Lamb Demand Analysislambresourcecenter.com/.../09/ALB_Lamb_Demand_Analysis__March_2015.pdf · i...

Lamb demand is as critical

today—as it was yesterday--and

will be tomorrow.

Lamb Demand

Analysis Julie Stepanek Shiflett, PhD Juniper Economic Consulting, Inc. [email protected] Deborah Marsh, Consultant [email protected]

March 2015

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1989 – “An increase in the demand for lamb is one avenue for reversing the long-

term decrease in sheep and lamb numbers and the falling share of lamb in the meat

case.” (Purcell, W.D. “Analysis of Demand for Beef, Pork, Lamb and Broilers: Implications for the Future.” Research

Institute on Livestock Pricing, Virginia Tech. Research Bulletin 1-89, July, 1989.)

1993 - “The level of demand for lamb and/or changes in that level over time are

important determinants of the long term economic viability of the lamb industry.” (Byrne, P., O. Capps, G. Williams. “U.S. Demand for Lamb: The Other Red Meat.” Journal of Food Distribution Research.

February 1995.)

2001 - “Understanding major determinants of, and trends, in consumer demand for

lamb is critical for the industry to develop appropriate production and marketing

strategies.” (Schroeder, T. C, R. J. Jerrick, R. Jones, and C. Spaeth. “U.S. Lamb Demand.” Sheep and Goat Research

Journal. May 21, 2001.)

2008 - “The level of demand for lamb and changes in that level over time are key

determinants of the long-run economic viability of the lamb industry.” (National Research

Council. Changes in the Sheep Industry in the United States: Making the Transition from Tradition. 2008.)

2013 - High-Level Goal: “Achieve a significant increase in demand for American lamb

meat as measured by the Demand Index.” (The Hale Group. “The American Lamb Industry Roadmap

Project, Draft Final Report.” September-October 2013.)

2015 – “Elasticities of demand vary by cut and by region. Knowledge of own-price

and cross-price elasticity estimates has implications for effective pricing strategies.” (Shiflett, J. and D. Marsh, “Lamb Demand Analysis.” March 2015)

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Executive Summary

This project updates the 2007 lamb demand study by Shiflett, et al., and addresses the question,

“What happened to demand?” More specifically, what has happened to retail lamb demand since the

2007 study was published? To help answer this question, the study updates the Retail Lamb Demand

Index as recommended in The Hale Group’s 2013 industry-wide assessment final report to the

American Lamb Board titled, “The American Lamb Industry Roadmap Project.” Demand research

opportunities identified in the 2008 National Academy of Sciences comprehensive study, “Changes in

the Sheep Industry in the United States: Making the Transition from Tradition,” are also addressed.

Specifically, these include 1) updating own-price and cross-price elasticities of demand to better

position lamb in the U.S. meat market, 2) conducting a sensitivity analysis of the retail lamb demand

index to changes in the own-price elasticity measures used and 3) conducting base-line research on

demand for specific cuts of lamb.

Key findings from this study include:

The own-price elasticity of demand for lamb was estimated at -0.76, indicating that for a 10 percent increase in the retail price of lamb, the quantity demanded decreases by 7.6 percent, and vice versa.

The updated Demand Index showed that between 2002 and 2010 demand remained relatively

stable. Demand increased slightly over the 2011-2014 period.

Retail demand was down five percent from the 1990 reference year, but up six percent over

the 2002 level.

Record high lamb prices in 2011 reflect a combination of tight supplies and increased demand.

General trends in demand are fairly robust to different elasticity estimates. However,

elasticity estimates do impact index results for a particular year relative to the base year.

Own-price elasticity estimates for individual retail cuts of lamb were found to be generally

more elastic than elasticity estimates for lamb in aggregate (composite of all cuts), with leg-

of-lamb being the most elastic (price-sensitive).

Elastic demand for specific cuts of lamb means that price promotions (price discounts) will

increase both sales volume and total expenditures on those cuts. Inelastic demand for specific

cuts means that price discounts will increase sales volume, but will reduce total expenditures

on those cuts.

Easter continues to exert a strong seasonal influence. During Easter, the price of legs is on

average 15 percent lower and sales volume 359 percent higher. Total lamb expenditures rise

sharply during Easter from an average of $6.5 million weekly to $23.9 million (2009-2014

FreshLook retail outlet data).

The lamb industry continues to face data challenges. However, there are opportunities available that could help the industry gain a better understanding of the relative value differences between specific cuts of domestic and imported lamb, and that could more precisely identify specific substitutes for lamb on a cut-by-cut basis.

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TABLE OF CONTENTS

1 Introduction .................................................................................................................................................. 1

2 Interrogation of Lamb Industry Data ............................................................................................................ 4

2.1 Introduction .......................................................................................................................................... 4

2.2 Public Sources of Retail Price Data ....................................................................................................... 4

2.3 Private Sources of Retail Price Data ...................................................................................................... 5

2.4 BLS Indexed Retail Price Data ............................................................................................................... 6

2.5 Imputed Retail Prices for Lamb ............................................................................................................. 8

2.6 Capita Consumption Data ..................................................................................................................... 9

2.7 Study Data ........................................................................................................................................... 13

3 Modeling Demand, 1990-2014 ................................................................................................................... 15

3.1 Demand Function ................................................................................................................................ 15

3.2 The OLS Aggregate Demand Model .................................................................................................... 16

3.3 Data ..................................................................................................................................................... 17

3.4 Statistical Results ................................................................................................................................ 18

3.5 Conclusion ........................................................................................................................................... 20

4 Demand Index Update ................................................................................................................................ 21

4.1 Introduction ........................................................................................................................................ 21

4.2 Demand Index Update ........................................................................................................................ 22

4.3 Beef and Pork Demand Index Comparison ......................................................................................... 24

4.4 Changes in Elasticity Over Time .......................................................................................................... 25

4.5 Conclusion ........................................................................................................................................... 27

4.6 Total Disappearance ........................................................................................................................... 27

4.6.1 Total Disappearance OLS Model ................................................................................................. 31

4.6.2 Total Disappearance Demand Index ........................................................................................... 33

4.6.3 Conclusion ................................................................................................................................... 34

5 2009-2014 Scanner-Data Lamb Cut Model ................................................................................................. 35

5.1 Introduction ........................................................................................................................................ 35

5.2 Literature Review ................................................................................................................................ 35

5.3 Background ......................................................................................................................................... 36

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5.4 Model .................................................................................................................................................. 37

5.5 Data ..................................................................................................................................................... 40

5.6 Results ................................................................................................................................................. 43

5.7 Own-Price and Cross-Price Elasticities ................................................................................................ 45

5.8 Expenditure Elasticity .......................................................................................................................... 49

5.9 Conclusion ........................................................................................................................................... 50

6 Recommendations ...................................................................................................................................... 52

7 Further Reading .......................................................................................................................................... 55

7.1 Literature Review ................................................................................................................................ 55

7.2 What is Demand? ................................................................................................................................ 61

7.3 Elasticity .............................................................................................................................................. 67

References .......................................................................................................................................................... 71

Appendix A. Retail Lamb Prices Source Summary ......................................................................................... 76

Appendix B. Analysis of BLS CPI-Imputed Retail Prices ................................................................................... 77

Appendix C. Beef, Pork and Lamb Demand Indices Values ............................................................................ 80

Appendix D. Lamb Demand Index Values with Alternative Elasticities .......................................................... 81

Appendix E. Lamb Cut Model Statistics and Model Parameters .................................................................... 82

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List of Figures

Figure 2-1 Historical Retail Lamb Prices (nominal) from Public and Private Sources ........................................... 6

Figure 2-2 BLS 'Lamb and Organ Meats' and 'Lamb and Mutton' Consumer Price Indices (2009=100) .............. 8

Figure 2-3 Public, Private and BLS CPI-Imputed Retail Lamb Prices (nominal) .................................................... 9

Figure 2-4 Annual per Capita Retail Lamb Consumption (lbs.), 1980-2014 ........................................................ 10

Figure 2-5 Lamb and Mutton in Cold Storage ..................................................................................................... 11

Figure 2-6 Cold Storage Lamb & Mutton, Annual Average (million pounds) ..................................................... 11

Figure 2-7 Commercial Slaughter and Estimated Nontraditional Market Slaughter .......................................... 12

Figure 2-8 Annual FreshLook 'Pounds Sold' as a Percent Total Retail Disappearance ....................................... 13

Figure 4-1 Inflation-adjusted Lamb Retail Price and Per Capita Consumption, 1990-2014 ............................... 21

Figure 4-2 Demand Index, Elasticity = -0.76, 1990=100 ..................................................................................... 23

Figure 4-3 Beef, Pork and Lamb Demand Indexes, 1990=100 ............................................................................ 24

Figure 4-4 Lamb Demand Index under Different Elasticity Measures ................................................................ 26

Figure 4-5 Beef, Pork and Lamb Demand Indexes, 1990=100, E = -0.75 ............................................................ 27

Figure 4-6 Inflation-adjusted Retail Lamb Prices (2009=100) and Per Capita Retail Consumption (1978-2014)

............................................................................................................................................................................ 28

Figure 4-7 Inflation-adjusted Retail Lamb Prices (2009=100) and Total Retail Disappearance (1978-2014) ..... 29

Figure 4-8 BLS All Items Consumer Price Index and Lamb Organ Meats Consumer Price Index for All Urban

Consumers (1982-84=100) .................................................................................................................................. 30

Figure 4-9 Total Retail Disappearance Demand Index, 1990-2014, 1990=100 .................................................. 33

Figure 4-10 Per Capita and Total Disappearance Index Values, 1990=100 ........................................................ 34

Figure 5-1 Easter Leg Demand, 2009-2013 ......................................................................................................... 36

Figure 5-2 Leg of Lamb Expenditure, 2009-2013 ................................................................................................ 38

Figure 5-3 Total Expenditure and Leg Budget Share .......................................................................................... 39

Figure 5-4 Leg of Lamb Price and Quantity Demanded ...................................................................................... 39

Figure 5-5 Leg and Shoulder Budget Shares ....................................................................................................... 40

Figure 5-6 Budget Share by Cut .......................................................................................................................... 41

Figure 5-7 FreshLook Regional Map .................................................................................................................... 42

Figure 5-8 Percent of Weekly Sales by Region, 2009-2013 ................................................................................ 43

Figure 5-9 Inflation-adjusted Ground Lamb Price and Quantity......................................................................... 48

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List of Tables

Table 3-1 Review of Lamb Demand Models ....................................................................................................... 16

Table 3-2 Descriptive Statistics for the Quarterly Continuous Variables ............................................................ 18

Table 3-3 Retail Lamb Demand OLS Regression Model: Parameter Estimates and Associated Statistics .......... 19

Table 4-1 Descriptive Statistics for the Quarterly Continuous Variables --Total Disappearance Model ............ 32

Table 4-2 Total Retail Disappearance Dependent Regression Model, Quarterly, 1990-2014 ............................ 32

Table 5-1 Cut and Regional Own-Price and Cross-Price Elasticities .................................................................... 46

Table 5-2 Cut and Regional Expenditure Elasticities ........................................................................................... 49

_____________________________________________________________________________

The authors would like to thank Dr. Wayne Purcell, Alumni Distinguished Professor Emeritus of

Agricultural and Applied Economics at Virginia Polytechnic Institute and State University (Virginia

Tech), and Mr. Paul Rodgers, Deputy Director of Policy, American Sheep Industry Association (ASI)

for their review of this study and helpful comments.

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1 INTRODUCTION

The American Lamb Board (ALB) is charged with increasing demand for American lamb. Demand is the underlying force that drives the entire production, processing, distribution and marketing chain and determines the profitability potential for the entire lamb industry. The Hale Group’s 2013 industry-wide analysis, “The American Lamb Industry Roadmap Project,” points to “Demand Creation” as a “High-Level Goal” and recommends a quantitative analysis of demand as measured by the Demand Index. The National Academy of Sciences (NAS) comprehensive 2008 study, “Changes in the Sheep Industry in the United States: Making the Transition from Tradition,” also recommends a number of research needs and opportunities specific to demand analysis. Three of those recommendations are investigated here, including own-price and cross-price elasticities of demand for better positioning of lamb in the U.S. meat market, the sensitivity of meat demand indices to changes in the own-price elasticity measures used and baseline research on the demand for specific cuts of lamb.

What happened to demand? This project provides an update of the 2007 lamb demand study. The project also addresses a number of specific recommendations as cited in the Hale Report and in the National Academies Study with respect to demand analysis. The overarching objective of this study is, however, to answer the question, “What happened to demand?” To help answer this question:

1) The study provides an updated review of the research literature. 2) The study provides an overview of the historical retail price information, both public and

private, available to the lamb industry and underscores deficiencies in the data that have hindered demand research and analysis for lamb. The data section also highlights some of the relative advantages and disadvantages of publically available Bureau of Labor Statistics (BLS) and Economic Research Service (ERS) data versus scanner-based data available from private sources such as the FreshLook Marketing Group.

3) Using publically-sourced retail price and quantity information, a quarterly double-log constant elasticity form of the demand function was estimated applying the ordinary least squares (OLS) regression technique and updated estimates of the own-price, cross-price and income elasticities of demand for lamb are reported.

4) The Demand Index for retail lamb demand is updated. 5) A sensitivity analysis of the Demand Index to various measures of the own-price elasticity of

demand is presented. 6) The updated Demand Index for lamb is compared with Demand Indices published for beef and

pork. 7) Using the FreshLook scanner-based data for individual retail cuts of lamb, a variation of the

AIDS model, the Quadratic Almost Ideal Demand System (QUAIDS), is estimated and own-price

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and cross-price elasticity estimates for the major retail cuts of lamb are presented for the U.S. and for each of the eight FreshLook marketing regions.

8) For those interested, a section titled “Further Reading” is also included that provides more detailed information on the basics of demand analysis.

Basic Economic Concepts

An understanding of demand is important because it is key to the development of sound pricing strategies that lead to profitability, to the development and targeting of effective advertising campaigns, promotional activities, and educational efforts, and because it provides a means for evaluating the effectiveness of the lamb check-off dollars invested. There are a number of basic economic concepts important to understanding demand and to interpreting research on demand. These key concepts are summarized briefly below and, for those interested, are presented in greater detail in the “Further Reading” section at the end of this report. The important economic concepts are:

Demand is a price-quantity relationship. The Law of Demand states that price and quantity are inversely related. Per capita consumption is not a measure of demand. Per capita consumption is a measure

of supply. A demand curve represents a schedule of the quantity of goods or services that consumers

are willing and able to purchase at various prices. A supply curve represents a schedule of the goods or services that producers are willing and

able to produce at various prices. The interaction of supply and demand jointly determine the market equilibrium price or the

market clearing price. The equilibrium price (own-price) changes in response to shifts in demand and/or shifts in

supply, but does not cause these shifts. Demand shifters include:

Changes in the prices of substitute or complement goods (cross-price),

Changes in income,

Changes in consumer tastes and preferences,

Holidays and other seasonal influences,

Health attributes or concerns,

Advertising,

Population (changes in the number of buyers). Supply shifters include:

Changes in input prices,

Changes in returns from commodities that compete for resources,

Changes in technology,

Changes in taxes, subsidies and risk,

Changes in the number of sellers.

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Elasticity of demand is a measure of price sensitivity. How sensitive is the quantity demanded by consumers to changes in price?

The own-price elasticity of demand is defined as the percentage change in the quantity demanded divided by the percentage change in price: %ΔQ/%ΔP.

An elasticity value greater than one (in absolute value) is termed elastic. Elastic means that the percentage change in the quantity demanded is greater than the percentage change in price, and indicates that consumers are price-sensitive.

An elasticity value less than one (in absolute value) is termed inelastic. Inelastic means that the percentage change in the quantity demanded is less than the percentage change in price and indicates that consumers are not very price-sensitive.

When demand is elastic, a price increase leads to a decrease in total revenue/expenditures (and vice versa).

When demand is inelastic, a price increase leads to an increase in total revenue/expenditures (and vice versa).

Cross-price elasticity measures the change in the demand for good A (lamb), in response to a change in the price of good B (beef).

Income elasticity measures the change in the demand for a good (lamb) as income changes.

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2 INTERROGATION OF LAMB INDUSTRY DATA

2.1 INTRODUCTION

Most demand studies provide only a relatively short paragraph identifying the data used in the analysis. However, because the U.S. lamb industry faces some rather unique data challenges at the retail level, both in relationship to the other meats and with respect to imported lamb products, a more in-depth discussion of the retail data available to the lamb industry is warranted. Just as meat quality is important to the consumer, data quality is important to industry analysts. The quality of the data inputs affects the quality of the analytical outputs.

2.2 PUBLIC SOURCES OF RETAIL PRICE DATA

Demand research and analysis for the lamb industry has been hindered by the lack of a consistent long-standing source of retail price information. The 2008 NAS study explicitly states that a major problem for both research on demand and decision-making in the lamb industry is the absence of a long-standing retail price series. Other meats that compete for the consumer’s dollar, including beef, pork and chicken, have readily available on-line through the USDA’s Economic Research Service (ERS) and the Livestock Marketing Information Center (LMIC), monthly, quarterly and annual retail price series dating back to January 1950 -- lamb does not. These retail price series are calculated using data collected by the U.S. Department of Labor’s Bureau of Labor Statistics (BLS) and are periodically reviewed and updated. Previously, the ERS published a comparable retail price series for lamb, also dating back to January 1950. The retail lamb series, however, was discontinued in April 1987 and the historical series is no longer readily available. Between January 1991 and January 1994, the BLS published “monthly” U.S. city average price data for lamb and mutton. This series, however, is characterized by large gaps in the data and is of limited practical application for demand analysis. More recently, the Livestock Mandatory Reporting Act of 1999 (LMRA) required the USDA to acquire an alternative measure of retail meat prices independent of the BLS data. To fulfill the requirements of the LMRA, the ERS developed a database of monthly average retail prices and indexed volume information for selected cuts of red meat and poultry, including beef, pork, chicken, turkey, veal and lamb. The methodology was developed and the database built using retail supermarket scanner information obtained from private sources. The scanner data on meat sales came from national and regional chain stores that accounted for about 20 percent of the value of all U.S. supermarket sales. However, the percentage of total U.S. meat sales represented by these data is not known. Maintenance and oversight of the ERS database were later transferred to the LMIC. Reporting of the ERS scanner-based retail series began in January 2001, and was terminated in April 2008. The ERS scanner database was unique in its attempt to capture and make publically available monthly retail prices for both domestic and imported lamb. The scanner-based retail prices for lamb were reported for ‘All Lamb’, ‘Domestic Lamb’, ‘Imported Lamb’, and for a number of domestic cuts including legs, loins, shoulders, chops and roasts. Previously, this type of differentiated price information had been captured and reported only rarely and generally under special circumstances,

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e.g., U.S. International Trade Commission (USITC) investigations. The loss of this valuable public source of comparative domestic and import retail price information has yet to be recovered and utilized by the lamb industry. Currently, the only public source of actual retail lamb prices, is through the UDSA’s Agricultural Marketing Service (AMS) which reports weekly feature activity. Featuring refers to the price discounts offered to consumers through retailers' weekly feature advertisements. The feature reports include advertised prices for lamb at major retail supermarket outlets with information gathered from publicly available sources, including store circulars, newspaper ads and retailer websites. Again, this type of series is not well-suited to the retail-level demand analysis.

2.3 PRIVATE SOURCES OF RETAIL PRICE DATA

Because retail lamb prices (aside from feature prices) are no longer publically available through the USDA, the lamb industry has had to rely on privately-owned information as its sole source of actual retail lamb prices. During the years 1987-1996, the American Sheep Industry Association (ASI), contracted with a private market research and information firm to provide first monthly, then bi-monthly, then quarterly retail price information. Prices were based on survey information and market coverage was limited. More recently, the American Lamb Board (ALB) has contracted with the FreshLook Marketing Group (now part of Information Resources, Inc. (IRI)) to provide scanner-based retail price information. The IRI FreshLook Perishable Service (FreshLook) provides scanner-based, point-of-sale information for perishable retail items sold in the U.S. The defined number of stores in the Multi-outlet definition is around 100,000 stores.1 FreshLook currently provides the ALB with quarterly retail sales information that includes average price per pound, sales volume (pounds), and total dollar sales. Sales are summarized by region which includes the Northeast, California, Southwest, Mid-south, West, Great Lakes, South Central, and Plains. Lamb sales are reported for all lamb and also are differentiated by cut – leg, loin, shoulder, rib, ground, miscellaneous and variety. The historical retail price series for lamb, both public and private, are summarized in Figure 2-1. The data shown are nominal historical monthly retail prices. Significant gaps in the data are evident as are volatility differences between the older BLS/ERS sample-based series and ASI private series, and the more recent ERS and FreshLook scanner-based series, as well as the AMS feature series. The historical and current retail price information available to the lamb industry is also summarized in table form in Appendix A.

1 Source: IRI FreshLook Perishable Service; www.iriworld.com .

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Figure 2-1 Historical Retail Lamb Prices (nominal) from Public and Private Sources

2.4 BLS INDEXED RETAIL PRICE DATA

The BLS collects a wide-range of retail prices from a variety of retail outlets, then uses that data to calculate commodity-specific consumer price indexes (CPI). The CPI is a measure of inflation that focuses on the buying habits of urban consumers. The BLS not only publishes the widely recognized “All Items” CPI, but also provides a number of other CPIs, covering a variety of goods and services, including food and beverages, meats, poultry, as well as housing, apparel and transportation, to name a few. In December 1977, the BLS began publishing a monthly CPI for Lamb and Organ Meats. The index runs continuously from December 1977 through the present - with the exception of a two-year period, January 2006 through December 2007, during which nearly half of the monthly observations are missing. The index represents the longest-standing and most complete source of historical retail lamb price information available. One obvious weakness of this index, however, is the unlikely combination of disparate meat products - lamb and organ meats – represented as a single price index based on a common ‘small sample size’ criteria. Further, the ‘organ meats’ classification includes not only lamb organ meats, but organ meats of any kind from multiple species – beef, pork, veal and lamb.2

2 Personal communication. BLS, June 20, 2014.

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More recently, beginning December 1997, the BLS started publishing a second CPI for Lamb and Mutton that does not include organ meats. This later series should provide a more accurate reflection of retail lamb prices as very little mutton is sold at retail in the U.S. However, this latter series is characterized by frequent gaps in the monthly data – particularly for the years prior to 2009. Both the BLS Lamb and Organ Meats CPI and the BLS Lamb and Mutton CPI are subsets of a larger Other Meats BLS index. Gaps appear in the two lamb series during periods when the sample size is not large enough for the BLS to publish reliable results. According to the BLS, both the Lamb and Organ Meats index and the Lamb and Mutton index contain the same lamb and mutton price information. The two series differ only in the inclusion/exclusion of the organ meats price information. As a result, the Lamb and Organ Meats index, the more commonly used index for research purposes, gives only the appearance of a more complete series. The Lamb and Organ Meats index appears more complete precisely because it includes organ meat price information across multiple species which serves to ‘fill-in-the-gaps’ in the lamb and mutton price information. Figure 2-2 highlights the differences between the BLS Lamb and Organ Meats and the BLS Lamb Mutton CPIs, and provides some indication of the extent to which organ meats price data is used to supplement lamb and mutton price data. Given that both indices include the same lamb and mutton price information, periods when the combined Lamb and Organ Meats index is greater than the Lamb and Mutton index value, (converted to a common base period), would suggest that organ meat prices were higher than lamb meat prices during those periods. This is counter intuitive, and raises some concern about the reliability of these indices for research application. Note that starting around May 2011 through May 2012, the Lamb and Mutton index is markedly higher than the Lamb and Organ Meats index. This corresponds to the period of historically high prices in the lamb market. In contrast, from September 2013 through December 2014, the Lamb and Mutton index trends markedly lower than the Lamb and Organ Meats index.

We asked the BLS to comment specifically

on how it calculates the monthly average

retail price index for lamb – i.e., what cuts or

mix of cuts are included in the index. The

BLS responded:

We are not calculating an average price, but

instead picking a specific item and following

that item’s price as it changes over time. The

price changes themselves are used to create

the index. A data collector probabilistically

chooses which item to price, based on sales

data that the outlet provides. So if ground

lamb is the best seller in that outlet, then

there is a better chance that we will select

ground lamb. We might have none, one, or

many lamb quotes in a given outlet,

depending on our survey data indicating

where people purchase lamb. – BLS, June 2014.

This methodology would seem to further

compromise the consistency of the BLS lamb

CPIs depending on the particular cuts or mix

of cuts being tracked during certain months,

and potentially, the mix of imported and

domestic product.

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Figure 2-2 BLS 'Lamb and Organ Meats' and 'Lamb and Mutton' Consumer Price Indices (2009=100)

2.5 IMPUTED RETAIL PRICES FOR LAMB

Prices imputed from the BLS Lamb and Organ Meats CPI have been used in a number of previous retail lamb studies, including Shiflett et al. (2007), Capps et al. (2010) and Schroeder et al. (2001). To create the retail price series from the BLS Lamb and Organ Meats CPI for the purpose of this study, the index was first converted to a 2009 base year (2009 = 100). The index was then converted to a monthly retail price series using the FreshLook scanner 2009 annual average price for all lamb (aggregate of all cut of lamb) as the base price. Figure 2-3 compares the monthly BLS CPI-imputed retail prices with a composite of the monthly public and private retail prices presented earlier (excluding the AMS feature activity series). The imputed series tracks well with recent FreshLook scanner prices in terms of general price level, which is not surprising given that the index was transformed using a FreshLook 2009 base price. Over the 2009-2014.Q3 period, the correlation coefficient between the BLS CPI-imputed retail series and the FreshLook scanner-based retail series is 0.97, indicating that the imputed price series provides a reasonable representation of retail lamb prices over recent years. The fit, however, is not as good relative to the other public and privately-sourced retail series. The imputed retail lamb price series is generally lower and less volatile than the other retail series, and notably lower and less volatile than the 2001-2008 ERS scanner-based retail series3.

3 Further analysis of BLS-CPI-imputed price series, ERS reported retail prices and FreshLook scanner-based retail prices is provides in Appendix B.

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Figure 2-3 Public, Private and BLS CPI-Imputed Retail Lamb Prices (nominal)

2.6 CAPITA CONSUMPTION DATA

Aggregate demand models are commonly estimated using per capita consumption as a measure of quantity demanded. Per capita consumption data for lamb – like retail price data for lamb – can be problematic and is often characterized by a lack of precision. Per capita retail consumption is measured as:

Commercial Production + Farm Production = Total Production Total Production + Beginning Stocks + Imports = Total Supply Total Supply – Exports – Ending Stocks = Total Disappearance (Total Disappearance ÷ Total Population) x Retail Conversion Factor = Per Capita Retail Consumption.

A number of different factors contribute to the lack of precision in the per capita retail consumption measure for lamb. Product movement in and out of cold storage affects both the volume and mix of lamb available at the retail level at any given point in time and can influence aggregate estimates of retail prices. The growing nontraditional lamb markets direct lambs away from the more traditional commercial markets in a manner that is difficult to capture. The inability to differentiate volume and price measures for domestic and imported product, and for food at home (FAH) and food away from home (FAFH) also contributes to the complexity of the price and quantity relationships that demand analysis seeks to identify and measure. Figure 2-4 shows annual per-capita retail consumption estimates for 1980-2014.

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Figure 2-4 Annual per Capita Retail Lamb Consumption (lbs.), 1980-2014

Consumption is essentially a measure of supply. The phase-out of the National Wool Act, 1993-1995, resulted in a substantial drop in the supply of domestic lamb and a commensurate “shift” of the total supply curve. Between 1993 and 1994, total supplies contracted approximately 26.4 million pounds, a decline of about seven percent. Of that, approximately 87 percent was due to a decrease in domestic supply. Between 2007 and 2008, total supplies contracted approximately 28.7 million pounds, again about seven percent. However, this time imports accounted for the largest share of the decline - about 67.5 percent. Following the initial effects of the phase-out of the National Wool Act, annual per capita consumption showed a general leveling off, stabilizing at an annual average of about 1.1 pounds per capita. Per capita consumption again trended lower following a slight increase in 2007. In 2009 annual retail consumption estimates dipped below one pound per capita for the first time, and, to date, have remained below the one pound mark. The ‘Beginning and Ending Stocks’ estimates used in the per capita consumption calculation are estimates of the amount of lamb and mutton in cold storage. Cold storage is used to help manage supplies and includes both domestic and imported product. The relative proportions of domestic and imported lamb and mutton in cold storage are not known and may affect national retail price averages vis-á-vis product mix and availability at any given time. In recent years, cold storage estimates have increased significantly. Over the five-year period, 2009 to 2013, for any given month, cold storage volume exceeded the average monthly domestic production of lamb and mutton by 44 percent. Reported cold storage volume increased significantly during 2014. Figure 2-5 shows the increase in cold storage volume for 2014 relative to 2012 and 2013 levels.

Source: USDA, BEA, LMIC

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Figure 2-5 Lamb and Mutton in Cold Storage

Source: USDA/NASS, ASI

In September 2006, under the LMRA, the USDA’s National Agricultural Statistics Service (NASS) identified additional supplies of lamb product in cold storage. As a result, cold storage estimates for 2006 were revised upward by approximately 4 million pounds. NASS began publishing a new cold storage series in 2007, while cold storage figures prior to 2006 continue to reflect the older series (Figure 2-6).

Figure 2-6 Cold Storage Lamb & Mutton, Annual Average (million pounds)

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

'000 Lbs.

2012 2013 2014

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Lamb slaughter for nontraditional markets also impacts estimates of per capita consumption through the ‘Total Supply’ side of the equation. Shiflett and Williams (2010) estimated that in 2009, 1.3 million head of sheep and lambs were either direct marketed or sold into ethnic markets from auction -- close to the calculated 1.2 million head statistical difference between the estimated lamb crop and commercial slaughter. These unreported lambs contribute to the lack of precision in the per capita consumption measure as they are not counted in the ‘Total Supply’ estimate. Figure 2-7 shows commercial slaughter (July – June) and slaughter for the nontraditional market estimated as the difference between the annual lamb crop and commercial slaughter with a six month lag imposed on commercial slaughter. In 2011, the number of lambs diverted to slaughter for nontraditional markets was estimated at 65 percent of the commercial slaughter – further exacerbating short supplies in 2011 and likely contributing to record-high lamb prices for the year.

Figure 2-7 Commercial Slaughter and Estimated Nontraditional Market Slaughter

Another limitation of the per capita retail consumption data, is that the estimates do not differentiate between ‘food at home’ (FAH) and ‘food away from home’ (FAFH) purchases of lamb – i.e., between grocery and food service sales. Per capita retail consumption is a composite disappearance estimate (FAH plus FAFH), whereas, the retail price of lamb reflects only FAH purchases. Here again, the two series, per capita consumption and retail lamb price, do not map well, with retail prices describing only a subsector of per capita consumption. Industry experts estimate that approximately 65 percent of the value of domestic lamb goes to the FAFH or the food service sector.4 Similar estimates of FAFH sales volume are not available.

4 Personal communication.

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To gain some perspective, nationally, the FreshLook retail scanner data represents about 83 percent of the total ‘All Commodity Volume’5. However, the percentage of the total volume of retail meat sales that this figure represents is not known. Using ERS annual ‘Total Retail Disappearance’ estimates and annual FreshLook ‘Total Pounds Sold’, over the 2009-2013 period, the FreshLook retail scanner data captured, on average, roughly 17, 28, 21 and 18 percent of the total retail disappearance of lamb, beef, pork and chicken, respectively (Figure 2-8). In addition, in the case of lamb, the percentage and cut profile of domestic and imported lamb directed to FAH versus FAFH is also unknown.

Figure 2-8 Annual FreshLook 'Pounds Sold' as a Percent Total Retail Disappearance

Finally, per capita consumption estimates for lamb are often reported with only one significant digit, such as 1.1 or 0.9 pound. As noted in our 2007 analysis of demand, this lack of precision, can affect a regression model’s ability to sort out the individual effects that the explanatory variables have on the dependent variable, per capita retail consumption. The per capita retail consumption estimates used in this study were obtained from the LMIC and include 15 decimal places.

2.7 STUDY DATA

Two different sources of retail lamb price data were utilized for this study. The first is the retail price series imputed from the BLS Lamb and Organ Meats CPI. Despite its deficiencies, the series constitutes the longest-standing and most complete series of retail price information available to the lamb industry - and it remains current. Over the 2009-2014 period, the BLS Lamb and Organ Meats CPI-imputed retail price series was highly correlated with the FreshLook retail scanner price data for lamb. The BLS CPI-imputed retail series was used for the primary purpose of updating the demand

5 Josh Grove, FreshLook, Manager, Client Services, Personal communication 1/20/2015.

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index. Despite its limitations, the series appears to provide a reasonable long-standing proxy for aggregate retail lamb prices. The second retail price series employed for this study is the FreshLook sales-weighted scanner data. A detailed weekly FreshLook retail scanner data set for lamb, that includes price, quantity and expenditure information by region and by retail cut, was generously provided by the American Lamb Board. The FreshLook data has the advantage of representing actual retail transactions, providing greater product detail, providing actual raw retail price and quantity information, and providing direct linkages between price and quantity observations. However, the FreshLook data is a much shorter series (01/11/2009 - 11/03/2013), which limits its value for identifying long-run trends and for tracking changes in demand over time. A second potential weakness of the FreshLook series is that the range of the data is dominated by a period of unsettled economic conditions and unusual price and market activity, particularly for lamb. The data span a unique period whereby the lamb industry saw record-high prices prompted by a supply squeeze, a growing supply of over-fat lambs and quality concerns. The data also overlaps the period dubbed the ‘Great Recession’, with its broader impact on the economy as a whole. As more data become available, the usefulness of the FreshLook series for analyzing and tracking retail demand will likely improve.

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3 MODELING DEMAND, 1990-2014

3.1 DEMAND FUNCTION

A demand function is a mathematical equation used to estimate or describe the relationship between the quantity of a good that consumers are willing and able to purchase and those factors that influence their purchase decisions. Demand functions are frequently used to estimate price and income or expenditure elasticities. The own-price elasticity of demand is one of the inputs required in the estimation of a demand index. The demand index, in turn, can then be used to track changes in consumer demand over time. The sources of the data inputs, range of the data analyzed, and type of modeling technique selected all can affect the output of the demand function. Modeling techniques can range from very simple to extremely complex. Taljaard et al. (2006) note that the use of different methodological frameworks in demand analysis is largely responsible for differences in estimated demand relations. In reference to demand elasticity estimates for Australian meat products, Griffith et al. (2001) similarly state that the major difficulty in forming any consensus opinion on domestic retail demand elasticity values is the diversity of models, variables and assumptions used and the data period, which effectively precludes a straight comparison of like with like. The same is true across U.S. studies. Table 3-1 summarizes some of the own-, cross-, and income elasticity estimates that have been reported in the literature. Modeling differences aside, one important attribute that all demand studies and demand models do have in common, is that the quality of the data inputs affects the quality of the estimated outputs.

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Table 3-1 Review of Lamb Demand Models

Timeframe Studied, Level of

Aggregation

Own-Price Elasticity

Cross-price elasticity:

Beef


Pork


Poultry

Income

elasticity

Capps, et al., 2011 (2 models)

1978/79-2009-10

-0.7258 -0.6452

0.3062 0.2683

-- --

-- --

-- --

Capps et al., 2010

1978/79-2008/09

-0.75 0.626 0.405 -- 0.266 (Not Sig.)

Shiflett, et al., 2007

1980-2005, Quarterly

-0.665 0.486 0.179, Weak

Substitute.

Not Sig. 0.684

RTI International (Montana State), 2007

1970-2003, annual

-0.523 short-run,

-1.108 long-run

Not Sig. Not Sig. 0.35 Not Sig.

Paarlberg & Lee, 2001


-0.437

--

--

--

--

Schroeder, et al., 2001

1978-1999, Quarterly,

-1.09 0.57 Weak Substitute.

Not Sig. -0.54

Byrne, et al., 1993

1978-1990, Bi-monthly

-0.62 short-run; long-run: -0.79

Not Sig. 0.131 Not Sig. Not Sig.

TAMRC, 1991 1978-1990, Bi-monthly

-0.6248 Not Sig 0.1312 Not Sig. Not Sig.

Purcell, 1989 1970-1987, Quarterly

-0.511 Not Sig. Not Sig. Not Sig. Not Sig.

Whipple and Menkhaus, 19891

1950-1987, Annual

-3.96 0.281 Not sig. Not Sig. 0.156

George and King, 1971

Quarterly, 1946-1968

-2.6252 0.5895 0.8914 0.2336 0.571

Notes: Not sig. = Not significant at 5 percent. -- = not considered. 1 Model price dependent so elasticities are calculated from flexibilities. 2 Statistical significance not reported.

3.2 THE OLS AGGREGATE DEMAND MODEL

Regression analysis using ordinary least squares (OLS) has been one of the more common modeling techniques applied to demand analysis. For the primary purpose of updating the demand index, a double-log constant elasticity form of the demand function was estimated. This is essentially the same specification of the demand function that was used in our previous demand study (Shiflett, et al. 2007) and is similar to the approaches used by Capps, et al. (2010), Schroeder, et al. (2001), Byrne, et al. (1993), TAMRC (1991) and Purcell (1989). The double-log constant elasticity functional form allows the elasticity estimates to be observed directly from the coefficient estimates.

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A simple demand function for lamb can be written:

QL = f(PL, PB, PP, PC, DPI, ε). The general form of the constant elasticity demand equation is then:

LnPCCRL = α + β1LnPL + β2LnPB + β3LnPP + β4LnPC + β5LnPCDPI + β6Q2 + β7Q3 + β8Q4 + ε. Where,

α is a constant or intercept term; PCCRL is per-capita retail consumption of lamb and mutton, in pounds; PL is the retail price of lamb in dollars per pound; PB is the retail price of beef in dollars per pound; PP is the retail price of pork in dollars per pound; PC is the retail price of chicken in dollars per pound; PCDPI is per-capita disposable income in dollars; Qi are seasonal dummy variables, where i = quarters 2, 3, and 4; ε is an error term that picks up the variation in per capita consumption of lamb not

captured by the other variables; Ln is the natural logarithm;

D indicates that all price and income variable are deflated to 2009 dollars; βi are the parameter coefficients, and for logarithmic variables, are the constant

elasticity estimates.

3.3 DATA

For the aggregate OLS demand model, this study utilizes quarterly historical data for the years 1990 -2014. Data used for ‘Per Capita Consumption Retail Lamb’ are available from the LMIC at http://www.lmic.info. The lamb retail price series was imputed from the BLS Lamb and Organ Meats CPI as previously described. The BLS Lamb and Organ Meats CPI is available at http://www.bls.gov. Retail price data for beef, pork and chicken are available from the LMIC. The ERS/LMIC retail price series used were the ‘All Fresh Retail Beef’, ‘Pork Retail’, and ‘Broiler Composite Retail’ series. Disposable personal income data are available at the both the BLS and the LMIC websites. All prices and income were deflated to 2009 dollars year using the consumer price index available from the BLS (also posted by the LMIC). Descriptive statistics for the quarterly continuous variables are summarized in Table 3-2.

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Table 3-2 Descriptive Statistics for the Quarterly Continuous Variables

Variable Mean Minimum Maximum Std. Dev.

PCCLR 0.2766 0.1702 0.3892 0.0435

DPL 5.14 4.40 6.82 0.70

DPB 3.93 3.31 5.40 0.41

DPP 3.19 2.82 3.84 0.22

DPC 1.93 1.63 2.43 0.19

DPCDPI 32546 27524 37618 3188

3.4 STATISTICAL RESULTS

Statistical results for the OLS regression model are summarized in Table 3-3. The model explains about 85 percent of the variability in quarterly per-capita retail consumption of lamb over the 1990-2014 period. The own-price elasticity of demand at retail was estimated at -0.76, slightly more elastic than reported in our 2007 study at -0.67, and not significantly different from the more recent own-price elasticity estimates reported by Capps, et al., (2010, OLS model 1978/79–2008/09) at -0.75 and Capps and Williams, (2011, Polynomial Distributed Lag model 1978/79–2009/10) at -0.73.

The -0.76 own-price elasticity finding indicates that a one percent increase in the retail price of lamb leads to a 0.76 percent decrease in the quantity demanded. Or, equivalently, that a one percent decrease in the retail price of lamb leads to a 0.76 percent increase in the quantity demanded.

Beef was shown to be a significant substitute for lamb with a cross-price elasticity of 0.274, meaning that a one percent increase in the price of beef leads to a 0.274 percent increase in per capita lamb consumption6. This cross-elasticity value is similar to that reported by Capps and Williams (2011) at 0.268 and 0.306 for their contemporaneous specification and distributed lag models, respectively, and is slightly lower than reported in our 2007 study at 0.486 and by Capps, et al. (2010) at 0.63. Neither pork nor chicken were shown to be significant substitutes for lamb in the aggregate demand model.

6 The intuition is that when the price of beef increases, lamb becomes relatively less expensive by comparison.

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Table 3-3 Retail Lamb Demand OLS Regression Model: Parameter Estimates and Associated Statistics

Dependent Variable: LnPCCRL, Quarterly Observations (1990-2014)

Variable Coefficient Std Error t-Statistic Prob.

LnDPL -.7576643 .1558637 -4.86 0.000

LnDPB .273933 .0982456 2.79 0.006

LnDPP .1228337 .1375698 0.89 0.374

LnDPC .0303434 .2097797 0.14 0.885

LnPCDDPI .0619831 .168831 0.37 0.714

LnPCCRL-1 .372053 .093216 3.99 0.000

Q2 -.071075 .0173923 -4.09 0.000

Q3 -.1412279 .0176397 -8.01 0.000

Q4 .0287938 .0209643 1.37 0.173

constant -.7160483 1.775541 -0.40 0.688

R-squared 0.8677 Shapiro-Wilk W test for normal data

Adj. R-squared 0.8543 Variable res

F(10, 96) 64.86 Obs 99

Prob > F 0.0000 W 0.98938

Root MSE 0.06006 V 0.870

Durbin-Watson d-statistic (10,99) 2.047998 z -0.309

Prob>z 0.62136

Variable VIF 1/VIF

LnDPL 11.03 0.090623

LnDPC 10.21 0.097974

LnPCDDPI 7.59 0.131677

LnPCCRL-1 6.02 0.166227

LnDPB 2.74 0.365563

Q4 2.28 0.439269

LnDPP 2.21 0.452916

Q3 1.61 0.620459

Q2 1.57 0.638235

Mean VIF 5.03

The coefficient on the income variable is positive but insignificant. This finding is consistent with a number of previous studies and indicates that lamb is a normal good, but that income is not a major determinant of retail level demand. In this respect, the 2008 National Academies study speculated that the lack of broad evidence of a statistically significant relationship between lamb consumption and income may reflect either the relatively small amount of lamb purchased or, “the fact that most lamb is purchased for special occasions”. The lack of significance on the income variable may, in part, also reflect the strong ethnic nature of the consumer base for lamb and the fact that FAFH purchases are not explicitly captured by the imputed retail price variable. FAFH lamb purchases tend to be associated with fine-dining, full-service-type establishments.

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A lagged dependent variable is sometimes included in an OLS regression with the dual intent of capturing the effects of habit persistence and as a means of addressing autocorrelation, which is prevalent in times series data. Following the example of Byrne, et al. (1993) and Schroeder et al. (2001), per capita retail consumption with a one-quarter lag was included in the model. Byrne et al., found that lagged lamb consumption was positive and significant over the 1978-1990 period, supporting an expectation of habit persistence among ethnic consumers. In contrast, Schroeder et al., estimated two partial-adjustment models, one using a one-quarter lag and another using a one-year lag, but concluded that habit persistence was not significant during the 1978 – 1999 period. The current model (1990-2014) supports the finding of habit persistence in lamb consumption, with the coefficient on lagged consumption both positive and less than one - consistent with a partial adjustment hypothesis. The dummy variables for quarters two and three were statistically significant and confirm that demand varies seasonally, although first and fourth quarter demand are not statistically different. The quarterly dummy variables indicate that per capita retail consumption is the greatest during the first and fourth quarters, with per capita retail consumption 6.9 percent, and 13.0 percent lower during the second and third quarters, respectively, relative to first quarter consumption, cet. par. However, given the traditionally strong influence of the Easter holiday on lamb consumption, the slight weakening of demand reflected during the second quarter was somewhat unexpected. The Easter holiday always falls between March 22 and April 25. Over the range of the data, Orthodox Easter was observed entirely during the second quarter, whereas, Western Easter was observed 19 of 25 years (76 percent of years) during the second quarter and 6 of 25 years at the end of the first quarter. Given the traditional influence of the Easter holidays on lamb consumption, relatively higher second quarter consumption was anticipated. However, monthly per capita consumption data are not available and in the context of quarterly demand analysis, it is difficult to more precisely isolate the influence of Easter. This is also true for other religious celebrations that include lamb as part of the traditional holiday meal - the Muslim festivals of Eid-al-Fitr and Eid-al-Adah, for example. While these two festivals are on the same day each year of the Islamic calendar, the specific effects are difficult to capture in a quarterly model as dates vary year-to-year using the Western calendar.

3.5 CONCLUSION

Elasticity estimates vary across studies, modeling methods and across different time periods. However, an own-price elasticity of -0.76 was found to be relatively robust across different model specifications tested for this study and is consistent with other recent demand studies for lamb in the U.S. In recent years, demand appears to have become slightly more elastic, meaning that consumers have become somewhat more price-sensitive. Since 2002, per capita retail consumption of lamb has declined, but this doesn’t necessarily indicate a commensurate decline in demand. An own-price elasticity estimate of -0.76 provides a credible framework for updating the demand index and measuring changes in demand.

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4 DEMAND INDEX UPDATE

4.1 INTRODUCTION

A demand index is a straight forward easy-to-interpret measure of how the demand for lamb is changing over time. Only increased demand will foster reinvestment, propel industry growth and improve profitability across sectors. Demand is a price-quantity relationship. Figure 4-1 shows per capita retail consumption and inflation-adjusted retail lamb prices for the years 1990-2014 in the form of a scatter diagram. Each point in the diagram represents the intersection of supply and demand and the equilibrium price for a particular year.

Figure 4-1 Inflation-adjusted Lamb Retail Price and Per Capita Consumption, 1990-2014

The diagram clearly shows that per capita lamb consumption has declined sharply over the past 25 years. The diagram can also easily give the impression that demand has experienced a similar dramatic decline over the same 1990-2014 period - but has it?

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In general, supply contractions put upward pressure on prices. However, increased demand also puts upward pressure on prices. In 1989, Purcell observed, “Consumption is down because lamb availability is down due to contractions in inventory and thus production, not necessarily because lamb demand is down.” For demand is to increase consumers must be both willing and able to: 1) purchase given amount of product at a higher price, or 2) purchase more of that product at the prevailing price. An increase in demand shifts the demand curve up and to the right. Conversely, a decrease in demand is reflected in a shift of the demand curve down and to the left such that: 1) consumers purchase the same given amount of product, but only at a lower price, or 2) consumers purchase less of a that product at the prevailing price. The scatter diagram alone does not definitively identify shifts in demand. More accurately, the scatter diagram traces out shifts in supply. The scatter diagram can, however, suggest a couple of potential shifts in demand over the 1990 to 2014 period. For example, between 1993 and 1994 per capita retail consumption fell 10 percent, from 1.30 to 1.17 pounds per capita, while the inflation-adjusted retail price for lamb remained constant at $4.48 per pound. The 1994-2001 period suggests a different demand surface to the left of the earlier 1990-1993 period – a potential decrease in demand? Between 2001 and 2002, per capita consumption increased slightly from 1.15 to 1.17 pounds per capita and the inflation–adjusted price also increased slightly from $4.63 to $4.96 cents per pound, suggesting a shift in the demand surface up and to the right – a potential increase in demand? From the scatter diagram alone, it is difficult to speculate about what happened to demand over the 2008-2014 period. Total supplies declined each year from 2008 to 2011, with inflation-adjusted prices reaching year-on-year highs over the same period. Questions were raised, “What happened to demand?” Did the record-high prices reflect a supply shift? A demand shift? Or both? Did lower prices in 2012-2014 reflect a decrease in demand, an increase in supply, or both?” “What happened to demand?” 4.2 DEMAND INDEX UPDATE

By teasing out the direct demand effect, the updated demand index can help answer the question, “What happened to demand?” The demand index essentially takes the same information that is summarized visually in a scatter diagram – including domestic production, imports, exports, cold storage, retail prices, inflation and population growth – filters it through a series of mathematical equations and presents it in a different manner – as a quantitative measure in the form of an index. A demand index is calculated relative to a particular base year, e.g., 1990. After selecting a base year, and adjusting for inflation, an elasticity measure is used to estimate the inflation-adjusted price that would have been expected in different years if demand is held constant at the base year level and the only thing changing is per capita supply. This gives the demand constant price, or DCP. The index for a particular year is then calculated as the ratio of the observed inflation-adjusted price and the DCP, multiplied by 100. For example, a demand index of 90 indicates that retail prices for a particular year were ten percent lower than they would have been if demand that year was at the same level as it was during the base year.

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The retail lamb demand index was updated using a 1990 base year and applying the updated elasticity estimate of -0.76. The demand index helps define and clarify the changes in demand between 1990 and 2014 suggested in the scatter diagram above. The demand index answers the question, “What happened to demand?” Figure 4-2 shows the updated demand index for retail lamb for the years 1990 to 2014. The years 2002 to 2014 have been highlighted to indicate the period of ALB operations.

Figure 4-2 Demand Index, Elasticity = -0.76, 1990=100

The demand index shows that demand did in fact decrease rather significantly from the early to the mid-1990s. This period coincides with the phase-out of the National Wool Act, 1993-1995. Between 1990 and 1994, domestic production dropped by 15 percent with total supplies contracting 13 percent. The scatter diagram clearly illustrates this drop in total supplies. However, not only was there a significant supply shift during this period, but the demand index indicates that demand also shifted, with a ten percent drop between 1993 and 1994 alone, and 19 percent decline between 1990 and 1994. The index indicates that demand remained relatively stable over the 1994 – 2001 period, with the exception of a slight increase evidenced in 1998. In 2002, demand began making some gains, jumping nine percent between 2001 and 2002. From 2002 through 2010, demand again remained relatively stable, but at a somewhat higher level than during the previous 1994-2001 period. In 2011, demand increased 7 percent, and through 2014, has remained at a slightly higher level – ending the period down only five percent from the 1990 level.

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4.3 BEEF AND PORK DEMAND INDEX COMPARISON

Figure 4-3 presents the demand index for lamb together with the demand indices for beef and pork (Tonsor, 2015)7 over the same 1990 – 2014 period (1990 = 100).

Figure 4-3 Beef, Pork and Lamb Demand Indexes, 1990=100

In general, beef, pork and lamb have followed similar trends in demand, but with two fairly pronounced periods of divergence. From the mid-1990s through 2001, pork enjoyed increased demand whereas demand for both lamb and beef was down. More recently, lamb has shown greater strength than either the beef or pork sectors, although demand for both beef and pork was up during 2013 and 2014. Relative to 1990, beef demand was down about 14 percent in 2014, pork was down 10 percent, while lamb ended the period down only about 5 percent. The 2014 index values for retail beef, pork and lamb were 86.2, 90.3 and 94.6, respectively. Over the 25-year period, none of the three meats recovered their 1990 demand level. Demand for lamb reached its lowest level with an index value of 79.7, in 1996 and again in 2000. Beef and pork lows were more recent, both in 2010, at 75.0 and 78.5, respectively.

7 The beef and pork demand indices used are available on-line at www.agmanager.info/livestock/marketing/graphs at

the meat demand charts site, maintained by the Agricultural Economics Department at Kansas State University. The

comparative index values are provided in Appendix C.

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4.4 CHANGES IN ELASTICITY OVER TIME Elasticity is an important input for the demand index algorithm and it should be noted that elasticity estimates can vary year-to-year. Elasticity estimates can also vary across the different ranges of data analyzed and with the variables, assumptions and modeling techniques selected. Historically, demand for lamb has been estimated in the inelastic range. The 2008 National Academies study pointed out:

[The] demand index is often calculated using a single estimate of own-price elasticity for a given time period. Estimates of own-price elasticities, however, can range rather widely and can be quite different for different time periods. No research has been done to investigate the sensitivity of the various meat demand indices to changes in the own-price elasticity measures used.

Given the range of elasticity estimates reported in the research literature, three different elasticity estimates were selected to examine the sensitivity of the demand index to changes in the own-price elasticity measure used. Capps and Williams (2011) reported elasticity estimates for the time period 1978/79 to 2009/10 of -0.726 and -0.645 (both inelastic) using two different model specifications. Schroeder, et al. (2001) reported an elasticity estimate of -1.09 for the period 1978 to 1999. Shiflett et al. (2007) reported an elasticity estimate of -0.66 for the period 1980 to 2005. An elasticity of -0.645 was selected to represent the lower range in the analysis, -0.76 estimated in this study was selected as a mid-range elasticity estimate, and -1.09 was selected to represent an upper range elasticity measure. The sensitivity analysis shows that changing the elasticity value does not affect the overall pattern and general direction of changes in demand (Figure 4-4)8. However, as the absolute elasticity value increases -- moving from inelastic to elastic -- the relative level of the index values also increases. For example, note that for each of the three elasticity values, demand showed an increase in 2011 over 2010. However, using the elastic measure of -1.09, there was an estimated eight percent demand increase in 2011 relative to 1990, whereas, using the two inelastic values, there was an estimated decrease in demand of nine percent and three percent, respectively for the -0.645 and the -0.76 elasticity measures. The sensitivity analysis indicates that although general trends in demand are fairly robust to different elasticity estimates, the magnitude of the percentage change in demand for a particular year relative to the base year is sensitive to the elasticity estimate applied and underscores the need to periodically re-evaluate the own-price elasticity of demand.

8 The comparative index values for each of the three elasticity measures are provided in Appendix D.

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Figure 4-4 Lamb Demand Index under Different Elasticity Measures

Some market analysts choose to apply a constant elasticity estimate across commodities when examining relative changes in demand for those commodities. For example the Daily Livestock Report, sponsored by the Chicago Mercantile Exchange (CME) Group, Inc. uses an across-commodity assumed elasticity of -0.75.9 Figure 4-5 shows what happens to the relative changes in demand when a constant across-commodity elasticity value of -0.75 is applied to all three meats. Results show that here again, the overall across-commodity demand patterns remain fairly consistent, with the single across-commodity elasticity estimate mitigating the relative differences.

9 Personal communication, Steve Meyer, July 2014.

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Figure 4-5 Beef, Pork and Lamb Demand Indexes, 1990=100, E = -0.75

4.5 CONCLUSION

The demand index is a tool used to measure changes in demand. While the demand index measures both the direction and the magnitude of changes in demand, it does not provide any information as to why those changes have occurred. It does, however, provide some indication of the industry’s responsiveness to changes in demand and of the success or failure of that response. It is likely that multiple factors have contributed to the year-to-year and period-to-period changes in demand. Recall that a shift in the demand for lamb does not come from changes in the price of lamb or from changes in supply (per capita consumption). Changes in demand come from changes in prices of competing meats, demographics including consumer incomes, consumer eating experiences and attractiveness of product offerings or health or food safety concerns. The demand index reflects changes in consumer tastes and preferences, but says nothing about why tastes and preferences have changed.

Since elasticity values can vary over time, and because elasticity estimates help drive the demand index, it is important to periodically update and re-evaluate these estimates.

4.6 TOTAL DISAPPEARANCE

It has been common practice to measure changes in demand for commodity meats such as beef, pork and chicken, on a per capita basis. The lamb industry has also assumed this convention. The demand index then reflects changes in the average individual, or per capita, demand for a particular meat. Aggregate demand, or total disappearance, is then simply the sum of the individual demand curves (price –quantity schedules) across the entire population.

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Increasingly, the U.S. lamb market is being characterized by many as a specialty or niche-type market. A number of studies have pointed to both the regional and ethnic nature of lamb consumption in the U.S. The 2008 National Academies study stated:

The traditional argument that American tastes and preferences have moved away from lamb may no longer be applicable, given the steady level of [total] consumption in recent years despite declining production. More appropriate now may be the argument that lamb is consumed fairly consistently by a small group of consumers and not at all by most consumers.

While per capita consumption is currently less than 1 lb. nationally, it has been documented that among ethnic groups, per capita consumption is over 3 lbs. at home and over 2 lbs. away from home (Shiflett, et al., 2010). Nationally, per capita consumption measures may tend to mask growth in the ethnic and niche or specialty markets for lamb. In this context, the conventional per capita-based demand index may not be the most appropriate barometer of the health of the U.S. sheep and lamb industry. If the lamb market is indeed defined by a number of smaller and more diverse specialty or niche markets, a total disappearance-based demand index may be a more appropriate means of capturing changes in demand. Consider the following scatter diagrams of 1) inflation-adjusted retail prices and per capita retail consumption over the 1978–2014 period (Figure 4-6), and 2) inflation-adjusted retail prices and total retail disappearance over the same 1978–2014 period (Figure 4-7). Figure 4-6 Inflation-adjusted Retail Lamb Prices (2009=100) and Per Capita Retail Consumption (1978-2014)

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Figure 4-7 Inflation-adjusted Retail Lamb Prices (2009=100) and Total Retail Disappearance (1978-2014)

Note in particular what happens to the 1978-1984 demand surface identified in Figure 4-7 when consumption is reported in terms of total retail disappearance rather than on a per capita basis. In Figure 4-6, on a per capita basis, the 1978-1984 demand surface lies far to the right of the 2002-2014 demand surface, whereas, in Figure 4-7, on a total retail disappearance basis, the difference is much less pronounced. The near-overlay of the 1978-84 and 2002-14 demand surfaces may suggest that retail lamb prices in general have kept pace with the rate of inflation, but that 1) the rate of expansion of the consumer base for lamb has not kept pace with the rate of population growth and/or 2) the growth in lamb consumption among ethnic consumers is under-reported, as Shiflett, et al. assert in their 2010 study of the nontraditional lamb market in the U.S. Figure 4-8 shows the All Items Consumer Price Index for all urban consumers and the Lamb and Organ Meats Consumer Price Index for all urban consumers reported by the BLS (1982-84 =100). Note that during the initial period, 1978-1983, the Lamb and Organ Meats CPI, is slightly higher than the All Items CPI. The two indices track fairly closely between 1984 and 2001, however, in 2002, the two indices begin to diverge with growth in the Lamb and Organ Meats CPI far out-pacing growth in the All Items CPI. This would indicate that, over the 2002-2014 period, the rate of increase in retail lamb prices far exceeded the general rate of inflation for the economy as a whole.

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Figure 4-8 BLS All Items Consumer Price Index and Lamb Organ Meats Consumer Price Index for All Urban Consumers (1982-84=100)

Looking once again at Figures 4-6 and 4-7, similar demand surfaces are apparent in both the per capita retail consumption and total retail disappearance diagrams for the 1985-2001 period, which appear distinct from both the earlier 1978-1984 and the later 2002-2014 periods. The 1985-2001 demand surface generally coincides with the period when changes in retail lamb prices track fairly closely with the overall rate of inflation (Figure 4-8). A number of potential demand shifters were at work helping to define these different periods. On the negative side:

Beginning in the early to mid-1980s, health information linking cholesterol and fat to heart disease weakened demand across all of the red meats.

The phase-out of the National Wool Act (1993-1995) and subsequent failure of the 1996 industry-wide check-off referendum, left the U.S. sheep and lamb industry with very few resources available for advertising and promotion or for research and development.

Through the mid to late 1990s, the lamb industry lagged behind the beef industry in the adoption of new technologies and development of more consumer-friendly products.

With the advent of gas-flush and cryovac packaging technologies, imports increasingly began entering the U.S. as fresh-chilled cuts around the mid-1990s, making imports more competitive with domestic product. Prior to this time, imports primarily entered the U.S. as frozen carcasses and half-carcasses.

On the positive side:

In the late 1990s, U.S. lamb packers retooled plants and began fabricating more lamb in order to compete with imported case-ready products.

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The successful 201 trade case filed in response to a surge of cheap imports in the late 1990s, resulted in temporary industry safeguards put being put into place and in an infusion of federal dollars that included additional resources for promotion, research and development.

The sheep and lamb industry Lamb Promotion, Research, and Information Order (American Lamb Check-off Program) was successfully passed in 2001 and in July 2002, the American Lamb Board (ALB) began operations. The ALB was created to administer the check-off program and is charged with increasing demand for American lamb.

In concert, these later developments, along with an increasing ethnic population, have likely had a positive effect on consumer tastes and preferences, again calling to task the familiar, but overly-simplistic assertion that “American tastes and preferences have moved away from lamb.”

4.6.1 TOTAL DISAPPEARANCE OLS MODEL

Total retail disappearance was evaluated to determine what effect, if any, this alternate measure might have on the elasticity measures for lamb and on the demand index. The aggregate OLS demand model was re-estimated using total retail disappearance as the dependent variable and the resulting own-price elasticity was used to calculate an aggregate retail demand index. The results were then compared against the per capita retail model findings. Descriptive statistics for the quarterly continuous variables for the total disappearance OLS regression model are summarized in Table 4-1. Statistical results of the regression are summarized in Table 4-2.

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Table 4-1 Descriptive Statistics for the Quarterly Continuous Variables --Total Disappearance Model

Variable Mean Minimum Maximum Std. Dev.

TDisR 78.6 53.1 102.2 8.620

DPL 5.14 4.40 6.82 0.70

DPB 3.93 3.31 5.40 0.41

DPP 3.19 2.82 3.84 0.22

DPC 1.93 1.63 2.43 0.19

DDPI 9420.7 6934.3 11952.0 1595.8

Table 4-2 Total Retail Disappearance Dependent Regression Model, Quarterly, 1990-2014

Variable Coefficient Std Error t-Statistic Prob.

LnDPL -.7421798 .1535227 -4.83 0.000

LnDPB .2866989 .0961344 2.98 0.004

LnDPP .1270617 .1343726 0.95 0.347

LnDPC -.0421862 .2127757 -0.20 0.843

LnDDPI .229181 .117206 1.96 0.054

LnTDisR-1 .3197554 .0957631 3.34 0.001

Q2 -.0697058 .0170818 -4.08 0.000

Q3 -.1422439 .0173288 -8.21 0.000

Q4 .0223168 .0209058 1.07 0.289

constant 1.616101 1.082502 1.49 0.139

R-squared 0.7424 Shapiro-Wilk W test for normal data

Adj. R-squared 0.7163 Variable res

F(10, 96) 28.49 Obs 99

Prob > F 0.0000 W 0.98922

Root MSE 0.05895 V 0.882

Durbin-Watson d-statistic (10,99) 2.020006 z -0.277

Prob>z 0.60919

Variable VIF 1/VIF

LnDDPI 11.56 0.086540

LnDPL 11.11 0.089971

LnDPC 10.90 0.091731

LnTDisR-1 3.23 0.309310

LnDPB 2.72 0.367747

Q4 2.35 0.425478

LnDPP 2.19 0.457257

Q3 1.61 0.619261

Q2 1.57 0.637299

Mean VIF 5.25

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The model explains about 72 percent of the variability in the total retail disappearance of lamb and mutton lamb over the 1990-2014 period. The own-price elasticity of demand is estimated at-0.74, not significantly different from that of the per-capita consumption dependent model. Notably, income elasticity in the total disappearance model is not only positive, but is also statistically significant. Beef is a significant substitute for lamb in both models. The cross-elasticity measure for beef is similar between the two models, at 0.27 and 0.29, for the per capita and total disappearance models, respectively. Pork and chicken remain insignificant.

4.6.2 TOTAL DISAPPEARANCE DEMAND INDEX

Using the -0.74 elasticity of demand estimate for total disappearance, an aggregate demand index based on total retail disappearance was calculated. The results are shown in Figure 4-9, below.

Figure 4-9 Total Retail Disappearance Demand Index, 1990-2014, 1990=100

The general pattern of changes in demand for the total retail disappearance demand index is similar to that of the per capita retail demand index presented previously – although in recent years the ‘total disappearance’ index indicates that somewhat greater gains have been made. The ‘total disappearance’ index again shows demand declining rather significantly between 1990 and 1994, holding relatively steady but at a lower level between 1994 and 1997, increasing slightly over the 1998-2001 period, then showing a general sustained increase between 2002 and 2010 and another slightly smaller but sustained increase 2011-2014. With the exception of 2005, the total disappearance index shows demand consistently higher over the 2002-2014 relative to the 1990 base year. In contrast, the per capita index indicates that demand over the entire 1991-2014 period was

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lower than for the 1990 base level (Figure 4-10). On a per capita basis, the demand index shows a demand increase of about six percent between 2002 and 2014. In terms of total disappearance, the index shows a nine percent increase over the same period.

Figure 4-10 Per Capita and Total Disappearance Index Values, 1990=100

4.6.3 CONCLUSION

Given that the lamb market in the U.S. is increasingly characterized as a specialty or niche market, a total retail disappearance-based demand index in conjunction with the more conventional per capita-based demand index may provide a more balanced reflection of changes in demand in the U.S. than does either index alone.

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5 2009-2014 SCANNER-DATA LAMB CUT MODEL

5.1 INTRODUCTION

The American Lamb Board currently receives quarterly market snapshots of trends in scanner lamb retail prices and volume by cut and by region of the country from Information Resources, Inc.’s (IRI) FreshLook Marketing Group. This study builds upon that analysis, using the same scanner data -- actual prices and volumes consumers face at the check-out counter – to estimate point-of-purchase retail lamb cut demand. The 2008 National Research Council Changes in the Sheep Industry in the U.S. highlighted lack of research for specific cuts of lamb as one of the major opportunities and challenges facing the U.S. lamb industry. The study contended that this type of information is needed to assist retailers and foodservice purveyors in pricing and price-based promotion of lamb cuts so as to maximize lamb sales revenue,” (2008). The key to exploring more cut-level demand in the industry is retail scanner data. The objective of this chapter is to estimate the demand for lamb cuts across the U.S. and by region using retail scanner data from IRI’s FreshLook. Six cuts including ground lamb, leg, loin, misc. (e.g. stew meat), rib and shoulder were studied across eight U.S. regions and nationally. 5.2 LITERATURE REVIEW

There are few demand studies for meat cuts and even fewer for lamb. It is hypothesized that the demand for lamb cuts is more price elastic than observed in demand models for aggregated lamb. Hermann and Roeder (1998) explain:

“Despite this evidence on price-inelastic food demand, it is well known that food retailers compete strongly by adopting very active pricing strategies. The latter observation might imply that food consumption in industrialized countries is price-inelastic at the aggregate level of market demand functions, but not necessarily at the point of sale.”

Historically, lamb in aggregate has an inelastic demand, with a few older studies indicating elastic demand. Individual lamb cuts are thought to have a more elastic demand. This is because at the cut level closer substitutes are available. If one lamb cut is thought to be priced too high, consumers can switch to another, lower-priced cut. By contrast, for aggregate lamb consumption, if a consumer has his or her heart set on having lamb for dinner, substituting beef, pork or chicken might not be an acceptable option. Research on the demand for different cuts of lamb has been extremely limited. In 1991 the TAMRC Lamb Industry Assessment Team from Texas A&M University, University of Wyoming and Colorado State University used a seemingly unrelated regression (SUR) procedure to model different lamb cuts. The cut model utilized weekly scanner data at a Houston-based retail supermarket chain to analyze specific cuts of lamb at the local market level from January 1987 to November 1988. Cuts included

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shoulder chops, round bone chops, rib chops, sirloin chops, loin chops, leg-of-lamb, shank, breast and ground lamb. With the exception of sirloin chops and breast roasts, all cuts were price elastic. Elasticities ranged from -0.77 (breast) to -3.17 (leg of lamb). In general, the study found that most cuts were significant substitutes. Three cut relationships were considered complements. Cross-cut price elasticities for lower value cuts, including the breast and ground lamb, were not significant. Consumers in the Houston market studied were less sensitive to changes in cross-cut prices than they were to own-price changes (1991). Hays et al. (2009) found that the beef chuck had an elasticity of -1.167 while the Rib Eye steak had an elasticity of -2.140 and the Porter House steak had an elasticity of -2.568. Hays et al. commented that the “higher elasticity for Porter House steaks seems consistent with theories related to the purchase of higher priced goods,” (2009). 5.3 BACKGROUND

The interaction of demand and supply of each cut defines price in a competitive market. Similar to lamb in the aggregate, the demand for each cut can contract or expand based upon changes in traditional demand shifters of prices of substitutes and complements, income and tastes and preferences.

Scatter plots again can reveal price-quantity relationships for individual cuts and possible demand surfaces. For example, a scatter plot of inflation-adjusted lamb prices and volume of legs sold reveals that lamb demand for legs expands at Easter (orange dots in Figure 5-1). The scatter points for price and quantity consumed at Easter lie on a higher demand surface indicating a higher level of demand, holding all else constant.

Figure 5-1 Easter Leg Demand, 2009-2013

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5.4 MODEL The model used to estimate cut demands is the quadratic version of Deaton and Muellbauer’s original almost-ideal demand-system model (AIDS). It is a popular model often used in applied consumer demand theory to study broad classifications of goods. The model estimates consumer behavior for a commodity group such as meats. The Deaton and Muellbauer (1980) AIDS model is specified as follows:

𝑤𝑖 = ∝𝑖+ ∑ 𝛾𝑖𝑗𝑗 log 𝑝𝑗 + 𝛽𝑖 log{𝑥

𝑃}

where wi is the share associated with the ith good, 𝛼𝑖 (alpha) is the constant coefficient in the ith share equation, 𝛾𝑖 (gamma) is the slope coefficient associated with the jth good in the ith share equation, pj is the price on the j th good. X is the total expenditure on the system of goods given by:

𝑋 = ∑ 𝑝𝑖

𝑛

𝑖=1

𝑞𝑖

in which qi is the quantity demanded for the ith good. The model is derived from economic theory: it represents the minimum expenditure necessary to achieve a certain level of utility, or satisfaction. In the AIDS model, the alphas (α) represent budget shares, betas (β) are expenditure coefficients and gammas (γ) are own- and cross-price coefficients. The model represents the final stage in a multiple-stage budgeting process. The first budgeting decision might be how much income to allocate to rent, food, transportation and entertainment, for example. The second stage might be how much income to allocate to meat versus fruits and vegetables. Last, a consumer will decide how much income to allocate to different meats. This is the decision modeled here and is called ‘weakly separable’ from other budgeting decisions. The quadratic variant of AIDS– called QUAIDS -- was pioneered by Banks, Blundell, and Lewbel (1997). QUAIDS can improve the income – expenditure relationship and thus improve the model fit and results. In a QUAIDS model, a quadratic term is added to the log of income which leads to increased flexibility in the representation of income effects. The QUAIDS model allows the relationship between income and the quantity consumed to change as income rises. Income and the quantity consumed might first be positively related at lower income levels (consumption of a good rises with income), but then at some point, the quantity consumers buy begins to fall as income continues to expand. The demand system examined here consists of six budget share equations: ground, leg, loin, misc., rib and shoulder. The model estimates the variation in the share of total lamb expenditures spent on each cut. The leg budget share, for example, is estimated as a function of the price of legs, the prices of all other cuts and total expenditure on lamb.

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The model explores the seasonal effect of holidays in explaining expenditures on lamb cuts. The National Research Council (2008) found that there appears to be a discernable impact of Muslim and Christian holiday periods and of Western and Orthodox Easter in particular on the disappearance levels of lamb (2008). Although there are a number of holidays that influence lamb consumption, given the limitations of the data set and the magnitude of the impact of Easter on prices, consumption and expenditures, only the specific effects of the Easter holiday are captured in this model. Lamb expenditures rise sharply during Easter from an average $6.5 million weekly to $23.9 million due to heightened leg sales (Figure 5-2).

Figure 5-2 Leg of Lamb Expenditure, 2009-2013

During this period there is an adjustment in budget shares with the leg increasing from an average of 21 percent of the total budget to 65 percent during Easter over the years 2009 to 2013 (Figure 9-4). At the higher expenditure levels during Easter, the budget share to the leg rises at the expense of the share to the loin, rib and shoulder.

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Figure 5-3 Total Expenditure and Leg Budget Share

The leg of lamb sees an average 15 percent price discount at Easter – compared to its annual average (Figure 5-4). The leg of lamb is also featured in December, but at a lower discount rate of 8 percent. On average, between 2009 and 2013, 1.1 million lbs. of leg of lamb sell in a given month, but during Easter, that volume jumps by 359 percent to 4.1 million lbs. (Figure 5-4).

Figure 5-4 Leg of Lamb Price and Quantity Demanded

Graphical analysis of cuts can give us a quick look at relationships between cuts that can be empirically tested later. It appears that in the decision to buy the lamb leg a consumer will consider prices and his or her budget constraint, but also how much purchasing the leg at Easter will fulfill some level of satisfaction defined by cultural factors. The data also reveal that consumers typically trade the shoulder for the leg at Easter (Figure 5-5). The loin and rib see similar drops in budget share at the leg’s expense, but not as pronounced. The

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shoulder averages about 25 percent of a consumer’s lamb budget for most of the year, but that share drops to less than one percent during Easter as the leg takes a greater share.

Figure 5-5 Leg and Shoulder Budget Shares

The QUAIDS model is specified as follows where expenditure shares are functions of all cut prices and total lamb expenditures and a variable denoting when Easter fell each year. w_ground = f(Pground, Pleg, Ploin, Pmisc, Prib, Pshoulder, Exp, Easter) w_leg = f(Pground, Pleg, Ploin, Pmisc, Prib, Pshoulder, Exp, Easter) w_loin = f(Pground, Pleg, Ploin, Pmisc, Prib, Pshoulder, Exp, Easter) w_misc = f(Pground, Pleg, Ploin, Pmisc, Prib, Pshoulder, Exp, Easter) w_rib = f(Pground, Pleg, Ploin, Pmisc, Prib, Pshoulder, Exp, Easter) w_should = f(Pground, Pleg, Ploin, Pmisc, Prib, Pshoulder, Exp, Easter) Where:

w_ground = the share of the total lamb expenditure to ground lamb. Similarly for other cuts. Pground= price of ground and prices of all other cuts Exp = total expenditures on ground, leg, loin, misc., rib and shoulder

Easter = 1 for the week before Western Easter and 0 otherwise.

5.5 DATA Retail scanner data used in this model were provided by the American Lamb Board. The data were collected by IRI and its FreshLook Marketing Group. The data - - from 2009 through 11/3/2013 -- represents weekly prices, volume, and expenditures by cut (for 252 weekly observations). The cuts include ground lamb, leg, loin, misc., rib and shoulder. Variety lamb accounted for an average of only 0.04 percent of the lamb budget and was omitted from this analysis. Miscellaneous lamb includes cubes, stew meat, shank and breast. FreshLook refers to misc. lamb as ingredient items. The natural log of cut prices was used in the model estimation to allow for nonlinear relationships between prices and budget shares.

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The data includes the mid-2011 period of tightening lamb supplies and record-high prices. The data includes domestic and imported product, but does not differentiate between sources. The data also does not delineate feature pricing. On average, nominal lamb cut prices gained 21 percent in the five years 2009 to 2013. The rib and shoulder saw the steepest gain at 28 percent while the loin saw the smallest increase at 15 percent. By comparison, the inflation rate during this period was 9 percent, indicating that lamb prices saw a real price increase. The summary statistics for the eight models are presented in Appendix E.a. The loin, shoulder, leg and rib account for 86 percent of consumers total lamb budget. Over the course of the 2009-2013 study period, the rib accounted for 19 percent of total lamb expenditures with an average price of $13.16 per lb. By contrast, the leg accounted for 24 percent of total expenditures and an average price of $5.55 per lb. Together, the rib and leg account for 48 percent of total expenditures. Ground lamb accounts for 5 percent, misc. lamb including stew meat acocutns for 9 percent and variety meats, 0.04 percent (Figure 5-6). Variety lamb meat was unavailable in many markets -- consisted of less than 1 percent of lamb’s budget share -- and therefore was omitted from the analysis.

Figure 5-6 Budget Share by Cut

According to FreshLook Marketing Group in the 52 weeks ending October 5, 2014, the leg produced $86.6 million in sales followed by the loin ($85.8 million), the shoulder ($73.1), the rib ($70.5 million), misc. lamb ($31.9 million) and ground lamb ($22.4 million). The data were collected for the U.S. and by region. The eight regions include the West, California, Great Lakes, Plains, South Central, Northeast, Mid-South and Southeast (Figure 5-7). On average, the Plains represents the region with the lowest average weekly expenditure on lamb at under $200,000 and the Northeast is the highest sales region at $2.3 million per week.

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Figure 5-7 FreshLook Regional Map

Budget shares to lamb cuts differ considerably across regions. The share to the rib ranges from 23 to 25 percent in the Northeast and South Central, respectively, compared to 13 to 16 percent in the West and California, respectively. The share to the loin ranges from 17 percent in California to nearly double that, 32 percent, in the Great Lakes region. The share to ground lamb in the Great Lakes is 7 percent, three times higher than the 2 percent calculated in the Southeast. Lamb sales across regions vary considerably. For example, based on the FreshLook sampling, Northeast average weekly sales on all lamb cuts were over 10 times that of sales in the Plains states (Figure 5-8). The Northeast accounted for 36 percent of total – across regions -- weekly average lamb expenditures, the Southeast, 15 percent. Weekly average sales in the Northeast were over two times that of the second-ranking region by sales, the Southeast.

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Figure 5-8 Percent of Weekly Sales by Region, 2009-2013

In the year ending October 5, 2014, the Northeast accounted for 33 percent of the U.S.’s total fresh lamb sales at $122.5 million.10 The Southeast was second at $57.1 million, the Mid-South was third at $44.2 million and California ranked fourth at $42.4 million followed by the West at $36.5 million. The Great Lakes ranked sixth followed by South Central at $21.0 million and last in sales was the Plains at $10.4 million.

5.6 RESULTS A demand system was estimated for each of the eight regions plus the U.S. The parameter results -- shown in Appendix E.b. – are not as important or intuitive as the elasticity estimates that will follow, but are important in estimating statistical significance of relationships between variables. The parameter estimates identify significant quantity demanded response (that is not random) to changes in relative prices and expenditure such that the change in price levels leads to systematic changes in budget shares for each cut.11 In the parameter table Appendix E.b., the alpha (α) are the estimated budget shares of each commodity and should sum to 1 to satisfy the adding-up condition. The beta (β) represents the commodity expenditure coefficient, that is, variation in a good’s expenditure when real income changes. In the U.S. model, a positive coefficient and less than one –leg, loin and rib -- is indicative of a normal necessity good. A negative coefficient – as in ground lamb, misc. lamb and the shoulder --represents an inferior good – the quantity consumed falls as incomes rise.

10 IRI, FreshLook Marketing Group, “Fresh Meat and Lamb Review, Multi-Outlet Data Ending 10/5/2014.” 11 Common to time series analysis, some of the cut prices exhibited unit roots (display trending behavior over time).

Presence of unit roots justifies the QUAIDS which is an estimated nonlinear seemingly unrelated (NLSUR) model whereby the errors for each equation are allowed to be correlated across equations in the system.

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The inferior good label among lamb cuts modeled for ground lamb, shoulder and misc. lamb is counter-intuitive. The unexpected signs might be a function of data limitations -- particularly for regional models with limited lamb availability -- limited number of observations, unusual time period and no information about price featuring. Clearly, as total expenditures to lamb increase (proxy for income), the quantity demanded of the leg increases, not decreases. Changes in relative prices work through the demand system. The gamma (γ) coefficient shows how the budget share of a good i changes due to a percent change in the price of a good j, holding real expenditure constant. 12 That is, how the budget share to the leg changes with a change in the price of shoulder. ‘Gamma_rib_ground’ = 0.11 implies that the rib price and the budget share of ground are positively correlated. That is, as the rib price increases, the quantity of ground also increases (cross-price elasticities support this, which will be shown later). The U.S. average ground price and average leg prices are fairly close. So, as ground price increases, consumers switch to legs as legs are now relatively cheaper compared with ground. So an increase in the price of ground means less ground is purchased and more legs are purchased which increases the budget share for legs. A Wald test revealed that the quadratic term on expenditure was significant and positive in explaining the variation of lamb cut budget shares (all models were significant at the 5 percent level).13 The test therefore validated the choice of the QUAIDS model functional form over the AIDS model, justifying the more flexible functional form for expenditure. This means that the income effect in the demand for lamb (how lamb demand changes with income) may differ depending upon income level. In the QUAIDS model, goods that have a positive β-coefficient (coefficient for total expenditure), and a negative λ-coefficient (coefficient for squared total expenditure), are considered to be luxury goods at low expenditure levels, becoming necessity goods as the total food expenditure grows (indicating rising incomes). The loin and rib fulfill this criteria: as incomes rise to higher levels, consumers will increase loin and rib consumption at a lower rate than at lower income levels. The model shows that Easter positively affects lamb demand for all cuts across the U.S. and in individual regions, but with differing degrees of significance. Easter is highly significant in all regions except for the West and Plains.14 The effect of Easter on demand differs across cuts and across regions. In the U.S. in aggregate, Northeast, Southeast and Mid-South, the effect of Easter is positive and significant on leg demand, but not significant in other regions. The effect of Easter on shoulder demand was negatively significant in the Southeast and Mid-South and marginally negatively significant in the U.S. in aggregate and Northeast. In the Southeast and Mid-South, shoulder demand falls during Easter. Rib

12 Changes in relative prices work through the demand system. Each gamma ( γij ) represents 102 times the effect on the

ith budget share of a 1 percent increase in the jth price with (X/P) held constant (Deaton and Muellbauer, 1980). Thus, isolating the effect of a change in the price of legs as it works through the demand system, a 1% decrease in the leg price brings about a 19% (0.190*100) decrease in the budget share of ribs, ceteris paribus. 13 The Wald test indicates that the lambda coefficients in the parameter results in Appendix E.b. are jointly significantly different from zero. 14 A high degree of significance is defined by a 5% significance level.

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demand also falls significantly during Easter in the U.S., California, Great Lakes, Mid-South and Southeast. 5.7 OWN-PRICE AND CROSS-PRICE ELASTICITIES

Table 5-1 presents the own-price and cross-price elasticities that are derived from the QUAIDS model parameters in the previous section. An own-price elasticity tells us the magnitude of which the quantity consumed of one cut will be affected by a change in its price. The own-price elasticities in the table are in red typeface. Own-Price Elasticities. As expected, the own-price elasticities of lamb cuts is more elastic than for aggregated lamb. Apart from an inelastic misc. lamb, including stew meat, and ground lamb, all cuts in the U.S. are elastic ranging from -1.688 for the loin to -2.409 for the leg. The elastic demand tells us the change in quantity demanded will be in greater proportion to the change in price. As the number of substitutes increases, the elasticity – or price sensitivity – will increase. For the segment of the population that buys lamb, if the price of one cut rises, then these elasticity findings tell us that the consumer will reduce purchases of the one cut in favor of another lamb cut. Elastic demand means that price decreases – or promotions – can increase total sales revenues because the quantity purchased is significantly high to offset the revenue-reduction effect of a price drop. This is particularly evident for leg promotions at Easter: price promotions prompt a spike in consumption and sales. The leg is the most elastic cut, according to the model. The leg therefore holds the greatest potential to increase revenue through a price promotion such as during the Easter and December holidays. The own-price elasticity for the leg ranged from a low of -0.961 in South Central to a high of -2.831 in the Southeast and -2.861 in the Northeast. Across the U.S., the own-price elasticity for the leg was –2.409. A 10-percent price feature for the leg will result in a 24-percent increase in its quantity demanded. The quantity response to price featuring is sufficiently large to offset the lower price and revenues will increase. The own-price elasticity for the loin ranged from a low of -0.632 in South Central and -0.656 in the Plains, but most elasticities hovered around the U.S. result of -1.688 (from -1.088 in the West to a high of -2.205 in the Northeast). These results suggest that a 1-percent price feature of the loin will yield the greatest loin consumption increase in the Northeast (by 2.2 percent) thereby increasing loin revenues.

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Table 5-1 Cut and Regional Own-Price and Cross-Price Elasticities

Ground price

Leg price

Loin price

Misc. price

Rib price

Shoulder price

U.S. Ground quantity 0.748 0.429 -0.542 -0.729 -0.403* 0.342*

Leg quantity 0.008 -2.409* 0.234* -0.071 -0.024* 0.226

Loin quantity -1.146 0.480 -1.168* -0.065* 0.441 0.221

Misc. quantity -0.454 0.134 -0.139 0.371* -0.378 -0.124

Rib quantity -0.154 0.190 0.492 -0.209 -1.740* 0.394*

Shoulder quantity 0.058 0.530 0.285 -0.049 0.430 -1.845*

California Ground quantity -1.225* 1.244* -0.593* 0.215* -0.186* -0.139*

Leg quantity 0.361 -2.085* -0.166 -0.075 -0.132 0.145*

Loin quantity -0..231 0.040 -1.686* 0.053 0.356* 0.680*

Misc. quantity 0.097 0.124 0.081 -0.925 0.455* -0.536*

Rib quantity -0.093 0.037 0.347 0.336 -1.989* 0.373*

Shoulder quantity -0.037 0.315 0.436 -0.289 0.256 -1.432*

West Ground quantity -2.329* 1.442* 0.159 -0.754* -0.695* 1.400*

Leg quantity 0.329 -2.403* 0.156* 0.269* -0.325* 0.362*

Loin quantity 0.070 0.464 -1.088* -0.332* 0.514* -0.164*

Misc. quantity -0.314 0.515 -0.498 -0.830 0.003 0.000*

Rib quantity -0.394 -0.561 0.597 -0.045 -1.479* 0.475*

Shoulder quantity 0.543 0.813 -0.137 0.139 0.487 -2.176*

Plains Ground quantity -1.055 0.718* 0.350* -0.844* -0.116 0.193

Leg quantity 0.191 -1.260 -0.422 0.272* -0.095 -0.397*

Loin quantity 0.104 -0.115 -0.655* -0.219* 0.054 0.718

Misc. quantity -0.940 0.946 -0.823 -0.317* 0.210* -0.004

Rib quantity -0.104 -0.003 0.015 0.107 -1.199 0.105

Shoulder quantity 0.127 -0.302 0.200 0.031 0.177 -0.756

South Central Ground quantity -0.886 0.272* 0.324 0.024 -0.686* 0.678*

Leg quantity -0.030 -0.960 -0.240 -0.167* -0.119 -0.367*

Loin quantity 0.059 0.123 -0.631* -0.097* -0.755* 0.840*

Misc. quantity -0.048 -0.583 -0.673 0.183* 0.199* -0.593*

Rib quantity -0.192 0.122 -0.911 0.088 0.163* -0.202*

Shoulder quantity 0.301 -0.418 1.784 -0.241 -0.294 -1.591*

Great Lakes Ground quantity -0.231* 0.354* -0.060* -0.260* 0.025 -0.129*

Leg quantity -0.013 -2.418* 0.144* 0.090* 0.185* -0.029*

Loin quantity -0.046 0.408 -1.703* -0.028 0.273* 0.365*

Misc. quantity -0.389 0.653 -0.196 -0.158* 0.056 -0.806*

Rib quantity -0.039 0.534 0.507 0.012 -1.249* -0.766*

Shoulder quantity -0.067 0.322 0.750 -0.232 -0.559 -0.676*

Northeast Ground quantity 0.159* 0.054 -0.028 -0.294* -0.528* 0.079*

Leg quantity -0.066 -2.861* 0.621* -0.031 0.381* 0.417*

Loin quantity -0.041 0.679 -2.205* 0.101 0.448* 0.218*

Misc. quantity -0.204 0.177 0.127 -0.329* -0.146 -0.145*

Rib quantity -0.051 0.207 0.458 -0.079 -1.830* 0.306*


Mid-South Ground quantity 0.099* 0.935 -0.350 0.380 -0.598 -0.396

Leg quantity 0.151 -2.540* 0.426* -0.138* 0.197* 0.260*

Loin quantity -0.142 0.532 -1.495* -0.237* 0.177 0.241

Misc. quantity 0.298 -0.162 -0.724 0.918* -0.167 -0.517*

Rib quantity -0.307 0.391 0.225 -0.134 -1.969* 0.601*


Southeast Ground quantity -1.198 0.289 0.915* 0.217* -0.676* 0.056*

Leg quantity 0.005 -2.831* 0.325* 0.078* 0.449* 0.441

Loin quantity 0.069 0.415 -1.592* 0.154 -0.316* 0.209*

Misc. quantity 0.043 0.313 0.441 -1.588* -0.150* -0.166

Rib quantity -0.082 0.581 -0.355 -0.054 -1.579 0.421*

Shoulder quantity 0.003 0.582 0.312 0.000 0.442 -1.816*

Notes: Own-price elasticities are in red and * indicates significance at 5%. Due to the Slutsky symmetry restriction of QUAIDS (The estimated effect of real price of good 1 on the expenditure share of good 2 is the same as the estimated effect of real price of good 2 on the expenditure share of good 1) only the cross-price elasticities corresponding to parameter results are reported.

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The rib elasticities range from a low of -1.249 in the Great Lakes to a high of -1.989 in California with -1.746 in the U.S. After the leg, consumers are very price sensitive to changes in the rib price: drop the price of the rib and a significant increase in sales will follow. In the U.S. the shoulder has an own-price elasticity of -1.845. Elasticities range from -0.676 in the Great Lakes region to -2.176 in the West, indicating that shoulder price featuring will have the greatest impact on sales in the West. If further analysis over time repeatedly finds that the shoulder has an inelastic demand in the Great Lakes region (-0.676) then it could be useful to determine whether unique shoulder cuts or packaging in the region could explain the inelastic demand (consumers relatively insensitive to changes in price). Alternatively, it is perhaps the lack of lamb substitutes in the region that is causing the inelastic demand of the shoulder. The variety of product offering across regions is likely highly variable. Ground lamb in the Northeast and Mid-South have positive own-price elasticities of 0.159 and 0.099, respectively. This is a rare case where it appears that demand is not downward sloping as theory dictates, but upward sloping: as prices increases, so too does quantity demanded. Figure 5-9 shows a positive relation between ground lamb prices and quantity consumed nationally suggesting an upward sloping demand curve. It is possible that significant demand expansion for ground lamb produced this anomaly. For every purchase, a substitution and income effect come into play. A rising price might cause a consumer to switch to a lower-price alternative (substitution effect); however, if incomes are simultaneously rising, then consumers might buy more of a good even though its price is rising (income effect). For the case of ground lamb, the income effect appeared greater than the substitution effect. It is possible that the income effect had a demand-expanding effect on ground lamb. It is also possible that the increase in quantity demanded as prices rise is a reflection of a change in tastes and preferences for the good which is shifting the demand curve rather than a direct response to a price increase. A scatter plot of price versus total expenditures on ground lamb indicated inelastic demand which suggests that ground lamb is not very price sensitive.

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Figure 5-9 Inflation-adjusted Ground Lamb Price and Quantity

Cross-Price Elasticities. Cross-price elasticities tell us how the quantity demanded of one cut changes with the change in price of another cut. A consumer might trade up or trade down depending upon relative price levels. If the loin is priced too high for an individual, he or she might choose shoulder blade chops as the favored summer grilling option. From cross elasticities we can then predict how a price promotion of the leg will affect the consumption of other cuts such as the shoulder. For the estimates of cross-price elasticities, the positive signs imply the cuts are substitutes and the negative signs imply the cuts are complements. As legs become relatively cheaper during Easter featuring, the quantity demanded of the leg increases at the expense of other cuts, or substitutes. For example, when the leg is priced 1-percent lower, ground lamb consumption will fall by 4.3 percent, the quantity demanded of the loin will fall 4.8 percent, the rib will fall 1.9 percent and shoulder consumption will fall 5.3 percent. During Easter leg featuring, shoulder sales will be the most impacted among lamb cuts in the aggregated U.S. model. Similarly, all cuts are substitutes to the leg in the largest Northeast market. However, in the Northeast the loin is the one cut that sees the greatest decline in consumption from leg featuring. While we primarily expect to see positive signs on cross-price elasticities of lamb cuts indicating the two cuts are substitutes in consumption, negative signs do occur, signifying the two cuts are complements. Different lamb cuts are typically considered competitors for the consumer’s lamb dollars and thus this complementary result appears to counter theory. For example, as the loin price increases 1 percent, ground lamb consumption falls 5.4 percent. Negative cross-price elasticities are counter-intuitive and warrant further investigation. Menkhaus et al. (1985) explain that negative cross-price elasticities are explained by separating out the income and substitution effects embedded in one cross-price elasticity measure. The income effect states that higher (lower) income levels will raise (lower) quantity demanded for a good. The substitution effect

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means that a higher price will result in consumers trading down to a lower-valued good (holding income constant). Simultaneously, because the loin price rose, the consumer is worse off because he or she can’t buy as much as before. Now the consumer is at an effective lower income level. That is, the income effect will also affect how the consumer chooses to allocate this smaller lamb budget among lamb cuts and hence, ground lamb consumption falls. Ground lamb is the one cut that has the most negative cross-price elasticities, signifying complements, not substitutes. Among the five substitute cuts, ground lamb has 4 cuts that are identified as complements. Ground lamb is an easy, every-day option that can be traded up for loins or leg-of-lamb for weekend company. Ground lamb experienced rising prices and increased quantity demanded, suggesting ground lamb demand increased over this time period. This increased demand has important implications for other lamb cut dynamics. In theory, if the price of ground lamb rises, it is expected that its quantity demanded will fall and the quantity demanded of another cut will rise: we expect to see a positive cross-price elasticity. However, if ground lamb demand is expanding while ground lamb prices are rising, we might see higher, not lower, ground lamb. It is the higher total income allocated to ground lamb that trumps the substitution to lower-priced cuts. We therefore see a negative cross-price elasticity. 5.8 EXPENDITURE ELASTICITY

An expenditure elasticity is used as a proxy for income elasticity – how quantity demanded changes with income. 15 The expenditure elasticity describes how a 1 percent increase in total lamb expenditure will change lbs. purchased by the corresponding lamb cut. Expenditure elasticities are estimated from the QUAIDS parameter estimates. Table 5-2 Cut and Regional Expenditure Elasticities

U.S. California West South Central

Plains Great Lakes

Northeast Mid-South

Southeast

Ground 0.114 0.636 0.732 0.256 0.679 0.291 0.089 -0.08 0.359

Leg 1.949 2.031 1.615 1.915 1.742 2.198 1.978 1.652 1.559

Loin 0.852 0.775 0.527 0.455 0.735 0.692 0.877 0.894 1.027

Misc. 0.550 0.699 1.112 1.577 0.921 0.830 0.500 0.328 1.098

Rib 1.001 0.989 1.419 0.923 1.081 0.996 0.978 1.196 1.062

Shoulder 0.637 -2.723 0.312 0.414 0.468 0.434 0.668 0.762 0.437

Most lamb cuts estimated by region were identified as normal goods: as income rises, the quantity consumed also rises. Within the category of normal goods, goods are either normal necessities or normal luxuries, or superior goods. The quantity demanded for normal necessities will increase with income, but at a slower rate than with luxury – or superior -- goods. This is because rather than buying more necessities as incomes grow, consumers will likely use their increased income to purchase more

15 If the assumption that lamb purchases are separate from other meat purchases does not hold, then the expenditure elasticity might not be a good proxy for the income elasticity.

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superior goods, consumers use extra income to trade up. The quantity demanded for luxury goods is very sensitive to changes in income. Superior goods are lamb cuts that consumers can do without during periods of reduced incomes and consumer confidence. In periods of rising incomes (lamb expenditures) consumers have the confidence to buy certain lamb cuts. If incomes fall, these lamb cuts might be the first to get cut from the food budget. The leg and rib are luxury goods denoted by expenditure elasticities greater than one while ground lamb, loin, shoulder and misc. lamb are normal necessities (expenditure elasticities less than one). The leg has an expenditure elasticity of 1.949 which means that as lamb expenditures rise by 1 percent the quantity demanded of the leg rises by 1.9 percent – greater than one percent. Said differently, when consumers choose to expand their lamb budget they first choose to spend the extra budget on the leg and second, on the rib – with an expenditure elasticity of 1.001. The leg is considered a luxury good across the U.S. with the Great Lakes regions recording the greatest expenditure elasticity of 2.198 and the Southeast the lowest at 1.558. The largest lamb market – the Northeast – has an expenditure elasticity of 1.978. As incomes rise and consumers spend more on lamb they will spend proportionally more on the leg in the Northeast than in the Southeast. As incomes rise, consumers will spend differing proportions of that increase on the rib depending upon region of the country. In the Plains, for example, as incomes rise 1 percent, the quantity demanded of the rib will rise by 1 percent, but in the West consumers will increase rib consumption by 1.4 percent. 5.9 CONCLUSION

The model shows that Easter positively affects lamb demand for all cuts across the U.S. and in individual regions, but with differing degrees of significance. Easter is highly significant in all regions except for the West and Plains. Easter is positively associated with leg expenditures in the U.S. while simultaneously significantly reducing rib spending. The significance of Easter across regions in demand modeling efforts is one tool to monitor the promotion effects on lamb consumption throughout the year. The model revealed that all lamb cuts except ground lamb and misc. lamb are elastic. The elastic demand for lamb legs at –2.409 is the highest own-price elasticity reported in the U.S. and confirms that the leg holds the most promise to increasing revenues through price featuring. Indeed, we see this in the market: leg price featuring of an average 15 percent occurs and leg consumption rises over 4-fold. When the leg is featured at Easter, the shoulder (cross-price elasticity 0.530) and the loin (0.480) are the two cuts that see the sharpest drop in consumption: Leg consumption rises at the expense of these cuts. It appears that from 2009 to 2013 ground lamb saw increased demand. This is likely due to increased tastes and preference for ground lamb that could have been motivated by the relative value of lamb

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compared to already high-priced ground beef and a desire for convenience meats. This finding explains the positive sign of its own-price elasticity of 0.748 and the negative cross-price elasticity of many other cuts, signifying ground lamb complements. It is plausible even when ground lamb prices were rising, we saw increased ground quantity demanded (rather than the expected decline) due to higher demand. Simultaneously we saw consumers buy more ground lamb at the expense of other cuts. Ground lamb, loin, shoulder and misc. lamb are considered normal necessities, while the leg and rib

are considered luxury goods. The expenditure elasticities tell us that as incomes rise consumers will

increase leg and rib consumption at a faster rate than other cuts.

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6 RECOMMENDATIONS

The 2014 Industry Roadmap study and the 2008 National Research Council sheep industry assessment recommended continued monitoring of lamb demand. Understanding and tracking demand is key to implementing lamb industry growth measures. This American Lamb Board study serves as a stepping-stone in a long-term commitment to monitor lamb demand.

Continue to track lamb demand. Through an updated lamb demand index the ALB should continue to monitor trends and changes in demand. While the demand index does not provide information as to why changes in demand have occurred, it does, however, provide some indication of the industry’s responsiveness to those changes and of the success or failure of that response. The National Research Council has stated that attention to demand can help in shaping the long-range price outlook and provides the foundation for long-term investment decisions (2008:200).

Continue to conduct periodic updates of demand elasticities and educate stakeholders of the

in-market effects of these measures.

Elasticity values can, and do, vary over time. Elasticity estimates help drive the demand index and it

is important to periodically update and re-evaluate these estimates. Elasticities provide a measure

of how sensitive consumers are to changes in price and income. Elasticities provide a measure of how

changes in supply will affect price. At retail, elasticities provide a measure of how a change in price

through feature activities will affect sales volume and revenue. Cross-price elasticities provide an

indication of how changes in the price of beef, for example, will impact lamb sales. During periods of

economic downturn, elasticities also provide an indication of how changes in consumer incomes will

affect demand.

Continue to update and analyze retail scanner data regularly. The lamb industry continues to face data challenges. Both the publically available BLS retail data and the private FreshLook scanner-based retail data have advantages and disadvantages for research purposes. One notable advantage of the BLS-based data is the span of the data which facilitates the identification of industry-wide long-term trends and changes in demand. On-the-other-hand, the FreshLook scanner data has the distinct advantage of capturing actual retail transactions and providing direct linkages between price and quantity observations. However, the scanner data available for this study spanned a relatively short time period, five years, and that five-year period was dominated by unsettled economic conditions nationally and unusual price and market activity in the lamb industry sector. As more data become available, the usefulness of the FreshLook series for analyzing and tracking retail demand will continue to improve.

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Continue to track lamb demand by cut and by region through the use of scanner data.

Lamb is not widely available in the U.S. nor is it widely consumed among the general population. Nationally, lamb is a heterogeneous product with market dynamics that differ by region. Continued tracking of demand elasticities by region and by cut can lead to sound pricing strategies and to the development and targeting of effective advertising campaigns, promotional activities, and educational efforts. Price specials will not be very effective in moving specific cuts of lamb when demand is inelastic but would be relatively more effective when demand is elastic. Price specials are more effective for cuts with elastic demand because consumers are relatively more price-sensitive. The cut model estimated for this study indicates that the leg holds the most promise for price promotions increasing total sales revenues. Over the past five years, legs were featured at Easter and, as the price of legs was lowered, consumption spiked, as did revenues. Cut market dynamics can also provide information about which cuts will likely be impacted the most when the price of another cut is discounted. The cut model found that shoulder consumption sees the greatest impact (decline) from leg features during Easter. Retail lamb cut dynamics also revealed that sales of ground lamb increased as prices increased, (contrary to theory). This suggests that over the past five years, the demand for ground lamb has been expanding. Three factors may have been important here, 1) consumers wanting to trade up for a summer grilling option chose lamb, 2) ground lamb is an easy substitute for ground beef in popular recipes, and 3) consumers may be telling the industry that they crave convenience in lamb product offerings.

Utilize retail scanner data to more effectively identify and delineate product substitution and improve estimates of cross-price elasticities.

This study investigated substitution across different cuts of lamb. However, scanner data can also provide insight into how the prices of specific cuts of other meats impact retail sales of lamb. Changes in the prices of substitutes (and/or complements) can lead to changes in demand for lamb. Aggregate demand models are limited in their ability to identify substitutes for lamb, such as beef or pork. It is likely that substitute relationships are more specifically defined across particular cuts of beef and lamb, for example, rather than across beef and lamb in general. Having simultaneous quantity and expenditure data provides the opportunity to more precisely identify and track the substitution of consumers away from a particular meat or cut when its price increases – consider for example, prime rib and rack of lamb, Easter hams and leg-of-lamb, or veal and other specialty meats as substitutes for particular cuts of lamb. Knowledge of specific cross-price and seasonal cross-price elasticities could help direct more effective advertising and promotional activities.

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Obtain retail scanner data for domestic and imported products separately. Scanner data also holds a great deal of promise for the lamb industry in terms of improving our understanding of the substitution between domestic and imported lamb and value-based pricing. It also holds a great deal of promise for the ALB in terms of evaluating the success of its different promotional activities on its mission to increase the demand for American lamb. The domestic share of the U.S. lamb market is currently around 50 percent. It is commonly held that American lamb constitutes a unique product offering, different from that of its imported competitors -- fresh with distinctly larger cuts. It is also widely held that American lamb has continued to dominate market share for specific cuts in some segments of the market such as racks at foodservice, however, empirical study has been lacking. In addition to price and volume information, retail scanners also collect data about various other product attributes. Meat Solutions, Inc. is a private company that adds value to the FreshLook scanner data by grouping and categorizing the data based on specific product attributes – including country of origin. Meat Solutions is able to provide sales data and average retail pricing for imported lamb from Australia and New Zealand. Over the range of the FreshLook data used for this study, Meat Solutions identified that approximately 40% of the lamb data was for Australian lamb, and less than 1% was for New Zealand lamb, with the remaining 59% of the data for U.S. product. A hypothesis to test is whether American and imported lamb operate in the same markets. Furthermore, to what extent are the two complements or substitutes? How do pricing strategies domestically affect imported product and vice versa?

Study food service lamb demand. Data limitations have constrained demand analysis to the retail sector. Given that an estimated 65% of the value of domestic product goes to food service, a means of capturing and characterizing the food service/food away from home sector would enhance the industry’s efforts to promote American lamb and increase demand in this important sector. It is recommended that the ALB survey the largest lamb packers regarding price sensitivities and popularity of cuts to the food service sector by regions. It is hypothesized that traditional demand shifters of income and price of substitute meats might have very different effects at food service relative to retail.

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7 FURTHER READING

7.1 LITERATURE REVIEW

Introduction

In 1989 Dr. Wayne Purcell wrote: “Lamb is not available in all markets, tends to be consumed on a regional basis by ethnic groups, and price-quantity relationships for lamb cannot be influenced by the traditional economic forces that act on beef, pork, and chicken,” (1989: 34). Modeling lamb as a commercial meat akin to studies done for beef, pork and poultry has been challenging. Economic models are estimated to determine the factors affecting lamb demand. That is, the models first help identify lamb demand determinants, such as the price of lamb and demand shifters. Second, the models determine the strength of the relationships between lamb consumption and other identified factors and whether the association is positively related or inversely related. Demand shifters can help expand or contract the demand for lamb. Traditional demand shifters include the price of substitute meats, income and population. Another important demand shifter for lamb is seasonality. Other possible demand determinants include habit persistence, the percent of females in the workforce to capture the demand for convenience in food preparation, advertising and quality. Quantitative lamb demand studies spanning 60 years of data were reviewed. Over this 60-year period, lamb has undergone significant fundamental changes with lamb consumption dropping by half, imports surging to account for half of the U.S. market and the U.S. processing sector consolidating sharply. Past lamb demand studies have found significant relationships between lamb consumption and the price of lamb, the price of beef and seasonality. Findings with respect to the relationship between income and lamb consumption have not been conclusive. Contributions of Qualitative Studies

There have been several studies that are not quantitative in nature, but qualitatively adding value to the study of lamb demand in the U.S. Most recently, The American Lamb Industry Roadmap Project by the Hale Group (January, 2014) set demand creation as one of the industry’s four high-level goals The Roadmap prioritized achieving a significant increase in demand for American lamb meat as measured by the Demand Index. This finding was the conclusion of a working team that served all segments of the industry – from producers to processors – and which conducted surveys of a larger group of stakeholders. The Roadmap recommended meeting this goal through the following. First, create a consumer-recognized and valued American lamb brand limited to American lamb products of a defined quality; 2. Develop innovative value-added products; 3. Support nontraditional sheep producers across the country through a series of niche marketing activities; 4. Explore the benefits and costs of alternative

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paths to market for American Lamb; and 5. Build the volume and value of the export market for American Lamb. In 2014, The American Lamb Board developed teams to take action on the Roadmap’s stated demand creation goals. In 2008 The National Research Council was charged with reviewing the development and current status of the sheep industry in the U.S. and with examining challenges and opportunities for the future. It found that “the level of demand for lamb and the changes in that level over time are key determinants of the long-run economic viability of the lamb industry (2008: 200). Further, it found that the assumption that American tastes and preferences have caused the long-term decline in lamb consumption is no longer valid given the steady level of consumption in recent years, in spite of declining domestic production. Rather, it explained, lamb is consumed regularly by a small segment of the population and not at all by most Americans. The National Research Council highlighted another important lamb demand issue: the U.S. lamb industry might be comprised of two markets: feeders fed to heavier weights in feedlots destined to the traditional market and lambs sold direct to consumers at lighter weights (the nontraditional market). Demand studies in general have focused on the commercial retail market, with the impact of the nontraditional market more difficult to capture and report. The U.S. International Trade Commission (USITC) study, Lamb Meat (2000), was primarily qualitative in nature, but lends insight into lamb demand determinates. The USITC’s investigative report on the U.S. import duty for lamb in 1999 applied a range of retail demand elasticities (–0.75 to –1.25) in its impact analysis. One objective of the project was to provide information on retail and wholesale price trends for domestic and imported lamb meat and to identify and assess variables that may have influenced those trends. Growers and feeders, as well as purchasers and retailers, were interviewed. The USITC survey results indicated that factors affecting lamb prices included prices of imported lamb meat, prices of other meat products, income and preferences for lamb meat (2000). In addition, higher retail prices possibly of beef and veal substitutes may have contributed to high lamb prices. Through the survey responses, it was found that lamb buyers had differing opinions on how the price of other meats affected the volume of lamb sold. One buyer responded that changes in the prices of other meats do affect the price of lamb meat and that other meats are featured because of their lower costs. When buyers were asked if they would offer more shelf space to lamb if it were priced closer to other meats, 57 percent said that they would while 43 percent said no. Purchasers were divided on whether the price of lamb affected the quantity of lamb demanded. The Effect of Lamb Price: Own-Price Elasticity

Other lamb-demand studies have been more rigorous in nature, studying the mathematical relationship between the quantity of lamb demanded and lamb price and demand shifters. These

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econometric models allowed for the estimation of the own-price elasticity of demand for lamb (Table 1). Own-price elasticity of demand is the percentage change in quantity demanded for a 1-percent change in price. An elasticity greater than one in absolute value indicates that the quantity demanded varies significantly as price changes, whereas a low price elasticity (elasticity less than one in absolute value, also termed inelastic) is an indicator that quantity changes are less than proportional to a change in price. Table 1 Review of Lamb Demand Models

Timeframe Studied, Level of

Aggregation

Own-Price Elasticity


Beef


Pork


Poultry

Income

elasticity

Capps et al. 2011

1978/79 to 2009/10, Annual (2 models)

-0.65 to -0.73 0.27 to 0.31

0.31 to 0.49

Not Sig. Not Sig.

Capps et al., 2010

1979-2010, Annual

-0.75 0.67 0.40 NA Not Sig.

Shiflett, et al., 2007


-0.665 0.486 0.179, Weak

Substitute.

Not Sig. 0.684

RTI International (Montana State), 2007

1970-2003, annual

-0.523 short-run,

-1.108 long-run

Not Sig. Not Sig. 0.35 Not Sig.

Paarlberg & Lee, 2001


-0.437

--

--

--

--

Schroeder, et al., 2001

1978-1999, Quarterly,

-1.09 0.57 Weak Substitute.

Not Sig. -0.54

Byrne, et al., 1993

1978-1990, Bi-monthly

-0.62 short-run; long-run: -0.79

Not Sig. 0.131 Not Sig. Not Sig.

Purcell, 1989 1970-1987, Quarterly

-0.511 Not Sig. Not Sig. Not Sig. Not Sig.

Whipple and Menkhaus, 19891

1950-1987, Annual

-3.96 0.281 Not sig. Not Sig. 0.156

George and King, 1971

Quarterly, 1946-1968

-2.6252 0.5895 0.8914 0.2336 0.571

Notes: Not sig. = Not significant at 5 percent. -- = not considered. 1 Model price dependent so elasticities are calculated from flexibilities. 2 Statistical significance not reported. Studies captured in this review span sixty years, from 1946 to 2010. Among lamb demand studies reviewed, most studies found that lamb demand is price inelastic (ranging from -0.51 to -0.75) while only three estimated an elastic demand (George and King, -2.6; Whipple and Menkhaus, -3.18; and Schroeder et al., -1.09).

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All studies found that the price of lamb is significant in explaining variations in lamb consumption. In theory, the law of demand states that price and consumption are inversely related: price goes down, more lamb is consumed and vice versa. The modeling technique used to determine the factors affecting lamb demand quantifies the own-price elasticity of demand. It tells us how sensitive lamb consumption is to the price of lamb. Montana State University (for RTI International) estimated lamb demand in its effort to measure the economic effects of restricting alternative marketing arrangements. It developed an equilibrium displacement model that models the lamb marketing chain as four distinct sectors: retail (consumer), wholesale (processor), slaughter (lamb feeding), and farm (feeder lamb). Demand Shifters

Changes in lamb demand is a function of demand shifters. Price of substitutes, income and advertising have all be explored in the literature. Among recent studies, Capp et al. (2011) found a cross-price elasticity with beef of 0.57; Shiflett et al. (2007) found a 0.34 elasticity and Schroder et al. (2001) estimated 0.57. Beef was a significant substitute in lamb consumption with the anticipated positive sign: i.e., as the price of beef increased, lamb consumption also increased because lamb, relative to beef, is now more competitive. Many studies – such as Capps et al. -- found pork to be a significant substitute although less significant than beef. Purcell (1989) found that lamb didn’t have any important substitutes. No single issue has challenged lamb demand modeling like the role of income. It is hypothesized that as incomes rise, so too will lamb consumption and yet, demand models have not generally identified this relationship. Income has ranged from being positively significant to negatively significant to insignificant. Capps, et al. (2011 and 2010), Montana State (2007), Purcell (1989) and Byrne, et al. (1993) all found that income was not a significant determinant of lamb demand. Schroeder et al. (2001) found that lamb demand declined as incomes increased. Purcell (1998) had the same finding: income was significant and negative, which identifies lamb as an inferior meat product. On-the-other-hand, Shiflett, et al. (2007) found income to be both a positive and significant determinant of lamb consumption. In 1989 Purcell wrote: “Since per capita disposable income is a “national” number, there is reason to speculate that regional consumption of lamb does not respond in the traditional way to changes in income,” (1989:35). Increased lamb consumption and increased incomes in one region might be masked from the overall declining trend of lamb consumption nationally and the increasing trend in incomes nationally. In a Texas Agribusiness Market Research Center (TAMRC) at Texas A&M University report to the American Lamb Board, Capps and Williams estimated a lamb demand model in an effort to determine the relationship between lamb demand and industry promotional efforts (2011). Over the period

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1978/1979 to 2009/2010, they found that significant factors affecting lamb consumption included lamb price, beef and pork prices and advertising and promotion expenditures. The primary objective of the TAMRC report was to determine whether lamb advertising and promotional activities were beneficial to the industry. Neither income nor chicken prices were important determinants of lamb consumption. Given the inconclusiveness of traditional demand factors, other demand shifters have been explored – to a lesser extent -- in modeling efforts. Byrne et al. (1993) found that habit persistence was positive and significant in explaining lamb consumption. Their hypothesis was that given that lamb consumption occurs primarily among certain ethnic groups of the population, lamb consumption might be a habit, -- or cultural. Habit persistence was captured in the model through the use of the previous period’s consumption. Other analysts, such as Schroeder et al. (2001) tested Byrne et al.’s hypothesis, but didn’t find the same positive and significant influence. Byrne et al. also added a trend variable to their model, but found it was not significant. They had hoped to capture possible industry influences such as trends in diet, health and nutrition as well as the possible effect on lamb consumption of away-from-home food markets. Purcell (1989) also found that trend was an important negative influence of lamb consumption. For the period 1970 to 1987, Purcell found that none of the traditional factors that cause demand to shift -- income and price of substitutes -- were important influences of the decline in per capita lamb consumption. He therefore concluded that shifts in preference patterns might have caused lamb consumption to decline in the early 1980s. Shiflett et al. (2007) also included a trend variable in their demand model. Lamb consumption has seen a long-term decline and simultaneously incomes have risen. The two variables are so strongly negatively correlated that is becomes difficult to separate the individual effects. So long as time trend was not in the model as an explanatory variable, the coefficient on consumer incomes was negative indicating that per capita consumption would decline as incomes go up. With a time trend variable in the model, the strong negative correlation between the steady and sustained increase in incomes and the steady and sustained declines in per capita consumption was offset. The decline over time in per capita consumption was picked up by the new trend variable. Another factor affecting lamb consumption is Easter and the religious holidays of December. Lamb consumption spikes during Easter. This effect is captured through the incorporation of seasonal dummy variables. Lamb consumption is found to be the highest during Easter, followed by the December holidays. The National Academy tested the effect of religious holidays on lamb slaughter. It found that “there appears to be a discernable impact of Muslim holiday periods and the Christian and Orthodox Easter holiday periods on the disappearance levels of lamb and yearlings. As well, the impact of these holidays appears to be increasing with time,” (2008: 331).

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Why Do Model Results Differ?

Different data sources and missing data as well as different modeling approaches have likely contributed to the differences in elasticity estimates found in the literature. Of necessity, retail prices were often imputed due to the lack of a long-standing formal series. Purcell (1989) used wholesale prices to fill in for missing retail prices with the inclusion of an intercept shift to account for the sharp change in price levels. Byrne et al. (1993) used an “auxiliary” regression model to impute, or predict, missing retail prices based upon wholesale prices. Schroeder, et al. (2001) and Shiflett et al. (2007) used a longer-standing Bureau of Labor Statistics (BLS) lamb and organ meats price index and available retail prices to impute retail prices. Differences in the reported elasticities may also be partly attributed to the time frame over which the models were estimated, and therefore reflect a real change in consumers’ behavior.

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7.2 WHAT IS DEMAND? Demand is a schedule of the quantities of goods and services that consumers are willing and able to purchase at alternative prices. An increase in the quantity sold does not necessarily mean that demand has increased – nor does an increase in price. When measuring demand, both price and quantity must be considered together. The law of demand states that as prices fall, consumers will buy more of a good or service, and vice versa. At a specific point in time, given that all other prices and income remain constant, consumers will purchase more lamb only at lower prices. Thus, the relationship between price and quantity of lamb purchased is inverse or negative (Figure 1). This is why demand curves are downward sloping. Demand is constant along any one demand curve, but quantity demanded and consumption can and will change as price changes.

Figure 1 Demand Curve

A change in demand refers to a shift in the demand curve to the right (up) or left (down). A shift in demand means that at any given price, the quantity demanded will change. Thus, if demand increases (curve shifts right), it means the quantity consumed at each price is greater. Figure 2 shows an increase in demand. When the demand curve shifts to the right, from D1 to D2, the quantity demanded of lamb increases from Q1 to Q2 for the same price level, P1. More lamb is consumed at the same price.

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Figure 2 Shift in Demand

Factors that can alter the level of demand (or shift the demand curve) are income, consumer tastes and preferences and prices of substitute meats. For example, if lamb and beef are substitute meats and the price of beef increases, then the demand for lamb will increase. The rising price of beef makes lamb relatively more affordable and more lamb is consumed. Another example of an increase in lamb demand could be prompted by an influx of ethnic groups into the United States that eat lamb regularly in their respective cultures. This shift in tastes for lamb within the population would influence the overall taste and preferences pattern and could cause an increase in lamb demand. For a normal good, rising incomes also prompt an increase in demand. Mistakenly, a surge in quantity sold at retail is sometimes taken to mean that lamb demand has increased. The omission of the price at which the lamb was sold is significant. For example, if an increased quantity of lamb was sold, but prices took a plunge, then demand definitely did not increase. However, if an increased quantity of lamb was sold and prices remained stable or even increased, then it is likely that demand has increased. It is important to remember that any amount of lamb can be sold at some price. Demand is defined by price and quantity, not just quantity and not just price. Similarly, per capita consumption is often mistakenly thought to be synonymous with demand. Per capita consumption is calculated as cold storage lamb stocks at the beginning of the year plus production plus imports minus ending stocks and exports, divided by the population of the United States. A decline in per capita consumption says nothing about demand, but it can tell us that the lamb industry is contracting--that is, per capita availability is decreasing and the industry is losing resources. If anything, per capita consumption is synonymous to per capita supply. Figure 3 shows graphically three demand expansion scenarios with different impacts on price and quantity:

1.) Demand expands, quantity demanded remains constant and prices rise (P3, Q1);

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2.) Demand expands, quantity demanded increases and prices remain constant (P1, Q3); and

3.) Demand expands and both price and quantity increase (P2, Q2).

Figure 3 Effect of Increased Demand on Prices and Quantity

A desirable demand expansion for industry growth occurs under the two scenarios in which more

lamb is sold (points Q2 and Q3) at equal or higher prices (points P2 or P3). It is under these scenarios

in which the industry can raise returns across industry participants and promote industry growth. If

prices are higher (point P3) and the quantity demand remains constant (Q1) then demand has

increased, but the industry is not growing.

Changes in the Quantity Demanded of Lamb

The concept of lamb demand should not be confused with the quantity demanded of lamb. An increase or decrease in demand is represented by a shift in the demand curve when the demand curve moves from line D1 to line D2 in the figures above. According to FreshLook Marketing, in September 2014, 23.5 million lbs. of lamb were sold through the retail outlets represented at an average $7.42 per lb. The 23.5 million lbs. represents the quantity demanded (Figure 4).

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Figure 4 Quantity Demanded

However, if we were to move along the demand curve, say from point A to point B as along a single demand curve as in Figure 5, we would be observing a change in the quantity demanded. If price and quantity are traced out on the graph it can be seen that consumers are buying more lamb at lower prices in a movement along the demand curve from point A to point B. This concept is referred to as a change in the quantity demanded and illustrates the law of demand.

Figure 5 Changes in Quantity Demanded

Price determination is a function of both demand and supply. A supply curve illustrates how much lamb producers are willing and able to offer to the market at different prices. Predictably, there is a positive relationship between the quantity supplied and price. As prices change, producers will offer

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more or fewer lambs to the market and we get a movement along the supply curve as a result of these changes in the quantity supplied. Like the demand curve, the supply curve can also shift to the right or to the left. In the U.S. sheep and lamb industry the amount of lamb supplied to the market has been contracting over the past 50 years. The supply curve can shift due to changes in costs, technology or the number of competitors in the market. If production or fabrication costs rise and it costs more to get lamb to retail then the supply curve will shift to the left. Alternatively, if there production costs decline or there are cost-saving technology improvements in lamb processing, then the supply curve could shift to the right – more lambs will be offered in the market. In Figure 6 the interaction of the supply and demand curve jointly determine the price -- $6.54 per lb. – and the amount of lamb supplied at retail and captured by FreshLook Marketing and the amount of lamb consumed, 6.28 million lbs.

Figure 6 Demand and Supply Curves

In 2011 the sheep industry saw record-high prices and a simultaneous supply squeeze (Figure 7). A supply reduction can put upward pressure on prices, holding demand constant (Figure 8). The sheep industry has seen periods of supply expansion and contractions. Additionally, lamb imports account for about half of the U.S. market. Relatively small changes in domestic or imported supplies can generate proportionately larger swings in prices. The bottom line is that higher prices are not necessarily due to increased demand, but tighter supplies, or a combination of both.

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Figure 7 FreshLook 2009-2013 Retail Price and Quantity

Figure 8 Supply Shift Raises Prices

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7.3 ELASTICITY

What is Elasticity?

Economists frequently refer to the elasticity of demand. Elasticity is simply a measure of how sensitive consumers are to changes in price. If demand is elastic, consumers are more sensitive to changes in price than if demand is inelastic. Elasticity, as one might expect, has to do with the notion of “stretchability”. For example, take a bungee cord and pull. A bungee cord generally stretches quite easily. If, on-the-other-hand, you pull on a similar length of rope, the rope probably isn’t going to stretch very much. The bungee cord is relatively elastic, the rope is relatively inelastic. In economics, this same concept applies to the elasticity of demand. If the price of a product changes – i.e., is “pulled” higher or lower, and the quantity demanded by consumers changes (stretches or contracts) a lot, then demand is said to be relatively elastic. If, on-the-other-hand, the price of a product is “pulled” higher or lower and the quantity demanded changes (stretches or contracts) very little, then demand is said to be relatively inelastic. Thus, elastic demand means that consumers are relatively sensitive to changes in price and, for a given change in price, the quantity demanded changes a lot, like pulling on a bungee cord. Inelastic demand means that consumers are not very sensitive to changes in price and, for a similar change in price, the quantity demanded doesn’t change very much, like pulling on a rope. More formally, the price elasticity of demand is the percentage change in the quantity demanded associated with a given percentage change in price. The elasticity measure is often summarized by a single number represented by the ratio between percentage change in quantity demanded and percentage change in price:

Price elasticity = %Δ Quantity/%Δ Price A convenient way to think of price elasticity is simply the percentage change in quantity demanded associated with a one percent change in price. Because price and quantity demanded almost always move in the opposite direction, the own-price elasticity of demand is almost always negative. In practice, however, the negative sign is often ignored, and attention is focused on the absolute magnitude of the elasticity value. The concept of elasticity is important because it provides a framework for summarizing the cause and effect relationship between changes in price and changes in quantity. Elasticity provides a QUANTITATIVE structure that can help identify and measure changes in demand. The elasticity measure is one of the inputs used in the calculation of a demand index, which in turn is used to identify and track changes in demand over time.

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Elasticity Values

Elasticity values can range from zero to infinity (0 to ∞). An elasticity greater than one (in absolute

value) is in the “elastic” range (think bungee cord) and an elasticity value less than one is in the

“inelastic” range (think rope). Table 1 summarizes these different elasticity ranges.

Table 1 Elasticity Interpretation

Price Elasticity Coefficient Demand is: Interpretation

|E| > 1 Elastic %Δ Quantity > %Δ Price Consumers are sensitive to changes in price.

|E|= 1 Unit Elastic %Δ Quantity = %Δ Price

|E| < 1 Inelastic %Δ Quantity < %Δ Price Consumers are not very sensitive to changes in price.

Note: The “|E|” symbol means “absolute value”, such that all elasticity values are positive.

Common Types of Demand Elasticities

There are three common types of elasticities used in the demand analysis, 1) own-price elasticity of

demand, 2) cross-price elasticity of demand, and 3) income or expenditure elasticity of demand.

Own-price elasticity of demand is a measure of the responsiveness of the quantity demanded for a good to a change in the price of that good.

Cross-price elasticity of demand is a measure of the responsiveness of the quantity demanded for one good to a change in the price of another good.

o Substitute goods have positive cross-price elasticities of demand – the quantity demanded of a particular good increases as the price of a substitute good increases.

o Compliments have negative cross-price elasticities of demand – the quantity demanded of a particular good increases as the price of a compliment good decreases.

Income elasticity of demand is a measure of the responsiveness of the quantity demanded to changes in income (Table 2).

o Normal goods have a positive income elasticity of demand - as the consumers’ income increases, more is demanded at each price.

o Necessities have an income elasticity of demand of between 0 and +1, o Luxury goods have income elasticities of demand > +1, and o Inferior goods have a negative income elasticity of demand, meaning that the quantity

demanded falls as income rises.

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o Expenditure elasticity is a measure of the responsiveness of demand to changes in expenditure on a bundle of similar goods and can be used as a proxy for income elasticity.

Table 2 Income Elasticity of Demand

Interpretation

EIncome > 0 Positive: Normal Good An increase in income leads to an increase in quantity demanded.

0 < EIncome < 1

Necessity: Goods consumers do not want to do without and will continue to buy even if incomes fall, e.g., food & rent.

EIncome > 1

Luxury good

EIncome < 0 Negative: Inferior Good An increase in income leads to a decrease in quantity demanded and may lead to changes to higher quality substitutes, e.g. margarine to butter.

Factors That Can Affect Demand Elasticity

A number of different factors can affect the elasticity of demand, including time period, availability

of substitutes, and the proportion of the consumer’s budget.

Time period: In general, the longer the time period, the more responsive quantity demanded is to changes in price, i.e. consumers have time to seek out substitutes and identify alternatives.

Availability of substitutes: In general, the number of close substitutes or comparable products

and the ease with which consumers can switch between products affects the elasticity of demand. The greater the availability of close substitutes, the greater the elasticity of demand.

Proportion of budget: In general, the larger the share of the consumer’s budget required for a purchase, the more sensitive consumers are to changes in price, and the more elastic the demand.

Table 3 provides a few examples of the relative differences in elasticity that would be anticipated for select items or categories. For example, food is relatively more inelastic than meat as there are a large number of different food choices available to consumers apart from meat. Meat, however, is relatively more inelastic than lamb, as there are a number of different of meats from which consumers can choose. Domestic supply of lamb is fixed in the short run and therefore is relatively more inelastic than import supplies which can respond more readily to changes in price, etc.

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Table 3 Summary of Select Relative Elasticities of Demand

Inelastic (less sensitive to changes in price) Elastic (more sensitive to changes in price)

Food Meat

Meat Lamb

Lamb Carcass Individual Cuts

Brand Name Generic

Holiday Purchases Everyday Purchases

Wholesale Retail

Domestic Supply Import Supply

Smaller percentage of budget Larger percentage of budget

Short run Long run

Why is Elasticity Important?

The concept of elasticity provides a quantitative framework for understanding how changes in price affect changes in quantity demanded, and in turn, changes in consumer spending. Elasticity also provides a quantitative framework for understanding how changes in supply will affect equilibrium prices if demand is held constant. For example, if the price per pound is reduced ten percent through price feature activity, how much of an increase in the quantity demanded would we anticipate and would we anticipate an increase or a decrease in total revenue as a result? Or, if short supplies threaten to drive up prices by ten percent, how much will consumers likely cut-back on the quantity demanded as a result, and again, what impact will this cut-back have on total revenue? By definition, when demand is price elastic, a ten percent change in price will result in a greater than ten percent change in the quantity demanded. When demand is price elastic, changes in price and changes in total expenditures move in the opposite direction, i.e., a price decrease leads to an increase in total expenditures, and vice versa. Conversely, when demand is price inelastic, a ten percent change in price will result in a less than ten percent change in the quantity demanded. When demand is price inelastic, price and total expenditures move in the same direction, i.e., a price decrease leads to a decrease in total expenditures, and vice versa. Elasticity then is key to understanding how changes in price and quantity can affect an industry’s profitability.

When Demand is: A Price Increase will: A Price Decrease will:

Elastic Decrease Total Revenue Increase Total Revenue

Inelastic Increase Total Revenue Decrease Total Revenue

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APPENDIX A. RETAIL LAMB PRICES SOURCE SUMMARY

Source

Time Frame

Items

Notes

PUBLIC SOURCES

ERS from BLS January 1950-April 1987 1. Monthly

2. BLS-based

3. Weighted average retail prices

from surveys.

BLS January 1991 – January 1994

Monthly bone-in lamb and mutton retail prices.

Large gaps in data: 17 (sporadic) monthly prices reported

ERS and later, LMIC January. 2001 – April 2008 1. Monthly average domestic

and imported retail prices

from retail supermarket

scanner data from private

sources.

2. Indexed volume.

3. Selected cuts (legs, loins,

shoulders, chops and roasts).

1. Unique: Provided domestic

and imported prices.

2. Scanner-based.

3. Feature-weighted.

AMS January 2007 - current 1. Monthly and weekly retail

feature lamb cut prices

national and by region (about

22 primals and subprimals)

2. Feature rate, %

3. Activity index

4. Simple average price observed

in grocery ads. Not prices

paid.

Publicly available sources: store circulars,

newspaper ads, retailer websites

Simple averages

PRIVATE SOURCES

FreshLook Marketing Group (Information Resources, Inc.)

2009-2013 1. Weekly

2. Lamb –random weight

packages;

3. Cuts (ground, leg, loin, misc.,

rib, shoulder, variety)

4. Regional

1. Scanner-based

2. Weighted average can be

computed.

3. Simple average is often higher

than weighted average.

ASI 1987 monthly; 1988-June 1993 and Sept & Dec 1994 bimonthly; 1995-1996 quarterly

Mix includes whole legs, boneless legs, shanks, sirloin half, center cut leg, rack roast, square-cut shoulder, loin chop, sirloin steaks, neck slices, stew meat, breast, riblets, ground lamb and all other cuts.

1. Survey-based.

2. Market coverage limited.

PRICE INDEXES

BLS Consumer Price Indices: 1. Lamb and Organ Meats 2. Lamb and Mutton

1. Lamb & organ meats (Dec

1977-present; Jan. 2006-

Dec. 2007 many missing

observations)

2. Lamb & mutton (Dec.

1997 – present (many

gaps in the data,

particularly prior to 2009)

1. Monthly and annual.

2. Organ meats include beef,

pork, lamb and veal organ

meats.

1. Statistical sampling.

2. Based on price changes rather

than average prices.

3. Difference in the two series is

organ meat prices.

4. No quantity information.

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APPENDIX B. ANALYSIS OF BLS CPI-IMPUTED RETAIL PRICES

To gain some perspective of how well BLS CPI-imputed retail prices compare with retail prices reported by the ERS and with FreshLook retail scanner prices, the same methodology for imputing lamb prices was applied to the BLS CPIs for beef, pork and chicken. Two different series were imputed for these three meats - the first using their respective 2009 annual average FreshLook retail scanner price, and the second using the 2009 annual average prices reported by the ERS for ‘All Fresh Retail Beef’, ‘Pork Retail’, and ‘Broiler Composite Retail’, respectively. A second BLS CPI-imputed index was also created for lamb using the BLS Lamb and Mutton CPI where available, and again the FreshLook 2009 annual average price for all lamb. In that monthly FreshLook data were not available across all four meats evaluated, all prices were aggregated to quarterly. The quarterly BLS CPI-imputed retail prices were then compared with the quarterly retail prices published by the ERS for the period 1990.Q1 – 2014.Q3 (beef, pork, chicken), and with quarterly retail scanner prices collected by FreshLook for the period 2009-2014.Q3 (lamb, beef, pork, chicken). The analysis showed that ERS retail prices were consistently higher than the FreshLook scanner prices for beef and pork, but lower for chicken. The analysis also found that the margin between the ERS retail series and the BLS CPI-imputed series tended to widen as the BLS CPI-imputed series moved further away from the base date and price. That is, the difference between the two price series tended to be greatest at the extremes. Across all meats, the FreshLook scanner series was more volatile than either the ERS series or the BLS CPI-imputed series. The analysis indicates that some of the discrepancies identified between the BLS CPI-imputed retail price series and the FreshLook retail scanner data are not unique to lamb, but can be observed across meats. Figures B1-4 compare the different price series for lamb, beef, pork and chicken, respectively. These findings were similar to those reported in the 2009 ERS study cited earlier, which found, in part, that sales-weighted scanner prices showed greater [month-to-month] variation than BLS-based prices and that the use of BLS data may lead to ERS overstate its retail meat price estimates. The study also suggested that the sales-weighted average retail scanner price may provide a more accurate measure of the “true” average prices consumers pay. The correlation coefficient between the BLS-imputed series and the scanner-based FreshLook series is the highest for beef at 0.97, followed by lamb (from the Lamb and Organ Meats CPI) and chicken, at 0.96 and 0.91, respectively. Pork had the lowest correlation coefficient between the two series, at 0.83. Surprisingly, for the period 2009-2014, the correlation coefficient between the FreshLook scanner series and the BLS imputed Lamb and Organ Meats series is greater than the correlation coefficient between the FreshLook scanner series and the BLS imputed Lamb and Mutton series, at 0.96 and 0.84, respectively.

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Figure B1 Nominal BLS CPI-Imputed Retail Lamb and FreshLook Scanner Retail Lamb Prices

Figure B2 Nominal BLS CPI-Imputed Retail Beef, ERS All Fresh Beef Retail and FreshLook Scanner Retail Beef Prices

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Figure B3 Nominal BLS CPI-Imputed Retail Pork, LMIC/ERS Pork Retail and FreshLook Scanner Retail Pork Prices

Figure B4 Nominal BLS CPI-Imputed Retail Chicken, LMIC/ERS Broiler Composite Retail and FreshLook Scanner Retail Chicken Prices

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APPENDIX C. BEEF, PORK AND LAMB DEMAND INDICES VALUES

All Fresh Retail Beef

Retail Pork

Retail Lamb

1990 100.0 100.0 100.0

1991 96.6 97.3 96.9

1992 91.4 95.9 91.4

1993 87.1 90.8 89.7

1994 87.1 90.7 80.6

1995 83.9 85.0 80.7

1996 80.9 84.9 79.9

1997 76.7 86.0 80.1

1998 77.9 94.2 85.2

1999 80.6 95.3 80.6

2000 79.7 90.9 79.9

2001 81.2 89.8 81.8

2002 84.3 90.5 89.4

2003 83.2 89.4 88.7

2004 91.2 90.2 89.0

2005 87.7 84.8 85.8

2006 84.8 80.3 88.0

2007 84.8 83.0 88.6

2008 80.6 78.6 87.7

2009 76.4 79.9 87.6

2010 75.0 78.5 90.2

2011 76.4 79.4 96.8

2012 79.2 79.0 94.5

2013 80.5 83.8 93.7

2014 86.2 90.3 95.0

81

APPENDIX D. LAMB DEMAND INDEX VALUES WITH ALTERNATIVE ELASTICITIES

E= -0.645 E= -0.76 E= -1.09

1990 100.0 100.0 100.0

1991 96.6 96.9 97.5

1992 90.4 91.4 93.2

1993 88.2 89.7 92.3

1994 78.1 80.6 85.5

1995 78.0 80.7 85.8

1996 76.8 79.9 85.8

1997 76.9 80.1 86.3

1998 82.4 85.2 90.5

1999 77.8 80.6 85.9

2000 76.9 79.9 85.5

2001 78.9 81.8 87.0

2002 86.6 89.4 94.7

2003 85.5 88.7 94.8

2004 85.8 89.0 95.0

2005 82.2 85.8 92.6

2006 84.3 88.0 95.1

2007 85.5 88.6 94.5

2008 83.6 87.7 95.7

2009 83.3 87.6 96.0

2010 85.4 90.2 99.9

2011 91.2 96.8 108.1

2012 89.1 94.5 105.4

2013 88.7 93.7 103.7

2014 89.9 95.0 105.1

82

APPENDIX E. LAMB CUT MODEL STATISTICS AND MODEL PARAMETERS

Appendix E.a. Summary Statistics

Ave. Weekly

Expenditure

ground leg loin misc. rib shoulder variety ground leg loin misc. rib shoulder variety

U.S. Ave. 0.051 0.213 0.241 0.087 0.191 0.217 0.000 $5.78 $6.02 $9.41 $3.49 $13.33 $5.14 $1.76 $6,464,486

Min. 0.014 0.138 0.103 0.042 0.115 0.066 0.000 $4.94 $3.90 $6.50 $2.96 $10.71 $3.64 $1.22 $5,085,818

Max. 0.074 0.647 0.335 0.112 0.242 0.290 0.003 $6.74 $7.34 $10.82 $4.76 $16.09 $6.22 $2.51 $23,908,505

St. Dev. 0.012 0.087 0.038 0.012 0.018 0.038 0.000 $0.49 $0.85 $0.78 $0.28 $1.45 $0.62 $0.25 $2,491,464

California Ave. 0.065 0.182 0.173 0.143 0.162 0.274 0.001 $5.87 $6.65 $9.96 $3.50 $13.74 $5.38 $1.99 $669,783

Min. 0.021 0.106 0.075 0.077 0.059 0.000 0.000 $5.08 $4.43 $2.97 $2.18 $4.74 $1.76 $0.00 $97,011

Max. 0.244 0.559 0.234 0.280 0.333 0.419 0.002 $8.23 $10.80 $11.51 $15.91 $16.24 $6.67 $2.94 $1,940,232

St. Dev. 0.021 0.080 0.030 0.032 0.032 0.062 0.000 $0.63 $1.15 $1.15 $1.26 $1.64 $0.81 $0.42 $217,342

Great Lakes Ave. 0.074 0.230 0.318 0.055 0.146 0.175 0.000 $5.56 $5.59 $9.26 $3.77 $12.02 $5.45 $1.39 $634,894

Min. 0.017 0.117 0.108 0.020 0.078 0.048 0.000 $4.58 $3.28 $5.99 $3.04 $9.37 $4.41 $0.00 $433,584

Max. 0.112 0.704 0.569 0.095 0.218 0.241 0.005 $6.90 $7.33 $10.67 $5.10 $15.37 $6.24 $2.08 $3,253,388

St. Dev. 0.018 0.116 0.070 0.014 0.022 0.038 0.001 $0.57 $0.85 $0.84 $0.35 $1.68 $0.36 $0.42 $357,382

Midsouth Ave. 0.059 0.223 0.256 0.070 0.153 0.239 0.000 $6.01 $5.90 $9.43 $3.33 $12.99 $4.83 $1.18 $753,715

Min. 0.015 0.145 0.110 0.032 0.104 0.075 0.000 $5.17 $3.77 $7.58 $2.73 $9.97 $3.79 $0.00 $535,039

Max. 0.100 0.655 0.345 0.110 0.232 0.309 0.000 $7.28 $7.55 $10.64 $5.10 $16.03 $6.46 $2.71 $2,720,138

St. Dev. 0.016 0.088 0.043 0.015 0.020 0.044 0.000 $0.57 $0.88 $0.75 $0.37 $1.69 $0.59 $0.53 $293,928

Northeast Ave. 0.044 0.194 0.247 0.071 0.229 0.214 0.000 $5.67 $6.09 $8.96 $3.53 $14.14 $5.16 $1.64 $2,288,295

Min. 0.011 0.103 0.075 0.029 0.125 0.051 0.000 $4.41 $3.37 $5.34 $2.94 $10.98 $2.74 $1.16 $1,531,345

Max. 0.065 0.682 0.450 0.108 0.295 0.367 0.009 $6.84 $7.59 $11.11 $4.50 $16.89 $6.50 $2.52 $9,249,911

St. Dev. 0.010 0.096 0.051 0.014 0.028 0.043 0.001 $0.70 $0.90 $1.08 $0.32 $1.58 $0.76 $0.27 $962,424

Plains Ave. 0.090 0.232 0.291 0.082 0.145 0.160 0.000 $5.71 $6.07 $10.54 $3.45 $11.67 $6.02 $0.06 $182,607

Min. 0.016 0.148 0.095 0.036 0.083 0.000 0.000 $4.31 $4.79 $2.88 $2.64 $6.41 $0.00 $0.00 $25,479

Max. 0.265 0.677 0.411 0.179 0.213 0.243 0.001 $7.22 $11.23 $12.04 $12.28 $15.31 $7.12 $1.99 $926,655

St. Dev. 0.024 0.084 0.052 0.029 0.019 0.035 0.000 $0.58 $0.84 $0.75 $0.71 $1.61 $0.55 $0.29 $100,074

So. Central Ave. 0.055 0.258 0.257 0.063 0.246 0.121 0.001 $5.61 $6.16 $9.81 $2.85 $12.14 $5.63 $2.33 $376,026

Min. 0.018 0.185 0.123 0.033 0.148 0.041 0.000 $4.81 $4.51 $8.69 $2.00 $10.34 $4.26 $0.00 $279,517

Max. 0.076 0.606 0.348 0.167 0.363 0.185 0.009 $6.77 $7.88 $11.03 $5.95 $15.26 $6.79 $3.42 $1,174,600

St. Dev. 0.011 0.065 0.039 0.019 0.040 0.032 0.002 $0.48 $0.97 $0.53 $0.55 $1.31 $0.75 $0.92 $128,359

Southeast Ave. 0.020 0.215 0.225 0.077 0.201 0.263 0.000 $6.06 $6.15 $10.08 $3.91 $13.43 $4.89 $1.90 $949,501

Min. 0.006 0.124 0.115 0.043 0.119 0.091 0.000 $4.59 $3.65 $7.63 $3.13 $10.11 $3.37 $0.00 $647,937

Max. 0.035 0.584 0.364 0.166 0.271 0.376 0.000 $6.74 $7.57 $10.93 $4.80 $16.49 $5.94 $2.80 $2,962,093

St. Dev. 0.004 0.086 0.036 0.012 0.024 0.054 0.000 $0.59 $0.88 $0.57 $0.29 $1.85 $0.79 $0.59 $326,340

West Ave. 0.067 0.250 0.197 0.172 0.132 0.182 0.001 $6.22 $6.17 $10.57 $3.54 $12.18 $5.60 $1.98 $589,494

Min. 0.018 0.165 0.091 0.085 0.105 0.071 0.000 $5.62 $4.71 $8.87 $2.99 $10.72 $4.23 $0.00 $429,156

Max. 0.115 0.612 0.246 0.226 0.213 0.227 0.003 $6.91 $7.56 $12.21 $4.76 $14.54 $6.83 $2.98 $1,924,167

St. Dev. 0.021 0.070 0.028 0.022 0.016 0.031 0.001 $0.34 $0.80 $0.78 $0.33 $1.04 $0.81 $0.56 $193,699

Ave. Weekly Budget Shares Ave. Weekly Nominal Prices

83

Appendix E.b. Parameter Results

U.S.

CA

West

Plains

So. Central

Great Lakes

NE

Mid-South

SE

Alpha (α) (Budget shares)

alpha_ground 0.490* 0.104* 0.079 0.058* 0.124* 0.017* 0.252* 0.283* 0.048*

alpha_leg -0.386 0.145* 0.305 0.209* 0.053 -0.182* -0.087 0.190* 0.390*

alpha_loin 0.359* 0.187* 0.255 0.238* 0.503* 0.465* 0.286* 0.133* 0.061

alpha_misc. 0.283* 0.157* 0.054 0.146* 0.074* 0.089* 0.199* 0.272* -0.012

alpha_rib -0.219* 0.265* -0.049 0.146* 0.162* 0.121* 0.074 0.124* 0.208*

alpha_shoulder 0.472* 0.141* 0.354 0.200* 0.083* 0.335* 0.275* -0.005 0.304*

Beta (β) (Expenditure)

beta_ground -0.216* 0.013* 0.011 -0.014* -0.054* -0.088* -0.138* -0.176* -0.018*

beta _leg 0.052 -0.122* -0.141 0.031 0.176* 0.224* -0.046 -0.310* -0.691*

beta _loin 0.002 0.080* -0.123* 0.003 -0.187* -0.027 0.036 0.223* 0.529*

beta_misc. -0.015 -0.070* 0.238* -0.014 0.092* -0.009 -0.042 -0.085* 0.086*

beta _rib 0.304* 0.083* 0.206* 0.045* 0.040 0.024 0.275* 0.165* 0.210*

beta _shoulder -0.126 0.016 -0.191* -0.049* -0.067* -0.124* -0.085* 0.183* -0.117

Gamma (γ) (Prices)

Gamma_ ground_ -0.015 -0.016* -0.089* -0.005 0.002 0.046* 0.019* 0.030* -0.005

Gamma_ leg_ ground 0.057 0.081* 0.095* 0.061* 0.011* 0.035* -0.004 0.002 -0.007

Gamma_ loin_ ground -0.042 -0.043* 0.007 0.023* 0.002 -0.025* -0.006 -0.003 0.025*

Gamma_ misc._ ground -0.051 0.011* -0.054* -0.078* 0.001 -0.023* -0.026* 0.002 0.005*

Gamma_ rib_ ground 0.109* -0.016* -0.049* -0.013 -0.048* -0.004 0.043* -0.018 -0.012*

Gamma_ shoulder_ ground

-0.057* -0.016* 0.091* 0.012 0.031* -0.028* -0.026* -0.013 -0.006*

Gamma_ leg_leg -0.362* -0.201* -0.342* -0.035 0.039 -0.342* -0.373* -0.414* -0.849*

Gamma_ loin _ leg 0.130* 0.012 0.066* -0.044 0.019 0.127* 0.172* 0.195* 0.454*

Gamma_ misc_leg 0.022 0.010 0.115* 0.077* -0.034* 0.036* 0.012 -0.038* 0.083*

Gamma_ rib_leg 0.009 0.013 -0.046* 0.001 0.025 0.074* 0.066* 0.107* 0.261*

Gamma_ shoulder_leg 0.151* 0.085* 0.112* -0.059* -0.057* 0.067* 0.128* 0.148* 0.059

Gamma_ loin_loin -0.187* -0.131* -0.051* 0.077* 0.040* -0.257* -0.307* -0.176* -0.404*

Gamma_ misc_loin -0.025* 0.007 -0.060* -0.069* -0.026* -0.014 0.001 -0.046* -0.009

Gamma_ rib_loin 0.094 0.050 0.109* 0.006 -0.226* 0.074* 0.089* 0.010 -0.178*

Gamma_ shoulder_loin 0.030 0.104 -0.073* 0.007 0.191* 0.094* 0.049* 0.020 0.114*

Gamma_ misc_misc 0.112* -0.000 -0.006 0.056* 0.073* 0.045* 0.041* 0.122* -0.051*

Gamma_rib_misc -0.029 0.062* -0.031 0.016* 0.019 0.002 -0.001 -0.005 -0.027*

Gamma_ shoulder_misc -0.029 -0.090* 0.037* -0.002 -0.030* -0.047* -0.026* -0.035* 0.001

Gamma_ rib_rib -0.334* -0.166* -0.087* -0.028 0.281* -0.036* -0.301* -0.168* -0.157*

Gamma_ shoulder_rib 0.158* 0.057* 0.104* 0.018 -0.051* -0.110* 0.103* 0.074* 0.114*

Gamma_ shoulder_ -0.253* -0.141* -0.271* 0.022 -0.082* 0.024* -0.229* -0.194* -0.283*

Lambda (λ) (Quadratic)

Lambda_ground 0.027* -0.014* -0.009 -0.006* 0.008* 0.014* 0.022* 0.041* 0.002

Lambda_leg 0.026 0.117* 0.104* 0.078* 0.032* 0.006 0.049* 0.164* 0.310*

Lambda_loin -0.009 -0.047* 0.011 -0.042* 0.030* -0.022 -0.014 -0.087* -0.199*

Lambda_misc -0.003 0.011* -0.076* 0.005 -0.034* 0.000 0.002 0.014 -0.030*

Lambda_rib -0.047 -0.035* -0.054* -0.019* -0.036* -0.009 -0.063* -0.049* -0.076*

Lambda_shoulder 0.006 -0.033* 0.024* -0.015* 0.001 0.011* 0.004 -0.082* -0.007

Eta (η)

Eta_Easter_ground -0.004 -0.019 -0.005 -0.003 -0.005 -0.000 -0.001 -0.009 -0.007*

Eta_Easter_leg 0.035* 0.114 0.020 0.026 -0.036 0.055 0.023* 0.059* 0.100*

Eta_Easter_loin -0.011 -0.008 -0.005 -0.015 0.001 -0.033 -0.008 -0.013 -0.019*

Eta_Easter_misc. -0.002 -0.039 -0.001 0.005 -0.013 0.001 0.000 -0.003 0.016*

Eta_Easter_rib -0.005* -0.019* -0.004 -0.018 -0.033 -0.015 -0.007* -0.010 -0.018*

Eta_Easter_shoulder -0.012 -0.027 -0.005 0.005 0.014 -0.007 -0.007 -0.023 -0.073*

Rho (ρ)

Rho_Easter 0.575 1.268 0.116 0.041 0.045 0.029 0.085 0.324 1.583*

Note: * denotes significant at 5% level of confidence.

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