Econ 191: Background material for Prof. Gorodnichenko's ...

Econ 191: Background material for Prof.Gorodnichenko’s Lecture on Optimal Inflation Rates

Owen Zidar

University of California, Berkeley

[email protected]

November 20, 2012

Owen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 1 / 41

Overview of Today’s Lecture

1 Skills: Brief Review of Data, Model, & Results Sections

1 Data: Summary Stats2 Empirical Model: Explicit regressions3 Results: Key point, graphs, supporting detail

2 Background for Gorodnichenko Lecture1 Definition: What is inflation?2 Motivation: Why study it?3 History: How has it evolved over time?4 Theory: What determines inflation - a brief review of macro theory5 Costs & Benefits of inflation


I.1) Final paper: Summary Stats example

Variable Mean Std. Dev. Min. Max. NI(Exogenous Tax Change) 0.424 0.498 0 1 66I(Payroll Tax Change) 0.242 0.432 0 1 662 year Change in Unemployment Rate 0.118 1.624 -2.767 4.658 632 year Growth in Employment 2.885 2.465 -4.334 8.218 632 year Growth in Real GDP 6.265 4.435 -11.74 17.156 642 year Growth in Consumption 7.005 3.245 -2.434 14.591 642 year Growth in Investment 10.242 22.899 -32.66 146.291 642 year Growth in Durable Goods Consumption 12.661 16.275 -10.313 111.883 642 year Growth in Non-durable Goods Cons. 5.101 2.649 -2.914 10.877 642 year Growth in Residential Investment 44.282 21.392 2.94 100 66∆TaxROMER,t -0.099 0.472 -1.858 0.858 66∆TaxINCOME,t -0.089 0.33 -1.516 0.631 66∆TaxNONINCOME,t -0.009 0.285 -0.869 0.643 66∆TaxTop30,t -0.052 0.231 -0.833 0.58 66∆TaxBottom70,t -0.038 0.12 -0.691 0.153 66∑t

t−2 ∆TaxROMER -0.305 0.804 -2.609 1.009 64∑tt−2 ∆TaxINCOME -0.277 0.512 -1.625 0.631 64∑tt−2 ∆TaxNONINCOME -0.028 0.498 -1.169 0.955 64∑tt−2 ∆TaxTop10 -0.081 0.267 -0.823 0.546 64∑tt−2 ∆TaxBottom90 -0.196 0.315 -1.04 0.34 64∑tt−2 ∆TaxTop30 -0.16 0.372 -1.3 0.58 64∑tt−2 ∆TaxBottom70 -0.117 0.186 -0.691 0.153 64

Note that the units for all of the ∆Tax variables are percent of GDP (i.e. 100× ∆τY

).


I.2) Final paper: Empirical Model example

Output growth & exogenous tax changes for different income groups

GrowthY ,t = β0 + βBOT90(∆TaxB90,t) + βTOP10(∆TaxT10,t) + Xtλ+ εt

∆TaxB90 and ∆TaxT10 are changes in income and payroll taxes as ashare of GDP for the bottom 90% and top 10% respectively

Xt is a vector of controls such as non-income and payroll tax changesand lagged GDP growth

Assume Cov(∆Taxg ,t , εt) = 0 ∀g ∈ (BOT 90,TOP10,NONINCOME )following Romer & Romer AER 2010


I.3) Results: Effects of Tax ∆s on Output & Emp Growth

(1) (2) (3) (4) (5) (6)VARIABLES GrowthY GrowthY GrowthY GrowthY GrowthE GrowthE∑t

t−2 ∆TaxROMER -0.853**

(0.362)∑tt−2 ∆TaxINCOME -1.373*

(0.780)∑tt−2 ∆TaxTop10 0.199 0.605 0.373 0.241

(0.992) (0.932) (0.735) (0.791)∑tt−2 ∆TaxBottom90 -2.725** -2.543** -1.851** -1.899**

(1.162) (1.139) (0.789) (0.801)∑tt−2 ∆TaxNONINCOME -0.738 0.243

(0.476) (0.420)Constant 2.491*** 2.090** 1.963* 2.204* 0.201 0.123

(0.905) (1.012) (1.026) (1.106) (0.640) (0.693)

Control for serial corr. Y Y Y Y Y YObservations 61 61 61 61 61 61R-squared 0.578 0.573 0.588 0.596 0.577 0.579Controlled for serial correlation by including ∆ lnYt−k for k ∈ (1, 2, 3) in regressionRobust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1


1.3) Graph Example: Employment & Top 10%


1.3) Graph Example: Employment & Bottom 90%


I. Final Paper Components

Takeaways for your Final Paper1 Data:

Show summary stats for relevant variablesDescribe in data sectionUse graphs to show interesting trends in variables of interest

2 Empirical Model:Explicitly write out regression specification and assumptionsDiscuss drawbacks and limitations

3 Results:Present Results in a regression tableUse graphs where possible to show your pointFocus on big picture question first!Then analyze mechanisms and robustness


II. Background for Gorodnichenko Lecture

Optimal Inflation Rates

1 Definition: What is inflation?

2 Motivation: Why study it?

3 History: How has it evolved over time?

4 Theory: What determines inflation - a brief review of macro theory

5 Costs & Benefits of inflation


1) What is Inflation?

Inflation, π, is an increase in the average price of goods and servicesin terms of money.”1

Consumers’ Price Index (CPI)2

CPIt =p1,tq1,0 + p2,tq2,0 + ...+ pj ,tqj ,0

p1,0q1,0 + p2,0q2,0 + ...+ pj ,0qj ,0(1)

the CPI is the ratio between the time t and the time 0 value of thetypical basket of goods purchased by households at time 0. Time 0 iscalled the base year.

The change in the CPI is used to measure inflation.

πt,t+1 =CPIt+1 − CPIt

CPIt=

CPIt+1

CPIt− 1 =

p1,t+1q1,0 + ...+ pj ,t+1qj ,0

p1,tq1,0 + ...+ pj ,tqj ,0

(2)

1David Romer’s Definition in Advanced Macroeconomics2Source: Violante (NYU) Notes



Inflation, π, is an increase in the average price of goods and servicesin terms of money.”1

Consumers’ Price Index (CPI)2

CPIt =p1,tq1,0 + p2,tq2,0 + ...+ pj ,tqj ,0

p1,0q1,0 + p2,0q2,0 + ...+ pj ,0qj ,0(1)

the CPI is the ratio between the time t and the time 0 value of thetypical basket of goods purchased by households at time 0. Time 0 iscalled the base year.

The change in the CPI is used to measure inflation.

πt,t+1 =CPIt+1 − CPIt

CPIt=

CPIt+1

CPIt− 1 =

p1,t+1q1,0 + ...+ pj ,t+1qj ,0

p1,tq1,0 + ...+ pj ,tqj ,0

(2)1David Romer’s Definition in Advanced Macroeconomics2Source: Violante (NYU) Notes



Some Issues3

Substitution Bias: “An oil-shock (like in the 1970s) ⇒ POIL

skyrockets, so households reduce the demand for gasoline & cars andincrease the use of substitute means of transportation, like thesubway. Then, at time t+1 the actual basket of goods includes muchless gasoline than at time zero. But the CPI measure does not take itinto account, so it will overstate inflation”

Quality Bias: “Suppose the price of a computer in 1993 and in 2003has always been $1,000. The standard PC in 2003 has 256 MB ofRAM, while in 1993 it used to have only 128 MB. This means that ifwe keep “constant” the quality of PC throughout the last decade, theprice of PC has fallen by 50%!”

Volatility: Fed also uses core inflation (because food and fuel pricesare volatile and fluctuations are often temporary).

New Goods3Source: Violante (NYU) Notes


2) Motivation

Why Study Inflation?

1 Prices: P & Q are central to economics ⇒ ∆ P is important

2 Historic Importance: Weimar Republic, US Continental Congress,the Cross of Gold, Confederate Graybacks during US Civil War, WINin 1970s

3 Potentially Large Costs: Some argue that inflation erodespurchasing power, causes arbitrary redistribution of wealth, increasesuncertainty, reduces investment, etc

4 Potentially Large Gains: Some argue that debt burdens are holdingback recovery - US and Euro could use a bit more inflation at times.Can grease the wheels of the labor market.

5 Policy & Markets: Half of the Fed’s mandate. The stock marketreacts to changes in inflation. Many social benefits are indexed toCPI.


3) Inflation in the US


3) Whip Inflation Now in the 1970s


3) What Determines Inflation?

1 Irving Fisher (1920): “The ups and downs of prices roughlycorrespond with the ups and downs of the money supply. Throughoutall history this has been so.”

2 Milton Friedman (1970): “Inflation is always and everywhere amonetary phenomenon.”


3) Always: US Inflation and Money Growth


3) Everywhere: Inflation and Money Growth


3) German Hyperinflation in 1923


4) Real Money Balances4

MP , is called real money balances, which measure the purchasing powermoney can buy in terms of goods and services.

Demand: L(Y , i)

First, lets focus on the first variable Y

Suppose that demand for real money balances is linear in Y , i.e.MP = kY , where k is positive

We can rearrange this equation to put it in a classic velocity of moneyexpression:

M1

k︸︷︷︸V

= PY (3)

4Material from Greg Mankiw & David RomerOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 20 / 41


MV = PY (4)

Suppose V is roughly fixed and that, at a point in time, inflation isgiven

When Y > Y , inflation gradually rises

When Y < Y , inflation gradually falls

When Y = Y , inflation is constant

where Y is normal or potential output, i.e., the level of output thatprevails when prices are fully flexible.

5Material from Greg Mankiw & David RomerOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 21 / 41


6Material from David RomerOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 22 / 41


7Material from David Romer



Two Key Points to Remember

Inflation does not respond immediately to deviations of output frompotential. But eventually Y = Y and V ≈ constant, so gM = π

We are talking about inflation, not prices. Output below potentialcauses the rate of inflation to fall from one positive number to asmaller positive number.



Now bring in second variable, nominal interest rates

M

P= L(Y , i) (5)

Higher interest rates, i , increase the opportunity cost of holdingmoney so higher i means lower demand for real balances, i.e. Li < 0

Fisher identity: i ≡ r + πe

So now we have:M

P= L(Y , r + πe) (6)



Summary - some potential sources of inflation

P =M

L(Y , r + πe︸︷︷︸i

)(7)

Increases in the money supply M.

Increases in interest rates i , which can be from increases in πe .

Decreases in output Y .

Decreases in money demand for a given Y and i . (e.g. ATMsinvented)

Over the long term, the main focus is the money supply M


5) Costs & Benefits of Inflation

Costs

1 Standards: Standards should remain standard (LHS)

2 Stability, Uncertainty & Relative Price Variability (LHS)12

3 Tax System: Indexing issues & magnified distortions (Feldstein)

4 Utility loss: People don’t like it (Romer)

Benefits

1 Grease the Wheels (LHS, cited in Romer)

2 Credibility (LHS)

3 Avoid ZLB (Williams)

12Also Okun & Carlton cited in RomerOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 28 / 41

5) Costs of Inflation

1.Standards should remain standard13

1 Thought Experiment: Depreciate the pound (lbs) by 10% everyyear so that what is a pound today would be 14.4 ounces next yearand 12.96 ounces two years from now, and so on.

2 Incentive to Delay: While you could write contracts in renominatedunits, but costly to write. If I owed you one “pound” of sugar,delaying as long as I could would benefit me.

3 Accounting & Planning for Future If you don’t know that thepound will change by 10%, but some other number, accounting andplanning for the future may become more difficult

13From LHS paper on the reading listOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 29 / 41


2.Stability, Uncertainty & Relative Price Variability14

“Significant rates of inflation are likely to accelerate, that they cannotaccelerate forever, and that when they are brought down, the ultimaterecession will cost more in output than was gained in the process ofgoing up”

Uncertainty: Higher uncertainty is costly

Prices: Relative prices provide market participants valuableinformation, which can be less informative in periods with increasedprice variability



Two Other Costs

1 Tax System: Indexing issues & magnified distortions (Feldstein)

2 Utility loss: People don’t like it (Romer, Shiller)


5) Benefits of Inflation

Benefits

1 Grease the Wheels (LHS, cited in Romer)

2 Credibility (LHS)

3 Avoid ZLB (Williams)



1A.Grease the Wheels15

Distribution of observed nominal wage changes

15http://www.frbsf.org/publications/economics/letter/2012/el2012-10.htmlOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 33 / 41


1B.“Greece” the Wheels

1 Wage Rebalancing: One rationale for inflation (in Europe now) isthat wage increases (in Germany) are an easier way of rebalancing theeurozone than wage reductions (in Greece)

2 Nominal Debts: A second rationale is to lower the debt/GDP ratiowhen debt is long term and not inflation indexed.



2.Credibility, Dynamic Consistency & Money Rules16

Exam Example: it looks good ex post to cancel exams so I don’thave to grade them. You have already studied.

Expectations: Likewise, it always looks good to inflate a little morethan people expect. Thus, a solution to these issues are rules whichyou are absolutely committed to, so cheating ex-post is impossible

More Credible if small, positive target

Note that some prominent commentators argue for more inflation inorder to ease real debt burdens in Europe and the US



3.Avoiding the Zero Lower Bound17

Idea: “Icarus, my son, I charge you to keep at a moderate height, forif you fly too low the damp will clog your wings, and if too high theheat will melt them.”

Experience of Japan in the 90s and Current Recession may havechanged thinking on frequency and duration of ZLB events

17From John Williams paper on the reading listOwen Zidar (Econ 191) Background for Gorodnichenko November 20, 2012 36 / 41

5) Benefits of Inflation: Avoiding ZLB (Williams)


Next Time

Prof. Gorodnichenko will discuss Optimal Inflation Rates, whichbalance these costs and benefits


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