“How much drag on the future economic growth of the developed world is likely to be exerted by the narrowing of its resource base, assuming indeed that the resource base is narrowing?”Solow (1978)

Nov, 2009

Capital-Energy Relationships: An Analysis of Three Panel Data Estimation Methods

Miguel A.Tovar, University of Essex

Motivation

According to Saunders (2000), the design of policies that aim to reduce energy consumption in the industrial sector requires knowledge of the Elasticity of Substitution (EoS) between capital and energy. If it is close to zero, then policies must encourage technological diffusion. However, if the elasticity is close to one, taxes could then be used to reduce energy consumption.

Miguel A.Tovar, University of Essex

Previous estimations

Berndt and Wood (1975) found that energy price shocks will prompt a shrinkage in the investment of capital for the USA economy. They used a KLME model with aggregate data of 24 years (1947-71).

Griffin and Gregory (1976) found that changes in energy prices will encourage investment in capital to reduce energy consumption. The authors used a KLE model for an international panel data of nine manufacturing countries over 14 years from 1955 to 1969

The first estimations were based on flexible forms that are considered an approximation of a general cost function

Miguel A.Tovar, University of Essex

More recently, Frondel and Schmidt (2002) pointed out that in fact none of these arguments were important. They found that, under certain circumstances, the elasticities obtained by the Translog Cost Function (TCF) ended up being close to the ratio of the factor costs and the total cost, and therefore, the TCF cannot provide reliable estimates

Previous estimations

Apostolakis (1990) analysed several estimations, finding that generally, studies based on time series estimations classified capital and energy as complements whereas the opposite conclusion was reached by panel data studies.

Miguel A.Tovar, University of Essex

Summary

Furthermore, Popp (1997) argues that using a time trend, as a regular practice in the previous estimations, cannot capture technological changes especially for energy efficiency.

After thirty years of studying EoS issues, researchers have learned that substitutability is a relative concept that depends on the country, Pindyck (1979), industry and the kind of capital, Field (1980) and Morrison (1993).

Thomsen (2000) suggested a two-step procedure to estimate Cross Price Elasticities (CPEs) based on the shadow price concept.

Miguel A.Tovar, University of Essex

Goal of this exercise

1. To estimate Cross Price Elasticities by using different approaches on a panel data of eight UK industries

2. To estimate a TCF to find evidence of the arguments in the literature (see e.g. Berndt and Wood (1979), Apostolakis (1990) and Frondel and Schmidt (2002)

3. To extend Thomsen’s methodology to a panel data setting and estimate an Error Correction Model (ECM) using investment in R&D for energy efficiency (IR&DEF)

4. To find out which is the more suitable policy to reduce energy consumption in the industrial sector for the UK economy based on empirical evidence.

Miguel A.Tovar, University of Essex

Data set

The analysis is based on both a cost and production context, and therefore the data set that it is used contains information of factors and their prices from 1970 to 2006 for 8 UK industries.

Additionally, I consider the following industries: basic metals, chemical, non-metallic minerals, transport equipment, machinery, textiles, food and paper. I also used five factors: "net capital stock" divided into buildings (K1) and machinery and equipment (K2), labour (L) and intermediate materials (M) together with energy (E) and IR&DEF. Regarding ( E), it comprises four fuels, electricity, natural gas, coal and oil.

The information about E, L ,M and R&D and their prices are obtained from the Economic and Social data Service, while the information related to capital is obtained from the National Statistics for the UK.

Miguel A.Tovar, University of Essex

Models

The TCF assumes symmetry, monotonicity and concavity

t

Miguel A.Tovar, University of Essex

Models

The Generalized Leontief assumes also symmetry, monotonicity and concavity

Following Thomsen (2000) the estimation is a two step procedure where in the first step a System of Input-Output Equations (SIOE) is estimated for the Long Run (LR) parameters. For the short run a SIOE is estimated using a price function for the quasi-fixed factors that is obtained based on the LR parameters. Moreover an error correction equation for the capital motion has to be included in the estimation for the short run.

Miguel A.Tovar, University of Essex

Models

The Error Correction Model (ECM)

In this estimation N=5 and π is the general technological change in the economy.The estimation is carried out based on a Cobb-Douglas production function and in the concept of substitution proposed by Frondel (2004)

TESihjh ih jh

jhih

lnih lnjh

. #

The estimation methods used in the described models are the Seemingly Unrelated Regression method, the General Method of Moments for dynamic panel data and cointegration and unit root tests for panel data

Miguel A.Tovar, University of Essex

Results

K11pE1

-0.1646*** (0.0464) K21pE1

-1.7064*** (0.4598)

K12pE2

-0.2388*** (0.0668) K22pE2

-1.1845*** (0.3466)

K13pE3

-0.1900*** (0.0593) K13pE3

-0.4697*** (0.1753)

K14pE4

-0.1592*** (0.0437) K14pE4

-2.6993*** (0.6982)

Some of the CPE estimated for the TCF

Standard errors are given in parenthesis. "*": significant at 5 percent level. "**": significant at 1% percent level. "***": significant at 0.1 % percent level.

Miguel A.Tovar, University of Essex

Results

K11pE1

-0.0820 (0.2754) K21pE1

-0.6185 (2.9585)

K12pE2

-0.1168 (0.3843) K22pE2

-0.2903 (2.2765)

K13pE3

-0.0778 (0.3869) K13pE3

0.0633 (1.0108)

K14pE4

-0.0878 (0.2669) K14pE4

-1.1789 (4.6816)

Some of the CPE estimated for the TCF (KLE model)

Miguel A.Tovar, University of Essex

Results

EE -0.0077 (0.0119)

EK1 0.0252** (0.0089)

EK2 0.0251* (0.0105)

EL 0.0115 (0.0064)

EM -0.0288** (0.0095)

K1K1 -0.0641* (0.0260)

K1K2 0.0937*** (0.0178)

Some of coefficients estimated for the GL in the long run

Miguel A.Tovar, University of Essex

Results

K11pE1

0.0962** (0.0339) K21pE1

0.0430* (0.0180)

K12pE2

0.0918** (0.0324) K22pE2

0.0415* (0.0174)

K13pE3

0.0980** (0.0345) K23pE3

0.0424* (0.0177)

K14pE4

0.0852** (0.0300) K24pE4

0.0398* (0.0166)

Some of CPE estimated for the GL in the long run

Miguel A.Tovar, University of Essex

Results

K11pE1

0.1714 (0.1005) K21pE1

0.0090 (0.0683)

K12pE2

0.1648 (0.0966) K22pE2

0.0087 (0.0656)

K13pE3

0.1768 (0.1036) K23pE3

0.0089 (0.0670)

K14pE4

0.1533 (0.0899) K24pE4

0.0083 (0.0630)

Some of CPE estimated for the GL in the short run (preliminary results)

Miguel A.Tovar, University of Essex

Results

Unit root test for the series in first differences

First differences

E -7.8269 113.9340 91.8918

K1 -9.3789 104.2700 49.5041

K2 -3.7331 46.5842 43.4554

L -6.2217 65.3152 87.7057

M -8.4268 92.2833 198.439

IR&DEF -12.8364 171.0940 175.431

y -7.2094 77.0375 87.0090

IPSW ADF-Fisher PP- Fisher

Miguel A.Tovar, University of Essex

Results

Alternative hypothesis: common autoregressive coefficients (within-dimension)

Panel v-Statistic 2.0895*

Panel rho-Statistic 0.3065

Panel PP-Statistic -2.8598*

Panel ADF-Statistic 0.3754

The Pedroni test for within dimension in the autorregresive coefficient of the residuals

"*": used when the probability that the null cannot be rejected is equal or larger than 1 per cent.

Miguel A.Tovar, University of Essex

Results

Null: Unit root (assumes common unit root process)

Levin, Lin & Chu t* -19.1334

Null: Unit root (assumes individual unit root process)

ADF - Fisher Chi-square 481.4740

PP - Fisher Chi-square 432.9090

Unit root test for the residuals of the ECM

Miguel A.Tovar, University of Essex

Results

TESE1K110.4353 (0.2557) TESE2K21

1.5887*** (0.3264)

TESE2K120.0523 (0.2085) TESE2K22

1.4008* (0.5624)

TESE3K130.5039*** (0.1420) TESE3K13

-1.1477** (0.4003)

TESE4K140.0765 (0.1766) TESE4K14

1.4034*** (0.2960)

Elasticities estimated for the ECM in the short run

TESEK 1

LR 0.1162 (0.3845) TESEK2

LR 1.3924*** (0.5159)

Elasticities estimated for the ECM in the long run

Miguel A.Tovar, University of Essex

Conclusion

In conclusion, from the different specifications used, I find clear evidence of complementarity when using the TCF and the ECM, while when using the GL, the results support weak substitutability between capital and energy specially for industries basic metals, chemical and machinery. Moreover, it was found that the TCF and the ECM point out a stronger relationship between energy and investment in machinery than in buildings. Therefore I find evidence that a policy that aims to diminish energy consumption via changes in energy prices will have a more severe contraction in capital demand for those three industries.