Methodology to estimate the effect of energy efficiency on growth

Transcription

1 Methodology to estimate the effect of energy efficiency on growth Report prepared for The Climate Institute March 2013

2 2 Contents 1 Introduction Energy efficiency and economic growth Data Estimation Discussion References Appendix... 16

3 3 List of tables Table 1. Table 2. Table 3. Table 4. There is evidence that higher levels of energy efficiency have an effect on economic growth For most countries, data is available from 1978 until 2011, but the time frames are shorter for developing and Eastern European countries The data varies sufficiently per country as the snapshot in 2010 shows17 Countries differ significantly in their levels of energy productivity and GDP per capita List of figures Figure 1. Energy efficiency is a factor in energy productivity... 6 Figure 2. Real PPP adjusted retail energy price indices are strong instruments for energy productivity in the panel Figure 3. Levels of retail PPP adjusted retail energy price indices are strong instruments for the change in energy productivity Figure 4. Panel unit root tests fail to reject the non-stationarity of GDP per capita and energy productivity, although evidence in the literature points towards the stationarity of energy productivity Figure 5. The pooled OLS instrumental variable model shown in this figure is invalid due to the presence of unobserved country and time specific effects Figure 6. Wooldridge s test for unobserved individual effects and King and Wu s test confirm the presence of country and time specific effects. 22 Figure 7. The estimate of 0.1 is significant Figure 8. The error terms are serially correlated, requiring robust standard errors in the estimation... 23

4 4 Figure 9. The error terms are heteroskedastic, requiring robust standard errors in the estimation Figure 10. If both GDP per capita and energy productivity are differenced, no connection can be detected... 23

5 5 1 Introduction This document is the technical part of a report which investigates the relationship between energy efficiency and economic growth. Energy plays a significant role in the economy as a major factor of production. The more efficient use of energy can contribute positively to economic growth. Three points are to be considered to evaluate the effect of energy efficiency measures on economic growth: first, the relationship between energy use and economic output; second, the effect of energy efficiency on economic growth; and third, the country specific energy efficiency potential. The relationship between economic growth and energy use has been investigated before; however, less work has been published on the second and third relationships. This report adds to the literature by investigating the second point: what is the effect of energy efficiency on economic growth? This report presents the methodology used to estimate the effects of energy efficiency on economic growth. The literature on economic growth focuses on determinants such as technological change, capital accumulation and the quantity and quality of labour supply but not on energy efficiency. This analysis investigates whether energy efficiency influences economic growth. Two concepts which are central to this analysis are energy productivity and energy efficiency. Energy productivity is defined as GDP per unit of energy used and is a measure of the economic value associated with energy use. It is the inverse of the well-known energy intensity. Energy efficiency, on the other hand, measures the amount of energy used in the production of a specific service, such as a unit of residential lighting. Energy efficiency is one determinant of the overall energy productivity in an economy. The remaining determinants are energy prices, which influence the allocation between energy and other production resources, the composition of GDP and social preferences as shown in Figure 1. It is difficult to obtain comparable data on energy efficiency across countries (for example, see Kuramochi, 2006 and Stern, 2012), whereas energy productivity data is readily available. The use of statistical techniques can allow the impact of energy efficiency to be isolated. This paper suggests one approach. It takes into account the economy- and time-specific factors influencing energy productivity, singling out the effect of energy efficiency on economic growth. There is a relationship between economic growth and energy productivity but there could be causation in both directions. For example: energy efficiency reduces production costs, boosting factor productivity and therefore growth; and economic growth may lead to an increase in the share of less energy-intensive sectors, such as financial services, increasing observed energy productivity in an economy.

6 6 This study aims to quantify the effect of energy efficiency on economic growth. As data on energy efficiency is not available, energy productivity is used as a proxy. The analysis accounts for other factors, such as the sectoral composition of GDP, to single out the contribution of energy efficiency to energy productivity. The remaining effect of energy productivity on economic growth can be attributed to energy efficiency improvements. Figure 1. Energy efficiency is a factor in energy productivity Energy productivity Energy efficiency Sectoral and social factors Energy prices Source Vivid Economics

7 7 2 Energy efficiency and economic growth This report aims to identify and quantify the potential effect of energy efficiency on economic growth. The approximate level of energy efficiency and the per capita rate of economic growth are used in the analysis. This report investigates the empirical effect of energy efficiency on economic growth without identifying the exact mechanism underlying it. The estimates are based on historic evidence; any future gains in economic growth due to energy efficiency might be different. The analysis considers the causality between energy efficiency and economic growth over the last three decades. It may not offer a guide to the contribution of energy efficiency measures to economic growth in the future since the underlying factors of the relationship are open to change. Analysis of the group of 28 countries considered as a whole will produce the most accurate estimate of the effects of energy efficiency, yet this estimate is not applicable to each country individually. The use of the whole group of 28 countries results in over 550 observations, which is a reasonable size for a data set. The obtained estimate shows the results for the group of countries. It is not representative of a single country. Individual country estimates are less accurate but provide more insight for specific countries. As the number of data points is much smaller for an individual country, 1 these estimates provide some insight into the relationship between energy efficiency and economic growth for each country that would otherwise be aggregated in the overall effect. Although this is useful, it is far less accurate than the overall estimate. 1 There are less than 30 data points for the average single country whereas there are over 550 for the group of 28 countries.

8 8 3 Data The data used in the analysis is: real GDP per capita ($US PPP adjusted); energy productivity (GDP in PPP $US produced per kg of oil equivalent); share of service sector (per cent of GDP); share of industry (per cent of GDP); and real energy retail price indices, specifically for oil, gas and electricity (PPP adjusted). The data is gathered from two sources: the World Development Indicators (WDI) database of the World Bank for GDP, energy productivity and the shares of the service sector and industry in GDP and the statistics of the International Energy Agency for real energy retail price indices. The resulting dataset is an unbalanced panel with dimensions N equal 28 and T varying between 6 and 32. Details of the variables are shown in Appendix A. The availability of energy prices limits the choice of countries which can be included, whereas data varies sufficiently between countries and over time. Countries range from low income to high income, from energy intensive to low energy, and encompass Asia, Europe, the Pacific and North America. 3.1 Data and initial analysis The data is summarised in Appendix A. Variables are transformed into logarithms to improve the statistical properties of the data and enable an intuitive interpretation of the final estimations as percentage changes. This specification is common in the economic growth literature. It assumes constant elasticities between the variables (Easterly & Levine, 2001; Hall & Jones, 1999). This transformation results in reduced non-linearity, heteroskedasticity and less pronounced effects of outliers. An additional benefit is that the coefficients become elasticities, which facilitates comparisons between countries of quite different levels of energy productivity and GDP per capita. 3.2 Endogeneity of energy productivity By definition, energy productivity (GDP divided by energy use) is endogenous to GDP per capita. Instrumental variable techniques can be used to overcome the problem of endogeneity and enable conclusions to be drawn about causality (Wooldridge, 2002). The goal is to use strong, exogenous instruments to evaluate the causal effect of energy productivity on economic growth. An instrumental variable has to be correlated with the variable of interest, energy productivity, but not with the error term. The instrument under consideration is the real retail prices for electricity, gas, and oil products (fuel oil, heating oil and so forth). This should fulfil three properties by being: i. exogenous to GDP per capita; ii. correlated with energy productivity; and

9 9 iii. affect GDP per capita only through energy productivity and not correlated with any omitted variable that affects GDP. For point (i), energy prices will reflect tax levels, resource endowment, trade and geography. The level and growth of energy prices have common factors, such as underlying fossil fuel prices. However, their level and growth differs based on the level of taxation, resource endowment, trade and geography. Countries with higher energy taxes might be expected to have higher energy productivity, whereas the growth rate of a country should not have a systematic impact on the country-specific price factors such as resource endowment and geography. On a global scale, growth can influence energy prices, but this effect can be assumed to be uniform across countries for traded energy products for which there are liquid, international markets. This variation is picked up by allowing for common effects over time. Correlation tests and regression analysis of energy productivity and energy prices deal with point (ii). Instrumental variables have to be correlated with energy productivity to be strong instruments. A regular ordinary least squares regression is performed of energy productivity on the instruments. If the inclusion of an instrument yields significant extra information, it is regarded as a strong instrument. If the additional information provided is only modest, it is a weak instrument. For a detailed treatment refer to Stock, Wright, and Yogo (2002). Real energy prices for electricity, gas and oil are strong instruments for energy productivity. The proposed instruments are highly correlated with energy productivity and strong instruments as their correlation coefficients and explanatory power are significant as shown in Appendix B. For point (iii), energy prices influence the amount of energy used in economic activity and, through it, GDP per capita. Energy productivity influences the factor productivity and input costs, both of which have an impact on economic growth. Academic evidence points towards this as the main channel of how energy prices feed into GDP per capita growth. The analysis controls for other channels by which prices might affect GDP, specifically by including the ratio between services and industry. Real PPP adjusted retail prices for electricity, gas and oil are found to be viable instruments and are used in the analysis. Individual and panel regressions show the high and significant correlation of retail energy prices with energy productivity as shown in Appendix C. Wholesale prices and the retail price of coal are found to be insignificant. 3.3 Time series properties Time series properties are important for a panel which has approximately equal dimensions in units and time. The most important property is whether the series is stationary as this determines the validity of the models. Individual time series of all variables are tested using the augmented Dickey & Fuller (1979) test and a unit root test developed by Kwiatkowski, Phillips, Schmidt, and Shin (1992). In addition, the series are examined for structural breaks and a Zivot-Andrews unit root test with breaks is conducted if applicable. The time series for each country show mixed evidence. In addition to some countries being trend-stationary under a certain lag specification and some being non-stationary, there are structural breaks present for some.

10 10 For the panel, GDP per capita is found to be non-stationary. The first difference of GDP per capita is therefore stationary. In addition, the difference of the logarithmic GDP per capita is equivalent to the growth rate, which is the ultimate variable of interest. Energy productivity is taken to be trend-stationary as previous academic studies found evidence that energy and GDP are cointegrated (for example Belke, Dobnik, & Dreger (2011) and Smyth & Narayan (2008). Although the panel cointegration tests cannot reject non-stationarity of energy productivity in the sample, the ratio of two non-stationary, cointegrated variables itself are stationary. Since both energy and GDP per capita are non-stationary and previous papers find a cointegration relationship between the two, the analysis proceeds with energy productivity taken as trend-stationary.

11 11 4 Estimation The estimation section describes the methodology and the estimation results for the panel and for selected individual countries. 4.1 Methodology This section describes the proposed course of the analysis Potential issues First, potential data and model issues encountered in the analysis are: heterogeneity between countries; heterogeneity over time; heteroskedasticity; cross-sectional dependence; and serial correlation. Heterogeneity between countries and over time is explicitly dealt with using a fixed effects model. Fixed effects models capture country and time specific effects by time demeaning the data for each country and adding country-specific intercepts. The appropriateness of fixed effects models is tested by comparing it with a pooled ordinary least squares (OLS) regression to test for country and time specific effects. Each regression model is assessed according to the following criteria using formal and descriptive tests to cover the remaining issues: 2 residual normality: a quantile plot, non-parametric kernel density estimate (a formal normality test is omitted due to rather poor size and power properties, even for the Shapiro-Wilk test); heteroskedasticity: Studentized Breusch-Pagan test; cross sectional dependence: a test by Pesaran (2006); and serial correlation: Durbin-Watson and Breusch-Godfrey/Wooldridge test Modelling path The analysis considers three variables: GDP per capita; the ratio between services and industry for each country; energy productivity. Further variables, such as the fuel mix, are not explicitly in the model. However, the fixed-effects specification captures some of these effects by allowing for country and time specific effects. 2 For a detailed treatment of these tests, please refer to Wooldridge (2002).

12 12 The analysis starts with a pooled instrumental variable (IV) pooled regression to test for unobserved effects using a test developed by Wooldridge (Wooldridge, 2002) and a Lagrange multiplier (LM) test following King and Wu (1997). A pooled model is only valid if there are no unobserved effects that are country or time specific. The main reason to implement the pooled OLS is to test for unobserved effects using the King and Wu LM test. Initial analysis confirms the presence of country and time specific unobserved effects as the hypothesis of no unobserved effects can be rejected at the five per cent level, as shown in Appendix D. As a consequence, pooled OLS is invalid and other techniques are used. The share of industry and services in GDP is a control variable added to the analysis to account for the composition of the economy. The composition of GDP is one of the main factors influencing energy productivity. Countries in which industry constitutes a large share of GDP will achieve less GDP per energy use than countries relying more on services: the addition of these variables accounts for these differences. Other country and time specific factors are accounted for by the fixed effects model specification. The final estimation is an instrumental variable fixed effects model with additional control variables as shown in Appendix E. The model is estimated using energy prices as instrumental variables for energy productivity to overcome endogeneity. The final FE model is: log( gdp. pc) = β 1 log( services / industry) + β 2 log( energy. prod) + u it it 1 it it (2) where each variable is transformed into logarithms, log(gdp.pc) is the yearly difference in the log of GDP per capita, services and industry are the share of these sectors in GDP and energy.prod is the energy productivity defined as the amount of GDP produced per unit of energy use. The last term, log(energy.prod), is estimated using real PPP adjusted energy (oil products, gas and electricity) price indices as instruments. The bar above the variable indicates the time demeaned version of the variable according to the fixed effects method. Specifically: x it x it T T 1 t= 1 x it (3) Robust standard errors are used to mitigate the effects of serial correlation and heteroskedasticity on the significance of the estimation results. 4.2 Estimation results The analysis finds evidence that higher levels of energy efficiency caused higher levels of GDP per capita growth, as shown in Table 1. Appendix E summarises the results for the panel and shows a significant coefficient of 0.1 for the effect of energy efficiency on economic growth. Due to the log difference transformation of GDP per capita and the log transformation of energy efficiency, the interpretation of this coefficient is as follows: a 1 per cent increase in the level of energy efficiency implies a 0.1 percentage point increase in the growth rate of GDP per capita.

13 13 Table 1. There is evidence that higher levels of energy efficiency have an effect on economic growth Estimate Significance level 0.1 <1 per cent Interpretation a 1 per cent increase in the level of energy efficiency causes a 0.1 percentage point increase in the growth rate of GDP per capita (for example from a growth rate of 2 per cent per annum to 2.1 per cent per annum) Note: Significance level means the likelihood this estimate has been obtained by chance and that there is no relationship. A lower number implies a higher statistical significance of the estimate. Vivid Economics There is serial correlation and some non-normality in the error terms. Robust standard errors are used to mitigate their effect on the significance of the results. The OLS estimate itself remains unbiased by both serial correlation and non-normality in the error terms. Additional estimation using the difference of energy productivity shows a positive but statistically insignificant effect. As the panel unit root test fails to reject the non-stationarity of energy productivity, another model specified in differences both for GDP per capita and energy productivity is considered. This model finds an estimate of 1.76, which is insignificant at the 10 per cent level. This implies that if the growth rate of energy efficiency increases by 1 percentage point, the growth rate of GDP per capita increases by 1.76 percentage points. This effect is larger, but the significance is far lower. The results are indicative of the sign and magnitude of the effect of energy efficiency on economic growth; however, more detailed academic work would be needed to pinpoint the exact relationship. The statistical analysis uses a model in which the true extent of energy efficiency gains is approximated by energy productivity, with the limitation that energy productivity accounts for factors beyond energy efficiency. Individual country estimates are not as robust as, and harder to identify than, the average estimate. Each individual country has a maximum of 30 observations available. 3 The relative scarcity of data contributes to less robust results and further analysis is required before these results can be used to evaluate and guide policy decisions. 3 The dataset spans 32 years. One year each is lost by using the lag of the ratio of services and industry and by differencing GDP per capita.

14 14 5 Discussion 5.1 Limitations of the methodology The analysis considers only indirectly the effect of energy efficiency on economic growth. There exists no usable observed data on energy efficiency. The analysis considers energy productivity and its effect on economic growth. As energy efficiency is a sub-part of energy productivity, the estimates do not show its effect on economic growth separately from other factors which underlie energy productivity. By including the share of services of GDP we account for part of multiple other variables affecting energy productivity. Only a few selected variables are included in the analysis. Although the fixed effects specification picks up a large amount of country and time specific variations, the inclusion of further variables might strengthen the robustness of the results. The estimated effects are time constant and linear. Like any average effect regression model, it does not capture non-linear effects. The effects are also constant over time for this estimation and not changing, which is due to the specification as a fixed effects model. Individual country estimations use a relatively small sample. All individual country samples have less than 30 data points. The law of large numbers is not applicable under these circumstances and the distribution of estimates can therefore be non-standard, resulting in the possible overstatement of significance. 5.2 Extensions In addition to the changes in GDP per capita and the effect of energy productivity on it, the contribution of energy efficiency to total factor productivity (TFP) could be estimated. TFP is a measurement of economic growth but its estimation presents challenges of its own. If the data and estimation allows for it, the effect of energy productivity on TFP can be estimated using the methodology proposed in this paper. If the effect of energy efficiency on TFP is estimated, a growth accounting exercise could show the magnitude of the contribution of a change in energy efficiency to GDP. Growth accounting measures the contribution of growth in different factors such as labour and capital to total factor productivity growth. The effect of energy efficiency on economic growth can be calculated by multiplying the effect of energy efficiency on TFP and the effect of TFP on growth. With more data for a longer timeframe and more countries, different model specifications become available, such as cointegration and dynamic models.

15 15 6 References Arellano, M., & Bond, S. (1991). Some Tests for Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. The Review of Economic Studies, 58(2), Carrion-i-Silvestre, J., Barrio, T., & López-Bazo, E. (2005). Breaking the Panels: An Application to GDP per capita. Econometrics Journal, 8, Dickey, D. A., & Fuller, W. A. (1979). Estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, Easterly, W., & Levine, R. E. (2001). It s Not Factor Accumulation: Stylized Facts and Growth Models. The World Bank Economic Review, 15(2), doi: /ssrn Hall, R. E., & Jones, C. I. (1999). Why Do Some Countries Produce So Much More Output Per Worker Than Others? Quarterly Journal of Economics, 114(1), doi: / </p> Im, K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels. Journal of Econometrics, 115(1), King, M. L., & Wu, P. X. (1997). Locally Optimal one-sided Tests for Multiparameter Hypothesis. Econometric Reviews, 33, Kuramochi, T. (2006). Differentiation of greenhouse gas emissions reduction commitments based on a bottom-up approach: Focus on industrial energy efficiency benchmarking and future industrial activity indicators. Copernicus Institute. Kwiatkowski, D., Phillips, P., Schmidt, P., & Shin, Y. (1992). Testing the Null Hypothesis of Stationary Against the Alternative of a Unit Root. Journal of Econometrics, 54, Pesaran, M. (2006). Estimation and Inference in Large Heterogenous Panels with a Multifactor Error Structure. Econometrica, 74(4), Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics, 22(2), Stock, J., Wright, J., & Yogo, M. (2002). A Survey of Weak Instruments and Weak Identification in Generalised Methods of Moments. Journal of the American Statistical Association, 20(4), Wooldridge, J. M. (2002). Econometric Analysis of Cross-Section and Panel Data.

16 16 7 Appendix 7.1 Appendix A: data description Table 2. For most countries, data is available from 1978 until 2011, but the time frames are shorter for developing and Eastern European countries GDP per Energy Country capita productivity Share of GDP (per cent) Price indices (constant 2000 USD) industry services electricity gas oil Australia complete complete complete complete complete complete complete Austria complete complete complete complete Belgium complete complete complete complete Bulgaria Canada complete complete complete complete complete complete complete Croatia Cyprus complete complete complete complete Czech Rep complete complete complete Denmark complete complete complete complete Estonia France complete complete complete complete complete complete 1980 Germany complete complete complete complete Greece complete complete complete complete Hungary complete complete complete complete complete complete complete Ireland complete complete complete complete complete Italy complete complete complete complete Japan complete complete complete complete complete complete complete Kazakhstan South Korea complete complete complete complete complete complete 1985 Latvia complete Lithuania Luxembourg complete complete complete complete Malta complete complete complete complete Netherlands complete complete complete complete New Zealand complete complete complete complete complete complete complete Poland Portugal complete complete complete complete Romania Slovak Rep Slovenia Spain complete complete complete complete Sweden complete complete complete complete Switzerland complete complete complete complete 1993

17 17 Turkey complete complete complete complete UK complete complete complete complete complete complete complete United States complete complete complete complete complete complete complete Vivid Economics Table 3. The data varies sufficiently per country as the snapshot in 2010 shows Variable Mean Median Minimum Maximum GDP per capita (2005 USD PPP) 35,967 35,798 11,589 93,949 retail electricity price index retail gas price index retail oil price index Note: Data is for 2010 only. Vivid Economics

18 18 Table 4. Countries differ significantly in their levels of energy productivity and GDP per capita Country GDP per capita in 2009 (constant 2000 Energy productivity in 2009 (constant 2000 USD) USD per kg oe) Australia 40, Australia 41, Austria 38, Belgium 35, Canada 37, Czech Republic 23, Denmark 33, Estonia 17, Finland 32, France 31, Germany 34, Greece 25, Hungary 16, Ireland 34, Italy 28, Japan 31, Korea, Rep. 26, Luxembourg 75, Netherlands 38, New Zealand 27, Norway 50, Poland 16, Portugal 19, Slovak Republic 19, Slovenia 24, Spain 27, Sweden 36, Switzerland 39, Turkey 10, United Kingdom 34, United States 41, Vivid Economics based on World Bank data

19 Appendix B: instrument estimation Figure 2. Real PPP adjusted retail energy price indices are strong instruments for energy productivity in the panel Equation: log(energy.prod) ~ log(retail.gas) + log(retail.oil) + log(retail.elec) Model: fixed effects Unbalanced Panel: n = 28, T = 6-33, N = 591 Coefficients: Estimate Std. Error t-value Pr(> t ) log(retail.gas) <0.001 *** log(retail.oil) <0.001 *** log(retail.elec) Total Sum of Squares: Residual Sum of Squares: R-Squared: Adj. R-Squared: F-statistic: on 3 and 560 DF, p-value: < 2.22e-16 Note: Although electricity prices are not statistically significant in the panel, they have been found to be significant on the country level and are included in the analysis. Vivid Economic

20 20 Figure 3. Levels of retail PPP adjusted retail energy price indices are strong instruments for the change in energy productivity Equation: diff(log(energy.prod)) ~ log(retail.gas) + log(retail.oil) + log(retail.elec) Model: fixed effects Unbalanced Panel: n = 28, T = 6-32, N = 583 Coefficients: Estimate Std. Error t-value Pr(> t ) log(retail.gas) log(retail.oil) log(retail.elec) ** Total Sum of Squares: Residual Sum of Squares: R-Squared: Adj. R-Squared: F-statistic: on 3 and 552 DF, p-value: Note: Although oil prices are not statistically significant in the panel, they have been found to be significant on the country level and are included in the analysis. Vivid Economics 7.3 Appendix C: unit root tests Individual unit root tests are ambiguous as some countries show either unit roots or trend-stationarity when accounting for breaks. Details of this are omitted for brevity. Panel unit root tests such as the modified Im, Pesaran and Shin (Im, Pesaran, & Shin, 2003; M. H. Pesaran, 2007) test fail to reject non-stationarity. The test is robust to country specific heterogeneity and crosssectional dependence. However, it does not take into account potential breaks.

21 21 Figure 4. Panel unit root tests fail to reject the non-stationarity of GDP per capita and energy productivity, although evidence in the literature points towards the stationarity of energy productivity Pesaran s CIPS test for unit roots in GDP per capita CIPS test = , lag order = 2, p-value > 0.1 alternative hypothesis: trend stationarity Pesaran s CIPS test for unit roots in energy productivity CIPS test = , lag order = 2, p-value > 0.1 alternative hypothesis: trend stationarity Note: Although the CIPS test fails to reject non-stationarity for energy productivity, the analysis proceeds under the assumption that energy productivity is trend-stationary as recent academic papers have found a cointegration relationship between energy and GDP, which implies the stationarity of the ratio. Vivid Economics 7.4 Appendix D: initial regression results Figure 5. The pooled OLS instrumental variable model shown in this figure is invalid due to the presence of unobserved country and time specific effects Equation: diff(log(rgdp.pc.pwt)) ~ lag(log(services/industry)) + log(energy.prod) with instruments log(retail.gas) + log(retail.oil) + log(retail.elec) Model: pooled OLS Coefficients: Estimate Std. Error t-value Pr(> t ) (Intercept) <0.001 *** lag(log(services/industry) log(energy.prod) * --- Signif. codes: 0 *** ** 0.01 * 0.05 Total Sum of Squares: Residual Sum of Squares: 0.69 R-Squared: Adj. R-Squared: F-statistic: 28.9 on 2 and 554DF, p-value: < Vivid Economics

22 22 Figure 6. Wooldridge s test for unobserved individual effects and King and Wu s test confirm the presence of country and time specific effects Wooldridge s test for unobserved individual effects z = 2.82 p-value = alternative hypothesis: unobserved effect Lagrange Multiplier Test - two-ways effects (King and Wu) normal = 71 df = 2 p-value < alternative hypothesis: significant effects Vivid Economics 7.5 Appendix E: final instrumental variable model estimation Fixed effects model with GDP per capita in differences and energy productivity in levels Figure 7. The estimate of 0.1 is significant Equation: diff(log(rgdp.pc.pwt)) ~ lag(log(services/industry)) + log(energy.prod) with instruments log(retail.gas) + log(retail.oil) + log(retail.elec) Model: fixed effects Unbalanced Panel: n=28, T=6-32, N=557 Coefficients: Estimate Std. Error t-value Pr(> t ) lag(log(services/industry)) log(energy.prod) ** Vivid Economics

23 23 Figure 8. The error terms are serially correlated, requiring robust standard errors in the estimation Breusch-Godfrey/Wooldridge test for serial correlation in panel models chisq = df = 6 p-value = < alternative hypothesis: serial correlation in idiosyncratic errors Durbin-Watson test for serial correlation in panel models DW = p-value = <0.001 alternative hypothesis: serial correlation in idiosyncratic errors Vivid Economics Figure 9. The error terms are heteroskedastic, requiring robust standard errors in the estimation studentized Breusch-Pagan test BP = df = 5 p-value = <0.01 Vivid Economics Fixed effects model with both GDP per capita and energy productivity in differences Figure 10. If both GDP per capita and energy productivity are differenced, no connection can be detected Equation: diff(log(rgdp.pc.pwt)) ~ lag(log(services/industry)) + diff(log(energy.prod)) with instruments log(retail.gas) + log(retail.oil) + log(retail.elec) Model: fixed effects Unbalanced Panel: n=28, T=6-32, N=557 Coefficients: Estimate Std. Error t-value Pr(> t ) lag(log(services/industry)) diff(log(energy.prod)) Vivid Economics

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