Longitudinal analysis (panel data regression)
Prior research acknowledges that determining the influence of policy measures on investments in RE capacity is challenging since spatial and temporal effects could overlap (Marques & Fuinhas, 2012a; Marques, Fuinhas, & Pires Manso, 2010). Following their work we assume panel auto-correlation and contemporaneous correlations as similarities in policy design (e.g. in EU countries) and a tendency to increase the number of policy measures which can be observed throughout the data. The literature reviewed in section 4.2 analyses policy measures that are conducive to RE investments, which are included in the model (see section 4.3.3.2). The best fitting econometric technique is to use a panel data approach under the conditions resulting from characteristics of policy making (Marques & Fuinhas, 2012a).
We estimate panel corrected standard error (PCSE), ordinary least squares (OLS) and random effects estimator (REE) models. Following Marques and Fuinhas (2012a) and to mitigate errors resulting from the data structure, we use several econometric treatments: Heteroskedasticity, panel autocorrelation, and contemporaneous correlation are addressed through fitting approaches (Reed & Ye, 2011). Thus, we circumvent inefficient coefficient estimation and a biased estimation of standard errors (Marques & Fuinhas, 2012a). We do not focus on OLS or REE as they do not address serial correlation and contemporaneous correlation, however, we include the estimates for reasons of robustness (Marques & Fuinhas, 2012a, 2012b).
Our analysis proceeds as suggested by Marques and Fuinhas (2012a) : 1. We observe the quality and nature of the data; 2. We test the presence of heteroskedasticity, panel autocorrelation and contemporaneous correlation; 3. If the results do not conform to standard assumptions about errors (i.e. if the error terms are Independent and identically distributed - iid), we employ the PCSE estimator, which is a suitable solution to improve the accuracy of the estimators; 4. We compare the results with those derived from OLS and REE to check the robustness.
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Random effects / Pooled OLS |
Fixed effects |
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Multiple RE |
Solar |
Wind |
Biomass |
Multiple RE |
Solar |
Wind |
Biomass |
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Modified Wald test |
- |
- |
- |
- |
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Wooldridge test |
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1.22 |
- |
- |
- |
- |
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F(N(0,1)) |
(OLS) |
(OLS) |
(OLS) |
(OLS) |
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Pesaran’s test |
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Frees’ test |
3 00*** |
1.03*** |
2.49*** |
0.90*** |
2.34*** |
0.22 |
1.87*** |
0.63** |
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Friedman’s test |
78.00*** |
30.63*** |
63.77*** |
38.51*** |
25.35** |
45.38** |
27.18* |
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Notes: The Wald test has a Chi2 distribution and tests the null hypothesis that none of the independent variables are significant; The Wooldridge test is N(0,1) distributed and tests the null hypothesis that there is no serial correlation. Pesaran and Frees’ tests examine the null hypothesis that there is cross-sectional independence; Pesaran’s test is a parametric procedure which follows a standard normal distribution; Frees’ test employs Frees’ Q-distribution; Friedman’s test is a non-parametric estimation based on Spearman’s rank correlation coefficient (Aguirre and Ibikunle, 2014; Hoyos and Sarafidis, 2006; Marques and Fuinhas, 2012 a). ***, **, *, denote 1, 5 and 10% significance level, respectively. xtcsd and xtserial commands were used. |
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Table 9 — Specification tests for the quantitative model
Table 9 presents results from the estimations of the specification tests regarding quality and nature of the data and confirms that especially the policy data is heteroskedastic (i.e. has a common variance) and that panel autocorrelation and contemporaneous correlation is present. Hence we use PCSE estimator as main econometric analysis technique.
As public policy effects differ across RE subsectors (e.g. solar, wind, biomass) we carried out the further analysis sector by sector and also aggregated the data (Multiple
RE sources) to analyse effects that are similar across sectors. Thereby, we can also distinguish policy instruments between the sectors as well as policies that apply to all sectors.
Panel data estimation without lag procedure (I)
Panel data estimation with lag procedure (II-IV)
lCjk is the aggregated installed capacity financed by institutional investors per country j per year k. is a vector of i explanatory variables representing policy measures
based on the IEA/IRENA scheme (per country per year). Cjk consists of a number of control variables (Model I). For the analyses of time-dependent phenomenon we include lags l of one to three years in the regressions (Model II-IV). The dummy variables dj and dk refer to country and time, respectively. The PCSE estimator permits the error term ?jk to be correlated over the cases (i.e. countries). Moreover a first-order autoregression for ?jk over time can be used. Finally the estimator allows ?jk to be heteroskedastic (Cameron & Trivedi, 2009; Marques & Fuinhas, 2012a).
