The threat of the negative consequences of global warming makes the discussion about the relationship between economic growth, productivity, and increasing renewable energy involvement an important topic. Hence, the aim of this study is to analyze the impact of renewable energy and energy supply on economic growth and productivity at the national level using stochastic frontier analysis and the aggregate production function framework. In doing so, we analyzed a panel of annual data from 133 countries from 2008 to 2014. We apply a generalized stochastic frontier model, which allows us to differentiate between persistent and transient inefficiency, as well as individual effects. Our results indicate a threshold level in terms of a country’s development that needs to be obtained to benefit from increasing renewable energy involvement over time. However, if this threshold level is obtained, productivity gains are evident. We also found that the role of the energy supply in aggregate production is nontrivial. That is, its inclusion changes the relationship between key input factors (capital and labor) by decreasing their overall elasticities and increasing the observed economies of scale.

Advanced efficiency measurement methods usually fall within Stochastic Frontier Analysis (SFA), Data Envelopment Analysis (DEA), or their derivatives. Although SFA has some theoretical advantages, it has been criticized for relying on arbitrary and potentially restrictive assumptions about model specification. One strand of the literature suggests the use of nonparametric SF models to cope with the issue. We follow an alternative path and demonstrate that it is possible to deal with specification uncertainty and potentially restrictive assumptions while maintaining the advantages of the parametric approach. First, we develop a flexible stochastic model based on generalized t and generalized beta of second kind distributions, which encompasses virtually all known parametric SFA specifications. Second, we apply Bayesian inference methods, which are less restrictive than those used so far, and propose feasible approximate alternatives based on maximum likelihood. Third, we pool results from alternative specifications using model averaging. Our focus is on the distributional assumptions regarding the compound error in SFA since this aspect has not been addressed so far in a satisfactory way. However, extensions to other elements of specification uncertainty, like the choice of the frontier functional form, are straightforward. Finally, we show simulations results and analyze two well-researched datasets, for which we obtain probabilistic (density) estimates of efficiency scores that take into account the estimation error and model uncertainty in a formally justified manner.

This paper discusses Bayesian model averaging (BMA) in Stochastic Frontier Analysis and investigates inference sensitivity to prior assumptions made about the scale parameter of (in)efficiency. We turn our attention to the “standard” prior specifications for the popular normal-half-normal and normal-exponential models. To facilitate formal model comparison, we propose a model that nests both sampling models and generalizes the symmetric term of the compound error. Within this setup it is possible to develop coherent priors for model parameters in an explicit way. We analyze sensitivity of different prior specifications on the aforementioned scale parameter with respect to posterior characteristics of technology, stochastic parameters, latent variables and—especially—the models’ posterior probabilities, which are crucial for adequate inference pooling. We find that using incoherent priors on the scale parameter of inefficiency has (i) virtually no impact on the technology parameters; (ii) some impact on inference about the stochastic parameters and latent variables and (iii) substantial impact on marginal data densities, which are crucial in BMA.

Research background: The probabilistic setup and focus on evaluation of uncertainties and risks has become more widespread in modern empirical macroeconomics, including the analysis of business cycle fluctuations. Therefore, forecast-based indicators of future economic conditions should be constructed using density forecasts rather than point forecasts, as the former provide description of forecast uncertainty. Purpose of the article: We discuss model-based probabilistic inference on business cycle fluctuations in Poland. In particular, we consider model comparison for probabilistic prediction of growth rates of the Polish industrial production. We also develop a class of indicators of future economic conditions constructed using probabilistic information on the rates (that make use of joint predictive distribution over several forecast horizons). Methods: We use Bayesian methods (in order to capture the estimation uncertainty) and consider two groups of models. The first group consists of Dynamic Conditional Score models with the generalized t conditional distribution (with conditional heteroskedasticity and heavy tails, being important for modelling of extreme observations). Another group of models relies on deterministic cycle modelling using Flexible Fourier Form. Ex-post density forecasting performance of the models is compared using the criteria for probabilistic pre-diction: Log-Predictive Score (LPS) and Continuous Ranked Probability Score (CRPS). Findings & value added: The pre-2013 data support the deterministic cycle models whereas more recent observations can be explained by a simple mean-reverting Gaussian AR(4) process. The results indicate a structural change affecting Polish business cycle fluctuations after 2013. Hence, forecast pooling strategies are recommended as a tool for further research. We find rather limited support in favor of the first group of models. The probabilistic indicator of future economic conditions considered here leads actual phases of the growth cycle quite well, though the effect is less obvious after 2013.

We demonstrate that analysis of long series of daily returns should take into account potential long-term variation not only in volatility, but also in parameters that describe asymmetry or tail behaviour. However, it is necessary to use a conditional distribution that is flexible enough, allowing for separate modelling of tail asymmetry and skewness, which requires going beyond the skew- t form. Empirical analysis of 60 years of S&P500 daily returns suggests evidence for tail asymmetry (but not for skewness). Moreover, tail thickness and tail asymmetry is not time-invariant. Tail asymmetry became much stronger at the beginning of the Great Moderation period and weakened after 2005, indicating important differences between the 1987 and the 2008 crashes. This is confirmed by our analysis of out-of-sample density forecasting performance (using LPS and CRPS measures) within two recursive expanding-window experiments covering the events. We also demonstrate consequences of accounting for long-term changes in shape features for risk assessment.