Abstract
From the early beginning of economics as a science, estimation of production functions has been a central topic in the relevant literature. Understanding the behavior of firms in various economic environments, knowing the elasticity parameters of inputs or the overall returns to scale parameter, estimating the efficiency of firms relatively possibly to a frontier that designates the optimal performance in the sector or, finally, evaluating the links between productivity and input decisions have proved to be major challenges in the contemporary economics. In the field of production microeconometrics two independent research areas have been developed, namely the stochastic frontier models (see Kumbhakar and Lovell, 2000) and the standard productivity models (see Griliches and Mairesse, 1998). Although the ultimate goal of estimation is not always the same for these two approaches, they do suffer in estimation from common aggravating factors, the most significant of all that of the endoge ...
From the early beginning of economics as a science, estimation of production functions has been a central topic in the relevant literature. Understanding the behavior of firms in various economic environments, knowing the elasticity parameters of inputs or the overall returns to scale parameter, estimating the efficiency of firms relatively possibly to a frontier that designates the optimal performance in the sector or, finally, evaluating the links between productivity and input decisions have proved to be major challenges in the contemporary economics. In the field of production microeconometrics two independent research areas have been developed, namely the stochastic frontier models (see Kumbhakar and Lovell, 2000) and the standard productivity models (see Griliches and Mairesse, 1998). Although the ultimate goal of estimation is not always the same for these two approaches, they do suffer in estimation from common aggravating factors, the most significant of all that of the endogeneity of regressors (inputs or/and outputs). Endogeneity of the regressors can arise when inputs are correlated with productivity or when there are more than one outputs in the production function even in the absence of productivity. No matter what factor causes the endogeneity, the resolution has been equally problematic.To this end, this thesis proposes two models towards a consistent estimation of the production function, one for each field, and sets a third theoretical model to unveil the deeper implications of the problem of endogeneity. The present thesis presents two papers on consistently estimating the production functions accounting explicitly for the endogeneity of the regressors, while relying on basic principles of economic theory. We are mixing ideas from finance, where prices are random variables, and finally we develop maximum likelihood and bayesian MCMC techniques for conducting inference. Additionally, a novel theoretical model is developed where, apart from various theoretical issues, it is shown that identifying the production function is closely related to the specification of the stochastic volatility process of productivity. In general, Monte Carlo tests and empirical applications are executed throughout the thesis providing strong evidence in favor of our proposed models. Specifically, the thesis is organized as follows. Chapter 2 provides an overview of the existing literature on the issue of the consistently estimating production functions. It discusses how the problem of endogeneity naturally arises in multiple output stochastic frontier models and the stochastic frontier literature is presented in the first half of the chapter. In the remaining chapter the productivity factor comes into play, the way how productivity renders inputs endogenous is addressed and an exposition of the related productivity literature is given. Chapter 3 proposes a novel way to properly estimate a standard multiple – output stochastic frontier model introducing for the first time random prices. What is mainly proposed is to complete the model with the first order conditions (FOC) as delivered from the optimization problem each time (cost minimization, revenue maximization or profit maximization; in our case we applied the revenue maximization environment) and make inference on structural parameters of the model by treating prices as latent, that is unobserved to econometrician, variables. Chapter 4 proposes a new model for consistently estimating the Cobb – Douglas production function. Profit maximization is assumed and productivity follows a panel autoregressive scheme, whereas log - relative prices follow an AR(1). Highly efficient bayesian Markov Chain Monte Carlo methods are developed to estimate this model, since one has to encompass the autoregressive nature of productivity and overcome constraints imposed by the most difficult, for estimation, economic environment, namely that of profit maximization. The extensive Monte Carlo and real data results are truly encouraging on the effectiveness of the estimation scheme. Finally, Chapter 5 reexamines the issue of endogeneity of inputs using a theoretical model with stochastic volatility in the productivity process. Through this theoretical model a deep search on the identification problem is undertaken, where the issue of identifying the production function boils down to specifying the drift of the stochastic volatility of productivity.
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