Essays on the Use of Duality, Robust Empirical Methods, Panel Treatments, and Model Averaging with Applications to Housing Price Index Construction and World Productivity Growth

This dissertation focuses on analyzing the production side of the economy, and aims to provide robust estimates of the parameters of interest. In a production process, the output level is mainly determined by two parts: inputs and productivity. Compared with the inputs, which are concrete and measurable, productivity is an unobservable factor that relies on economic models for estimation. An appropriate and robust modeling method is essential if we want to accurately capture the productivity term. Chapter 1 reviews the research on productivity with a focus on stochastic frontier analysis, which is a classic framework in the productivity literature. This chapter starts with the definition and decomposition of productivity. Measured as a ratio of the outputs to the inputs, productivity can be divided into two main parts: innovations and technical efficiencies. The growth of technologies and innovations depends heavily on education and research, and the technical efficiencies of firms vary with their administration, management skills, and allocation of inputs etc. In studies analyzing these two components, stochastic frontier models have gradually become the standard method. This chapter briefly introduces the development of stochastic frontier models, with an emphasis on the panel data setting. Twelve specifications, as well as their implementation methods, are then discussed in detail. These representative models make different assumptions about the efficiency term, aiming to provide better approximations of the underlying data generating process without adding too many constraints. Comparing all these models, we expect different estimates of productivity from different specifications. The evaluation and selection of a suitable model for empirical analysis become a problem. Standard information criteria provide measures of the performance of each candidate model, but multiple criteria can lead to contradicting conclusions about which model is the best one. In addition, the model selection approach itself ignores the risk of model uncertainty. This issue of dealing with multiple competing models will be addressed in Chapter 3. While Chapter 1 concentrates on the methods of estimating productivity, Chapter 2 focuses on the role of proper specification of the inputs used in generating the output. Though the inputs of a production process are usually observable, their effects on the outputs are often not clear and straightforward. The allocation of different inputs are affected by both the production technology and market prices. Chapter 2 utilizes the duality between the production maximization problem and cost minimization problem to uncover the shadow prices of inputs, and constructs corresponding price indexes for further analysis. This chapter is motivated by recent housing bubbles and considers the housing market for the empirical application. The housing market is an important component of the economy, and constantly attracts interests of researchers. Diewert (2010) for example has provided a comparison of various methods of constructing property price indexes using index number and hedonic regression methods, which he illustrates using data over a number of quarters from a small Dutch town. Chapter 2 provides an alternative approach based on Shephard's dual lemma and I apply it to the same data used by Diewert. This method avoids the multicollinearity problem associated with traditional hedonic regression, and the resulting prices of property characteristics show smoother trends than Diewert's results. The chapter also revisits the Diewert and Shimizu (2013) study that employed hedonic regressions to decompose the price of residential property in Tokyo into land and structure components and that constructed constant quality indexes for land and structure prices respectively. I use three models from Diewert and Shimizu (2013) to fit our real estate data from town ‘A’ in Netherlands, and also construct the price indices for land and structure, which are compared with results derived using the duality theory. Again, we have multiple models in the study of housing market. As in the case of productivity, the shadow prices of property characteristics are unobservable (due to the nature of the input or intermediate good, there may not exist an explicit market.) Thus, we rely on certain methods for estimation, and there are a set of candidate models. Chapters 1 and 2 leave us in a dilemma. Which model is correct? Which model do we choose? Is any model actually the correct one or are we choosing among misspecified models? Do we simply choose one model and ignore results from the others? These issues are addressed in Chapter 3 wherein a model averaging approach is explored to provide estimates that are robust to various model specifications. Model averaging methods can be used to provide robust estimates by combining a set of competing models through certain optimization mechanisms. Chapter 3 pursues robust estimates of world productivity levels as well as its growth rates. Various structural and reduced form models of productivity growth have been proposed in the literature. In either class of models, reduced form measurements of productivity and efficiency are obtained. As the true data generating process of productivity cannot be observed, this chapter examines model averaging approaches that can provide a vehicle to weight predictions (in the form of productivity and efficiency measurements) from different reduced form methods. The reduced form models, typically stochastic frontier methods, have a variety of different settings, which have been discussed in Chapter 1. This chapter considers the jackknife model averaging estimator proposed by Hansen and Racine (2012) and illustrates how to apply the technique to a set of competing stochastic frontier estimators. The derived method is employed to analyze the productivity and efficiency development in three country groups worldwide. The results of the empirical application show that the model averaging method provides more stable estimates. The model selection method, on the other hand, tends to select a model with superficially high goodness of fit, which results from the match between some specific model setting and the data set. A brief discussion of alternative structural models from which a reduced form forecast can be derived is provided to illustrate a different perspective for productivity analysis