Essays on Treatments of Cross-Section Dependence in Panel Data Models
Sickles, Robin C
Doctor of Philosophy
The dissertation consists of three essays on the treatments of cross-sectional dependence in panel data models especially oriented to spatial econometric approaches. The first essay aims to investigate spillover effects of public capital stock in a production function model that accounts for spatial dependencies. In many settings, ignoring spatial dependency yields inefficient, biased and inconsistent estimates in cross country panels. Although there are a number of studies aiming to estimate the output elasticity of public capital stock, many of those fail to reach a consensus on refining the elasticity estimates. We argue that accounting for spillover effects of the public capital stock on the production efficiency and incorporating spatial dependences are crucial. For this purpose, we employ a spatial autoregressive stochastic frontier model based on a number of specifications of the spatial dependency structure. Using the data of 21 OECD countries from 1960 to 2001, we estimate a spatial autoregressive stochastic frontier model and derive the mean indirect marginal effects of public capital stock, which are interpreted as spillover effects. We found that spillover effects can be an important factor explaining variations in technical inefficiency across countries as well as in explaining the discrepancies among various levels of output elasticity of public capital stock in traditional production function approaches. The second essay examines aggregate productivity in the presence of intersectoral linkages. Cross-sectional dependence is inevitable among industries as each sector serves as supplier to other sectors immediately and the chains of the interconnection cause indirect relationship among industries. Spatial analysis is one of the approaches that address cross-sectional dependence using a priori specified spatial weights matrices. We exploit the linkage patterns from the Input-Output table and use the patterns to assign spatial weights that describe the interdependency in economic space. Us- ing the spatial weights matrix, we estimate industry-level production function and productivity of the U.S. for the period from 1947 to 2010. Our main results indicate that the output elasticity estimates are larger when we consider cross-sectional dependence, which is the consequence of indirect effects reflecting interactions among industries. The productivity estimates, however, are found to be comparable across the estimation techniques. The third essay considers a panel data model addressing the issues of endogeneity and cross-sectional dependence together. Unobserved heterogeneity may cause two different results: endogeneity and cross-sectional dependence. In this essay, we model both endogeneity and cross-sectional dependence expanding a spatial error model with a control function on the productivity component. In particular, we found that the two-step estimation procedure for a typical control function approach is not required when it is used with a Spatial Error Model. We estimate a production function and efficiency scores by applying our model to Spanish Dairy farm data in a panel setting for a period of 1999 - 2010. We compare the results from a variety of specifications with and without incorporating endogeneity and cross-sectional dependence. We found that the Spanish Dairy farms shows increasing returns to scale and the yearly average efficiency level decreases with time.
Cross-Section Dependence; Panel Data; Spatial Analysis; Productivity; Stochastic Frontier Analysis