Sample selection and spatial models of housing price indexes, and, A disequilibrium analysis of the U.S. gasoline market using panel data

This dissertation consists of two parts. The first part studies the sample selection and spatial models of housing price index using transaction data on detached single-family houses of two California metropolitan areas from 1990 through 2008. House prices are often spatially correlated due to shared amenities, or when the properties are viewed as close substitutes in a housing submarket. There have been many studies that address spatial correlation in the context of housing markets. However, none has used spatial models to construct housing price indexes at zip code level for the entire time period analyzed in this dissertation to the best of my knowledge. In this paper, I study a first-order autoregressive spatial model with four different weighing matrix schemes. Four sets of housing price indexes are constructed accordingly. Gatzlaff and Haurin (1997, 1998) study the sample selection problem in housing index by using Heckman's two-step method. This method, however, is generally inefficient and can cause multicollinearity problem. Also, it requires data on unsold houses in order to carry out the first-step probit regression. Maximum likelihood (ML) method can be used to estimate a truncated incidental model which allows one to correct for sample selection based on transaction data only. However, convergence problem is very prevalent in practice. In this paper I adopt Lewbel's (2007) sample selection correction method which does not require one to model or estimate the selection model, except for some very general assumptions. I then extend this method to correct for spatial correlation.In the second part, I analyze the U.S. gasoline market with a disequilibrium model that allows lagged-latent variables, endogenous prices, and panel data with fixed effects. Most existing studies (see the survey of Espey, 1998, Energy Economics) of the gasoline market assume equilibrium. In practice, however, prices do not always adjust fast enough to clear the market. Equilibrium assumptions greatly simplify statistical inference, but are very restrictive and can produce conflicting estimates. For example, econometric models of markets that assume equilibrium often produce more elastic demand price elasticity than their disequilibrium counterparts (Holt and Johnson, 1989, Review of Economics and Statistics, Oczkowski, 1998, Economics Letters). The few studies that allow disequilibrium, however, have been limited to macroeconomic time-series data without lagged-latent variables. While time series data allows one to investigate national trends, it cannot be used to identify and analyze regional differences and the role of local markets. Exclusion of the lagged-latent variables is also undesirable because such variables capture adjustment costs and inter-temporal spillovers. Simulation methods offer tractable solutions to dynamic and panel data disequilibrium models (Lee, 1997, Journal of Econometrics), but assume normally distributed errors. This paper compares estimates of price/income elasticity and excess supply/demand across time periods, regions, and model specifications, using both equilibrium and disequilibrium methods. In the equilibrium model, I compare the within group estimator with Anderson and Hsiao's first-difference 2SLS estimator. In the disequilibrium model, I extend Amemiya's 2SLS by using Newey's efficient estimator with optimal instruments.