The dissertation consists of three parts and the theme is to deal with heterogeneity ineconometrics models for positive response variables. The first part studies the models withmultiplicative heterogeneity for cross sectional data; the multiplicative heterogeneity canbe transformed from the log linear model with additive heterogeneity. We introduce thenotion of Average Partial Effect (APE) and Conditional APE (CAPE); the estimators andtheir asymptotic distribution are proposed. In order to catch the positivity of the unknownconditional expectation function of the unobserved heterogeneity, we borrow the idea ofpower series approximation of unknown function in Newey (1993, 1994) and develop an\exponential sieves" estimator for CAPE suggested in Wooldridge (1992a).The second part of the dissertation pertains to extending results for CAPE in chapter 1for panel data sets. First, Using the models in Wooldridge (1999), We compare three mainestimation methods for positive response variable{ FE method for log linear model (LFE),Poisson Quasi-Maximum Likelihood (PQML) and Generalized Method of Moment (GMM){ by Monte Carlo Simulation and real life data set. It is not surprising that LFE estimatoris not consistent when PQML is; however, we do find circumstance where both LFE andPQML estimators are consistent plus LFE is more efficient. With this regard, we introduceGMM to improve the efficiency of PQML estimator as well as keeping the consistency; thisway also finds a solution to the problem raised in Wooldridge (1999). From the simulationresults, we find that GMM can reduce the standard error of PQML estimator by almosta half. Second, an \exponential sieves" estimator for CAPE is proposed under panel datasetting; the result automatically extends the results in Ai and Norton (2008) from crosssectional setting to panel data models. Third, We also apply the GMM to a US domesticairlines data set and the result shows that GMM improves the efficiency by 10% comparedwith PQML.The third part investigates the effect of spatial correlation for fractional response variable.By a MEAP data of Michigan in 2009/2010 school year, we investigate again the effect ofschool financing reform on school performance which is studied by Papke (2005, 2008), Pakeand Wooldridge (2008); we use both level math test pass rate (linear case)and its log oddsratio (nonlinear) as dependent variable to run OLS and GLS regression; Conley (1999)'sspatial dependence corrected standard errors are calculated and nd that the statistical significance for some regressors hinges on the choice of cut o points ; however there do existother factors whose statistical significance is robust to the choice. This way we shed somelight on how to pick the right window size. Moreover, by transforming LOR back to levelrate, we find the spending effect estimated from linear model is about 4 6% higher thanfrom nonlinear one.
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