Essays in econometrics and entrepreneurship

This thesis proposes new semiparametric methods for estimation and testing of conditional moments restrictions models, develops third-order likelihood based techniques for inference in small sample models, and analyzes entrepreneurship in Africa. The research proceeds along five chapters. The first chapter develops a Hausman-type specification test statistic for conditional moment restrictions (CMR) models. The proposed test statistic is asymptotically chi-squared distributed under correct specification. A general bootstrap procedure for computing critical values in small samples is also proposed. The test statistic is easy to implement and simulations show that it works well in small samples. The second and third chapters develop third-order likelihood based procedures for estimation and inference in small sample models. Chapter two proposes a statistical technique to derive highly accurate p-value approximations when testing for autocorrelation in dynamic nonlinear regression models. The proposed techniques are particularly accurate for small samples whereas commonly used methods could be misleading. Monte Carlo simulations are provided to show how the proposed method outperforms existing ones and an empirical example is given. Likewise, Chapter three uses similar techniques to develop a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability with independent normal variables of unknown means and variances. The proposed method is compared to existing ones and its superior accuracy in terms of coverage probability and error rate is confirmed by numerical simulations. The fourth and fifth chapters examine entrepreneurial choice in Africa. The fourth chapter investigates how skills and limited access to credit influence occupational patterns and explain the heterogeneity observed in the informal sector of developing countries using a cross-sectional sample of households from the Cameroon informal sector. Structural estimates and counterfactual numerical simulations are then used to show that microfinance can improve entrepreneurship and income. The fifth chapter argues that the culture of "forced mutual help" (Firth 1951), that obliges wealthy Africans to share their resources with their needy relatives and extended family, also discourages entrepreneurship. The study combines theoretical and empirical analysis to show how this mutual help constraint adversely affects entrepreneurship, using a database compiling enterprises surveys from several African countries.