Estimating non-linear models with applications to health, labor and education economics

Resumen

This dissertation is composed of three studies of non-linear econometric models, with applications to Health, Labor and Education Economics. Chapter 1 studies the differences in the proportion of temporary employees of domestic and foreign firms in the Spanish manufacturing sector. The objective of the chapter is to determine if, after controlling for a large set of observable firm characteristics and unobservable firm-specific time-invariant components, there is still a relationship between firm nationality and the type of employment contracts that firms offer. For that purpose, I estimate standard censored Tobit and Heckman sample selection models (also known as type I Tobit and Heckman two-step models, respectively), using data from the Survey of Managerial Strategies (Encuesta sobre Estrategias Empresariales, ESEE), which includes a representative number of Spanish firms in the manufacturing sector during 1991-2005. The estimations show that firm nationality has a significant effect over the probability that firms hire temporary workers and over the proportion of temporary workers for firms that choose to hire temporary workers. The size and significance of the effects depend on firm size. In the case of the Heckman estimations, for example, a higher proportion of foreign capital implies a lower average probability of hiring temporary workers for small and medium firms, but not for large firms. Likewise, a higher proportion of foreign capital implies a decrease in the average proportion of temporary workers (for firms who choose to hire temporary workers) for medium and large firms, but not for small firms. Chapter 1 provides two contributions to the literature. First, it presents a further account of the differences between domestic and foreign firms. In particular, I show that domestic and foreign firms do not differ only in wages and productivity, but also on the types of labor contracts that they offer. Second, the chapter provides a detailed study of the determinants of temporary employment in the Spanish manufacturing sector, focusing in particular on firm nationality and firm size. My findings indicate that a labor reform trying to reduce the use of fixed-term employment contracts should provide different incentives to firms of different size. Chapter 2 considers the estimation of a dynamic ordered probit with fixed effects, and its application to the study of the determinants of self-assessed health status (SAH). SAH has been used as a proxy for true overall individual health status in many socioeconomic studies. Moreover, it has been shown to be a good predictor of mortality and of subsequent demand of medical care (see for example van Doorslaer, Koolman and Jones 2004). Contoyannis, Jones and Rice (2004) studied the dynamics and effects of socioeconomic variables on SAH for the British Household Panel Survey, by performing a random effects analysis on a dynamic ordered probit model. Among other aims, they tried to determine the relative contribution of state dependence and unobserved heterogeneity in explaining the observed persistence in SAH. This chapter applies a 'fixed effects' approach instead, which allows us to leave unrestricted the joint distribution of the two individual effects and their correlation with the explanatory variables, and to avoid the initial conditions problem. In addition to accounting for unobserved factors that affect health status (index shifts), it is also important to take into account the possible heterogeneity in reporting behavior (cut-point shifts), which may occur if individuals use different thresholds when assessing their health and reporting it in the SAH categorical variable (i.e. two individuals may report a different value of SAH even though they have the same level of true health). Despite the advantages of fixed effects over random effects estimations, there have been only few applications in non-linear models in health economics (as can be seen by reading Jones's 2007 handbook chapter). This is due to the difficulty in dealing with the incidental parameters problem, which is specially severe in the model studied in the chapter because it contains two fixed effects (index and cut-point shifts). To account for the incidental parameters problem, we apply Carro's (2007) approach to bias reduction. We compare the resulting estimators with the 'standard' Maximum Likelihood estimators, and with the bias-corrected estimators proposed by Bester and Hansen (2009). In Montecarlo simulations, we show that both Maximum Likelihood and Bester and Hansen's estimators under-perform relative to the estimators obtained by following Carro's approach. Moreover, we also find that large biases remain in the case of Bester and Hansen's estimator, even for relatively large panel sizes. We estimate the model using the British Household Survey in the period 1991-2006. Based on our best estimates, the two fixed effects exhibit important variation so it is relevant to account for both when estimating the effect of other variables. Our estimates also show that state dependence is very important even though we have controlled for unobserved heterogeneity and some forms of objective health measures. The latter are the variables with higher marginal effects. The contributions of this chapter are twofold. First, the chapter contributes to the recent literature on bias correction in nonlinear panel data models by applying and studying the finite sample properties of two of the existing proposals to the ordered probit case. We find that the most direct and easily applicable correction to our model is not the best one and still has important biases in our sample sizes. Second, we contribute to the literature that studies the determinants of Self-Assessed Health measures by applying the previous analysis on estimation methods to the British Household Panel Survey. Finally, in Chapter 3, I study gender differences in major choice and college entrance probabilities in the University of Campinas, a Brazilian public university dependent on the State of Sao Paulo. As with most Brazilian public universities, candidates for entry into University of Campinas first select a major, and then compete for a place in that major by taking a major-specific entrance exam. This singular characteristic of the Brazilian case allows me to differentiate the effect of gender on major-specific entrance probabilities and preferences. I propose a model and econometric strategy which can account for two important issues, selectivity bias and the fact that expected utility depends on the probability of entering the different majors. I estimate this model using a novel dataset obtained from University of Campina's Permanent Commission for Vestibular Exams (Comvest). I find evidence of gender differences in preferences and entrance probabilities. For most majors, gender differences in major choice are mostly explained by differences in preferences. However, for the most demanding majors (those that require higher grades from students), differences in major choice are explained in a large proportion by differences in entrance probabilities. Finally, I find that gender has important interactions with other variables. In particular, gender effects depend on education, socioeconomic characteristics and family background. This chapter has three contributions. First, the econometric model is able to account for selection bias, in contrast to previous papers, which have assumed that the errors of the probability of entry and choice equations were independent, i.e. there was no selectivity bias by assumption (see for example, Montmarquette et al. 2002). Second, the chapter introduces a novel database, which can be used to disentangle the differential effects of probability of entry and preferences in gender differences in major choice. Third, this chapter provides the first detailed analysis of the determinants of major choice in Brazil. A few papers analyze the determinants of performance in Entrance Test Exams (Guimaraes and Sampaio 2007, 2008, Calvacanti et al. 2009), but the choice of major has not been analyzed in detail. Performing such analysis is important because of its possible relation with gender inequality, which is an important issue for the Brazilian Federal Government. For example, the Federal Government has recently introduced over 400 projects directed at enhancing equal opportunities for men and women, which will be performed by 22 government institutions between 2008 and 2011 (Pinheiro et al. 2008).