Identification and estimation of endogenous selection models in the presence of misclassification errors

This paper shows the semi-parametric identification and estimation of sample selection models when the primary equation contains a discrete mismeasured endogenous covariate. Assuming that appropriate instruments for the presence of endogeneity are available, I apply a control function approach to remove the possible endogeneity. Based on the conditional mean independence between the model error and the selection error, the model can be regarded as a semi-parametric regression model with a discrete mismeasured covariate, thereby permitting a non-classical measurement error. Additional identification assumptions include monotonicity restrictions on the regression function and an empirical testable rank condition. I then use the identification result to construct a sieve maximum likelihood estimation estimator to estimate the model parameters consistently and recover the selection rule and joint probabilities of the accurately measured endogenous variable and the mismeasured observed variable. The proposed estimation method allows for a rather flexible functional form of the mismeasured endogenous covariate, requires only one valid instrument to control for both endogeneity and measurement errors for the variable of interest, and imposes no distribution assumptions on the selection rule.     

Estimating gravity equation models in the presence of sample selection and heteroscedasticity

Gravity models are widely used to explain patterns of trade. However, two stylized features of trade data, sample selection and heteroscedasticity challenge the estimation of gravity models. We propose a two-step method of moments (TS-MM) estimator that deals with both issues. The Monte-Carlo experiments show that the TS-MM estimates are resistant to various combinations of sample selection and heteroscedasticity. Moreover, the TS-MM estimator performs reasonably well even when the data generating process deviates from the TS-MM assumptions. We revisit the world trade in 1990 to illustrate the usefulness of the proposed model, with emphasis on the identification of the extensive margin of trade.     

The competence-loyalty tradeoff in China's political selection

This paper studies the competence-loyalty tradeoff and its evolution in China's political system characterized by hierarchical selection. From the eyes of the central controllers, the rational selection rule is to mix competence and loyalty when officials are selected to fill lower-tier positions and to select from them the more loyal to fill higher-level positions. Measuring competence by an official's contribution to local economic growth and loyalty by his work experience (connection) with central leaders, our empirical analysis finds that ability strongly matters and connection weakly matters for city officials promoted to provincial positions, but only connection matters for provincial officials promoted to central positions. Moreover, ability matters more in the early years, and connection matters more in the later years.     

An MPEC estimator for misclassification models

In this paper, we propose a constrained maximum likelihood estimator for misclassification models, by formulating the estimation as an MPEC (Mathematical Programming with Equilibrium Constraints) problem. Our approach improves the numerical accuracy and avoids the singularity problem. Monte Carlo simulations confirm that the proposed estimator reduces bias and standard deviation of the estimator, especially when the sample is small/medium and/or the dimension of latent variable is large.     

Model Uncertainty in Characterizing Recreation Demand

A Bayesian variable selection procedure is used to control for uncertainty in the specification of a recreational demand model. Specifically, we propose a model that draws on the Bayesian paradigm to integrate the variable selection process into model estimation and to reflect the accompanying uncertainty about which is the best specification in subsequent counterfactual predictions. The advantage of this procedure over previous non-Bayesian approaches is that it overcomes the problem of pre-testing in specification searches. In our application, evaluating demand for recreational lake usage in Iowa, we find clear evidence that site attributes, such as lakes size, handicap facilities and wake restrictions, do impact lake usage. There is also evidence that water quality matters in household recreation choices. Indeed, contrary to Abidoye et?al. (Am J Agricult Econ, 2012), in which only a single functional form is considered, we find clear evidence that water quality matters, with posterior probability of less that 10 % associated with a model without any water quality variables. This suggests that the flexibility that the Bayesian variable selection model affords in capturing the linkage between recreation demand and site characteristics can be important.     

Interval regression models with endogenous explanatory variables

We consider the estimation of linear models where the dependent variable is observed by intervals and some continuous regressors may be endogenous. Our approach, an IV version of the technique devised by Stewart (Rev Econ Stud 50(3):737?C753, 1983), is fully parametric and two estimators are proposed: a two-step estimator and a limited-information maximum-likelihood estimator. The results can be summarized as follows: the two-step estimator has an intuitive appeal, and a Monte Carlo experiment suggests that its relative efficiency is rather satisfactory. The limited-information maximum-likelihood estimator, however, is probably simpler to implement and has the advantage of providing a framework in which several testing procedures are more straightforward to perform. The application of two-stage least squares to a proxy of the dependent variable built by taking midpoints, on the other hand, leads to inconsistent estimates; Monte Carlo evidence suggests that the bias arising from the ??midpoint?? technique is much worse than the effect of distributional misspecification. An example application is also included, which uses Australian data on migrants?? remittances; endogeneity effects are substantial and using conventional estimation methods leads to substantially misleading inference.     

Testing exclusion restrictions and additive separability in sample selection models

Standard sample selection models with non-randomly censored outcomes assume (i) an exclusion restriction (i.e., a variable affecting selection, but not the outcome) and (ii) additive separability of the errors in the selection process. This paper proposes tests for the joint satisfaction of these assumptions by applying the approach of Huber and Mellace (Testing instrument validity for LATE identification based on inequality moment constraints, 2011) (for testing instrument validity under treatment endogeneity) to the sample selection framework. We show that the exclusion restriction and additive separability imply two testable inequality constraints that come from both point identifying and bounding the outcome distribution of the subpopulation that is always selected/observed. We apply the tests to two variables for which the exclusion restriction is frequently invoked in female wage regressions: non-wife/husband’s income and the number of (young) children. Considering eight empirical applications, our results suggest that the identifying assumptions are likely violated for the former variable, but cannot be refuted for the latter on statistical grounds.     

Semiparametric Difference-in-Differences Estimators

The difference-in-differences (DID) estimator is one of the most popular tools for applied research in economics to evaluate the effects of public interventions and other treatments of interest on some relevant outcome variables. However, it is well known that the DID estimator is based on strong identifying assumptions. In particular, the conventional DID estimator requires that, in the absence of the treatment, the average outcomes for the treated and control groups would have followed parallel paths over time. This assumption may be implausible if pre-treatment characteristics that are thought to be associated with the dynamics of the outcome variable are unbalanced between the treated and the untreated. That would be the case, for example, if selection for treatment is influenced by individual-transitory shocks on past outcomes (Ashenfelter's dip). This article considers the case in which differences in observed characteristics create non-parallel outcome dynamics between treated and controls. It is shown that, in such a case, a simple two-step strategy can be used to estimate the average effect of the treatment for the treated. In addition, the estimation framework proposed in this article allows the use of covariates to describe how the average effect of the treatment varies with changes in observed characteristics.     

Optimal Time Interval Selection in Long-Run Correlation Estimation

This paper presents an asymptotically optimal time interval selection criterion for the long-run correlation block estimator (Bartlett kernel estimator) based on the Newey–West and Andrews–Monahan approaches. An alignment criterion that enhances finite-sample performance is also proposed. The procedure offers an optimal alternative to the customary practice in finance and economics of heuristically or arbitrarily choosing time intervals or lags in correlation studies. A Monte Carlo experiment using parameters derived from Dow Jones returns data confirms that the procedure can be MSE-superior to alternatives such as aggregation over arbitrary time intervals, parametric VAR, and Newey–West covariance matrix estimation with automatic lag selection.

     

Inverse probability weighted M-estimators for sample selection, attrition, and stratification

I provide an overview of inverse probability weighted (IPW) M-estimators for cross section and two-period panel data applications. Under an ignorability assumption, I show that population parameters are identified, and provide straightforward -consistent and asymptotically normal estimation methods. I show that estimating a binary response selection model by conditional maximum likelihood leads to a more efficient estimator than using known probabilities, a result that unifies several disparate results in the literature. But IPW estimation is not a panacea: in some important cases of nonresponse, unweighted estimators will be consistent under weaker ignorability assumptions.JEL Classification: C13, C21, C23I would like to thank Bo Honoré, Christophe Muller, Frank Windmeijer, and the participants at the CeMMAP/ESCR Econometric Study Group Microeconometrics Workshop for helpful comments on an earlier draft.     

Estimation of a Tobit model with unknown censoring threshold

Conventional wisdom suggests that only the estimated intercept is affected by imposition of a zero censoring threshold on a Tobit model. This is true for Heckman-Lee estimation. For maximum likelihood (ML) estimation, however, it is only true if the censoring threshold is known and is subtracted from the dependent variable. Failure to properly transform the dependent variable prior to ML estimation of a zero threshold Tobit model will generally bias the coefficient estimates. A long neglected topic is ML estimation of a Tobit model with common, but unknown, censoring threshold. This paper shows that the ML estimator of the censoring threshold is the minimum order statistic from the observed subsample, and that existing software for estimation of a zero-threshold Tobit model is easily adapted to include estimation of the censoring threshold.     

The Impact of Inequality and Redistribution on Growth

In this paper, we reassess the impact of inequality on growth. The majority of previous papers have employed (system) GMM estimation. However, recent simulation studies indicate that the problems of GMM when using non‐stationary data such as GDP have been grossly underestimated in applied research. Concerning predetermined regressors such as inequality, GMM is outperformed by a simple least‐squares dummy variable estimator. Additionally, new data have recently become available that not only double the sample size compared to most previous studies, but also address the substantial measurement issues that have plagued past research. Using these new data and an LSDV estimator, we provide an analysis that both accounts for the conditions where inequality is beneficial or detrimental to growth and distinguishes between market‐driven inequality and redistribution. We show that there are situations where market inequality affects growth positively while redistribution is simultaneously beneficial.     

Semiparametric Estimation of the Intercept of a Sample Selection Model

This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to infinity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept has typically been subsumed in the nonparametric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the "wage gap" between unionized and nonunionized workers, decompose the wage differential between different socio-economic groups (e.g. male–female and black–white), and evaluate the net benefits of a social programme.     

Returns to women’s education using optimal IV selection

This paper investigates returns to women’s education by applying an optimal IV selection approach, post-Lasso IV estimation, which improves the first-stage predictive relationship between an endogenous regressor and instruments. Using the 2010 American Community Survey, we find that an extra year of education increases married women’s own income by $4,480 and spouse income by $8,822. Our findings indicate that 53% of the increase in women’s consumption by education is attributed to the marriage market, and thus, we conclude that the marriage market is the primary channel through which education improves women’s well-being. The results demonstrate the advantages of the post-Lasso approach: The resulting two-stage least squares estimator maintains efficiency without increasing finite sample bias and is less subject to the inconsistency problem when some instruments are invalid; This differs from the results using the instrument of birth quarters only, which is mostly applied in studies on returns to education.     

Simulated Non-Parametric Estimation of Dynamic Models

This paper introduces a new class of parameter estimators for dynamic models, called simulated non-parametric estimators (SNEs). The SNE minimizes appropriate distances between non-parametric conditional (or joint) densities estimated from sample data and non-parametric conditional (or joint) densities estimated from data simulated out of the model of interest. Sample data and model-simulated data are smoothed with the same kernel, which considerably simplifies bandwidth selection for the purpose of implementing the estimator. Furthermore, the SNE displays the same asymptotic efficiency properties as the maximum-likelihood estimator as soon as the model is Markov in the observable variables. The methods introduced in this paper are fairly simple to implement, and possess finite sample properties that are well approximated by the asymptotic theory. We illustrate these features within typical estimation problems that arise in financial economics.     

Catching Growth Determinants with the Adaptive Lasso

Abstract. This paper uses the adaptive Lasso estimator to determine variables important for economic growth. The adaptive Lasso estimator is a computationally very efficient procedure that simultaneously performs model selection and parameter estimation. The computational cost of this method is negligibly small compared with standard approaches in the growth regressions literature. We apply this method for a regional dataset for the European Union covering the 255 NUTS2 regions in the 27 member states over the period 1995–2005. The results suggest that initial GDP per capita (with an implied convergence speed of about 1.5% per annum), human capital (proxied by the shares of highly and medium educated in the working age population), structural labor market characteristics (the initial unemployment rate and the initial activity rate of the low educated) as well as being a capital region are important for economic growth.     

The asymptotic efficiency of semiparametric estimators for censored linear regression models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantite, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.     

Efficiency of two-step estimators for censored systems of equations: Shonkwiler and Yen reconsidered

This study analyses a parametric estimator for a system of equations with limited dependent variables that was recently proposed. Its performance is compared with those of alternative estimation procedures using Monte Carlo methods. The comparison shows that this new estimator is less efficient for a wide range of parameter regions than multivariate generalizations of the classical Heckman model. This result can be explained by its variance depending on the squared conditional mean of the dependent variables. Additionally, it turns out that within the class of generalized Heckman estimators, rather simple ones display the best performance.     

Semiparametric Estimation of Simultaneous-Equation Microeconometric Models with Index Restrictions

This article introduces semiparametric methods for the estimation of simultaneous-equation microeconometric models with index restrictions. The methods are motivated by a semiparametric minimum-distance procedure, which unifies the estimation of both regression-type and linear or nonlinear simultaneous-equation models without emphasis on the construction of instrumental variables. Single-equation and systematic estimation methods and optimal weighting procedures are considered. The estimators are √ n -consistent and asymptotically normal. For the estimation of nonparametric regression and some sample selection models where the variances of disturbances are functions of the same indices, the optimal weighted estimator attains Chamberlain's efficient bound for models with conditional moment restrictions. The weighted estimator is shown to be optimal within a class of semiparametric instrumental variables estimators.
JEL classification numbers: C14, C24, C34.     

A Note on Estimating Unemployment Duration

A focal point of a number of recent studies of unemployment duration has been the estimation of the unobserved average completed duration (ACD) of an unemployment spell using groped data on observed incomplete spells. Both parametric and non-parametric methods are available. This note compares the assumptions underlying the two approaches and argues for the use of a non-parametric estimator, specifically the Kaplan-Meier estimator, on grounds of its use of the weaker assumptions. In an actual application of the Kaplan-Meier estimator to some data from the Australian Labour Force Survey a Number of problems are experienced due to the fact that the estimator is intended for data in a life table format. The note briefly discusses the resolution of these problems and related statistical issues.