Inference on an extended Roy model,with an application to schooling decisions in France

This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangling the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the selection equation, we show that this component is point identified from the knowledge of the covariate effects on earnings, as soon as one covariate is continuous. Notably, and in contrast to most results on the identification of Roy models, this implies that identification can be achieved without any exclusion restriction nor large support condition on the covariates. As a by-product, bounds are obtained on the distribution of the ex ante   monetary returns. We propose a three-stage semiparametric estimation procedure for this model, which yields root-n$n$ consistent and asymptotically normal estimators. Finally, we apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.     

A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom

This paper is concerned with developing a semiparametric panel model to explain the trend in UK temperatures and other weather outcomes over the last century. We work with the monthly averaged maximum and minimum temperatures observed at the twenty six Meteorological Office stations. The data is an unbalanced panel. We allow the trend to evolve in a nonparametric way so that we obtain a fuller picture of the evolution of common temperature in the medium timescale. Profile likelihood estimators (PLE) are proposed and their statistical properties are studied. The proposed PLE has improved asymptotic property comparing the sequential two-step estimators. Finally, forecasting based on the proposed model is studied.     

On efficient estimation of the ordered response model

In this paper, we derive efficiency bounds for the ordered response model when the distribution of the errors is unknown. Furthermore, we develop an estimator that is efficient under suitable conditions. Interestingly, neither the bounds nor the estimator are trivial extensions of what has been proposed in the literature for the binary response model. The estimator is composed of quadratic B-splines, and estimation is performed by the method of sieves. In addition, the estimator of the distribution function is restricted to be a proper distribution function. An empirical example on the effect of fees on attendance rates at universities and community colleges is also included; we get substantively different results by relaxing the assumption that the distribution of the errors is normal.     

Efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood

This paper presents efficient semiparametric estimators for endogenously stratified regression with two strata, in the case where the error distribution is unknown and the regressors are independent of the error term. The method is based on the use of a kernel-smoothed likelihood function which provides an explicit solution for the maximization problem for the unknown density function without losing information in the asymptotic limit. We consider both standard stratified sampling and variable probability sampling, and allow for the population shares of the strata to be either unknown or known a priori.     

Wages and Ageing: Is There Evidence for the ‘Inverse‐U’ Profile?*

How individual wages change with time is one of the crucial determinants of labour market decisions including the timing of retirement. The focus of this paper is the relationship between age and wages with special attention given to individuals nearing retirement. The analysis is presented in a comparative context for Britain and Germany looking at two longitudinal data sets (BHPS and SOEP, respectively) for the years 1995–2004. We show the importance of cohort effects and selection out of employment which determine the downward‐sloping part of the ‘inverse‐U’ profile observed in cross‐sections. There is little evidence that wages fall with age.     

Asymptotic theory for nonparametric regression with spatial data

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.     

A smoothed least squares estimator for threshold regression models

We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen [2000. Sample splitting and threshold estimation. Econometrica 68, 575–603] to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold effect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the slope and threshold parameters.     

Nonparametric identification of a binary random factor in cross section data

Suppose V and U are two independent mean zero random variables, where V has an asymmetric distribution with two mass points and U has some zero odd moments (having a symmetric distribution suffices). We show that the distributions of V and U are nonparametrically identified just from observing the sum V+U, and provide a pointwise rate root n estimator. This can permit point identification of average treatment effects when the econometrician does not observe who was treated. We extend our results to include covariates X, showing that we can nonparametrically identify and estimate cross section regression models of the form Y=g(X,D^∗)+U, where D^∗ is an unobserved binary regressor.     

Estimating semiparametric panel data models by marginal integration

We propose an alternative method for estimating the nonlinear component in semiparametric panel data models. Our method is based on marginal integration that allows us to recover the nonlinear component from an additive regression structure that results from the first differencing transformation. We characterize the asymptotic behavior of our estimator. We also extend the methodology to treat panel data models with two-way effects. Monte Carlo simulations show that our estimator behaves well in finite samples in both random effects and fixed effects settings.     

Inference in semiparametric binary response models with interval data

This paper studies the semiparametric binary response model with interval data investigated by Manski and Tamer (2002). In this partially identified model, we propose a new estimator based on MT’s modified maximum score (MMS) method by introducing density weights to the objective function, which allows us to develop asymptotic properties of the proposed set estimator for inference. We show that the density-weighted MMS estimator converges at a nearly cube-root-n rate. We propose an asymptotically valid inference procedure for the identified region based on subsampling. Monte Carlo experiments provide supports to our inference procedure.     

Semiparametric robust estimation of truncated and censored regression models

Many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares (SCLS) are sensitive to outliers and data contamination as we document. Therefore, we propose a semiparametric general trimmed estimator (GTE) of truncated and censored regression, which is highly robust but relatively imprecise. To improve its performance, we also propose data-adaptive and one-step trimmed estimators. We derive the robust and asymptotic properties of all proposed estimators and show that the one-step estimators (e.g., one-step SCLS) are as robust as GTE and are asymptotically equivalent to the original estimator (e.g., SCLS). The finite-sample properties of existing and proposed estimators are studied by means of Monte Carlo simulations.     

Identification and nonparametric estimation of a transformed additively separable model

Let r(x,z)$r(x,z)$ be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses the identification and consistent estimation of the unknown functions H$H$, M$M$, G$G$ and F$F$, where r(x,z)=H[M(x,z)]$r(x,z)=H\left[M(x,z)\right]$, M(x,z)=G(x)+F(z)$M(x,z)=G\left(x\right)+F\left(z\right)$, and H$H$ is strictly monotonic. An estimation algorithm is proposed for each of the model’s unknown components when r(x,z)$r(x,z)$ represents a conditional mean function. The resulting estimators use marginal integration to separate the components G$G$ and F$F$. Our estimators are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We apply our results to estimate generalized homothetic production functions for four industries in the Chinese economy.     

Censored regression quantiles with endogenous regressors

This paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous (and continuously distributed) and instrumental variables are available for them. A “distributional exclusion” restriction is imposed on the unobservable errors, whose conditional distribution is assumed to depend on the regressors and instruments only through a lower-dimensional “control variable,” here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments. This assumption, which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable, is used to motivate a two-stage estimator of the censored regression coefficients. In the first stage, the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated, as are the first-stage reduced-form residuals to be used as control variables. The second-stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors, using only pairs of observations for which both estimated quantiles are positive (i.e., in the uncensored region) and the corresponding difference in estimated control variables is small. The paper gives the form of the asymptotic distribution for the proposed estimator, and discusses how it compares to similar estimators for alternative models.     

Partial maximum likelihood estimation of spatial probit models

This paper analyzes spatial Probit models for cross sectional dependent data in a binary choice context. Observations are divided by pairwise groups and bivariate normal distributions are specified within each group. Partial maximum likelihood estimators are introduced and they are shown to be consistent and asymptotically normal under some regularity conditions. Consistent covariance matrix estimators are also provided. Estimates of average partial effects can also be obtained once we characterize the conditional distribution of the latent error. Finally, a simulation study shows the advantages of our new estimation procedure in this setting. Our proposed partial maximum likelihood estimators are shown to be more efficient than the generalized method of moments counterparts.     

Partial identification of probability distributions with misclassified data

This paper addresses the problem of data errors in discrete variables. When data errors occur, the observed variable is a misclassified version of the variable of interest, whose distribution is not identified. Inferential problems caused by data errors have been conceptualized through convolution and mixture models. This paper introduces the direct misclassification approach. The approach is based on the observation that in the presence of classification errors, the relation between the distribution of the ‘true’ but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations, in which the coefficient matrix is the matrix of misclassification probabilities. Formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities. Such information can have strong identifying power. The direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest. A method for estimating the identification regions and construct their confidence sets is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.     

Structural vs. atheoretic approaches to econometrics

In this paper I attempt to lay out the sources of conflict between the so-called “structural” and “experimentalist” camps in econometrics. Critics of the structural approach often assert that it produces results that rely on too many assumptions to be credible, and that the experimentalist approach provides an alternative that relies on fewer assumptions. Here, I argue that this is a false dichotomy. All econometric work relies heavily on a priori assumptions. The main difference between structural and experimental (or “atheoretic”) approaches is not in the number of assumptions but the extent to which they are made explicit.     

An integrated maximum score estimator for a generalized censored quantile regression model

Quantile regression techniques have been widely used in empirical economics. In this paper, we consider the estimation of a generalized quantile regression model when data are subject to fixed or random censoring. Through a discretization technique, we transform the censored regression model into a sequence of binary choice models and further propose an integrated smoothed maximum score estimator by combining individual binary choice models, following the insights of Horowitz (1992) and Manski (1985). Unlike the estimators of Horowitz (1992) and Manski (1985), our estimators converge at the usual parametric rate through an integration process. In the case of fixed censoring, our approach overcomes a major drawback of existing approaches associated with the curse-of-dimensionality problem. Our approach for the fixed censored case can be extended readily to the case with random censoring for which other existing approaches are no longer applicable. Both of our estimators are consistent and asymptotically normal. A simulation study demonstrates that our estimators perform well in finite samples.     

A family of empirical likelihood functions and estimators for the binary response model

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance.