Summary This paper introduces measures for how each moment contributes to the precision of parameter estimates in generalized method of moments settings. For example, one of the measures asks what would happen to the variance of the parameter estimates if a particular moment was dropped from the estimation. The measures are all easy to compute. We illustrate the usefulness of the measures through two simple examples as well as an application to a model of joint retirement planning of couples. We estimate the model using the British Household Panel Survey, and we find evidence of complementarities in leisure. Our sensitivity measures illustrate that the estimate of the complementarity is primarily informed by the distribution of differences in planned retirement dates. The estimated econometric model can be interpreted as a bivariate ordered-choice model that allows for simultaneity. This makes the model potentially useful in other applications.
It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. The additional structure can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one-dimensional line segment in the parameter space, and we demonstrate that this line segment can be short in practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. We also provide non-sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.
This paper investigates identification in binary response models with panel data. Conditioning on sufficient statistics can sometimes lead to a conditional maximum likelihood approach that can be used to identify and estimate the parameters of interest in such models. Unfortunately it is often difficult or impossible to find such sufficient statistics, and even if it is possible, the approach sometimes leads to conditional likelihoods that do not depend on some interesting parameters. Using a range of different data generating processes, this paper calculates the identified regions for parameters in panel data logit AR(2) and logit VAR(1) models for which it is not known whether the parameters are identified or not. We find that identification might be more common than was previously thought, and that the identified regions for non-identified objects may be small enough to be empirically useful.
This paper introduces a bivariate version of the generalized accelerated failure time model. It allows for simultaneity in the econometric sense that the two realized outcomes depend structurally on each other. Another feature of the proposed model is that it will generate equal durations with positive probability. Our approach takes a stylized economic model that leads to a univariate generalized accelerated failure time model as a starting point. In this model, agents decide when to transition from an initial state to a new one, and the covariates influence the difference in the utility flow in the two states. We introduce simultaneity by allowing the utility flow to depend on the status of the other person. The econometric model is then completed by assuming that the observed outcome is the Nash bargaining solution in that simple economic model. The advantage of this approach is that it includes independent realizations from the generalized accelerated failure time model as a special case, and deviations from this special case can be given an economic interpretation. We established identification under assumptions that are similar to those in the literature on nonparametric estimation of duration models. We illustrate the model by studying the joint retirement decisions in married couples using the Health and Retirement Study. In that example, it seems reasonable to allow for the possibility that each partner's optimal retirement time depends on the retirement time of the spouse. Moreover, the data suggest that the wife and the husband retire at the same time for a nonnegligible fraction of couples. The main empirical finding is that the simultaneity is economically important. In our preferred specification, the indirect utility associated with being retired increases by approximately when one's spouse retires.
The bootstrap is a convenient tool for calculating standard errors of the parameter estimates of complicated econometric models. Unfortunately, the bootstrap can be very time-consuming. In a recent paper, Honoré and Hu (2017), we propose a “Poor (Wo)man’s Bootstrap” based on one-dimensional estimators. In this paper, we propose a modified, simpler method and illustrate its potential for estimating asymptotic variances.
This paper constructs estimators for panel data regression models with individual specific heterogeneity and two-sided censoring and truncation. Following Powell the estimation strategy is based on moment conditions constructed from re-censored or re-truncated residuals. While these moment conditions do not identify the parameter of interest, they can be used to motivate objective functions that do. We apply one of the estimators to study the effect of a Danish tax reform on household portfolio choice. The idea behind the estimators can also be used in a cross sectional setting.
This paper considers estimation of a dynamic discrete choice model with second order state dependence in the presence of strictly exogenous time-varying explanatory variables. We propose a new method for estimating such models, and a small Monte Carlo study suggests that the method performs well in practice. The method is used to test for duration dependence in labour market spells for young people in France. The novelty in the application is that we are able to control for time-varying explanatory variables. In a discrete time duration model, duration dependence will result in second order state dependence, and the paper therefore also adds to the literature on estimation of duration models with unobserved heterogeneity.
This paper studies the identification of a simultaneous equation model involving duration measures. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of the generalized accelerated failure time model. In its most general form, the system resembles a classical simultaneous equation model in which endogenous variables interact with observable and unobservable exogenous components to characterize an economic environment. In this paper, the endogenous variables are the individually chosen equilibrium durations. Even though a unique solution to the game is not always attainable in this context, the structural elements of the economic system are shown to be semi-parametrically identified. We also present a brief discussion of estimation ideas and a set of simulation studies on the model.
This article considers instrumental variables versions of the quantile and rank regression estimators. The asymptotic properties of the estimators are discussed, and a small-scale Monte Carlo study is used to illustrate the potential advantages of the approach. Finally, the proposed methods are implemented for two empirical examples.
It is very difficult to deal with endogeneity in limited dependent variables models. Unless strong assumptions are made on the exact relationship between the endogenous regressors and the instruments, it is generally not possible to apply instrumental variable type techniques. This paper derives moment conditions that are useful in estimating censored regression models with endogenous regressors. These moment conditions are motivated by panel data censored regression models with predetermined (but not strictly exogenous) explanatory variables, but the main insight is also applicable to cross sectional models with endogenous explanatory variables.
Panel data play an important role in empirical economics. With panel data one can answer questions about microeconomic dynamic behavior that could not be answered with cross sectional data. Panel data techniques are also useful for analyzing cross sectional data with grouping. This paper discusses some issues related to specification and estimation of nonlinear models using panel data.
Censored regression models have received a great deal of attention in both the theoretical and applied econometric literature. Most of the existing estimation procedures for either cross-sectional or panel data models arc designed only for models with fixed censoring. In this paper, a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed. This procedure is then applied to the CLAD and quantile estimators of Powell (1984, 1986) to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring. The resulting estimator is shown to have desirable asymptotic properties, and performs well in a small-scale simulation study.
We consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables, lags of the endogenous dependent variable as well as unobservable individual-specific effects. For the logit specification we propose an estimator that is consistent and asymptotically normal, although its rate of convergence is slower than the inverse of the square root of the sample size. In the semiparametric case the proposed estimator is shown to be consistent. The finite sample properties of the proposed estimators are investigated in a small Monte Carlo simulation study.
The aim of this paper is two-fold. First, we review recent estimators for censored regression and sample selection panel data models with unobservable individual specific effects, and show how the idea behind these estimators can be used to construct estimators for a variety of other Tobit-type models. The estimators presented in this paper are semiparametric, in the sense that they do not require the parametrization of the distribution of the unobservable. The second aim of the paper is to introduce a new class of estimators for the censored regression model. The advantage of the new estimators is that they can be applied under a stationarity assumption on the transitory error terms, which is weaker than the exchangeability assumption that is usually made in this literature. A similar generalization does not seem feasible for the estimators of the other models that are considered.
Building on the work of Chay (1995), this study examines the impact of civil rights policies on black economic progress using individual-level panel data. Many earnings records are censored and the degree of censoring changed during the period of interest. Consequently, valid estimates of the program effects must account for this censoring. Maximum likelihood estimation can be used if the error terms of the model are identically normally distributed. The authors investigate the value of using weaker assumptions on the error process to estimate the laws impact. The analysis shows that there was significant black-white earnings convergence in the South during the 1960s. They also find that semiparametric estimation methods are informative in pinpointing which parts of the model are misspecified.
This paper considers estimation of the semiparametric type 3 Tobit model. The authors construct two-step estimators that use the ideas of symmetric trimming and pairwise comparisons that have been proposed for the censored regression model by J. L. Powell (1986) and B. E. Honore and J. L. Powell (1994). The estimators are consistent and asymptotically normal under two identifying assumptions: conditional symmetry and independence between the errors and regressors. The ideas and techniques are also implementable in other selection models that are variations of the basic type 3 Tobit model. The authors demonstrate this by applying the proposed method in estimating an empirical model considered by C. Udry (1994).
This paper presents orthogonality conditions for censored regression models with fixed effects and lagged dependent variables. The orthogonality conditions can be used to construct method of moments estimators of the parameters of the model. Nonlinear fixed effects models are usually estimated by maximum likelihood, with fixed effects treated as parameters to be estimated. Monte Carlo results indicate that in a Tobit model with fixed effects and lagged dependent variables, the maximum likelihood estimator of the effect of the lagged dependent variable performs poorly. The method of moments estimator based on the orthogonality conditions presented here, however, performs quite well.
The purpose of this paper is to investigate the identifiability of duration models with multiple spells. The author proves that the results of C. Elbers and G. Ridder (1982) and J. J. Heckman and B. Singer (1984) can be generalized.to multispell models with lagged duration dependence. He also proves that, without lagged duration dependence, the identification result does not depend on moment conditions or tail conditions on the mixing distribution. This resul t is in contrast to Ridder's (1990) result for single-spell models.
This paper considers estimation of truncated.and censored regression models with fixed effects. Up until now, no estimator has been shown to be consistent as the cross-section dimension increases with the time dimension fixed. Trimmed least absolute deviations and trimmed least squares estimators are proposed for the case where the panel is of length two, and it is proven that they are consistent and asymptotically normal. It is not necessary to maintain parametric assumptions on the error terms to obtain this result. A small scale Monte Carlo study demonstrates that these estimators can perform well in small samples.
This paper explores the robustness of the essential economic conclusions of the Roy model of self-selection and income inequality to relaxation of its normality assumptions. A log concave version of the model reproduces most of the main results. Log convex cases offer counterexamples. The authors show that in a Roy economy, random assignment is inegalitarian and Pareto inefficient. They consider nonparametric identifiability of latent skill distributions with cross-section and panel data. The authors' analysis proves nonparametric identifiability for the closely related competing risks model.
This paper presents a simple estimator of the shape parameter in a Weibull duration model with unobserved heterogeneity. The estimator is consistent and asymptotically normal under mild conditions, and a consistent estimator of the asymptotic variance is available. A Monte Carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution. The estimation strategy can be extended to a model with regressors and to a log-logistic model with unobserved heterogeneity. The advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived.
This paper considers the consequences for identifiability of introducing regressors into the competing risks model of multistate duration analysis. We establish conditions under which access to regressors overturns the nonidentification theorem of Cox and Tsiatis for both proportional and accelerated failure time models.