Geert Ridder

Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

We are interested in estimating the average effect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pretreatment variables, biases associated with simple treatment-control average comparisons can be removed by adjusting for differences in the pre-treatment variables. Rosenbaum and Rubin (1983, 1984) show that adjusting solely for differences between treated and control units in a scalar function of the pre-treatment, the propensity score, also removes the entire bias associated with differences in pre-treatment variables. Thus it is possible to obtain unbiased estimates of the treatment effect without conditioning on a possibly high-dimensional vector of pre-treatment variables. Although adjusting for the propensity score removes all the bias, this can come at the expense of efficiency. We show that weighting with the inverse of a nonparametric estimate of the propensity score, rather than the true propensity score, leads to efficient estimates of the various average treatment effects. This result holds whether the pre-treatment variables have discrete or continuous distributions. We provide intuition for this result in a number of ways. First we show that with discrete covariates, exact adjustment for the estimated propensity score is identical to adjustment for the pre-treatment variables. Second, we show that weighting by the inverse of the estimated propensity score can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score. Finally, we make a connection to results to other results on efficient estimation through weighting in the context of variable probability sampling.

True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model

Lancaster and Nickell (1980) have argued that in the proportional hazard model the effects of time dependence (true duration dependence) and unobserved sample heterogeneity (spurious duration dependence) cannot be distinguished. We show that both effects can be distinguished if the model allows for observed explanatory variables in the hazard. We also discuss the application of our result to practical situations.

Pooling states in the multinomial logit model

The distinction of separate states in a multinomial logit model can be tested by a likelihood ratio test that is easy to apply.

The Non-Parametric Identification of Generalized Accelerated Failure-Time Models

We consider a class of models that generalizes the popular Mixed Proportional Hazard (MPH) model for duration data: the Generalized Accelerated Failure-Time (GAFT) model. We show that the GAFT model is non-parametrically identified (up to a normalization). We then reconsider the non-parametric identification of the MPH model. We show that the class of MPH models is not closed under normalization. This implies that a finite mean of the mixing distribution is a necessary condition for (non-parametric) identification of the MPH model. It is impossible to test this hypothesis without imposing arbitrary restrictions on the base-line hazard and/or the regression function.

Combining Panel Data Sets with Attrition and Refreshment Samples

In many fields researchers wish to consider statistical models that allow for more complex relationships than can be inferred using only cross-sectional data. Panel or longitudinal data where the same units are observed repeatedly at different points in time can often provide the richer data needed for such models. Although such data allows researchers to identify more complex models than cross-sectional data, missing data problems can be more severe in panels. In particular, even units who respond in initial waves of the panel may drop out in subsequent waves, so that the subsample with complete data for all waves of the panel can be less representative of the population than the original sample. Sometimes, in the hope of mitigating the effects of attrition without losing the advantages of panel data over cross-sections, panel data sets are augmented by replacing units who have dropped out with new units randomly sampled from the original population. Following Ridder (1992), who used these replacement units to test some models for attrition, we call such additional samples refreshment samples. We explore the benefits of these samples for estimating models of attrition. We describe the manner in which the presence of refreshment samples allows the researcher to test various models for attrition in panel data, including models based on the assumption that missing data are missing at random (MAR, Rubin, 1976; Little and Rubin, 1987). The main result in the paper makes precise the extent to which refreshment samples are informative about the attrition process; a class of non-ignorable missing data models can be identified without making strong distributional or functional form assumptions if refreshment samples are available.

Stratified Partial Likelihood Estimation

When multiple durations are generated by a single unit, they may be related in a way that is not fully captured by the regressors. The omitted unit-specific variables might vary over the durations. They might also be correlated with the variables in the regression component. The authors propose an estimator that responds to these concerns and develop a specification test for detecting unobserved unit-specific effects. Data from Malaysia reveal that concentration of child mortality in some families is imperfectly explained by observed explanatory variables, and that failure to control for unobserved heterogeneity seriously biases the parameter estimates.

The Distribution of Single-Spell Duration Data

This paper is concerned with the statistical analysis of single-spell duration data. However, many points also apply to the analysis of other duration data. The interest among econometricians into the analysis of single-spell duration data was greatly enhanced by a series of papers by Lancaster and Nickell (Lancaster (1979), Nickell (1979), Lancaster and Nickell (1980)). Since then there has been a considerable growth in the number of statistical tools as well as in their application, mainly in labor economics. However, there are a number of problems in the application of these methods to the kind of data usually available. The connection between the models proposed by Lancaster and Nickell and the data which are used to estimate them is less direct than in most econometric analyses. To be more precise, different aspects of the same data can be used to estimate the same model. For instance, Nickell estimated his model using observations on elapsed durations of unemployment, while Lancaster used data on residual durations obtained from a repeated survey. Each analysis used only part of the information contained in completed spells.

Job matching and job competition: Are lower educated workers at the back of job queues?

Abstract During the cyclical downturn of the 1980s unemployment in the Netherlands increased substantially, with unemployment rates of lower educated workers increasing more than those of higher educated workers. A possible explanation of this phenomenon is job competition between workers with different levels of education. Another explanation of the diverging unemployment rates is that employers dismiss replaceable lower educated workers before irreplaceable higher educated workers. In this paper we scrutinize the job competition explanation. Our results show that there only is job competition between unemployed workers with an academic and a higher vocational education. There is no job competition at lower levels of education.

Measuring Labor Market Frictions: A Cross-Country Comparison

In this paper we define and estimate measures of labor market frictions using data on job durations. We compare different estimation methods and different types of data. We propose and apply an unconditional inference method that can be applied to aggregate duration data. It does not require wage data, it is invariant to the way in which wages are determined, and it allows workers to care about other job characteristics. The empirical analysis focuses on France, but we perform separate analyses for the USA, the UK, Germany and the Netherlands. We quantify the monopsony power due to search frictions and we examine the policy effects of the minimum wage, unemployment benefits and search frictions.

Mean-squared-error Calculations for Average Treatment Effects

This paper develops a new efficient estimator for the average treatment effect, if selection for treatment is on observables. The new estimator is linear in the first-stage nonparametric estimator. This simplifies the derivation of the means squared error (MSE) of the estimator as a function of the number of basis functions that is used in the first stage nonparametric regression. We propose an estimator for the MSE and show that in large samples minimization of this estimator is equivalent to minimization of the population MSE.