Tony Lancaster

The Incidental Parameter Problem Since 1948

This paper was written to mark the 50th anniversary of Neyman and Scotts Econometrica paper defining the incidental parameter problem. It surveys the history both of the paper and of the problem in the statistics and econometrics literature.

Combining Micro and Macro Data in Microeconometric Models

Census reports can be interpreted as providing nearly exact knowledge of moments of the marginal distribution of economic variables. This information can be combined with cross-sectional or panel samples to improve accuracy of estimation. In this paper we show how to do this efficiently. We show that the gains from use of marginal information can be substantial. We also discuss how to test the compatibility of sample and marginal information.

Efficient Estimation and Stratified Sampling

Abstract In this paper we investigate estimation of a class of semi-parametric models. The part of the model that is not specified is the marginal distribution of the explanatory variables. The sampling is stratified on the dependent variables, implying that the explanatory variables are no longer exogenous or ancillary. We develop a new estimator for this estimation problem and show that it achieves the semi-parametric efficiency bound for this case. In addition we show that the estimator applies to a number of sampling schemes that have previously been treated separately.

Instrumental variables and inverse probability weighting for causal inference from longitudinal observational studies

Inferring causal effects from longitudinal repeated measures data has high relevance to a number of areas of research, including economics, social sciences and epidemiology. In observational studies in particular, the treatment receipt mechanism is typically not under the control of the investigator; it can depend on various factors, including the outcome of interest. This results in differential selection into treatment levels, and can lead to selection bias when standard routines such as least squares regression are used to estimate causal effects. Interestingly, both the characterization of and methodology for handling selection bias can differ substantially by disciplinary tradition. In social sciences and economics, instrumental variables (IV) is the standard method for estimating linear and nonlinear models in which the error term may be correlated with an observed covariate. When such correlation is not ruled out, the covariate is called endogenous and least squares estimates of the covariate effect are typically biased. The availability of an instrumental variable can be used to reduce or eliminate the bias. In public health and clinical medicine (e.g., epidemiology and biostatistics), selection bias is typically viewed in terms of confounders, and the prevailing methods are geared toward making proper adjustments via explicit use of observed confounders (e.g., stratification, standardization). A class of methods known as inverse probability weighting (IPW) estimators, which relies on modeling selection in terms of confounders, is gaining in popularity for making such adjustments. Our objective is to review and compare IPW and IV for estimating causal treatment effects from longitudinal data, where the treatment may vary with time. We accomplish this by defining the causal estimands in terms of a linear stochastic model of potential outcomes (counterfactuals). Our comparison includes a review of terminology typically used in discussions of causal inference (e.g., confounding, endogeneity); a review of assumptions required to identify causal effects and their implications for estimation and interpretation; description of estimation via inverse weighting and instrumental variables; and a comparative analysis of data from a longitudinal cohort study of HIV-infected women. In our discussion of assumptions and estimation routines, we try to emphasize sufficient conditions needed to implement relatively standard analyses that can essentially be formulated as regression models. In that sense this review is geared toward the quantitative practitioner. The objective of the data analysis is to estimate the causal (therapeutic) effect of receiving combination antiviral therapy on longitudinal CD4 cell counts, where receipt of therapy varies with time and depends on CD4 count and other covariates. Assumptions are reviewed in context, and resulting inferences are compared. The analysis illustrates the importance of considering the existence of unmeasured confounding and of checking for ‘weak instruments.’ It also suggests that IV methodology may have a role in longitudinal cohort studies where potential instrumental variables are available.

Case-Control Studies with Contaminated Controls

Abstract This paper considers inference about a parametric binary choice model when the data consist of two distinct samples. The first is a random sample from the people who made choice 1, say, with all relevant covariates completely observed. The second is a random sample from the whole population with only the covariates observed . This is called a contaminated sampling scheme. An example might be where we have a random sample of female labor force participants and their covariate values and a second random sample of working age women, with covariates, whose participant status is unknown. We consider the cases in which the fraction of the population making choice 1 is known and that in which it is not. For both cases we give semiparametrically efficient procedures for estimating the choice model parameters.

The Estimation of Models of Labour Market Behaviour

In this paper we view the labour market experience of individuals as a process of movement between the states of employment and unemployment. We note that there are three main ways of sampling members of the labour force namely sampling the members of a specific state, sampling the people entering or leaving a state and sampling the population regardless of state. The joint distribution of observable and unobservable characteristics of individuals depends on the mode of sampling adopted. We examine this dependence and its implications for the interpretation of estimates of models of labour market behaviour.

Panel Data with Survival: Hospitalization of HIV-Positive Patients

Abstract This article provides an analysis of the hospitalization experience of a panel of HIV-positive patients. It is part of a program of work designed to study the medical expenditures of such patients and their variation both between people and over time. We model the joint distribution of the inpatient episodes and the survival times of a panel of patients over 15 months. The model induces correlation between hospitalization and death via an unmeasured, person-specific, frailty term, and it allows rates of hospitalization and of death each to be affected by time-invariant and time-varying covariates. We subject the model to a variety of predictive tests and show that it is generally consistent with the data. We study and present estimates of the time variation in the rate of hospitalization. We also report the effects of a large number of covariates on rates of hospitalization and mortality. The model generalizes fairly easily in a number of ways, one of which is to handle vector-valued measures of ...

Exact Structural Inference in Optimal Job Search Models

This article is a study of the exact posterior distributions of parameters appearing in a stationary optimal job-search model I exploit the simple latent structure of the search model when all job offers are observed to simulate posterior distributions of structural parameters when the latent structure is imperfectly observed. These simulations enable me to show the exact, and unusual, shape of the job-search likelihood when the data are durations and accepted wages. I also develop an algorithm to resample simulated posterior distributions to impose on the model the implications of fully optimal, utility-maximizing search. The methods are illustrated using simulated data.

Simultaneous Equations with Endogenous Hazards

Suppose that one samples unemployed job seekers and observes their current job search policy and their elapsed duration of search: this paper is a study of the econometric problems that arise in using such data to investigate inter-individual and inter-temporal differences in search policy and the effect of such policies on the probability of leaving unemployment. In particular we study the implications of the distinction between sampling the stock and sampling the flow of unemployed people and we propose a particular model. The theory is illustrated by some calculations using data on ‘reservation wages’ and elapsed durations reported by two samples of British unemployed people. These calculations are consistent with the job search model, but suggest that the effect of selectivity in prolonging unemployment for our samples was small.

Residual analysis for censored duration data

Abstract In this note we show how residuals defined for right censored duration data, such as arise in, for example, labour market studies, feature in diagnostic statistics to detect omitted covariates and neglected heterogeneity.