Regressor and random-effects dependencies in multilevel models

The objectives of this paper are (1) to review methods that can be used to test for different types of random effects and regressor dependencies, (2) to present results from Monte Carlo studies designed to investigate the performance of these methods, and (3) to discuss estimation methods that can be used when some but not all of the random effects and regressor independence assumptions, are violated. Because current methods are limited in various ways, we will also present a list of open problems and suggest solutions for some of them. As we will show, the issue of regressor random-effects independence has received some attention in the econometrics literature, but this important work has had little impact on current research practices in the social and behavioral sciences.     

The Reliability of Family Background Effects on Status Attainment: Multiple Informant Models

This article sets out to investigate to what extent conventional retrospective measurement of family background leads to biases in the effects of family background in status attainment research. Multiple informant models show that the effect of father’s educational attainment on respondent’s educational attainment is 41% greater than conventional research suggests, and that the effect of father’s occupational status on respondent’s educational attainment becomes zero. The direct effect of respondent’s educational attainment on respondent’s occupational status is 21% greater after the unreliability in the respondent’s answers has been taken into account. We conclude that measurement error seriously biases conclusions about the status attainment process in the Netherlands.     

Estimating the returns to education for Australian youth via rank-order instrumental variables

This paper employs the rank-order instrumental variable (IV) procedure of Vella and Verbeek [Vella, F., Verbeek, M., 1997. Using rank order as an instrumental variable: an application to the return to schooling, CES Discussion Paper 97.10, K.U. Leuven.] to estimate the returns to education for Australian youth. The attraction of this approach is that it can account for the endogeneity of schooling in the wage equation via the use of instrumental variables without the use of exclusion restrictions. We find, after accounting for the endogeneity of schooling, that an additional year of schooling is associated with an increase in wages of approximately 8%. Furthermore, we find that the rank-order IV approach is able to identify the presence of endogeneity in this particular empirical example. However, despite this, the adjusted estimate of how schooling affects wage is close to the ordinary least squares (OLS) estimate.     

Instrumental variable quantile regression: A robust inference approach

In this paper, we develop robust inference procedures for an instrumental variables model defined by Y=D^′α(U)$Y=D^{\prime }\alpha (U)$ where D^′α(U)$D^{\prime }\alpha (U)$ is strictly increasing in U and U is a uniform variable that may depend on D but is independent of a set of instrumental variables Z. The proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression. Our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely. The use of the proposed procedures is illustrated through two empirical examples.     

Tests with correct size when instruments can be arbitrarily weak

This paper applies classical exponential-family statistical theory to develop a unifying framework for testing structural parameters in the simultaneous equations model under the assumption of normal errors with known reduced-form variance matrix. The results can be divided into the limited-information and full-information categories. In the limited-information model, it is possible to characterize the entire class of similar tests in a model with only one endogenous explanatory variable. In the full-information framework, this paper proposes a family of similar tests for subsets of endogenous variables’ coefficients. For both limited- and full-information models, there exist power upper bounds for unbiased tests. When the model is just-identified, the Anderson–Rubin, score, and (pseudo) conditional likelihood ratio tests are optimal. When the model is over-identified, the (pseudo) conditional likelihood ratio test has power close to the power envelope when identification is strong.     

Latent variables in econometrics

Unobservable variables in econometrics are represented in one of three ways: by variables contaminated by measurement errors, by proxy variables, or by various manifest indicators and/or causes. This paper contains a discussion of models involving each of these representations, and highlights certain interesting implications that have been insufficiently emphasized or completely unrecognized in the literature.     

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative

This paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test is not subject to the ill-posed inverse problem of nonparametric instrumental variable estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is proportional to n^−1/2, where n is the sample size. Monte Carlo simulations illustrate the finite-sample performance of the test.     

Do demand curves for stocks slope down?: Evidence from aggregate data

We examine whether the aggregate demand curve for stocks is downward sloping. As a proxy for aggregate demand, we use net outflows (dividends plus repurchases less net issues) from the stock market scaled by the previous year's market capitalization. To disentangle the information and price pressure effects from the demand curve effects, we use an information-free demographic variable as an instrument and look at the relation between annual changes in aggregate demand and excess market return. We find that information-free changes in the annual aggregate demand for stocks do not lead to changes in the annual excess market return. This finding supports long-term horizontal demand curves for stocks.     

Estimation methods for male labor supply functions How to take account of nonlinear taxes

Nonlinear taxes create econometric difficulties when estimating labor supply functions. One estimation method that tackles these problems accounts for the complete form of the budget constraint and uses the maximum likelihood method to estimate parameters. Another method linearizes budget constraints and uses instrumental variables techniques. Using Monte Carlo simulations I investigate the small-sample properties of these estimation methods and how they are affected by measurement errors in independent variables. No estimator is uniquely best. Hence, in actual estimation the choice of estimator should depend on the sample size and type of measurement errors in the data. Complementing actual estimates with a Monte Carlo study of the estimator used, given the type of measurement errors that characterize the data, would often help interpreting the estimates. This paper shows how such a study can be performed.