Multidimensional skills and the returns to schooling: Evidence from an interactive fixed-effects approach and a linked survey-administrative data set

This paper presents new evidence on returns to schooling based on an interactive fixed-effects framework that allows for multiple unobserved skills with potentially time-varying prices as well as individual-level heterogeneity in returns. This constitutes a substantive generalization of most existing approaches. Our empirical analysis employs a unique linked survey-administrative panel data set on education and earnings. We find average marginal returns to schooling of about 2.8–4.4% relative to least squares/instrumental variable estimates between 7.7% and 12.7%. Omitted ability accounts for a larger fraction of the aggregate least squares bias compared to heterogeneity. We also find considerable heterogeneity in individual returns.     

On efficient estimation with panel data: An empirical comparison of instrumental variables estimators

This paper attempts a replication of the Cornwell and Rupert (1988) study—hereafter CR. The CR study investigated the efficiency gains in a returns to schooling example by applying alternative sets of instrumental variables estimators for panel data regressions proposed by Hausman and Taylor (1981), Amemiya and MaCurdy (1986), and Breusch, Mizon, and Schmidt (1989). Corrections on the CR data set lead to changes in the legitimate set of instruments, when the time dummies are excluded from the regression, and to much lower empirical gains in efficiency than those reported in CR. If the time dummies are retained in the wage equation, the experience coefficient is not estimable by the within regression, and the empirical gains in efficiency from using the IV procedures are not limited to the time-invariant education coefficient.     

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.     

A simple framework for analysing bull and bear markets

Bull and bear markets are a common way of describing cycles in equity prices. To fully describe such cycles one would need to know the data generating process (DGP) for equity prices. We begin with a definition of bull and bear markets and use an algorithm based on it to sort a given time series of equity prices into periods that can be designated as bull and bear markets. The rule to do this is then studied analytically and it is shown that bull and bear market characteristics depend upon the DGP for capital gains. By simulation methods we examine a number of DGPs that are known to fit the data quite well—random walks, GARCH models, and models with duration dependence. We find that a pure random walk provides as good an explanation of bull and bear markets as the more complex statistical models. In the final section of the paper we look at some asset pricing models that appear in the literature from the viewpoint of their success in producing bull and bear markets which resemble those in the data. Copyright © 2002 John Wiley & Sons, Ltd.     

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

Age of Menarche,Adolescent Sexual Intercourse and Schooling Attainment of Women

We use data from the 1970 British Cohort Study to measure the effect of adolescent sexual intercourse on female schooling attainment. We emphasize the appropriate use of menarcheal age as an instrumental variable (IV) for early intercourse. Our analysis suggests that developmental trajectories vary with menarcheal age and, therefore, capturing variations in individual cognitive capacities induced by pubertal timing is crucial for the validity of the IV identification strategy. Our empirical results indicate that adolescent sexuality reduces full‐time education by approximately one year. Given that 37 percent of females in our data exited virginity in adolescence, the aggregate loss of human capital as measured by average years of female schooling could be up to one‐third of a year.     

A structural analysis of the correlated random coefficient wage regression model

We estimate a dynamic programming model of schooling decisions in which the log wage regression function is set within a correlated random coefficient model. We show that estimates of the dynamic programming model can be used to obtain a number of treatment effects, including the local average treatment effect (LATE). However, unlike LATE parameters obtained in a standard IV framework, our LATE estimates are obtained without imposing separability between individual specific heterogeneity and schooling choices and are therefore not subject to a “monotonicity” restriction. We find that returns to schooling are characterized by a high degree of dispersion across individuals.     

Testing for random effects in panel models with spatially correlated disturbances

In the empirical analysis of panel data the Breusch–Pagan (BP) statistic has become a standard tool to infer on unobserved heterogeneity over the cross-section. Put differently, the test statistic is central to discriminate between the pooled regression and the random effects model. Conditional versions of the test statistic have been provided to immunize inference on unobserved heterogeneity against random time effects or patterns of spatial error correlation. Panel data models with spatially correlated error terms are typically set out under the presumption of some known adjacency matrix parameterizing the correlation structure up to a scaling factor. This paper delivers a bootstrap scheme to generate critical values for the BP statistic allowing robust inference under misspecification of the adjacency matrix. Moreover, asymptotic results are derived for the case of a finite cross-section and infinite time dimension. Finite sample simulations show that misspecification of spatial covariance features could lead to large size distortions, while the robust bootstrap procedure retains asymptotic validity.     

A Bounded Model of Time Variation in Trend Inflation,Nairu and the Phillips Curve

In this paper, we develop a bivariate unobserved components model for inflation and unemployment. The unobserved components are trend inflation and the non‐accelerating inflation rate of unemployment (NAIRU). Our model also incorporates a time‐varying Phillips curve and time‐varying inflation persistence. What sets this paper apart from the existing literature is that we do not use unbounded random walks for the unobserved components, but rather bounded random walks. For instance, NAIRU is assumed to evolve within bounds. Our empirical work shows the importance of bounding. We find that our bounded bivariate model forecasts better than many alternatives, including a version of our model with unbounded unobserved components. Our model also yields sensible estimates of trend inflation, NAIRU, inflation persistence and the slope of the Phillips curve. Copyright © 2015 John Wiley & Sons, Ltd.     

Literacy and earnings: an investigation of the interaction of cognitive and unobserved skills in earnings generation

This paper uses direct measures of literacy to examine the influence of cognitive and unobserved skills on earnings. We find that cognitive skills contribute significantly to earnings and that their inclusion in earnings equations reduces the measured impact of schooling. The impact of literacy on earnings does not vary across quantiles of the earnings distribution, schooling and literacy do not interact in influencing earnings, and introducing literacy has little effect on the estimated impact of experience. Our findings suggest that cognitive and unobserved skills are both productive but that having more of one skill does not enhance the other's productivity.     

Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables

The aim of this paper is to convey to a wider audience of applied statisticians that nonparametric (matching) estimation methods can be a very convenient tool to overcome problems with endogenous control variables. In empirical research one is often interested in the causal effect of a variable X on some outcome variable Y . With observational data, i.e. in the absence of random assignment, the correlation between X and Y generally does not reflect the treatment effect but is confounded by differences in observed and unobserved characteristics. Econometricians often use two different approaches to overcome this problem of confounding by other characteristics. First, controlling for observed characteristics, often referred to as selection on observables, or instrumental variables regression, usually with additional control variables. Instrumental variables estimation is probably the most important estimator in applied work. In many applications, these control variables are themselves correlated with the error term, making ordinary least squares and two-stage least squares inconsistent. The usual solution is to search for additional instrumental variables for these endogenous control variables, which is often difficult. We argue that nonparametric methods help to reduce the number of instruments needed. In fact, we need only one instrument whereas with conventional approaches one may need two, three or even more instruments for consistency. Nonparametric matching estimators permit     consistent estimation without the need for (additional) instrumental variables and permit arbitrary functional forms and treatment effect heterogeneity.     

Estimation of Dynamic Nonlinear Random Effects Models with Unbalanced Panels

This paper presents estimation methods for dynamic nonlinear models with correlated random effects (CRE) when having unbalanced panels. Unbalancedness is often encountered in applied work and ignoring it in dynamic nonlinear models produces inconsistent estimates even if the unbalancedness process is completely at random. We show that selecting a balanced panel from the sample can produce efficiency losses or even inconsistent estimates of the average marginal effects. We allow the process that determines the unbalancedness structure of the data to be correlated with the permanent unobserved heterogeneity. We discuss how to address the estimation by maximizing the likelihood function for the whole sample and also propose a Minimum Distance approach, which is computationally simpler and asymptotically equivalent to the Maximum Likelihood estimation. Our Monte Carlo experiments and empirical illustration show that the issue is relevant. Our proposed solutions perform better both in terms of bias and RMSE than the approaches that ignore the unbalancedness or that balance the sample.     

Weak‐instrument robust inference for two‐sample instrumental variables regression

Instrumental variable (IV) methods for regression are well established. More recently, methods have been developed for statistical inference when the instruments are weakly correlated with the endogenous regressor, so that estimators are biased and no longer asymptotically normally distributed. This paper extends such inference to the case where two separate samples are used to implement instrumental variables estimation. We also relax the restrictive assumptions of homoskedastic error structure and equal moments of exogenous covariates across two samples commonly employed in the two‐sample IV literature for strong IV inference. Monte Carlo experiments show good size properties of the proposed tests regardless of the strength of the instruments. We apply the proposed methods to two seminal empirical studies that adopt the two‐sample IV framework.     

Two applications of wild bootstrap methods to improve inference in cluster‐IV models

Microeconomic data often have within‐cluster dependence, which affects standard error estimation and inference. When the number of clusters is small, asymptotic tests can be severely oversized. In the instrumental variables (IV) model, the potential presence of weak instruments further complicates hypothesis testing. We use wild bootstrap methods to improve inference in two empirical applications with these characteristics. Building from estimating equations and residual bootstraps, we identify variants robust to the presence of weak instruments and a small number of clusters. They reduce absolute size bias significantly and demonstrate that the wild bootstrap should join the standard toolkit in IV and cluster‐dependent models.     

Addressing Unobserved Selection Bias in Accounting Studies: The Bias Minimization Method

This note explains the minimum-biased estimator (MBE), which accounting researchers can use to analyze the robustness of regression or propensity score-matched treatment estimates to unobserved selection (endogeneity) bias. Based on the principles of the Heckman treatment model, the MBE entails estimating matched treatment effects within a range of propensity scores that minimizes unobserved selection bias. A major advantage of the MBE is that an instrumental variable is not required. The potential utility of the MBE in accounting studies is highlighted, and a familiar empirical illustration is provided.     

The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics

The Beveridge–Nelson (BN) decomposition is a model-based method for decomposing time series into permanent and transitory components. When constructed from an ARIMA model, it is closely related to decompositions based on unobserved components (UC) models with random walk trends and covariance stationary cycles. The decomposition when extended to I(2)$I\left(2\right)$ models can also be related to non-model-based signal extraction filters such as the HP filter. We show that the BN decomposition provides information on the correlation between the permanent and transitory shocks in a certain class of UC models. The correlation between components is known to determine the smoothed estimates of components from UC models. The BN decomposition can also be used to evaluate the efficacy of alternative methods. We also demonstrate, contrary to popular belief, that the BN decomposition can produce smooth cycles if the reduced form forecasting model is appropriately specified.     

GMM with Multiple Missing Variables

We consider efficient estimation in moment conditions models with non‐monotonically missing‐at‐random (MAR) variables. A version of MAR point‐identifies the parameters of interest and gives a closed‐form efficient influence function that can be used directly to obtain efficient semi‐parametric generalized method of moments (GMM) estimators under standard regularity conditions. A small‐scale Monte Carlo experiment with MAR instrumental variables demonstrates that the asymptotic superiority of these estimators over the standard methods carries over to finite samples. An illustrative empirical study of the relationship between a child's years of schooling and number of siblings indicates that these GMM estimators can generate results with substantive differences from standard methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Empirical Tests of the Pollution Haven Hypothesis When Environmental Regulation is Endogenous

The pollution haven hypothesis (PHH) posits that production within polluting industries will shift to locations with lax environmental regulation. While straightforward, the existing empirical literature is inconclusive owing to two shortcomings. First, unobserved heterogeneity and measurement error are typically ignored due to the lack of a credible, traditional instrumental variable for regulation. Second, geographic spillovers have not been adequately incorporated into tests of the PHH. We overcome these issues utilizing two novel identification strategies within a model incorporating spillovers. Using US state‐level data, own environmental regulation negatively impacts inbound foreign direct investment. Moreover, endogeneity is both statistically and economically relevant. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling and calculating the effect of treatment at baseline from panel outcomes

We propose and examine a panel data model for isolating the effect of a treatment, taken once at baseline, from outcomes observed over subsequent time periods. In the model, the treatment intake and outcomes are assumed to be correlated, due to unobserved or unmeasured confounders. Intake is partly determined by a set of instrumental variables and the confounding on unobservables is modeled in a flexible way, varying both by time and treatment state. Covariate effects are assumed to be subject-specific and potentially correlated with other covariates. Estimation and inference is by Bayesian methods that are implemented by tuned Markov chain Monte Carlo methods. Because our analysis is based on the framework developed by Chib [2004. Analysis of treatment response data without the joint distribution of counterfactuals. Journal of Econometrics, in press], the modeling and estimation does not involve either the unknowable joint distribution of the potential outcomes or the missing counterfactuals. The problem of model choice through marginal likelihoods and Bayes factors is also considered. The methods are illustrated in simulation experiments and in an application dealing with the effect of participation in high school athletics on future labor market earnings.