Intergenerational mobility and sample selection in short panels

Using data from the first 11 waves of the BHPS, this paper measures the extent of the selection bias induced by standard coresidence conditions—bias that is expected to be severe in short panels—on measures of intergenerational mobility in occupational prestige. We try to limit the impact of other selection biases, such as those induced by labour market restrictions that are typically imposed in intergenerational mobility studies, by using different measures of socio‐economic status that account for missing labour market information. We stress four main results. First, there is evidence of an underestimation of the true intergenerational elasticity, the extent of which ranges between 12% and 39%. Second, the proposed methods used to correct for the selection bias seem to be unable to attenuate it, except for the propensity score weighting procedure, which performs well in most circumstances. This result is confirmed both under the assumption of missing‐at‐random data as well as under the assumption of not‐missing‐at‐random data. Third, the two previous sets of results (direction and extent of the bias, and differential abilities to correct for it) are also robust when we account for measurement error. Fourth, restricting the sample to a period shorter than the 11 waves under analysis leads to a severe sample selection bias. In the cases when the analysis is limited to eight waves, this bias ranges from about 40% to 65%. Copyright © 2006 John Wiley & Sons, Ltd.     

Two-step estimation of panel data models with censored endogenous variables and selection bias

This paper presents some two-step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias. Our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity/selection bias to include as additional explanatory variables in the primary equation. These are obtained through a decomposition of the reduced form residuals. The panel nature of the data allows adjustment, and testing, for two forms of endogeneity and/or sample selection bias. Furthermore, it incorporates roles for dynamics and state dependence in the reduced form. Finally, we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions.     

The nonrandom selection of don't knows in binary and ordinal responses: Corrections with the bivariate probit model with sample selection

On social surveysdon't knows are a common answer to attitudinal questions, which often have binary or ordinal response categories.Don't knows can be nonrandomly selected according to certain demographic or socioeconomic characteristics of the respondent. To model the sample selection and correct for its bias, this paper discusses two types of bivariate models —binary-probit and the ordinal probit model with sample selection. The difference between parameter estimates and predicted probabilities from the analysis modelling the sample selection bias ofdon't knows and those from the analysis not modellingdon't knows is emphasized. Two empirical examples using the 1989 General Social Survey data demonstrate the necessity to correct for the bias in the nonrandom selection ofdon't knows for binary and ordinal attitudinal response variables. A replication of the analyses using the 1990 and 1991 General Social Survey data helps demonstrate the reliability of the sample selection bias ofdon't knows.     

Bayesian Inference in Spatial Sample Selection Models

In this study, we consider Bayesian methods for the estimation of a sample selection model with spatially correlated disturbance terms. We design a set of Markov chain Monte Carlo algorithms based on the method of data augmentation. The natural parameterization for the covariance structure of our model involves an unidentified parameter that complicates posterior analysis. The unidentified parameter – the variance of the disturbance term in the selection equation – is handled in different ways in these algorithms to achieve identification for other parameters. The Bayesian estimator based on these algorithms can account for the selection bias and the full covariance structure implied by the spatial correlation. We illustrate the implementation of these algorithms through a simulation study and an empirical application.     

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.     

Retirement Choices in Italy: What an Option Value Model Tells Us*

Using Italian data, we estimate an option value model to quantify the effect of financial incentives on retirement choices. As far as we know, this is the first empirical study to estimate the conditional multiple‐years model put forward by Stock and Wise (1990) . This implies that we account for dynamic self‐selection bias. We also present an extended version of this model in which the marginal value of leisure is random. For the female sample, the model is able to predict almost perfectly the age‐specific hazard rates. For the male sample, we obtain a good fit. Dynamic self‐selection results in a downward bias in the estimate of the marginal utility of leisure. We perform a simulation study to gauge the effects of a dramatic pension reform. Underestimation of the value of leisure translates into sizeable over‐prediction of the impact of reform. Due to lack of data, results for males should be interpreted with caution since we are not able to fully correct for dynamic self‐selection bias.     

Market efficiency and NCAA college basketball gambling

The betting market for NCAA college basketball is examined from the 1996–97 season through 2003–04. In the overall sample, market efficiency cannot be rejected. For big favorites, specifically those favorites of 20 or more, a simple strategy of betting the underdog in these games is shown to reject the null hypothesis of a fair bet since the underdog wins more than implied by efficiency. This bias appears to be the same as in other sports. The home-team bias in college basketball is shown to be the opposite of the other sports, however, since big favorites win more often than implied by efficiency. Potential reasons for this bias such as NCAA tournament incentives and uniformity of playing conditions are discussed.     

Binary response panel data models with sample selection and self‐selection

We consider estimating binary response models on an unbalanced panel, where the outcome of the dependent variable may be missing due to nonrandom selection, or there is self‐selection into a treatment. In the present paper, we first consider estimation of sample selection models and treatment effects using a fully parametric approach, where the error distribution is assumed to be normal in both primary and selection equations. Arbitrary time dependence in errors is permitted. Estimation of both coefficients and partial effects, as well as tests for selection bias, are discussed. Furthermore, we consider a semiparametric estimator of binary response panel data models with sample selection that is robust to a variety of error distributions. The estimator employs a control function approach to account for endogenous selection and permits consistent estimation of scaled coefficients and relative effects.     

Estimation of the threshold stochastic frontier model in the presence of an endogenous sample split variable

Heterogeneity among firms has been an important issue in studying firms’ technical efficiencies. If firms do not randomly fall into different groups with different technologies but by self-selection, statistically it implies the data are subject to the sample selection bias. In this paper, we generalize the stochastic frontier (SF) model to accommodate heterogeneous technologies among firms by considering the threshold SF model with an endogenous threshold variable. We discuss the econometric techniques appropriate for the threshold SF model with panel data. To determine the optimal number of regimes, we use modified the model selection criteria of Gonzalo and Pitarakis (J Econom 110(2):319–352, 2002) and investigate their finite sample performance by some Monte Carlo experiments. Finally, we also demonstrate our approach by an empirical example.     

Sample selection bias with multiple selection rules: An application to student aid grants

This paper extends the sample selection bias correction procedure, developed by James J. Heckman, to the case of multiple selection rules. Estimators are presented for independent selection rules and a consistent estimator for the variance-covariance matrix is derived. The methodology is applied to the problem of estimating the financial aid available to U.S. highschool students for college education. In order to be observed in receipt of financial aid, a student has to be both enrolled in college and to have had an expected value of aid in excess of the costs of applying. Both of these sources of selection bias were found to be important.     

Measuring a boom and bust: The Sydney housing market 2001–2006

The Sydney housing market peaked in 2003. The period 2001–2006 is, therefore, of particular interest since it captures a boom and bust in the housing market. We compute hedonic, repeat-sales and median price indexes for five regions in Sydney over this period. While the three approaches are in broad agreement regarding the timing of the turning point in the housing market, some important differences also emerge. In particular, we find evidence of sample selection bias in our hedonic and repeat-sales data sets (with the former focusing more on better quality dwellings and the latter more on lower quality dwellings). These sample selection biases could in turn cause bias (in opposite directions) in our hedonic and repeat-sales indexes. Median indexes may likewise be biased as a result of an apparent decline in the average quality of dwellings sold in the latter part of the sample. We also find evidence of convergence in prices across regions during the boom and divergence in the subsequent bust.     

Tackling selection bias in sentencing data analysis: a new approach based on a scale of severity

For reasons of methodological convenience statistical models analysing judicial decisions tend to focus on the duration of custodial sentences. These types of sentences are however quite rare (7% of the total in England and Wales), which generates a serious problem of selection bias. Typical adjustments employed in the literature, such as Tobit models, are based on questionable assumptions and are incapable to discriminate between different types of non-custodial sentences (such as discharges, fines, community orders, or suspended sentences). Here we implement an original approach to model custodial and non-custodial sentence outcomes simultaneously avoiding problems of selection bias while making the most of the information recorded for each of them. This is achieved by employing Pina-Sánchez et al. (Br J Criminol 59:979–1001, 2019) scale of sentence severity as the outcome variable of a Bayesian regression model. A sample of 7242 theft offences sentenced in the Crown Court is used to further illustrate: (a) the pervasiveness of selection bias in studies restricted to custodial sentences, which leads us to question the external validity of previous studies in the literature limited to custodial sentence length; and (b) the inadequacy of Tobit models and similar methods used in the literature to adjust for such bias.     

Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models

This paper develops estimators for dynamic microeconomic models with serially correlated unobserved state variables using sequential Monte Carlo methods to estimate the parameters and the distribution of the unobservables. If persistent unobservables are ignored, the estimates can be subject to a dynamic form of sample selection bias. We focus on single‐agent dynamic discrete‐choice models and dynamic games of incomplete information. We propose a full‐solution maximum likelihood procedure and a two‐step method and use them to estimate an extended version of the capital replacement model of Rust with the original data and in a Monte Carlo study. Copyright © 2015 John Wiley & Sons, Ltd.     

Moving Towards Estimating Sons' Lifetime Intergenerational Economic Mobility in the UK

Estimates of intergenerational economic mobility that use point in time measures of income and earnings suffer from lifecycle and attenuation bias. They also suffer from sample selection issues and further bias driven by spells out of work. We consider these issues together for UK data, the National Child Development Study and British Cohort Study, for the first time. When all three biases are considered, our best estimate of lifetime intergenerational economic persistence in the UK is 0.43 for children born in 1970. Whilst we argue that this is the best available estimate to date, we discuss why there is good reason to believe that this is still a lower bound, owing to residual attenuation bias.     

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis (DEA). In this study, we focus on a “big data” problem related to the considerably large dimensions of the input-output data. The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation, including principal component analysis (PCA-DEA), which is based on the idea of aggregating input and output, efficiency contribution measurement (ECM), average efficiency measure (AEC), and regression-based detection (RB), which is based on the idea of variable selection. We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test. In addition, we discuss the effect of initial variable selection in RB for the first time. Based on the results, we offer guidelines that are more reliable on how to choose an appropriate method.     

Choice of employment status and the wages of employees and the self-employed: Some further evidence

Using US data drawn from the 1978 young men NLS sample, this paper replicates a key finding reported by Rees and Shah in their analysis of self-employment using large-scale British data. A wage equation, which allows for sample selectivity, is estimated for subsamples of employees and the self-employed. Despite differences between the data sets and the variables analysed, the NLS results support Rees and Shah's conclusion that there is positive selection bias in the observed earnings of employees.     

The effect of adverse impact in selection practices on organizational diversity: a field study

Based on a sample of 154 organizations across Canada, we examined the influence of the use of different employee selection methods on workplace minority representation rates. Results indicated that usage of cognitive ability and personality testing significantly influences minority representation after controlling for other diversity management practices. In particular, cognitive ability testing appears to be associated with lower levels of minority group representation in organizations as a whole and in their management ranks; personality testing is associated with higher levels of minority representation in organizations. To advance our understanding of the organizational factors that influence minority group representation and the use of different selection practices, we also examined HR manager perceptions of test bias and the effects of employment equity (EEA) legislation on selection test usage. Results indicated that firms covered under employment equity legislation were less likely to use cognitive ability tests. Interestingly, HR managers reported that personality tests may be more biased against minorities than cognitive ability tests. Implications for research and practice are discussed.     

Bootstrap Co‐integration Rank Testing: The Effect of Bias‐Correcting Parameter Estimates

Bootstrap‐based methods for bias‐correcting the first‐stage parameter estimates used in some recently developed bootstrap implementations of co‐integration rank tests are investigated. The procedure constructs estimates of the bias in the original parameter estimates by using the average bias in the corresponding parameter estimates taken across a large number of auxiliary bootstrap replications. A number of possible implementations of this procedure are discussed and concrete recommendations made on the basis of finite sample performance evaluated by Monte Carlo simulation methods. The results show that bootstrap‐based bias‐correction methods can significantly improve the small sample performance of the bootstrap co‐integration rank tests.     

Statistical Analysis with Linked Data

Computerised Record Linkage methods help us combine multiple data sets from different sources when a single data set with all necessary information is unavailable or when data collection on additional variables is time consuming and extremely costly. Linkage errors are inevitable in the linked data set because of the unavailability of error‐free unique identifiers. A small amount of linkage errors can lead to substantial bias and increased variability in estimating parameters of a statistical model. In this paper, we propose a unified theory for statistical analysis with linked data. Our proposed method, unlike the ones available for secondary data analysis of linked data, exploits record linkage process data as an alternative to taking a costly sample to evaluate error rates from the record linkage procedure. A jackknife method is introduced to estimate bias, covariance matrix and mean squared error of our proposed estimators. Simulation results are presented to evaluate the performance of the proposed estimators that account for linkage errors.     

Bias corrections for two-step fixed effects panel data estimators

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.