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.     

Temporary Help Agencies and Occupational Mobility*

This paper analyses the effects of Temporary Help Agencies (THA) on occupational mobility by performing an empirical comparison of the job‐to‐job upgrading chances of agency and regular (non‐agency) workers in Spain. We estimate a switching regression model to allow for self‐selection into agency work because of, for instance, more motivated workers being more likely to search for jobs through a THA. We find evidence in favour of the existence of self‐selection in all qualification groups considered. Concerning mobility, we find that agency workers in intermediate qualification levels are less likely to experience demotions than regular workers. THA increase the probability of high‐skilled workers achieving a permanent contract in Spain.     

Demand and supply estimation biases due to omission of durability

We build a dynamic equilibrium model of a durable goods oligopoly with a competitive secondary market to evaluate the bias in estimating the structural parameters of demand and supply when durability is omitted. We simulate data from our dynamic model and use them to estimate the model’s static counterpart. We find that the static estimate of the elasticity of demand is an overestimate of the true elasticity and that the static estimate of the markup is an underestimate. Our results provide a benchmark on the magnitude and sign of the bias when static models are used for economic inference.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.     

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 sample selection models with spatial dependence

We consider the estimation of a sample selection model that exhibits spatial autoregressive errors (SAE). Our methodology is motivated by a two‐step strategy where in the first step we estimate a spatial probit model and in the second step (outcome equation) we include an estimated inverse Mills ratio (IMR) as a regressor to control for selection bias. Since the appropriate IMR under SAE depends on a parameter from the second step, both steps are jointly estimated employing the generalized method of moments. We explore the finite sample properties of the estimator using simulations and provide an empirical illustration. Copyright © 2010 John Wiley & Sons, Ltd.     

Exact Skewness–Kurtosis Tests for Multivariate Normality and Goodness‐of‐Fit in Multivariate Regressions with Application to Asset Pricing Models*

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross‐equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared with a simulation‐based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal and stable error distributions. In the Gaussian case, finite‐sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi‐stage Monte Carlo test methods. For non‐Gaussian distribution families involving nuisance parameters, confidence sets are derived for the nuisance parameters and the error distribution. The tests are applied to an asset pricing model with observable risk‐free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over 5‐year subperiods from 1926 to 1995.     

Estimation of linear dynamic panel data models with time‐invariant regressors

We present a sequential approach to estimating a dynamic Hausman–Taylor model. We first estimate the coefficients of the time‐varying regressors and subsequently regress the first‐stage residuals on the time‐invariant regressors. In comparison to estimating all coefficients simultaneously, this two‐stage procedure is more robust against model misspecification, allows for a flexible choice of the first‐stage estimator, and enables simple testing of the overidentifying restrictions. For correct inference, we derive analytical standard error adjustments. We evaluate the finite‐sample properties with Monte Carlo simulations and apply the approach to a dynamic gravity equation for US outward foreign direct investment.     

TECHNOLOGICAL INNOVATION AND EMPLOYMENT IN DERIVED LABOUR DEMAND MODELS: A HIERARCHICAL META‐REGRESSION ANALYSIS

The effect of technological innovation on employment is of major concern for workers and their unions, policy makers and academic researchers. We meta‐analyse 570 estimates from 35 primary studies that estimate a derived labour demand model. We contribute to existing attempts at evidence synthesis by addressing the risks of selection bias and that of data dependence in observational studies. Our findings indicate that: (i) hierarchical meta‐regression models are sufficiently versatile for addressing both selection bias and data dependence in observational data; (ii) innovation's effect on employment is positive but small and highly heterogeneous; (iii) only a small part of residual heterogeneity is explained by moderating factors; (iv) selection bias tends to reflect preference for upholding prevalent hypotheses on the employment effects of process and product innovations; (v) country‐specific effect‐size estimates are related to labour market and product market regulation in six OECD countries in a U‐shaped fashion; and (vi) OLS estimates reflect upward bias whereas those based on time‐differenced or within estimators reflect a downward bias. Our findings point out to a range of data quality and modelling issues that should be addressed in future research.     

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.     

Competing for Consumers with Self‐Control Problems

I examine strategic implications of competing for consumers with self‐control problems. For investment goods, like health clubs, I find that the equilibrium sign‐up (lump‐sum) fees decrease when competition intensifies, similarly to prices in standard oligopoly models. However, the equilibrium attendance (per‐unit) price increases due to firms' deteriorated ability to take advantage of consumers' self‐control problems. Moreover, firms earn less profit due to consumers' self‐control problems—the firms have a unilateral incentive to charge per‐unit fees lower than the marginal cost; however, they cannot make up the lost margins by increasing the lump‐sum fee, due to competition. I also show that for plausible parameter regions the market adjusts to consumers' self‐control problem in such a way that firms play the standard equilibrium strategies that they would have engaged in with fully rational consumers, with identical market outcomes. Most of the results are qualitatively the same for leisure goods (for example, credit cards); however, some results are reversed: the per‐unit fees are higher than marginal cost and decrease as competition intensifies.     

Quasi-structural estimation of a model of childcare choices and child cognitive ability production

This article evaluates the effects of maternal vs. alternative care providers’ time inputs on children’s cognitive development using the sample of single mothers in the National Longitudinal Survey of Youth. To deal with the selection problem created by unobserved heterogeneity of mothers and children, we develop a model of mother’s employment and childcare decisions. We then obtain approximate decision rules for employment and childcare use, and estimate these jointly with the child’s cognitive ability production function. To help identify our selection model, we take advantage of the plausibly exogenous variation in employment and childcare choices of single mothers generated by the variation in welfare rules across states and over time created by the 1996 welfare reform legislation and earlier State waivers.     

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.     

Regression density estimation using smooth adaptive Gaussian mixtures

We model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of the covariates. The model extends the existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need fewer components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mechanism that prevents overfitting and makes it feasible to fit flexible high-dimensional surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities, but also that special cases of the general model are interesting models for economic data.     

Bayesian estimation and model selection for spatial Durbin error model with finite distributed lags

In this paper we investigate a spatial Durbin error model with finite distributed lags and consider the Bayesian MCMC estimation of the model with a smoothness prior. We study also the corresponding Bayesian model selection procedure for the spatial Durbin error model, the spatial autoregressive model and the matrix exponential spatial specification model. We derive expressions of the marginal likelihood of the three models, which greatly simplify the model selection procedure. Simulation results suggest that the Bayesian estimates of high order spatial distributed lag coefficients are more precise than the maximum likelihood estimates. When the data is generated with a general declining pattern or a unimodal pattern for lag coefficients, the spatial Durbin error model can better capture the pattern than the SAR and the MESS models in most cases. We apply the procedure to study the effect of right to work (RTW) laws on manufacturing employment.     

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.     

Model identification for infinite variance autoregressive processes

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.     

Estimation and model selection of semiparametric multivariate survival functions under general censorship

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n$n$ asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple consistent estimator of its asymptotic variance, allowing for a first-step nonparametric estimation of the marginal survivals. We establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application is provided.     

Using the Fraction of Missing Information to Identify Auxiliary Variables for Imputation Procedures via Proxy Pattern‐mixture Models

In many surveys, imputation procedures are used to account for non‐response bias induced by either unit non‐response or item non‐response. Such procedures are optimised (in terms of reducing non‐response bias) when the models include covariates that are highly predictive of both response and outcome variables. To achieve this, we propose a method for selecting sets of covariates used in regression imputation models or to determine imputation cells for one or more outcome variables, using the fraction of missing information (FMI) as obtained via a proxy pattern‐mixture (PMM) model as the key metric. In our variable selection approach, we use the PPM model to obtain a maximum likelihood estimate of the FMI for separate sets of candidate imputation models and look for the point at which changes in the FMI level off and further auxiliary variables do not improve the imputation model. We illustrate our proposed approach using empirical data from the Ohio Medicaid Assessment Survey and from the Service Annual Survey.     

GMM estimators with improved finite sample properties using principal components of the weighting matrix,with an application to the dynamic panel data model

GMM estimators have poor finite sample properties in highly overidentified models. With many moment conditions the optimal weighting matrix is poorly estimated. We suggest using principal components of the weighting matrix. This effectively drops some of the moment conditions. Our simulations, done in the context of the dynamic panel data model, show that the resulting GMM estimator has better finite sample properties than the usual two-step GMM estimator, in the sense of smaller bias and more reliable standard errors.