Classification Error in Dynamic Discrete Choice Models: Implications for Female Labor Supply Behavior

Two key issues in the literature on female labor supply are (i) whether persistence in employment status is due to unobserved heterogeneity or state dependence, and (ii) whether fertility is exogenous to labor supply. Until recently, the consensus was that unobserved heterogeneity is very important and fertility is endogenous. Hyslop (1999) challenged this. Using a dynamic panel probit model of female labor supply including heterogeneity and state dependence, he found that adding autoregressive errors led to a substantial diminution in the importance of heterogeneity. This, in turn, meant he could not reject that fertility is exogenous. Here, we extend Hyslop (1999) to allow classification error in employment status, using an estimation procedure developed by Keane and Wolpin (2001) and Keane and Sauer (2005). We find that a fairly small amount of classification error is enough to overturn Hyslop's conclusions, leading to overwhelming rejection of the hypothesis of exogenous fertility.     

Dynamic Financial Constraints: Distinguishing Mechanism Design From Exogenously Incomplete Regimes

We formulate and solve a range of dynamic models of constrained credit/insurance that allow for moral hazard and limited commitment. We compare them to full insurance and exogenously incomplete financial regimes (autarky, saving only, borrowing and lending in a single asset). We develop computational methods based on mechanism design, linear programming, and maximum likelihood to estimate, compare, and statistically test these alternative dynamic models with financial/information constraints. Our methods can use both cross‐sectional and panel data and allow for measurement error and unobserved heterogeneity. We estimate the models using data on Thai households running small businesses from two separate samples. We find that in the rural sample, the exogenously incomplete saving only and borrowing regimes provide the best fit using data on consumption, business assets, investment, and income. Family and other networks help consumption smoothing there, as in a moral hazard constrained regime. In contrast, in urban areas, we find mechanism design financial/information regimes that are decidedly less constrained, with the moral hazard model fitting best combined business and consumption data. We perform numerous robustness checks in both the Thai data and in Monte Carlo simulations and compare our maximum likelihood criterion with results from other metrics and data not used in the estimation. A prototypical counterfactual policy evaluation exercise using the estimation results is also featured.     

Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables

This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high‐dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure.     

Informal Caregiving and Women's Work Choices: Lessons from the Netherlands

This paper focuses on the effects of Dutch long‐term care and labour market policies on women's labour market participation and informal caregiving decisions. Labour market participation and informal caregiving are estimated jointly through a multivariate dynamic binary probit on European Community Household Panel data. Under Dutch policy, informal care decisions appear to be independent of household non‐labour income and no significant impediment seems to hinder the contemporaneous practice of work activities and care. However, past informal care provision still slightly reduces the probability of currently working and vice versa, leaving room for policy improvements to enhance labour market participation.     

Sequential Estimation of Dynamic Discrete Games

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems, and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two‐step PML estimators, which, although they are attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always available; and they are asymptotically inefficient. Second, we show that a recursive extension of the two‐step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.     

Bayesian Inference for Hospital Quality in a Selection Model

This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom selection. Mortality rates in patient discharge records are widely used to infer hospital quality. However, hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others. In this situation the assumption of random admission leads to spurious inference about hospital quality. This study controls for hospital selection using a model in which distance between the patient's residence and alternative hospitals are key exogenous variables. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator, and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals. The study uses data on 74,848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia. It finds the smallest and largest hospitals to be of the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study's selection model.     

Looks and Labor: Do Attractive People Work More?

Using the German General Social Survey (ALLBUS) 2008, I investigate how looks affect an individual's labor supply decision. My results are, by and large, in line with predictions derived from the neoclassical model of labor supply. Applying regular probit, bivariate probit, Tobit and Heckman selection regression models, I find that good looks go hand in hand with higher employment probabilities and more hours of market work. Furthermore, physical attractiveness is positively associated with spousal income and spousal employment. Hence, beauty appears to affect labor supply decisions both directly and through the marriage market.     

Finite Mixture Distributions,Sequential Likelihood and the EM Algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log‐likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.     

Accuracy of Simulations for Stochastic Dynamic Models

This paper is concerned with accuracy properties of simulations of approximate solutions for stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then show that the statistics generated by any sufficiently good numerical approximation are arbitrarily close to the set of expected values of the model's invariant distributions. Also, under a contractivity condition on the dynamics, we establish error bounds. These results are of further interest for the comparative study of stationary solutions and the estimation of structural dynamic models.     

基于SV-SGED模型的动态VaR测度研究

本文针对金融资产收益展现出“有偏”及“厚尾”分布特征,引入有偏广义误差分布（SGED）来描述资产收益,继而提出SV-SGED模型对资产收益波动率建模,并以此来测度动态风险值（VaR）,进而采用后验测试技术对风险测度模型的精确性进行检验。同时,为了估计SV模型的参数,提出基于有效重要性抽样（EIS）技巧的极大似然（ML）估计方法。最后,给出了基于上证综合指数的实证研究。结果表明,SV-SGED模型比正态分布假定下的SV（SV-N）和广义误差分布假定下的SV（SV-GED）模型具有更好的波动率描述能力,SV-SGED模型展现出比SV-N和SV-GED模型更优越的风险测度能力。     

加权复合分位数回归方法在动态VaR风险度量中的应用

风险价值(VaR)因为简单直观,成为了当今国际上最主流的风险度量方法之一,而基于时间序列自回归(AR)模型来计算无条件风险度量值在实业界有广泛应用。本文基于分位数回归理论对AR模型提出了一个估计方法--加权复合分位数回归(WCQR)估计,该方法可以充分利用多个分位数信息提高参数估计的效率,并且对于不同的分位数回归赋予不同的权重,使得估计更加有效,文中给出了该估计的渐近正态性质。有限样本的数值模拟表明,当残差服从非正态分布时,WCQR估计的的统计性质接近于极大似然估计,而该估计是不需要知道残差分布的,因此,所提出的WCQR估计更加具有竞争力。此方法在预测资产收益的VaR动态风险时有较好的应用,我们将所提出的理论分析了我国九只封闭式基金,实证分析发现,结合WCQR方法求得的VaR风险与用非参数方法求得的VaR风险非常接近,而结合WCQR方法可以计算动态的VaR风险值和预测资产收益的VaR风险值。     

Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure

This paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure. The unobserved factors and the individual‐specific errors are allowed to follow arbitrary stationary processes, and the number of unobserved factors need not be estimated. The basic idea is to filter the individual‐specific regressors by means of cross‐section averages such that asymptotically as the cross‐section dimension (N) tends to infinity, the differential effects of unobserved common factors are eliminated. The estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross‐sectional averages of the dependent variable and the individual‐specific regressors. A number of estimators (referred to as common correlated effects (CCE) estimators) are proposed and their asymptotic distributions are derived. The small sample properties of mean group and pooled CCE estimators are investigated by Monte Carlo experiments, showing that the CCE estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics, and for relatively small values of N and T.     

Should I Text or Call Here? A Situation‐Based Analysis of Drivers’ Perceived Likelihood of Engaging in Mobile Phone Multitasking

This study investigated how situational characteristics typically encountered in the transport system influence drivers’ perceived likelihood of engaging in mobile phone multitasking. The impacts of mobile phone tasks, perceived environmental complexity/risk, and drivers' individual differences were evaluated as relevant individual predictors within the behavioral adaptation framework. An innovative questionnaire, which includes randomized textual and visual scenarios, was administered to collect data from a sample of 447 drivers in South East Queensland‐Australia (66% females; n = 296). The likelihood of engaging in a mobile phone task across various scenarios was modeled by a random parameters ordered probit model. Results indicated that drivers who are female, are frequent users of phones for texting/answering calls, have less favorable attitudes towards safety, and are highly disinhibited were more likely to report stronger intentions of engaging in mobile phone multitasking. However, more years with a valid driving license, self‐efficacy toward self‐regulation in demanding traffic conditions and police enforcement, texting tasks, and demanding traffic conditions were negatively related to self‐reported likelihood of mobile phone multitasking. The unobserved heterogeneity warned of riskier groups among female drivers and participants who need a lot of convincing to believe that multitasking while driving is dangerous. This research concludes that behavioral adaptation theory is a robust framework explaining self‐regulation of distracted drivers.     

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K–stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz–Miller estimator (for K=1) and Rust's nested fixed point estimator (in the limit when K→∞). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade–off between finite sample precision and computational cost in the sequence of policy iteration estimators.     

End‐of‐Sample Instability Tests

This paper considers tests for structural instability of short duration, such as at the end of the sample. The key feature of the testing problem is that the number, m, of observations in the period of potential change is relatively small—possibly as small as one. The well‐known F test of Chow (1960) for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors, even when the total number of observations, n+m, is large. We generalize the F test to cover regression models with much more general error processes, regressors that are not strictly exogenous, and estimation by instrumental variables as well as least squares. In addition, we extend the F test to nonlinear models estimated by generalized method of moments and maximum likelihood. Asymptotic critical values that are valid as n→∞ with m fixed are provided using a subsampling‐like method. The results apply quite generally to processes that are strictly stationary and ergodic under the null hypothesis of no structural instability.     

Estimation and Inference With Weak,Semi‐Strong,and Strong Identification

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments, generalized empirical likelihood, minimum distance, and semi‐parametric estimators. The consistency/lack‐of‐consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic sizes (in a uniform sense) of standard and identification‐robust tests and CS's are established. The results are applied to the ARMA(1, 1) time series model estimated by ML and to the nonlinear regression model estimated by LS. In companion papers, the results are applied to a number of other models.     

国内外原油价格关系的动态分析

以2000年1月~2006年12月国内原油和国际原油现货FOB月价格为变量,分析了两者的动态关系:首先,通过Johansen和Juselius的极大似然法对2个变量进行了协整检验,结果显示2个变量之间可能存在动态均衡关系;其次,通过G ranger因果检验和建立误差修正模型对两者的动态均衡关系进行了检验,证明这2个变量间存在均衡关系;然后,运用脉冲响应函数和预测误差分解技术对这种动态均衡关系进行了分解,分析了国内外原油价格之间的相互作用机制和影响程度。在此基础上,从我国石油价格形成机制方面讨论了增强国内原油价格对国际原油价格定价的发言权、避免国际原油价格的波动风险的途径。     

Information‐Sensitive Replenishment when Inventory Records Are Inaccurate

Inspired by recent empirical work on inventory record inaccuracy, we consider a periodic review inventory system with imperfect inventory records and unobserved lost sales. Record inaccuracies are assumed to arrive via an error process that perturbs physical inventory but is unobserved by the inventory manager. The inventory manager maintains a probability distribution around the physical inventory level that he updates based on sales observations using Bayes Theorem. The focus of this study is on understanding, approximating, and evaluating optimal forward‐looking replenishment in this environment. By analyzing one‐ and two‐period versions of the problem, we demonstrate several mechanisms by which the error process and associated record inaccuracy can impact optimal replenishment. Record inaccuracy generally brings an incentive for a myopic manager to increase stock to buffer the added uncertainty. On the other hand, a forward‐looking manager will stock less than a myopic manager, in part to improve information content for future decisions. Using an approximate partially observed dynamic programming policy and associated bound, we numerically corroborate our analytical findings and measure the effectiveness of an intelligent myopic heuristic. We find that the myopic heuristic is likely sufficiently good in practical settings targeting high service levels.     

Marital Instability,Reproductive Behaviour and Women's Labour Force Participation Decisions

ABSTRACT The subject of this paper is the relationship between female labour force participation, fertility decisions and marital instability and pursues a two-fold objective: to explain the nature of the interdependences between participation and procreation decisions; and to look for, through empirical evidence, an explanation for women's labour force participation and fertility dynamics over the last 20 years. The empirical evidence, based on a panel of 19 countries over the period 1965–1989, shows that variables representing marital instability have an important role in woman's labour supply and fertility dynamics during this period.     

COMPETING WITH MENUS OF TARIFF OPTIONS

The nature of numerous strategies of firms is often discrete or countable. This adds difficulty to measuring and testing for the existence of complementarities among several strategies. This paper introduces a generalized multivariate count data model that allows estimating correlations of any sign among the pricing decisions of competing firms in a manner that is robust to the existence of unobserved heterogeneity leading to either over‐ and underdispersion of the distribution of counts. Thus, it is possible to overcome a major challenge in testing whether two decisions are strategic complements or substitutes, namely, dealing with the effect of unobserved heterogeneity. I study how firms actually compete in nonlinear tariffs by analyzing the interrelation between the incumbent and entrant's decisions to offer a given number of tariff options. Results document the existence of complementarity among tariff options regardless of whether they are dominated or not. This result supports the view that the implementation of nonlinear tariffs by means of a menu of self‐selecting two‐part tariffs has some strategic competitive value. (JEL: C35, D43, M21)