SIMULATED MAXIMUM LIKELIHOOD ESTIMATION BASED ON FIRST‐ORDER CONDITIONS*

I describe a strategy for structural estimation that uses simulated maximum likelihood (SML) to estimate the structural parameters appearing in a model's first‐order conditions (FOCs). Generalized method of moments (GMM) is often the preferred method for estimation of FOCs, as it avoids distributional assumptions on stochastic terms, provided all structural errors enter the FOCs additively, giving a single composite additive error. But SML has advantages over GMM in models where multiple structural errors enter the FOCs nonadditively. I develop new simulation algorithms required to implement SML based on FOCs, and I illustrate the method using a model of U.S. multinational corporations.     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

We propose a generalized method of moments (GMM) estimator with optimal instruments for a probit model that includes a continuous endogenous regressor. This GMM estimator incorporates the probit error and the heteroscedasticity of the error term in the first‐stage equation in order to construct the optimal instruments. The estimator estimates the structural equation and the first‐stage equation jointly and, based on this joint moment condition, is efficient within the class of GMM estimators. To estimate the heteroscedasticity of the error term of the first‐stage equation, we use the k‐nearest neighbour (k‐nn) non‐parametric estimation procedure. Our Monte Carlo simulation shows that in the presence of heteroscedasticity and endogeneity, our GMM estimator outperforms the two‐stage conditional maximum likelihood estimator. Our results suggest that in the presence of heteroscedasticity in the first‐stage equation, the proposed GMM estimator with optimal instruments is a useful option for researchers.     

The Impact of Inequality and Redistribution on Growth

In this paper, we reassess the impact of inequality on growth. The majority of previous papers have employed (system) GMM estimation. However, recent simulation studies indicate that the problems of GMM when using non‐stationary data such as GDP have been grossly underestimated in applied research. Concerning predetermined regressors such as inequality, GMM is outperformed by a simple least‐squares dummy variable estimator. Additionally, new data have recently become available that not only double the sample size compared to most previous studies, but also address the substantial measurement issues that have plagued past research. Using these new data and an LSDV estimator, we provide an analysis that both accounts for the conditions where inequality is beneficial or detrimental to growth and distinguishes between market‐driven inequality and redistribution. We show that there are situations where market inequality affects growth positively while redistribution is simultaneously beneficial.     

Convenient estimators for the panel probit model: Further results

Bertschek and Lechner (1998) propose several variants of a GMM estimator based on the period specific regression functions for the panel probit model. The analysis is motivated by the complexity of maximum likelihood estimation and the possibly excessive amount of time involved in maximum simulated likelihood estimation. But, for applications of the size considered in their study, full likelihood estimation is actually straightforward, and resort to GMM estimation for convenience is unnecessary. In this note, we reconsider maximum likelihood based estimation of their panel probit model then examine some extensions which can exploit the heterogeneity contained in their panel data set. Empirical results are obtained using the data set employed in the earlier study. Helpful comments and suggestions by Irene Bertschek and Michael Lechner are gratefully acknowledged. This paper has also benefited from comments by two anonymous referees and from seminar participants at the Center for Health Economics at the University of York. Any remaining errors are the responsibility of the author.     

Orthogonal Parameters and Panel Data

This paper describes a class of consistent estimators for short panels with fixed effects. The method is to find an orthogonal reparametrization of the fixed effects and then to integrate the new effects from the likelihood with respect to an appropriately chosen prior density. The resulting marginal posterior densities of the common parameters have modes that are shown to be consistent in the models examined here. The main result concerns the first-order autoregressive model with agent specific intercepts where the likelihood is conditional on the set of initial observations. This paper provides a consistent likelihood-based estimator for this model. Some numerical illustrations are given. The first-order conditions for the posterior mode can also be thought of as new moment conditions for GMM estimation.     

Redundancy of Moment Conditions in Restricted GMM Estimation

Using a novel approach to calculating the rank of the difference of two asymptotic variance matrices, The author derives the necessary and sufficient conditions for an extra set of moment conditions to be redundant given a set of moment conditions in GMM estimation with general nonlinear restrictions. The necessary and sufficient conditions derived in this paper include as a special case the redundancy of moment conditions for GMM estimation without restrictions that was first derived by Breusch et al. (1999). Therefore this paper advances the research on redundancy of moment conditions from unrestricted GMM estimation to a larger class of GMM estimation. To show their usefulness, the main results of the current paper are applied to instrumental variables estimation of linear regression models and the efficient estimation of seemingly unrelated regressions models, subject to restrictions.     

GMM estimation of panel data models with time-varying slope coefficients

A difference/system generalized method of moments (GMM) model that imposes time-constant coefficients is common in empirical studies using panel data. However, a rejection by the Sargan–Hansen test is sometimes a serious concern for researchers. We highlight the fact that the Sargan–Hansen test for GMM estimators applied to panel data is a joint test of valid orthogonality conditions and coefficient stability over time. A possible reason for a rejection is therefore that the slope coefficients vary over time. One solution is to estimate an empirical model in which the coefficients are time specific. We apply this solution to the system GMM estimator of simple nondynamic Cobb–Douglas production functions for a selection of Swedish industries and find that relaxing the assumption of constant slope coefficients results in more satisfactory outcomes of the Sargan–Hansen test.     

Grouped coefficients to reduce bias in heterogeneous dynamic panel models with small T

We propose the grouped coefficients estimator to reduce bias in dynamic panels with small T that have a multilevel structure to the coefficient and factor loading heterogeneity. If groups are chosen such that the within-group heterogeneity is small, then the grouped coefficients estimator can lead to substantial bias reduction compared to pooled GMM dynamic panel estimators. We also propose using a Wald test that can be used to assess whether pooled estimators suffer from heterogeneity bias. We illustrate the usefulness of grouped coefficients with an application to labour demand in which the coefficients are grouped by sub-sector. Our results suggest that the standard pooled estimates are substantially biased.     

Macroeconomic outcomes,collective bargaining and intersectoral productivity differentials: a panel approach

Using a sample of 19 advanced countries from 1990 to 2014 and an Arellano–Bover/Blundell–Bond linear dynamic GMM estimator along with a bootstrap-based bias correction fixed effects estimator for dynamic panels, the paper examines the macroeconomic impact of collective bargaining structures in a context of varying intersectoral heterogeneity in productivity growth among the exposed and sheltered sectors of the economy. Results show a dampening impact of pattern and centralized bargaining structures on unemployment. However, strong domestic demand is a key precondition for such a favourable effect to materialize. Uncoordinated and centralized bargaining structures are the most efficient in terms of labour cost restraint while industry bargaining moderates labour cost growth as intersectoral productivity differentials widen.     

On IV,GMM and ML in a dynamic panel data model

For the basic dynamic panel data model we give an expression for the optimal instrumental variable (IV) estimator and show that the generalized method of moments (GMM) does not add to the asymptotic efficiency. It is recommended to exploit the full set of orthogonality conditions as given by Ahn and Schmidt.     

SINGLE MOMS AND DEADBEAT DADS: THE ROLE OF EARNINGS,MARRIAGE MARKET CONDITIONS,AND PREFERENCE HETEROGENEITY

Why do some men father children outside of marriage without providing support? Why do some women have children outside of marriage when they receive little support from fathers? Why is this behavior more common among Blacks than Whites? We estimate a dynamic equilibrium model of marriage, employment, fertility, and child support decisions. We consider the extent to which low earnings, marriage market conditions, and preference heterogeneity explain nonmarital childbearing, deadbeat fatherhood, and racial differences in these outcomes. We find the Black–White earnings gap and preference heterogeneity explain a substantial portion of racial differences, whereas marriage market conditions are less important.     

Generalized least squares and maximum likelihood estimation of the logistic function for technology diffusion

Given a simple stochastic model of technology adoption, we derive a function for technological diffusion that is logistic in the deterministic part and has an error term based on the binomial distribution. We derive two estimators—a generalized least squares (GLS) estimator and a maximum likelihood (ML) estimator—which should be more efficient than the ordinary least squares (OLS) estimators typically used to estimate technological diffusion functions. We compare the two new estimators with OLS using Monte-Carlo techniques and find that under perfect specification, GLS and ML are equally efficient and both are more efficient than OLS. There was no evidence of bias in any of the estimators. We used the estimators on some example data and found evidence suggesting that under conditions of misspecification, the estimated variance-covariance of the ML estimator is badly biased. We verified the existence of the bias with a second Monte-Carlo experiment performed with a known misspecification. In the second experiment, GLS was the most efficient estimator, followed by ML, and OLS was least efficient. We conclude that the GLS estimator of choice.     

扁平证券市场线和融资限制——中国股票市场的实证检验

资本资产定价模型（CAPM)在国际金融市场的实证检验结果往往呈现扁平证券市场线现象。一些学者认为融资限制是该现象的产生原因。本文旨在研究扁平证券市场线现象是否存在于中国股市,同时分析融资限制对中国股市证券市场线的影响。本文采用投资组合分析法对A股主板市场进行实证检验。本文研究发现：（1)扁平的证券市场线现象同样存在于中国股票市场中;（2)在中国股票市场中,融资限制与证券市场线的斜率呈负相关,与截距呈正相关,这符合融资限制理论;（3)以上两点发现同样存在于多因子定价模型中,这表明本文研究结果具有稳健性。       

Subsidised Training and Youth Employment: Distinguishing Unobserved Heterogeneity from State Dependence in Labour Market Histories

Using the 1990–2 wave of the French Labour Force Survey to study the employment histories of young people I consider transitions between six labour market states: employment contracts whether permanent or temporary, unemployment, training, education and non-participation. I use a fixed effect estimator in a dynamic multinomial logit model which can accommodate any form of unobserved heterogeneity in levels. This analysis can be extended to Markov processes of any order. I relate heterogeneity components to individual and family characteristics by using simulated maximum likelihood methods. These procedures allow evaluation of the effects training schemes have on youth employment histories.     

Globalization and labor market institutions: International empirical evidence

A widespread concern is that labor market institutions erode in the course of globalization, which, in turn, decreases employment and wages. By using panel data and cross-sectional data, I investigate the influence of globalization on labor market regulation. I use the indicators of labor market institutions by Gwartney et al. (2012) and the KOF indices of globalization. To deal with potential reverse causality, I employ a system GMM panel estimator and use a constructed trade share as proposed by Frankel and Romer (1999) as an instrumental variable for globalization in cross-sectional models. The results do not show that globalization induced labor market deregulation.     

外商在华直接投资决定因素的阶段性差异研究——基于面板数据的系统GMM估计

现有实证研究忽视了在华外商直接投资的阶段性,导致数据异质而估计偏误.为避免数据异质和其他计量问题,本文细分数据并采用系统GMM进行估计.结果表明,外商在华直接投资的决定因素存在阶段性差异,其表现为:外资集聚效应和市场规模的作用增强,开放度的促进作用开始显现,工资负效应、非市场化的阻碍作用减弱,税收优惠作用由正变负,交通基础设施正效应、非国有内资企业的集聚效应消失.最后,据此提出了政策性的建议.     

中国反倾销申诉寒蝉效应的实证分析——基于动态面板模型的GMM检验

本文基于中国2001年-2008年对外反倾销案例的面板数据,通过构造横截面单元为中国对外反倾销调查的动态面板数据模型,应用一阶差分广义矩估计方法考察了中国实施反倾销措施及其贸易自由化对中国进口贸易的影响。实证结果表明,贸易自由化对中国进口贸易的促进作用效果非常显著;中国反倾销立案调查对进口贸易有一定的震慑作用,但并未起到限制进口贸易的作用,也就是说中国对外反倾销并非是要构筑贸易壁垒体系,更没有将之作为抵消贸易自由化效应的政策工具。     

Semiparametric estimation of conditional mean functions with missing data

A new semiparametric estimator for estimating conditional expectation functions from incomplete data is proposed, which integrates parametric regression with nonparametric matching estimators. Besides its applicability to missing data situations due to non-response or attrition, the estimator can also be used for analyzing treatment effect heterogeneity and statistical treatment rules, where data on potential outcomes is missing by definition. By combining moments from a parametric specification with nonparametric estimates of mean outcomes in the non-responding population within a GMM framework, the estimator seeks to balance a good fit in the responding population with low bias in the non-responding population. The estimator is applied to analyzing treatment effect heterogeneity among Swedish rehabilitation programmes.

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A generalized method of moments estimator for a spatial model with moving average errors, with application to real estate prices

This paper proposes a new GMM estimator for spatial regression models with moving average errors. Monte Carlo results are given which suggest that the GMM estimates are consistent and robust to non-normality, and the Bootstrap method is suggested as a way of testing the significance of the moving average parameter. The estimator is applied in a model of English real estate prices, in which the concepts of displaced demand and displaced supply are introduced to derive the spatial lag of prices, and the moving average error process represents spatially autocorrelated unmodelled variables.