The maximum number of parameters for the Hausman test when the estimators are from different sets of equations

Hausman (1978) developed a widely-used model specification test that has passed the test of time. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Three illustrative examples are used, namely an exogeneity test for the linear regression model, a test for the Box–Cox transformation, and a test for sample selection bias.     

On Liu estimators for the logit regression model

This paper introduces a shrinkage estimator for the logit model which is a generalization of the estimator proposed by Liu (1993) for the linear regression. This new estimation method is suggested since the mean squared error (MSE) of the commonly used maximum likelihood (ML) method becomes inflated when the explanatory variables of the regression model are highly correlated. Using MSE, the optimal value of the shrinkage parameter is derived and some methods of estimating it are proposed. It is shown by means of Monte Carlo simulations that the estimated MSE and mean absolute error (MAE) are lower for the proposed Liu estimator than those of the ML in the presence of multicollinearity. Finally the benefit of the Lie estimator is shown in an empirical application where different economic factors are used to explain the probability that municipalities have net increase of inhabitants.     

A demand system for input factors when there are technological changes in production

In a system with n input factors there are n − 1 independent cost shares. An often-used approach in estimating factor demand systems is to (implicitly or explicitly) assume that there is a (independent) cointegrating relationship for each of the n − 1 independent cost shares. However, due to technological changes, there might not be as many cointegrating relationships as there are (independent) cost shares. This article presents a flexible demand system that allows for both factor neutral technological changes as well as technological changes that affect the relative use of the different factors. The empirical tests indicate that there are fewer cointegrating relationships than usually implied using conventional estimation approaches. This result is consistent with technological changes that affect the relative use of the different input factors. I argue that, since such unexplained technological changes are likely to affect input factor decisions, a demand system that allows for such changes should be preferred.     

On ridge estimators for the negative binomial regression model

The negative binomial (NB) regression model is very popular in applied research when analyzing count data. The commonly used maximum likelihood (ML) estimator is very sensitive to highly intercorrelated explanatory variables. Therefore, a NB ridge regression estimator (NBRR) is proposed as a robust option of estimating the parameters of the NB model in the presence of multicollinearity. To investigate the performance of the NBRR and the traditional ML approach the mean squared error (MSE) is calculated using Monte Carlo simulations. The simulated result indicated that some of the proposed NBRR methods should always be preferred to the ML method.     

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.     

Consistency of Heckman-type two-step estimators for the multivariate sample-selection model

This analysis shows that multivariate generalizations to the classical Heckman (1976 Heckman, JJ. 1976. The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. Annals of Economics and Social Measurement, 5: 475–92.  [Google Scholar], 1979) two-step estimator that account for cross-equation correlation and use the inverse Mills ratio as correction term are consistent only if certain restrictions apply to the true error-covariance structure. An alternative class of generalizations to the classical Heckman two-step approach is derived that condition on the entire selection pattern rather than selection in particular equations and, therefore, use modified correction terms. It is shown that this class of estimators is consistent. In addition, Monte-Carlo results illustrate that these estimators display a smaller mean square prediction error.     

Consumption externalities: a representative consumer model when agents are heterogeneous

We examine a growth model with consumption externalities where agents differ in their initial capital endowment and their reference group. We show under which conditions the aggregate equilibrium with heterogeneous agents replicates that obtained with a representative consumer, despite the fact that different individuals have different consumption levels. Next we consider the implications of the presence of consumption externalities for the long-run distributions of income and wealth. We find that, in a growing economy, “keeping up with the Joneses” results in less inequality than would prevail in an economy with no consumption externalities.     

Testing for complementarity when strategies are dichotomous

We show that it is not possible to extend Arora (1996) reduced form test for the existence of complementarity to evaluate the relationship between a couple of dichotomous strategies as it leads to an incoherent simultaneous discrete response model.     

Maximum likelihood estimators of the dagum model parameters

This paper will show the sample size needed to provide good maximum likelihood estimators of the Dagum model parameters. The principal goal of this study is to verify the asymptotic properties of these estimators for finite sample sizes comparable to the ones employed in the real surveys (for example, the Labor Force Survey).     

Comparison of SML and GMM estimators for the random coefficient logit model using aggregate data

A simulated maximum likelihood (SML) estimator for the random coefficient logit model using aggregate data is found to be more efficient than the widely used generalized method of moments estimator (GMM) of Berry et?al. (Econometrica 63:841?C890, 1995). In particular, the SML estimator is better than the GMM estimator in recovery of heterogeneity parameters which are often of central interest in marketing research. With the GMM estimator, the analyst must determine what moment conditions to use for parameter identification, especially the heterogeneity parameters. With the SML estimator, the moment conditions are automatically determined as the gradients of the log-likelihood function, and these are the most efficient ones if the model is correctly specified. Another limitation of the GMM estimator is that the product market shares must be strictly positive while the SML estimator can handle zero market share observations. Properties of the SML and GMM estimators are demonstrated in simulated data and in data from the US photographic film market.     

Wealth transfers and the role of collateral when lifetimes are uncertain

We develop a general equilibrium model of wealth transfers in the presence of uncertain lifetimes and default. Without introducing exogenous debt constraints, agents are allowed to make collateral-backed promises at any state of their life span.     

Measuring the cost of capital when taxes are changing with foresight

The familiar Hall-Jorgenson (1967) cost of capital perturbation is not a uniquely feasible one. Because of institutional features of actual tax systems, the optimal holding time for an incremental unit of capital will generally be infinite. The impossibility of an optimal rule for recapturing excess depreciation allowances on disposal is demonstrated. When tax changes are foreseen, the ‘error’ in the traditional measure of cost of capital can become highly significant. Ignorance of this effect led to underestimates of the extent to which the radical changes to the U.K. Corporation Tax in 1984 would affect cost of capital and incentives to forestall planned investment.     

Population-monotonic solutions to the problem of fair division when preferences are single-peaked

Summary We consider the problem of fairly allocating an infinitely divisible commodity among agents with single-peaked preferences. First, we examine the implications of the requirement that a change in the population affect all agents that are present before and after the change in the same direction. We show that this requirement is met by no selection from the no-envy solution. In the face of this impossibility, we limit our attention to changes that are not so disruptive, in the following sense: if initially there is not enough to bring all agents to their satiation points, then this still is the case after the change, and if initially there is so much that agents have to be brought beyond their satiation points, then again, this remains the case. The requirement is that such changes affect all agents that are present before and after the change in the same direction. Our main result is that there is essentially only one selection from the envy-free and efficient solution satisfying this property. It is the solution known as the uniform rule.The comments of T. Yamato, T. Sönmez and two referees, and support from NSF under Grant No. 8809822 and SES 9212557, are gratefully acknowledged.     

Valuing the Incremental Benefits of Groundwater Protection when Exposure Levels are Known

Both economic theory and psychological research indicate that benefit functions for reductions in health risk exposures may be conditional on current exposures. Using nitrates found in household wells, it is demonstrated that perceptions of health risks across exposure levels are affected by the individual's current exposure level, thus providing support for a conditional benefits function approach. Functions of conditional incremental benefits are estimated from a contingent valuation study of households that had been informed of their water test results. Incremental benefits reach a peak at an intermediate level of nitrates and then decline. Possible explanations for this non-convexity are provided.     

矿山资源整合的三方博弈及其策略研究

设租、寻租等投机行为是造成资源整合效率损失,进而埋下安全、环保隐患的重要原因之一.文章借助博弈论的分析工具,首先分析了中央政府、地方政府和开采企业基于资源整合监管力度的支付函数,并以此为基础对参与方同步行动时的不完全信息动态子博弈分别进行了研究,得到精炼纳什均衡策略.进而基于博弈的过程为参与方不断利用扰动进行策略调整,且博弈的结果都为采取0-1的纯策略决策,构建涉及剩余价值"扰动"的策略演进博弈模型,而使得中央政府信息劣势的不利程度得到一定程度的缓解,且策略明显得到改善.     

Testing for cointegration using the Johansen methodology when variables are near-integrated: size distortions and partial remedies

We investigate the properties of Johansen’s (J Econ Dyn Control 12:231–254, 1988; Econometrica 59:1551–1580, 1991) maximum eigenvalue and trace tests for cointegration under the empirically relevant situation of near-integrated variables. Using Monte Carlo techniques, we show that in a system with near-integrated variables, the probability of reaching an erroneous conclusion regarding the cointegrating rank of the system is generally substantially higher than the nominal size. The risk of concluding that completely unrelated series are cointegrated is therefore non-negligible. We suggest ways of identifying the problem and different approaches to reduce the size distortions of the tests.     

Monetary and fiscal policy interactions in the EMU when cyclical conditions are uncertain

This paper examines economic policy interactions in the Economic and Monetary Union when the assessment of cyclical conditions in real time is surrounded by uncertainty. On the basis of a simple stylised model it shows that with a Nash-type of interaction different views about the output gap on the side of the policy players—the Council of the European Union, the European Commission and the European Central Bank—can give rise to excessive activism with policy players pushing economic variables into opposite directions. It argues that the costs of such policy conflicts can be reduced by agreeing on a common assessment of the cycle, by constraining policy variables, and/or by increasing the weight of fiscally conservative institutions. An alternative option to sidestep policy conflicts ensuing from diverging views of the cycle is to take policy decisions sequentially, as is the case in a Stackelberg-type of interaction. The paper shows that for a given misperception of the cycle, the impact on the policy instruments and on output and inflation are generally smaller in the Stackelberg equilibrium as compared to a Nash outcome. Alternative allocations of roles—that is leader versus follower—are discussed and assessed.

A monte carlo study of the small sample properties of various estimators of Solow's distributed lag model

The results of some Monte Carlo experiments investigating the small sample properties of estimators ofSolow's distributed lag model are presented. In general, the relative efficiency of an estimation technique depends on the true values of the parameters being estimated. But if the assumptions of the model are not violated, then the maximum and mean likelihood and the Bayesian estimators are best.