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Abstract:
We detail the basic theory for models of discrete choice. This encompasses methods of estimation and analysis of models with discrete dependent variables. Entry level theory is presented for the practitioner. We then describe a few of the recent, frontier developments in theory and practice.

Abstract:
We detail the basic theory for models of discrete choice. This encompasses methods of estimation and analysis of models with discrete dependent variables. Entry level theory is presented for the practitioner. We then describe a few of the recent, frontier developments in theory and practice.

Abstract:
We detail the basic theory for regression models in which dependent variables are censored or underlying distributions are truncated. The model is extended to models for counts, sample selection models, and models hazard models for duration data. Entry level theory is presented for the practitioner. We then describe a few of the recent, frontier developments in theory and practice.

Censoring, Truncation, Maximum likelihood, Attenuation, Regression, Bias, Sample selection, Panel data, Semiparametric

Abstract:
We survey the literature on models for ordered choices, including ordered logit and probit specifications. The contemporary form of the model is presented and analyzed in detail. The historical development of the model is presented as well. We detail a number of generalizations that have appeared in the recent literature. Finally, we propose a new form of the model that accommodates in a natural, internally consistent form, functional form flexibility and individual heterogeneity. Much of this study is pedagogical. However, the last few sections propose new model formulations, and illustrate them with an application to self reported health satisfaction.

Abstract:
Undergraduate students typically are able to regurgitate basic rules and formulas for probability. They also have little trouble following the cookbook steps for estimation and hypothesis testing. Microsoft Excel has empowered them to run regressions. We are not persuaded, however, that these advances have markedly improved student understanding of the underlying principles of statistics. Nor are we convinced that advances made by scholars working with quantitative methods and real economic data are making their way into classrooms and computer laboratories. In this piece, we show how the work of Nobel Laureates in economics can be used to enhance student understanding and bring students up to date on topics such as probability, uncertainty and decision theory, hypothesis testing, regression to the mean, instrumental variable techniques, discrete choice modeling and time-series analysis.

Abstract:
The most familiar fixed effects (FE) and random effects (RE) panel data treatments for count data were proposed by Hausman, Hall and Griliches (HHG) (1984). The Poisson FE model is particularly simple and is one of a small few known models in which the incidental parameters problem is, in fact, not a problem. The same is not true of the negative binomial (NB) model. Researchers are sometimes surprised to find that the HHG formulation of the FENB model allows an overall constant a quirk that has also been documented elsewhere. We resolve the source of the ambiguity, and consider the difference between the HHG FENB model and a true FENB model that appears in the familiar index function form.The familiar RE Poisson model using a log gamma heterogeneity term produces the NB model. The HHG RE NB model is also unlike what might seem the natural application in which the heterogeneity term appears as an additive common effect in the conditional mean. We consider the lognormal model as an alternative RENB model in which the common effect appears in a natural index function form.

Poisson regression, Negative binomial, Panel data, Heterogeneity;, Lognormal;, Fixed effects, Random effects

Abstract:
The most familiar fixed effects (FE) and random effects (RE) panel data treatments for count data were proposed by Hausman, Hall and Griliches (HHG) (1984). The Poisson FE model is particularly simple and is one of a small few known models in which the incidental parameters problem is, in fact, not a problem. The same is not true of the negative binomial (NB) model. Researchers are sometimes surprised to find that the HHG formulation of the FENB model allows an overall constant - a quirk that has also been documented elsewhere. We resolve the source of the ambiguity, and consider the difference between the HHG FENB model and a "true" FENB model that appears in the familiar index function form.

The familiar RE Poisson model using a log gamma heterogeneity term produces the NB model. The HHG RE NB model is also unlike what might seem the natural application in which the heterogeneity term appears as an additive common effect in the conditional mean. We consider the lognormal model as an alternative RENB model in which the common effect appears in a natural index function form.

Poisson regression, Negative binomial, Panel data, Heterogeneity, Lognormal, Fixed effects, Random effects

Abstract:
Heckman s (1979) sample selection model has been employed in three decades of applications of linear regression studies. The formal extension of the method to nonlinear models, however, is of more recentvintage. A generic solution for nonlinear models is proposed in Terza (1998). We have developed simulation based approach in Greene (2006). This paper builds on this framework to obtain a sample selection correction for the stochastic frontier model. We first show a surprisingly simple way to estimate the familiar normal-half normal stochastic frontier model (which has a closed form log likelihood) using maximum simulated likelihood. The next step is to extend the technique to a stochastic frontier modelwith sample selection. Here, the log likelihood does not exist in closed form, and has not previously been analyzed. We develop a simulation based estimation method for the stochastic frontier model. In an application that seems superficially obvious, the method is used to revisit the World Health Organization data [WHO (2000), Tandon et al. (2000)] where the sample partitioning is based on OECD membership. The original study pooled all 191 countries. The OECD members appear to be discretely different from therest of the sample. We examine the difference in a sample selection framework.

Stochastic Frontier, sample Selection, Simulation, Efficiency

Abstract:
Heckman's (1979) sample selection model has been employed in three decades of applications of linear regression studies. The formal extension of the method to nonlinear models, however, is of more recent vintage. A generic solution for nonlinear models is proposed in Terza (1998). We have developed simulation based approach in Greene (2006). This paper builds on this framework to obtain a sample selection correction for the stochastic frontier model. We first show a surprisingly simple way to estimate the familiar normal-half normal stochastic frontier model (which has a closed form log likelihood) using maximum simulated likelihood. The next step is to extend the technique to a stochastic frontier model with sample selection. Here, the log likelihood does not exist in closed form, and has not previously been analyzed. We develop a simulation based estimation method for the stochastic frontier model. In an application that seems superficially obvious, the method is used to revisit the World Health Organization data [WHO (2000), Tandon et al. (2000)] where the sample partitioning is based on OECD membership. The original study pooled all 191 countries. The OECD members appear to be discretely different from the rest of the sample. We examine the difference in a sample selection framework.

Stochastic Frontier, sample Selection, Simulation, Efficiency

Abstract:
We derive a model for consumer loan default and credit card expenditure. The default model is based on statistical models for discrete choice, in contrast to the usual procedure of linear discriminant analysis. The model is then extended to incorporate the default probability in a model of expected profit. The technique is applied to a large sample of applications and expenditure from a major credit card company. The nature of the data mandates the use of models of sample selection for estimation. The empirical model for expected profit produces an optimal acceptance rate for card applications which is far higher than the observed rate used by the credit card vendor based on the discriminant analysis.I am grateful to Terry Seaks for valuable comments on an earlier draft of this paper and to Jingbin Cao for his able research assistance. The provider of the data and support for this project has requested anonymity, so I must thank them as such. Their help and support are gratefully acknowledged. Participants in the applied econometrics workshop at New York University also provided useful commentary.

Abstract:
This paper derives the marginal effects for a conditional mean function in the bivariate probit model. A general expression is given for a model which allows for sample selectivity and heteroscedasticity. The computations are illustrated using microeconomic data from a study on creditscoring.

Marginal effects, Bivariate probit

Abstract:
The roughly 9.5 percent of all U.S. families that are without some type of transaction account (unbanked) are disproportionately represented by minorities. The unbanked often must rely on alternative ways to carry out basic financial transactions such as cashing payroll checks and paying bills. This study analyzes unique survey data and finds that a consumer's decision to patronize check-cashing businesses is jointly made with the decision to be unbanked. For the unbanked, these businesses are an important source for financial services.
Attributes that contribute to these decisions, however, vary for each racial/ethnic group. Latent preference effects are also observed to influence this joint decision for Blacks and Hispanics. These findings may explain in part why the provisions of the Debt Collection Improvement Act (DCIA) of 1996 have not been more successful in bringing unbanked federal benefits recipients into the financial mainstream.

Consumer participation in mainstream financial markets can improve their ability to build assets and create wealth, protect them from theft and discriminatory, predatory or unsavory lending practices, and may promote economic stability and vitality in the communities where they reside. By more fully understanding a consumer's financial decisions, policies can be better directed to improve the effectiveness of legislation such as the DCIA of 1996 in encouraging mainstream financial market participation.

unbanked, check-cashing business, currency exchanges, bivariate probit model

Abstract:
We present several modifications of the Poisson and negative binomial models for count data to accommodate cases in which the number of zeros in the data exceed what would typically be predicted by either model. The excess zeros can masquerade as overdispersion. We present a new test procedure for distinguishing between zero inflation and overdispersion. We also develop a model for sample selection which is analogous to the Heckman style specification for continuous choice models. An application is presented to a data set on consumer loan behavior in which both of these phenomena are clearly present.

Abstract:
This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well known variants of the negative binomial model (the NB1 and NB2 forms). We then propose some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these models. The lognormal model provides a versatile alternative specification that is more flexible (and more natural) than the log gamma form, and provides a platform for several â¬Stwo partâ¬? extensions, including zero inflation, hurdle and sample selection models. We also resolve some features in Hausman, Hall and Grilichesâ¬"s (1984) widely used panel data treatments for the Poisson and negative binomial models that appear to conflict with more familiar models of fixed and random effects. Finally, we consider a bivariate Poisson model that is also based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed methods using the data employed in one of the two aforementioned bivariate Poisson studies.

Poisson regression, Negative binomial, Panel data, Heterogeneity, Lognormal, Bivariate Poisson, Zero inflation, Two part model, Hurdle model

Abstract:
This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well known variants of the negative binomial model (the NB1 and NB2 forms). We then propose some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these models. The lognormal model provides a versatile alternative specification that is more flexible (and more natural) than the log gamma form, and provides a platform for several "two part" extensions, including zero inflation, hurdle and sample selection models. We also resolve some features in Hausman, Hall and Griliches's (1984) widely used panel data treatments for the Poisson and negative binomial models that appear to conflict with more familiar models of fixed and random effects. Finally, we consider a bivariate Poisson model that is also based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed methods using the data employed in one of the two aforementioned bivariate Poisson studies.

Poisson regression, Negative binomial, Panel data, Heterogeneity, Lognormal, Bivariate Poisson, Zero inflation, Two part model, Hurdle model

Abstract:
This paper surveys recently developed approaches to analyzing panel data with nonlinear models. We summarize a number of results on estimation of fixed and random effects models in nonlinear modelingframeworks such as discrete choice, count data, duration, censored data, sample selection, stochastic frontier and, generally, models that are nonlinear both in parameters and variables. We show thatnotwithstanding their methodological shortcomings, fixed effects are much more practical than heretofore reflected in the literature. For random effects models, we develop an extension of a random parametersmodel that has been used extensively, but only in the discrete choice literature. This model subsumes the random effects model, but is far more flexible and general, and overcomes some of the familiar shortcomings of the simple additive random effects model as usually formulated. Once again, the range of applications is extended beyond the familiar discrete choice setting. Finally, we draw together several strands of applications of a model that has taken a semiparametric approach to individual heterogeneity inpanel data, the latent class model. A fairly straightforward extension is suggested that should make this more widely useable by practitioners. Many of the underlying results already appear in the literature, but,once again, the range of applications is smaller than it could be.

Panel data, random effects, fixed effects, latent class, random parameters

Abstract:
This paper examines the effectiveness of multinational enterprises capital budgeting decisions as compared to the decisions of purely domestic enterprises. This is an important question because of multinationals role in allocating capital globally. Answering this question may also shed light on whether multinationals are indeed better managed than are purely domestic firms. We examine this question empirically using the deviation of a firm s estimated marginal Tobin s q from an appropriate benchmark as an indicator of effective resource allocation. We find that multinationals make more efficient capital budgeting decisions than do purely domestic firms. The result stems from multinational enterprises exercising greater restraint on over-investment, but is not due to looser liquidity constraints. In obtaining the result, we account for the impact of institutional ownership, managerial ownership, and managerial entrenchment. We also test whether multinationals greater capital budgeting efficiency might be due to their investment locations, since they might thereby be monitored by more agents and also may be more successful in resisting pressures from special interest groups and governments to adopt practices that are not consistent with firm value maximization. We do not find support for the monitoring and bargaining hypotheses. Our observations therefore suggest that multinationals may be intrinsically better managed firms than are purely domestic firms.

Abstract:
We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employed in one of the two aforementioned bivariate Poisson studies.

Poisson regression, Heterogeneity, Lognormal, Bivariate Poisson, Simulation

Abstract:
This essay examines the role of data and program-code archives in making economic research "replicable." Throughout science, replication of published results is recognized as an essential part of the scientific method. Yet, historically, both the "demand for" and "supply of" replicable results in economics has been minimal. Previous authors have interpreted this absence of replication as a market failure in which the rational choices of individual researchers do not achieve the same equilibrium as would an omnipotent social planner. In this equilibrium, "respect for the scientific method" is not sufficient to motivate either economists or editors of professional journals to ensure the replicability of published results. We enumerate the costs and benefits of mandatory data and code archives, and argue that the benefits far exceed the costs. Progress has been made since the gloomy assessment of Dewald, Thursby and Anderson some twenty years ago in the American Economic Review, but much remains to be done before empirical economics ceases to be a "dismal science" when judged by the replicability of its published results.

Data archives, replication, epistemology

Abstract:
The most commonly used approaches to parametric (stochastic frontier) analysis of efficiency in panel data, notably the fixed and random effects models, fail to distinguish between cross individual heterogeneity and inefficiency. This blending of effects is particularly problematic in the World Health Organization s (WHO) panel data set on health care delivery, which is a 191 country, five year panel. The wide variation in cultural and economic characteristics of the worldwide sample of countries produces a large amount of unmeasured heterogeneity in the data. Familiar approaches to inefficiency estimation mistakenly measure that heterogeneity as inefficiency. This study will examine a large number of recently developed alternative approaches to stochastic frontier analysis with panel data, and apply some of them to the WHO data. A more general, flexible model and several measured indicators of cross country heterogeneity are added to the analysis done by previous researchers. Results suggest that in these data, there is considerable evidence of heterogeneity that in other studies using the same data, has masqueraded as inefficiency. Our results differ substantially from those obtained by several earlier researchers.

Panel data, fixed effects, random effects, random parameters, technical efficiency, stochastic frontier, heterogeneity, health care

Abstract:
Received analyses based on stochastic frontier modeling with panel data have relied primarily on results from traditional linear fixed and random effects models. This paper examines extensions of these models that circumvent two important shortcomings of the existing fixed and random effects approaches. The conventional panel data stochastic frontier estimators both assume that technical or cost inefficiency is time invariant. In a lengthy panel, this is likely to be a particularly strong assumption. Second, as conventionally formulated, the fixed and random effects estimators force any time invariant cross unit heterogeneity into the same term that is being used to capture the inefficiency. Thus, measures of inefficiency in these models may be picking up heterogeneity in addition to or even instead of technical or cost inefficiency. In this paper, a true fixed effects model is extended to the stochastic frontier model using results that specifically employ the nonlinear specification. The random effects model is reformulated as a special case of the random parameters model that retains the fundamental structure of the stochastic frontier model. The techniques are illustrated through two applications, a large panel from the U.S. banking industry and a cross country comparison of the efficiency of health care delivery.

Panel data, fixed effects, random effects, random parameters, computation, Monte Carlo, maximum simulated likelihood, technical efficiency, stochastic frontier

Abstract:
Recent studies in econometrics and statistics include many applications of randomparameter models. There is some ambiguity in how estimation results in these modelsare interpreted. The underlying structural parameters are often not informative about the statistical relationship of interest. As a result, standard significance tests of structural parameters in random parameter models do not necessarily indicate the presence or absence of a significant relationship among the model variables. This note offers some suggestions on how to interpret and use the results of estimation of a general form of random parameter model and how simulation based estimates of parameters in conditional distributions can be used to examine the influence of model covariates.

Panel data, random effects, random parameters, maximum simulated likelihood, posterior mean, posterior variance, marginal effects, confidence interval

Abstract:
Recent studies in econometrics and statistics include many applications of random parameter models. The underlying structural parameters in these models are often not directly informative about the statistical relationship of interest. As a result, standard significance tests of structural parameters in random parameter models do not necessarily indicate the presence or absence of a significant relationship among the model variables. This note offers a suggestion on how to examine the results of estimation of a general form of random parameter model. We also extend results on computing individual level parameters in a random parameters setting and show how simulation based estimates of parameters in conditional distributions can be used to examine the influence of model covariates (marginal effects) at an individual level

Panel data, random effects, random parameters, maximum simulated likelihood, conditional mean, conditional variance, marginal effects, confidence interval

Abstract:
The nonlinear fixed effects models in econometrics has often been avoided for two reasons one practical, one methodological. The practical obstacle relates to the difficulty of estimating nonlinear models with possibly thousands of coefficients. In fact, in a large number of models of interest to practitioners, estimation of the fixed effects model is feasible even in panels with very large numbers of groups. The more difficult, methodological question centers on the incidental parameters problem that raises questions about the statistical properties of the estimator. There is very little empirical evidence on the behavior of the fixed effects estimator. In this note, we use Monte Carlo methods to examine the small sample bias in the binary probit and logit models, the ordered probit model, the tobit model, the Poisson regression model for count data and the exponential regression model for a nonnegative random variable. We find three results of note: A widely accepted result that suggests that the probit estimator is actually relatively well behaved appears to be incorrect. Perhaps to some surprise, the tobit model, unlike the others, appears largely to be unaffected by the incidental parameters problem, save for a surprising result related to the disturbance variance estimator. Third, as apparently unexamined previously, the estimated asymptotic estimators for fixed effects estimators appear uniformly to be downward biased.

Panel data, fixed effects, computation, Monte Carlo

Abstract:
We detail the basic theory for regression models in which dependent variables are censored or underlying distributions are truncated. The model is extended to models for counts, sample selection models, and models hazard models for duration data. Entry level theory is presented for the practitioner. We then describe a few of the recent, frontier developments in theory and practice.

Censoring, Truncation, Maximum likelihood, Attenuation, Regression, Bias, Sample selection, Panel data, Semiparametric

Abstract:
Obesity is a major risk factor for several diseases including diabetes, heart disease and stroke. Increasing rates of obesity internationally are set to cost health systems increasing resources. In the US a conservative estimate puts resources already spent on obesity at $120 billion annually. Given scarce health care resources it is important that categorisation of the overweight and obese is accurate, such that health promotion and public health targeting can be as effective as possible. To test the accuracy of current categorisation within the overweight and obese we extend the discrete data latent class literature by explicitly defining a latent variable for class membership as a function of both observables and unobservables, thereby allowing the equations defining class membership and observed outcomes to be correlated. The procedure is then applied to modeling observed obesity outcomes, based upon an underlying ordered probit equation. We find the standard boundaries for converting.

Abstract:
We present a correction for sample selectively in the poisson regression model for count data. The model is similar to that devised by Heckman for the linear regression model. Estimation by a two step method is suggested using nonlinear least squares at the second step.The model described here was presented in Greene(1994). Terza(1995) describes an alternative approach that has more orthodox specification of the regression function. We show in this note that Terza's approach is essentially the same as Greene's.

Abstract:
Random effects estimates using panel data for 42 colleges and universities over 16 years reveal that the economics faculty size of universities offering a Ph.D. in economics is determined primarily by the long-run average number of Ph.D. degrees awarded annually; the number of full-time faculty increases at almost a one-for-one pace as the average number of Ph.D.s grows. Faculty size at Ph.D. granting universities is largely unresponsive to changes in the number of undergraduate economics degrees awarded at those institutions. In contrast, faculty size at colleges where a bachelor's is the highest degree awarded is responsive to the average number of economics degrees awarded annually, growing by about one for each additional eleven graduating economics majors.

student body, faculty size, Ph.D. degrees, bachelor degrees

Abstract:
The normal-gamma stochastic frontier model was proposed in Greene (1990) and Beckers and Hammond (1987) as an extension of the normalexponential proposed in the original derivations of the stochastic frontier byAigner, Lovell, and Schmidt (1977). The normal-gamma model has the virtue ofproviding a richer and more flexible parameterization of the inefficiencydistribution in the stochastic frontier model than either of the canonical forms,normal-half normal and normal-exponential. However, several attempts to operationalize the normal-gamma model have met with very limited success, as the log likelihood is possesed of a significant degree of complexity. This note will propose an alternative approach to estimation of this model based on the method of simulated maximum likelihood estimation as opposed to the received attempts which have approached the problem by direct maximization.

Abstract:
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.

Panel probit model, Multivariate probit, GMM, Simulated likelihood, Latent class, Marginal effects

Abstract:
We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employed in one of the two aforementioned bivariate Poisson studies.

Poisson regression., Heterogeneity, Lognormal, Bivariate Poisson, Simulation

Abstract:
This paper explores the application of several panel data models in measuring productive efficiency of the electricity distribution sector. Stochastic Frontier Analysis has been used to estimate the cost-efficiency of 59 distribution utilities operating over a nine-year period in Switzerland. The estimated coefficients and inefficiency scores are compared across three different panel data models. The results indicate that individual efficiency estimates are sensitive to the econometric specification of unobserved firm-specific heterogeneity. This paper shows that alternative panel models such as the 'true' random effects model proposed by Greene (2005) could be used to explore the possible impacts of unobserved firm-specific factors on efficiency estimates. When these factors are specified as a separate stochastic term, the efficiency estimates are substantially higher suggesting that conventional models could confound efficiency differences with other unobserved variations among companies. On the other hand, refined specification of unobserved heterogeneity might lead to an underestimation of inefficiencies by mistaking potential persistent inefficiencies as external factors. Given that specification of inefficiency and heterogeneity relies on non-testable assumptions, there is no conclusive evidence in favour of one or the other specification. However, this paper argues that alternative panel data models along with conventional estimators can be used to obtain approximate lower and upper bounds for companies' efficiency scores.

Abstract:
The nonlinear fixed-effects model has two shortcomings, one practical and one methodological. The practical obstacle relates to the difficulty of computing the MLE of the coefficients of non-linear models with possibly thousands of dummy variable coefficients. In fact, in many models of interest to practitioners, computing the MLE of the parameters of fixed effects model is feasible even in panels with very large numbers of groups. The result, though not new, appears not to be well known. The more difficult, methodological issue is the incidental parameters problem that raises questions about the statistical properties of the ML estimator. There is relatively little empirical evidence on the behaviour of the MLE in the presence of fixed effects, and that which has been obtained has focused almost exclusively on binary choice models. In this paper, we use Monte Carlo methods to examine the small sample bias of the MLE in the tobit, truncated regression and Weibull survival models as well as the binary probit and logit and ordered probit discrete choice models. We find that the estimator in the continuous response models behaves quite differently from the familiar and oft cited results. Among our findings are: first, a widely accepted result that suggests that the probit estimator is actually relatively well behaved appears to be incorrect; second, the estimators of the slopes in the tobit model, unlike the probit and logit models that have been studied previously, appear to be largely unaffected by the incidental parameters problem, but a surprising result related to the disturbance variance estimator arises instead; third, lest one jumps to a conclusion that the finite sample bias is restricted to discrete choice models, we submit evidence on the truncated regression, which is yet unlike the tobit in that regardit appears to be biased towards zero; fourth, we find in the Weibull model that the biases in a vector of coefficients need not be in the same direction; fifth, as apparently unexamined previously, the estimated asymptotic standard errors for the ML estimators appear uniformly to be downward biased when the model contains fixed effects. In sum, the finite sample behaviour of the fixed effects estimator is much more varied than the received literature would suggest.

Panel data, fixed effects, computation, Monte Carlo, tobit, truncated regression, bias, finite sample

Abstract:
This paper introduces a four-state failure model to depict a wider range of distress scenarios that public companies typically face in the real world. We use a multinomial error component logit model to analyse firm failure, a major advance on the modelling techniques used in previous research. The error component logit model, being an extension of the more familiar mixed logit model, relaxes several questionable statistical assumptions associated with standard models. Using a sample of Australian firms we provide an interpretative illustration of the error component logit model and contrast its behavioural performance with the standard logit model widely used in previous research.

Abstract:
We further examine the interaction effect in nonlinear models that has recently been discussed by Ai and Norton (2003). Statistical tests about partial effects and interaction terms are not necessarily informative in the context of the estimated model. We suggest more useful ways that do not involve statistical testing to examine the interaction effect in binary choice models.

Interaction effect, Interaction term, Partial effect, Probit, Logit, Nonlinear Models