Abstract
This paper shows that the LM test for the validity of the logistic distribution commonly assumed in Binary Dependent Variable Models (i.e., the logit model) developed by Poirier (1980) can be obtained from a simple artificial regression. Monte Carlo simulations examine the small sample behaviour of the test statistic in comparison to the Information Matrix test for the logit model developed by Orme (1988) and Davidson and MacKinnon (1989), and two versions of the Reset test for limited dependent variable models suggested by Pagan and Vella (1989). Our results suggest that the LM test compares favourably under the null. The tests also appear to have varying power properties against different alternatives which suggests that they should all be used in investigating the validity of the logit model.
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References
Abramovitz M, Segun IA (1964) Handbook of Mathematical Functions. New York, Dover
Arabmazar A, and Schmidt P (1982) An Investigation into the Robustness of the Tobit Estimator to Non-Normality. Econometrica 50: 1055–1063
Bera AK, Jarque CM, Lee LF (1984) Testing the Normality Assumption in Limited Dependent Variable Models. International Economic Review 25: 563–578
Chesher A (1984) Testing for Neglected Heterogeneity. Econometrica 52: 865–872
Chesher A, Spady R (1991) Asymptotic Expansions of the Information Matrix Test Statistic. Econometrica 59: 787–815
Davidson R, MacKinnon JG (1983) Small Sample Properties of Alternative Forms of the Lagrange Multiplier Test. Economic Letters: 12: 269–275
Davidson R, MacKinnon JG (1984). Convenient Specification Tests for Logit and Probit Models. Journal of Econometrics 25: 241–262
Davidson R, MacKinnon JG (1987) Testing for Consistency Using Artificial Regressions. Discussion Paper No. 687, Queen's University
Davidson R, MacKinnon JG (1989) Testing for Consistency Using Artificial Regressions. Econometric Theory 5: 363–384
Fry T (1987) Some Aspects of a Tobit Model. Discussion Paper No. ES 181. Department of Economics, University of Manchester
Gabler S, Laisney F, Lechner, M (1991), Semi-Nonparametric Maximum Likelihood Estimation of Binary Choice Models with an Application to Labour Force Participation. Discussion Paper No. 430-90. University of Mannheim
Gourireoux C, Monfort A (1991) Simulation Based Inference in Models with Heterogeneity. Annales D'Economie et de Statistique 20/21: 69–107
Klein R, Spady R (1987) An Efficient Semiparametric Estimator for Discrete Choice Models. Mimeo, Bellcore
Lancaster T (1990) The Econometric Analysis of Transition Data Econometric Society Monograph, No. 17. Cambridge University Press
Laisney F, Lechner M, Strom S (1991) Lessons from Specification Tests for a Labour Supply Model. Annales D'Economie et de Statistique 20/21: 193–217
Lechner M (1991) Testing Logit Models in Practice. Discussion Paper No. 408-90. University of Mannheim
Lechner M (1991a) Testing Logit Models in Practice. Empirical Economics 16: 177–198
Manski C (1975) Maximum Score Estimation of the Stochastic Utility Model of Choice. Journal of Econometrics 3: 205–28
Newey W (1985) Maximum Likelihood Specification Testing and Conditional Moment Tests. Econometrica 53: 1047–1070
Orme C (1988) The Calculation of the Information Matrix Test for Binary Data Models. The Manchester School 61: 370–376
Orme C (1990) The Small-Sample Performance of the Information-Matrix Test. Journal of Econometrics 46: 309–331
Pagan A, Vella F (1989) Diagnostic Tests for Models Based on Individual Data: A Survey. Journal of Applied Econometrics Supplement 4: S29-S59
Poirier DJ (1980) A Lagrange Multiplier Test for Skewness in Binary Logit Models. Economics Letters 5: 141–143
Smith RJ (1989) On the Use of Distributional Misspecification Checks in Limited Dependent Variable Models. The Economic Journal 99: 178–192
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Work on this paper began at Queen's University, Ontario. I am grateful to James MacKinnon, Michael Lechner, Stephen Pudney, Hashem Pesaran, Chris Orme, two anonymous referees and especially Richard Smith for useful comments and suggestions. Financial support from Queen's, the AUCC and the DAE is gratefully acknowledged. All errors are mine.