Abstract
Heteroscedasticity and autocorrelation typically are assumed to be absent in econometric models. Linear regression models are forgiving if these assumptions fail: ordinary least squares (OLS) estimates remain consistent if errors are not homoscedastic or are autocorrelated. Estimators for models with discrete data are not always as forgiving as OLS. For example, the Standard probit estimator continues to provide consistent estimates when error terms are autocorrelated, but the estimates are inconsistent as well as inefficient when errors have non-constant variances. Failure of the homoscedasticity assumption also leads to inconsistent estimates in such common models as tobit and logit. Thus, heteroscedasticity is a serious problem in models with discrete data.
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References
Anderson, J.E., Estimating Generalized Urban Density Functions, Journal of Urban Economics18, 1–10, 1985.
Anselin, L., Spatial Econometrics: Methods and Models, Dordrecht: Kluwer Academic Publishers, 1988.
Anselin, L., Some Robust Approaches to Testing and Estimation in Spatial Regression Analysis, Regional Science and Urban Economics, 20, 141–163, 1990a.
Anselin, L., Spatial Dependence and Spatial Structural Instability in Applied Regression Analysis, Journal of Regional Science, 30, 185–207, 1990b.
Anselin, L., Spatial Dependence and Spatial Heterogeneity: Model Specification Issues in the Spatial Expansion Paradigm, in: J.P. Jones III and E. Casetti (eds.), Applications ofthe Expansion Method, New York: Routledge, 1992.
Anselin, L. and D.A. Griffith, Do Spatial Effects Really Matter in Regression Analysis?, Papers ofthe Regional Science Association, 65, 11–34, 1988.
Avery, R.B., L.P. Hansen and V.J. Hotz, Multiperiod Probit Models and Orthogonality Condition Estimation, International Economic Review, 24, 21–35, 1983.
Besag, J.E., Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data, Journal ofthe Royal Statistical Society, Series B, 34, 75–83, 1972.
Breusch, T. and A. Pagan, A Simple Test for Heteroscedasticity and Random Coefficient Variation, Econometrica, 47, 1287–1294, 1979.
Case, A., Neighborhood Influence and Technological Change, Regional Science and Urban Economics, 22, 491–508, 1992.
Casetti, E., Generating Models by the Spatial Expansion Method: Applications to Geographical Research, Geographical Analysis, 4, 81–91, 1972.
Davidson, R. and J.G. MacKinnon, Convenient Specification Tests for Logit and Probit Models, Journal of Econometrics, 25, 241–262, 1984.
Dubin, R.A., Estimation of Regression Coefficients in the Presence of Spatially Autocorrelated Error Terms, Review of Economics and Statistics, 70, 466–474, 1988.
Dubin, R.A., Spatial Autocorrelation and Neighborhood Quality, Regional Science and Urban Economics, 22, 433–452, 1992.
Engle, R.F., D.F. Hendry and D. Trumble, Small-Sample Properties of ARCH Estimators and Tests, Canadian Journal of Economics, 18, 66–93, 1985.
Ericsson, N.R., Post-Simulation Analysis of Monte Carlo Experiments: Interpreting Pesaran’s Study of Non-Nested Hypothesis Test Statistics, Review of Economic Studies, 53, 691–707, 1986.
Griffith, D.A., Modelling Urban Population Density in a Multicentered City, Journal of Urban Economics, 9, 298–310, 1981.
Griffiths, W.E. and K. Surekha, A Monte Carlo Evaluation of the Power of Some Tests for Heteroscedasticity, Journal of Econometrics, 31, 219–231, 1986.
Haining, R., Estimating Spatial Means with an Application to Remotely Sensed Data, Communications in Statistics, 17, 573–597, 1988.
Heckman, J.J., The Common Structure of Statistical Models of Truncation, Sample Selection, and Limited Dependent Variables and a Simple Estimator for such Models, Annals of Economic and Social Measurement, 5, 475–492, 1976.
Hendry, D.F., Monte Carlo Experimentation in Econometrics, in: Z. Griliches and M.D. Intriligator (eds.), Handbook of Econometrics, vol. II, Amsterdam: North- Holland, 1984.
Johnston, J., Econometric Methods, New York: McGraw-Hill, 1984.
Jones III, J.P. and E. Casetti, Applications of the Expansion Method, New York: Routledge, 1992.
Judge, G.G., R.C. Hill, W.E. Griffiths, H. Lütkepohl and T.C. Lee, Introduction to the Theory and Practice of Econometrics, New York: John Wiley & Sons, 1988.
Lahiri, K. and R.P. Numrich, An Econometric Study on the Dynamics of Urban Spatial Structure, Journal of Urban Economics, 14, 55–79, 1983.
Maddala, G.S., Limited-Dependent and Qualitative Variables in Econometrics, New York: Cambridge University Press, 1983.
Maddala, G.S., Introduction to Econometrics, New York: Macmillan Publishing Company, 1988.
McMillen, D.P., Probit with Spatial Autocorrelation, Journal of Regional Science, 32, 335–348, 1992.
Mizon, G.E. and D.F. Hendry, An Empirical Application and Monte Carlo Analysis of Tests of Dynamic Specification, Review of Economic Studies, 47, 21–45, 1980.
Poirier, D.J. and P.A. Ruud, Probit with Dependent Observations, Review of Economic Studies, 55, 593–614, 1988.
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McMillen, D.P. (1995). Spatial Effects in Probit Models: A Monte Carlo Investigation. In: Anselin, L., Florax, R.J.G.M. (eds) New Directions in Spatial Econometrics. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79877-1_9
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