Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter January 5, 2015

Spatial Errors in Count Data Regressions

Marinho Bertanha and Petra Moser


Count data regressions are an important tool for empirical analyses ranging from analyses of patent counts to measures of health and unemployment. Along with negative binomial, Poisson panel regressions are a preferred method of analysis because the Poisson conditional fixed effects maximum likelihood estimator (PCFE) and its sandwich variance estimator are consistent even if the data are not Poisson-distributed, or if the data are correlated over time. Analyses of counts may however also be affected by correlation in the cross-section. For example, patent counts or publications may increase across related research fields in response to common shocks. This paper shows that the PCFE and its sandwich variance estimator are consistent in the presence of such dependence in the cross-section – as long as spatial dependence is time-invariant. We develop a test for time-invariant spatial dependence and provide code in STATA and MATLAB to implement the test.

JEL Classifications: C10; C12; C23; O31; O33

Corresponding author: Marinho Bertanha, Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA, 94305, USA, E-mail:


We thank Han Hong, Guido Imbens, Aprajit Mahajan, and Scott Stern for helpful conversations and comments. Moser gratefully acknowledges support through NSF CAREER grant 1151180; Bertanha gratefully acknowledges the financial support received as a B.F. Haley and E.S. Shaw Fellow from the Stanford Institute for Economic Policy Research.


Andersen, E. B. 1972. “The Numerical Solution of a Set of Conditional Estimation Equations.” Journal of the Royal Statistical Society. Series B (Methodological) 34 (1): 42–54.10.1111/j.2517-6161.1972.tb00887.xSearch in Google Scholar

Azoulay, P., J. G. Zivin, and J. Wang. 2010. “Superstar Extinction.” The Quarterly Journal of Economics 125 (2): 549–589.10.1162/qjec.2010.125.2.549Search in Google Scholar

Borjas, G. J., and K. B. Doran. 2012. “The Collapse of the Soviet Union and the Productivity of American Mathematicians.” The Quarterly Journal of Economics 127 (3): 1143–1203.10.1093/qje/qjs015Search in Google Scholar

Cameron, A. C., and P. K. Trivedi. 2005. Microeconometrics: Methods and Applications. Cambridge University Press.10.1017/CBO9780511811241Search in Google Scholar

Conley, T. G. 1999. “Gmm Estimation with Cross Sectional Dependence.” Journal of Econometrics 92 (1): 1–45.10.1016/S0304-4076(98)00084-0Search in Google Scholar

Furman, J. L., and S. Stern. 2011. “Climbing Atop the Shoulders of Giants: The Impact of Institutions on Cumulative Research.” The American Economic Review 101 (5): 1933–1963.10.1257/aer.101.5.1933Search in Google Scholar

Gourieroux, C., A. Monfort, and A. Trognon. 1984. “Pseudo Maximum Likelihood Methods: Theory.” Econometrica 52 (3): 681–700.10.2307/1913471Search in Google Scholar

Hall, B. H., Z. Griliches, and J. Hausman. 1986. “Patents and R&D: Is there a Lag?” International Economic Review 27 (2): 265–283.10.2307/2526504Search in Google Scholar

Hausman, J., B. H. Hall, and Z. Griliches. 1981. “Econometric Models for Count Data with an Application to the Patents-R&D Relationship.” NBER Technical Working Paper No. 17.Search in Google Scholar

Hausman, J., B. H. Hall, and Z. Griliches. 1984. “Econometric Models for Count Data with an Application to the Patents-R&D Relationship.” Econometrica 52 (4): 909–938.10.2307/1911191Search in Google Scholar

Jaffe, A. B., M. Trajtenberg, and R. Henderson. 1993. “Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations.” The Quarterly Journal of Economics 108 (3): 577–598.10.2307/2118401Search in Google Scholar

Kogan, L., D. Papanikolaou, A. Seru, and N. Stoffman. 2012. “Technological Innovation, Resource Allocation, and Growth.” NBER working paper 17769.10.3386/w17769Search in Google Scholar

Marshall, A. Principles of Economics. MacMillan, London, 1890.Search in Google Scholar

Moser, P., A. Voena, and F. Waldinger. 2014. “German-Jewish Emigres and U.S. Invention.” Forthcoming in the American Economic Review.10.3386/w19962Search in Google Scholar

Moser, P., and A. Voena. 2012. “Compulsory Licensing: Evidence from the Trading with the Enemy Act.” The American Economic Review 102 (1): 396–427.10.1257/aer.102.1.396Search in Google Scholar

Williams, H. L. 2013. “Intellectual Property Rights and Innovation: Evidence from the Human Genome.” Journal of Political Economy 121 (1): 1–27.10.1086/669706Search in Google Scholar

Wooldridge, J. M. 1999. “Distribution-Free Estimation of Some Nonlinear Panel Data Models.” Journal of Econometrics 90 (1): 77–97.10.1016/S0304-4076(98)00033-5Search in Google Scholar

Supplemental Material

The online version of this article (DOI: 10.1515/jem-2014-0015) offers supplementary material, available to authorized users.

Published Online: 2015-1-5
Published in Print: 2016-1-1

©2016 by De Gruyter