In many cases, only an unbalanced panel data set with some observations missing at random is available. This note derives a Cliff and Ord test for spatially autocorrelated disturbances for such data. In a small Monte Carlo simulation exercise, the performance of the proposed test is similar to its balanced counterpart. In almost all simulation experiments, the test is properly sized. Naturally, the lower the power of the test, the higher the share of missing data.
AnselinL.Le GalloJ.JayetH.. 2008. “Spatial Panel Econometrics.” In The Econometrics of Panel Data: Fundamentals and Recent Developments in Theory and Practice, edited by L. Mátyás and P. Sevestre, chapter 19. Berlin, Heidelberg, Germany: Springer: 625–660.
4.
BaltagiB. H.2008. Econometric Analysis of Panel Data. 4th ed. Chichester, UK: John Wiley.
5.
BaltagiB.H.LongLiu. 2012. “Random Effects, Fixed Effects and Hausman's Test for the Generalized Spatial Panel Data Regression Model”. Working paper WP # 0029ECO-661-2012. The University of Texas at San Antonio, College Business.
6.
BaltagiB. H.SongS. H.KohW.. 2003. “Testing Panel Data Models with Spatial Error Correlation.”Journal of Econometrics117:123–50.
7.
BurridgeP.1980. “On the Cliff-Ord Test for Spatial Correlation.”Journal of the Royal Statistical Society Series B (Methodological).” 42:107–8.
8.
CornwellC.SchmidtP.. 1992. “Models for Which the MLE and the Conditional MLE Coincide.”Empirical Economics17:67–75.
9.
HainingR.GriffithD.BennettD.. 1989. “Maximum Likelihood with Missing Spatial Data and with an Application to Remotely Sensed Data.”Communications in Statistics—Theory and Methods18:1875–94.
10.
KapoorM.KelejianH. H.PruchaI. R.. 2007. “Panel Data Models with Spatially Correlated Error Components.”Journal of Econometrics140:97–130.
11.
KelejianH. H.PruchaI. R.. 2001. “On the Asymptotic Distribution of the Moran I Test with Applications.”Journal of Econometrics104:219–57.
12.
KelejianH. H.PruchaI. R.. 2010a. “Spatial Models with Spatially Lagged Dependent Variables and Incomplete Data.”Journal of Geographical Systems12:241–57.
13.
KelejianH. H.PruchaI. R.. 2010b. “Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances.”Journal of Econometrics157:53–67.
14.
KhatriC. G.1968. “Some Results for the Singular Normal Multivariate Regression Models.”Sankhya: The Indian Journal of Statistics Series A30:267–80.
15.
KieferN. M.1980. “Estimation of Fixed Effect Models for Time Series of Cross-Sections with Arbitrary Intertemporal Covariance.”Journal of Econometrics14:195–202.
16.
LeeL.YuJ.. 2010a. “Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects.”Journal of Econometrics154:165–85.
17.
LeeL.YuJ.. 2010b. “Some Recent Developments in Spatial Panel Data Models.”Regional Science and Urban Economics40:255–71.
18.
LeSageJ. P.PaceR. K.. 2004. “Models for Spatially Dependent Missing Data.”Journal of Real Estate Finance and Economics29:233–54.
19.
LittleR. J. A.RubinD. B.. 2002. Statistical Analysis with Missing Data. 2nd ed. New Jersey: John Wiley.
20.
MagnusJ. R.NeudeckerH.. 2007. Matrix Differential Calculus with Applications in Statistics and Econometrics. 2nd ed. New York: John Wiley.
21.
MartinR. J.1984. “Exact Maximum Likelihood for Incomplete Data from a Correlated Gaussian Process.”Communications in Statistics—Theory and Methods13:1275–88.
22.
MoranP.1950. “Notes on Continuous Stochastic Phenomena.”Biometrika37:17–23.
23.
MutlJ.PfaffermayrM.. 2010. “A Note on the Cliff and Ord Test for Spatial Correlation n Panel Models.”Economics Letters108:225–28.
24.
NicolettiC.2006. “Nonresponse in Dynamic Panel Data Models.”Journal of Econometrics132:461–89.
25.
RaoR. C.1973. Linear Statistical Inference and its Applications. 2nd ed. New Jersey: John Wiley.
26.
RubinD. B.1976. “Inference and Missing Data.”Biometrika63:581–92.