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  • "Estimation and Inference in Spatial Models with Dominant Units", by M. Hashem Pesaran and Cynthia Fan Yang,, forthcoming in Journal of Econometrics, April 2020

    Abstract: In spatial econometrics literature estimation and inference are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of units, n, in the network. This paper relaxes this restriction and allows for one or more units to have pervasive effects in the network. The linear-quadratic central limit theorem of Kelejian and Prucha (2001) is generalized to allow for such dominant units, and the asymptotic properties of the GMM estimators are established in this more general setting. A new bias-corrected method of moments (BMM) estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both cases of homoskedastic and heteroskedastic errors are considered and the associated estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of GMM and BMM estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre-and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input-output tables, despite the evidence of dominant sectors being present in the US economy.
    JEL Classifications: C13, C21, C23, R15.
    Key Words: SAR models, central limit theorems for linear-quadratic forms, dominant units, heteroskedastic errors, bias-corrected method of moments, US input-output tables, capital share
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  • "Estimation and Inference for Spatial Models with Heterogeneous Coefficients: An Application to U.S. House Prices", by Michele Aquaro, Natalia Bailey and M. Hashem Pesaran, forthcoming in Journal of Applied Econometrics, CESifo WP Series No. 7542. This paper was previously titled “Quasi-maximum likelihood estimation of spatial models with heterogeneous coefficient” (CESifo WP Series No. 5428)

    Abstract: This paper considers the estimation and inference of spatial panel data models with heterogeneous spatial lag coefficients, with and without weakly exogenous regressors, and subject to heteroskedastic errors. A quasi maximum likelihood (QML) estimation procedure is developed and the conditions for identification of the spatial coefficients are derived. The QML estimators of individual spatial coefficients, as well as their mean group estimators, are shown to be consistent and asymptotically normal. Small sample properties of the proposed estimators are investigated by Monte Carlo simulations and results are in line with the paper's key theoretical findings even for panels with moderate time dimensions and irrespective of the number of cross section units. A detailed empirical application to U.S. house price changes during the 1975-2014 period shows a significant degree of heterogeneity in spatio-temporal dynamics over the 338 Metropolitan Statistical Areas considered.
    JEL Classifications: C21, C23
    Key Words: Spatial panel data models, heterogeneous spatial lag coefficients, identification, quasi maximum likelihood (QML) estimators, house price changes, Metropolitan Statistical Areas.
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  • "Detection of Units with Pervasive Effects in Large Panel Data Models", by George Kapetanios, M. Hashem Pesaran and Simon Reese, forthcoming in Journal of Econometrics, CESifo Working Papers No. 7401, May 2020

    Abstract: The importance of units that influence a large number of other units in a network has become increasingly recognized in the literature. In this paper we propose a new method to detect such pervasive units by basing our analysis on unit-specific residual error variances subject to suitable adjustments due to the multiple testing issues involved. Accordingly, a sequential multiple testing (SMT) procedure is proposed, which allows identification of pervasive units (if any) without a priori knowledge of the interconnections amongst cross-section units or availability of a short list of candidate units to search over. The proposed method is applicable even if the cross section dimension exceeds the time series dimension, and most importantly it could end up with none of the units selected as pervasive when this is in fact the case. The SMT procedure exhibits satisfactory small-sample performance in Monte Carlo simulations and compares well relative to existing approaches. We apply the SMT detection method to sectoral indices of U.S. industrial production, U.S. house price changes by states, and the rates of change of real GDP and real equity prices across the world's largest economies.
    JEL Classifications: C18, C23, C55.
    Key Words: Pervasive units, factor models, systemic risk, multiple testing, sequential procedure, cross-sectional dependence.
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  • "General Diagnostic Tests for Cross-sectional Dependence in Panels", by M. Hashem Pesaran, forthcoming in Empirical Economics, May 2020, Volume 35, Issue 3, pp. 294-314.

    Abstract: This paper proposes simple tests of error cross-sectional dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short T and large N. The proposed tests are based on the average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel and can be used to test for cross-sectional dependence of any fixed order p, as well as the case where no a priori ordering of the cross-sectional units is assumed, referred to as CD(p) and CD tests, respectively. Asymptotic distribution of these tests is derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed N and T and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and, as predicted by the theory, they are quite robust to the presence of unit roots and structural breaks. The use of the CD test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross-dependence in output innovations across many countries and regions in the World.
    JEL Classifications: C12, C13, C33
    Key Words: Cross-sectional dependence; Spatial dependence; Diagnostic tests; Dynamic heterogenous panels; Empirical growth.
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