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Handbook of Regional Science pp 1–21Cite as

Instrumental Variables/Method of Moments Estimation

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Abstract

The chapter discusses generalized method of moments (GMM) estimation methods for spatial models. Much of the discussion is on GMM estimation of Cliff-Ord-type models where spatial interactions are modeled in terms of spatial lags. The chapter also discusses recent developments on GMM estimation from data processes which are spatially α-mixing.

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Notes

  1. 1.

    Lee (2004) gives, to the best of our knowledge, first formal results for the maximum likelihood estimator of a spatial-autoregressive model. The maintained assumptions are similar to those introduced in Kelejian and Prucha (1998, 1999).

  2. 2.

    Let u = [u1, …, un]′, then the above moment condition can be rewritten as E[n−1u′Aqu] = tr[n−1AqEuu′] = n−1σ2tr(Aq) = 0, since under the maintained assumptions Euu′ = σ2In.

  3. 3.

    Recall, e.g., that there are more than 33,000 zip codes in the U.S.

  4. 4.

    To obtain the estimator of Kelejian and Prucha (1998, 1999) the matrix A1 has to be scaled by v = 1/[1 + [n−1tr(M′M)]2]. Of course, the scaling factor only comes into play if the moment conditions are not optimally weighted, as was the case in the early literature.

  5. 5.

    Lin and Lee (2010) also allow for heteroskedastic innovations for model (22) with ρ0 = 0.

  6. 6.

    For an incomplete list of empirical work see, e.g., Kelejian and Prucha (2010).

  7. 7.

    Quasi-ML and Bayesian MCMC methods are not covered by this review. For recent papers employing those methods within the context of dynamic panel data models, see, e.g., Yu et al. (2008) and Parent and LeSage (2012), respectively. There is also an important literature on testing for spatial dependence in a panel context, which is not part of this review. For a partial review of this literature see, e.g., Baltagi (2011).

  8. 8.

    In the following vecD (A) refers to the column vector containing the diagonal elements of the matrix A.

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Acknowledgments

I would like to thank James LeSage and Pablo Salinas Macario for their helpful comments on this chapter.

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Authors and Affiliations

  1. Department of Economics, University of Maryland, College Park, MD, USA

    Ingmar R. Prucha

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  1. Ingmar R. Prucha
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Correspondence to Ingmar R. Prucha .

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Editors and Affiliations

  1. Institute for Economic Geography and GIScience, Vienna University of Economics and Business, Vienna, Austria

    Manfred M. Fischer

  2. and Business Administration Department of Spatial Economics, Free University Faculty of Economics, Amsterdam, The Netherlands

    Peter Nijkamp

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Prucha, I.R. (2019). Instrumental Variables/Method of Moments Estimation. In: Fischer, M., Nijkamp, P. (eds) Handbook of Regional Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36203-3_90-1

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  • DOI: https://doi.org/10.1007/978-3-642-36203-3_90-1

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  • Print ISBN: 978-3-642-36203-3

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