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Empirical Economics

Erschienen in:

30.01.2023

Spatial panel simultaneous equations models with error components

verfasst von: Marius C. O. Amba, Taoufiki Mbratana, Julie Le Gallo

Erschienen in: Empirical Economics | Ausgabe 3/2023

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Abstract

This paper develops limited and full information estimators for a simultaneous panel data model with spatial lags on the dependent variables and spatially autocorrelated error processes in the form of spatial autoregressive or spatial moving average processes. The spatial error components are estimated with various generalized moment procedures. Monte Carlo experiments show that the proposed estimators outperform traditional estimators and also provide results on the impact of misspecifying the error process. We illustrate the various estimators on an empirical example pertaining to competition in current and capital expenditure between French municipalities in the capital region of Ile-de-France.

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In the paper, we use the abbreviations GM and GMM to, respectively, refer to the generalized moments estimator (for stochastic components) proposed by Kelejian and Prucha (1998) and the generalized method of moments estimator (for structural parameters) proposed by Lee (2007a).

A list of frequently used notations is provided in Appendix A.1 for easy reference.

In this paper, we assume that the system involves the same weight matrix across equations. This also seems to be the typical specification in applied works (Gebremariam et al. 2011; Jeanty et al. 2010; Lambert et al. 2014).

The weight \(\omega _{ij}\) represents the proximity between cross-sectional units i and j. The notion of proximity is not limited to the geographical sense. Indeed, it can be economic, technology, or social proximity, although endogeneity issues might arise when dealing with non-geographic weight matrices.

Note that since \({\textbf{A}}\) is assumed to be diagonal, the specification relates the disturbance vector in the l-th equation only to its own spatial lag. Allowing \({\textbf{A}}\) to be nondiagonal is beyond the scope of our paper.

Matrices \(Q_0\) and \(Q_1\) are standard transformation matrices used in the error component literature, with the appropriate adjustments implied by our adopted ordering of the data; compared to, e.g., Baltagi (2008). They are symmetric, idempotent and orthogonal to each other. Furthermore, \(Q_0+Q_1=I_{nT}\) and \(\text {tr}(Q_{nT,h})=n(T-1)^{1-h}\).

The limited GMM is obtained by considering each equation separately. This estimator is the same as the one proposed by Lee (2007b).

We follow Kelejian and Prucha (1998) and compute the adjusted \(\text {RMSE}^*({\hat{\lambda }}_k) =\left[ \text {bias}^2({\hat{\lambda }}_k) + \left( {\text {IQ}({\hat{\lambda }}_k)} /{1.35}\right) ^2\right] ^{1/2}\), where median is used instead of mean for bias. \(\text {IQ}\) is the inter-quartile range and \({\hat{\lambda }}_k\) is the estimator of kth parameter \(\lambda _k\).

Here, we used the comprehensive criteria proposed by Sasser (1969): \(\text {NOMAD}({\hat{\lambda }})=\frac{1}{RK}\sum _{k=1}^K\sum _{r=1}^R\left| \frac{{\hat{\lambda }}_{k,r}-\lambda _k}{\lambda _k}\right| \) where K is the number of parameters, R is the number of replications, \({\hat{\lambda }}_{k,r}\) is the estimator of kth parameter in rth replication.

The results obtained with the SMA specification are available upon request.

The départements are the middle-tier level of local governments in France.

Note that for \(m=0\), \([\text {E}(W_{nT}y_1),\ldots ,\text {E}(W_{nT}y_{m}),{\textbf{X}}]={\textbf{X}}\) by convention.

Agrawal DR, Hoyt WH, Wilson JD (2022) Local policy choice: theory and empirics. J Econ Lit 60(4):1378–1455

Allers MA, Elhorst JP (2011) A simultaneous equations model of fiscal policy interactions. J Reg Sci 51(2):271–91CrossRef

Amba MCO, Le Gallo J (2022) Specification and estimation of a periodic spatial panel autoregressive model. J Spat Econom 3(1):1–34

Baltagi B (2008) Econometric analysis of panel data. Wiley, Hoboken

Baltagi BH, Deng Y (2015) Ec3sls estimator for a simultaneous system of spatial autoregressive equations with random effects. Econom Rev 34(6–10):659–94CrossRef

Baltagi BH, Egger P, Pfaffermayr M (2013) A generalized spatial panel data model with random effects. Econom Rev 32(5–6):650–85CrossRef

Cliff AD, Ord JK (1973) Spatial autocorrelation. Pion, London

Cliff AD, Ord JK (1981) Spatial processes: models & applications. Taylor & Francis, London

De Graaff T, Van Oort FG, Florax RJ (2012) Regional population-employment dynamics across different sectors of the economy. J Reg Sci 52(1):60–84CrossRef

Drukker DM, Egger PH, Prucha IR (2022) Simultaneous equations models with higher-order spatial or social network interactions. Econom Theory 1–48. https://doi.org/10.1017/S026646662200007X

Fingleton B (2008) A generalized method of moments estimator for a spatial panel model with an endogenous spatial lag and spatial moving average errors. Spat Econ Anal 3(1):27–44CrossRef

Fingleton B, Le Gallo J (2008) Estimating spatial models with endogenous variables, a spatial lag and spatially dependent disturbances: finite sample properties. Pap Reg Sci 87(3):319–39CrossRef

Gebremariam GH, Gebremedhin TG, Schaeffer PV (2011) Employment, income, and migration in Appalachia: a spatial simultaneous equations approach. J Reg Sci 51(1):102–20CrossRef

Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econom J Econom Soc 50(4):1029–1054

Hauptmeier S, Mittermaier F, Rincke J (2012) Fiscal competition over taxes and public inputs. Reg Sci Urban Econ 42(3):407–19CrossRef

Jeanty PW, Partridge M, Irwin E (2010) Estimation of a Spatial Simultaneous Equation Model of Population Migration and Housing Price Dynamics. Regional Science and Urban Economics 40(5):343–52CrossRef

Kapoor M, Kelejian HH, Prucha IR (2007) Panel data models with spatially correlated error components. J Econom 140(1):97–130CrossRef

Kelejian HH, Prucha IR (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. J Real Estate Finance Econ 17(1):99–121CrossRef

Kelejian HH, Prucha IR (2004) Estimation of simultaneous systems of spatially interrelated cross sectional equations. J Econom 118(1):27–50CrossRef

Lambert DM, Wan X, Florax RJGM (2014) Partial adjustment analysis of income and jobs, and growth regimes in the Appalachian region with smooth transition spatial process models. Int Reg Sci Rev 37(3):328–64CrossRef

Le Gallo J, Fingleton B (2019) Endogeneity in spatial models. In: Fischer MM, Nijkamp P (eds) Handbook of regional science. Springer, Berlin, pp 1–29. https://doi.org/10.1007/978-3-642-36203-3_122-1CrossRef

Lee L (2003) Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econom Rev 22(4):307–35CrossRef

Lee L (2007) GMM and 2sls estimation of mixed regressive, spatial autoregressive models. J Econom 137(2):489–514CrossRef

Lee L (2007) The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models. J Econom 140(1):155–89CrossRef

LeSage J, Pace RK (2009) Introduction to spatial econometrics, 1st edn. Chapman and Hall/CRC. https://doi.org/10.1201/9781420064254

Liu X (2014) Identification and efficient estimation of simultaneous equations network models. J Bus Econ Stat 32(4):516–36CrossRef

Liu X, Saraiva P (2019) GMM estimation of spatial autoregressive models in a system of simultaneous equations with heteroskedasticity. Econom Rev 38(4):359–385CrossRef

Sasser WE (1969) A finite-sample study of various simultaneous equation estimators... Duke University, Durham

Wang W, Lee L-F, Bao Y (2018) GMM estimation of the spatial autoregressive model in a system of interrelated networks. Reg Sci Urban Econ 69:167–98CrossRef

Yang K, Lee L (2017) Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models. J Econom 196(1):196–214CrossRef

Yang K, Lee L (2019) Identification and estimation of spatial dynamic panel simultaneous equations models. Reg Sci Urban Econ 76(C):32–46CrossRef

Zhang Z, Zhu P (2010) A more efficient best spatial three-stage least squares estimator for spatial autoregressive models. Ann Econ Finance 11(1):155–184

Titel: Spatial panel simultaneous equations models with error components
verfasst von: Marius C. O. Amba
Taoufiki Mbratana
Julie Le Gallo
Publikationsdatum: 30.01.2023
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 3/2023
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-023-02368-z

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