Simultaneous equation models with spatially autocorrelated error components

AMBA OYON, Claude Marius and Mbratana, Taoufiki (2017): Simultaneous equation models with spatially autocorrelated error components.

Abstract

This paper develops estimators for simultaneous equations with spatial autoregressive or spatial moving average error components. We derive a limited information estimator and a full information estimator. We give the generalized method of moments to get each coefficient of the spatial dependence of each equation in spatial autoregressive case as well as spatial moving average case. The results of our Monte Carlo suggest that our estimators are consistent. When we estimate the coefficient of spatial dependence it seems better to use instrumental variables estimator that takes into account simultaneity. We also apply these set of estimators on real data.

• Item Type: MPRA Paper
• Language: English
• Keywords: Panel data, SAR process, SMA process, Simultaneous equations, Spatial error components
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C33 - Panel Data Models ; Spatio-temporal Models

References

Allers, M. A. and Elhorst, J. P. (2011). A simultaneous equations model of fiscal policy interactions. Journal of regional science, 51(2):271–291.

Anselin, L. (1988). Model validation in spatial econometrics: a review and evaluation of alternative approaches. International Regional Science Review, 11(3):279–316.

Anselin, L. (2006). Spatial econometrics in: Mills tc, patterson k (eds) palgrave handbook of econometrics: Volume 1, econometric theory.

Anselin, L. and Bera, A. K. (1998). Spatial dependence in linear regression models with an introduction to spatial econometrics. Statistics Textbooks and Monographs, 155:237–290.

Balestra, P. and Varadharajan-Krishnakumar, J. (1987). Full information estimations of a system of simultaneous equations with error component structure. Econometric Theory, 3(02):223–246.

Baltagi, B. (2008). Econometric analysis of panel data. John Wiley & Sons.

Baltagi, B. H. (1981). Simultaneous equations with error components. Journal of econometrics, 17(2):189–200.

Baltagi, B. H. (1984). A monte carlo study for pooling time series of cross-section data in the simultaneous equations model. International Economic Review, pages 603–624.

Baltagi, B. H. and Bresson, G. (2011). Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris. Journal of Urban Economics, 69(1):24–42.

Baltagi, B. H. and Deng, Y. (2015). Ec3sls estimator for a simultaneous system of spatial autoregressive equations with random effects. Econometric Reviews, 34(6-10):659–694.

Baltagi, B. H., Egger, P., and Pfaffermayr, M. (2013). A generalized spatial panel data model with random effects. Econometric Reviews, 32(5-6):650–685.

Baltagi, B. H. and Li, Q. (1992). A note on the estimation of simultaneous equations with error components. Econometric Theory, 8(1):113–119.

Baltagi, B. H. and Pirotte, A. (2011). Seemingly unrelated regressions with spatial error components. Empirical Economics, 40(1):5–49.

Barro, R. and Sala-i Martin, X. (1995). Economic growth. ed.

Cliff, A. D. and Ord, J. K. (1973). Spatial autocorrelation. Technical report, London: Pion.

Cliff, A. D. and Ord, J. K. (1981). Spatial processes: models & applications. Taylor & Francis.

Cornwell, C., Schmidt, P., and Wyhowski, D. (1992). Simultaneous equations and panel data. Journal of Econometrics, 51(1-2):151–181.

Cressie, N. (2015). Statistics for spatial data. John Wiley & Sons.

De Graaff, T., Van Oort, F. G., and Florax, R. J. (2012). Regional population–employment dynamics across different sectors of the economy. Journal of Regional Science, 52(1):60–84.

Doğan, O. and Taşpınar, S. (2013). Gmm estimation of spatial autoregressive models with moving average disturbances. Regional Science and Urban Economics, 43(6):903–926.

Fingleton, B. (2008). A generalized method of moments estimator for a spatial model with moving average errors, with application to real estate prices. Empirical Economics, 34(1):35–57.

Gebremariam, G. H., Gebremedhin, T. G., and Schaeffer, P. V. (2011). Employment, income, and migration in appalachia: A spatial simultaneous equations approach. Journal of Regional Science, 51(1):102–120.

Goldsmith-Pinkham, P. and Imbens, G. W. (2013). Social networks and the identification of peer effects. Journal of Business & Economic Statistics, 31(3):253–264.

Haining, R. (1978). The moving average model for spatial interaction. Transactions of the Institute of British Geographers, pages 202–225.

Hauptmeier, S., Mittermaier, F., and Rincke, J. (2012). Fiscal competition over taxes and public inputs. Regional science and urban economics, 42(3):407–419.

Hepple, L. W. (2003). Bayesian and maximum likelihood estimation of the linear model with spatial moving average disturbances. School of Geographical Sciences, University of Bristol, Working Papers Series, University of Bristol, School of Geographical Sciences.

Hitiris, T. and Posnett, J. (1992). The determinants and effects of health expenditure in developed countries. Journal of health economics, 11(2):173–181.

Ho, C.-S. and Hite, D. (2008). The beneft of environmental improvement in the southeastern united states: Evidence from a simultaneous model of cancer mortality, toxic chemical releases and house values. Papers in Regional Science, 87(4):589–604.

Jeanty, P. W., Partridge, M., and Irwin, E. (2010). Estimation of a spatial simultaneous equation model of population migration and housing price dynamics. Regional Science and Urban Economics, 40(5):343–352.

Kapoor, M., Kelejian, H. H., and Prucha, I. R. (2007). Panel data models with spatially correlated error components. Journal of econometrics, 140(1):97–130.

Kelejian, H. H. and Prucha, I. R. (1998). A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. The Journal of Real Estate Finance and Economics, 17(1):99–121.

Kelejian, H. H. and Prucha, I. R. (1999). A generalized moments estimator for the autoregressive parameter in a spatial model. International economic review, 40(2):509–533.

Kelejian, H. H. and Prucha, I. R. (2004). Estimation of simultaneous systems of spatially interrelated cross sectional equations. Journal of econometrics, 118(1):27–50.

Kelejian, H. H., Prucha, I. R., and Yuzefovich, Y. (2004). Instrumental variable estimation of a spatial autoregressive model with autoregressive disturbances: Large and small sample results. In James, P. L. and Kelley, R. P., editors, Spatial and spatiotemporal econometrics, volume 18, pages 163–198. Emerald Group Publishing Limited.

Kelejian, H. H. and Robinson, D. P. (1992). Spatial autocorrelation: A new computationally simple test with an application to per capita county police expenditures. Regional Science and Urban Economics, 22(3):317–331.

Lee, L.-f. (2003). Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econometric Reviews, 22(4):307–335.

LeSage, J. P. and Pace, R. K. (2009). Introduction to Spatial Econometrics (Statistics, textbooks and monographs). CRC Press.

Liu, X. (2014). Identifcation and efcient estimation of simultaneous equations network models. Journal of Business & Economic Statistics, 32(4):516–536.

Liu, X. and Saraiva, P. (2017). Gmm estimation of spatial autoregressive models in a system of simultaneous equations with heteroskedasticity. Econometric Reviews, (just-accepted).

Lu, L. (2017). Simultaneous spatial panel data models with common shocks. Working Paper.

O’Connell, J. M. (1996). The relationship between health expenditures and the age structure of the population in oecd countries. Health economics, 5(6):573–578.

Parkin, D., McGuire, A., and Yule, B. (1987). Aggregate health care expenditures and national income: is health care a luxury good? Journal of health economics, 6(2):109–127.

Prucha, I. R. (1985). Maximum likelihood and instrumental variable estimation in simultaneous equation systems with error components. International Economic Review, pages 491–506.

Prucha, I. R., Drukker, D. M., and Egger, P. H. (2016). Simultaneous equations models with higher-order spatial or social network interactions. Technical report, Working paper, Department of Economics, University of Maryland.

Sasser, W. E. (1969). A fnite-sample study of various simultaneous equation estimators...Duke University.

Solow, R. M. (1956). A contribution to the theory of economic growth. The quarterly journal of economics, 70(1):65–94.

Wang, L., Li, K., and Wang, Z. (2014). Quasi maximum likelihood estimation for simultaneous spatial autoregressive models. University Library of Munich, Germany.

Whittle, P. (1954). On stationary processes in the plane. Biometrika, pages 434–449.

Yang, K. and Lee, L.-f. (2017). Identifcation and qml estimation of multivariate and simultaneous equations spatial autoregressive models. Journal of Econometrics, 196(1):196–214.

Zenou, Y. (2017). Multivariate choices and identifcation of social interactions. Journal of Applied Econometrics, pages 1–37