×

Modeling US housing prices by spatial dynamic structural equation models. (English) Zbl 1288.62197

Summary: This article proposes a spatial dynamic structural equation model for the analysis of housing prices at the State level in the USA. The study contributes to the existing literature by extending the use of dynamic factor models to the econometric analysis of multivariate lattice data. One of the main advantages of our model formulation is that by modeling the spatial variation via spatially structured factor loadings, we entertain the possibility of identifying similarity “regions” that share common time series components. The factor loadings are modeled as conditionally independent multivariate Gaussian Markov random fields, while the common components are modeled by latent dynamic factors.
The general model is proposed in a state-space formulation where both stationary and nonstationary autoregressive distributed-lag processes for the latent factors are considered. For the latent factors which exhibit a common trend, and hence are cointegrated, an error correction specification of the (vector) autoregressive distributed-lag process is proposed. Full probabilistic inference for the model parameters is facilitated by adapting standard Markov chain Monte Carlo (MCMC) algorithms for dynamic linear models to our model formulation. The fit of the model is discussed for a data set of 48 States for which we model the relationship between housing prices and the macroeconomy, using State level unemployment and per capita personal income.

MSC:

62P20 Applications of statistics to economics
62M40 Random fields; image analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Software:

bvarsv; spBayes
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] Ahn, S. K. and Reinsel, G. C. (1990). Estimation for partially nonstationary multivariate autoregressive models. J. Amer. Statist. Assoc. 85 813-823. · Zbl 0705.62081
[2] Anselin, L. (1988). Spatial Econometrics : Models and Applications . Kluwer Academic, Dordrecht, The Netherlands. · Zbl 1328.62406
[3] Apergis, N. and Payne, J. E. (2012). Convergence in U.S. housing prices by state: Evidence from the club convergence and clustering procedure. Letters in Spatial and Resource Sciences 5 103-111.
[4] Banerjee, S., Carlin, B. P. and Gelfand, A. E. (2004). Hierarchical Modeling and Analysis for Spatial Data . Chapman & Hall/CRC, Boca Raton, FL. · Zbl 1053.62105
[5] Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994). Time Series Analysis : Forecasting and Control , 3rd ed. Prentice Hall Inc., Englewood Cliffs, NJ. · Zbl 0858.62072
[6] Brown, P. J., Vannucci, M. and Fearn, T. (1998). Multivariate Bayesian variable selection and prediction. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 627-641. · Zbl 0909.62022
[7] Cameron, G., Muellbauer, J. and Murphy, A. (2006). Was There a British House Price Bubble? Evidence from a Regional Panel. Mimeo . Oxford Univ. Press, London.
[8] Capozza, D. R., Hendershott, P. H., Mack, C. and Mayer, C. J. (2002). Determinants of real house price dynamics. NBER Working Paper 9262.
[9] Carter, C. K. and Kohn, R. (1994). On Gibbs sampling for state space models. Biometrika 81 541-553. · Zbl 0809.62087
[10] Case, K. E. and Shiller, R. J. (2003). Is there a bubble in the housing market? Brookings Papers on Economic Activity 2 299-362.
[11] Cho, S. (2010). Inference of cointegrated model with exogenous variables. SIRFE Working Paper 10-A04.
[12] Clayton, J., Miller, N. and Peng, L. (2010). Price-volume correlation in the housing market: Causality and co-movements. Journal of Real Estate Finance and Economics 40 14-40.
[13] Cressie, N. A. C. (1993). Statistics for Spatial Data. Wiley Series in Probability and Mathematical Statistics : Applied Probability and Statistics . Wiley, New York. · Zbl 0799.62002
[14] Dawid, A. P. (1981). Some matrix-variate distribution theory: Notational considerations and a Bayesian application. Biometrika 68 265-274. · Zbl 0464.62039
[15] Debarsy, N., Ertur, C. and LeSage, J. P. (2012). Interpreting dynamic space-time panel data models. Stat. Methodol. 9 158-171. · Zbl 1248.62167
[16] Di Giacinto, V., Dryden, I., Ippoliti, L. and Romagnoli, L. (2005). Linear smoothing of noisy spatial temporal series. J. Math. Stat. 1 299-311. · Zbl 1141.62076
[17] Durbin, J. and Koopman, S. J. (2001). Time Series Analysis by State Space Methods. Oxford Statistical Science Series 24 . Oxford Univ. Press, Oxford. · Zbl 0995.62504
[18] Elhorst, J. P. (2001). Dynamic models in space and time. Geographical Analysis 33 119-140.
[19] Engle, R. F., Hendry, D. F. and Richard, J.-F. (1983). Exogeneity. Econometrica 51 277-304. · Zbl 0528.62093
[20] ESRI. (2009). ArcMap 9.2. Environmental Systems Resource Institute, Redlands, California.
[21] Frühwirth-Schnatter, S. (1994). Data augmentation and dynamic linear models. J. Time Series Anal. 15 183-202. · Zbl 0815.62065
[22] Gallin, J. (2008). The long run relationship between housing prices and income: Evidence from local housing markets. Real Estate Economics 36 635-658.
[23] Gelfand, A. E. and Ghosh, S. K. (1998). Model choice: A minimum posterior predictive loss approach. Biometrika 85 1-11. · Zbl 0904.62036
[24] Gelman, A. (1996). Inference and Monitoring Convergence. In Introducing Markov Chain Monte Carlo . · Zbl 0839.62020
[25] George, E. I., Sun, D. and Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. J. Econometrics 142 553-580. · Zbl 1418.62322
[26] Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian Statistics , 4 ( PeñíScola , 1991) (J. Bernardo, J. Berger, A. Dawid and A. Smith, eds.) 169-193. Oxford Univ. Press, New York.
[27] Gilks, W. R., Richardson, S. and Spiegelhalter, D. J., eds. (1996). Markov Chain Monte Carlo in Practice. Interdisciplinary Statistics . Chapman & Hall, London. · Zbl 0832.00018
[28] Giussani, B. and Hadjimatheou, G. (1991). Modeling regional housing prices in the United Kingdom. Papers In Regional Science 70 201-219.
[29] Gourieroux, C. S. and Monfort, A. (1997). Time Series and Dynamic Models . Cambridge Univ. Press, Cambridge. · Zbl 0861.62077
[30] Holly, S., Pesaran, M. H. and Yamagata, T. (2010). A spatio-temporal model of house prices in the USA. J. Econometrics 158 160-173. · Zbl 1431.62627
[31] Ippoliti, L., Valentini, P. and Gamerman, D. (2012). Space-time modelling of coupled spatio-temporal environmental variables. J. R. Stat. Soc. Ser. C. Appl. Stat. 61 175-200.
[32] Jochmann, M., Koop, G., Leon-Gonzalez, R. and Strachan, R. (2013). Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy. J. Appl. Econometrics 28 62-81.
[33] Johansen, S. (1988). Statistical analysis of cointegration vectors. J. Econom. Dynam. Control 12 231-254. · Zbl 0647.62102
[34] Jones, G. L., Haran, M., Caffo, B. S. and Neath, R. (2006). Fixed-width output analysis for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 101 1537-1547. · Zbl 1171.62316
[35] Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773-795. · Zbl 0846.62028
[36] Kim, H., Sun, D. and Tsutakawa, R. K. (2001). A bivariate Bayes method for improving the estimates of mortality rates with a twofold conditional autoregressive model. J. Amer. Statist. Assoc. 96 1506-1521. · Zbl 1051.62112
[37] Koop, G., León-González, R. and Strachan, R. W. (2010). Efficient posterior simulation for cointegrated models with priors on the cointegration space. Econometric Rev. 29 224-242. · Zbl 1185.62157
[38] Koop, G. M., Strachan, R. W., Van Dijk, H. and Villani, M. (2006). Bayesian approaches to cointegration. In The Palgrave Handbook of Theoretical Econometrics 871-898. Palgrave Macmillan, Basingstoke, UK.
[39] Kuethe, T. and Pede, V. (2011). Regional housing price cycles: A spatio-temporal analysis using US state-level data. Regional Studies 45 563-574.
[40] Lopes, H. F., Salazar, E. and Gamerman, D. (2008). Spatial dynamic factor analysis. Bayesian Anal. 3 759-792. · Zbl 1330.62356
[41] Lopes, H. F. and West, M. (2004). Bayesian model assessment in factor analysis. Statist. Sinica 14 41-67. · Zbl 1035.62060
[42] Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis . Springer, Berlin. · Zbl 1072.62075
[43] Malpezzi, S. (1999). A simple error correction model of housing prices. Journal of Housing Economics 8 27-62.
[44] Mardia, K. V. (1988). Multidimensional multivariate Gaussian Markov random fields with application to image processing. J. Multivariate Anal. 24 265-284. · Zbl 0637.60065
[45] Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis . Academic Press, London. · Zbl 0432.62029
[46] Meen, G. (1999). Regional house prices and the ripple effect: A new interpretation. Housing Studies 14 733-753.
[47] Meen, G. (2001). Modelling Spatial Housing Markets : Theory , Analysis and Policy . Kluwer, Dordrecht, The Netherlands.
[48] Moench, E. and Ng, S. (2011). A hierarchical factor analysis of U.S. housing market dynamics. Econom. J. 14 C1-C24.
[49] Muellbauer, J. and Murphy, A. (1997). Booms and busts in the UK housing market. Econom. J. 107 1701-1727.
[50] Osiewalski, J. and Steel, M. F. J. (1996). A Bayesian analysis of exogeneity in models pooling time-series and cross-sectional data. J. Statist. Plann. Inference 50 187-206. · Zbl 0888.62025
[51] Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74 967-1012. · Zbl 1152.91718
[52] Pfeifer, P. E. and Deutsch, S. J. (1980). A three-stage iterative procedure for space-time modeling. Technometrics 22 35-47. · Zbl 0429.62066
[53] Pfeifer, P. E. and Deutsch, S. J. (1981). Space-time ARMA modeling with contemporaneously correlated innovations. Technometrics 23 401-409.
[54] Primiceri, G. E. (2005). Time varying structural vector autoregressions and monetary policy. Rev. Econom. Stud. 72 821-852. · Zbl 1106.91047
[55] Rosenberg, B. (1973). Random coefficients models: The analysis of a cross-section of time series by stochastically convergent parameter regression. Annals of Economic and Social Measurement 60 399-428.
[56] Sain, S. R. and Cressie, N. (2007). A spatial model for multivariate lattice data. J. Econometrics 140 226-259. · Zbl 1418.62368
[57] Sain, S. R., Furrer, R. and Cressie, N. (2011). A spatial analysis of multivariate output from regional climate models. Ann. Appl. Stat. 5 150-175. · Zbl 1220.62152
[58] Sims, C. A. and Zha, T. (1999). Error bands for impulse responses. Econometrica 67 1113-1155. · Zbl 1056.62533
[59] Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 583-639. · Zbl 1067.62010
[60] Strickland, C. M., Simpson, D. P., Turner, I. W., Denham, R. and Mengersen, K. L. (2011). Fast bayesian analysis of spatial dynamic factor models for large space time data sets. J. R. Stat. Soc. Ser. C. Appl. Stat. 60 1-16.
[61] Sugita, K. (2009). A Monte Carlo comparison of Bayesian testing for cointegration rank. Economics Bulletin 29 2145-2151.
[62] van Dijk, B., Franses, P. H., Paap, R. andvan Dijk, D. J. C. (2011). Modeling regional house prices. Applied Economics 43 2097-2110.
[63] Vermeulen, W. and Van Ommeren, J. (2009). Compensation of regional unemployment in housing markets. Economica 76 71-88.
[64] Wang, F. and Wall, M. M. (2003). Generalized common spatial factor model. Biostatistics 4 569-582. · Zbl 1197.62067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.