Common factors and spatial dependence: an application to US house prices

Abstract

This paper considers panel data models with cross-sectional dependence arising from both spatial autocorrelation and unobserved common factors. It derives conditions for model identification and proposes estimation methods that employ cross-sectional averages as factor proxies, including the 2SLS, Best 2SLS, and GMM estimations. The proposed estimators are robust to unknown heteroskedasticity and serial correlation in the disturbances, unrequired to estimate the number of unknown factors, and computationally tractable. The paper establishes the asymptotic distributions of these estimators and compares their consistency and efficiency properties. Extensive Monte Carlo experiments lend support to the theoretical findings and demonstrate the satisfactory finite sample performance of the proposed estimators. The empirical section of the paper finds strong evidence of spatial dependence of real house price changes across 377 Metropolitan Statistical Areas in the US from 1975Q1 to 2014Q4. The results also reveal that population and income growth have significantly positive direct and spillover effects on house price changes. These findings are robust to different specifications of the spatial weights matrix constructed based on distance, migration flows, and pairwise correlations. . This work was carried out during my doctoral study at the University of Southern California.(ii) The error term e it has absolutely summable cumulants up to the fourth order.Assumption 3. The factor loadings, γ i and A i , are independently and identically distributed across i, and independent of e jt , v jt , and f t , for all i, j, and t. Both γ i and A i have fixed means, which are given by γ and A, respectively, and finite variances. In particular, for all i,where Ω η is a symmetric non-negative definite matrix, γ < K, A < K, andAssumption 4. The true parameter vector, δ 0 = ρ 0 , β ′ 0 ′ , is in the interior of the parameter space, denoted by ∆ sp , which is a compact subset of the (k + 1)-dimensional Euclidean space, R k+1 .Assumption 5. The matrixC, given by (7), has full row rank for all N , including N → ∞. Assumption 6. The N × N nonstochastic spatial weights matrix, W = (w ij ), has bounded row and column sum norms, namely, ||W|| ∞ < K and ||W|| 1 < K, respectively, andfor all values of ρ. In addition, the diagonal entries of W are zero, that is, w ii = 0, for all i = 1, 2, . . . , N . Assumption 7. The N × q matrix of instrumental variables, Q .t , for t = 1, 2, . . . , T , is composed of a subset of the columns of X .t , WX .t , W 2 X .t , . . . , and its column dimension q is fixed for all N and t. The matrix Q = (Q ′ .1 , Q ′ .2 , . . . , Q ′ .T ) ′ represents the IV matrix of dimension N T × q. Assumption 8. (i) There exists N 0 and T 0 , such that for all N > N 0 and T > T 0 , the matrices (N T ) −1 Q ′ M b Q and (N T ) −1 Q ′ M b f Q exist and are nonsingular.

Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices

“…Spatial parameter estimates are positive and statistically significant for all regions. The average estimate of the spatial lag obtained for the U.S. (around 0.51) is lower than the estimate of around 0.65 reported by Yang (2018) who considers a homogeneous SAR specification estimated on a similar data set. The differences between the two estimates could be due to the considerable degree of heterogeneity that we observe across the regions in the U.S., which is being neglected under the homogeneity assumption.…”

“…BHP distinguish between spatial dependence that originates from economy-wide common shocks such as changes in interest rates, oil prices and technology, and the dependence across MSAs due to local spill-over effects arising from differences in house prices, incomes and demographics across MSAs. 13 Here, we use an extended version of the panel dataset employed by BHP and further augmented with population and per capita real income data by Yang (2018) to estimate HSAR models, after filtering out the effects of common factors on house price changes. 14 We provide MSA specific estimates of spill-over effects, as well as population and income elasticities of house prices as compared to the homogeneous spatial parameter estimates obtained in Yang (2018).…”

“…13 Here, we use an extended version of the panel dataset employed by BHP and further augmented with population and per capita real income data by Yang (2018) to estimate HSAR models, after filtering out the effects of common factors on house price changes. 14 We provide MSA specific estimates of spill-over effects, as well as population and income elasticities of house prices as compared to the homogeneous spatial parameter estimates obtained in Yang (2018). To compare our individual estimates with those of Yang, we also report MG estimates both at the national and regional levels.…”

“…20 (67) is in accordance with the theoretical model (1) analyzed in Sections 2 and 3. 21 With regard to the construction of the weights matrix W = (w ij ), we consider a distance based weighting scheme implemented in Yang (2018), which is common in the spatial econometrics literature. More precisely, the calculation of the geodesic distance between each pair of latitude/longitude coordinates for the MSAs included in our sample uses the Haversine formula.…”

“…For a theoretical analysis of the interactions between regional house prices, migration flows and income shocks seeCun and Pesaran (2018).14 The authors would like to thank Cynthia Yang for providing them with the updated dataset originally used inYang (2018).15 The February 2013 delineation states that 'metropolitan statistical areas have at least one urbanised area of 50,000 or more population, plus adjacent territory that has a high degree of social and economic integration with the core as measured by commuting ties'. For further details see:https://www.whitehouse.gov/sites/whitehouse.gov/files/omb/bulletins/2013/b13-01.pdf 16 This excludes the non-contiguous states of Alaska (2 MSAs) and Hawaii (2MSAs) and all other off-shore insular areas.17 The quarterly figures for nominal house prices (HP ) are arithmetic averages of monthly observations of HP .…”