Shocking Regions: Estimating the Temporal and Spatial Effects of One-Time Events Hebrew University of Jerusalem Michael Beenstock Daniel Felsenstein

2 The Issues Rising interest in the spatial dynamics of shocks and disasters (Katrina, Tsunami, acts of warfare and terrorism). Shocks have a spatial and temporal impact: one- time effect and cumulative effects Much interest in the temporal effects: can cities bounce back? how long does it take? is there a size threshold for shocks? 2

3 The Methods Control groups and trend analysis (Bram et al 2002, WTC 9/11). Expanded I-O models (SIM) (Okuyama, Hewings and Sonis 2004, Kobe earthquake 1995) CGE models (Rose et al 2004, electricity losses from Tennesse earthquake) NEG models- path dependence and temporary equilibria (Brakman et al 2004, Davis and Weinstein 2002, wars and bombing damage: Hiroshima, Dresden) What about abrupt socio-econ processes and not just natural and man-made ‘disasters’? 3

The State of the Literature Static Spatial Panel Models: Elhorst (2003) SAC and spatial lags Elhorst (2004) SAC and TAC Spatial Panel Models: Pfeifer & Deutsch (1980), univariate context temporal lags, ‘lagged’ spatial lags 4

The State of the Literature (cont.) Dynamic Spatial Panel Models – joint estimation, multivariate Spatial lags and spatial (auto)correlation estimated jointly with temporal lags and temporal autocorrelation. Beenstock and Felsenstein (2007) Dynamic Spatial Panel Models – 2 stage process 1.spatial filtering 2.estimate dynamic panel Badinger, Muller and Tondl (2004) 5

The Questions Method: can temporal and spatial dynamics of shocks be integrated (using spatial panel data)? Temporary or permanent effects: What are the impulse responses? How long do they last? Spatial issues: are shocks independent or spatially correlated? 6

Notation Regions:n = 1, 2, ….., N Time Periods:t = 1, 2,..…, T Endogenous Variables (Y k )k = 1, 2,..…, K Exogenous Variables (X P )p = 1, 2,..…, P Temporal Lag (Y t-q )q = 1, 2,..…, Q 7

8 Time Series (Temporal lag): Integrating Temporal and Spatial Dynamics in Spatial Panel Data Cross Section (Spatial lag):

9 Identification Problem In Time Series (TS): VARs under-identify the structural parameters. In Cross Section (CS): Identification problem Provided β = 0 ML IV SpVAR (CS + TS): Structural identification remains a problem.

Temporal and Spatial Dynamics (‘Lagged’ spatial lag) Notation:  – spatial lag  – temporal lag – lagged spatial lag Error Structure:  – spatial autocorrelation (SAC)  – lagged SAC (LSAC)  – temporal autocorrelation (TAC)  nr – spatial correlation (SC = SUR) 10

11 Weak Exogeneity (K=1) Are Y nt-1 and instruments for  ? 1.  =  = 0Y nt-1 weakly exogenous 2.  =  = 0Y nt-1 weakly exogenous 3.  = θ = 0u nt-1   u nt Y nt-1 

The SpVAR Model In Matrix Form: where:  ’s are region specific effects, δ’s are temporal lag coefficients  ’s are spatial lag coefficients ’s are lagged spatial lag coefficients When =  = 0, this equation reverts to an SVAR. 12

13 Data Sources 9 regions, variables: Earnings: Household Income Surveys (CBS) Population: Central Bureau of Statistics House Prices: Central Bureau of Statistics Housing Stock: Housing Completions (CBS)

14 Spatial Weights Asymmetric spatial weights based on distance and population size where: d ni = distance between regions n and i, Z= variable that captures scale effects.

15 Data Housing Stock (th sq m) Real Earnings (1991 prices)

16 Data (cont.) House Prices (1991 prices) Population (th)

17 Panel Unit Root Tests Auxiliary regression:  d lnY knt =  kn + kn  d-1 lnY knt-1 +  kn  d lnY knt-1 +  knt. Critical values of t-bar with N = 9 and T = 18 are –2.28 at p = 0.01 and –2.17 at p = We estimate SpVAR in log first differences Ln(Y j )d = 0d = 1d=2 Earnings Population House Prices Housing Stock

18 Estimating the SpVAR EarningsPopulationHouse PricesHousing Stock Temporal Lag(δ) Unrestricted Model Restricted Model Unrestricted Model Restricted Model Unrestricted Model Restricted Model Unrestricted Model Restricted Model Earnings **- Population *-0.112** House Prices ** ** Housing Stock ** Lagged Spatial Lag (λ) Earnings 0.131**-0.018** **- Population ** ** *-0.605* House Prices 0.205**0.196** **- Housing Stock R 2 adjusted Panel DW F statistic SBC unrestricted SBC restricted

19 Spatial Lag and Spatial Autocorrelation Coefficients EarningsPopulationHouse PricesHousing Stock Spatial Lag (  ) * * Error Parameters  TAC *-0.034**0.0094**0.0443**  SAC  LSAC 0.118**-.0400** ** **  (Determinant of correlation matrix) *Coefficients significant at 0.05<p<0.1 ** Coefficients significant at p>0.1

20 Spatial Correlation (SC): SUR Estimates JerusalemTel AvivHaifaKrayotDanCenterSouthSharon Tel Aviv Earnings Population Housing Prices Haifa Earnings Population Housing Prices Krayot Earnings Population Housing Prices Dan Earnings Population Housing Prices Center Earnings Population Housing Prices South Earnings Population Housing Prices Sharon Earnings Population Housing Prices North Earnings Population Housing Prices

21 SpVAR Impulse Response Simulations: The effect of shocks to variable k in region n on: The shocked variable in the region in which the shock occurred Other variables in which the shock occurred The shocked variable in other regions Other variables in other regions 21

22 Simulated Impulse Responses: 2% Earnings Shock in Jerusalem

23 Simulated Impulse Responses: 2% Population Shock in Tel Aviv

24 Impulses 1991 With and Without SC (a) 2% Earnings Shock in Jerusalem (b) 2% Population Shock in Tel Aviv (a)EarningsPopulationPricesHousing Stock Jerusalem Dan South (b)EarningsPopulationPricesHousing Stock Tel Aviv Dan Krayot

Main Results Evidence of temporal lags, spatially autocorrelated errors and ‘lagged’ spatial lags. Impulses: reverberate across space and time, feedback effects. But die out quite quickly Impulse response across regions: dictated by spatial weighting system, eg Jerusalem has greater spillover effect on South than on Dan region Spillover effects from Tel Aviv: reflects spatial lag coefficients in magnitude and sign 25

Conclusions Integration of time series and spatial econometrics Joint estimation in SpVAR (not 2-stage estimation) Difference between spatially correlated errors (SC) and spatially autocorrelated errors (SAC) and lagged SAC Impulse responses – ripple-through effect within and between regions 26