Shocking Regions: Estimating the Temporal and Spatial Effects of One-Time Events

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

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

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

5. The State of the Literature (cont.) • Dynamic Spatial Panel Models – 2 stage process • 1. spatial filtering • 2. estimate dynamic panel • Badinger, Muller and Tondl (2004) • 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) 5

6. 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

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

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

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

10. 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.  =  = 0 Ynt-1 weakly exogenous •  =  = 0 Ynt-1 weakly exogenous •  = θ = 0 unt-1   unt • Ynt-1  Weak Exogeneity (K=1) Are Ynt-1 and instruments for ?

12. 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. 9 regions, 1987-2004 4 variables: Earnings: Household Income Surveys (CBS) Population: Central Bureau of Statistics House Prices: Central Bureau of Statistics Housing Stock: Housing Completions (CBS) Data Sources

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

15. Data Housing Stock (th sq m) RealEarnings (1991 prices)

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

17. Panel Unit Root Tests • Auxiliary regression: dlnYknt = kn + knd-1lnYknt-1 + kndlnYknt-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 = 0.05. • We estimate SpVAR in log first differences

18. Estimating the SpVAR

19. Spatial Lag and Spatial Autocorrelation Coefficients *Coefficients significant at 0.05<p<0.1 ** Coefficients significant at p>0.1

20. Spatial Correlation (SC): SUR Estimates

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. (a) 2% Earnings Shock in Jerusalem (b) 2% Population Shock in Tel Aviv Impulses 1991 With and Without SC

25. 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

26. 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