Measurement and Inference on Cross Section

and Spatial Interactions

Arnab Bhattacharjee Sean Holly

(ab102@st-andrews.ac.uk) (sean.holly@econ.cam.ac.uk)

University of St. Andrews University of Cambridge

NTTS 2009 Conference, Brussels

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1 Outline

� The research question

� Example 1: Di¤usion in excess housing demand

� Example 2: Interactions in a monetary policy committee

� Example 3: Convergence and inequality across regions

� Estimation of spatial weights matrix

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� Understanding interactions in committees

� Spatial dependence driven by factor structures

� Sampling of spatial units

� Further research

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2 The research question

� Substantial cross section and spatial dependence in many applications

� Spatial weights matrix

representing spatial dependence

notions of geographic/ economic/ socio-cultural ditance

imperfect measurements and uncertainty about drivers

huge implications for spatial dependence models

� Key Question: Can we understand spatial interaction without assum-ing specic drivers of di¤usion?

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� Emerging literature: Estimating spatial weights without a priori notionsof distance

consistent with observed pattern of spatial dependence

using estimates to identify true drivers of di¤usion

� In this presentation

Review three new methods

Motivate using examples

Identify new research questions

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3 Example 1: Di¤usion in excess housing de-

mand

3.1 Structural economic model

� Prices, Demand and Supply (Wheaton, 1990; Hendershott et al., 2002)Three behavioural relationships:1. Rate of change of price = f (deviation of vacancy rate from naturalvacancy rate, deviation of price from equilibrium price)

(Vt � Vt�1) =Vt�1 = �1 (�� � �t�1) + �2�V �t�1 � Vt�1

�:

2. Demand = f (Price, Neighbourhood conditions, Market conditions)

Dt = �0:X�1t :V

�2t :Y

�3t :

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3. In equilibrium, Demand = Supply times Occupancy rate

Dt � (1� �t) :St:

� Price-setting through search and matching(Wheaton, 1990; Krainer, 2001; Anglin et al., 2003)

Degree-of-overpricing = Listing price / Final sales price4. Degree-of-overpricing (DOP) = f (Neighbourhood conditions, Mar-ket conditions, Demand)

lnDOPt � lnVt � lnV Lt = �0 + �1:Xt + �2: lnYt + �3: lnDt:

5. Time on the market (TOM) = f (Market conditions, Degree-of-overpricing, Occupancy rate)

lnTOMt = �0 + �1: lnYt + �2: lnDOPt � �3: ln(1� �t):

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� In logs and rst di¤erences all vars. stationary in temporal dimension

� We assume: (a) natural value (V �) xed (temporally) in the short run,(b) exogenous supply, neighbourhood conditions and market conditions.

� lnDt = �0�Dt�1 � �1�Xt � �2� lnVt + �3� lnYt + ut (1)

� lnVt = 0+ 1:� lnDt�1+ 2:� lnVt�1� 3:� lnSt�1+ �1t (2)

� lnDOPt = �1�Xt+�2� lnYt+�3:� lnDt��4� lnVt+ �3t (3)

�TOMt = �1� lnYt+�2� lnDOPt��3� lnDt+�4� lnSt+�4t (4)

� Structural equations are identied.

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3.2 Spatial di¤usion in excess demand

� Stack up demand for all regions into a vector

� Spatial error model with autoregressive errors (SEM-AR)

Dt = Zt:� + ut; t = 1; : : : ; T;

ut = R:W :ut + "t (5)) Dt = Zt:� + (I �R:W )�1 :"t

T time periods (t = 1; : : : ; T ) and K regions,W : an unknown spatial weights matrix (K �K),R = diag (�1; �2; : : : ; �K): diagonal matrix containing spatial autore-gression parameters for each region, and"t: K�1 vector of independent but possibly heteroscedastic spatial errors

� = E�":"0

�= diag

��21; �

22; : : : ; �

2K

�:

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� Arbitrary spatial interaction (di¤usion) subject to identication constraint:(I �R:W ) nonsingular.

� Objective: to estimateW .

3.3 What use are such estimates?

� Suppose housing shocks originate from London

� How do the shocks then propagate through space?

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� In other words, which is closer to London Hertfordshire, Buckinghamshireor Birmingham?

Geographic distance: Hertfordshire and Buckinghamshire are closerthan Birmingham

Sociocultural distance: Birmingham may be closer.

� Bhattacharjee and Jensen-Butler (2005)

Spatial spillover from excess housing demand in London higher for theSouth East (Buckinghamshire) and West Midlands (Birmingham) thanEast of England (Hertfordshire).

Hence, geographic distance useful in some cases (London and the SouthEast), not appropriate for others (London and West Midlands, Londonand East of England).

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4 Example 2: Decision making in committees

� Economics of networks: pattern of connections between individual rationalagents shapes their actions and determines their rewards.

� An important examples is a monetary policy committee (ECB or Bank ofEngland)

Members may hold either partisan views depending on region/constituencyor vote strategically.

� Like the previous example

Membersvoting behaviour represented by regression model includingination, output gap and markets

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Deviations from such votes may be explained by cross-member inter-actions through connections weights (similar to spatial weights)

� Bhattacharjee and Holly (2008):

Decision making within the Bank of Englands monetary policy com-mittee (MPC)

Personalities of members reected in heterogeneity in the policy reac-tion functions

In addition, signicant interactions among members either strategicor likemindedness

Network architectures o¤er interesting insights into capacity constraints,transaction costs and incentives.

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5 Example 3: Convergence and inequality

� Stable di¤erences in productivity across regions in the EU.

� Explanations: innovative capacity, technology transfer/ absorption

� Many possible drivers for each, also potentially institutional features

� In empirical studies

Useful to allow for relatively unrestricted technology transfer

Further, infer on strength and direction of inter-region di¤usion ...... while being agnostic about the specic drivers of such interaction.

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6 Estimation of spatial weights matrix

� Bhattacharjee and Jensen-Butler (2005) consider estimation of a spatialweights matrix

� Spatial error model with spatial autoregressive errors (5).

� Estimation problem is only partially identied, up to an orthogonal trans-formation of interactions.Symmetry of spatial weights matrix valid identifying restrictions.

� Proposed algorithm for estimation, bootstrap for standard errors.Easy to use, but symmetry assumption may be too strong

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Figure 1: Government O¢ ce Regions (GORs) in England and Wales

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Figure 2: Topological Map of England and Wales based on spatial weights

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7 Understanding interactions in committees

� Bhattacharjee and Holly (2008) develop an alternative GMM based method

� Spatial or interaction weights matrices here are unrestricted ...... except for the validity of the included instruments and other momentconditions.

� The method assumes a nonempty set of other cross section units, ...... correlated with the units under consideration, ...... but may change over time, expand or some units may even drop out.

� Application to MPC voting behaviour suggest asymmetry, incomplete con-nectivity, and heterogeneity in inuence.Further, negative interaction weights point to strategic voting.

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Figure 3: Connections weights within the Bank of Englands MPC

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8 Spatial dependence driven by factor structures

� The above methodologies are based on an important assumption:Spatial interactions are structural not driven by unobserved factors.This assumption can sometimes be tenuous!

� Holly, Pesaran and Yamagata (2008) develop a method for factor models,based on the common correlated e¤ects (CCE) method (Pesaran, 2006).

� Application to changes in real house prices in the UK, nd evidence that1. Adjustment to shocks involve both region specic and spatial e¤ects2. Shocks to London propagated contemporaneously and spatially to otherregions, but they impact on other regions with a delay.3. New York house prices have direct but lagged e¤ect on London prices.

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9 Sampling of spatial units

� Important both for credible data analyses and e¤ective collection of spatialdata by statistical agencies.

� Guard against potential sample selection biasesNot very well understood research potential!

� Methods considered here explicitly account for endogeneity in selection ofunits.Selection endogenously related to the size and importance of spatial unitsTherefore, sample selection bias is potentially limited.Nevertheless, these issues need to be quantied and addressed.

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� Selection models can in turn be used to classify core and periphery.Useful for developing appropriate survey designs for spatial data.Above methods can identify such units and help e¤ective survey design

� (Longitudinal) panel nature of the data need to be preserved. Important for addressing unobserved xed and random e¤ects at thecross section level, ...... but also for accumulating evidences of spatial interaction and di¤usionpatterns over time.Therefore, very important for research that sampling of the same spatialunits is continued over substantial time.

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10 Further research

� Estimation of interactions provide useful understanding and insights

� Available methods assume either (a) purely structural interactions, or(b) purely factor driven dependence.Combination of the two an important direction of future research

� Study of sampling issues requiredDesign of spatial surveys Implications (sample selection, endogeneity) for inference Implications of estimated interactions for rening surveys

� Further applications: convergence and related issues, and beyond.

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