Diversication of Geographic Risk in Retail Networks: Evidence from Bank Expansion after Riegle-Neal Victor Aguirregabiria, Robert Clark, and Hui Wang IU - Kelley 04/18/2014 Aguirregabiria, Clark, and Wang () Geographic Risk Diversication IU - Kelley 04/18/2014 1 / 48
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Diversi�cation of Geographic Risk in Retail Networks:Evidence from Bank Expansion after Riegle-Neal
Victor Aguirregabiria, Robert Clark, and Hui Wang
IU - Kelley 04/18/2014
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 1 / 48
Introduction Retail Networks and Geographic Risk
Motivation: Retail Networks and Geographic Risk
Role of Geographic Risk Diversi�cation (GRD) in growth andspatial con�guration of Retail Chains.
Retail Chain: Collection of stores at di¤erent geographic markets.
Geographic Risk: Revenues and costs in a geographic marketdepend on idiosyncratic risk.
Diversi�cation: By opening branches in multiple local markets aretail chain can reduce the risk in its pro�ts.
Other factors (e.g., diseconomies of scale in the number of stores,economies of density, adjustment costs) can counterbalance GRD.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 2 / 48
Introduction Our Application
Our Application
We study the US retail banking industry during 1994-2006, beforeand after policy change (the Riegle-Neal Act) that eliminated verystrong restrictions to geographic expansion of retail banks.
Ideal setting to study GRD of retail networks.
Main empirical questions:
(a) Does bank expansion after Riegle-Neal reveal banksconcern for diversi�cation of liquidity risk?
(b) What were the e¤ects of this deregulation on bankscompetition for liquidity, and on liquidity risk?
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 3 / 48
Outline
Outline
[1] Riegle-Neal Act
[2] Data
[3] Measuring Geographic Risk: A Factor Model
[4] Evolution of Banks�Geographic Risk
[5] Model of Bank Branch Networks
[6] Summary of Results and Conclusions
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 4 / 48
In markets within the same state as bank HQs 60.9 49.7 43.1 33.3 32.8In markets in di¤erent state than bank HQs 82.7 91.0 75.7 65.2 67.9
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 14 / 48
Data
05
1015
20pe
rcen
tage
1994 1997 2000 2003 2006year
Among banks with nbr>4 (quartile4 in 1994)Among banks with 2<nbr<=4 (quartile3 in 1994)Among banks with 1<nbr<=2 (quartile2 in 1994)Among banks with 0<nbr<=1 (quartile1 in 1994)
Percentage of multistate banks
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 15 / 48
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 16 / 48
Measuring Geographic Risk: Factor Model
Factor Model
Regression model for log-deposits-per-branch:
ln (dmt ) = αm(Xt ) + βm(Xt ) ft + umt ,
Xt represents a vector of variables with all the information availableto banks at period t,
αm(.) is a deterministic function of Xt ,βm(.) is a 1� F vector of deterministic functions of Xtft is an F � 1 vector of random variables or factors that are commonto all the markets.
umt is a random variable that is market speci�c.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 17 / 48
Measuring Geographic Risk: Factor Model
Main Results form Factor Model
The estimated level of liquidity risk is quite substantial.
Systematic risk is between 0.6 and 2.3 percentage points;
Diversi�able risk is between 1.1 and 3.1 percentage points (This isthe level of risk that a bank would have if it operates only in onecounty).
Very substantial cross-state heterogeneity in the possibilities for GRDbefore RN, both for large banks and for small banks.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 18 / 48
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 27 / 48
Model
Main purpose of structural model
RN expanded banks�possibilities of GRD but most banks did not takeadvantage of these possibilities.
One explanation for this �nding is that banks are not seriouslyconcerned about GRD.
An alternative explanation is that other factors, such as diseconomiesof scale, economies of density, merging costs, and local market powerhave counterbalanced banks�concern for GRD.
We propose and estimate a structural model of competition betweenbranch networks where banks are (potentially) concerned withgeographic risk.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 28 / 48
Model
Model of bank competition
The model has two levels of competition between retail banks.
- Local competition: Branches in the same local market(county).compete for deposits.
- National competition between bank networks: Bankschoose the number of branches at each geographic local market.
Liquidity from deposits can be transferred between branches of thesame bank at a very low cost.
Banks can obtain additional liquidity in the interbank money marketbut this is costly. This cost generates a bank�s concern for liquidityrisk.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 29 / 48
Model Local Market Competition
Local Market Competition
Number of branches of each bank in a local market is determined inthe game of network competitionand it is exogenous in this game oflocal market competition.
Branches compete for the supply of deposits from households andbusinesses in the market.
The Nash equilibrium in this model of local competition impliesequilibrium functions that relate the deposits and the pro�ts of abank in a local market with the number of branches, their ownershipstructure, and exogenous market characteristics:
Dimt = fd (nimt ,nmt ,Xmt )
πimt = fπ(nimt ,nmt ,Xmt )
For the purpose of this paper, we are interested in the equilibriumfunctions fd and fπ more than in the structural estimation of demandand supply of deposits at the local market level.Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 30 / 48
Model Local Market Competition
Local Market Competition (2)
Cournot model with multiple branches, linear consumer supply ofdeposits, and a convex cost function that is consistent with thedescriptive evidence.
Consumer supply of deposits in market m at period t is described bythe equation: rmt = αmt + β Dmt .
Variable pro�t of this bank is:
πimt = (pmt � rmt ) Dimt � Cmt (Dimt , nimt ) .pmt represents the return from the best lending options in thismarket, and we assume that it is exogenously given.
Cmt (D, n) represents the variable cost of the bank for managing avolume of deposits D using n branches. We consider the followingspeci�cation of this cost function:
Cmt (D, n) � γmt D + [δ(n)/2] D2
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 31 / 48
Model Local Market Competition
Local Market Competition (3)
Equilibrium amount of deposits of a bank:
D�imt =�pmt � αmt � γmt
β(I �mt + 1)
� 0@ 1
1+ δ(nimt )β
1A ,where I �mt � ∑It
j=11
1+δ(njmt )/βcan be interpreted as the "e¤ective"
number of banks in the local market.
The equilibrium value of variable pro�ts is:
π�imt = β
�1+
δ(nimt )2β
�(D�imt )
2.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 32 / 48
Model Local Market Competition
Number of Branches and Deposits for a Bank in a CountyDependent variable: ln(Dimt )
Time dummies (#) YES (11) YES (10)County � Bank FEs YES YES
Number of observations 277,408 232,812
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 33 / 48
Model Local Market Competition
Model: Branch Network
A bank chooses its branch network nit to maximize its expectedvalue, E(Vit jXt ):
E(Vit jXt ) =M∑m=1
π�imt � FCit (nit )� ACit (nit ,nit�1)� ρit Pr(Dit � Li � Ei j Xt ).
(a) Variable pro�t. ∑Mm=1 π�imt , is the sum of variable pro�ts from
all the local markets where the bank is active.
(b) Fixed operating costs. FCit (nit ) captures economies of scaleand density in the operation of a branch network.θFC1 [#branches] +θFC2 [#branches]2 + θFC3 [#branches *distance-to-HQs] +θFC4 [#branches * (distance-to-HQs)2]
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 34 / 48
Model Local Market Competition
Model: Branch Network (2)
(c) Adjustment costs. ACit (nit ,nit�1) includes costs of adjusting orchanging the branch network, including merging costs and costs ofdenovo branching.θAC1 [# new branches via denovo, within HQs state] + θAC2 [# newbranches via denovo, outside HQs state] + θAC3 [# new branches viamerger, within HQs state] + θAC4 [# new branches via merger,outside HQs state].
(d) Cost of liquidity shortage. Pr(Dit � Li � Ei j Xt ) is theprobability of liquidity shortage.
Φ
Li � Ei � E(Dit jXt )p
V(Dit jXt )
!
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 35 / 48
Model Local Market Competition
Model: Branch Network (3)
Expected value of a bank
E (Vit j Xt ) = Wit (nit )θ+εit (nit )
Wit (nit ) is the vector of known functions fΠit (nit ), �ΦitΠit (nit ),[#branches], [#branches]2, [#branches * distance-to-HQs],[#branches * (distance-to-HQs)2], [# new branches via denovo,within HQs state], [# new branches via denovo, outside HQs state],[# new branches via merger, within HQs state], [# new branches viamerger, outside HQs state]g
θ is the vector of parameters (β, ρ̄, θFC1 , θFC2 , θFC3 , θFC4 , θAC1 , θAC2 ,θAC3 , θAC4 )0
εit (nit ) represents other factors that are unobservable to theresearcher but known to the bank
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 36 / 48
Model Local Market Competition
Model: Branch Network (4)
We apply the principle of revealed preference to estimate (up to scale)the vector of parameters θ.
nit = arg maxn2Ait
fWit (n) θ+ εit (n)g ,
We estimate the structural parameters of our model using a MomentInequalities estimator (MIE).
E
�Zit
�(Wit (nit )�Wit (n))
θ0
σε+K
��� 0,
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 37 / 48
Model Local Market Competition
Estimation of Bank Network Costs and Bene�ts
Parameter Estimate (s.e.)(1)
β/σε (in million $) 3.2135 (0.8720)
Cost of Insolvency Parameter ρ 8.4380�� (1.5200)
Branch network diseconomies of scale:
Number of branches (in million $ per branch) -1.9802�� (0.6163)
Number of branches square (in million $ per branch sq.) -0.0706� (0.0620)
Number of observations (#banks) 120,812 (14,127)
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 38 / 48
Model Local Market Competition
Estimation of Bank Network Costs and Bene�ts
Parameter Estimate (s.e.)(1)
Branch network economies of density:
Average distance to county HQs -0.1435�� (0.0387)
(in million $ per 100 miles and per branch)
Average distance to county HQs square 0.0050 (0.0063)
Branch network adjustment costs. Denovo branching
Denovo Branch Creation within state (in million $ per branch) -1.3325�� (0.2803)
Denovo Branch Creation out state (in million $ per branch) -2.1597�� (0.4239)
Branch network adjustment costs. Merger
Merger within state (in million $ per new branch) -0.6480�� (0.3985)
Merger out state (in million $ per new branch) -1.1871�� (0.4200)
Merger within state � small bank (in million $ per new branch) -1.4410� (0.9106)
Merger out state � small bank (in million $ per new branch) -2.4309�� (0.6767)
Number of observations (#banks) 120,812 (14,127)
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 39 / 48
Model Local Market Competition
Estimation Results
ρ̄ : statistically and economically signi�cant. Each percentage pointof probability of liquidity shortage is equivalent to an ad valorem taxon deposits of 8.4%.
Fixed costs: signi�cant diseconomies of scale. Fixed cost of the �rstbranch is $1.98 millions, and the cost per branch increases with thenumber of branches;
Fixed costs: economies of density. The operating cost increases withthe average distance of the branch network to the county with bank�sheadquarters. Every 100 miles of average distance to theheadquarters implies an increase in the cost-per-branch of $143, 000.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 40 / 48
Model Local Market Competition
Estimation Results
Costs of denovo branching and merging are sizeable. There aresigni�cant di¤erences in these costs if the expansion is within thesame state or to another state.
The estimated merging cost per acquired branch is smaller than thecost of denovo branching especially for out of state expansions.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 41 / 48
Model Local Market Competition
Counterfactual experiments
Experiment 1: Shut down the e¤ect of GRD by making theparameter ρ̄ equal to zero.
Experiment 2: We eliminate economies of density by �xing θFC3 andθFC4 to zero.
We focus on the following predictions: (a) average annual probabilityof adding new branches (through denovo or merger) outside the homecounty; (b) average annual probability of adding new branches outsideof the home state; and (c) average annual change in geographicdeposit risk. We distinguish between small banks (i.e., three branchesor less), medium (4 to 20 branches), and large banks (21 or morebranches).
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 42 / 48
Model Local Market Competition
Counterfactual experiments: Results
Experiment 1: Eliminating banks�concern for risk has a veryimportant impact on the network expansion of small banks, but anegligible e¤ect on medium and large banks.
For small banks, the probability of increasing the number of brancheswithin the home state goes from 5.2% to 1.8%, and the probability ofexpanding out of the home state becomes practically zero.
Experiment 2: Shutting down economies of density has a veryimportant e¤ect on the network expansion of all the banks, thoughthe stronger e¤ect is for banks of medium size.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 43 / 48
Model Local Market Competition
Counterfactual Experiments using Model of Branch Networks
Actual Model Exp. 1 Exp. 2
Statistic Value Prediction ρ̄ = 0 θFC3 = θFC4 = 0
Small banks (#branches� 3)Prob. new br. outside home county (%) 4.97 5.20 1.83 6.47
Prob. new br. outside home state (%) 0.36 0.43 0.02 0.75
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 46 / 48
Model Local Market Competition
Main Empirical Findings
1. There is signi�cant location-speci�c geographic risk.
2. Before RN, there was large between-state heterogeneity in thepossibilities of GRD.
3. RN has expanded signi�cantly the possibilities of GRD of banks withHQs in small/homogeneous states.
4. However, very few banks have taken advantage of RN to reducedgeographic risk. Out-of-state branch expansion accounts for a verysmall fraction of the change in the distribution of banks�risks.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 47 / 48
Model Local Market Competition
Main Empirical Findings (II)
5. There has been a signi�cant reduction in banks geographic risk during1995-2006. However, most of this reduction can be explained by: (a)an exogenous decline in risk associated to growth of relatively smallmarkets; and (b) within-state branch expansion.
6. Our estimates of banks�preferences show a signi�cant banks�concernfor GRD.
7. Nevertheless, this concern for GRD has been counter-balanced by fourimportant factors: (1) economies of density; (2) large costs ofout-of-state de-novo branching; (3) large costs of mergers, especiallyfor small banks; and (4) in general, banks in small states are not themost attractive partners for a merger because they are small with lowrates of return and high risk.
Aguirregabiria, Clark, and Wang () Geographic Risk Diversi�cation IU - Kelley 04/18/2014 48 / 48