Bank Geographic Diversification and Systemic Risk: A Gravity-Deregulation Approach. (Abstract)

Bank Geographic Diversification and Systemic Risk: A Gravity-Deregulation Approach (Abstract) Using the gravity-deregulation model to construct the time-varying and bankspecific exogenous instrument of geographic diversification following Goetz, Laeven, and Levine (2013), we examine the causal relationship between geographic diversification and systemic risk using publicly traded bank holding companies (BHCs) in the U.S. as the sample. We find that bank geographic diversification leads to higher systemic risk across all three proxies including systemic expected shortfall (SES), conditional capital shortfall (SRISK), and conditional value at risk (ΔCoVaR). The results continue to hold with several robustness checks. Furthermore, we find that the impact of geographic diversification on systemic risk is more pronounced in BHCs that are located in states that commove less with the aggregate U.S. economy, suggesting state and U.S. economy comovement is a potential channel to explain the results. Cross sectional analyses reveal that the impact of geographic diversification on systemic risk is more pronounced in BHCs that are larger, have lower capital adequacy ratio and liquidity position, engage in more non-interest income activities, and have higher non-performing loan ratio and growth opportunity. Key Words: geographic diversification, systemic risk, gravity-deregulation, exogenous instrument JEL Classification: G21, G28 1

Bank Geographic Diversification and Systemic Risk: A Gravity-Deregulation Approach I. Introduction The recent global financial crisis of 2007-2009 created systemic risk marked by widespread failures and gigantic losses in the banking industry as well as huge negative externalities to the real economy. 1 It is crucial for policy makers, regulators and financial institutions to understand the various determinants of systemic risk of the financial system. In this study we construct an exogenous instrument of geographic diversification based on the gravity-deregulation model, and examine the causal relationship between bank geographic diversification and systemic risk of the entire financial system. We examine this important issue for two reasons: First, due to deregulation, technological advancement, and financial innovation, the US banking industry has experienced a tremendous level of geographic expansion via mergers and acquisitions and establishment of new branches/subsidiaries across state borders during the recent decades. Wagner (2010) demonstrates that bank diversification may reduce the probability of bank failure while simultaneously increase systemic risk, as diversification makes banks more similar to each other by exposing them to the same risks. As banks expand their footprints nationwide, they are exposed to the same risk from the same regions they operate subsidiaries or branches. As a result, it is likely that economic shocks at individual institutions may be spread to the whole financial system, leading to a greater systemic risk. Goetz, Laeven, and Levine (2016) examine geographic diversification and firm-specific 1 The International Monetary Fund (IMF), Bank of International Settlements (BIS) and Financial Stability Board (FSB) define systemic risk as the risk of disruption to financial services that (i) is caused by an impairment of all parts of the financial system and (ii) has the potential to have serious negative consequences for the real economy. 2

risk in the banking industry and find that geographic diversification reduces bank-specific risk. However, there is scant empirical evidence on how bank geographic diversification affects systemic risk. Our study intends to fill this gap. Second, an empirical challenge of conducting such research is that bank geographic diversification could be endogenous as there may be unobservable variables (to researchers) that affect both bank geographic diversification and systemic risk. To overcome this challenge, we employ the gravity-deregulation model by integrating the dynamic cross-state and cross-time variation in the interstate bank deregulation with a gravity model of BHC geographic expansion to construct an exogenous time-varying BHCspecific instrumental variable for bank geographic diversification, following Goetz, Laeven, and Levine (2013), then examine the causal relationship between geographic diversification and systemic risk using publicly traded bank holding companies (BHCs) in the U.S. as the sample. The advantage of gravity-deregulation model is that it provides a time-varying BHC-specific exogenous instrument of geographic diversification, based on which we can draw causal relationship between bank geographic diversification and systemic risk. A valid instrument must satisfy both relevance and exclusion restrictions. We find the instrumental component of geographic diversification is positively and significantly related to the actual cross-state asset dispersion of a BHC, satisfying the relevance restriction. In addition, the instrumental variable passes both under-identification and weak identification tests, suggesting the validity of the instrument. Moreover, our instrument is constructed from two plausibly exogenous sources of variation: the staggered process of interstate bank deregulation and pre-determined geographic distance between a 3

BHC s home state and the state capital of a foreign state, as well as state population, satisfying the exclusion restriction. Following Acharya, Pedersen, Philippon, and Richardson (2010) and Adrian and Brunnermeier (2011), we construct three variables to measure systemic risk: systemic expected shortfall (SES), normalized conditional capital shortfall (SRISK), and conditional value at risk (CoVaR). SES is the loss of a bank experiences when a crisis occurs. It is related to marginal expected shortfall and a bank s leverage. SRISK measures capital shortfall during crisis. We measure the marginal contribution of an institution to the overall systemic risk using the difference between CoVaR conditional on the distress of institution and the CoVaR conditional on the normal state of the institution (ΔCoVaR). We find that bank geographic diversification leads to higher financial instability across all three proxies of systemic risk. The empirical results lend support to Wagner (2010). The results are robust to several sensitivity checks, including using an alternative way of constructing instrument based on a more parsimonious gravity-deregulation model that only use distance while excluding relative market size in coming up with the predicted shares of BHC expansion, removing BHCs headquartered in New York City, excluding BHCs primarily engage in foreign operations, and including additional control variable. Moreover, we document that geographic diversification has a more pronounced impact on systemic risk for BHCs that are located in a home state that commoves less with the rest of the economy. The reason is that as these BHCs expand geographically, their asset return commoves more with the whole economy and expose them to the same risk, which leads to higher systemic risk. We also perform several cross sectional analyses to examine whether the influence of geographic diversification on systemic risk varies with BHC- 4

specific characteristics. We document that the impact of geographic diversification on systemic risk is more pronounced in BHCs that are larger, operate at lower capital adequacy ratio and liquidity position, engage in more non-interest income activities, and have higher non-performing loan ratio and growth opportunity. We contribute to the literature in the following ways: first, ours is the first study that examine bank geographic diversification and systemic risk, using the gravity deregulation model to construct an exogenous instrument of geographic diversification following Goetz, Laeven and Levine (2013). This allows us to draw causal relationship between bank geographic diversification and financial instability. 2 Existing studies on bank geographic diversification focus on firm-specific risk and provide mixed empirical results. For example, Akhigbe and Whyte (2003), Hughes, Lang, Mester, and Moon (1999), Deng and Elyasiani (2008), and Goetz et al. (2016) all find that bank geographic diversification is associated with a lower level of firm risk, consistent with the view that diversification may reduce earnings volatility through coinsurance effect documented in Lewellen (1971) and Boot and Schmeits (2000). In contrary, Winton (1999), and Berger, Clarke, Cull, Klapper, and Udell (2005) suggest that diversification may increase organizational complexity and intensify agency problem, leading to higher firm risk. Along the same line, Demsetz and Strahan (1997), and Chong (1991) show that bank diversification does not result in lower risk because diversified banks may raise leverage and pursue riskier activities due to competitive pressures. Second, we document that bank geographic diversification positively and significantly contributes to systemic risk, which complements Goetz, Laeven and Levine 2 We describe these three proxies of systemic risk in more detail in Section 3.2.2. 5

(2016) reporting that geographic diversification leads to reduced bank-specific risk. Combined with Goetz, Laeven and Levine (2016), our study provides empirical support to Wagner (2010) s theoretical prediction that diversification may reduce firm-specific risk while simultaneously increase systemic risk, which challenges the conventional wisdom that diversification reduces firm-specific risk, which in turn may benefit financial stability. Third, we add to existing literature on determinants of bank systemic risk by documenting geographic diversification as an additional factor that influences bank systemic risk. Therefore our study complements prior studies that examine various determinants of bank systemic risk, including bank size, derivatives holding, nonperforming loan ratios, non-interest income activities, and consolidation (Bayazitova & Shivdasani, 2012; Brunnermeier, Dong, & Palia, 2012; De Jonghe, Diepstraten, & Schepens, 2015; Mayordomo, Rodriguez-Moreno, & Peña, 2014; Weiß, Neumann, & Bostandzic, 2014). Our study is related to Goetz, Laeven, and Levine (2013), Goetz, Laeven and Levine (2016) and Levine, Lin and Xie (2016), all of which use gravity-deregulation model to construct exogenous component of geographic diversification. More specifically, Goetz, Laeven, and Levine (2013) find that the exogenous component of geographic diversification reduces BHC valuation. Goetz, Laeven and Levine (2016) document that the exogenous instrument based geographic expansion reduces bank-specific risk proxied by stock return volatility, stock return residual, and Z-score. Levine, Lin and Xie (2016) discover that the exogenous component of geographic diversification lowers bank funding costs. Our work complements these studies by probing the causal relationship between bank geographic diversification and systemic risk, using the gravity-deregulation model to 6

construct an exogenous component of geographic diversification. We find that bank geographic diversification contributes more to systemic risk of the financial system. The study proceeds as follows. Section II sketches the institutional background of bank interstate deregulation. Section III discusses data and methodology. Section IV presents the gravity-deregulation model and empirical results, as well as channel effect and cross sectional analyses. Section V concludes. II. Institutional Background of U.S. bank interstate deregulation Our identification strategy exploits the dynamic process of time varying and statespecific interstate bank deregulation, which generates an exogenous shock to the geographic diversification of U.S. banks. This section briefly provides some institutional background of U.S. bank interstate deregulation. Before the 1970s, U.S. banks were largely prohibited from expanding across state borders by laws. In 1978 Maine became the first state that lifted restriction on the entry of banks from foreign states, Alaska and New York followed suit in 1982. Over the following decade or so, states removed entry restrictions in a dynamic time-varying and state-specific process, either by unilaterally opening state borders and allowing the entry of foreign state BHCs, or by signing reciprocal bilateral and multilateral agreements with other states allowing interstate banking. The wave of bank deregulation continued until mid-1990s, which culminated in the passage of Riegle-Neal Interstate Banking and Branching Efficiency Act (IBBEA) of 1994. The IBBEA removed all of the remaining restrictions on interstate banking by 1995, afterwards nation-wide interstate banking becomes a reality. Over this two decade evolution of interstate bank deregulation, states not only started eliminating out- 7

of-state bank entry restrictions in different years, but also signed reciprocal bilateral and multilateral agreements with other states on interstate banking in a chaotic manner over time. Therefore, the evolution of interstate bank deregulation is a dynamic process that varies across states and time, which generates an exogenous shock to the geographic diversification and hence provides us a useful laboratory to assess the impact of BHC geographic diversification on systemic risk. In the dynamic deregulation process, we identify whether a state can legally enter other states for each state-pair over time based on Amel (1993), and determine the actual date that Riegle-Neal Act of 1994 becomes effective based on Rice and Strahan (2010). III. Data and methodology 3.1 Sample selection We obtain data from three main sources, including bank holding companies (BHC) database, and Report of Condition and Income (Call Report), both are provided by Federal Reserve Bank of Chicago, as well as the Center for Research in Security Prices (CRSP) database provided by the University of Chicago. BHC database provides BHC-specific information such as total assets, total loans, and total equity, etc., as well as structural variables. Call Report provides bank-specific information for bank subsidiaries of BHCs. CRSP database provides information on share price and market capitalization. Additional data item such as risk-free rate is from Federal Reserve Board, and state population is from U.S. Bureau of Economic Analysis (BEA). We obtain CoVaR related data from Professor Markus K. Brunnermeier s website. We use the following procedure to construct the sample. First, following Goetz, Laeven, and Levine (2013), we use RSSD9364 in the Call Report to identify the parent 8

BHCs of bank subsidiaries. A commercial bank subsidiary is linked to its parent BHC identified by (non-zero) RSSD9364 and when shares of higher holding (RSSD9365) is larger than 50%. The accounting and structural information of the parent companies are from FR Y-9C form. we eliminate observations with missing values of total assets, state code or zip code, etc. Consistent with prior studies on bank branching deregulation (Jayaratne & Strahan, 1996), we focus on BHCs headquartered in the 48 contiguous states and the District of Columbia while excluding the state of Delaware and South Dakota. 3 Next, we merge the dataset with CRSP database by using the link file provided by Federal Reserve Bank of New York, which documents the historical linkage between regulatory entity codes from FR Y-9C Form and the permanent company number (permco) from CRSP database. After deleting the observations with missing values, our final sample includes 967 unique BHCs and 35,906 BHC-quarter observations over a sample period of 1986 to 2006. All variables are winsorized at 1% and 99% level to eliminate outliers. We start the sample period in the third quarter of 1986 when the BHC database begins coverage, and end our sample in 2006 to avoid the confounding effect of the recent 2007~2009 financial crisis. 3.2. Variable construction 3.2.1 Geographic diversification We use asset dispersion index as a measure of geographic diversification, which is similar to a Herfindahl-Hirschman index, described as one minus the sum of the squared 3 South Dakota and Delaware removed usury ceilings on credit card loans and other types of consumer loans in 1980 and 1981 respectively, shortly before these two states removing bank branching restrictions, we exclude them to avoid any confounding effects. 9

ratios of the assets of subsidiaries in each state to the sum of the total assets in all of the states where a BHC operates (1 HHI). This index ranges from zero to one, with larger values indicating greater extent of geographic diversification. 3.2.2 Systemic risk measures We employ three main measures of systemic risk to assess the extent of a bank s contribution to the systemic risk of the financial system, including systemic expected shortfall (SES), normalized conditional capital shortfall (SRISK), and the value at risk of the financial system conditional on institutions being under distress (CoVaR). We measure the marginal contribution of an institution to the overall systemic risk using the difference between CoVaR conditional on the distress of institution and the CoVaR conditional on the normal state of the institution (ΔCoVaR). We detail how we construct each of these measures below. 3.2.2.1 Systemic Expected Shortfall According to Acharya, Pedersen, Philippon, and Richardson (2016), systemic expected shortfall (SES) measures an institution s propensity to be undercapitalized when the system as a whole is undercapitalized. It is a linear function of an institutions marginal expected shortfall (MES) and leverage. MES is the average loss of market equity when the market return is in its 5% lower tail based on previous one year horizon. The details of computing MES and Leverage are as follows: MES i ( i m t = E Rt Rt isin5 % Tail) (1) 10

LVG i t = i i Book assetst Book Equityt + Market Equity Market Equity i t i t (2) Acharya, Pedersen, Philippon, and Richardson (2016) regress the percentage of stock returns of large US institutions against the above two components during the recent 2007~2009 financial crisis and derive Realized SES as follows: Realized SES = 0.15MES + 0.04LVG (3) We use the fitted value of SES for each bank-quarter observation to proxy for a bank s contribution to systemic risk, with a higher value of SES indicating greater systemic risk. 3.2.2.2 Expected Capital Shortfall Expected capital shortfall (SRISK) is about how much capital a bank would need in the time of crisis to maintain a given capital adequacy ratio. Below we use the V. Acharya, Engle, and Richardson (2012) measure which was further refined by Brownlees and Engle (2015) to compute SRISK: i SRISK = E( Capital Shortfall Crisis) t = E( k( Debt + Equity) Equity Crisis) (4) = kdebt (1 k)(1 LRMES ) Equity i t i t i t i Where k is a prudential capital adequacy ratio set at 8% following Brownlees and Engle (2015). LRMES stands for long-run marginal expected shortfall, which is approximated as LRMES = 1 exp( 18 MES), with MES being the marginal expected shortfall. Following Berger, Roman, and Sedunov (2016), we scale SRISK by market cap to make it comparable across banks. 3.2.2.3. Conditional Value at Risk 11

Developed by Adrian and Brunnermeier (2011), conditional value at risk (CoVaR) is the value at risk of the entire financial sector conditional on an institution being in distress. We measure the marginal contribution of an institution to the overall systemic risk using the difference between CoVaR conditional on the distress of institution and the CoVaR conditional on the normal state of the same institution (ΔCoVaR) following Adrian and Brunnermeier (2011). More specifically CoVaR and ΔCoVaR are constructed as follows 4 : X = α + γ M + ε (5a) i i i i t t 1 t X = α + β X + γ M + ε (5b) system system i system i i system i system i t t t 1 t VaR ( q) = ˆ α + ˆ γ M (6a) i i i t q q t 1 CoVaR ( q) = ˆ α + ˆ β VaR ( q) + ˆ γ M (6b) i system i system i i system i t q q t q t 1 i i i CoVaR (5%) = CoVaR (5%) CoVaR (50%) (7) t t t where X is the weekly market value based asset returns for a firm; M is a set of macro variables. 5 We assume the worst 5% of macro variables and worst 5% of financial system returns when estimating VaR and CoVaR using quantile regression. VaR captures the loss of an individual institution conditional on crisis, while CoVaR captures the systemic loss conditional on the distress of an institution. ΔCoVaR is the marginal contribution of an institution on the overall systemic risk, which is defined as the difference between CoVaR conditional on the distress of an institution i (q=5%, i.e., using the worst 4 We obtain CoVaR and ΔCoVaR data from Professor Markus K. Brunnermeier s website at http://scholar.princeton.edu/markus/publications?page=1. 5 This set of variables include CBOE Volatility index (VIX), liquidity spread (3-month repo minus 3-month bill rate), change in 3-month Treasury bill rate, term spread (10-year Treasury rate minus 3-month bill rate), credit spread (10 Year BAA rated bonds minus 10-year Treasury rate), and return of the MSCI world index. 12

5% of macro variables and the worst 5% financial system returns in the quantile regression) and CoVaR conditional on the normal state of the institution (q=50%). 6 3.2.3. Control variables Following Berger, Roman, and Sedunov (2016), we include a set of BHC-specific characteristics as control variables, including CAMELS which serve as indicators of a bank s financial health, bank size, bank age, and growth opportunity. CAMELS include capital adequacy, asset quality, management, earnings, liquidity, and sensitivity to market risk. Capital adequacy is measured by total equity divided by gross total assets. We expect capital adequacy is inversely related to systemic risk, since capital acts as a buffer to absorb systemic shocks. Asset quality is proxied by the ratio of nonperforming loans to total loans. We expect it is positively related to systemic risk. Management quality is measured by the ratio of non-interest expense divided by total operating income. We expect it is negatively related to systemic risk. Liquidity is proxied by liquid assets divided by total assets. 7 We expect it is negatively related to systemic risk as banks with better liquidity position contribute less to systemic risk. Sensitivity to market risk is proxied by one-year GAP ratio, which is measured by (earning assets repriced within one year interest-bearing deposit liabilities repriced within one year long-term debt repriced within one year)/total assets. We expect it is positively related to systemic risk. Bank size is positively related to systemic risk as large banks may operate at lower capital ratio and rely more on short term funding, and conduct more risky activities. Older banks and banks with greater growth opportunity contribute more to systemic risk. 3.3 Sample descriptive statistics 6 The results are qualitatively similar when we compute ΔCoVaR using the worst 1% of macro variables. 7 Liquid assets consist of cash and balances, federal funds sold, and securities purchased to resell. 13

Table 1 presents the sample descriptive statistics. We divide the sample into diversified and non-diversified BHC-quarter observations. As BHCs expand geographically at different time, the same BHC can be categorized as a non-diversified BHC in the quarters before it expands geographically and a diversified BHC in the quarters after it diversifies. On average diversified BHC-quarter observations have 6.773 subsidiaries in 2.848 states, and 47.5% of subsidiary assets in foreign states. Moreover, compared to non-diversified BHC-quarter observations, diversified BHC-quarter observations are larger and older, have greater systemic risk, higher profitability, growth opportunity and market risk sensitivity, as well as higher non-performing loan ratio (poorer asset quality). On the other hand, these observations have lower capital adequacy ratio, liquidity position, and management quality. All these differences are statistically significant at 1% level. Insert Table 1 here IV. Gravity-deregulation model and empirical results 4.1 Identification strategy To address the concern that geographic diversification may be endogenous, we follow Goetz, Laeven, and Levine (2013) and employ a gravity-deregulation model to construct the time-varying BHC-specific exogenous instrument of geographic diversification, and then examine its causal relationship with systemic risk of the financial system. The nutshell of the gravity-deregulation model is to integrate the dynamic crossstate and cross-time variation in the interstate bank deregulation with a gravity model of BHC geographic expansion to construct an exogenous time-varying BHC-specific 14

instrumental variable for bank geographic diversification. Since interstate bank deregulation occurs at state level, we examine BHC expansion across states. We summarize how we perform this task in the following steps. Step one, we exploit the state-specific dynamic process of interstate bank deregulation from 1970s until mid-1990s which provides state-year information on whether BHCs in one state can establish subsidiaries in other states. This interstate bank deregulation process alone does not provide us an instrument that varies among BHCs in the same state. Therefore, in step two, we combine this state-specific dynamic process of eliminating interstate bank restrictions into a gravity model of BHC asset expansion across state borders to construct a BHC-specific instrumental variable of geographic diversification. More specifically, we project the share of assets a BHC in its home state entering a foreign state based on a gravity-deregulation model. Step three, we use one minus the Herfindahl index based on projected share as the instrument for the first stage model of observed actual geographic diversification based on asset dispersion across states, along with a set of control variables. Lastly, we apply the predicted value of the actual geographic diversification obtained from stage one in the second stage model of systemic risk, and estimate the two models simultaneously using a two-stage least squares (2SLS) regression framework. In the next section we detail how we implement this task. 4.2 Gravity-deregulation model The gravity model is used in international trade literature (Frankel & Romer, 1999; Helpman, Melitz, & Rubinstein, 2008). More specifically, Frankel and Romer (1999) develop the gravity model to construct instrumental variable of bilateral trade volume between countries, then estimate the causal relationship between international trade and income. They 15

argue that geographic characteristics such as country size, geographic distance between countries are highly correlated to bilateral trade volume between countries, yet they do not influence income, and hence they are valid instruments for international trade across countries. They find that a country far from other countries experience less international trade, and a country with more population experience more international trade. We integrate the state-specific dynamic process of interstate bank deregulation into the gravity model with following Goetz, Laeven, and Levine (2013), and Levine, Lin and Xie (2016). We reason that the distance between BHC headquarters and a foreign state into which a BHC can legally enter matters in a BHC s expansion decision, i.e., a BHC is more likely to expand to a neighboring state as the cost of doing so is lower. Moreover, BHCs maybe more attracted to larger markets than smaller ones. Therefore, we consider both distance between states and relative market size when projecting a BHC s expansion into a foreign state. In the first step (stage zero), we estimate the following model: Sharebijt =αjdistancebij +βjln(populationit/populationjt)+εbijt, (8) Where Sharebijt is the proportion of assets of BHC b, headquartered in state i, held in its subsidiaries in state j in quarter t; Distancebij is the distance between BHC b s headquarters and state j s capital (in 100s of miles), which is assumed to be the market center of a state. We expect the coefficient on distance to be negative since banks are less likely to expand to far away states. Ln(Populationit/Populationjt) is the natural logarithm of the population of BHC s home state i divided by the population of a foreign state j in quarter t, which is a proxy for the relative market size of home state to the foreign state. We expect the coefficient to be negative as BHCs headquartered in a smaller market will be more likely to expand geographically to a relatively larger foreign market. We also add state and quarter fixed effects. 16

The percentage of assets that a subsidiary of BHC can have in a certain state naturally ranges from zero to one. Since many BHCs do not diversify across states and the sample median number of states BHCs expand to is 3, OLS estimation is unsuitable. Following Papke and Wooldridge (1996, 2008), we employ a fractional logit model to estimate model (4) that addresses the relationship between distance, population and a BHC s shares of assets in a state. We only include observations in which it is legal for BHC b with headquarters in state i to enter state j in quarter t. Column (1) and (2) of Table 2 present the results on the extent to which distance and market size can project BHCs expansion decision across state border. We cluster standard errors at state-year level. There is a negative and significant relationship between a BHC s assets in a state and the distance between the BHC headquarters and the state capital where the BHC expands into, suggesting that the impact of interstate bank deregulation on BHCs in one state depends on the distance between the BHCs and a foreign state. Moreover, the coefficient on the foreign market size is negative and significant indicating foreign state market size matters too in that BHCs are less likely to expand into a relatively small state. We use the predicted value of column (2) because adding fixed effects in the construction of instrument variable will bias the estimation of the second-stage (Rubinstein, 2011). Based on the numbers in column (2) of Table 2, an increase of 100 miles in distance between a bank s headquarters and a state s capital leads to a decline of 1.8% shares allocated to the foreign state. We also estimate model (8) using fractional Probit, Tobit, and OLS regressions to check the robustness of results. The results are qualitatively similar, as shown in Column (3)- (6) of Table 2. Insert Table 2 here 17

4.3 Two-stage least squares (2SLS) regression We employ the predicted share of BHC expansion into foreign states obtained from estimating model (8) using fractional logit regression to compute the predicted Herfindahl index of assets across states for each BHC (Predicted HHI). Then we construct the instrumental variable, i.e., the predicted diversification measure for each BHC in each quarter, as one minus the predicted Herfindahl index of assets across states (1 Predicted HHI). To generate Predicted HHI, we use the projected proportion of a BHC s assets in a state for periods (the coefficient estimates from column (2) of Table 2) when it is legal for a BHC to expand in that state. For observations in which regulations restrict a BHC from operating a subsidiary in a state, we set the projected proportion to zero. Then, we use these projected percentages based on model (8) to compute predicted Herfindahl index of assets across states for each BHC in each quarter. Lastly, we use one minus the predicted Herfindahl index of assets across states (1 Predicted HHI) as the exogenous instrument of actual diversification in the first-stage model, along with a set of control variables. The variable (1 Predicted HHI) is the state-varying and time-varying BHC-specific exogenous instrument of actual diversification. We also include both BHC and quarter fixed effects. In the last step, we apply the predicted value of actual geographic diversification obtained from stage-one model in the second stage model of systemic risk, then estimate both models simultaneously using a 2SLS regression framework. Below is our two-stage model: (1 HHI) it α1 β1(1 Predicted HHI) it γ1x it δ i η t ε it = + + + + + (9) Systemic Risk it = α + β (1 HHI ) it + γ X it + δ i + η t + π it (10) 2 2 2 Where systemic risk is proxied by multiple variables including SES, SRISK and ΔCoVaR discussed in the previous section, as well as the principal component based on the 18

three systemic risk measures. Xit is a set of control variables discussed Section 3.2.3. We also include both BHC and quarter fixed effects. 4.4 Empirical results The first-stage results as reported in Panel B of Table 3 indicate that the instrument, 1 Predicted HHI, is positively and significantly (at 1%) related to actual degree of geographic diversification, suggesting that this instrument can explain diversification at BHC level very well. The second-stage results of estimating model (10) are presented in Panel A of Table 3. The coefficient on predicted geographic diversification from stage one is positive and significant at 5% or better level across all three models using alternative systemic risk measures including SES, SRISK and ΔCoVaR, suggesting bank geographic diversification contributes more to systemic risk of the financial system (Column 1-3, Panel A of Table 3). The 2SLS results are consistent with Wagner (2010) in that bank diversification may reduce the probability of bank failure while simultaneously increase systemic risk, as diversification makes banks more similar to each other by exposing them to the same risks. The results are also economically significant. One standard deviation increase in geographic diversification will cause a 1.33 standard deviation increase in SES, 8 and 1.13 standard deviation increase in SRISK, and 0.52 standard deviation increase in ΔCoVaR. We also investigate the reduced form relationship between systemic risk and the predicted geographic diversification from stage one of the gravity-deregulation model. The results 8 The coefficient on 1-HHI, in column (1), Panel A of Table 3 is 3.72, the standard deviation of 1-HHI is 0.12 for the sample BHCs, the standard deviation of SES is 0.3352 for the sample BHCs, so an increase of one standard deviation of 1-HHI leads to an increase of 1.33 standard deviation increase in SES (3.72 0.12/0.3352 =1.33). Other numbers are calculated similarly. 19

reported in Panel C of Table 3 are consistent with our main results, indicating that BHC geographic diversification is positively and significantly associated with systemic risk. The signs of most control variables are consistent with our expectation. Capital adequacy ratio is negatively associated with systemic risk as BHCs with better capital position can better weather the storm. Asset quality proxied by non-performing loan ratio is positively related to systemic risk, consistent with Mayordomo et al. (2014). Management quality is negatively associated with systemic risk. Earnings and liquidity position are both negatively related to systemic risk. BHC size and growth opportunity are both negatively related to systemic risk. On the other hand, sensitivity to market risk and bank age are largely insignificant. To address the concern that none of the systemic risk proxies can perfectly measure a bank s contribution to systemic risk, we perform principle component analysis and extract common factors based on SES, SRISK and ΔCoVaR to capture the common variation among the three proxies. We retain the first two factors which explain 99% of total variations, indicating a high comovement among the three variables. Results based on principle component analysis are reported in Column (4) of Table 3, which continue to show that geographic diversification contributes more to systemic risk of the entire financial system. One standard deviation increase in geographic diversification will cause a 1.79 standard deviation increase in PCA. There is a concern that in addition to promoting geographic expansion, deregulation may lead to more competition among BHCs which in turn may affect BHC systemic risk. To address this concern and ensure the validity of the instrument based on gravityderegulation model, we include BHC and quarter fixed effects, as well as state-year fixed 20

effects to control for all time-varying factors that influence all BHCs in the same state, including the threat of the entry of out-of-state banks. Results are displayed in Columns (5) to (8) of Table 3. We continue to find that geographic diversification contributes more to systemic risk. We also perform under-identification and weak identification tests to check the validity of our instrumental variable. For SES model (Column 1 of Table 3), the results indicate that this instrument passes the under-identification test with Kleibergen- Paap rk LM statistic being 10.106 (p-value < 1%). It also passes the weak identification test with Cragg-Donald Wald F statistic being 28.029, much greater than the critical value of 16.38 for the 10% maximal IV size based on Stock and Yogo (2005). To further ensure the validity of our results we perform several robustness checks in the following section, including alternative way of constructing instrumental variable, removing BHCs headquartered in New York city, dropping BHCs primarily engaging in foreign activities, and including additional control variable. Insert Table 3 here 4.5 Robustness checks 4.5.1 Alternative way of constructing instrumental variable In the first step of the above gravity-deregulation model, we account for both distance and relative market size when projecting a BHC s expansion to a foreign state. The results shown in Table 2 indicate that both distance and market size are statistically and economically significant factors in explaining a BHC s expansion across state borders. When we include both home state and quarter fixed effects, the effect of market size weakens. Following Goetz, Laeven, and Levine (2016), we use a more parsimonious gravity model with only distance while omitting market size in the model to project the share of assets in 21

foreign states (Projected Share). Then we compute the projected Herfindahl index of assets across states (Projected HHI) based on Projected Share. We construct the instrument as one minus the projected HHI (1 Projected HHI). Then we use (1 Projected HHI) as an instrument for the model of actual geographic diversification based on deposit dispersion across states (1-HHI) in stage one, along with a set of control variables. We then estimate model (9) and (10) simultaneously using a 2SLS regression framework to evaluate the causal relationship between geographic diversification and systemic risk. Results in Panel A of Table 4 shows that geographic diversification is still positively related to systemic risk, suggesting our results are robust to such exercise of alternative way of constructing the instrument of geographic expansion. 4.5.2 Removing BHCs headquartered in New York city To address the concern that BHCs headquartered in New York city may have different geographic expansion pattern and risk profile, we exclude 18 BHCs headquartered in New York city with 681 BHC-quarter observations from the sample, and re-estimate the models. The results are reported in Panel B of Table 4. We continue to find that BHC geographic expansion contribute more to systemic risk, suggesting that our results are robust to excluding BHCs headquartered in New York city. 4.5.3. Dropping BHCs primarily engage in foreign activities Since we only focus on BHC s domestic diversification in the 48 contiguous states and the District of Columbia, we exclude BHCs that primarily engage in foreign activities. We define a BHC as mainly engaging in foreign activities if more than 50% of its total deposits are from foreign offices. We lose about 27% of total observations when dropping 22

such BHCs. We still find a positive and significant relationship between geographic diversification and systemic risk (Panel C of Table 4). 4.5.4 Including an additional control variable De Jonghe et al. (2015) and Brunnermeier et al. (2012) find that bank non-interest income activities may influence systemic risk. To address the concern that our results might be driven by omitted variables, we include non-interest income activities as an additional control variable in the 2SLS regression model. Results are presented in Panel D of Table 4. We continue to find that geographic diversification leads to a positive and significant increase in systemic risk across all systemic risk measures. Insert Table 4 here 4.6 Channel effect: state and U.S. economy comovement Wagner (2010) predicts that bank geographic diversification may lead to greater systemic risk as diversification makes banks more similar to each other by exposing them to the same risks. Our empirical results support such prediction. Furthermore, we expect when BHCs that are located in a home state that commoves less with the rest of the economy expand across states, this would have a bigger impact on systemic risk as banks asset return will commove more with the whole economy and expose them to the same risk, which leads to higher systemic risk. On the other hand, when BHCs that are headquartered in a home state that commoves more with the aggregate U.S. economy diversify across state borders, it should have a smaller impact on systemic risk as the banks asset return will covary less with the whole economy and expose them to less systemic risk. In other words, the marginal effect of geographic diversification on systemic risk is 23

greater for BHCs that are located in a home state that commoves less with the rest of the economy. In this section we test this potential channel effect. To proxy for the degree of comovement between the economy of a state and the rest of the U.S., we follow Levine, Lin and Xie (2016) and use the correlation of a state economy with the U.S. economy. More specifically, we obtain the monthly Coincident index produced by Federal Reserve Bank of Philadelphia, for each of the 50 states and the U.S. 9 Based on the monthly Coincident index of each state and the overall U.S. economy, we compute the correlation between a state and the U.S. economy for each quarter using a rolling window of 12 quarters. A higher correlation indicates a greater comovement between a state and the aggregate U.S. economy (Comovement). We interact 1-HHI and Comovement and include the interaction as well as 1- Predicted HHI as the instruments in the 2SLS framework. We expect the coefficient on this interaction term to be negative as the marginal effect of geographic diversification on systemic risk is greater when a BHC is headquartered in a state that commoves less with the aggregate U.S. economy. The second stage results are reported in Panel A of Table 5. The coefficient on stand-alone 1-HHI continues to be positive and significant across all models using four different measures of systemic risk. On the other hand, the coefficient on the interaction term between 1-HHI and Comovement is negative and significant across all models, suggesting that when a BHC is headquartered in a state that commoves less with the U.S. 9 The coincident indexes summarize the current economic conditions of a state in a single index by combining four state-level indicators, which consist of nonfarm payroll employment, average hours worked in manufacturing by production workers, the unemployment rate, and wage and salary disbursements scaled by the consumer price index (U.S. city average). The trend for each state s index is set to the trend of its gross state product (GSP), so long-term growth in the state s index matches long-term growth in its GSP. 24

economy, geographic expansion leads to greater systemic risk. In other words, the impact of geographic diversification on systemic risk is less pronounced among BHCs that are located in states which strongly commove with the overall U.S. economy. We also perform the reduced-form analyses and report the results in Panel B of Table 5. The reduced form results are qualitatively similar, with the coefficient on 1-HHI (1-HHI Comovement) being positive (negative) and significant across all models. Collectively, the results presented in Table 5 lend support to our conjecture that state and U.S. economy comovement is an important channel through which bank geographic diversification increases financial instability. Insert Table 5 here 4.7 Cross sectional analyses Bayazitova and Shivdasani (2012), and Mayordomo et al. (2014) suggest that larger banks may pose greater systemic risk to the financial system. De Jonghe et al. (2015) and Brunnermeier et al. (2012) find that bank non-interest income activities may influence systemic risk. Laeven, Ratnovski, and Tong (2015) find that bank capital is inversely related to systemic risk. To check whether the relationship between geographic diversification and systemic risk varies across these BHC-specific characteristics, including bank size, capital, non-interest income activities, as well as liquidity, nonperforming loan ratio, and growth opportunity, we perform several cross-sectional analyses. Bank size, capital, liquidity, non-performing loan ratio, and growth opportunity are defined in Section 3.2.3. In addition, non-interest income activities are measured by total non-interest income divided by total assets. We partition our sample into two subsamples 25

based on the sample medians of the above bank characteristics. If a bank-quarter observation is greater than the sample median, it is assigned to the Higher subsample, otherwise Lower subsample. We present the results in Panel A to Panel F of Table 5. Panel A of Table 6 indicates that indeed geographic expansion by larger banks contribute more to systemic risk, while the impact of geographic diversification on systemic risk in smaller BHCs becomes insignificant. Panel B of Table 6 shows that geographic expansion contributes more to systemic risk in both highly- and lowlycapitalized BHCs, though the economic magnitude of the impact of geographic expansion on systemic risk is greater for lowly-capitalized banks than highly-capitalized ones. The above two results are consistent with Laeven et al. (2015) who document bank size (capital) is directly (inversely) related to systemic risk. Panel C of Table 6 suggests geographic expansion by banks with lower liquidity position contribute more to systemic risk, while the influence of geographic diversification on systemic risk in BHCs with higher liquidity becomes insignificant. Panel D of Table 6 indicates that indeed geographic expansion by banks engaging more non-interest income activities contribute more to systemic risk, while the impact of geographic diversification on systemic risk in BHCs with less non-traditional banking activities becomes insignificant. The result is consistent with Brunnermeier et al. (2012). Panel E of Table 6 suggests geographic expansion by banks with higher nonperforming loan ratio contribute more to systemic risk, while the influence of geographic diversification on systemic risk in BHCs with lower non-performing loan ratio becomes insignificant. The result is consistent with Mayordomo et al. (2014). Panel F of Table 6 suggests geographic expansion by banks with higher growth potential contribute more to 26

systemic risk, while the influence of geographic diversification on systemic risk in BHCs with less growth potential is insignificant. Insert Table 6 here V. Conclusion Using the gravity-deregulation model, we construct the time-varying and bankspecific exogenous instrument of geographic diversification following Goetz, Laeven, and Levine (2013), we examine the causal relationship between geographic diversification and systemic risk using publicly traded bank holding companies (BHCs) in the U.S. as the sample. We employ three variables to measure systemic risk: systemic expected shortfall (SES), normalized conditional capital shortfall (SRISK), and the value at risk of the financial system conditional on institutions being under distress (ΔCoVaR). We find that bank geographic diversification leads to higher systemic risk across all three proxies of systemic risk as well as the principal components based on the above mentioned three systemic risk measures. The results continue to hold with to several robustness checks, including using an alternative way of constructing instrument based on a more parsimonious gravity-deregulation model that only use distance while excluding market size in coming up with the predicted shares of BHC expansion, removing BHCs headquartered in New York City, excluding BHCs primarily engage in foreign operations, and including additional control variable. Moreover, we find that the impact of geographic diversification on systemic risk is more pronounced in BHCs that are located in states that commove less with the overall U.S. economy, suggesting state and U.S. economy 27

comovement is a potential channel to explain the results. The cross-sectional analyses reveal that the impact of geographic diversification on systemic risk is more pronounced in BHCs that are larger, have lower capital adequacy ratio and liquidity position, engage in more non-interest income activities, have higher non-performing loan ratio and growth opportunity. Our results have important implications. Conventional wisdom suggests that diversification may reduce firm-specific risk and individual bank insolvency risk, which may contribute to the financial stability of the financial system. However, our results indicate that geographic diversification may increase systemic risk as banks expand their footprints to more regions with the same risk. References Acharya, V., Engle, R., & Richardson, M. (2012). Capital shortfall: A new approach to ranking and regulating systemic risks. The American Economic Review, 102(3), 59-64. Acharya, V., Pedersen, L. H., Philippon, T., Richardson, M. (2016). Measuring systemic risk. Review of Financial Studies. Forthcoming. Adrian, T., & Brunnermeier, M. K. (2011). CoVaR. Working paper. Princeton University. Akhigbe, A., & Whyte, A. M. (2003). Changes in market assessments of bank risk following the Riegle Neal Act of 1994. Journal of Banking & Finance, 27(1), 87-102. Amel, D. F. (1993). State laws affecting the geographic expansion of commercial banks. Bayazitova, D., & Shivdasani, A. (2012). Assessing tarp. Review of Financial Studies, 25(2), 377-407. Berger, A. N., Clarke, G. R., Cull, R., Klapper, L., & Udell, G. F. (2005). Corporate governance and bank performance: A joint analysis of the static, selection, and 28