TY - JOUR
AU - Xia,, Cong
AB - Abstract Exploiting staggered interstate banking deregulation as exogenous shocks to bank geographic expansion, we examine the causal effect of geographic diversification on systemic risk. Using the gravity-deregulation approach, we find that bank geographic diversification leads to higher systemic risk measured by the change in conditional value at risk (⁠|$\Delta$|CoVaR) and financial integration (Logistic(⁠|$R^{2}))$|⁠. Furthermore, we document that geographic diversification affects systemic risk via its impact on asset similarity. The impact of geographic diversification on systemic risk is stronger in BHCs located in states comoving less with the U.S. aggregate economy. Geographic expansions allow banks to diversify assets and reduce idiosyncratic risk (Hughes et al. 1999; Akhigbe, and Whyte 2003; Deng and Elyasiani 2008; Goetz, Laeven, and Levine 2016). At the same time, however, diversification may increase systemic risk as it makes banks more similar to each other by holding similar portfolios, exposing them to the same risks. A negative shock may force one bank to liquidate assets to meet regulatory capital or macroprudential requirements. Because other banks hold similar asset portfolios, this may trigger joint liquidation, which may depress asset prices such that banks are forced to sell assets at deep fire sale discounts, generating financial distress at other banks holding the common assets. The affected banks could in turn sell other assets to shore up balance sheets, further depressing asset prices. Such liquidation spirals create interdependency and contagion, resulting in systemic risk (Wagner 2008, 2011; Allen, Babus, and Carletti 2012; Greenwood, Landier, and Thesmar 2015). Most existing studies focus on how diversification affects stand-alone risk, so there is a dearth of empirical evidence on the effect of diversification on systemic risk.1|$^{,}$|2 We try to fill this gap in the literature by examining the causal effect of bank geographic diversification on systemic risk. Identifying the causal effect of bank diversification on systemic risk is empirically challenging due to endogeneity concerns. First, the decision to diversify is often endogenous as banks may strategically choose to diversify when the benefits outweigh the costs of doing so (Matsusaka 2001). Second, omitted variables may drive both bank diversification and systemic risk (Campa and Kedia 2002). To overcome these empirical challenges, we exploit the staggered interstate banking deregulation as exogenous shocks to bank geographic expansion and use an instrumental variable approach based on the gravity-deregulation approach developed by Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016) to examine the causal effect of bank geographic diversification on systemic risk. Following Adrian and Brunnermeier (2016), we construct the change in conditional value at risk (⁠|$\Delta $|CoVaR) as our main measure of systemic risk. CoVaR is the value at risk of the financial system conditional on an institution being in distress. |$\Delta $|CoVaR, computed as the difference between the CoVaR conditional on the distress of an institution and the CoVaR conditional on the normal state of the institution, measures the marginal contribution of an institution to systemic risk. Following Karolyi et al. (2012) and Anginer, Demirguc-Kunt, and Zhu (2014), we use financial integration, proxied by the logistic transformation of |$R^{2}$| (Logistic(R|$^{2}))$|⁠, as an alternative measure of systemic risk. The |$R^{2}$| measure is developed by Pukthuanthong and Roll (2009), following which we obtain the |$R^{2}$| by regressing a bank’s daily stock returns against the four common factors extracted from the principal component analysis using the daily stock returns of the top 20 banks. A higher value of |$R^{2}$| indicates that a bank is exposed to more common risks, and hence is more integrated with other banks in the financial system. We find that bank geographic diversification leads to a higher systemic risk measured by both the change in conditional value at risk (|$\Delta $|CoVaR) and financial integration (Logistic(R|$^{2})).$| A 1-standard-deviation increase in geographic diversification results in an increase in |$\Delta $|CoVaR by 13.39% of its standard deviation and an increase in Logistic(R|$^{2}) $|by 7.3% of its standard deviation. The results remain valid with several robustness checks including reverse causality, additional control variables, alternative instruments, alternative frequency samples, and addressing the location heterogeneity in BHC expansion. Our results, together with those of Goetz, Laeven, and Levine (2016), lend support to the theoretical prediction in Wagner (2010) and Ibragimov, Jaffee, and Walden (2011) that bank diversification may result in lower stand-alone bank risk and higher systemic risk simultaneously. Bank geographic diversification may increase systemic risk because of greater asset similarity. As banks expand geographically and operate in multiple markets, their asset portfolios become similar to each other, leading to greater asset similarity among banks. The similar asset holdings may expose banks to common shocks, which in turn increase the probability of joint liquidation and cascading failures (Wagner 2008, 2011; Allen, Babus, and Carletti 2012). We label this channel the asset similarity channel. We follow Girardi et al. (2018) and construct the cosine similarity measures based on asset classes, loan types, and geographic distributions of mortgage loans to proxy for asset similarity. Indeed, we find that bank geographic expansions lead to a higher similarity in asset classes, loan types, and mortgage loan geographic distribution, consistent with the asset similarity channel. Furthermore, we find that the impact of geographic diversification on systemic risk is more pronounced for BHCs located in home states less correlated with the rest of the U.S. economy. The reason is that as these BHCs expand geographically, their asset returns comove more with the whole economy, which exposes them to the common risk in the economy, propagating systemic risk. To the best of our knowledge, our paper is the first to examine the causal effect of bank geographic diversification on systemic risk using the identification strategy based on the gravity-deregulation approach developed in Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016). We show that bank geographic diversification is an important determinant of systemic risk, adding to the existing studies that identify bank size, capital adequacy ratio, derivatives holding, nonperforming loans, and noninterest income activities, among others, as important factors affecting systemic risk (Bayazitova and Shivdasani 2012; Brunnermeier, Dong, and Palia 2012; De Jonghe, Diepstraten, and Schepens 2015; Mayordomo, Rodriguez-Moreno, and Peña 2014; Weiß, Neumann, and Bostandzic 2014). Second, we document that bank geographic diversification positively affects systemic risk, complementing Goetz, Laeven, and Levine (2016), who find that geographic diversification lowers banks’ stand alone risk. Collectively, Goetz, Laeven, and Levine (2016) and our study suggest that diversification may reduce stand alone risk, while increasing systemic risk. We thus contribute to the existing literature by providing a complete picture of how bank geographic diversification affects risk and lending empirical support to the theoretical prediction in Wagner (2010) and Ibragimov, Jaffee, and Walden (2011). Our study also complements Nijskens and Wagner (2011), who find that bank credit risk transfer mechanisms, such as credit default swaps and collateralized loan obligations, may shed individual bank risk while increasing systemic risk as bank returns become more correlated. Third, we provide the first empirical exercise to identify asset similarity as a channel through which bank geographic diversification positively affects systemic risk. On the policy front, the results suggest a tradeoff between stand alone risk and systemic risk associated with bank geographic diversification, suggesting that effective regulation should not only target stand alone bank risk but also address systemic risk. Fourth and finally, our study is also related to Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016), and Levine, Lin, and Xie (2016), who also use the gravity-deregulation model to construct the instrument of geographic diversification but instead examine the effect of bank geographic diversification on firm valuation, stand alone risk, and funding costs, respectively. Our work complements these studies by documenting the causal effect of bank geographic diversification on systemic risk. 1. Data and Variables 1.1 Sample selection Our sample construction starts with all bank holding companies (BHCs) filing the FR Y-9C form provided by the Federal Reserve Bank of Chicago. Following prior studies on bank branching deregulation (e.g., Jayaratne and Strahan 1996), we focus on BHCs headquartered in the 48 contiguous states and the District of Columbia while excluding the states of Delaware and South Dakota.3 We then merge the data set with the FDIC’s Summary of Deposits (SOD) database to compute deposit dispersion across metropolitan statistical areas (MSAs).4 Finally, we merge the data set with the CRSP database by using the link file provided by Federal Reserve Bank of New York. The final sample consists of 392 unique BHCs and 9,638 BHC-quarter observations over the sample period from 1986 to 1997. All continuous variables are winsorized at the top and bottom 1% levels. We follow Goetz, Laeven, and Levine (2016) to start the sample period in the third quarter of 1986, when the BHC database began coverage, and to end our sample in 1997, when the process of state-level changes in interstate banking deregulation ended. 1.2 Variable construction 1.2.1 Bank geographic diversification The FDIC’s Summary of Deposits (SOD) database provides deposits data at the branch and subsidiary level for each BHC, as well as information about the structure of the BHCs. Following Goetz, Laeven, and Levine (2016), we use deposit dispersion across MSAs as the measure of geographic diversification. It is defined as one minus the Herfindahl-Hirschman index of deposit shares across MSAs (1-HHI). This index ranges from zero to one, with larger values corresponding to greater degrees of geographic diversification. 1.2.2 Systemic risk measures To measure an institution’s contribution to systemic risk, we follow Adrian and Brunnermeier (2016) and use the change in conditional value at risk (|$\Delta $|CoVaR) as the main measure of systemic risk. CoVaR is the conditional value at risk of the financial system. |$\Delta $|CoVaR, defined as the difference between the CoVaR conditional on the distress of an institution and the CoVaR conditional on the normal state of the institution, measures the marginal contribution of an institution to the overall systemic risk. Specifically, |$\Delta $|CoVaR is constructed as follows. First, we run quantile regressions of market returns on individual bank returns as follows: $$\begin{equation} R_{mt} =\alpha _{system\vert i} +\beta _{system\vert i} R_{it} +\varepsilon _{it}, \end{equation}$$ (1) where |$R_{it} $| is the weekly stock returns of bank i, and |$R_{mt}$| is the weekly market returns. We then calculate CoVaR as the predicted value from the quantile regressions: $$\begin{equation} CoVaR_{it}^q =\hat {\alpha }_{system\vert i}^q +\hat {\beta }_{system\vert i}^q VaR_{it}^q, \end{equation}$$ (2) where |$VaR_{it}^q $| is the |$q$| percentile value at risk of bank |$i$| at time t. Finally, the change in CoVaR (|$\Delta $|CoVaR) is the difference between the CoVaR conditional on the distress of an institution |$i$| (⁠|$q$|=5%, that is, using the worst 5% financial system returns in the quantile regression) and CoVaR conditional on the normal state of the institution (⁠|$q$|=50%). |$\Delta $|CoVaR measures the marginal contribution of an institution to the overall systemic risk. We use return losses (return multiplied by |$-1$|⁠) to compute CoVaR, so a higher value of |$\Delta $|CoVaR indicates greater systemic risk: $$\begin{equation} \Delta CoVaR_{it}^{5\% } =-(CoVaR_{it}^{5\% } -CoVaR_{it}^{50\% } ). \end{equation}$$ (3) We modify the conditional value at risk in two ways based on Adrian and Brunnermeier (2016). First, we compute |$\Delta $|CoVaR based on a 3-year forward-looking rolling window while Adrian and Brunnermeier (2016) use the entire sample period. We do this to avoid the look-ahead bias in the regressions. Second, because we use the 3-year forward-looking rolling window and the time variation comes from the 3-year rolling window, we do not include state variables in the computation of either |$\beta _{System\vert i} $| or |$CoVaR_{it}^q .$| In other words, the variation in |$\Delta $|CoVaR comes entirely from the tail dependence, instead of from the time variation of the state variables. We also follow Karolyi et al. (2012) and Anginer, Demirguc-Kunt, and Zhu (2014) to use the logistic transformation of |$R^{2}$| (Logistic(R|$^{2}))$|⁠, computed as log(R|$^{2}/(1-R^{2}))$|⁠, as an alternative measure for systemic risk. |$R^{2}$|⁠, developed by Pukthuanthong and Roll (2009), measures the degree of financial integration of an individual bank with large banks in the system. A higher |$R^{2}$| indicates that a bank is more integrated with other banks. Specifically, the |$R^2$| is obtained by estimating the following model: $$\begin{equation} R_{it} =\alpha +\sum\limits_{k=1}^4 {\beta _{ikt} } Factor_{kt} +\varepsilon _{it}, \end{equation}$$ (4) where |$R_{it} $|is bank |$i$|’s daily equity return, and Factor|$_{kt}$| are the first four factors extracted from the principal component analysis using the daily stock returns of the 20 largest banks ranked by assets. To measure individual banks’ exposure to systemic risk (instead of its contribution to systemic risk), we use the marginal expected shortfall (MES) and the expected capital shortfall (SRISK) following Acharya, Pedersen, Philippon, and Richardson (2017), Acharya, Engle, and Richardson (2012), and Brownlees and Engle (2017). MES measures the average loss of market equity of a firm when the market return is in its 5% lower tail in a given year based on a 1-year forward-looking rolling window. According to Acharya et al. (2017), MES is defined as $$\begin{equation} MES_{it} =E(-R_{it} \vert R_{mt}~~\mbox{is in 5% tail)}, \end{equation}$$ (5) where |$R_{it} $| is firm |$i$|’s stock return on day |$t$|⁠, and |$R_{mt} $| is the market return on day |$t.$| Specifically, we compute the MES of a bank as the average stock return during the days when the market return is at the worst 5% in a given year during the sample period using a 1-year forward-looking rolling window. SRISK measures how much capital a bank needs at the time of crisis to maintain a given capital adequacy ratio. Below, we construct SRISK following Acharya, Engle, and Richardson (2012), further refined by Brownlees and Engle (2017): $$\begin{equation} \begin{array}{l} SRISK_{it} =E(Capital~Shortfall_{it} \vert Crisis) \\ ~~~~~~~~~~~~~~\mbox{=}E(k(Debt_{it} +Equity_{it} )-Equity_{it} \vert Crisis) \\ ~~~~~~~~~~~~~~\mbox{=}kDebt_{it} -(1-k)(1-LRMES_{it} )\times Equity_{it} \\ \end{array}\!, \end{equation}$$ (6) where |$k$| is the capital adequacy ratio set at 8% following Brownlees and Engle (2017); and LRMES is the long-run marginal expected shortfall, calculated as |$LRMES=1-exp\left( {-18\times MES} \right).$| We scale SRISK by the sum of all positive SRISK at time |$t$| following Brownlees and Engle (2017). 1.2.3 Control variables Following Anginer, Demirguc-Kunt, and Zhu (2014), we include a set of BHC-specific characteristics as control variables, including bank size, funding structure, profitability, market-to-book ratio, noninterest income share, and loan loss provision. Bank size is calculated as the natural logarithm of total assets (Size). We also include the squared term of bank size (Size|$^{2})$| to account for any nonlinear effect. Reliance on nondeposit short-term funding is computed as the sum of interbank borrowing, certificates of deposits, and short-term bonds (nondeposit short-term funding) divided by the sum of deposits and nondeposit short-term funding (ST_funding); profitability is measured as the return on assets (ROA); market-to-book ratio is the market value of equity divided by book value of equity (Market_to_book); noninterest income share is noninterest income divided by total operating income (Noninterest); and provision is loan loss provision divided by total loans (Provision). To account for banks’ business activity diversification that may be correlated with geographic diversification and may potentially affect systemic risk, we include income diversity (Income_diversity) and asset diversity (Asset_diversity) as additional control variables. Following Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016), we define Income_diversity as 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert$|⁠, and Asset_diversity as 1-|$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$| Income diversity measures the degree to which bank income is diversified between interest and noninterest income, and asset diversity measures the degree to which bank assets are diversified between traditional lending and nontraditional banking activities. 1.3 Descriptive statistics Table 1 presents the sample descriptive statistics. We divide the sample into diversified and nondiversified BHC-quarter subsamples. As BHCs expand geographically at different times, the same BHC can be categorized as a nondiversified BHC in the years before it expands geographically and a diversified BHC in the years afterward. The diversified BHC-quarter observations contribute to greater systemic risk, measured by both the change in conditional value at risk (|$\Delta $|CoVaR) and financial integration (Logistic(R|$^{2}))$|⁠, than nondiversified BHC-quarter observations. The diversified BHC-quarter observations are also more exposed to systemic risk, measured by both the marginal expected shortfall (MES) and the expected capital shortfall (SRISK), than nondiversified BHC-quarter observations. On average, the diversified BHC-quarter observations have 88.3 branches (# branches) in 7.568 MSAs (# MSAs) and 36.5% of deposits in foreign MSAs (Share). Nondiversified BHC-quarter observations have 11.233 branches in a single MSA with no deposits in foreign MSAs. Moreover, compared with nondiversified BHC-quarter observations, diversified BHC-quarter observations are larger, engage in more noninterest income activities, set aside more loan loss provision, use more nondeposit short-term funding, and have higher income diversity. On the other hand, these observations have lower profitability, market-to-book ratio, and asset diversity. All these differences are statistically significant at the 5% level. Table 1 Summary statistics . Diversified bank-quarters . Nondiversified bank-quarters . Difference in mean . Difference in median . Variable . N . Mean . SD . Median . N . Mean . SD . Median . |$t$|-stat . Wilcoxon Z-value . |$\Delta $|CoVaR 5,788 0.337 0.263 0.307 3,780 0.207 0.203 0.18 25.815*** 24.846*** |$R^{2}$| 5,753 0.085 0.08 0.065 3,714 0.067 0.046 0.057 12.035*** 8.326*** Logistic(R|$^{2})$| 5,753 -2.706 0.929 -2.669 3,714 -2.878 0.82 -2.801 9.238*** 8.326*** MES 5,767 0.009 0.01 0.008 3,768 0.006 0.009 0.004 18.68*** 18.9*** SRISK 5,789 0.149 0.843 -0.099 3,803 0.091 0.85 -0.133 3.33*** 6.19*** 1–HHI 5,805 0.491 0.267 0.489 3,833 0.000 0.000 0.000 113.953*** 85.966*** Size 5,805 14.63 1.576 14.51 3,833 13.15 0.844 12.97 53.489*** 49.482*** Size|$^{2}$| 5,805 216.5 47.51 210.4 3,833 173.5 23.16 168.3 52.131*** 49.482*** ROA 5,805 0.005 0.006 0.005 3,833 0.006 0.008 0.006 -3.175*** -2.9 Market_to_book 5,805 1.032 0.049 1.025 3,833 1.038 0.244 1.019 -2.037*** 5.534*** Noninterest 5,805 0.136 0.082 0.12 3,833 0.108 0.092 0.088 15.579*** 24.867*** ST_funding 5,805 0.005 0.008 0.002 3,832 0.004 0.007 0.002 3.537** 8.271*** Provision 5,805 0.023 0.038 0.007 3,833 0.02 0.044 0 4.463*** 13.173*** Income_diversity 5,805 0.68 0.116 0.681 3,833 0.619 0.107 0.621 25.824*** 26.004*** Asset_diversity 5,806 0.372 0.105 0.353 3,833 0.39 0.137 0.369 -7.343*** -4.876*** #Branches 5,805 88.3 192.313 25 3,833 11.233 10.742 8 23.350*** 46.100*** #MSAs 5,805 7.568 11.163 3 3,833 1 0 1 35.818*** 79.832*** Share 5,805 0.365 0.238 0.336 3,833 0 0 0 113.20*** 76.43*** . Diversified bank-quarters . Nondiversified bank-quarters . Difference in mean . Difference in median . Variable . N . Mean . SD . Median . N . Mean . SD . Median . |$t$|-stat . Wilcoxon Z-value . |$\Delta $|CoVaR 5,788 0.337 0.263 0.307 3,780 0.207 0.203 0.18 25.815*** 24.846*** |$R^{2}$| 5,753 0.085 0.08 0.065 3,714 0.067 0.046 0.057 12.035*** 8.326*** Logistic(R|$^{2})$| 5,753 -2.706 0.929 -2.669 3,714 -2.878 0.82 -2.801 9.238*** 8.326*** MES 5,767 0.009 0.01 0.008 3,768 0.006 0.009 0.004 18.68*** 18.9*** SRISK 5,789 0.149 0.843 -0.099 3,803 0.091 0.85 -0.133 3.33*** 6.19*** 1–HHI 5,805 0.491 0.267 0.489 3,833 0.000 0.000 0.000 113.953*** 85.966*** Size 5,805 14.63 1.576 14.51 3,833 13.15 0.844 12.97 53.489*** 49.482*** Size|$^{2}$| 5,805 216.5 47.51 210.4 3,833 173.5 23.16 168.3 52.131*** 49.482*** ROA 5,805 0.005 0.006 0.005 3,833 0.006 0.008 0.006 -3.175*** -2.9 Market_to_book 5,805 1.032 0.049 1.025 3,833 1.038 0.244 1.019 -2.037*** 5.534*** Noninterest 5,805 0.136 0.082 0.12 3,833 0.108 0.092 0.088 15.579*** 24.867*** ST_funding 5,805 0.005 0.008 0.002 3,832 0.004 0.007 0.002 3.537** 8.271*** Provision 5,805 0.023 0.038 0.007 3,833 0.02 0.044 0 4.463*** 13.173*** Income_diversity 5,805 0.68 0.116 0.681 3,833 0.619 0.107 0.621 25.824*** 26.004*** Asset_diversity 5,806 0.372 0.105 0.353 3,833 0.39 0.137 0.369 -7.343*** -4.876*** #Branches 5,805 88.3 192.313 25 3,833 11.233 10.742 8 23.350*** 46.100*** #MSAs 5,805 7.568 11.163 3 3,833 1 0 1 35.818*** 79.832*** Share 5,805 0.365 0.238 0.336 3,833 0 0 0 113.20*** 76.43*** This table provides summary statistics for diversified and nondiversified banks. The full sample ranges from 1986Q3 to 1997Q4. A bank is classified as diversified if it has branches in more than one MSAs. The sample is at the bank-quarter level. A bank can be diversified in 1 year and nondiversified in another year, so it may appear in both groups. |$\Delta $|CoVaR is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis of daily equity return of top-20 largest banks. MES is the marginal expected shortfall, defined as the average stock return of a bank when the market return is in its 5% lower tail in a given year. SRISK is the capital shortfall of a bank in time of crisis. We scale capital shortfall by the sum of all positive SRISK during a quarter. Size is the logarithm of total assets. ROA is net income divided by total assets. Market_to_book is the market value of equity divided by book value of equity. Noninterest is noninterest income divided by total operating income. Provision is loan loss reserves divided by gross loans. ST_funding is nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding. Income_diversity is 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|Asset_diversity is 1-|$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$|#Branches is the number of branches a BHC operates. #MSAs is the number of MSAs a BHC operates. Share is the deposit share of a BHC in a foreign MSA. *|$p<.1$|⁠; **|$p <.05$|⁠; ***|$p< .01$|⁠. Open in new tab Table 1 Summary statistics . Diversified bank-quarters . Nondiversified bank-quarters . Difference in mean . Difference in median . Variable . N . Mean . SD . Median . N . Mean . SD . Median . |$t$|-stat . Wilcoxon Z-value . |$\Delta $|CoVaR 5,788 0.337 0.263 0.307 3,780 0.207 0.203 0.18 25.815*** 24.846*** |$R^{2}$| 5,753 0.085 0.08 0.065 3,714 0.067 0.046 0.057 12.035*** 8.326*** Logistic(R|$^{2})$| 5,753 -2.706 0.929 -2.669 3,714 -2.878 0.82 -2.801 9.238*** 8.326*** MES 5,767 0.009 0.01 0.008 3,768 0.006 0.009 0.004 18.68*** 18.9*** SRISK 5,789 0.149 0.843 -0.099 3,803 0.091 0.85 -0.133 3.33*** 6.19*** 1–HHI 5,805 0.491 0.267 0.489 3,833 0.000 0.000 0.000 113.953*** 85.966*** Size 5,805 14.63 1.576 14.51 3,833 13.15 0.844 12.97 53.489*** 49.482*** Size|$^{2}$| 5,805 216.5 47.51 210.4 3,833 173.5 23.16 168.3 52.131*** 49.482*** ROA 5,805 0.005 0.006 0.005 3,833 0.006 0.008 0.006 -3.175*** -2.9 Market_to_book 5,805 1.032 0.049 1.025 3,833 1.038 0.244 1.019 -2.037*** 5.534*** Noninterest 5,805 0.136 0.082 0.12 3,833 0.108 0.092 0.088 15.579*** 24.867*** ST_funding 5,805 0.005 0.008 0.002 3,832 0.004 0.007 0.002 3.537** 8.271*** Provision 5,805 0.023 0.038 0.007 3,833 0.02 0.044 0 4.463*** 13.173*** Income_diversity 5,805 0.68 0.116 0.681 3,833 0.619 0.107 0.621 25.824*** 26.004*** Asset_diversity 5,806 0.372 0.105 0.353 3,833 0.39 0.137 0.369 -7.343*** -4.876*** #Branches 5,805 88.3 192.313 25 3,833 11.233 10.742 8 23.350*** 46.100*** #MSAs 5,805 7.568 11.163 3 3,833 1 0 1 35.818*** 79.832*** Share 5,805 0.365 0.238 0.336 3,833 0 0 0 113.20*** 76.43*** . Diversified bank-quarters . Nondiversified bank-quarters . Difference in mean . Difference in median . Variable . N . Mean . SD . Median . N . Mean . SD . Median . |$t$|-stat . Wilcoxon Z-value . |$\Delta $|CoVaR 5,788 0.337 0.263 0.307 3,780 0.207 0.203 0.18 25.815*** 24.846*** |$R^{2}$| 5,753 0.085 0.08 0.065 3,714 0.067 0.046 0.057 12.035*** 8.326*** Logistic(R|$^{2})$| 5,753 -2.706 0.929 -2.669 3,714 -2.878 0.82 -2.801 9.238*** 8.326*** MES 5,767 0.009 0.01 0.008 3,768 0.006 0.009 0.004 18.68*** 18.9*** SRISK 5,789 0.149 0.843 -0.099 3,803 0.091 0.85 -0.133 3.33*** 6.19*** 1–HHI 5,805 0.491 0.267 0.489 3,833 0.000 0.000 0.000 113.953*** 85.966*** Size 5,805 14.63 1.576 14.51 3,833 13.15 0.844 12.97 53.489*** 49.482*** Size|$^{2}$| 5,805 216.5 47.51 210.4 3,833 173.5 23.16 168.3 52.131*** 49.482*** ROA 5,805 0.005 0.006 0.005 3,833 0.006 0.008 0.006 -3.175*** -2.9 Market_to_book 5,805 1.032 0.049 1.025 3,833 1.038 0.244 1.019 -2.037*** 5.534*** Noninterest 5,805 0.136 0.082 0.12 3,833 0.108 0.092 0.088 15.579*** 24.867*** ST_funding 5,805 0.005 0.008 0.002 3,832 0.004 0.007 0.002 3.537** 8.271*** Provision 5,805 0.023 0.038 0.007 3,833 0.02 0.044 0 4.463*** 13.173*** Income_diversity 5,805 0.68 0.116 0.681 3,833 0.619 0.107 0.621 25.824*** 26.004*** Asset_diversity 5,806 0.372 0.105 0.353 3,833 0.39 0.137 0.369 -7.343*** -4.876*** #Branches 5,805 88.3 192.313 25 3,833 11.233 10.742 8 23.350*** 46.100*** #MSAs 5,805 7.568 11.163 3 3,833 1 0 1 35.818*** 79.832*** Share 5,805 0.365 0.238 0.336 3,833 0 0 0 113.20*** 76.43*** This table provides summary statistics for diversified and nondiversified banks. The full sample ranges from 1986Q3 to 1997Q4. A bank is classified as diversified if it has branches in more than one MSAs. The sample is at the bank-quarter level. A bank can be diversified in 1 year and nondiversified in another year, so it may appear in both groups. |$\Delta $|CoVaR is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis of daily equity return of top-20 largest banks. MES is the marginal expected shortfall, defined as the average stock return of a bank when the market return is in its 5% lower tail in a given year. SRISK is the capital shortfall of a bank in time of crisis. We scale capital shortfall by the sum of all positive SRISK during a quarter. Size is the logarithm of total assets. ROA is net income divided by total assets. Market_to_book is the market value of equity divided by book value of equity. Noninterest is noninterest income divided by total operating income. Provision is loan loss reserves divided by gross loans. ST_funding is nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding. Income_diversity is 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|Asset_diversity is 1-|$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$|#Branches is the number of branches a BHC operates. #MSAs is the number of MSAs a BHC operates. Share is the deposit share of a BHC in a foreign MSA. *|$p<.1$|⁠; **|$p <.05$|⁠; ***|$p< .01$|⁠. Open in new tab 2. Bank Geographic Diversification and Systemic Risk: Ordinary Least Squares Regressions To understand the relationship between bank geographic diversification and systemic risk, we first run the ordinary least squares (OLS) regression. The dependent variable is systemic risk, including institutions’ contribution to systemic risk, measured by |$\Delta $|CoVaR and Logistic(R|$^{2})$|⁠, and institutions’ exposure to systemic risk, measured by MES and SRISK. The independent variable of interest is geographic diversification based on deposit dispersion across MSAs. Columns (1) – (4) of Table 2 report the results for |$\Delta $|CoVaR and Logistic(R|$^{2}).$| Without control variables, the coefficients on bank geographic diversification are positive and statistically significant at the 5% level or better (Columns 1 and 2). With the bank-specific controls, the coefficients on bank geographic diversification 1–HHI remain positive but become statistically insignificant (Columns 3 and 4). Table 2 Bank geographic diversification and systemic risk: OLS results . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . MES . SRISK . MES . SRISK . 1–HHI 0.161** 0.187*** 0.014 0.109 0.037*** 2.025*** -0.001 -0.024 (2.099) (3.669) (0.440) (1.426) (3.868) (3.860) (-0.575) (-0.189) Size -0.088 0.172 0.005 0.914 (-0.652) (0.300) (0.948) (1.327) Size|$^{2}$| 0.006 -0.006 -0.000 -0.023 (1.148) (-0.287) (-0.588) (-0.930) ROA 0.768** 2.616 -0.033* -13.373*** (2.129) (1.431) (-1.685) (-3.133) Market_to_book -0.054 0.414*** -0.002 -1.115 (-1.054) (3.836) (-0.524) (-1.256) Noninterest -0.090 -0.283 0.000 -2.919*** (-0.544) (-0.576) (0.054) (-3.744) Provision 0.793*** 4.946*** 0.075*** 16.106*** (2.738) (3.673) (3.152) (6.057) ST_funding -0.106 0.402 -0.009 -0.726 (-1.141) (1.134) (-1.398) (-1.408) Income_diversity -0.013 0.276 0.006 2.772*** (-0.143) (1.019) (1.101) (4.880) Asset_diversity -0.014 -0.244 -0.001 -0.221 (-0.234) (-1.353) (-0.343) (-0.912) State-year fixed effect Yes Yes Yes Yes Yes Yes Yes Yes BHC fixed effect Yes Yes Yes Yes Yes Yes Yes Yes N 9,467 9,568 9,567 9,466 9,654 9,652 9,593 9,591 . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . MES . SRISK . MES . SRISK . 1–HHI 0.161** 0.187*** 0.014 0.109 0.037*** 2.025*** -0.001 -0.024 (2.099) (3.669) (0.440) (1.426) (3.868) (3.860) (-0.575) (-0.189) Size -0.088 0.172 0.005 0.914 (-0.652) (0.300) (0.948) (1.327) Size|$^{2}$| 0.006 -0.006 -0.000 -0.023 (1.148) (-0.287) (-0.588) (-0.930) ROA 0.768** 2.616 -0.033* -13.373*** (2.129) (1.431) (-1.685) (-3.133) Market_to_book -0.054 0.414*** -0.002 -1.115 (-1.054) (3.836) (-0.524) (-1.256) Noninterest -0.090 -0.283 0.000 -2.919*** (-0.544) (-0.576) (0.054) (-3.744) Provision 0.793*** 4.946*** 0.075*** 16.106*** (2.738) (3.673) (3.152) (6.057) ST_funding -0.106 0.402 -0.009 -0.726 (-1.141) (1.134) (-1.398) (-1.408) Income_diversity -0.013 0.276 0.006 2.772*** (-0.143) (1.019) (1.101) (4.880) Asset_diversity -0.014 -0.244 -0.001 -0.221 (-0.234) (-1.353) (-0.343) (-0.912) State-year fixed effect Yes Yes Yes Yes Yes Yes Yes Yes BHC fixed effect Yes Yes Yes Yes Yes Yes Yes Yes N 9,467 9,568 9,567 9,466 9,654 9,652 9,593 9,591 This table reports the results from an OLS regression on how bank geographic diversification affects systemic risk. |$\Delta $|CoVaR is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis using daily equity return of top-20 largest banks. Size is the logarithm of total assets. MES is marginal expected shortfall, defined as the average stock return of a bank on condition that the overall market is under its 5% tail. SRISK is expected capital shortfall of a bank on conditional on crisis. We scale capital shortfall by the sum of all positive SRISK during a quarter. ROA is net income divided by total assets. Market_to_book is market value of equity divided by book value of equity. Noninterest is noninterest income divided by total operating income. Provision is loan loss reserves divided by gross loans. ST_funding is nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding. Income_diversity is 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|Asset_diversity is 1-|$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$| We cluster standard errors at the BHC level and report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab Table 2 Bank geographic diversification and systemic risk: OLS results . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . MES . SRISK . MES . SRISK . 1–HHI 0.161** 0.187*** 0.014 0.109 0.037*** 2.025*** -0.001 -0.024 (2.099) (3.669) (0.440) (1.426) (3.868) (3.860) (-0.575) (-0.189) Size -0.088 0.172 0.005 0.914 (-0.652) (0.300) (0.948) (1.327) Size|$^{2}$| 0.006 -0.006 -0.000 -0.023 (1.148) (-0.287) (-0.588) (-0.930) ROA 0.768** 2.616 -0.033* -13.373*** (2.129) (1.431) (-1.685) (-3.133) Market_to_book -0.054 0.414*** -0.002 -1.115 (-1.054) (3.836) (-0.524) (-1.256) Noninterest -0.090 -0.283 0.000 -2.919*** (-0.544) (-0.576) (0.054) (-3.744) Provision 0.793*** 4.946*** 0.075*** 16.106*** (2.738) (3.673) (3.152) (6.057) ST_funding -0.106 0.402 -0.009 -0.726 (-1.141) (1.134) (-1.398) (-1.408) Income_diversity -0.013 0.276 0.006 2.772*** (-0.143) (1.019) (1.101) (4.880) Asset_diversity -0.014 -0.244 -0.001 -0.221 (-0.234) (-1.353) (-0.343) (-0.912) State-year fixed effect Yes Yes Yes Yes Yes Yes Yes Yes BHC fixed effect Yes Yes Yes Yes Yes Yes Yes Yes N 9,467 9,568 9,567 9,466 9,654 9,652 9,593 9,591 . (1) . (2) . (3) . (4) . (5) . (6) . (7) . (8) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . MES . SRISK . MES . SRISK . 1–HHI 0.161** 0.187*** 0.014 0.109 0.037*** 2.025*** -0.001 -0.024 (2.099) (3.669) (0.440) (1.426) (3.868) (3.860) (-0.575) (-0.189) Size -0.088 0.172 0.005 0.914 (-0.652) (0.300) (0.948) (1.327) Size|$^{2}$| 0.006 -0.006 -0.000 -0.023 (1.148) (-0.287) (-0.588) (-0.930) ROA 0.768** 2.616 -0.033* -13.373*** (2.129) (1.431) (-1.685) (-3.133) Market_to_book -0.054 0.414*** -0.002 -1.115 (-1.054) (3.836) (-0.524) (-1.256) Noninterest -0.090 -0.283 0.000 -2.919*** (-0.544) (-0.576) (0.054) (-3.744) Provision 0.793*** 4.946*** 0.075*** 16.106*** (2.738) (3.673) (3.152) (6.057) ST_funding -0.106 0.402 -0.009 -0.726 (-1.141) (1.134) (-1.398) (-1.408) Income_diversity -0.013 0.276 0.006 2.772*** (-0.143) (1.019) (1.101) (4.880) Asset_diversity -0.014 -0.244 -0.001 -0.221 (-0.234) (-1.353) (-0.343) (-0.912) State-year fixed effect Yes Yes Yes Yes Yes Yes Yes Yes BHC fixed effect Yes Yes Yes Yes Yes Yes Yes Yes N 9,467 9,568 9,567 9,466 9,654 9,652 9,593 9,591 This table reports the results from an OLS regression on how bank geographic diversification affects systemic risk. |$\Delta $|CoVaR is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis using daily equity return of top-20 largest banks. Size is the logarithm of total assets. MES is marginal expected shortfall, defined as the average stock return of a bank on condition that the overall market is under its 5% tail. SRISK is expected capital shortfall of a bank on conditional on crisis. We scale capital shortfall by the sum of all positive SRISK during a quarter. ROA is net income divided by total assets. Market_to_book is market value of equity divided by book value of equity. Noninterest is noninterest income divided by total operating income. Provision is loan loss reserves divided by gross loans. ST_funding is nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding. Income_diversity is 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|Asset_diversity is 1-|$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$| We cluster standard errors at the BHC level and report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab We also estimate individual banks’ exposure to systemic risk proxied by MES and SRISK and report the results in Columns 5–8 of Table 2. Without control variables, the coefficients on bank geographic diversification 1–HHI are positive and statistically significant at the 1% level (Columns 5 and 6). With the bank-specific controls, the coefficients on 1–HHI become negative and insignificant (Columns 7 and 8). The OLS results are biased due to the endogenous decision to diversify. If bank geographic diversification increases systemic risk, a bank exposed to more systemic risk ex ante may choose to expand less to other regions; while a bank exposed to less systemic risk may choose to expand more. As a result, the OLS regressions may underestimate the effect of geographic diversification on systemic risk.5 In the next section, we employ an instrumental variable approach to address the endogeneity issue. 3. Identification Strategy and the Empirical Methodology 3.1 Identification strategy Before the 1970s, U.S. banks were largely prohibited from expanding across state borders by law. In 1978, Maine became the first state to lift the restriction on the entry of banks from foreign states. Alaska and New York followed suit in 1982. Over the following decade, many states removed entry barriers to out-of-state banks in a staggered time-varying and state-specific process. States either unilaterally opened state borders to allow the entry of banks from foreign states, or signed reciprocal bilateral or multilateral agreements with other states allowing interstate banking. The wave of interstate banking deregulation continued until the mid-1990s and culminated in 1994 when Congress passed the Riegle-Neal Interstate Banking and Branching Efficiency Act (IBBEA). The IBBEA removed all remaining restrictions on interstate banking by 1995 when nation-wide interstate banking became a reality. In summary, the evolution of interstate banking deregulation is a staggered process that varies across states and over time, generating exogenous shocks to bank geographic expansion. In this study, we follow Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016) and use the interstate banking deregulation as exogenous shocks to bank geographic expansion. Exploiting this staggered deregulation process, we identify whether banks in a home MSA can legally enter MSAs in other states for each MSA-pair over time based on Amel (1993), and determine the actual dates the Riegle-Neal Banking and Branching Efficiency Act of 1994 becomes effective based on Rice and Strahan (2010). This interstate banking deregulation process alone does not provide us an instrument that varies among BHCs in the same MSA. In the next step, we integrate this state-specific staggered process of interstate banking deregulation into a gravity model that uses predetermined variables, such as physical distance and relative market size, to project the deposit shares a BHC may receive in foreign MSAs, based on which we construct a time-varying BHC-specific instrumental variable for bank geographic diversification. There are two plausibly exogenous sources of variation in this instrument, the staggered process of interstate banking deregulation and the predetermined variables, including the physical distance between a BHC’s headquarters and the center of foreign MSAs, and the relative market size of home versus foreign MSAs. In the next section, we describe in detail how we construct the instrument using the gravity-deregulation approach and how we apply it in a framework to identify the causal effect of bank geographic diversification on systemic risk. 3.2 The gravity-deregulation model The gravity model is widely used in the international trade literature to construct instrumental variables for bilateral trade flows in assessing the relationship between international trade and income (Frankel and Romer 1999; Helpman, Melitz, and Rubinstein 2008). The gravity model employs predetermined characteristics, such as country size and the physical distance between countries, to project bilateral trade flows between countries. Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016) are among the first in the finance literature to integrate staggered interstate banking deregulation into the gravity model to project bank geographic expansion across state borders. Following Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016), we integrate the staggered interstate banking deregulation into the gravity model that includes both the physical distance between the BHC headquarters and the center of a foreign MSA and the relative market size between home and foreign MSAs to project the deposit share a BHC subsidiary may receive in each foreign MSA. We argue that a BHC is more likely to expand to a neighboring MSA as the cost of doing so is lower. Moreover, BHCs may be more attracted to larger markets than smaller ones. More specifically, we estimate the following model: $$\begin{equation} Share_{bijt} =\alpha Distance_{bij} +\beta ln(Population_{it} /Population_{jt} )+\varepsilon _{bijt}, \end{equation}$$ (7) where Share|$_{bijt}$| is the deposit share of BHC |$b$|⁠, headquartered in MSA |$i$|⁠, held in its subsidiaries in MSA |$j $|in quarter |$t$|⁠, and Distance|$_{bij}$| is the distance between BHC |$b$|’s headquarters in MSA |$i$| and the center of MSA |$j $|(in hundreds of miles) based on street addresses. We expect the coefficient on the distance to be negative as banks are less likely to expand to distant MSAs. ln(Population|$_{it}$|/Population|$_{jt})$| is the natural logarithm of the population of a BHC’s home MSA |$i$| divided by the population of foreign MSA |$j$| in quarter |$t$|⁠, a proxy for the relative market size of home versus foreign MSAs. We expect the coefficient to be negative as BHCs headquartered in a smaller market will be more likely to expand geographically to a relatively larger foreign market. The deposit share that a bank branch can receive in a certain MSA ranges from zero to one. Following Papke and Wooldridge (1996, 2008), we employ a fractional logit model to estimate model (5). Because we need the predicted shares to construct the instrument, we use the fractional logit model instead of OLS to ensure the predicted value is bounded between zero and one. We only include BHC-quarter observations in which it is legal for BHC |$b$| with headquarters in MSA |$i$| to enter MSA |$j$| in quarter |$t.$| Columns 1 and 2 of Table 3 present the results using the fractional logit model and OLS regression without fixed effects, respectively. Column 3 reports the OLS regression results with both home- and foreign-MSA fixed effects. We cluster standard errors at the MSA-quarter level. As expected, the distance between the BHC headquarters and the MSA where the BHC expands has a negative effect on the deposit share a BHC receives in that MSA, suggesting that a BHC is more likely to expand to geographically proximate foreign MSAs. Furthermore, the coefficient on the relative market size is negative and statistically significant, suggesting that BHCs are less likely to expand to relatively small MSAs. Table 3 Results for the gravity-deregulation model . (1) . (2) . (3) . |$~$| . Share . Share . Share . ln(Distance) -0.0056*** -0.023*** -0.024*** (-46.32) (-44.07) (-41.75) ln(Population|$_{i}$|/Population|$_{j})$| -0.0013*** -0.0018*** -0.0018*** (-21.33) (-16.05) (-16.61) Home-MSA fixed effects Yes Foreign-MSA fixed effects Yes N 728,809 728,809 728,809 . (1) . (2) . (3) . |$~$| . Share . Share . Share . ln(Distance) -0.0056*** -0.023*** -0.024*** (-46.32) (-44.07) (-41.75) ln(Population|$_{i}$|/Population|$_{j})$| -0.0013*** -0.0018*** -0.0018*** (-21.33) (-16.05) (-16.61) Home-MSA fixed effects Yes Foreign-MSA fixed effects Yes N 728,809 728,809 728,809 This table reports the average marginal effects from a fractional logit regression (Column 1) and OLS results for the gravity-deregulation model (Columns 2 and 3). The dependent variable Share is the deposit share a BHC has in a given MSA. ln(Distance) is the natural logarithm of the straight-line distance between a BHC’s headquarter and the center of an MSA. ln(Population|$_{i }$|/Population|$_{j})$| is the natural logarithm of the population of BHC’s home state |$i$| divided by the population of a foreign state |$j.$| We cluster standard errors at the MSA-quarter level and report t-values in parentheses. *|$p<.1$|⁠; **|$p<.05$|⁠; ***|$p<.01$|⁠. Open in new tab Table 3 Results for the gravity-deregulation model . (1) . (2) . (3) . |$~$| . Share . Share . Share . ln(Distance) -0.0056*** -0.023*** -0.024*** (-46.32) (-44.07) (-41.75) ln(Population|$_{i}$|/Population|$_{j})$| -0.0013*** -0.0018*** -0.0018*** (-21.33) (-16.05) (-16.61) Home-MSA fixed effects Yes Foreign-MSA fixed effects Yes N 728,809 728,809 728,809 . (1) . (2) . (3) . |$~$| . Share . Share . Share . ln(Distance) -0.0056*** -0.023*** -0.024*** (-46.32) (-44.07) (-41.75) ln(Population|$_{i}$|/Population|$_{j})$| -0.0013*** -0.0018*** -0.0018*** (-21.33) (-16.05) (-16.61) Home-MSA fixed effects Yes Foreign-MSA fixed effects Yes N 728,809 728,809 728,809 This table reports the average marginal effects from a fractional logit regression (Column 1) and OLS results for the gravity-deregulation model (Columns 2 and 3). The dependent variable Share is the deposit share a BHC has in a given MSA. ln(Distance) is the natural logarithm of the straight-line distance between a BHC’s headquarter and the center of an MSA. ln(Population|$_{i }$|/Population|$_{j})$| is the natural logarithm of the population of BHC’s home state |$i$| divided by the population of a foreign state |$j.$| We cluster standard errors at the MSA-quarter level and report t-values in parentheses. *|$p<.1$|⁠; **|$p<.05$|⁠; ***|$p<.01$|⁠. Open in new tab We first calculate the predicted value of a BHC’s deposit shares in foreign MSAs based on the fractional logit model, as reported in Column 1. We then construct the BHC-specific and time-varying instrumental variable of geographic diversification as one minus the Herfindahl index based on the projected deposit shares. We choose the model in Column 1, because adding too many fixed effects in the construction of the instrument variable may bias the second-stage estimation (Rubinstein 2011). For observations in which regulation prohibits a BHC from operating a subsidiary in a foreign MSA, we set the projected deposit share to zero. 3.3 Two-stage least squares regressions With the instrument constructed above, we implement the two-stage least squares (2SLS) regression as follows: $$\begin{equation} (1-HHI)_{it} =\beta _1 (1-Predicted~HHI)_{it} +\gamma _1 X_{it} +\delta _i +\eta _{kt} +\varepsilon _{it}, \end{equation}$$ (8) $$\begin{equation} Systemic~Risk_{it} =\beta _2 (1-HHI)_{it} +\gamma _2 X_{it} +\delta _i +\eta _{kt} +\pi _{it}. \end{equation}$$ (9) In the first stage, the actual geographic diversification (1–HHI) is regressed on one minus the predicted Herfindahl-Hirschman index based on projected deposit share (1–Predicted HHI). In the second stage, measures of systemic risk are regressed on the predicted value of geographic diversification from the first stage (Predicted (1–HHI)). Systemic risk is measured by |$\Delta $|CoVaR and Logistic(R|$^{2}) $|as discussed in Section 2.2.2. In addition, we use MES and SRISK to measure individual banks’ exposure to systemic risk, also discussed in Section 2.2.2. |$X_{it}$| is a set of control variables as discussed in Section 2.2.3. |$\delta _i $| is the BHC fixed effect, and |$\eta _{kt} $| is the state-year fixed effect for BHCs located in state |$k$| at time |$t.$| 4. Empirical Results from the 2SLS Regressions 4.1 Geographic diversification and systemic risk Panel B of Table 3 reports the first-stage results for estimating model (8) on geographic diversification.6 The coefficients on the instrument, 1-Predicted HHI, are all positive and statistically significant (at the 1% level), suggesting that this instrument satisfies the relevance requirement and explains bank geographic diversification well. Panel A of Table 4 presents the second-stage results for estimating model (9) of systemic risk.7 Because control variables can also potentially be affected by interstate banking deregulation, from which the main variation of the instrument comes, we estimate models (8) and (9) both with and without the controls to ensure that the results are not driven by bad controls. The coefficients on geographic diversification (1-HHI) are all positive and statistically significant across models using both |$\Delta $|CoVaR and Logistic(R|$^{2})$| as measures of systemic risk, suggesting that bank geographic diversification leads to higher systemic risk. The 2SLS results are consistent with the theoretical prediction in Wagner (2010) and Ibragimov, Jaffee, and Walden (2011) that bank diversification may reduce stand-alone risk, while increasing systemic risk. Table 4 Bank geographic diversification and systemic risk: 2SLS results A. Second-stage 2SLS results . . . . . . . . (1) . (2) . (3) . (4) . (5) . (6) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1-HHI) 1.009*** 1.929** 0.977*** 2.071** 0.911*** 1.813* (5.060) (1.979) (4.605) (1.977) (4.704) (1.897) Size -0.225** -0.207 -0.208** -0.141 (-2.468) (-0.506) (-2.381) (-0.359) Size|$^{2}$| 0.007** -0.001 0.006** -0.003 (2.245) (-0.062) (2.049) (-0.231) ROA 1.035*** 2.536 1.411*** 3.632** (2.954) (1.506) (3.859) (2.019) Tobin’s q -0.081** 0.338*** -0.063* 0.389*** (-2.257) (2.763) (-1.886) (3.260) Noninterst -0.242*** -0.207 -0.606*** -1.265* (-2.668) (-0.540) (-3.858) (-1.751) Provision 0.793** 4.683*** 0.889** 5.003*** (2.129) (2.891) (2.478) (3.150) Nondeposit -0.101 0.382 -0.142** 0.332 (-1.555) (1.153) (-2.173) (0.984) Income_diversity 0.306*** 0.899** (3.321) (2.041) Asset_diversity 0.014 -0.196 (0.315) (-0.983) State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes Kleibergen-Paap 69.29 69.38 65.22 64.39 74.97 74.07 rk LM statistic Cragg-Donald Wald 65.24 63.82 61.10 58.37 71.48 68.61 F statistic N 9,629 9,531 9,628 9,530 9,628 9,530 B. First-stage 2SLS results (1) (2) (3) (4) (5) (6) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) |$(1-$|Predicted HHI) 0.16*** 0.16*** 0.15*** 0.15*** 0.16*** 0.16*** (8.423) (8.369) (8.081) (7.958) (8.745) (8.611) Controls Yes Yes Yes Yes Yes Yes C. Reduced-form second-stage results (1) (2) (3) (4) (5) (6) |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$(1-$|Predicted HHI) 0.16*** 0.30** 0.15*** 0.31** 0.15*** 0.29* (5.677) (2.009) (5.321) (2.017) (5.314) (1.909) Controls Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes A. Second-stage 2SLS results . . . . . . . . (1) . (2) . (3) . (4) . (5) . (6) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1-HHI) 1.009*** 1.929** 0.977*** 2.071** 0.911*** 1.813* (5.060) (1.979) (4.605) (1.977) (4.704) (1.897) Size -0.225** -0.207 -0.208** -0.141 (-2.468) (-0.506) (-2.381) (-0.359) Size|$^{2}$| 0.007** -0.001 0.006** -0.003 (2.245) (-0.062) (2.049) (-0.231) ROA 1.035*** 2.536 1.411*** 3.632** (2.954) (1.506) (3.859) (2.019) Tobin’s q -0.081** 0.338*** -0.063* 0.389*** (-2.257) (2.763) (-1.886) (3.260) Noninterst -0.242*** -0.207 -0.606*** -1.265* (-2.668) (-0.540) (-3.858) (-1.751) Provision 0.793** 4.683*** 0.889** 5.003*** (2.129) (2.891) (2.478) (3.150) Nondeposit -0.101 0.382 -0.142** 0.332 (-1.555) (1.153) (-2.173) (0.984) Income_diversity 0.306*** 0.899** (3.321) (2.041) Asset_diversity 0.014 -0.196 (0.315) (-0.983) State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes Kleibergen-Paap 69.29 69.38 65.22 64.39 74.97 74.07 rk LM statistic Cragg-Donald Wald 65.24 63.82 61.10 58.37 71.48 68.61 F statistic N 9,629 9,531 9,628 9,530 9,628 9,530 B. First-stage 2SLS results (1) (2) (3) (4) (5) (6) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) |$(1-$|Predicted HHI) 0.16*** 0.16*** 0.15*** 0.15*** 0.16*** 0.16*** (8.423) (8.369) (8.081) (7.958) (8.745) (8.611) Controls Yes Yes Yes Yes Yes Yes C. Reduced-form second-stage results (1) (2) (3) (4) (5) (6) |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$(1-$|Predicted HHI) 0.16*** 0.30** 0.15*** 0.31** 0.15*** 0.29* (5.677) (2.009) (5.321) (2.017) (5.314) (1.909) Controls Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes This table reports the second-stage results from a 2SLS regression on how bank geographic diversification affects systemic risk. |$\Delta $|CoVaR is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis using daily equity return of top-20 largest banks. Independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. Size is the logarithm of total assets. ROA is net income divided by total assets. Market_to_book is the market value of equity divided by book value of equity. Noninterest is noninterest income divided by total operating income. Provision is loan loss reserves divided by gross loans. ST_funding is nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding. Income_diversity is 1-|$\vert $|(Net interest income –Total noninterest income)/(Total operating income)|$\vert .$|Asset_diversity is 1– |$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$| Panel A reports the 2SLS second-stage results for systemic risk; Panel B reports the first-stage 2SLS results for bank geographic diversification; and Panel C reports the reduced-form results for systemic risk. We cluster standard errors at the BHC level and report t-values in parentheses. *|$p<.1$|⁠; **|$p< .05$|⁠; ***|$p<.01$|⁠. Open in new tab Table 4 Bank geographic diversification and systemic risk: 2SLS results A. Second-stage 2SLS results . . . . . . . . (1) . (2) . (3) . (4) . (5) . (6) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1-HHI) 1.009*** 1.929** 0.977*** 2.071** 0.911*** 1.813* (5.060) (1.979) (4.605) (1.977) (4.704) (1.897) Size -0.225** -0.207 -0.208** -0.141 (-2.468) (-0.506) (-2.381) (-0.359) Size|$^{2}$| 0.007** -0.001 0.006** -0.003 (2.245) (-0.062) (2.049) (-0.231) ROA 1.035*** 2.536 1.411*** 3.632** (2.954) (1.506) (3.859) (2.019) Tobin’s q -0.081** 0.338*** -0.063* 0.389*** (-2.257) (2.763) (-1.886) (3.260) Noninterst -0.242*** -0.207 -0.606*** -1.265* (-2.668) (-0.540) (-3.858) (-1.751) Provision 0.793** 4.683*** 0.889** 5.003*** (2.129) (2.891) (2.478) (3.150) Nondeposit -0.101 0.382 -0.142** 0.332 (-1.555) (1.153) (-2.173) (0.984) Income_diversity 0.306*** 0.899** (3.321) (2.041) Asset_diversity 0.014 -0.196 (0.315) (-0.983) State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes Kleibergen-Paap 69.29 69.38 65.22 64.39 74.97 74.07 rk LM statistic Cragg-Donald Wald 65.24 63.82 61.10 58.37 71.48 68.61 F statistic N 9,629 9,531 9,628 9,530 9,628 9,530 B. First-stage 2SLS results (1) (2) (3) (4) (5) (6) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) |$(1-$|Predicted HHI) 0.16*** 0.16*** 0.15*** 0.15*** 0.16*** 0.16*** (8.423) (8.369) (8.081) (7.958) (8.745) (8.611) Controls Yes Yes Yes Yes Yes Yes C. Reduced-form second-stage results (1) (2) (3) (4) (5) (6) |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$(1-$|Predicted HHI) 0.16*** 0.30** 0.15*** 0.31** 0.15*** 0.29* (5.677) (2.009) (5.321) (2.017) (5.314) (1.909) Controls Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes A. Second-stage 2SLS results . . . . . . . . (1) . (2) . (3) . (4) . (5) . (6) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1-HHI) 1.009*** 1.929** 0.977*** 2.071** 0.911*** 1.813* (5.060) (1.979) (4.605) (1.977) (4.704) (1.897) Size -0.225** -0.207 -0.208** -0.141 (-2.468) (-0.506) (-2.381) (-0.359) Size|$^{2}$| 0.007** -0.001 0.006** -0.003 (2.245) (-0.062) (2.049) (-0.231) ROA 1.035*** 2.536 1.411*** 3.632** (2.954) (1.506) (3.859) (2.019) Tobin’s q -0.081** 0.338*** -0.063* 0.389*** (-2.257) (2.763) (-1.886) (3.260) Noninterst -0.242*** -0.207 -0.606*** -1.265* (-2.668) (-0.540) (-3.858) (-1.751) Provision 0.793** 4.683*** 0.889** 5.003*** (2.129) (2.891) (2.478) (3.150) Nondeposit -0.101 0.382 -0.142** 0.332 (-1.555) (1.153) (-2.173) (0.984) Income_diversity 0.306*** 0.899** (3.321) (2.041) Asset_diversity 0.014 -0.196 (0.315) (-0.983) State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes Kleibergen-Paap 69.29 69.38 65.22 64.39 74.97 74.07 rk LM statistic Cragg-Donald Wald 65.24 63.82 61.10 58.37 71.48 68.61 F statistic N 9,629 9,531 9,628 9,530 9,628 9,530 B. First-stage 2SLS results (1) (2) (3) (4) (5) (6) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) (1-HHI) |$(1-$|Predicted HHI) 0.16*** 0.16*** 0.15*** 0.15*** 0.16*** 0.16*** (8.423) (8.369) (8.081) (7.958) (8.745) (8.611) Controls Yes Yes Yes Yes Yes Yes C. Reduced-form second-stage results (1) (2) (3) (4) (5) (6) |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$\Delta $|CoVaR Logistic(R|$^{2})$| |$(1-$|Predicted HHI) 0.16*** 0.30** 0.15*** 0.31** 0.15*** 0.29* (5.677) (2.009) (5.321) (2.017) (5.314) (1.909) Controls Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes This table reports the second-stage results from a 2SLS regression on how bank geographic diversification affects systemic risk. |$\Delta $|CoVaR is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis using daily equity return of top-20 largest banks. Independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. Size is the logarithm of total assets. ROA is net income divided by total assets. Market_to_book is the market value of equity divided by book value of equity. Noninterest is noninterest income divided by total operating income. Provision is loan loss reserves divided by gross loans. ST_funding is nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding. Income_diversity is 1-|$\vert $|(Net interest income –Total noninterest income)/(Total operating income)|$\vert .$|Asset_diversity is 1– |$\vert $|(Net Loans–Other earning assets)/(Total earning assets)|$\vert .$| Panel A reports the 2SLS second-stage results for systemic risk; Panel B reports the first-stage 2SLS results for bank geographic diversification; and Panel C reports the reduced-form results for systemic risk. We cluster standard errors at the BHC level and report t-values in parentheses. *|$p<.1$|⁠; **|$p< .05$|⁠; ***|$p<.01$|⁠. Open in new tab To account for banks’ business activity diversification that might potentially influence systemic risk, we include income diversity (Income_diversity) and asset diversity (Asset_diversity) as additional control variables. Columns 5 and 6 of Table 4 present the results. The results show that neither income diversity nor asset diversity affects the change in conditional value at risk (⁠|$\Delta$| oVAR), while income diversity positively affects financial integration (Logistic(R|$^{2}$|)). We continue to find that geographic diversification results in a positive increase in systemic risk measured by both |$\Delta $|CoVAR and Logistic(R|$^{2}).$| Compared with the OLS results reported in Section 3, the coefficients on (1-HHI) are significant both economically and statistically using the 2SLS regressions. We also investigate the reduced-form relationship between geographic diversification and systemic risk by regressing systemic risk measures on (1- Predicted HHI). The results, as reported in Panel C of Table 4, show that BHC geographic diversification positively affects systemic risk, consistent with our main results. In terms of the economic magnitudes, a 1-standard-deviation increase in geographic diversification results in an increase in |$\Delta $|CoVaR by 13.39% of its standard deviation and an increase in Logistic(R|$^{2}) $|by 7.3% of its standard deviation.8 The signs of most control variables are consistent with our expectations. We perform the underidentification and weak identification tests to check the validity of our instrumental variable. Taking the |$\Delta $|CoVaR model as an example, the results in Column 3 of Table 4 indicate that this instrument passes both the underidentification test with Kleibergen-Paap rk LM statistic of 65.22 (⁠|$p$|-value |$<$| 1%) and the weak identification test with Cragg-Donald Wald F statistic of 61.1, much greater than the critical value of 16.38 for the 10% maximal IV size based on Stock and Yogo (2005). Columns 1–4 of Table 5 report the results for individual banks’ exposure to systemic risk. The coefficients on (1-HHI) are positive and statistically significant with BHC and quarter fixed effects. The coefficients on (1-HHI) are positive but statistically insignificant with state-year and BHC fixed effects.9 Table 5 Bank geographic diversification and individual bank’s exposure to systemic risk: 2SLS results . (1) . (2) . (3) . (4) . . MES . SRISK . MES . SRISK . (1–HHI) 0.028|$^{***}$| 0.857|$^{**}$| 0.011 0.099 (3.429) (1.978) (1.216) (0.929) Control variables Yes Yes Yes Yes Year fixed effects Yes Yes No No BHC fixed effects Yes Yes Yes Yes State-year fixed effects No No Yes Yes N 9,595 9,651 9,606 9,651 . (1) . (2) . (3) . (4) . . MES . SRISK . MES . SRISK . (1–HHI) 0.028|$^{***}$| 0.857|$^{**}$| 0.011 0.099 (3.429) (1.978) (1.216) (0.929) Control variables Yes Yes Yes Yes Year fixed effects Yes Yes No No BHC fixed effects Yes Yes Yes Yes State-year fixed effects No No Yes Yes N 9,595 9,651 9,606 9,651 This table reports the second-stage results from a 2SLS regression on how geographic diversification affects individual bank’s exposure to systemic risk. MES is the marginal expected shortfall, defined as the average stock return of a bank when the market return is in its 5% lower tail in a given year. SRISK is the capital shortfall of a bank in time of crisis. We scale capital shortfall by the sum of all positive SRISK during a quarter. Independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. We cluster standard errors at the BHC level and report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab Table 5 Bank geographic diversification and individual bank’s exposure to systemic risk: 2SLS results . (1) . (2) . (3) . (4) . . MES . SRISK . MES . SRISK . (1–HHI) 0.028|$^{***}$| 0.857|$^{**}$| 0.011 0.099 (3.429) (1.978) (1.216) (0.929) Control variables Yes Yes Yes Yes Year fixed effects Yes Yes No No BHC fixed effects Yes Yes Yes Yes State-year fixed effects No No Yes Yes N 9,595 9,651 9,606 9,651 . (1) . (2) . (3) . (4) . . MES . SRISK . MES . SRISK . (1–HHI) 0.028|$^{***}$| 0.857|$^{**}$| 0.011 0.099 (3.429) (1.978) (1.216) (0.929) Control variables Yes Yes Yes Yes Year fixed effects Yes Yes No No BHC fixed effects Yes Yes Yes Yes State-year fixed effects No No Yes Yes N 9,595 9,651 9,606 9,651 This table reports the second-stage results from a 2SLS regression on how geographic diversification affects individual bank’s exposure to systemic risk. MES is the marginal expected shortfall, defined as the average stock return of a bank when the market return is in its 5% lower tail in a given year. SRISK is the capital shortfall of a bank in time of crisis. We scale capital shortfall by the sum of all positive SRISK during a quarter. Independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. We cluster standard errors at the BHC level and report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab 4.2 The asset similarity channel Wagner (2010, 2011) and Allen, Babus, and Carletti (2012) argue that diversification may result in similar asset structures. Banks with similar assets may be subject to common shocks, which may trigger joint liquidation and in turn depress asset prices. The affected banks even may be forced to sell assets at fire sale discounts, generating negative externalities and financial fragility. In this section, we explore whether asset similarity serves as a channel through which geographic diversification affects systemic risk (the asset similarity channel). We follow Girardi et al. (2018) and construct the cosine similarity to proxy for asset similarity among banks. Specifically, we measure the asset similarity between bank A and bank B (Cos|$_{AB})$| as follows: $$\begin{equation} Cos_{AB} =\frac{\vec {A}.\times \vec {B}}{\left| {\vec {A}} \right|\times \left| {\vec {B}} \right|}, \end{equation}$$ (10) where |$\vec {A}$| is a 1 by N vector (item 1, item 2, …, item N), and item 1 to item N are N different asset items on bank A’s balance sheet. Each item is scaled by total assets and expressed as a percentage. |$\vec {B}$| is the vector for bank B defined in the same way. The “dot multiply,” “|$.\times$|⁠,” is an element by element multiplication of vectors |$\vec {A}$| and |$\vec {B}. \left| {\vec {A}} \right|$| and |$\left| {\vec {B}} \right|$| are vector lengths of |$\vec {A}$| and |$\vec {B}.$| The cosine similarity is between zero and one, with a cosine similarity of one corresponding to exactly the same asset structures between two banks, and zero corresponding to completely different asset structures. We compute the pairwise cosine similarity measure based on asset structures for all bank pairs in each quarter. The asset items include cash and balances due from depository institutions, securities, federal funds sold and securities purchased under agreements to resell, loans and lease financing receivables, and intangible assets. The asset similarity of a bank to other banks is the average of its cosine values with each of the other banks (Asset_simi). We also compute the weighted average asset similarity (Asset_simi_w), which is the weighted average cosine similarity of bank |$i$| with each of the other sample banks based on asset structure and is computed below: $$\begin{equation} ~Asset\_simi\_w_i =\mathop \sum \limits_{j\ne i} w_j Cos_{ij}, \end{equation}$$ (11) where |$w_j$| is the weight of bank |$j$|⁠, defined as bank |$j$|’s total assets divided by the total assets of all banks. We also compute the cosine similarity based on bank loan structure for all bank pairs in each quarter similarly, which is the average of the cosine value of an individual bank with each of the other banks based on loan structure (Loan_simi). The loan items include real estate loans, commercial and industrial loans, loans to depository institutions, agriculture loans, lease financing receivables, and all other loans. We also compute the weighted average loan similarity (Loan_simi_w), which is the weighted average cosine value of a bank with all other banks based on loan structure, with the weight based on the ratio of total loans of a bank to total loans of all banks in a quarter. To examine whether geographic diversification leads to more similar asset structures, we estimate the 2SLS regressions by replacing the dependent variables in Equation (9) with asset similarity measures. As in the baseline results, we also include BHC fixed effects and state-year fixed effects to account for any time-varying state effects and time-invariant BHC-specific effect. The second-stage results, as reported in Columns 1–4 of Table 6, show that the coefficients on (1-HHI) are positive and statistically significant in all models, suggesting that bank geographic expansion leads to higher asset similarity. To the extent that banks with similar asset structures are subject to common shocks, these findings are consistent with the idea that bank geographic diversification increases bank systemic risk through its effect on asset similarity. Table 6 Asset similarity channel effect . (1) . (2) . (3) . (4) . (5) . (6) . . Asset_simi . Asset_simi_w . Loan_simi . Loan_simi_w . Location_simi_num . Location_simi_amount . (1–HHI) 0.226|$^{***}$| 0.138|$^{**}$| 0.216|$^{**}$| 0.250|$^{***}$| 0.090|$^{**}$| 0.122|$^{***}$| (3.713) (2.380) (2.265) (2.671) (2.313) (2.887) Control variables Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes N 8,188 8,188 7,838 7,838 8,449 8,449 . (1) . (2) . (3) . (4) . (5) . (6) . . Asset_simi . Asset_simi_w . Loan_simi . Loan_simi_w . Location_simi_num . Location_simi_amount . (1–HHI) 0.226|$^{***}$| 0.138|$^{**}$| 0.216|$^{**}$| 0.250|$^{***}$| 0.090|$^{**}$| 0.122|$^{***}$| (3.713) (2.380) (2.265) (2.671) (2.313) (2.887) Control variables Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes N 8,188 8,188 7,838 7,838 8,449 8,449 This table reports the second-stage results from a 2SLS regression exploring the asset similarity channel to explain the causal impact of bank geographic diversification on systemic risk. Asset_simi is the cosine value of a bank with each of the other banks based on asset structure, and Asset_simi_w is the weighted average cosine value of a bank with each of the other banks based on asset structure with the weight based on bank total assets. Loan_simi is the cosine value of a bank with each of the other banks based on loan structure, and Loan_simi_w is the weighted average cosine value of a bank with each of the other banks based on loan structure with the weight based on bank total loans. Location_simi_num is the weighted average borrower MSA similarity based on the number of mortgage loans using HMDA data, with the weight being the size of paired banks. Location_simi_amount is the weighted average borrower MSA similarity based on the value of mortgage loans using HMDA data, with the weight being the size of paired banks. Independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. We cluster standard errors at the BHC level and report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab Table 6 Asset similarity channel effect . (1) . (2) . (3) . (4) . (5) . (6) . . Asset_simi . Asset_simi_w . Loan_simi . Loan_simi_w . Location_simi_num . Location_simi_amount . (1–HHI) 0.226|$^{***}$| 0.138|$^{**}$| 0.216|$^{**}$| 0.250|$^{***}$| 0.090|$^{**}$| 0.122|$^{***}$| (3.713) (2.380) (2.265) (2.671) (2.313) (2.887) Control variables Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes N 8,188 8,188 7,838 7,838 8,449 8,449 . (1) . (2) . (3) . (4) . (5) . (6) . . Asset_simi . Asset_simi_w . Loan_simi . Loan_simi_w . Location_simi_num . Location_simi_amount . (1–HHI) 0.226|$^{***}$| 0.138|$^{**}$| 0.216|$^{**}$| 0.250|$^{***}$| 0.090|$^{**}$| 0.122|$^{***}$| (3.713) (2.380) (2.265) (2.671) (2.313) (2.887) Control variables Yes Yes Yes Yes Yes Yes State-year fixed effects Yes Yes Yes Yes Yes Yes BHC fixed effects Yes Yes Yes Yes Yes Yes N 8,188 8,188 7,838 7,838 8,449 8,449 This table reports the second-stage results from a 2SLS regression exploring the asset similarity channel to explain the causal impact of bank geographic diversification on systemic risk. Asset_simi is the cosine value of a bank with each of the other banks based on asset structure, and Asset_simi_w is the weighted average cosine value of a bank with each of the other banks based on asset structure with the weight based on bank total assets. Loan_simi is the cosine value of a bank with each of the other banks based on loan structure, and Loan_simi_w is the weighted average cosine value of a bank with each of the other banks based on loan structure with the weight based on bank total loans. Location_simi_num is the weighted average borrower MSA similarity based on the number of mortgage loans using HMDA data, with the weight being the size of paired banks. Location_simi_amount is the weighted average borrower MSA similarity based on the value of mortgage loans using HMDA data, with the weight being the size of paired banks. Independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. We cluster standard errors at the BHC level and report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab To account for the heterogeneity in BHCs’ assets across MSAs, we examine whether diversified banks make mortgage loans to a similar pool of borrowers using the Home Mortgage Disclosure Act (HMDA) data from 1986 to 1997. The HMDA data provide detailed information on both the number of mortgage loans and the dollar amount of mortgage loans that a bank lends in each MSA.10 Similar to asset similarity measures, we construct two loan allocation similarity measures based on the cosine values. More specifically, we build a 1 by 374 vector based on MSAs (MSA1, MSA2, …, MSA374) for each BHC, with the values of the vector MSA1 to MSA374 being the percentages of mortgage loans that a bank makes to each of the 374 MSAs. The cosine value of two banks is the cosine value of the two vectors, and the loan-allocation similarity for a specific bank is the asset-weighted average of its cosine value with each of the other banks. We construct the 1 by 374 vector based on both the number of mortgage loans and dollar amount of mortgage loan a BHC makes in each MSA and denote the corresponding loan allocation similarity measures as Allocation_simi_num and Allocation_simi_amount. The results, as reported in Columns 5 and 6 of Table 6, show that the coefficients on bank geographic diversification are still positive and significant. The results also suggest that bank geographic diversification leads to a greater mortgage loan allocation similarity across MSAs, corroborating the asset similarity channel. 4.3 Cross-sectional analysis: State and U.S. economy comovement In this section, we conduct a cross-sectional analysis to investigate whether the causal effect of bank geographic diversification on systemic risk varies with the comovement between a state and the U.S. economy. If BHCs located in a home state less correlated with the rest of the economy expand across state borders, it would have a bigger impact on systemic risk because banks’ assets will comove more with the whole economy and expose them to greater common risks. To measure the degree of comovement between the economy of a state and the rest of the U.S. economy, we use the correlation of a state economy with the U.S. economy following Amore, Schneider, and Žaldokas (2013) and Levine, Lin, and Xie (2016). More specifically, we obtain the monthly Coincident index produced by Federal Reserve Bank of Philadelphia, for each of the 50 states and the United States.11 We then compute the correlation between a state and the rest of U.S. economy for each quarter using a rolling window of the previous 12 quarters based on the monthly Coincident index. A higher correlation indicates a greater comovement between a state and the aggregate U.S. economy, based on which we define a dummy variable High_comovement. This dummy variable equals one if the correlation of the Coincident index is larger than the sample median and zero otherwise. We interact (1-HHI) and High_comovement and include the interaction term in the regressions and use the interaction between (1-Predicted HHI) and High_comovement as well as (1- Predicted HHI) as the instruments in the 2SLS framework. High_comovement itself is subsumed by state-year fixed effects. We expect the coefficient on the 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 comoves less with the aggregate U.S. economy. Table 7 reports the second-stage results. The coefficients on (1-HHI) continue to be positive and statistically significant across the models using both |$\Delta $|CoVaR and Logistic(R|$^{2}) $|as measures of systemic risk. The coefficients on the interaction term between (1-HHI) and High_comovement are negative and significant in both the |$\Delta $|CoVaR and Logistic(R|$^{2}) $|models, suggesting that the impact of geographic diversification on systemic risk is more pronounced for BHCs located in states comoving less with the overall U.S. economy. On the other hand, for BHCs located in states comoving more with the U.S. economy, the sum of coefficients on (1–HHI)|$\times $|(High_comovement) and (1–HHI) is negative and small (i.e., the sum of coefficients = |$-$|49.58 + 48.508 = |$-$| 1.072), suggesting that for BHCs located in states with high comovement, the effect of diversification on systemic risk is small, and, if anything, it is negative. Table 7 Cross-sectional test: State and U.S. economy comovement . (1) . (2) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1–HHI)|$\times $|(High_comovement) |$-49.580^{***}$| |$-86.116^{*}$| (⁠|$-$|3.565) (⁠|$-$|1.780) (1–HHI) |$48.508^{***}$| |$87.680^{*}$| (3.504) (1.826) Control variables Yes Yes State-year fixed effects Yes Yes BHC fixed effects Yes Yes N 8,466 8,382 . (1) . (2) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1–HHI)|$\times $|(High_comovement) |$-49.580^{***}$| |$-86.116^{*}$| (⁠|$-$|3.565) (⁠|$-$|1.780) (1–HHI) |$48.508^{***}$| |$87.680^{*}$| (3.504) (1.826) Control variables Yes Yes State-year fixed effects Yes Yes BHC fixed effects Yes Yes N 8,466 8,382 This table reports the second-stage results from a 2SLS regression examining the relationship between bank geographic diversification and systemic risk conditional on state and U.S. economy comovement. |$\Delta $|CoVa is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis using daily equity return of top-20 largest banks. The independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. Comovement is the correlation between the Coincident index of the home state of a BHC and the Coincident index of the U.S. economy. High_comovement is a dummy variable that equals one if the correlation of Coincident index is larger than the sample median and zero otherwise. (⁠|$1-$|HHI)|$\times $|High_comovement is instrumented by (⁠|$1-$|PredictedHHI)*High_comovement and (1– Predicted HHI). (⁠|$1-$|HHI) is instrumented by (⁠|$1-$|PredictedHH)*High_comovement and (⁠|$1-$|PredictedHHI). We cluster standard errors at the BHC level and report t-values in parentheses. *|$p<.1$|⁠; **|$p<.05$|⁠; ***|$p<.01$|⁠. Open in new tab Table 7 Cross-sectional test: State and U.S. economy comovement . (1) . (2) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1–HHI)|$\times $|(High_comovement) |$-49.580^{***}$| |$-86.116^{*}$| (⁠|$-$|3.565) (⁠|$-$|1.780) (1–HHI) |$48.508^{***}$| |$87.680^{*}$| (3.504) (1.826) Control variables Yes Yes State-year fixed effects Yes Yes BHC fixed effects Yes Yes N 8,466 8,382 . (1) . (2) . . |$\Delta $|CoVaR . Logistic(R|$^{2})$| . (1–HHI)|$\times $|(High_comovement) |$-49.580^{***}$| |$-86.116^{*}$| (⁠|$-$|3.565) (⁠|$-$|1.780) (1–HHI) |$48.508^{***}$| |$87.680^{*}$| (3.504) (1.826) Control variables Yes Yes State-year fixed effects Yes Yes BHC fixed effects Yes Yes N 8,466 8,382 This table reports the second-stage results from a 2SLS regression examining the relationship between bank geographic diversification and systemic risk conditional on state and U.S. economy comovement. |$\Delta $|CoVa is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution, based on a 3-year forward-looking window. Logistic(R|$^{2}) $|is the logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|⁠, where |$R^{2}$| is obtained from a regression of an individual bank’s equity return on the first four common factors extracted from the principal component analysis using daily equity return of top-20 largest banks. The independent variable of interest is bank geographic diversification (1-HHI), which is one minus sum square of bank deposit share across MSAs. (1–HHI) is instrumented by (1– Predicted HHI) derived from the stage-zero gravity-deregulation model. Comovement is the correlation between the Coincident index of the home state of a BHC and the Coincident index of the U.S. economy. High_comovement is a dummy variable that equals one if the correlation of Coincident index is larger than the sample median and zero otherwise. (⁠|$1-$|HHI)|$\times $|High_comovement is instrumented by (⁠|$1-$|PredictedHHI)*High_comovement and (1– Predicted HHI). (⁠|$1-$|HHI) is instrumented by (⁠|$1-$|PredictedHH)*High_comovement and (⁠|$1-$|PredictedHHI). We cluster standard errors at the BHC level and report t-values in parentheses. *|$p<.1$|⁠; **|$p<.05$|⁠; ***|$p<.01$|⁠. Open in new tab 4.4 Robustness checks 4.4.1 Reverse causality test The Riegle-Neal Interstate Banking and Branching Efficiency Act (IBBEA) was passed in 1994 to provide a set of uniform rules regarding branching and interstate mergers and acquisitions in the financial services industry. Nonetheless, one may be concerned that the passage of IBBEA could be endogenous in that systemic risk might be a driver behind the timing of such interstate banking deregulation. In other words, IBBEA might be passed to address the systemic risk of the financial system. If that is the case, the results documented above can be driven by reverse causality. In addition, individual states’ decisions to allow interstate banking also may be driven by systemic risk to which the banks in those states are exposed. To address the possible reverse causality problem, we examine whether systemic risk affects the timing of interstate banking deregulation for each state pair. We follow Kroszner and Strahan (1999) and construct a Weibull model to investigate whether systemic risk drives the timing of state-pair banking deregulation (⁠|$T)$|⁠, with |$T $|being the timing of state-pair deregulation; that is, BHCs in state |$i$| can enter state |$j$| at time |$t.$| In carrying out this test, we keep observations that are either before deregulation or up to the year of deregulation; that is, we delete the observations after deregulation. We incorporate structural covariates as well as systemic risk to predict the expected time to deregulate for each state-pair, following Kroszner and Strahan (1999). Our Weibull model is as follows: $$\begin{eqnarray} \ln (T)_{ijt} &=&\beta _1 SystemicRisk_{it} +\beta _2 SystemicRisk_{jt} +StateControls_{it}\nonumber\\ &&+StateControls_{jt} +\eta _{ij} +\varepsilon _{ijt}, \end{eqnarray}$$ (12) where the dependent variable ln(T) is the log of the expected time to deregulate for each state pair, state |$i$| and state |$j$|⁠; that is, banks in state |$i$| can enter state|$ j.$|SystemicRisk is the weighted average state-level systemic risk measure based on either |$\Delta $|CoVaR or Logistic(R|$^{2}) $|of all BHCs in the same state, with the weights based on total assets of each BHC. We follow Kroszner and Strahan (1999) and include a set of state-level control variables, such as SmallShare, CapitalDiff, Unemp, and GSP. SmallShare is the percentage of banks with total assets below the median size of all banks in each state in each year. CapitalDiff is the capital ratio of small banks minus that of large banks; Unemp is the unemployment rate of a state; GSP is the gross state product; and |$\eta $| is year fixed effect. All covariates are constructed for each state-pair, state |$i$| and state |$j$|⁠, each year. The results presented in Table 8 show that the coefficients on state-pair systemic risk measures, |$\Delta $|CoVaR and Logistic(R|$^{2})$|⁠, are insignificant in predicting the timing of state-pair interstate banking deregulation, suggesting the causal effect of bank geographic diversification on systemic risk is unlikely to be driven by reverse causality. On the other hand, the coefficients on SmallShare and CapitalDiff are positive and significant, suggesting that both a higher small bank share and a larger difference in capital ratio between small and large banks delay the timing of state-pair deregulation, consistent with Kroszner and Strahan (1999). Table 8 Reverse causality test . (1) . (2) . . ln(T) . ln(T) . |$\Delta $|COVAR_i 1.704 (1.345) |$\Delta $|COVAR_j -1.540 (-1.101) Logistic(R|$^{2}$|)_i -0.166 (-0.574) Logistic(R|$^{2}$|)_j 0.195 (0.596) SmallShare_i 0.547*** 0.546*** (3.623) (3.555) SmallShare_j 2.543*** 2.571*** (14.668) (14.262) CapitalDiff_i 1.546*** 1.437*** (3.794) (3.487) CapitalDiff_j 5.208*** 4.673*** (11.169) (9.611) Unemp_i -0.019*** -0.020*** (-5.033) (-5.265) Unemp_j -0.017*** -0.027*** (-4.488) (-6.730) GDP_i 0.000 -0.000 (0.329) (-1.422) GDP_j 0.000 -0.000*** (0.938) (-2.965) Year fixed effects Yes Yes N 6,723 6,570 . (1) . (2) . . ln(T) . ln(T) . |$\Delta $|COVAR_i 1.704 (1.345) |$\Delta $|COVAR_j -1.540 (-1.101) Logistic(R|$^{2}$|)_i -0.166 (-0.574) Logistic(R|$^{2}$|)_j 0.195 (0.596) SmallShare_i 0.547*** 0.546*** (3.623) (3.555) SmallShare_j 2.543*** 2.571*** (14.668) (14.262) CapitalDiff_i 1.546*** 1.437*** (3.794) (3.487) CapitalDiff_j 5.208*** 4.673*** (11.169) (9.611) Unemp_i -0.019*** -0.020*** (-5.033) (-5.265) Unemp_j -0.017*** -0.027*** (-4.488) (-6.730) GDP_i 0.000 -0.000 (0.329) (-1.422) GDP_j 0.000 -0.000*** (0.938) (-2.965) Year fixed effects Yes Yes N 6,723 6,570 We estimate the following Weibull hazard model: |$\ln (T)_{ijt} =\beta _1 SystemicRisk_{it} +\beta _2 SystemicRisk_{jt} +StateControls_{it} +StateControls_{jt} +\eta _{ij} +\varepsilon _{ijt}$|⁠, where |$T$| is the expected time that banks in state |$i $|can enter state|$ j.$| SystemicRisk is systemic risk measures aggregated as state level. StateControls include SmallShare, CapitalDiff, Unemp, and GSP. SmallShare is the percentage of banking assets in the state held by banks below the median size of banks in each state in each year. CapitalDiff is the capital to assets ratio of small banks minus that of large banks; Unemp is the unemployment rate of a state; and GSP is the gross state product of a state. |$\eta $| is year fixed effect. The suffix “|$i$|” stands for state |$i$| and “_j” stands for state |$j.$| We report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab Table 8 Reverse causality test . (1) . (2) . . ln(T) . ln(T) . |$\Delta $|COVAR_i 1.704 (1.345) |$\Delta $|COVAR_j -1.540 (-1.101) Logistic(R|$^{2}$|)_i -0.166 (-0.574) Logistic(R|$^{2}$|)_j 0.195 (0.596) SmallShare_i 0.547*** 0.546*** (3.623) (3.555) SmallShare_j 2.543*** 2.571*** (14.668) (14.262) CapitalDiff_i 1.546*** 1.437*** (3.794) (3.487) CapitalDiff_j 5.208*** 4.673*** (11.169) (9.611) Unemp_i -0.019*** -0.020*** (-5.033) (-5.265) Unemp_j -0.017*** -0.027*** (-4.488) (-6.730) GDP_i 0.000 -0.000 (0.329) (-1.422) GDP_j 0.000 -0.000*** (0.938) (-2.965) Year fixed effects Yes Yes N 6,723 6,570 . (1) . (2) . . ln(T) . ln(T) . |$\Delta $|COVAR_i 1.704 (1.345) |$\Delta $|COVAR_j -1.540 (-1.101) Logistic(R|$^{2}$|)_i -0.166 (-0.574) Logistic(R|$^{2}$|)_j 0.195 (0.596) SmallShare_i 0.547*** 0.546*** (3.623) (3.555) SmallShare_j 2.543*** 2.571*** (14.668) (14.262) CapitalDiff_i 1.546*** 1.437*** (3.794) (3.487) CapitalDiff_j 5.208*** 4.673*** (11.169) (9.611) Unemp_i -0.019*** -0.020*** (-5.033) (-5.265) Unemp_j -0.017*** -0.027*** (-4.488) (-6.730) GDP_i 0.000 -0.000 (0.329) (-1.422) GDP_j 0.000 -0.000*** (0.938) (-2.965) Year fixed effects Yes Yes N 6,723 6,570 We estimate the following Weibull hazard model: |$\ln (T)_{ijt} =\beta _1 SystemicRisk_{it} +\beta _2 SystemicRisk_{jt} +StateControls_{it} +StateControls_{jt} +\eta _{ij} +\varepsilon _{ijt}$|⁠, where |$T$| is the expected time that banks in state |$i $|can enter state|$ j.$| SystemicRisk is systemic risk measures aggregated as state level. StateControls include SmallShare, CapitalDiff, Unemp, and GSP. SmallShare is the percentage of banking assets in the state held by banks below the median size of banks in each state in each year. CapitalDiff is the capital to assets ratio of small banks minus that of large banks; Unemp is the unemployment rate of a state; and GSP is the gross state product of a state. |$\eta $| is year fixed effect. The suffix “|$i$|” stands for state |$i$| and “_j” stands for state |$j.$| We report t-values in parentheses. *|$p< .1$|⁠; **|$p<.05$|⁠; ***|$p< .01$|⁠. Open in new tab 4.4.2 Including bank-specific risk as an additional control variable To address the concern that bank stand-alone risk may affect systemic risk, we include the stand-alone risk measures, the standard deviation of stock return (SD) or Z-score (Z-score) as an additional control variable in the systemic risk model (9). Columns 1 and 2 (Columns 3 and 4) of Panel A of Table IA2 in the Internet Appendix present the results after including SD (Z-score), respectively. The coefficient on SD (Z-score) is positive (negative) and significant, suggesting that stand-alone risk is positively associated with systemic risk. Meanwhile, we continue to find that geographic diversification leads to a positive and significant increase in systemic risk across both |$\Delta $|CoVaR and Logistic(R|$^{2}).$| 4.4.3 Using alternative samples Our main proxy of bank geographic diversification is computed as deposit dispersion across MSAs based on the FDIC’s Summary of Deposits (SOD) data. Because the SOD database is annual, our measure of geographic diversification is also measured at the annual frequency; however, other BHC-specific control variables are measured at the quarterly frequency. In the analyses above, we construct the sample at the quarterly frequency following Goetz, Laeven, and Levine (2016).12 To examine whether the results continue to hold at the annual frequency, we reconstruct our sample at the BHC-year level and reestimate Equations (8) and (9). The results, as reported in Columns 1 and 2 of Panel B of Table IA2 in the Internet Appendix, show that the coefficients on geographic diversification are still positive and significant for both |$\Delta $|CoVaR and Logistic(R|$^{2}).$| We also interpolate the annual deposits data to quarterly deposits using both linear interpolation and cubic spline interpolation. Based on the interpolated quarterly deposits, we compute the geographic diversification measure, which varies at the quarterly frequency, then reestimate Equations (8) and (9). Columns 3–6 of Panel B of Table IA2 in the Internet Appendix report the results. The coefficients on bank geographic diversification are still positive and significant in the |$\Delta $|CoVaR and Logistic(R|$^{2})$| models when using the sample based on either linear or cubic spline interpolation. 4.4.4 Addressing location heterogeneity in BHC expansion One may be concerned that the heterogeneity in the locations where BHCs expand to and hence their exposure to local shocks may differ and affect our results. Consider two BHCs, both located in Philadelphia. BHC A expands to New York City, and BHC B expands to Boston. While the gravity model predicts the extent of geographic expansion based on physical distance and market size, shocks to a BHC’s systemic risk may vary due to the differences in the BHCs’ exposure to these two different markets, namely, New York City and Boston. However, this effect that varies by the location where the BHC expands to is not captured by the time-varying state-year fixed effects.13 To address this potential effect, we include a set of dummy variables for each MSA where the BHC expands to in the models and estimate them using both OLS and 2SLS regressions.14 Panel C of Table IA2 in the Internet Appendix reports the OLS and the second-stage 2SLS results. In the OLS results, in Columns 1 and 2, the coefficients on bank geographic diversification are still positive but insignificant in Models of |$\Delta $|CoVaR and Logistic(R|$^{2}).$| The second-stage 2SLS results, as reported in Columns 3 and 4, show that the coefficients on bank geographic diversification are still positive and significant. To further address the potential time-varying changes at the MSA level, we follow Goetz (2018) and include some linear MSA time trends. Columns 5 and 6 of Panel C of Table IA2 in the Internet Appendix report the results. The coefficients on geographic diversification are still positive and statistically significant, consistent with our baseline results.15 As an additional robustness check, we cluster standard errors at the MSA-year level. Panel D of Table IA2 in the Internet Appendix reports the results. The coefficients on geographic diversification remain positive and statistically significant, corroborating our baseline results. 4.4.5 Using state-level instruments The gravity-deregulation model allows us to construct a time-varying and BHC-specific instrumental variable for bank geographic diversification; however, it also introduces variation not driven by interstate banking deregulation. To check the robustness of our results, we follow Goetz, Laeven, and Levin (2013) and employ three time-varying state-level instruments, including the number of years since a state first started interstate banking deregulation (Years_since), the square term of the number of years since deregulation (Years_since|$^{2})$|⁠, and ten dummy variables for each year since the state initially started lifting the interstate banking restrictions, from 1 year after to 10 or more years after deregulation (After1-After10). Our baseline sample period is from 1986 to 1997 and is too short to construct these nonparametric dummies as the state-level instruments. To mitigate this issue, we extend the sample period to 1986-2006 to conduct the tests with these state-level instruments. We end the sample period in 2006 to avoid the confounding effect of the 2007-2009 financial crisis.16 We replace the time-varying and BHC-specific instrumental variable based on the gravity-deregulation approach with the above-mentioned state-level instruments in Equation (8), and simultaneously estimate models (8) and (9) using the 2SLS technique. Table IA3 in the Internet Appendix reports the results. Columns 1 to 6 of Panel B of Table IA3 present the first stage results. We again find that interstate banking deregulation leads to an increase in bank geographic diversification. The second stage results, as shown in Columns 1 to 6 of Panel A of Table IA3, show that the impact of bank geographic diversification on systemic risk remains positive and statistically significant at the 1% level. 5. Conclusion In this study, we examine the causal effect of geographic diversification on systemic risk using an improved identification strategy based on the gravity-deregulation approach of Goetz, Laeven, and Levin (2013),Goetz, Laeven, and Levine (2016). More specifically, we exploit the staggered interstate banking deregulation as exogenous shocks to bank geographic expansion and integrate such deregulation into a gravity model to project bank deposit shares in foreign MSAs. Based on the deposit shares, we construct a time-varying and bank-specific instrument for geographic diversification and use an instrumental variable approach to estimate the causal effect of geographic diversification on systemic risk. We document that geographic diversification leads to significantly higher systemic risk measured by the change in conditional value at risk (|$\Delta $|CoVaR) and financial integration (Logistic(R|$^{2}$|)). Moreover, we find that geographic diversification leads to an increase in asset similarity, resulting in systemic risk. The result supports the asset similarity channel. Furthermore, the impact of geographic diversification on systemic risk is more pronounced on BHCs that are located in states comoving less with the rest of the U.S. economy. Our study complements Goetz, Laeven, and Levine (2016) by documenting the causal effect of bank geographic diversification on systemic risk. Collectively, our study and Goetz, Laeven, and Levine (2016) lend empirical support to the theoretical prediction of Wagner (2010) and Ibragimov, Jaffee, and Walden (2011) that diversification may reduce stand alone risk and increase systemic risk simultaneously, thus portraying a more complete picture of the effect of bank geographic diversification on risk. The results have important policy implications in that effective bank regulation should not only target bank stand alone risk but also address systemic risk. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. Acknowledgments We are grateful to Philip Strahan (editor) and two anonymous referees for their numerous insightful comments and suggestions. We thank Kandarp Srinivasan (discussant); participants at the FMA 2017 Annual Meeting; and seminar participants at Southern Illinois University, Temple University, University of Lethbridge, Central University of Finance and Economics, and Beijing Normal University for their helpful comments and discussions. We also thank Guangping Xie and Weidong Xiong for their excellent research assistance. All errors are solely our own. Supplementary data can be found on The Review of Financial Studies web site. Footnotes 1 Empirical evidence on how diversification affects firm-specific risk is inconclusive. The classical theory of finance suggests that diversification reduces idiosyncratic risk due to the “coinsurance effect” (Lewellen 1971; Boot and Schmeits 2000). The other strand of studies suggests that diversification may lead to higher firm risk because of increased organizational complexity and intensified agency problem (Berger et al. 2005; Winton 1999; Demsetz and Strahan 1997; Chong 1991). 2 The International Monetary Fund (IMF) defines 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” (IMF 2009, p. 2). The Bank of International Settlements (BIS) and the Financial Stability Board (FSB) use the same definition. 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 removed branching restrictions. We exclude both states to avoid any confounding effects. 4 The Summary of Deposits data before 1994 are obtained from Professor Christa Bouwman’s website https://sites.google.com/a/tamu.edu/bouwman/data. 5Goetz, Laeven, and Levine (2016) find that the coefficients of the OLS regressions are opposite to those of 2SLS after addressing the endogeneity issue. 6 To ensure that we accurately implement the gravity-deregulation approach developed in Goetz, Laeven, and Levine (2016), we replicate Goetz, Laeven, and Levine (2016) by assessing the relationship between geographic diversification and bank-specific risk. We present the description of the test and results in Internet Appendix A and Table IA1. 7 We replicate the results from Goetz, Laeven, and Levine (2016) and find that geographic diversification leads to a significant decline in stand-alone risk. Please refer to Internet Appendix A for the discussion and results for bank geographic diversification and idiosyncratic risk. 8 Given the standard deviation of |$1-$| Predicted HHI is 0.224, the standard deviation of |$\Delta $|CoVaR (Logistic(R|$^{2}))$| is 0.251 (0.89), and the coefficients on |$1-$| Predicted HHI are 0.15 and 0.29 for |$\Delta $|CoVaR and Logistic(R|$^{2})$|⁠, respectively, the economic magnitudes are computed as 0.15|$\times $|0.224/0.251= 13.39% for |$\Delta $|CoVaR and 0.29|$\times $|0.224/0.89= 7.3% for Logistic(R)|$^{2}$|⁠. 9 Because the results for both MES and SRISK are mostly insignificant, we focus on |$\Delta$|CoVAR and Logistic(R|$^{2}) $|hereafter. 10 The HMDA data provide information on mortgage applications and originations, which includes lender identity, the location of the property, loan amount, application year, and whether the loan was accepted or sold to a third party during the year of origination, as well as borrower-specific information, such as income, race, gender, and borrower location at the census tract level. 11 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. 12 Despite the annual frequency of actual bank geographic diversification, there are some quarterly variations in the predicted value of geographic diversification as other BHC-specific control variables in stage-one model are at a quarterly frequency. 13 We thank an anonymous referee for suggesting this test. 14 We use an OLS regression, because including those dummy variables may reintroduce endogeneity. The instruments need to be unrelated to a BHC’s actual choice as to which MSAs to enter. Nonetheless, we also use a 2SLS regression, because our baseline results are obtained by a 2SLS regression. 15 We tried to include MSA-quarter fixed effects in the model, because the coefficient estimates on |$1-$|HHI remain positive yet become insignificant. 16Goetz, Laeven, and Levin (2013) employ a sample period of 1986–2007. 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Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Appendix Table A.1 Variable definitions Systemic risk measures .  |$\Delta $|CoVaR Change in conditional value at risk following Adrian and Brunnermeier (2016), we define |$\Delta $|CoVaR as the marginal contribution of an individual bank to the overall systemic risk. It is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution. We calculate |$\Delta $|CoVaR based on a 3-year forward-looking window  Logistic(R|$^{2})$| Following Pukthuanthong and Roll (2009), we regress each bank’s equity return on the first four factors extracted from principal component analysis using daily equity return of top-20 largest banks from 1986 to 1997. The |$R^{2}$| from the above regression measure an individual bank’s integration with the overall banking system. |$R^{2}$| is computed based on a 1-year forward-looking window. We take a logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|  MES Marginal expected shortfall, defined as the average stock return of a bank on condition that the overall market is under its 5% tail  SRISK Expected capital shortfall of a bank on conditional on crisis, following Acharya, Engle, and Richardson (2012) and Brownlees and Engle (2017). We scale capital shortfall by the sum of all positive SRISK during a quarter Geographic diversification measures  (1–HHI) Bank geographic diversification measure, which is one minus the Herfindahl-Hirschman index of deposit shares across MSAs  # branches The number of branches a BHC operates  # MSAs The number of MSAs a BHC operates  Share The deposit share of a BHC in a foreign MSA Control variables  Size The logarithm of total assets  Size|$^{2}$| Size squared  ROA Return on assets, which equals net income divided by total assets  Market_to_book The market value of equity divided by book value of equity  Noninterest Noninterest income divided by total operating income  Provision Loan loss reserves divided by gross loans  ST_funding Nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding  Income_diversity 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|  Asset_diversity 1-|$\vert $|(Net loans–Other earning assets)/(Total earning assets)|$\vert $| Channel effects  Asset_simi Cosine similarity measure based on asset structure. We convert the percentage of N asset types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. The asset similarity of a bank to other banks is the average of its cosine value with each of the other banks  Asset_simi_w The weighted average of Asset_similarity with the weight based on bank total assets  Loan_simi Cosine similarity measure based on loan structure. We convert the proportion of N loan types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. Loan_similarity of an individual bank is the average of its cosine value with each of the other banks  Loan_simi_w The weighted average of Loan_similarity with the weight based on bank total loans  Location_simi_num Weighted average borrower MSA similarity based on the number of mortgage loans using HMDA data, with the weight being the size of paired banks  Location_simi_amount Weighted average borrower MSA similarity based on the amount of mortgage loans using HMDA data, with the weight being the size of paired banks Cross-sectional test  Comovement It is the correlation between the Coincident index of the home state of a BHC and the Coincident index of U.S. economy  High_comovement A dummy variable that equals one if the correlation of the Coincident index is larger than the sample median and zero otherwise. Reverse causality test  |$T$| The expected time that a state-pair deregulates  SmallShare Percent of banking assets in the state held by banks below the median size of banks in each state in each year  CapitalDiff Capital to assets ratio of small banks minus that of large banks  Unemp The unemployment rate of a state  GSP Gross state product of a state Variables used to replicate Goetz, Laeven, and Levine, Lin, and Xie (2016)  ln(SD) The logarithm of the standard deviation of weekly equity return during a quarter  ln(Residual) We first regress a bank’s weekly equity returns on the returns of the S&P 500, spread on BAA and AAA corporate bonds, and change in yield of a 3-month Treasury bill, we then calculate the standard deviation of the residuals from above regression  ln(Z-score) The logarithm of the Z-score, which is defined as (net income/book value of assets + capital/book value of assets) divided by the standard deviation of weekly market returns during a quarter  Loan_commitments Loan_commitments/(Loan_commitments+Loans)  Transaction_deposits Transaction_deposits/(total deposits)  Capital Capital/total assets  Operating_income The logarithm of total operating income  International A dummy variable that equals one if a BHC has subsidiaries that mainly engage in international activities, and zero otherwise State-level instruments  Year_since The number of years after the initial interstate banking deregulation of a BHC’s headquarter state  Year_since|$^{2}$| Year_since squared  After1 A dummy variable that equals one for 1 year after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise  After2(to After9) A dummy variable that equals one for 2 (to 9) years after the initial interstate banking deregulation of a BHC’s headquarter state, and zero otherwise  After10 A dummy variable that equals one for 10 or more years after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise Systemic risk measures .  |$\Delta $|CoVaR Change in conditional value at risk following Adrian and Brunnermeier (2016), we define |$\Delta $|CoVaR as the marginal contribution of an individual bank to the overall systemic risk. It is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution. We calculate |$\Delta $|CoVaR based on a 3-year forward-looking window  Logistic(R|$^{2})$| Following Pukthuanthong and Roll (2009), we regress each bank’s equity return on the first four factors extracted from principal component analysis using daily equity return of top-20 largest banks from 1986 to 1997. The |$R^{2}$| from the above regression measure an individual bank’s integration with the overall banking system. |$R^{2}$| is computed based on a 1-year forward-looking window. We take a logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|  MES Marginal expected shortfall, defined as the average stock return of a bank on condition that the overall market is under its 5% tail  SRISK Expected capital shortfall of a bank on conditional on crisis, following Acharya, Engle, and Richardson (2012) and Brownlees and Engle (2017). We scale capital shortfall by the sum of all positive SRISK during a quarter Geographic diversification measures  (1–HHI) Bank geographic diversification measure, which is one minus the Herfindahl-Hirschman index of deposit shares across MSAs  # branches The number of branches a BHC operates  # MSAs The number of MSAs a BHC operates  Share The deposit share of a BHC in a foreign MSA Control variables  Size The logarithm of total assets  Size|$^{2}$| Size squared  ROA Return on assets, which equals net income divided by total assets  Market_to_book The market value of equity divided by book value of equity  Noninterest Noninterest income divided by total operating income  Provision Loan loss reserves divided by gross loans  ST_funding Nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding  Income_diversity 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|  Asset_diversity 1-|$\vert $|(Net loans–Other earning assets)/(Total earning assets)|$\vert $| Channel effects  Asset_simi Cosine similarity measure based on asset structure. We convert the percentage of N asset types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. The asset similarity of a bank to other banks is the average of its cosine value with each of the other banks  Asset_simi_w The weighted average of Asset_similarity with the weight based on bank total assets  Loan_simi Cosine similarity measure based on loan structure. We convert the proportion of N loan types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. Loan_similarity of an individual bank is the average of its cosine value with each of the other banks  Loan_simi_w The weighted average of Loan_similarity with the weight based on bank total loans  Location_simi_num Weighted average borrower MSA similarity based on the number of mortgage loans using HMDA data, with the weight being the size of paired banks  Location_simi_amount Weighted average borrower MSA similarity based on the amount of mortgage loans using HMDA data, with the weight being the size of paired banks Cross-sectional test  Comovement It is the correlation between the Coincident index of the home state of a BHC and the Coincident index of U.S. economy  High_comovement A dummy variable that equals one if the correlation of the Coincident index is larger than the sample median and zero otherwise. Reverse causality test  |$T$| The expected time that a state-pair deregulates  SmallShare Percent of banking assets in the state held by banks below the median size of banks in each state in each year  CapitalDiff Capital to assets ratio of small banks minus that of large banks  Unemp The unemployment rate of a state  GSP Gross state product of a state Variables used to replicate Goetz, Laeven, and Levine, Lin, and Xie (2016)  ln(SD) The logarithm of the standard deviation of weekly equity return during a quarter  ln(Residual) We first regress a bank’s weekly equity returns on the returns of the S&P 500, spread on BAA and AAA corporate bonds, and change in yield of a 3-month Treasury bill, we then calculate the standard deviation of the residuals from above regression  ln(Z-score) The logarithm of the Z-score, which is defined as (net income/book value of assets + capital/book value of assets) divided by the standard deviation of weekly market returns during a quarter  Loan_commitments Loan_commitments/(Loan_commitments+Loans)  Transaction_deposits Transaction_deposits/(total deposits)  Capital Capital/total assets  Operating_income The logarithm of total operating income  International A dummy variable that equals one if a BHC has subsidiaries that mainly engage in international activities, and zero otherwise State-level instruments  Year_since The number of years after the initial interstate banking deregulation of a BHC’s headquarter state  Year_since|$^{2}$| Year_since squared  After1 A dummy variable that equals one for 1 year after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise  After2(to After9) A dummy variable that equals one for 2 (to 9) years after the initial interstate banking deregulation of a BHC’s headquarter state, and zero otherwise  After10 A dummy variable that equals one for 10 or more years after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise Open in new tab Table A.1 Variable definitions Systemic risk measures .  |$\Delta $|CoVaR Change in conditional value at risk following Adrian and Brunnermeier (2016), we define |$\Delta $|CoVaR as the marginal contribution of an individual bank to the overall systemic risk. It is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution. We calculate |$\Delta $|CoVaR based on a 3-year forward-looking window  Logistic(R|$^{2})$| Following Pukthuanthong and Roll (2009), we regress each bank’s equity return on the first four factors extracted from principal component analysis using daily equity return of top-20 largest banks from 1986 to 1997. The |$R^{2}$| from the above regression measure an individual bank’s integration with the overall banking system. |$R^{2}$| is computed based on a 1-year forward-looking window. We take a logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|  MES Marginal expected shortfall, defined as the average stock return of a bank on condition that the overall market is under its 5% tail  SRISK Expected capital shortfall of a bank on conditional on crisis, following Acharya, Engle, and Richardson (2012) and Brownlees and Engle (2017). We scale capital shortfall by the sum of all positive SRISK during a quarter Geographic diversification measures  (1–HHI) Bank geographic diversification measure, which is one minus the Herfindahl-Hirschman index of deposit shares across MSAs  # branches The number of branches a BHC operates  # MSAs The number of MSAs a BHC operates  Share The deposit share of a BHC in a foreign MSA Control variables  Size The logarithm of total assets  Size|$^{2}$| Size squared  ROA Return on assets, which equals net income divided by total assets  Market_to_book The market value of equity divided by book value of equity  Noninterest Noninterest income divided by total operating income  Provision Loan loss reserves divided by gross loans  ST_funding Nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding  Income_diversity 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|  Asset_diversity 1-|$\vert $|(Net loans–Other earning assets)/(Total earning assets)|$\vert $| Channel effects  Asset_simi Cosine similarity measure based on asset structure. We convert the percentage of N asset types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. The asset similarity of a bank to other banks is the average of its cosine value with each of the other banks  Asset_simi_w The weighted average of Asset_similarity with the weight based on bank total assets  Loan_simi Cosine similarity measure based on loan structure. We convert the proportion of N loan types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. Loan_similarity of an individual bank is the average of its cosine value with each of the other banks  Loan_simi_w The weighted average of Loan_similarity with the weight based on bank total loans  Location_simi_num Weighted average borrower MSA similarity based on the number of mortgage loans using HMDA data, with the weight being the size of paired banks  Location_simi_amount Weighted average borrower MSA similarity based on the amount of mortgage loans using HMDA data, with the weight being the size of paired banks Cross-sectional test  Comovement It is the correlation between the Coincident index of the home state of a BHC and the Coincident index of U.S. economy  High_comovement A dummy variable that equals one if the correlation of the Coincident index is larger than the sample median and zero otherwise. Reverse causality test  |$T$| The expected time that a state-pair deregulates  SmallShare Percent of banking assets in the state held by banks below the median size of banks in each state in each year  CapitalDiff Capital to assets ratio of small banks minus that of large banks  Unemp The unemployment rate of a state  GSP Gross state product of a state Variables used to replicate Goetz, Laeven, and Levine, Lin, and Xie (2016)  ln(SD) The logarithm of the standard deviation of weekly equity return during a quarter  ln(Residual) We first regress a bank’s weekly equity returns on the returns of the S&P 500, spread on BAA and AAA corporate bonds, and change in yield of a 3-month Treasury bill, we then calculate the standard deviation of the residuals from above regression  ln(Z-score) The logarithm of the Z-score, which is defined as (net income/book value of assets + capital/book value of assets) divided by the standard deviation of weekly market returns during a quarter  Loan_commitments Loan_commitments/(Loan_commitments+Loans)  Transaction_deposits Transaction_deposits/(total deposits)  Capital Capital/total assets  Operating_income The logarithm of total operating income  International A dummy variable that equals one if a BHC has subsidiaries that mainly engage in international activities, and zero otherwise State-level instruments  Year_since The number of years after the initial interstate banking deregulation of a BHC’s headquarter state  Year_since|$^{2}$| Year_since squared  After1 A dummy variable that equals one for 1 year after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise  After2(to After9) A dummy variable that equals one for 2 (to 9) years after the initial interstate banking deregulation of a BHC’s headquarter state, and zero otherwise  After10 A dummy variable that equals one for 10 or more years after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise Systemic risk measures .  |$\Delta $|CoVaR Change in conditional value at risk following Adrian and Brunnermeier (2016), we define |$\Delta $|CoVaR as the marginal contribution of an individual bank to the overall systemic risk. It is computed as the difference between CoVaR conditional on the distress of a bank and CoVaR conditional on the normal state of the institution. We calculate |$\Delta $|CoVaR based on a 3-year forward-looking window  Logistic(R|$^{2})$| Following Pukthuanthong and Roll (2009), we regress each bank’s equity return on the first four factors extracted from principal component analysis using daily equity return of top-20 largest banks from 1986 to 1997. The |$R^{2}$| from the above regression measure an individual bank’s integration with the overall banking system. |$R^{2}$| is computed based on a 1-year forward-looking window. We take a logistic transformation of |$R^{2}$| as log(R|$^{2}/(1-R^{2}))$|  MES Marginal expected shortfall, defined as the average stock return of a bank on condition that the overall market is under its 5% tail  SRISK Expected capital shortfall of a bank on conditional on crisis, following Acharya, Engle, and Richardson (2012) and Brownlees and Engle (2017). We scale capital shortfall by the sum of all positive SRISK during a quarter Geographic diversification measures  (1–HHI) Bank geographic diversification measure, which is one minus the Herfindahl-Hirschman index of deposit shares across MSAs  # branches The number of branches a BHC operates  # MSAs The number of MSAs a BHC operates  Share The deposit share of a BHC in a foreign MSA Control variables  Size The logarithm of total assets  Size|$^{2}$| Size squared  ROA Return on assets, which equals net income divided by total assets  Market_to_book The market value of equity divided by book value of equity  Noninterest Noninterest income divided by total operating income  Provision Loan loss reserves divided by gross loans  ST_funding Nondeposit short-term funding divided by the sum of total deposit and nondeposit short-term funding  Income_diversity 1-|$\vert $|(Net interest income–Total noninterest income)/(Total operating income)|$\vert .$|  Asset_diversity 1-|$\vert $|(Net loans–Other earning assets)/(Total earning assets)|$\vert $| Channel effects  Asset_simi Cosine similarity measure based on asset structure. We convert the percentage of N asset types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. The asset similarity of a bank to other banks is the average of its cosine value with each of the other banks  Asset_simi_w The weighted average of Asset_similarity with the weight based on bank total assets  Loan_simi Cosine similarity measure based on loan structure. We convert the proportion of N loan types of a bank into a 1 by N vector, the similarity of two banks can be measured by the cosine value of the angle between two vectors in an N-dimensional space. Loan_similarity of an individual bank is the average of its cosine value with each of the other banks  Loan_simi_w The weighted average of Loan_similarity with the weight based on bank total loans  Location_simi_num Weighted average borrower MSA similarity based on the number of mortgage loans using HMDA data, with the weight being the size of paired banks  Location_simi_amount Weighted average borrower MSA similarity based on the amount of mortgage loans using HMDA data, with the weight being the size of paired banks Cross-sectional test  Comovement It is the correlation between the Coincident index of the home state of a BHC and the Coincident index of U.S. economy  High_comovement A dummy variable that equals one if the correlation of the Coincident index is larger than the sample median and zero otherwise. Reverse causality test  |$T$| The expected time that a state-pair deregulates  SmallShare Percent of banking assets in the state held by banks below the median size of banks in each state in each year  CapitalDiff Capital to assets ratio of small banks minus that of large banks  Unemp The unemployment rate of a state  GSP Gross state product of a state Variables used to replicate Goetz, Laeven, and Levine, Lin, and Xie (2016)  ln(SD) The logarithm of the standard deviation of weekly equity return during a quarter  ln(Residual) We first regress a bank’s weekly equity returns on the returns of the S&P 500, spread on BAA and AAA corporate bonds, and change in yield of a 3-month Treasury bill, we then calculate the standard deviation of the residuals from above regression  ln(Z-score) The logarithm of the Z-score, which is defined as (net income/book value of assets + capital/book value of assets) divided by the standard deviation of weekly market returns during a quarter  Loan_commitments Loan_commitments/(Loan_commitments+Loans)  Transaction_deposits Transaction_deposits/(total deposits)  Capital Capital/total assets  Operating_income The logarithm of total operating income  International A dummy variable that equals one if a BHC has subsidiaries that mainly engage in international activities, and zero otherwise State-level instruments  Year_since The number of years after the initial interstate banking deregulation of a BHC’s headquarter state  Year_since|$^{2}$| Year_since squared  After1 A dummy variable that equals one for 1 year after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise  After2(to After9) A dummy variable that equals one for 2 (to 9) years after the initial interstate banking deregulation of a BHC’s headquarter state, and zero otherwise  After10 A dummy variable that equals one for 10 or more years after the initial interstate banking deregulation of a BHC’s headquarters state, and zero otherwise Open in new tab © The Author(s) 2020. 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TI - Bank Geographic Diversification and Systemic Risk
JO - The Review of Financial Studies
DO - 10.1093/rfs/hhz148
DA - 2011-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/bank-geographic-diversification-and-systemic-risk-fe8CLBI7rf
DP - DeepDyve
ER -