Keywords: Bank capital, bank lending
Abstract:
The effect of changes in bank capital on the extension of bank credit is a key determinant of the linkage between financial conditions and real activity. Quantifying this relation has therefore been one of the most important research questions of the recent financial crisis. For example, early in the crisiswhen the likelihood of a credit crunch was still under debatethe connection between bank capital and bank lending was central to any assessment of how losses in banks' mortgagerelated portfolios would affect lending and thus real activity. Likewise, when the Troubled Asset Relief Program (TARP) moved to inject capital into banks through the Capital Purchase Program (CPP), the impact of the program on real activity largely focused on the effect of these injections on bank lending. More recently, this question has reemerged in light of proposals announced by the Basel Committee on Banking Supervision to raise banks' capital requirements and limit leverage ratios. In this case, policymakers and regulators need to weigh the effects of stricter capital requirements on economic activity against the benefits that would result from greater financial and macroeconomic stability.
In principle, there is a wide range of possible values for effect of a change in bank capital on bank assets and lending. On the one hand, a wellcapitalized bank or a bank with access to additional sources of capital will be able to accommodate capital losses without reducing its assets (and hence its lending). By contrast, one could imagine a polar case in which banks very actively manage their assets in order to maintain a constant equitycapitaltoassets ratio (or "capital ratio")for example, because they cannot raise equity to offset declines in their capital. In this case, a capital loss results in a reduction in assets, with the required reduction equal to the size of the bank's capital loss scaled up by the inverse of its capital ratio (that is, its leverage ratio). Since observed bank capital ratios roughly range from 0.08 to 0.125, leverage ratios range from 8 (= 1/0.125) to 12.5 (= 1/0.08). This means that a dollar's reduction in capital results in an $8 to $12.50 reduction in bank assets.^{1} How close we will be to either case in practice is, of course, an empirical question.
Despite its importance, there are relatively few recent estimates for the United States of the effect of changes in bank capital on lending. This is somewhat surprising given the existence of an active earlier literature on this topic. In particular, during the sluggish recovery that followed the 199091 recession, many observers debated whether the newly introduced capital regulations associated with Basel I were inhibiting lending. Although this debate did not yield a definitive conclusion, it did result in the development of empirical models that expressly sought to quantify the effect of bank capital on bank lending. For example, Hancock and Wilcox (1993, 1994) estimated models relating changes in individual banks' loan growth to measures of loan demand and bank capital. Similarly, Berger and Udell (1994) specified an equation relating the growth rate of various bank assets to different measures of bank capital ratios. Finally, Bernanke and Lown (1991) developed statelevel equations linking bank loan growth to bank capital ratios and employment, along with banklevel equations for a single state (New Jersey).^{2}
This paper draws on this earlier literature, as well as more recent approaches, to examine how bank capital affects bank lending in the U.S. In all cases, we find relatively modest effects of bank capital on lending and more important roles for factors such as economic activity and increased perception of risk by banks. Using balancesheet data for large bank holding companies (BHCs), we consider variants of two of the approaches developed in the earlier literature: specifically, the Hancock and Wilcox (1993, 1994) and Bernanke and Lown (1990) models. For our purposes, the main difference between these two approaches is that the BernankeLown approach considers the effect of actual BHC capitaltoasset ratios on BHC loan growth while the HancockWilcox approach looks at the effect of deviations of BHC capital levels relative to an estimated target. Both approaches have merits and shortcomingswhich we will discuss at lengthbut both also agree in finding relatively small effects of BHC capital on loan growth.
A potential concern surrounding both sets of results is survivor bias: Our panel only includes BHCs that were still in operation at the end of our sample period (2008:Q3). We address this issue by also considering a more aggregate approach; namely, a modified variant of one of Lown and Morgan's (2006) vector autoregression (VAR) models. This allows us to investigate the dynamic and generalequilibrium effects of an exogenous change in bank capital ratios. Again, however, we find relatively modest effects of bank capitalratio changes on loan growth even using this very different approach.
Our estimates of the effect of bank capital on lending are considerably smaller than the effects suggested in recent statements by U.S. Treasury officials. For example, on the likely effects on lending of capital injections and anticipated capital raising following the stress tests, such statements suggest that a $1 capital injection generates between $8 to $12 of lending capacity.^{3} These magnitudes seem more consistent with the view described earlier that banks actively manage their assets to maintain constant bank capital ratios. This view has been quite prominent of late, and is apparently based on a scatterplot for aggregate leverage and commercialbank asset growth reported by Adrian and Shin (2007).^{4} This scatterplot for commercial banks is reproduced in the lowerleft panel of Figure 1 using our data; the figure also shows scatterplots for all of the other institutions that Adrian and Shin consider (specifically, households, nonfinancial and nonfarm corporate firms, and security brokers and dealers). The sample period used in Figure 1 is 1963 to 2006, the same as that employed by Adrian and Shin.^{5} The roughly constant leverage ratio apparent from the commercial bank panelespecially when compared to other classes of institutionssuggests a very active management of assets by commercial banks. This implies that a change in bank capital has a magnified effectwith the scaling factor equal to the leverage ratioon asset levels and lending volumes.
Adrian and Shin's scatterplots have also been quite influential in shaping forecasters' views. For example, in a note written early in the crisis, Hatzius (2007) used these commercialbank scatterplots to estimate the reduction in loan volumes that would result from banks' mortgagerelated portfolio losses. In a subsequent Brookings paper on the same issue, Hatzius (2008) again appealed to assetleverage scatterplots to inform revised estimates of the effect of bank capital losses on loans.
Interestingly, reconciling our regression results with the AdrianShin scatterplots turns out to be very simple: Because of the major structural changes that occurred in the banking sector following the adoption of the Basel Accord, our empirical analysis begins in the early 1990s; in contrast, Adrian and Shin's scatterplots span a much longer period that starts in 1963. To see what effect the choice of sample period has on the analysis, consider the two left panels of Figure 2, which give scatterplots for commercialbank asset and leverage growth over 1963:Q1 to 1989:Q4 (the top panel) and 1990:Q1 to 2008:Q3 (the bottom panel). As can be seen from comparing these plots, the feature of the data that has led to the view that commercial banks actively manage their assets to maintain constant leverage is much more of an artifact of the early part of the sample and is considerably less evident in the latter (postBasel) part, which is naturally more relevant for considering current questions. Indeed, in the latter part of the sample the scatterplot is merely a cloud of points with no obvious correlation. The two righthand panels of Figure 2 provide a different split of the sample; specifically, one that breaks the sample in 1985:Q1 and therefore uses a more equal number of observations (88 and 94 observations, respectively) for each plot. Again, the feature of the data reported by Adrian and Shin (2007) and emphasized by Hatzius (2007, 2008) is very evident in the first part of the sample and not at all evident in the second part.^{6} Clearly, the scatterplots shown in the lower panels of Figure 2 make the small effects of bank capital on loan growth found in our regressions less surprising.
A couple of other related recent studies are also worth noting. First, Francis and Osborne (2009) apply Hancock and Wilcox's approach to U.K. commercial bank data; like us, they find relatively modest effects of bank capital shortfalls on lending. Ciccarelli, Maddaloni, and Peydró (2010) build on Lown and Morgan's VAR modelalbeit along a different dimension than we doto study the credit channel of monetary policy in the Euro area and the U.S. (in this case using the European Bank Lending Survey or BLS and the U.S. Senior Loan Officer Opinion Survey or SLOOS). In contrast to our approach, however, Ciccarelli et al. do not explicitly consider the influence of bank capital by including a measure of it in their VAR model but rather rely on answers to "reasons for tightening/loosening lending standards" questions from the survey. Based on this approach, Ciccarelli, et al. conclude that bank capital and liquidity have significant effects on GDP.^{7}
Other methods for examining the effect of bank capital on lending have been pursued in a number of recent papers, albeit for countries other than the U.S. For example, following Peek and Rosengren (1997), Puri, Rocholl and Steffen (2010) use loan applications from German Landesbanks to examine the effect of shocks to capital on the supply of credit by comparing the performance of affected and unaffected banks. Gianetti and Simonov (2010) use Japanese data to perform a similar exercise concerning bank bailouts. These papers do find a relevant role for capital in determining loan volumes, although they do not explicitly compare the magnitudes of the effects they find with those implied by the constant leverage view. Another group of papers use firm and bank loanlevel data; these include Jiménez, Ongena, and Peydró (2010), who use Spanish data, and Albertazzi and Marchetti (2010), who use data on Italy. These papers find sizeable effects of low bank capitalization and scarce liquidity on credit supply. (We contrast our methodology with the approaches that use firm and bank loanlevel data later in the paper.)
We would note that although the abovementioned loanlevel studies for Spain and Italy suggest larger effects than what we find, other studies for the U.S. that use loanlevel data (albeit for syndicated loans only) matched to bank and firm variables, such as Santos and Winton (2010), obtain relatively small effects of bank capital on lending. In addition, Elliot (2010) uses simulationbased techniques and finds small effects of higher capital ratios on loan pricing and loan volumes for U.S. banks. Finally, De Nicolò and Lucchetta (2010) use aggregate data for the G7 countries and conclude that credit demand shocks are the main drivers of bank lending cycles. Thus, our empirical findings of modest effects of capital on total loan growth appear consistent with other papers that employ U.S. data.
Our findings have several interpretations. First, in making their lending decisions, BHCs might not actively manage their assets on the basis of their capital positions.^{8} If our results are correct, and other factors such as loan demand or increased bank risk play a more important role in determining BHC loan growth, then we have an explanation for the notable slowing of loan growth observed over the first three quarters of 2009: The impact of increases in the availability of loanable funds from various government actions was more than offset by weak economic conditions that reduced loan demand, as well as by increased risks (such as the reduced creditworthiness of borrowers).
Second, given the widespread consensus that banks entered the most recent crisis with too little capital relative to the riskiness of their portfolios (even though by most measures they were previously viewed as well capitalized), another interpretation of our results is that conventional measures of bank capitalsuch as those that we usemay not be relevant for assessing financial intermediaries' capital positions. If so, our results naturally call into question the prevailing riskbased measures employed by the regulatory capital framework and militate a strengthening in risk coverage, particularly in terms of incorporating capital requirements for offbalance sheet operations (such as securitization activities) and counterparty exposures.
The balance of the paper is organized as follows. We describe our data in Section 1. Section 2 contains empirical estimates of the relation between bank capital and bank loan growth at the institutional level, while section 3 presents our results using aggregate data. Sections 4 and 5 then use the models developed in sections 2 and 3 to address some questions of practical policy interest. Specifically, in section 4 we estimate the likely effect that TARP capital injections had on bank loans, and in section 5 we consider the factors underlying recent reductions in bank loan growth. Section 6 concludes.
Because we use both panel and timeseries methods, the paper employs a wide range of data sources. We discuss these data sources at length in this section.
For our panel regression, which we conduct at the institution level, we use bank holding company (BHC) data rather than data on the loans of individual commercial banks within a BHC. This reflects the observation that many decisions regarding a BHC's activities are taken for the institution as a whole rather than on a subsidiarybysubsidiary basis.^{9} Institutionlevel data are taken from the Consolidated Financial Statements for Bank Holding Companies (FR Y9C); the data cover the period 1992:Q1 to 2009:Q3, with the exception of the data series that are based on regulatory capital (and that appear in some of our BernankeLown type regressions), which begin only in 1996. Our sample consists of 165 large BHCs, all with total assets in excess of $3 billion as of 2008:Q3. This represents approximately 85 percent of the total assets in the banking sector.^{10}
Table 1 reports summary statistics for the variables used in the panel regressions. Although the sample only includes large BHCs, there is a sizable variation in total assets. The median BHC in the sample has assets above $3 billion. However, the standard deviation of $145 billion is consistent with the fact that the four largest institutions in the sample have assets above $1 trillion, whereas total assets for the smallest ones are below $1 billion.^{11} Quarterly growth in total and C&I loans averages 3 percent across all BHCs and over time. The distribution of variables scaled by assets such as capital, securities and net chargeoffs exhibit smaller variances. Both the mean and the median values for the equitytoassets (leverage) ratio are about 8 percent, while the mean and median of total and tier one riskbased capital ratios (measured as total and tier one capital over riskweighted assets) are 121/2 percent and 131/4 percent (for total) and 103/4 percent and 111/4 percent (for tier one). Finally, the Tangible Common Equity (TCE) ratio (measured as tangible common equity over tangible assets) for the mean and median BHC is about 7 percent.
The first four panels of Figure 3 depict the evolution of the average of different capital ratios over our sample. As is evident from the top two panels, throughout most of the sample period the average total and tier one riskbased capital ratios for large BHCs remained significantly above their wellcapitalized regulatory minima.^{12} Note also the divergent movements across different capitalratio measures: For example, while riskbased capital ratios have exhibited a downward trend since 2004, the capitaltoassets ratiothe middleleft panelremained on an upward trend until mid2007. This could partly reflect differences arising from the denominator of the capitalratio measures which, in turn, could be associated with increasing risktaking by banks during the last 5 years. In particular, excessive risktaking behavior could have made riskweighted assets increase faster than total assets.
As expected, the leverage ratio and the regulatory capital ratios all jump in 2008:Q4 after the implementation of the Treasury's capital injection program. (A vertical line is shown in the top four panels of Figure 3 at 2008:Q3, just before the capital injections.) However, because the Treasury injected capital through purchases of preferred stock with warrants rather than common equity, the TCE ratiothe middleright panelis not affected by TARP capital infusions and seems to have maintained the downward trend that it has displayed since 2003. Adverse market risk perceptions of the banking sector were more evident after the beginning of the financial crisis and this explains a deeper contraction in the average TCE ratio after the second half of 2007. This marketfocused measure of capitalization reached its lowest value in 2009:Q1 due to adverse market expectations in advance of the May 2009 release of the bank stress test results (the average TCE ratio was below 6 percent, with ratios below 2 percent for some of the largest BHCs).
The bottom two panels of Figure 3 plot the average fourquarter growth rate of total loans for the 165 BHCs in our sample, along with loan growth for all commercial banks and large banks only. As can be seen from these panels, commercialbank and BHC loan growth slowed notably in the 2001 recession but recovered rapidly thereafter, with the average fourquarter growth rate prior to 2007 fluctuating between 10 to 15 percent. Total growth in bank loans exhibits a severe contraction starting in early 2008, with a further slowing in growth following the ongoing deterioration in credit conditions during 2008. Negative fourquarter growth rates were evident in the first part of 2009.
Our panel regressions include a number of macroeconomic data series; these are plotted in Figure 4. Specifically, our panel regression loangrowth equations include real GDP growth (the topleft panel of Figure 4), as measured by the National Income and Product Accounts (NIPAs); inflation (the topright panel, solid line), as measured by the overall GDP deflator; the Federal funds rate (the middleleft panel); and (aggregate) net tightening of C&I lending standards (the bottomright panel), as reported by the Federal Reserve Board's Senior Officer Opinion Survey (SLOOS).
A large fraction of the aggregate variables that are included in the paper's panel regressions are also included in the VAR model that we consider in section 3. Indeed our panel equation for loan growth has a similar specification to our loangrowth equation in the VAR, albeit without the institutionspecific variables that the former equation has. In particular, our VAR model includes real GDP growth, along with inflation. However, the inflation measure used in the VAR is based on the GDP deflator excluding food and energy (see the dotted line in the topright panel of Figure 4). Our reason for using different inflation measures is attributable to some very large swings in overall GDP prices caused by swings energy prices at the end of our data. In our panel regressions, the difference between the two inflation measures has a minimal impact on our results since our estimation period stops at the third quarter of 2008, before we observe significant movements in energy prices. In the VAR, these swings were not important for our impulse response functions, but did influence (in an implausible way) the composition of estimated nonfinancial structural shocks being derived from our model over the 2008 to 2009 period.^{13}
Like the panel regression, our VAR model also includes the Federal Funds rate and the net tightening in C&I lending standards from the SLOOS. Our measure of the aggregate capitalasset ratio (the bottomleft panel) is for commercial banks and is taken from the Call Reports. Finally, for loan growth (the middleright panel) we use bank and thrift depository loan growth as reported by the Flow of Funds Accounts. Our principal motivation for using commercial bank and thrift loans in the VAR rather than just commercial bank loanswhich may seem more sensible given that all other bankingsector variables pertain only to commercial banksarises from some very sharp spikes in the latter series caused by purchases of large thrifts by commercial banks, such as Bank of America's purchase of Countrywide and JP Morgan's purchase of Washington Mutual. Using the aggregate bank and thrift data eliminates these swings and does not greatly alter the VAR's impulse response functions, although clearly it leads to more plausible estimated sequence of structural shocks.
In this section we use institutionlevel BHC data and panel regression techniques to study the effects of BHC capital on loan growth. The idea here is to model the loan growth of our panel of BHCs as a function of supply and demand factors, with one of our supply factors being BHC capital.
Specifically, the loan growth regressions that we estimate take the form
Because our loangrowth regression (1) controls for the effects of other supply and demand variables, we can interpret the coefficient on the capital term as the effect of BHC capital conditions on loan growth. We consider two ways that capital can affect loan growth. In the first casewhich corresponds to the approach of Hancock and Wilcox (1993, 1994)it is the divergence between a BHC's actual and target capital (i.e., its capital surplus or shortfall) that is important for determining loan growth. In the second casewhich corresponds to the approach of Bernanke and Lown (1991)a BHC's capitaltoassets ratio influences loan growth.
The BHC capitaltoassets ratio measures included in the BernankeLown regressions can be calculated from variables taken directly from the Consolidated Financial Statements for Bank Holding Companies (the FR Y9C data). By contrast, the capital measures used in the HancockWilcox regressions first requires us to create timevarying desired/target capital levels for each BHC in our panel. From these time series, we can compute the percentage surplus or shortfall of actual capital relative to target. (The precise method and results for this stage of the HancockWilcox estimation procedure are discussed in subsection 2.1.), Note that the estimation period for these regressions is 1992:Q1 to 2008:Q3; that is, we stop the analysis around when the crisis intensified in late September 2008 and just before TARP capital injections began to occur. This prevents the TARP capital injections from distorting our regression coefficients.
Following Hancock and Wilcox (1993, 1994) and Flannery and Rangan (2008) we use a partialadjustment model between actual and target capital holdings to estimate individual bankspecific capital targets. The target capital ratio, , is modeled as a linear function of a vector of control variables , which include bankspecific characteristics as well as institutional and aggregate determinants (so ). Based on the rationale that costs of altering bank capital prevent banks from moving capital to its target level immediately, the actual bank capital ratio is assumed to follow a partialadjustment process of the form
Substituting in our expression for , rearranging terms, and adding a bankspecific constant yields our estimation equation:The bankspecific variables in include the log of total assets, the return on assets, and the net chargeoff rate; these are intended to serve as proxies for size, earnings, and risk, respectively. Size captures the fact that larger banks are likely to face lower risks (due, for example, to greater diversification) and better access to sources of funding (thereby requiring less capital). Earnings are included because dividend payments are often slow to adjust; hence, an increase in earnings results in an accumulation of retained earnings and bank capital. Risk captures the fact that markets and regulators require more capital to be held against riskier assets. In the benchmark specification of our capital ratio equation we also include the loan/security composition of bank assets, which reflects the differential risk exposures implied by different types of assets, and the composition of bank loans, which for similar reasons could also affect target capital ratios. These terms are dropped in an alternative specification of equation (2) that we consider.^{14} The institutional variable, called "regulatory pressure," is a dummy variable that equals unity if the BHC's equity capital ratio is less than 1.5 percentage points above the minimum of 5 percent.^{15} We also include aggregate variables such as a measure of stockmarket volatility and the aggregate net chargeoff rate.
Note that the only measure of capital that we consider in deriving our surplus/shortfall estimates is equity capital. Consequently, we do not estimate models of the form described by equation (2) for the three other capital ratiosi.e., the total and tierone riskbased capital ratios and the tangible common equitytoassets ratiothat we reported in Figure 3 and discussed in section 1.1. (The full set of capital ratios is examined when we consider the BernankeLown version of equation 1.) We focus here on equity capital on the grounds that the HancockWilcox loangrowth regression implicitly seeks to capture a behavioral relation whereby BHCs alter the growth rate of their loan volumesthe dependent variable of equation (1)so as to obtain a desired level of capital. If this is the case, however, it would then be most likely that such an adjustment would involve a fairly broad measure of capital (such as, total equity capital) rather than a more narrow measure (such as, tangible common equity). Similarly, we do not consider total and tierone riskbased capital ratios because these are essentially regulatory concepts for which the relevant target is the threshold that determines whether a BHC is adequately or well capitalized. Thus, it makes less sense to try to develop a model of the target for these capital ratios. In addition, even if BHCs did seek to target these ratios, they would be more likely to adjust their riskbased assetsthat is, to adjust the composition of their loans as well as their volumewhich would make this a less useful tool for analyzing the growth of aggregate loan volumes (the ultimate focus of our analysis).
Table 2 provides the estimation results for equation (2) under two different specifications of the term. Other than the coefficients on bank size and aggregate stockmarket volatility, most of the coefficients reported in Table 2 are close to what might be expected a priori. Size receives a positive and significant coefficient in both specifications, which implies that larger BHCs have higher equity capital ratios. This contradicts previous findings that larger BHCs have lower capital ratios, and suggests that there are some economies of scale in holding capital at larger institutions.^{16} We also find that larger shares of each broad category of loans and of securities (relative to assets) are associated with lower capital ratios, which we interpret as indicating that BHCs with more portfolio diversification (loans categories and investment securities) hold less capital. The negative coefficient on stockmarket volatility appears to reflect the countercyclical nature of volatility and the procyclicality of bank capital. Both individual and aggregate net chargeoff rates are associated with higher capital ratios, though only the aggregate measure seems statistically significant. These two variables control for bank risks and suggest that BHCs hold additional capital during bad times, when the credit quality of loans deteriorates. Our dummycontrol for regulatory pressure has a negative coefficient but is statistically insignificant, which suggests that regulatory restrictions do not seem to bind in a way that affects equity capital ratios. Finally, BHCs with higher profits tend to hold more capital, but this result also appears to be statistically weak.
In addition to the usual candidate determinants of the target capital ratio, the regression equation includes bankspecific fixed effects to control for possible omitted variables and to capture heterogeneous characteristics such as different risk preferences, governance structures, and managerial skills. The fixed effects explain a large fraction of the crosssectional variation in target capital ratios without affecting the statistical significance of the other timevarying and firmspecific characteristics in the regression equation.^{17} Interestingly, the coefficient on the lagged capital ratio implies a relatively quick adjustment of capital ratios to target: Our estimated average speed of adjustment of 36 percent per year is smaller than the 49 percent per year rate found by Flannery and Rangan (2008) but within the range of 28 percent to 41 percent reported by Berger et al. (2008).
As in Hancock and Wilcox, the estimates of the coefficients in equation (1) are used to calculate a time series for each BHC's target capital ratio . These estimated target capital ratios are then used to construct target capital levels . Capital surpluses, denoted by , are calculated as deviations of actual capital levels relative to target; that is, .
Figure 5 plots the average actual and average target capital ratiosthat is, and over our estimation period, where the averages are computed over the entire sample of BHCs. Differences between the average actual and average target capital ratios appear quite pronounced and quite persistent; nonetheless they do appear to conform with certain aspects of the conventional wisdom concerning movements in these series. In particular, in line with the findings of the literature on bank capital management, we find that BHCs operated with significant capital surpluses over most of the late 1990s and early 2000s.^{18} Furthermore, BHCs appeared to have operated with large capital shortfalls between 1993 and 1995, which may have reflected widespread capital pressures after the implementation of the Basel I capital guidelines around 1992.^{19}
Figure 6 plots the average actual and average target capital ratios over our estimation period for subgroups of BHCs based on bank size. Differences between actual and target capital also seem apparent among the largest and smallest BHCs in our sample. The four largest BHCs (those with total assets above $1 trillion at the end of the sample) seemed to have operated with capital close to their target levels in the early 1990s (e.g., after the implementation of Basel I) and then to have accumulated large surpluses between 1995 and 2001. These plots suggest that most of the conventional wisdom regarding the emergence of large capital surpluses in the late 1990s and early 2000s is explained by the behavior of the largest BHCs. However, after 2002 the very large BHCs appear to suffer from the largest capital shortfalls, which became more pronounced during the recent financial turmoil. Unlike the largest institutions, smaller BHCs had relatively large capital shortfalls during the early 1990s, and gradually aligned their capital with their target during the late 1990s and early 2000s. The smallest 20 BHCs seemed to have conducted a quick capital adjustment during that period and began to be better capitalized with large surpluses between 2003 and 2006. However, the smallest institutions started to reduce their capital ratios around the middle of 2004, mainly as a result of a rapid balance sheet expansion; as in the case of the largest BHCs, these firms were operating substantially below target at the beginning of and during the recent financial crisis. In sum, the recent phenomena of large capital shortfalls that is apparent in the aggregate data (Figure 5) seems largely to reflect developments at the smallest and very largest BHCs.
To gauge the effects of capital surpluses or shortfalls on bank loans we include our estimates of bank capital surplusesdenoted by , abovein a regressions model of bank loan growth. Our model is similar in spirit to the loan growth regression of Hancock and Wilcox, who studied the link between bank capital and bank loan growth while controlling for macroeconomic conditions. Our particular specification is closer, however, to that used by Kashyap and Stein (1995, 2000), who modeled the growth rate of bank loans in terms of supply and demand factors.
We model the growth rate of BHC loans (
) as a function of its own lags, lags of aggregate economic growth (
), lags of the GDP price inflation rate (
), lags of the change in the federal funds rate (
), and lags of lending standards (). In addition, we include
lagged BHCspecific characteristics such as a control for bank liquidity (
), which is measured by the ratio of securities to total assets, and the ratio of net chargeoffs to total assets (). The last term we include is our estimates of bank capital surpluses/shortfalls (), which is the main variable of interest.
Thus, we fit the following panel regression equation
The model is specified in growth rates to deal with nonstationary variables; to avoid potential endogeneity issues, only lags of the explanatory variables are used. We also include quarterly dummies to control for possible seasonality in the data. In this specification, GDP growth is used to control for changes in loan demand, lending standards are used to control for credit supply changes that arise from changes in banks' lending behavior, and the federal funds rate controls for monetary policy changes. At the firm level, the liquidity variable is intended to capture the extent to which BHCs use their stock of securities to adjust their loan growth, all else equal (a point raised by Kashyap and Stein) while the fraction of chargeoffs to total assets is a proxy for risk, which should act as a drag on loan growth. Equation 3 is estimated with bank fixed effects in order to allow for potential omitted factors that vary across BHCs and are constant over time.
Table 3 presents the estimation results for equation (3).^{20} The first pair of columns gives results when total bank loans are used as the dependent variable, while the second pair of columns gives results when C&I loans are used as the dependent variable. For both total bank loans and C&I loans there is a positive and significant coefficient on capital surpluses, indicating that the growth rate of both total and C&I bank loans is larger for banks with greater amounts of excess capital. The effects, however, are small: The longrun impact of a capital surplus (shortfall) on both total and C&I BHC loan growth is roughly to increase (reduce) annualized loan growth by 0.25 percentage point when capital exceeds (falls short of) its target level by 1 percent.
Our estimate of the effects of a 1 percent capital surplus on loan growth canwith some manipulationbe compared to the effects found by Hancock and Wilcox, who looked at dollar amounts. Using a 10 percentage point average capitaltoassets ratio and a 60 percent average share of loans (as a fraction of bank assets), our model estimates imply that a $1 capital surplus results in a $1.86 boost in loan volumes.^{21} This is a touch higher than Hancock and Wilcox's estimates, which implied that a $1 surplus leads to a $1.50 boost in loan volumes, but it is not vastly different. Our estimate is, however, very differenti.e., about onesixth to onetenth the sizeto the $8 to $12.50 increase in loans that the constant leverage ratio assumption would imply.
The results in Table 3 suggest a notable role for demand shocks and exogenous changes in net chargeoffs in determining both total and C&I loan growth. The results imply that in the longrun a 1 percentage point reduction in GDP growth lowers the annualized growth rate of total loans by 4.1 percentage points and lowers the annualized growth rate of C&I loans by 9.4 percentage points. Furthermore, changes in net chargeoffs have a large and significant impact in both specifications. For example, a 1 percentage point increase in the net chargeoff ratio depresses (in the long run) the annualized growth rate of both total and C&I BHC loans by about 7 percentage points. Turning to the other regressors, although the coefficient on the securitiestoassets ratio is significant, the effect of increased holdings of securities on BHC loan growth is small: A 1 percentage point increase in the securitiestoassets ratio leads to about a 0.3 percentage point longrun increase in both total and C&I annualized loan growth. Finally, the coefficient on lending standards in both the total and C&I loan growth equations are negative (as expected) and statistically significant, but imply an impact on loan growth that is economically small: A 1 percentage point increase in lending standards leads to about a 0.1 percentage point decrease in annualized loan growth. The small effect of standards may be explained by the fact that the capital surplus measure and chargeoff ratio likely already capture changes in banks' willingness to lend.
As we will discuss in the next section (when we consider possible identification issues present in our panel regression analysis), one potential problem with the HancockWilcox approach is that the target capitaltoassets ratio equation could be misspecified. If we model the target poorly, our estimates of the effect of a capital surplus or shortfall on loans will also be poor, thereby biasing the estimated surplus/shortfall impact coefficient . (The direction of this bias will likely be downward for the usual errorsinvariables reasons.) An alternative approach to investigating the link between bank capital and bank lending that does not suffer from this issue involves focusing on the relationship between capital ratios and bank loan growth. For this purpose, we replace our measure of the capital surplus in equation (3) with the lagged value of different measures of the capital ratio. That is, we estimate:
using several measures of the capitaltoassets ratio for : the equity capitaltoassets ratio (the book leverage ratio); the total riskbased capital ratio; the tierone riskbased capital ratio; and the tangible common equity (TCE) ratio. We consider each capital ratio separately. The different capital ratios measure different dimensions of banks' balancesheet positions and thereby reflect different forces that act to influence lending. For example, by using the equity capital ratio we capture the impact of capitalization decisions on loan growth, while using the two riskbased capital ratios in our regression captures the effect on loan growth of both capital adequacy and portfolio composition because the riskbased measures also include offbalance sheet assets. The TCE ratio is a more conservative measure of bank capital, intended to represent the firstloss position in case of a bank's failure. We include this alternative measure of bank capital primarily because it was the focus of market participants in the quarters after October 2008 in evaluating the financial strength of banking institutions. (We would note that the specification implied by this equation 4 is broadly similar to the loan growth equation estimated in our VAR model in section 3.)
The estimation results for the effect of capitalratio shocks to capital ratios on BHC loan growth are reported in Table 4. As can be seen from the table, all variables enter with the expected sign and most are statistically significant. For example, there are positive and significant coefficients on the BHC capital ratios, which is consistent with the growth rate of bank loans being larger for banks with higher capital ratios. However, regardless of the capital ratio we use as our main explanatory variable, the effects of shocks to capital on BHC loan growth are small. Depending on the capital ratio employed, our results in Table 4 suggest that a 1 percentage point increase in the capital ratio leads to a longrun increase in annualized BHC loan growth that is only between 0.7 and 1.2 percentage points.
The largest estimated effect of capital shocks on BHC loan growth comes from the regression specification that uses the TCE ratio; as mentioned above, this measure received significant attention by market participants, especially during the weeks surrounding the bank stress tests in 2009. However, even this specification suggests that higher bank capitalization would have a very modest impact on BHC loan growth. In other words, in the event that BHCs managed to raise additional capital either by issuing more common stock or by converting preferred shares to common sharesas some proposals for regulatory reform have suggestedthe resulting increase in common equity would have only a minor impact on the growth rate of bank loans.
Our estimate of the longrun effect of a 1 percentage point increase in the equity capital ratio, which lies towards the lower end of the above range of estimates, can be compared with the effect obtained by Bernanke and Lown for their sample of New Jersey banks. Bernanke and Lown's reported estimates are notably larger than ours: For their full sample of 111 New Jersey banks, they found that a 1 percentage point increase in the equity capital ratio resulted in a 2 percentage point increase in loan growth, while the corresponding increase in loan growth for their sample of 90 small New Jersey banks was around 21/2 percentage points. Clearly, the size of the institutions considered is one reason why our estimates differ from Bernanke and Lown's; indeed, Bernanke and Lown's analysis does indicate a notably smaller degree of sensitivity of bank loans to equity capital ratios for larger banks. Note also, that because our analysis considers the largest 165 BHCs in the United States while Bernanke and Lown's analysis only considers banks that operate within the state of New Jersey, even the smallest institutions in our sample are larger than the "large" banks in Bernanke and Lown's sample.^{22} Of course, another reason why our estimate may be smaller than that of Bernanke and Lown's is that whereas our model of loan growth includes a number of controls (including bankspecific ones), Bernanke and Lown's model only includes the capital ratio, which could be capturing the effects of other variables.
While the effects of the equity capital ratio on bank loan growth that we obtain in our analysis are somewhat smaller than those estimated by Bernanke and Lown, they are notably smalleron the order of onetenth the sizethan the loangrowth impact that would be implied by the constant leverageratio assumption. That is, the constant leverageratio assumption would imply that the percentagepoint longrun increase in loan growth implied by a 1 percentage point increase in the equity capital ratio is equal to the capital ratioi.e., 8 percentage points for a 8 percent equity capital ratio and 12 percentage points for a 12 percent equity capital ratio.
As was the case for our analysis of the effects of capital shortfalls on loan growth, the model's estimation results suggest that demand shocks and exogenous changes in net chargeoffs play the most important role in determining total loan growth. The response of BHC loan growth to demand shocks (measured by changes in GDP growth), implies that a 1 percentage point reduction in GDP growth leads to about a 4 percentage point decline in annualized loan growth. Furthermore, the potential effects of continued writedowns through further increases in net chargeoffs imply a large and significant impact in all capitalratio specifications that we considered, as a 1 percentage point increase in the net chargeoff ratio reduces the annualized growth rate of total BHC loans by about 8 percentage points. As before, the coefficient on the securitiestoassets ratio is significant but the effect of increased holdings of securities is small and leads to only a 0.3 percentage point increase in BHC loan growth for every percentagepoint increase in the securitiestoassets ratio. Finally, the coefficient on lending standards is negative and significant but has also small impact on BHC loans. As before, this latter finding might be explained by the fact that the capital shock and changes in the chargeoff ratio already capture changes in banks' willingness to lend.
In the discussion of our estimation results in subsections 2.2 and 2.3 we interpreted our parameter as reflecting the magnitude of the increase in loan growth implied by a higher capital surplus or a higher capital ratio. Doing this, however, requires us to rule out other possible interpretations that could result in a relationship between a bank loan growth and bank capital.
One possible (and well recognized) reason why we might observe a positive correlation between a bank's loan growth and its capitalwhether lagged or notis that this correlation is driven by a third variable that affects both independently. It is likely that capital ratios will be positively correlated with the state of the economy (because of higher profits growth), which is in turn positively correlated with loan growth. Including macroeconomic variablesespecially, economic growthin our loan growth equation does limit this possibility, and the fact that the coefficients on lags of real GDP growth are so large in our loan growth equations suggests that we are in fact successfully capturing movements in loan growth that arise from fluctuations in economic activity.
A positive relationship between loan growth and lagged capital measures could also arise if banks preemptively increase their capital levels in anticipation of an increase in loan volumes (and hence balancesheet size). This response of bank capital levels to anticipated changes in loan volumes raises the possibility of an endogeneity issue in the Bernanke and Lown loangrowth equations. However, this endogeneity issue is not necessarily an overwhelming concern if we simply wish to determine whether the constant leverage assumption exaggerates the estimated response of loan growth to an increase in capital ratios, because this source of endogeneity would induce an upward bias in our estimates of . Nevertheless, to examine this further we considered an alternative specification that also includes the ratio of the BHC's cash dividends to its net income. To the extent that BHCs change their dividend policy so as to boost their capital in anticipation of future lending opportunities (for example, banks may cut dividends when they expect further increases in loan growth), the dividendtonetincome ratio would capture the endogenous variation in capital due to expected changes in loan volumes. Our estimates using this alternative specification of the BernankeLown equation (not reported) imply that, depending on the capital ratio employed, a 1 percentage point increase in the capital ratio leads to an increase in the annualized BHC loan growth rate of 0.5 to 1 percentage points. This is close to the 0.7 to 1.2 percentage point increase in BHC loan growth that we find when the benchmark BernankeLown specification is used.
To the extent that our implementation of the HancockWilcox approach correctly models the target capital level , this identification issue should be of limited concern. If the reason banks boost their capital is that they anticipate a future balance sheet expansion, this should also be reflected in an increase in their target capital, which implies no net change in the capital surplus or shortfall. Consequently, the possibility that banks increase their capital in response to an anticipated expansion in lending, does not generate a positive relationship between loan growth and capital surpluses or shortfalls, and the interpretation of is preserved. That said, the possibility remains that our model of banks' target capital is incorrect and thatperhaps because a forwardlooking component is absent from equation (2)we have not completely purged our parameter of this potential source of bias. Naturally, it would be possible to address this problem by introducing forwardlooking behavior to the target capital relation, although this would also require specifying simple forecasting equations for the explanatory variables, which could themselves be misspecified. Thus, we do not pursue this approach. Instead, we tolerate some possibility of an incorrectly modeled target capital inducing some modest amount of upward bias in the parameter , in part because the misspecification of the target capital ratio equation is always present (and always a vulnerability of this approach), and in part because it is not clear that omitting a forwardlooking component from the equation is necessarily the most important omission.
The preceding discussion highlights why we use both the HancockWilcox and BernankeLown approaches to analyze the effect of bank capital on bank lending. While we generally consider the HancockWilcox approach to be preferable inasmuch as it allows us to interpret the parameter as capturing the effect of an exogenous increase in capital on loan growth, it is vulnerable to the misspecification of its target capital equation, which can potentially reduce estimates of . In contrast, while the BernankeLown approach is not vulnerable to misspecifying a target capital variable it is susceptible to some endogeneity issues that could then limit the interpretation of the parameter . Again, however, these do not necessarily represent an overwhelming concern when our goal is to determine whether the constant leverage assumption exaggerates the estimated response of loan growth to an increase in capital ratios.
We conducted a number of robustness checks that ultimately leave our key conclusions unchanged.
First, we considered an alternative, atheoretic approach to calculating the capital surplus term used in the HancockWilcox regressions. Specifically, instead of estimating a model to calculate banks' capital targets, we used a onesided HodrickPrescott filter applied to each BHC's capital ratio. The capital surpluses and shortfalls implied by the filter's estimates are smaller and smoother than their modelbased counterparts, but are also less consistent with the conventional view of when the banking system was operating with capital surpluses or shortfalls. (Indeed, this is the main reason that we chose the modelbased target measure as our primary specification.) We found that the estimated effect of capital shortfalls on loan growth under the alternative measure was statistically significant and larger, implying roughly a 0.7 percentage point reduction in annualized loan growth when capital is 1 percent below its target level. Nevertheless, this is still small relative to the values that would be implied by the constant leverage assumption.
We also included four additional lags of our various capital measures in regression equations (3) and (4) to allow for a less parsimonious specification aimed at capturing richer dynamics and potentially more persistent effects of capital on loan growth. In both cases the coefficients on the capital terms were almost unchanged, so that we still obtained only a modest impact of capital on BHC loan growth.
In light of the plots in Figure 6, which suggested differences in the magnitude of capital deviations across BHCs grouped by size, we also conducted our regression analysis using subsamples of BHCs grouped into large (top 20), small (smallest 20), and mediumsized firms. We found little difference in the estimated impact of capital shortfalls or surpluses on loan growth: While the coefficient on our capital surplus measure was slightly bigger for large BHCs0.06 compared with 0.04 for smaller BHCsthis difference was not statistically significant. We also excluded the largest four BHCs from our sample to deal with potential outlier effects, but still found results that were qualitatively similar to those reported in tables 2 through 4.
We next performed rollingwindow panel regressions over the sample period to address the possibility that the effect of shocks to bank capital on loan growth has been declining.^{23} We used fixedsize rolling windows of six, seven, and eight years and quarterly data starting in 1992:Q1. In all cases, we found that the coefficients on our various capital terms were relatively stable and therefore continued to imply a small impact of capital on lending. For example, the coefficients (annualized) fluctuated between 0.2 and 0.4 for the capital surplus/shortfall (HancockWilcox) measures, and between 0.4 and 2.2 for the equitytoassets ratio (BernankeLown) regressions. For both sets of models, the largest coefficients obtained in the regressions whose estimation started between 1992 and 1995. We interpret this result as being consistent with the large rates of loan growth observed over the second half of the 1990s and the early 2000s, which was also the period during which large BHCs were holding significant capital surpluses.
Next, we considered variants of the regressions described in equations (3) and (4) over a shorter sample periodspecifically the most recent four years.^{24} In this case we obtained slightly larger coefficients on both the capital surplus term in equation (3) and the equitytoasset ratio in equation (4), although after rounding these coefficients still imply 0.4 and 1.4 percentage point reductions in annualized loan growth for a onepercent capital shortfall and a onepercent reduction in the capital ratio, respectively.
We also considered crosssectional regressions that relate 4quarter changes in BHC loan growth between 2007:Q3 and 2008:Q3 to the bankspecific variables in equations (3) and (4), lagged one year. In both cases, we found that the coefficients on our capital measures are slightly different but still imply a modest impact of capital on lending: The coefficient for the capital surplus measure implies a 0.2 percentage point reduction in annual loan growth for a onepercent capital shortfall. The coefficient for the equitytoasset ratio almost doubles but still only implies that a onepercent reduction in the capital ratio leads to a 1.4 percentage point contraction in the annual loan growth. Interestingly, in both crosssectional specifications the coefficient on the netchargeoffs ratio doubles too, implying a much stronger impact of bank risk perception on BHC loan growth. (In both cases, a onepercent rise in the netchargeoffs ratio is associated with a 15 percentage point contraction in annual loan growth.)
We also considered the possibility that the effect of capital on lending could vary with the state of the business cycle and that such effects could be diluted by estimating, as we do, the relationship between loan growth and capital over a long sample period. To test for this possibility in the fullsample model we interact the coefficient for the capital surplus in equation (3) and the coefficient for the equitytoasset ratio in equation (4) with the output gap (as measured by the U.S. Congressional Budget Office) to determine whether the size of the effect of capital on loan growth increases in slumps. Although we do obtain the correctly signed coefficient in both cases (bank capital seems to have a larger effect in "bad times"), the interaction term is statistically insignificant.
Finally, we examined the possibility that capital could have nonlinear effects on BHC loan growth by adding quadratic and/or cubic terms of the different capital measures to our loangrowth regressions. In every case we found that none of these terms was statistically significant. For the capital surplus/shortfall regressions we also considered differences in the impact of capital deviations on loan growth between BHCs operating with surpluses and those operating with shortfalls.^{25} Here we found no statistically significant difference between the separate surplus and shortfall coefficients.
While our combined methodology is able to address most forms of endogeneity and survivorship bias, it cannot deal with biases that might arise if bank and firm matches are not randomly formed. Addressing this bias requires bank lending and firm borrowing to be considered jointly, which in turn implies that individual loans must be modeled rather than aggregate lending by banks (or aggregate borrowing by firms). A number of recent papers pursue this approach using loanlevel data obtained from national credit registers; these include Jiménez, Ongena, and Peydró (2010), who use data collected by the Bank of Spain, and Albertazzi and Marchetti (2010), who use data collected by the Bank of Italy. These studies, which control for firmlevel characteristics, find larger effects of low bank capitalization and scarce liquidity on credit supply.
Matching bankloan information to borrower characteristics has a number of advantages in helping to identify causal effects since it allows the crosssectional heterogeneity of both banks and firms to be exploited. However, we believe that for considering the linkage between financial conditions and real activity this approach is only informative in practice if the matched sample is large and representative of the universe of lenders and borrowers. In the U.S., matchedsample analysis has only been applied to data on syndicated loans; specifically, bank loanlevel data from the Loan Pricing Corporation's (LPC) Dealscan database, which can be matched with BHC data from the FR Y9C form and data on firms from Compustat. In addition to representing a fairly narrow class of lending, these matched data have a number of problems such as important missing information and outliers, which may then further restrict (in some cases significantly) the number of available firmbankloan observations. That said, studies that use these firm and bank loanlevel data also seem to suggest relatively small effects of bank capital on lending. For example, Santos and Winton (2010) find that a 1 percent change in a bank's capitaltoassets ratio results in only a 3 basis point increase in loan rates, thus implying a relatively modest effect. This is consistent with our finding of a small effect of changes in bank capital on lending behavior.
As noted earlier, our panel estimation approach only uses BHCs that have existed over our entire sample period (or at least most of it). It could therefore potentially suffer from survivor bias, which would tend to lower the estimated effect of bank capital on loans.^{26} To address this concern, in this section we use aggregate data and a vector autoregression (VAR) model to study the effects of commercialbank capital ratios on bank loan growth. In our panel regressions, we specified BHC loangrowth equations that controlled for the effects of other supply and demand variables and so allowed us to interpret the coefficient on the equations' capital terms as the effect of BHC capital positions on loan growth. Here we take a different approach; specifically, we attempt to identify structural innovations in bank capital ratios and then examine the dynamic impact of these structural innovations on bank loan growth.
An important determinant of the influence that structural innovations to bankcapital ratios will have on bank loan growth is the effect that these innovations have on other variables in the modelsuch as real economic growth and bank lending standardsthat in turn feed back to lending. These indirect channels need to be borne in mind in considering how changes in bank capital affect loans; in particular, they must be accounted for in comparing the magnitudes of the effects found in the timeseries analysis with those obtained from the panel regressions. We therefore conduct additional exercises where we shut down these indirect effects.
The vector autoregression model that we use is a slightly modified version of the extended VAR model with bank capital considered by Lown and Morgan (2006). Our VAR consists of six variables: real GDP growth and GDP price inflation (excluding food and energy); the Federal funds rate; commercial bank and thrift loan growth; the aggregate capitaltoassets ratio of the commercial bank sector; and the net fraction of loan officers at commercial banks reporting a tightening of credit standards for C&I loans. The first three variables in the VAR are standard components of a monetarypolicy VAR, while the last three variablescommercial bank and thrift loan growth, the capitaltoassets ratio, and lending standardsare added to the model to allow us to study the interaction between banks and the macroeconomy. As in our panel regressions, we use the estimation period 1990:Q3 to 2008:Q3 for our VARs; that is, we end the VAR analysis just when the crisis intensified and just before TARP capital injections began to occur.
The residuals obtained from each of the estimated OLS regressions in the VAR system are combinations of underlying structural innovations. Importantly, the structural innovations have economic interpretations, such as exogenous shocks to monetary policy, technology, and the markup of prices over costs in the monetarypolicy portion of the model and exogenous shocks to bank lending standards (reflecting changes in cautiousness), bank capital ratios, and bank loan volumes (form changes in conditions in other credit markets) in the banking portion of the model. However, although structural innovations underlie the residuals from the estimated equation, they cannot, in the absence of any additional assumptions, be observed or inferred. A wide variety of assumptions can be used to identify structural innovations based on the estimated equation residuals; for our VAR we use a recursive identification scheme with the causal order given by the ordering of variables described above. We are primarily interested in separately identifying the three banking shocks in our model; for our purposes, it is sufficient to amalgamate the macroeconomic shocks into a single composite innovation.
Our identification procedure assumes that structural innovations to any of the model's banking variables do not contemporaneously affect the model's macro variables, but that innovations to the model's macroeconomic variables have a contemporaneous impact on the model's banking variables. One interpretation for this assumption as it relates to economic activity and inflation is that households, firms, and all levels of government can arrange their spending, production, and pricedetermination plans for the current period in such a way that surprise developments in the credit sector will not prevent these plans from taking place (at least in the aggregate). That said, such plans can be modified in response to surprise developments that are directly relevant for spending, production, and price determination (the macroeconomic shocks); moreover, these macro developments will contemporaneously affect variables in the banking sector. Likewise, monetary policymakers do not alter their interestrate setting decisions in response to withinquarter developments in the banking sector, although monetary policy surprises can have immediate effects on bankingsector variables.
Within the banking portion of the VAR our identification procedure assumes that structural innovations to loan volumes can affect bank capital ratios and lending standards immediately but that innovations to these latter variables do not have contemporaneous effects on loans. The first part of this assumption suggests that contemporaneous structural innovations to bank loan growth originate from the nonbanking part of the credit sector (as well as the real economy). Thus, a reasonable interpretation of these innovations (particularly in the context of the recent crisis) is that they reflect disruptions to segments of the financial system that can in turn impact bank loan volumes contemporaneously.^{27} The second part of the assumptionthat capital ratios and lending standards do not affect lending contemporaneouslyreflects the fact that it takes time to arrange a loan. This may at first appear to be at odds with our assumption that changes in the real economy can affect lending contemporaneously; however, for that case we have in mind households and firms drawing down or repaying prearranged lines of credit. Clearly, credit limits on loans that take the form of "on demand" credit lines (such as HELOCs, credit cards, or C&I commitment loans) can eventually be modified by banks in response to capitalratio or standards innovations, but these changes are difficult to implement quickly.
We would note that it is reasonable to assume that changes in lending standards have no contemporaneous impact on loan volumes inasmuch as there are many ways through which banks can alter lending standards other than contemporaneous changes in loan volumes; for example, banks can change the maturity of loans, the cost of credit lines, the spreads on loan rates, any covenants on the loan, and the loans' collateralization requirements. Our identifying assumption therefore implies that banks only make these changes in the period in which standards are altered.
Our identification method also assumes that innovations to lending standards do not affect bank capital ratios contemporaneously, although bank capital ratios do affect standards. The first part of this assumption makes sense given that we assume that innovations to standards have no contemporaneous effect on loan volumes, while the second part of the assumption reflects the fact that current lending standards are the most easily altered variable in the VAR.
Finally, note that we only separately identify structural innovations to loan volumes, bank capital, and lending standards, but do not identify the model's macroeconomic shocks separately. Thus, in our results we only report the combined effects of the model's macroeconomic shocks.
Figure 7 shows the responses of key model variablesspecifically, output growth, loan growth, the capitaltoassets ratio, and standardsto a onestandarddeviation structural innovation to the capitaltoassets ratio. This innovation implies an immediate 16 basis point increase in the capitaltoassets ratio, which then declines gradually back to its longrun level. Lending standards immediately loosen by about 2 percentage points in response to the increase in capital ratios and loan growth is boosted for about two years with a maximum response of about 1/2 percentage point two quarters after the impact of the shock. The (statistically insignificant) response of GDP growth is rapid and shortlived (about one year), peaking at 0.2 percentage point in the period immediately following the shock. One possible reason for the smaller and shorterlived response of output growth relative to loan growth is that some of the growth in loans may just represent substitution across institutions. Indeed, additional analysisshown in Figure 8that uses the sum of bank and thrift loans and ABS issuers' holdings of mortgage and consumer credit in the VAR in place of bank and thrift loans seems to support this view. Specifically, a shock to the capitaltoassets in this model has no effect on the broader aggregate of loan volumes while having similar effects on the other variables in the model. The fact that changes in capital ratios do appear to induce substitution between on and offbalancesheet credit is an interesting one; we do not pursue it here, however, since our principal focus in this paper is on bank capital and lending.
Our results imply that a one percentage point increase in the capitaltoassets ratio results in a 23/4 percentage point increase in loan growth that peaks about a year after the initial shock. This is almost four times as large as the corresponding response from the panel regressions. The relatively larger response implied by the VAR model is perhaps not surprising given that the VAR approach allows for the endogenous response of several variablesmost notably standards and real GDP growththat in turn have additional effects on loan growth. Given this, it is instructive to shut down these additional effects in the VAR so as to permit a more direct comparison with the results obtained using institutionlevel BHC data.^{28}
Figure 9 reports the responses to a one standard deviation capitaltoassets ratio shock that obtain when various endogenous responses of other model variables are eliminated. In particular, the red line in Figure 9 shuts down the response of standards to the capitaltoassets ratio shock; the blue line shuts down the response of real GDP growth to the capitaltoassets ratio shocks; and the green line shuts down both the standards and real GDP growth responses. These results suggest that in the absence of endogenous responses from other variables, bank loan growth should increase approximately 1.2 percentage points in response to a one percentage point capitaltoassets ratio shock. This increase is about twice as large as the increase in loan growth implied by the panel regressions, but is still considerably smaller than what would be predicted under the constantleverage assumption that is implied by the scatterplot approach.
We now use the models developed in sections 2 and 3 to estimate the likely effects of TARPrelated capital injections on bank loan growth.
The panel regression results from section 2 can be used to estimate the effect of the original TARP disbursement ($182 billion for our sample of large banks) on BHC loan volumes. The CPP capital infusions during 2008:Q4 raised the level of equity capital, yielding an increase in the capital surplus term of about 14 percentage points on average. Taken together with the estimation results of section 2.2, which indicate that a 1 percentage point increase in the capital surplus implies a 1/4 percentage point increase in annualized loan growth, this implies that the CPP injections increased loan growth by 31/2 percentage points at an annual rate in our sample of banks. In ratio terms the CPP injections raised the equitytoassets ratio by about 1.4 percentage points and the riskbased capital ratio by about 1.7 percentage points on average. Given the estimation results of section 2.3 this implies that the CPP injections boosted BHC loan growth by 1.0 to 1.3 percentage points.
In dollar terms, the results from the surplus/shortfall regressions imply that the $182 billion increase in capital that large BHCs in our sample received would have resulted in a $273 billion increase in these BHCs' loans over the following year. The results from the capitalratio regressions imply an increase in loan volumes for large BHCs of between $76 billion and $100 billion over the following year (depending on the measure of capital considered). These volumes are significantly less than the boost in lending capacity that would be implied by the U.S. Treasury's assumptions. Specifically, since the Treasury assumed that a dollar's increase in capital would generate between eight to twelve dollars of lending, a $182 billion capital injection should have resulted in a $11/2 to $21/4 trillion increase in lending.
We can also use the VAR model's impulse response functions to estimate the magnitude of the impact of CPP injections on commercial bank loan volumes. As noted above, capital injections under the CPP raised the equitytoassets ratio by 1.4 percentage points. The impulse response functions reported in Figure 7 imply that the CPP capital injections would boost loan growth by 3.7 percentage points over the first year. Cumulating the effect on loan growth implies a 5 percent increase in the level of loans or a $300 billion increase in commercial bank lending.
We can also use these models to ascertain the effect of recent changes in capital ratios on loan growth. First, we use results from the panel regressions to understand the causes of the recent decline in bank loan growth and to gauge whether the large decline in lending is mainly explained by supply or demand factors. We then use our VAR estimates to decompose changes in commercial bank lending across the various banking and nonfinancial shocks that we estimate.
We conduct outofsample forecasts of BHC loan growth using both our capital surplus/shortfall and capitalratio panel regressions and decompose the quarterly growth rate of BHC loans into supply and demand factors such as capital, lending standards, risk, and GDP growth. Figure 10 reports the results from the capitalratio panel regressions.
As can be seen in Figure 10, our capitalratio panel regression model performs relatively well in explaining the recent drop in the quarterly growth rate of BHC loans. The decomposition of the predicted growth rate confirms the importance of loan demand shocks and increased risk in accounting for most of the decline in BHC loan growth. Out of the 2.9 percentage point decline in the quarterly loan growth rate from 2008:Q4 to 2009:Q3of which the model explains 2.2 percentage points1.3 percentage points is accounted for by changes in GDP growth (the dark blue shaded area) and 1.1 percentage points is explained by changes in net chargeoff rates (the green shaded area), which captures the deterioration in loan quality. Tighter lending standards (the purple area) significantly restrained BHC loan growth during the first half of 2009 (by about 1.3 percentage points), though this effect lessened in 2009:Q3. On net, then, lending standards account for only 0.2 percentage point of the 2008:Q4 to 2009:Q3 reduction in BHC loan growth.
Figure 10 also confirms that changes in bank capital (the light blue area) had only a small impact on BHC loan growth. In particular, the changes in BHC capital ratios associated with both TARPrelated capital injections in 2008:Q4 and subsequent efforts to raise capital privately during the first half of 2009 made only a small positive contribution to bank loan growth (of only 0.1 percentage point) and were more than offset by adverse factors such as reduced loan demand, increased risk, and somewhat tighter lending standards.
The results from the capital surplus/shortfall model (not shown) indicate that this model does not perform as well as the capitalratio model in terms of predicting the 2008:Q4 to 2009:Q3 decline in BHC loan growth. In particular, the surplus/shortfall model explains only 1.3 percentage points of the 2.9 percentage point decline in loan growth over this period. That said, the conclusions obtained from the capitalratio model with respect to the relative importance of real GDP growth, net chargeoff rates, and capital in explaining BHC loan growth continue to hold.^{29}
The VAR model's identification procedure allows us to decompose movements in each variable into the portion attributable to the various shocks. This is done in Figure 11. In each panel of the chart we show the actual path of loan growth over the past three yearsthe solid black lineas well as the model's unconditional forecastthe dotted line. We also show the path of loan growth that would be implied by the unconditional forecast and a specific set of structural innovations. We find that structural innovations to capital ratios explain very little of the belowpar pace of loan growth over the past year (see the lowerleft panel). Prior to the rebound in economic growth following the sharp contractions in activity in 2008:Q4 and 2009:Q1, macro innovations appear to have accounted for much of the decline in loan growth (the lowerright panel), with standards innovations accounting for a portion as well (the upperleft panel). Finally, over the last two quarters of the simulation period, ownvariable innovations to loan growth account for the bulk of the series' decline (see the upperright panel).
To some extent the large recent contribution of the ownvariable loan growth innovations reflects the outofsample nature of our simulation exercise. The same exercise performed with a model estimated through to 2009:Q3see Figure 12attributes much less of the recent decline in loan growth to ownvariable shocks and much more to standards and macro shocks. Note, however, that capital ratio shocks continue to explain only a small portion of the decline in loan growth.
This paper has applied a number of different methods to examine how bank capital influences the extension of bank credit. An analysis based on panel data finds modest effects of BHC capitaltoasset ratios on BHC lending; using macroeconomic time series and aggregate commercial bank balancesheet data, we find largerbut still modesteffects of capital ratio shocks on loan growth.
These results stand in marked contrast to the constantleverage view, which has been quite influential of late in shaping forecasters' and policymakers' views regarding the size of the effect that bank capital changes have on loan growth. In particular, this view predicts effects of bank capitalratio changes on loan growth (that are six to ten times) larger than what we found in either our panel or timeseries estimation results. We attribute the difference to the fact that the simple correlation between asset growth and leverage growth for commercial banks that underpins the constantleverage view is not very robust across time, and especially fails to hold for the postBasel sample period over which our analysis is conducted.
While our empirical results suggest relatively modest effects of both capital shortfalls and capital ratios on loan growth, we find more important roles for other factors such as economic activity and increased perception of riskiness by banks. One interpretation of this result is that banks and BHCs give relatively little consideration to their capital position when deciding whether to lend and instead allow other factors such as loan demand and risk to guide their decisionmaking. If this is the case, it would provide one explanation for the slowdown in loan growth that took place over the first three quarters of 2009 despite the sizable capital injections that occurred in 2008:Q4 under the CPP. However, another interpretation of our results is that existing measures of bank capital do not capture the "true" capital position of banks that is relevant for determining bank behavior. If true, this interpretation calls into question whether existing riskbased regulatory capital measures are valid, and would suggest that such measures need to be improved.
Variable  No. Observations  Median  Mean  Std.Dev. 
Total Assets ($ million)  11107  3595.30  27302.91  145408.60 
Total Loan Quarterly growth  11107  2.15%  3.00%  5.03% 
C&I Loan Quarterly growth  11107  2.09%  2.91%  8.82% 
Equity/Assets  11107  8.17%  8.39%  2.16% 
Tier 1 Capital ratio  7320  10.72%  11.38%  3.29% 
Total Capital ratio  7320  12.54%  13.24%  2.20% 
TCE ratio  9139  6.83%  7.02%  2.20% 
Return on Assets  11107  0.1396  0.1296  0.8287 
Securities/Assets  9460  0.2257  0.2424  0.1131 
Net Chargeoffs/Assets  11099  0.1687  0.2963  0.4288 
Model 1
Estimate 
Model 1
tstat 
Model 2
Estimate 
Model 2
tstat 

Lagged capital ratio  0.9108***  (87.60)  0.9189***  (87.91) 
Size  0.0931***  (4.12)  0.0778***  (5.09) 
ROA  0.0356  (1.48)  0.0373*  (1.76) 
Aggregate Volatility  0.0053***  (4.67)  0.0035***  (4.09) 
C&I loan share  0.0097***  (2.95)  
Real Estate loan share  0.0065***  (3.20)  
Consumer loan share  0.0001  (0.01)  
Securities share  0.0059***  (2.92)  
Regulatory Pressure  0.0260  (0.58)  0.0159  (0.43) 
Sector Chargeoff/Loan  0.1074**  (2.45)  0.0781**  (2.58) 
Chargeoffs/Asset  0.0229  (0.60)  0.0094  (0.75) 
Intercept  0.1584  (0.42)  0.5334**  (2.56) 
0.852  0.870  
8706  10512 
Total Loans
Estimate 
Total Loans
stat 
C&I Loans
Estimate 
C&I Loans
stat 

Loan Growth Lags (sum)  0.1598***  (15.49)  0.0731  (1.34) 
Surplus capital  0.0523***  (75.98)  0.0602***  (24.78) 
Securities/Asset  0.0668***  (20.25)  0.0559**  (4.03) 
Net Chargeoffs/Asset  1.6177***  (25.02)  1.6410***  (8.59) 
Lending Standards (sum)  0.0181***  (8.24)  0.0274***  (6.47) 
GDP Growth Lags (sum)  0.8562**  (5.52)  2.1685***  (7.65) 
Fed Funds Lags (sum)  0.4534  (1.83)  0.0059  (0.00) 
Inflation Lags (sum)  0.1918  (0.07)  1.7849  (2.19) 
Intercept  0.5080  (0.42)  1.5000  (0.99) 
0.215  0.098  
7793  7760 
Eq.toAsset Ratio: Estimate  Eq.toAsset Ratio: t/Fstat  Riskbased Capital Ratio: Estimate  Riskbased Capital Ratio: t/Fstat  Riskbased Tier 1 Cap. Ratio: Estimate  Riskbased Tier 1 Cap. Ratio: t/Fstat  TCE Ratio: Estimate  TCE Ratio: t/Fstat  
Loan Gr. Lags (sum)  0.1648***  (33.04)  0.1583***  (24.22)  0.1571***  (24.07)  0.1743***  (37.66) 
Capital ratio  0.1450***  (3.23)  0.1572***  (4.69)  0.1674***  (4.98)  0.2521***  (5.75) 
Securities/Asset  0.0556***  (5.64)  0.0431***  (2.76)  0.0421***  (2.66)  0.0498***  (4.84) 
Net Chargeoffs/Asset  1.6835***  (6.75)  1.8524***  (6.92)  1.8346***  (6.86)  1.6832***  (6.65) 
Lending Stds (sum)  0.0135**  (10.46)  0.0130***  (7.09)  0.0130***  (7.09)  0.0131***  (9.89) 
GDP Gr. Lags (sum)  0.8628***  (10.41)  1.0884***  (9.61)  1.0684***  ( 9.25)  0.8508***  (10.67) 
Fed Funds Lags (sum)  0.1164  (0.28)  0.5391*  (2.88)  0.5696*  (3.17)  0.1792  (0.64) 
Inflation Lags (sum)  1.1988***  (6.65)  0.4573  (0.44)  0.3482  (0.26)  0.7072  (2.31) 
Intercept  0.1001  (1.90)  1.2893  (1.64)  1.1345  (1.49)  0.7761  (1.28) 
0.186  0.196  0.197  0.190  
8549  6658  6658  8549 