Anne-Laure Delatte

Pranav Garg

Jean Imbs

The Collateral Channel of Monetary Policy

Keywords: JEL Codes: E44, E58, G21, G32 Collateral constraints, unconventional monetary policy, credit supply, real effects

We present evidence that a loosening in collateral requirements instigated by the European Central Bank in 2012 did result in an expansion of credit, with real effects on firms' investment, productivity, and dividends. This is a novel result, obtained thanks to our identification methodology. We partition banks into categories according to the pre-reform distributions of their overall loan portfolios, so that the comparison is performed between banks with different exposures to the change in collateral constraint, but otherwise similar loan portfolios. The policy has economy-wide real effects that are economically significant: Relaxing collateral constraints by one standard deviation results in an increase of 0.3σ in investment and productivity, and of 0.26σ in dividends.

Introduction

A traditional task of central banks is to ensure the provision of liquidity in the banking system. They often do so by granting secured loans, i.e. loans that are conditioned by collateral [START_REF] Bindseil | The Eurosystem collateral framework explained[END_REF]. The collateral that banks post is subject to eligibility criteria, relating to issuers, asset classes, and credit risk. During episodes of financial crisis, a scarcity of high quality collateral imposes binding constraints on collateralized borrowing for banks. Consequently, a loosening of the collateral eligibility criteria can become an important tool for influencing refinancing conditions, a key transmission channel for monetary policy.

Since its very purpose is to ensure the provision of liquidity in the financial system, the collateral framework has become a prominent tool of monetary policy in most major central banks, especially during times when policy rates are close to the zero lower bound.1 Liquidity has been provided through non-standard open market operations, whereby the central bank increases the overall level of liquidity by exchanging central bank reserves against an expanding range of eligible private paper. Such pledgeable private paper includes loans originated by banks in the form of residential mortgages and to firms with sufficiently high credit ratings. The emergence of this new collateral channel has had permanent consequences on the conduct of monetary policy even well away from the zero lower bound.

In theory, liquidity injections by the central bank can have consequences on the real economy. For example, [START_REF] Kiyotaki | Liquidity, business cycles, and monetary policy[END_REF] introduce a liquidity constraint, consisting in heterogeneous "resalability" across assets in addition to a standard borrowing constraint. They show that if both constraints are high enough, the provision of central bank reserves increases investment and boosts aggregate activity. 2Empirically there is limited evidence that relaxing collateral constraints increases the supply of credit and affects the activity of some firms. The evidence is limited first by the existence of relevant quasi experiments, since changes in collateral requirements typically do not happen by chance. And second, it is limited by the conventional identification approach, which confines the detection of putative real effects to those firms that are affected by the change in collateral eligibility, i.e., those that receive the treatment. Little is known about real effects across the whole economy, via an expansion of credit at the bank level. Does broadening collateral have a macroeconomic impact via an increase in aggregate credit?

This paper contributes to the question by studying the effect of a now well-known overnight re-classification of loans into claims eligible as collateral with the Banque de France. In February 2012, the Banque de France announced that loans to firms with credit rating of 4 would become eligible as collateral, whereas previous eligibility stopped at 4+ (a rating of 4 on the Banque de France's scale is approximately equivalent to a Fitch rating of BB-, with 4+ being a loan of a lower credit risk). The cut-off implies variation in exposure across banks depending on the share of these newly eligible loans that were held on their loan portfolios prior to the announcement. This variation is largely exogenous to developments in the French economy: The European Central Bank announced at the end of 2011 that national central banks were allowed to implement the change at their leisure, which the Banque de France elicited to do in February 2012. The ECB announcement came as a surprise, as it was issued by the then President Mario Draghi barely one month after he took office. There were no observable changes in the weights of newly eligible loans in the interim period between the ECB's announcement and the Banque de France's implementation.

Like [START_REF] Mésonnier | The Interest of Being Eligible[END_REF] and [START_REF] Van Bekkum | Does a larger menu increase appetite? Collateral eligibility and credit supply[END_REF], we explore whether banks with a larger share of newly eligible loans react differently than others, a conventional difference-in-differences approach. The quasi-natural experiment does however present a serious complication: The "treated" banks choose to hold a large fraction of loans that were issued to risky firms (rated 4), which must be the outcome of a meaningful and systematic loan portfolio allocation strategy. In that sense, treated banks are likely to be fundamentally different from untreated ones, in ways that are not necessarily observable. Therefore, the conventional difference-in-differences approach applied to the fraction of eligible loans held by the universe of banks is inherently flawed, in the sense that these are not similar subjects. Identification rests on comparing banks with very diverse portfolios in all aspects beyond just the newly eligible loans. It is not an issue if these banks differ in levels, a difference taken into account by bank fixed effects, as long as they follow parallel trends. However, as one would expect, we rule out the presence of parallel trends when just bank fixed effects are employed. A significant estimate is at best inconclusive, which may explain why the literature so far has focused on the policy impact on loans from treated banks to newly eligible firms, rather than the loans from treated banks across the board.

An intuitive resolution of this problem is to focus the analysis on a homogeneous subset of treated banks (or firms), but doing so eschews the generality of the results, without guarantee that the problem is addressed decisively. Our first contribution is to adapt a methodology recently proposed by [START_REF] Carbonnier | Who benefits from tax incentives? The heterogeneous wage incidence of a tax credit[END_REF] in a different setting. Our idea is to partition all banks into categories that are determined by the overall composition of their loans portfolios: we compare banks that have a similar distribution of loans, except immediately around the newly eligible loans. We explain the construction of these categories in detail later. The estimation is then performed within these categories, i.e., holding constant features of their portfolios while using the universe of bank lending data made available to us. The categorization of the data can then be validated by verifying whether the (within-category) estimates are unaffected by the inclusion of bank-specific fixed effects: If such is the case, the categorization absorbs all the relevant time-invariant heterogeneity across banks and the treatment effect is well identified.3

Our second contribution is a consequence of the first one. Our estimation is performed on the universe of banks so we can identify the response of credit at the bank level. We then construct artificial firms, whose characteristics (investment, employment, etc) are given by a loan-weighted average of the firms borrowing from each bank. This generates an association between each bank and the average characteristics of the firms borrowing from it, which we then exploit to identify the real effects of the change in collateral requirements. The estimation is performed in a panel of banks, which makes it possible to identify any real effects within the bank categorization designed in the first step. In other words, we evaluate whether the average firm borrowing from a treated bank displays significantly different real responses than the average firm borrowing from an untreated bank. The estimation is performed within homogeneous categories of banks, which ensures identification of the treatment effect.

We document large and significant real effects of the change in collateral requirements: Treated firms have higher productivity and they increase investment as well as dividend distribution. There is no significant response of employment on impact but it is shown to decrease temporarily with a lag, so that the benefits of the new collateral policy seem to accrue to capital holders. The effects of a one standard deviation relaxation in collateral requirements are economically large: Between a quarter and a third of the standard deviation in the corresponding measure of real activity, depending on the specification. Interestingly, these effects are not confined to treated firms (i.e., those with the credit ratings that became eligible): They are statistically indistinguishable from the significant changes we identify among untreated firms. This documents the potentially powerful aggregate effects of collateral policies via an economy-wide expansion of credit.

Related literature Several papers have exploited the quasi-randomness of the 2011/2012 change in collateral eligibility instigated by the ECB. [START_REF] Van Bekkum | Does a larger menu increase appetite? Collateral eligibility and credit supply[END_REF] examine its impact in the Dutch context. Their analysis is specific to the market of residential mortgage-backed securities, a segment of which became eligible as collateral. They find that the banks that had issued the most newly eligible RMBS securities continued to do so with even more issuances, which they eventually securitized: The change in collateral requirement affected bank lending positively in the specific segment that became eligible (RMBS).

There are many papers that, like us, evaluate the impact of the new collateral framework in the French context. [START_REF] Mésonnier | The Interest of Being Eligible[END_REF] run treatment effect estimations within banks to identify the effect of the policy on the terms offered to newly eligible borrowing firms vs. (closely-comparable but) not newly eligible firms. They find that becoming eligible to the ECB collateral framework translates into a reduction in loan rates by 7 basis points. [START_REF] Cahn | Unconventional monetary policy and bank lending relationships[END_REF] discuss the heterogeneous effect on credit for singlebank vs. multiple-banks firms. [START_REF] Andrade | Can the provision of long-term liquidity help to avoid a credit crunch? Evidence from the Eurosystem's LTRO[END_REF] exploit firms that borrow from multiple banks to isolate the effect of the policy change on credit supply. They find that the relaxation of collateral requirements resulted in a large increase in lending that was focused on a few large firms.

Garcia-Posada and Marchetti (2016) exploit the policy change in Spain to evaluate the response of credit; They document heterogeneous responses, relatively small on average, and largest for illiquid banks. [START_REF] Carpinelli | The design and transmission of central bank liquidity provisions[END_REF] study the effect of the policy in Italy, where they show a significant positive response of the supply of credit and increased purchases of government bonds by liquid banks. [START_REF] Alves | Surviving the perfect storm: The role of the lender of last resort[END_REF] exploit an earlier move by the ECB allowing Portuguese banks to refinance themselves at the Banco de Portugal. They show once again an effect on the sustaining of credit supply in the context of the 2008 crisis in Portugal.

We differ from these papers in two ways: First, our estimations are run between banks (and within selected categories of banks). We use this approach to document the response of credit supply in the economy at large. Second, because of our identification approach we are able to identify precisely the real effects that the expansion in credit had on all firms, not only treated ones (i.e., not only firms whose loans became eligible for collateral). To our knowledge such consequences on the real economy have not been documented thus far, even though they appear to be highly relevant in theory. For example, Del [START_REF] Negro | The great escape? A quantitative evaluation of the Fed's liquidity facilities[END_REF] simulate a DSGE model with liquidity frictions to show that the liquidity facilities implemented by the Federal Reserve during the 2008-2009 crisis had large real effects. One would expect similar well-identified episodes should have real consequences in the data, too.

Pranav: I AM TAGGING SOME OTHER KEY PAPERS HERE: Lastly, our paper contributes to a strand of literature on credit supply shocks: driven by monetary policy [START_REF] Cetorelli | Banking Globalization and Monetary Transmission[END_REF], Gabriel [START_REF] Jimenez | Hazardous Times for Monetary Policy: What Do Twenty-Three Million Bank Loans Say About the Effects of Monetary Policy on Credit Risk-Taking?[END_REF]), government intervention [START_REF] Khwaja | Do Lenders Favor Politically Connected Firms? Rent Provision in an Emerging Financial Market*[END_REF], [START_REF] Paravisini | Local Bank Financial Constraints and Firm Access to External Finance[END_REF]), banking regulation [START_REF] Favara | Credit Supply and the Price of Housing[END_REF]), by regional variation in market structure [START_REF] Drechsler | The Deposits Channel of Monetary Policy[END_REF], [START_REF] Mian | Credit Supply and Housing Speculation[END_REF]). Further, we contribute to literature on real effects associated with credit shocks [START_REF] Amiti | How Much Do Idiosyncratic Bank Shocks Affect Investment? Evidence from Matched Bank-Firm Loan Data[END_REF], [START_REF] Acharya | Whatever it takes: The real effects of unconventional monetary policy[END_REF], [START_REF] Jiménez | The real effects of the bank lending channel[END_REF]). NEED TO DISCUSS: [START_REF] Ashcraft | Two Monetary Tools: Interest Rates and Haircuts[END_REF] makes a good point of how the shadow cost of the entire distribution of securities shifts in response to changes in the collateral framework. Their empirical evidence is restricted to the same thing as several other papers: effect on the security/borrower itself in response to a haircut decline. This is indeed starkly different from identifying an effect on lenders who issue these securities, which requires accounting for their entire pre-reform portfolio distribution.

Data and Methodology

A key methodological contribution of our paper is the discretization of banks into homogeneous categories, adapted from [START_REF] Carbonnier | Who benefits from tax incentives? The heterogeneous wage incidence of a tax credit[END_REF]. The purpose of the partition is to construct "buckets" that contain banks with some degree of homogeneity in their overall portfolio composition, while preserving dispersion in the exposure to the treatment, i.e., to 4-rated loans. We perform this discretization over a range of loan ratings that surrounds the threshold eligibility. We discretize banks according to ratings of 4+, 4, 5+, and 5, out of a scale that ranges from 3++ (safest) to 9 and P (bankruptcy). 4The categorization is two-dimensional and based on the proportion of banks loans that are below a certain category. The first dimension categorizes banks according to the percentage of loans below (and excluding) the 4+ rating (i.e., loans rated 3++, 3+, 3), the other dimension categorizes banks according to the percentage of loans below (and including) the 5 rating. Crossing these two criteria gives rise to 6 × 6 "buckets" corresponding to different percentage ranges for the holdings of loans between 4+ and 5 ratings. Figure 1 illustrates the discretization when there are six categories along each dimension. Each cell in the figure contains the percentage ranges of holdings of loans rated in the ratings range [4+, 5]. For example the upper left bucket in Figure 1 is populated by banks whose portfolios contain between 80 and 100 percent of loans with ratings between ratings range [4+, 5]. Banks that lend to risky firms are located in the lower left area of the figure, where holdings of loans below (and excluding) 4+ and below (and including) 5 are low (and therefore loans above 5 are prevalent). Similarly banks with conservative portfolios will be located in the upper right area of the figure. The two-dimensional discretization of banks sharpens identification: Our estimations are all run within bucket, i.e., within a group of banks whose loan portfolios are relatively homogeneous. This ensures the treatment effect is identified ceteris paribus, in comparison to banks with similar lending strategies. The resulting variation is more likely to be exogenous, as it is influenced by the arbitrary policy cutoff rather than by the bank's underlying lending function.

6 0 - 8 0 % 4 0 - 6 0 % 2 0 - 4 0 % 0 - 2 0 % 0 % 8 0 - 1 0 0 % 6 0 - 1 0 0 % 4 0 - 8 0 % 2 0 - 6 0 % 0 - 4 0 % 0 - 2 0 % 4 0 - 8 0 % 2 0 - 6 0 % 0 - 4 0 % 0 - 2 0 % 2 0 - 6 0 % 0 - 4 0 % 0 - 2 0 % 0 - 4 0 % 0 - 2 0 % 0 - 2 0 % 0% 0 -20% 20 -40% 40 -60% 60 -80% 80 -100% 0% 80 -100% 60 -80% 40 -60% 20 -40% 0 -20% < 4+ ≤ 5
It is still possible of course that observable (and non-observable) bank heterogeneity survives within bucket, such as by bank size or capital or deposits. That can be addressed with further controls that effectively split a bucket further into "cells". These are defined as the interaction of bucket categories with size categories. Within cell identification meaningfully captures heterogeneity across banks' portfolio distributions and across bank size. Ultimately, the question that needs answering in the data is whether heterogeneity between banks within a cell can still be detected empirically. A natural check is whether the inclusion of bank-specific intercepts changes the results of an estimation performed within cell. We find that our within-cell specification results are robust to the additional inclusion of bank-specific fixed effects. In contrast, relying on only bank fixed effects and omitting cell-specific fixed effects fails to satisfy parallel trends assumption.

Our approach presents an additional desirable feature when it comes to identifying shocks to the supply of credit with consequences on real activity. In terms of real effects, the literature has focused on conventional treatment effect estimations, where the credit conditions offered to treated firms (i.e., those rated 4) are compared with the conditions offered to other, untreated, firms. The approach potentially conflates supply and demand effects, since treated firms can simply respond to the policy change by demanding more credit, which complicates identification. The discretization performed here achieves identification within categories of banks and real effects are established across all firms, not only those whose loans have a 4-rating. It is difficult to think of reasons why firms that do not have a 4-rating should increase their credit demand in the face of the policy change, which does not concern them. This facilitates the identification of a credit supply shock and of its effects on the real economy.

Data

We merge the French national credit register (CCR), the credit rating database and the FIBEN financial statement database, all from the Banque de France (BdF).

The credit register contains data on corporate borrowers with total exposure (debt and guarantees) above 25,000 EUR toward financial intermediaries operating in France.

For each bank-firm pair, we recover the end-of-month total outstanding credit granted (whether drawn or undrawn) for each month from January 2011 till December 2014. The register reports a monthly average of 2.5 million bank-firm observations. The credit database provides information on all existing lines of credit of any type. The database also contains information on the geographical location of borrowers, the type of sector they belong to and the nature of ownership (private or public entities). Each bank and firm in the data is uniquely identified throughout the data based on anonymous identifiers (CIB for banks and SIREN for firms). These identifiers allow us to match firms in the credit registry one-to-one to firm balance sheet data reported in the FIBEN individual company database.

Credit rating information comes from the FIBEN internal credit rating database at Banque de France. The national central bank attributes credit ratings to around 270,000 companies on an annual basis. Information on a firms' riskiness is updated annually using firm accounting information, provided it is made available5 . Banque de France ratings indicate a company's ability to meet its financial commitments over a one to three-year horizon. Banque de France analysts' criteria for ratings rests on firms' earning power (net income, gross operating surplus, etc.), financial autonomy (self financing capacity, debt stability, etc.), liquidity (going concern) and solvency.

To compute the exposure to the policy at the bank level -the share of 4-rated loans in their pre-reform loan portfolio -we consider all credit lines (short-medium-and-long term loans and off-balance sheet credit) extended to every firm. Since we are interested in the share of targeted loans over the entire lending portfolio of banks, we include lending to any firm by a bank, regardless of whether the firm is listed on the FIBEN database.

Then, when we constitute the sample of bank-firms observations for our analysis, we exclude firms whose financial information has not been updated by Banque de France over the past 23 months or more. These firms receive a rating of "X0" on the FIBEN database and constitute a major fraction of aggregate lending. 6 We further exclude interbank lending. 7 Lastly, we exclude loans to investment trusts and funds that often benefit from preferential tax treatment. Similar data cleaning has been done in earlier works relying on the French credit register. Dropping inactive firms and lending to financial and insurance sector firms reduces our monthly bank-firm observations to a monthly average of around 460,000 observations out of 2.5 million observations. Lastly, we merge the data on bank lending with data on interest rates characteristics for a randomized representative sample of loans using the "New Contracts" dataset administered by the Banque de France.

The accounting data on firm balance sheets comes from FIBEN, a database compiled from tax returns by Banque de France. The database includes all firms whose turnover in a fiscal year is at least equal to 750,000 EUR. The cut-off of 750,000 EUR is inclusive of all but the smallest firms. 8 We drop firms with zero total assets. All firm characteristics are winsorized at the 0.5 and 99.5 percentile.

In addition to the full sample covering the universe of French banks, we consider two sub-samples centered on the loans ratings that define the discretization. The first one is focused on banks that have at least 20 percent of their portfolio in loans rated between 4+ and 5; The second one raises the fraction to 60 percent. Both sub-samples narrow the analysis onto banks that are substantially affected by the policy change, with the consequence that the discretization is focused on increasingly homogeneous groups of banks. This constitutes an interesting robustness check in the sense that it establishes the extent to which full sample results are due to residual unobserved heterogeneity in banks. There is no significant difference between median and average holdings in any of the three samples, suggesting relatively low skewness. The majority of banks hold less than 50 percent of 4-rated loans across all three panels. We perform a discretization of banks' portfolios according to the six categories in Figure 3. The categories are chosen to minimize bank heterogeneity within bucket while preserving enough observations for identification. Figure 3a reports the number of banks per bucket in the full sample on the basis of their average loan portfolios in the twelve months prior to the policy change. The figure suggests that a majority of banks in our sample are rather conservative in their lending strategies: They tend to hold relatively large proportions of loans with ratings between 4+ and 5 and are located on the upper region of the figure. Figures 3b and3c illustrate the assignment of banks to buckets in the two reduced samples we consider. The first sub-sample is focused on banks that hold a minimum of 20 percent of their portfolios in loans rated between 4+ and 5, which means the outer diagonal of Figure 3a is dropped and some banks are omitted from the new diagonal. The resulting matrix is not a complete upper triangular one because some bins are empty.

The second sub-sample is focused on banks that hold a minimum of 60 percent of their portfolio in loans rated between 4+ and 5, which means most of the buckets in the full sample have to be purged from banks with not enough such loans.

Identification

We document the average cumulative distribution of loan shares within bucket. In each bucket we compute the cumulative distribution of portfolio shares for all banks. And in each bucket we identify the bank with median holding of 4-rated loans. We then compute the cumulative distributions for the sub-samples constituted by banks whose holdings of 4-rated loans are above and below that median. Figure 4 plots the average of these three cumulative distribution functions across all buckets. Several aspects stand out.

Firstly, the discretization is performed so that the portfolio shares of loans weakly below 4+ and above 5 are very similar within bucket. This happens because by definition all banks in a given bucket hold the same proportion of loans below 4+ and below 5. It follows that the three CDFs in Figure 4 must be very close together from rating 3++ up to (and including) rating 4+, and also from (and including) rating 5 up to bankruptcy P. Secondly and therefore, within a bucket, most of the dispersion between banks must by definition happen for ratings 4 and 5+. These two facts are salient in the three samples considered in Figure 4: By construction, they are most evident in the sub-samples presented in panels (b) and (c), since they are focused on banks with large holdings of loans between 4+ and 5. Thirdly, in these two panels, the dispersion is largest for holdings of loans rated 4, because there is simply more loans at that rating level in our data.

Figure 4: Average dispersion within bucket

This figure shows the average cumulative distribution of loans across all buckets. The black line represents the cumulative distribution of loans for the full sample of banks, while the blue and red lines represent the cumulative distribution of banks whose holdings of 4-rated loans are above and below median respectively

Figure 4 illustrates how the discretization of banks sharpens the treatment effect estimation. The assignment of banks into buckets creates sub-sets of banks in which by construction loan portfolios are very similar but for the share of the loans rated 4. Since the estimation is performed within bucket, the approach holds constant bank portfolios outside of the rating segment that is affected by the change in collateral requirement.

As such it provides a rare ceteris paribus environment to estimate the treatment effect of interest.

The categorization of banks ensures some degree of homogeneity across banks' portfolios within each bucket. However, homogeneity serves little purpose for identification if differences in lending policies existed prior to the change in collateral requirement within bucket. Figure 5 documents average lending by banks with holdings of 4-rated loans above and below the median value within bucket. Lending is computed relative to January 2012, just prior to the policy change, when lending by both categories of banks is normalized to one. We then take the quarterly average of monthly data to smooth the time series. The three panels in Figure 5 suggest there are no pre-existing differences within bucket in lending patterns between treated and untreated banks prior to the date of the policy change. After February 2012, however, lending grew substantially faster in banks above median exposure to 4-rated loans than for banks below the median. That is true in all three considered samples, most saliently in the one restricted to banks that hold at least 60 percent of their portfolio in loans rated between 4 and 5. That is to be expected since this is the sample in which banks' portfolios are overall most affected by the policy change. We establish formally the absence of any significant pre-existing difference by estimating the well-known specification introduced by [START_REF] Autor | Outsourcing at Will: The Contribution of Unjust Dismissal Doctrine to the Growth of Employment Outsourcing[END_REF]:

L b,t = α c,t + α b + k={-12,...,36} k =-1 β k 1 • (T b × D 2012m2+k ) + β 2 • T b + ε b,t , (1)
where L b,t denotes the value of new loans originated by bank b at time t, T b denotes the fraction of 4-rated loans in bank b's portfolio, and D 2012m2+k is a binary variably taking value 1 for the month equal to 2012m2 + k. The term α c,t refers to cell × time fixed effects. We define cells as the interaction of bucket categories with size categories, where the latter are determined by creating septiles by bank assets as of January 2012.9 The inclusion of cell × time fixed effects implies that we are comparing ex-ante similar banks in terms of loans distribution between 4+ and 5 rated loans and size category. The common trend assumption needs only hold within-cell. We estimate equation ( 1) with and without a bank-specific intercept α b to gauge whether any meaningful heterogeneity survives between banks within a cell, i.e., whether the estimates for β 1 (and β 2 ) are affected by the inclusion of α b . We plot β k 1 and verify the lack of pre-existing trends by checking if it is not significantly different from zero in the pre-ACC period (i.e., for k < 0). Figure 6 confirms the lack of pre-existing trends via estimation of equation 1. In addition, we check the holdings of 4-rated loans in the few months between ECB announcement and the Banque de France implementation. Figure 7 displays the averages for above and below within bucket median of 4-rated holdings. Below-median show an increase after ACC, as expected, but no change between announcement and implementation.

Figure 7: The evolution of loan holdings between announcement and implementation

Table 1 presents a variance decomposition of bank treatment before the ACC was implemented in the three considered samples. The table shows that in the full sample 57.4% of the variation in the policy exposure is between firms of the same bucket. Logically the more concentrated the samples, the larger within cell variance.

Finally Table 2 checks whether the categorization into cells leaves any residual heterogeneity by measuring the correlation between T b , the fraction of 4-rated loans in bank b's portfolio, and three different bank size characteristics. The unconditional correlations are always large, as are the correlations within bucket ("bin" in the table). Both facts suggest portfolio allocation is not random, not a very surprising conclusion. However, the correlation within cell is considerably smaller in most cases and presumably insignificant, which indicates that identification within cell is indeed ceteris paribus.

Estimations and Results

Credit effects

We first estimate the consequences of the relaxation in collateral constraints on bank's credit supply. Identification is achieved within cell. We consider the following specification:

L b,t = α c,t + α b + β 1 • (T b × D 2012m2 ) + β 2 • T b + ε b,t , (2)
where L b,t denotes the value of new loans originated by bank b at time t, T b denotes the fraction of 4-rated loans in bank b's portfolio, and D 2012m2 is a binary variable taking value 1 after the relaxation in collateral requirements. All estimations are performed within cell with an intercept α c,t , which also allows for time-varying cell-specific developments. We estimate equation ( 2) with and without a bank-specific intercept α b to gauge whether any time-invariant unobserved heterogeneity survives between banks within a cell, i.e., whether the estimates for β 1 (and β 2 ) are affected by the inclusion of α b . 10 2), without and with bank fixed effects and for the three samples. Columns (1) and (2) reports the estimates in the full sample: β 1 is positive and significant at the 10 percent confidence level, with a magnitude that is unchanged whether α b is included or not. 11 β 1 is estimated imprecisely in the full sample, possibly because it contains many banks that are not much affected by the change in collateral requirements. For example one every five banks holds less than 20% 4-rated loans in their portfolio in the full sample.

Columns (3) and (4) in Table 3 report the estimates of equation ( 2) in the reduced sample formed by banks that have a minimum of 20 percent of their portfolio holdings in loans rated between 4+ and 5. Estimates of β 1 without and with bank fixed effect are 10 Another reason to include bank fixed effects is the fact that the banking sector in France is dominated by a few large networks of branches belonging to the same mother institution. The credit effect we document could be driven by a central decision-making process at the level of network headquarters, which would have a different interpretation. The irrelevance of bank fixed effects tells us that the credit effect occurs within bank network, since α b subsumes bank networks. 11 β 2 is subsumed in the bank fixed effect when it is included.

positive and significant, estimated with more precision than in the full sample, and not significantly different from each other. They are not significantly different from the full sample estimates neither. Finally columns ( 5) and ( 6) consider the narrowest sample where T b > 0.6: The estimates of β 1 are still positive and significant, point estimates are now 50 percent larger, and still not different from each other.

There is no observable residual heterogeneity between banks within a cell, which suggests the treated and control groups within cell are similar except for their holding of 4-rated loans, as they should. The relaxation of collateral constraints had significant consequences on the supply of credit, especially by banks that held a substantial proportion of their portfolios in 4-rated loans. The point estimates of β 1 in columns ( 3) and ( 5) suggest that a one standard deviation relaxation of collateral constraints results in a 12.9 and 28.9 percent increase in new loans, which corresponds to 0.12σ and 0.19σ increase in new loans.

Table 4:

The credit effect of collateral constraints -omitting 4-rated firms Dependent variable: Relaxing collateral constraints is a tool of monetary policy that purports to have economywide consequences: Credit could increase across the board, and not only towards those firms whose loans become eligible as collateral. Since we identify within bank categories, it is entirely possible to verify whether credit to newly eligible firms (rated 4) is actually driving the results. Table 4 presents the results of estimating equation ( 2) omitting all firms whose loans are rated 4. A quick comparison with Table 3 shows that the coefficient estimates are not significantly different. We conclude that the relaxation of collateral constraints does have aggregate consequences on credit.

Log(Loans) (1) (2) (3) (4) (5) (6)
Regulatory and financial conditions bind at the bank holding group level, and groups have active internal capital markets. Hence, our effects could be overstating the credit supply effect if some less-responsive sub-entities within a bank holding group undo the supply shocks of other more-responsive sub-entities. To check whether there is such undoing of lending happening within a bank holding group, we run our baseline estimation in the presence of holding group fixed effects. Results are reported in Table A2. We find no significant change in our baseline credit effect.

Tables 3 and4 focus on the impact effect of the change in collateral requirements. To investigate the evolution of this effect over time, we perform a local projection following Jorda, 2005. The specification becomes:

L b,t+h = α c,t + α b + β h • (T b × 2012m2 ) + β 2 • T b + ε b,t+h , (3)
for all h in {0, 1, ..., 36}. The estimates of β h are presented in Figure 8, in three panels corresponding to the three samples. The effect of the policy change on credit last between 6 and 10 months before becoming insignificant in the three samples. The analysis confirms that the relaxation of collateral requirements has a temporary positive effect on credit, which increases significantly over the few months that follow the policy announcement. As a result, the level of credit supply increases permanently to reach a higher level after the policy change.

Price effect

Our findings in the previous section identify a credit supply shock. Next, we turn to check whether there is a complementary price effect: Do more treated banks pass-through the decrease in cost of financing to borrowers? We test this using a randomized representative sample of new bank loans administered by the Banque de France. The specification resembles equation 2 with the dependent variable as the loan-weighted average rate of lending at the bank-level. As before, our identification comes from comparing banks with ex-ante similar loan portfolios in all regards except for immediately around the eligibility threshold. This implies that concerns of bank-level variation in shadow cost of financing induced in response to the ACC reform as unlikely to bias our results.

Table 5 captures our findings. Indeed, there is a significant pass-through in financing costs, and that this effect gets stronger as we zoom in on lenders with a greater policyinduced liquidity shock. The point estimates in columns (3) and ( 5) suggest that a one standard deviation relaxation of collateral constraints results in a 28 bps and a 60 bps decline in interest rates to borrowers on average. To conclude, ACC reform created both a volume and a price effect for lenders by unexpectedly increasing their existing stock of eligible collateral and by lowering their cost of financing. We find lenders pass-through to borrowers along both the quanity the price dimensions. [START_REF] Kashyap | Monetary Policy When the Central Bank Shapes Financial-Market Sentiment[END_REF] survey recent literature on the effect that both conventional and unconventional monetary policy have on risk tolerance in financial markets. Specifically for banks, [START_REF] Acharya | The Seeds of a Crisis: A Theory of Bank Liquidity and Risk-Taking Over the Business Cycle[END_REF] and [START_REF] Drechsler | A Model of Monetary Policy and Risk Premia[END_REF] note that an accommodative monetary policy lowers the cost of liquidity, which serves as an insurance against a potential disruptive liquidity shortfall as a result of excessive risk-taking. More broadly, the mechanism presented in [START_REF] Geanakoplos | The Leverage Cycle[END_REF] and [START_REF] Gorton | Securitized banking and the run on repo[END_REF] argues that a decline in leverage due to a tightening in collateral constraints (higher haircuts) decrease the risk-bearing capacity of the financial system.

Shifts in risk tolerance induced by monetary policy

There has been a lack of well-identified studies documenting shifts in risk tolerance for banks induced by monetary policy. [START_REF] Dell'ariccia | Bank Leverage and Monetary Policy's Risk-Taking Channel: Evidence from the United States[END_REF] find that when policy rate declines, banks extend more credit to riskier borrowers. Their findings extend to new loans and not just commitments prior to a policy change. [START_REF] Paligorova | Monetary policy and bank risktaking: Evidence from the corporate loan market[END_REF] use data on syndicated corporate loans in the US to show that loan spreads for riskier firms become relatively lower during periods of monetary policy easing compared to tightening. Their effects become stronger for banks with a greater risk appetite as proxied for by banks' answers to the Senior Loan Officers Opinion Survey. However, such existing work does not exploit an exogenous shift in bank liquidity as a result of monetary policy but rather reports linear relationships between the monetary policy rates and bank risk-taking.

In contrast, our work differentiates itself from prior work in its ability to isolate the effect of risk-taking entirely driven an exogenous shift in bank liquidity induced by (the collateral channel of) monetary policy. Our findings are strengthened by our reliance on granular credit register data for the near universe of corporate loans and our identification across banks with similar pre-reform portfolios in all regards expect immediately around the eligibility threshold. We estimate whether for banks with quasi-random variation in their policy exposures, their pricing of loans within the same credit risk profile varies depending on the liquidity induced by the policy shock. Absent any shifts in risk tolerance, lending to the same credit risk profile should not vary around the policy for high versus low exposure banks after adequately controlling for time-varying trends at the cell-and credit risk-level. The specification to test this then becomes:

i b,r,t = α c,t + α r,t + α b + β 1 • (T b × D 2012m2 ) + β 2 • T b + ε b,r,t , (4)
The dependent variable is interest rate on new loans offered by bank b to credit risk profile r in month t. Credit risk profiles are the ratings of Banque de France from 3++ to P described earlier. α r,t controls for economy-wide cyclical changes in price of risk associated with each credit risk profile, such as absorbing any demand variation from borrowers of credit risk profile r that is common to all banks each month that could possibly be co-varying with treatment timing. Identification still occurs within cell.

We estimate equation 4 for three sub-samples of borrowers. First, we consider the effect on risk profiles that are eligible post-reform (4 and above). Next, we look at the effect on only newly eligible 4-rated borrowers. Any effect in these sets of borrowers can be rationalized as a effect induced by a lowering their shadow price of credit simply because a shift in the eligibility threshold these borrowers more attractive. Finally, we focus on interest rates for loans riskier than 4-rated which were never eligible as collateral. Intuitively, interest rates to the borrowers within the same riskier credit risk profile would be lower for more treated banks only if these banks' tolerance for risk (and hence their compensation for risk in the form of lending rates) increases.

Table 6 reports our findings. We find that liquidity induced by the collateral channel results in a lower interest rate to safe (Panel A) and 4-rated (Panel B) firms only for the most treated subset (60% subsample) of banks. By contrast, for risky borrowers, there is a lowering in interest rates across the board. For a borrower of the same risk profile, banks with a one standard deviation higher ACC-induced liquidity shock lower interest rates by 116 bps (column 2) to 254 bps (column 6) across sub-samples. In conclusion, while there is a positive credit supply shock as a result of the collateral channel, there is also a heightened tolerance for risk that is a positive function of liquidity induced by a loose monetary policy.

Bank FE N Y N Y N Y Cell × Time FE Y Y Y Y Y Y Rating × Time FE Y Y Y Y Y Y

Real effects

We now turn to our analysis of the real effects engendered by the expansion of credit just documented. Thanks to our approach, we are able to examine whether real effects prevail across all firms, not only those that have the 4-rating affected by the policy. In particular, we estimate

Y b,t = α c,t + α b + β 1 • (T b × D 2012m2 ) + β 2 • T b + ε b,t , (5)
where Y b,t denotes the average real outcome (employment, investment, etc) in the synthetic firm that borrows from bank b. We know the outcomes of all borrowing firms so that we can pair them with banks (sometimes more than one), and compute an average of all borrowing firms' characteristics weighted by the share of each firm in bank b's portfolio. Formally,

Y b,t = f L 2011 b,f,t f L 2011 b,f,t Y f,t ,
where L 2011 b,f,t denotes the value of loans borrowed from bank b by firm f in each month t of 2011, and Y f,t denotes a characteristic of firm f at time t, e.g., employment, investment etc. The rest of the specification is unchanged relative to the previous section: Identification is still obtained within cell, and the consequences of including a bank fixed effect still help us gauge the extent of residual bank heterogeneity within cell.

An alternative approach to equation 5 is to perform the estimation at firm-level. For instance both Cingano, Manaresi and Sette (2016) and Jimenez, Ongena, Peydro, and Saurina (2012) identify at firm-level in matched bank-firm datasets akin to ours, in Italy and Spain, respectively. Firm-level identification is not natural in our context, since we must identify within cell. One intuitive option is to construct a synthetic cell for each firm, instead of a synthetic firm for each bank, computing a weighted average of the cells a given firm belongs to on the basis of the banks it borrows from. We explored this option and estimated a version of equation 5 modified accordingly. A salient empirical difficulty is that firm-level treatment then becomes a weighted average of bank-level treatments, which actually tends to average out the differences between banks: Following this approach, we find the empirical dispersion in firm treatment is a small fraction of the dispersion in bank treatment. Unsurprisingly, as a result no coefficient is estimated precisely.

An immediate issue with the specification in equation ( 5) comes from the fact that firms do not bank with a single bank. In fact, [START_REF] Andrade | Can the provision of long-term liquidity help to avoid a credit crunch? Evidence from the Eurosystem's LTRO[END_REF] exploit precisely the existence of multi-bank firms in their identification. This is an issue for us, since a firm could borrow from treated and untreated banks, which would pollute identification. We address the issue in two ways that create two different subsets of firms for our analysis. In the first subset, we confine the analysis to firms that borrow from banks that are all categorized above (or below) the within-cell median treatment. Here a firm may borrow from more than one bank, each potentially belonging to different cells, but all the banks that a firm borrows from have to be either above or below the median of the cell they are located in. In other words, the treatment of all the banks lending to a given firm must be homogeneous. This excludes 32,677 firms from the analysis, out of a total of 229,878. In the second subset, we limit the sample of firms to those that borrow at least 75 percent of their total borrowing from a single bank: We then assign this firm to that bank. This results in omitting 86,429 firms. To get a sense of the importance of these omissions we also present the estimation results for equation ( 5) on the full sample of firms.

The existence of a relationship between a firm and a bank is potentially time-varying, particularly in response to the change in collateral requirements. The characteristics of synthetic firms in equation ( 5) must therefore be computed on the basis of the bank-firm relationships observed prior to the policy change, lest the real effects we document be caused by new relationships that arise in response to the change in collateral requirements. In practice, we use the lending decisions made by banks in the 12 months that predate the policy change, from January 2011 to January 2012. But by doing this, we may be missing a substantial part of the expansion of credit that happened after the relaxation of collateral requirements. We now verify that the response of credit did in fact occur mostly at the intensive margin, with no significant increase in the number of firms banks lent to.

We estimate NFirms

b,t = α c,t + α b + β 1 • (T b × D 2012m2 ) + β 2 • T b + ε b,t , (6)
where NFirms b,t denotes the number of new firms borrowing from bank b. The rest of the specification is identical to equation (2) in the previous section.12

Table 7 presents the estimates of β 1 when the dependent variable is the number of new bank-firm relationships (to capture the extensive margin of lending) in response to the policy change. β 1 is insignificant across the three samples and whether bank fixed effects are included or not. We conclude that the credit expansion documented in the previous section happened at the intensive margin, as banks chose to lend more to their existing customers.

Table 7

Dependent variable: In fact, this is to be expected given the well-known persistence in bank-firm relationships (see for instance [START_REF] Petersen | Does Distance Still Matter? The Information Revolution in Small Business Lending[END_REF], Chodorow-Reich ( 2014)), which we expect to hold in our data as well. We perform a simple auto-regressive specification on a variable capturing the existence of a bank-firm relationship at time t, estimating

Log(Number of firms) Full sample 20% sample 60% sample (1) (2) (3) (4) (5) (6)
Active b,f,t = α b,f + α t + ρ • Active b,f,t-1 + ε b,f,t , (7)
where Active b,f,t takes value 1 if a relationship exists between bank b and firm f at time t, and zero otherwise. Table 8 reports estimates of ρ in the three samples, with or without time and bank-firm specific intercepts. All estimates are large, close to 0.9 without fixed effects, down to about 0.75 if α b,f and α t are included. Unsurprisingly, bank-firm relationships are highly persistent in French data as well.

Theory suggests that a relaxation of collateral requirements should result in an increase in activity (see [START_REF] Kiyotaki | Liquidity, business cycles, and monetary policy[END_REF]). We compute synthetic values for Y b,t using firm-specific data on tangible investment, employment, dividends, and productivity. Tangible investment I t is computed as a share of (lagged) total assets, employment dN t is in growth rates, dividends D t are computed as a share of total (lagged) liabilities, and The estimation of equation 6 is performed within cell, and therefore within samples of homogeneous banks prior to the modification of collateral requirements. However, there is no guarantee that the typical average firms within a cell are similarly homogeneous, since these are synthetic firms computed as weighted averages of many potentially very different firms. We need to know whether, before ACC, above and below median banks within a cell lend to firms with equal characteristics on average, since this is crucial to the identification of real effects. To establish this, we perform Welch two-sample t-tests of the null hypothesis that investment, employment, dividends, and productivity have equal means when comparing above versus below median banks within cell before February 2012. Table 9 presents the results for the 20 percent sample, Table 10 for the full sample, and Table 11 for the 60 percent sample. Each Table presents the results of the tests for the three samples of firms we consider. The null hypothesis is not rejected in 32 of the 36 cases considered in the three tables, and in the four cases where the null is rejected, it is at relatively low levels of confidence, i.e., always above 5 percent. We conclude that the within cell ex-ante differences between the firms borrowing from treated vs. untreated banks lend are insignificant. Table ?? presents the result of estimating equation 6 on the three samples of banks (i.e., the full sample, the 20, and the 60 percent samples), and on the three samples of firms (the full sample, firms with only treated or untreated lenders, and firms with a prime lender). Bank fixed effects are systematically included, as are cell-time fixed effects.

The results are unambiguous: In all but one specifications investment, dividends, and productivity increase significantly at conventional confidence levels.13

A key point of our study is to demonstrate that the real effects we identify are not confined to the firms that are treated. This is done in Table ??, which reproduces Table ?? omitting altogether firms whose loans are rated 4. The results are not significantly different, and all but two coefficients in Table ?? are positive and significant. We conclude that firms with a rating of 4 are not the ones that drive the response of investment, dividends, and productivity: The expansion of credit caused by a modification of collateral constraints benefit all firms.

How economically relevant are these responses? Tables 12 and13 report the standard deviations of the regressors across all specifications, which helps quantifying the economic significance of the effects in both tables. Applying a standard deviation of the treatment T b equal to its average across samples (0.22), the coefficient estimates reported in Table 13 imply that one standard deviation relaxation in collateral requirement increases tangible investment by an average of 0.3σ (ranging from 0.24σ to 0.39σ depending on the specification), dividends by an average of 0.26σ (ranging from 0.22σ to 0.29σ), and productivity by an average of 0.31σ (ranging from 0.23σ to 0.41σ).

Table 12 reports impact effects as predicted by equation 5. Figure 9 plots the corresponding linear projection estimates, up to 36 months after the policy change. All significant responses are relatively short-lived and stop being significant about year from the shock: 15 months for tangible investment, 6 months for dividends, and 8 months for productivity. Interestingly, there is a lagged and temporary negative response of employment growth. The implication is the credit expansion increased productivity and dividends via higher capital per worker, as the stock of capital increased while employment contracted.

(3) (4)

(5)

Conclusion

We document large and economy-wide effects in response to an episode of relaxation of collateral constraints instigated by the ECB in 2011. The effects can be interpreted as causal on the basis of the surprise move by the ECB in 2011 followed by the implementation by the French Central Bank in 2012. The relaxation of collateral constraints results in an economy-wide expansion of credit with positive and large consequences on all firms' productivity, investment, and dividends. These findings suggest that the collateral channel is a powerful tool of monetary policy, consistent with recent theoretical conjectures. An interesting question is whether the magnitude of this effect depends on the macroeconomic context, and in particular the proximity to the zero lower bound. We leave this question open for further research.

A4 Alternative credit line

Figure 1 :

 1 Figure 1: Loan shares in the bucket method

Figure 2 :Figure 2

 22 Figure 2: Distribution of treatment intensity size in 2011

  Figure 3: Bank Discretization

Figure 5 :

 5 Figure 5: Pre-existing trends within bucket This Figure plots the average lending by banks with holdings of 4-rated loans above and below the median value within bucket

Figure 6 :

 6 Figure 6: Pre-existing trends à la Autor (2003) This Figure plots the value of β 1 in equation 1 to check whether treated and non treated banks are similar before the policy is implemented.

Figure 8 :

 8 Figure 8: Local projections for credit effects

Figure 9 :

 9 Figure 9: Local projections for real effects: 75% sample of firms with fixed effects

Figure A1 :

 A1 Figure A1: Testing for pre-existing trends in the full sample

Table 2 :

 2 Correlations between treatment intensity and bank characteristics

				Table 1
	Sample		# Banks Std. Dev. Between Cell Within Cell
	Full sample	505	0.156	42.6%	57.4%
	20% sample	410	0.151	28.2%	71.8%
	60% sample	138	0.223	25.5%	74.5%
	Statistic		Sample	# Banks Unconditional Bin FEs Cell FEs
	ρ(T b ,Assets b )	Full sample	505	0.046	0.061	-0.006
	ρ(T b ,Capital b )	Full sample	505	0.130	0.134	0.013
	ρ(T b ,Deposits b ) Full sample	505	0.110	0.132	-0.018
	ρ(T b ,Assets b )	20% sample	410	0.040	0.069	-0.008
	ρ(T b ,Capital b )	20% sample	410	0.130	0.149	0.009
	ρ(T b ,Deposits b ) 20% sample	410	0.135	0.163	-0.036
	ρ(T b ,Assets b )	60% sample	138	0.299	0.300	0.080
	ρ(T b ,Capital b )	60% sample	138	0.318	0.323	0.072
	ρ(T b ,Deposits b ) 60% sample	138	0.298	0.313	0.115

Table 3 :

 3 The credit effects of collateral constraints

				Dependent variable:
				Log(Loans)
		Full sample	20% sample	60% sample
		(1)	(2)	(3)	(4)	(5)	(6)
	T b × D 2012m2	0.746 *	0.694 *	0.852 * *	0.656 *	1.297 * * 1.213 * *
		(0.272) (0.294) (0.280) (0.304) (0.297) (0.386)
	T b	-0.032		-0.372		-0.654
		(0.564) (0.000) (0.568) (0.000) (0.634) (0.000)
	Bank FE	N	Y	N	Y	N	Y
	Cell x Time FE	Y	Y	Y	Y	Y	Y
	Observations	18,960	18,960	15,752	15,752	4,837	4,837
	Adjusted R 2	0.619	0.971	0.601	0.975	0.439	0.957
	Note:

* p<0.1; * * p<0.05; * * * p<0.01 Table

3

reports the estimates of β 1 and β 2 in equation (

Table 5 :

 5 The price effect of collateral constraints

				Dependent variable:
				Interest rate
		Full sample	20% sample	60% sample
		(1)	(2)	(3)	(4)	(5)	(6)
	T b × D 2012m2	-1.807 (0.494)	(0.762)	(0.553)	(0.729)	(0.937)	(1.082)
	T b	2.367		2.409		1.813
		(1.483)	(0.000)	(1.533)	(0.000)	(2.297)	(0.000)
	Bank FE	N	Y	N	Y	N	Y
	Cell × Time FE	Y	Y	Y	Y	Y	Y
	Observations	2,987	2,987	2,754	2,754	394	394
	Adjusted R 2	0.378	0.781	0.333	0.767	0.109	0.780
	Note:

* * -0.680 -1.862 * * -0.685 -2.374 * -2.605 * * p<0.1; * * p<0.05; * * * p<0.01

Table 6 :

 6 Risk taking effect relaxing collateral constraints

				Dependent variable:
				Interest rate
		Full sample	20% sample	60% sample
		(1)	(2)	(3)	(4)	(5)	(6)
	Panel A: Ratings above (and including) 4-rated
	T b × D 2012m2	-0.067	-0.012	-0.096	-0.359	-8.929 * * *	-9.433 * * *
		(3.080)	(2.147)	(3.358)	(2.094)	(0.224)	(1.624)
	T b	2.575		3.230		3.558
		(2.838)	(0.000)	(3.001)	(0.000)	(2.729)	(0.000)
	Bank FE	N	Y	N	Y	N	Y
	Cell × Time FE	Y	Y	Y	Y	Y	Y
	Rating × Time FE	Y	Y	Y	Y	Y	Y
	Observations	10,182	10,182	9,565	9,565	747	747
	Adjusted R 2	0.519	0.643	0.489	0.621	0.811	0.859
	Panel B: Only 4-rated
	T b × D 2012m2	3.021	0.289	3.780	0.995	-4.267 * *	-3.730 * * *
		(2.911)	(3.743)	(2.438)	(3.421)	(1.113)	(0.000)
	T b	-0.323		-0.981		0.635
		(2.155)	(0.000)	(1.952)	(0.000)	(3.920)	(0.000)
	Bank FE	N	Y	N	Y	N	Y
	Cell × Time FE	Y	Y	Y	Y	Y	Y
	Observations	2,435	2,435	2,302	2,302	200	200
	Adjusted R 2	0.391	0.678	0.337	0.658	0.714	0.940
	Panel C: Ratings below (and excluding) 4-rated
	T b × D 2012m2	-7.099 * * * -7.457 * * * -5.792 * * * -7.795 * * *	-9.306 * *	-11.411 * * *
		(0.535)	(1.225)	(0.572)	(0.805)	(3.019)	(1.629)
	T b	3.467 * *		1.567		1.216
		(1.150)	(0.000)	(0.968)	(0.000)	(1.246)	(0.000)

Table 8 :

 8 The persistence of bank-firm relationships p<0.1; * * p<0.05; * * * p<0.01 productivity EBE t is measured by gross operating surplus to total (lagged) sales. The normalizations are introduced to bypass issues of non-stationarity.

				Dependent variable:
				Active
		Full sample	20% sample	60% sample
		(1)	(2)	(3)	(4)	(5)	(6)
	Active b,f,t-1	0.894 * * *	0.751 * * *	0.894 * * *	0.752 * * *	0.862 * * *	0.732 * * *
		(0.0001)	(0.0001)	(0.0001)	(0.0001)	(0.0004)	(0.0005)
	Bank x Firm FE	N	Y	N	Y	N	Y
	Time FE	Y	Y	Y	Y	Y	Y
	Observations	35,700,760 35,700,760 35,353,167 35,353,167 2,086,020 2,086,020
	Adjusted R 2	0.800	0.811	0.801	0.812	0.746	0.759
	Note:

*

Table 9

 9

	Variable	T-statistic	p-value	DoF
	Panel A: Full sample of firms
	I(T) t At-1	0.065	0.949	968
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	0.344 -1.404 -1.028	0.731 0.161 0.304	901 998 915
	Panel B: Firms borrowing from only treated or only control
	I(T) t At-1	1.101	0.271	982
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	0.679 -1.744 -0.721	0.498 0.081 0.471	934 973 893
	Panel C: Firms with a prime lender (75%)
	I(T) t At-1	0.307	0.759	824
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	1.344 -0.979 -1.011	0.179 0.328 0.312	802 797 850

Table 10

 10

	Variable	T-statistic	p-value	DoF
	Panel A: Full sample of firms
	I(T) t At-1	1.232	0.218	1, 180
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	0.222 -1.387 -0.518	0.824 0.166 0.604	1, 141 1, 197 1, 128

Panel B: Firms borrowing from only treated or only control

	I(T) t At-1	1.522	0.128	1, 165
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	1.178 -1.905 -0.658	0.239 0.057 0.511	1, 109 1, 149 1, 050
	Panel C: Firms with a prime lender (75%)
	I(T) t At-1	0.764	0.445	976
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	1.395 -1.666 -0.483	0.163 0.096 0.630	908 892 979

Table 11

 11

	Variable	T-statistic	p-value	DoF
	Panel A: Full sample of firms
	I(T) t At-1	-0.401	0.688	210
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	0.138 -1.613 -1.307	0.890 0.108 0.193	204 276 191
	Panel B: Firms borrowing from only treated or only control
	I(T) t At-1	-0.403	0.688	203
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	-0.021 -1.600 -1.530	0.983 0.111 0.128	183 266 182
	Panel C: Firms with a prime lender (75%)
	I(T) t At-1	-0.294	0.769	206
	Gr(Emp) t Divt Lt-1 EBEt Salest-1	-0.028 -1.566 -1.898	0.977 0.119 0.059	187 274 189

Table 12 :

 12 Real effects of relaxing collateral requirements

			EBEt Salest-1	(12)		0.090 * * *	(0.029)	799	0.214	0.056
		60% sample	Gr(Emp) t Divt Lt-1	(10) (11)		0.071 0.019 * *	(0.053) (0.018)	744 788	0.293 -0.026	0.076 0.014
			I(T) t At-1	(9)		0.038 * *	(0.016)	799	0.510	0.027
			EBEt Salest-1	(8)		0.084 * * *	(0.022)	2642	0.251	0.041
	Dependent variable:	20% sample	Gr(Emp) t Divt Lt-1	(6) (7)		-0.001 0.015 * * *	(0.047) (0.006)	2564 2628	0.246 0.038	0.063 0.011
			I(T) t At-1	(5)		0.031 * *	(0.012)	2642	0.512	0.019
			EBEt Salest-1	(4)		0.086 * * *	(0.022)	3179	0.238	0.046
		Full sample	t Lt-1 Divt I(T) t At-1 Gr(Emp)	(3) (1) (2)	Panel A: Full sample of firms	0.015 * * * 0.027 * * 0.011 T b × D 2012m2	(0.005) (0.012) (0.045)	3153 3179 3076 Observations	0.056 0.527 0.299 Adjusted R 2	0.012 0.020 0.066 σ(Y)	Panel B:

Firms borrowing from only treated or only control

	0.091 * * *	(0.028)	796	0.028	0.056		0.104 * * *	(0.035)	788	0.257
	0.018 * *	(0.008)	785	-0.030	0.014		0.016 *	(0.009)	776	-0.013
	0.064	(0.053)	741	0.336	0.075		0.059	(0.062)	731	0.344
	0.037 * *	(0.027)	796	0.496	0.027		0.036 * *	(0.017)	788	0.497
	0.086 * * *	(0.029)	2602	0.277	0.043		0.103 * *	(0.045)	2366	0.182
	0.012	(0.008)	2585	-0.026	0.013		0.018 * *	(0.008)	2325	0.014
	0.001	(0.054)	2516	0.242	0.070		-0.092	(0.076)	2236	0.184
	0.028 * *	(0.013)	2602	0.484	0.020		0.045 * * *	(0.016)	2366	0.340
	0.082 * * *	(0.023)	3079	0.212	0.048		0.102 * *	(0.045)	2688	0.207
	T b × D 2012m2 0.026 * * 0.003 0.015 * * *	(0.013) (0.053) (0.006)	Observations 3076 2967 3051	Adjusted R 2 0.503 0.294 0.057	σ(Y) 0.021 0.075 0.013	Panel C: Firms with a prime lender (75%)	0.044 * * * -0.108 0.020 * * T b × D 2012m2	(0.016) (0.077) (0.008)	2688 2532 2651 Observations	0.385 0.239 0.100 Adjusted R 2	σ(Y)

Table 13 :

 13 Real effects of relaxing collateral requirements excluding 4-rated firms

			EBEt Salest-1
		60% sample	Gr(Emp) t Divt Lt-1
			I(T) t At-1
			EBEt Salest-1
	Dependent variable:	20% sample	Gr(Emp) t Divt Lt-1
			I(T) t At-1
			EBEt Salest-1
		Full sample	Gr(Emp) t Divt Lt-1
			I(T) t At-1	(1)

Table 14 :

 14 R&D effect of relaxing collateral requirements

		Dependent variable:
		I(T) t A t-1
	Full sample 20% sample 60% sample
	(1)	(2)	(3)

* p<0.1; * * p<0.05; * * * p<0.01

In the US, see the Term Auction Facility, the Primary Dealer Credit Facility, and the Term Securities Lending Facility Del[START_REF] Negro | The great escape? A quantitative evaluation of the Fed's liquidity facilities[END_REF].

Additionally see ashcraft2011two;[START_REF] Holmström | Private and public supply of liquidity[END_REF]. On the role of central banks as lender of last resort, see[START_REF] Freixas | Systemic risk, interbank relations, and liquidity provision by the central bank[END_REF],[START_REF] Freixas | The lender of last resort: A twenty-first century approach[END_REF], and[START_REF] Rochet | Coordination failures and the lender of last resort: was Bagehot right after all?[END_REF].

In practice the criterion used for categorization involves the characteristics of each bank's portfolio "around" the treatment level, i.e. according to their holdings of loans above and below

rating.

Credit ratings are administrated by the Banque de France on a twelve point scale: 3++, 3+, 3, 4+, 4,

5+, 5, 6, 7, 8, 9, P. We experimented with alternative categorization ranges with no significant change in our findings.

Ratings are also updated throughout the year should there be an episode confirming the firms' inability (or ability) to deliver on its financial commitments.

Non-0 are firms on the FIBEN database are relatively larger firms that receive more credit-per-capita. However, around

70% of all observations are "X0" rated, and comprise around 60% of overall credit.7 Inter-bank lending refers to lending to other financial or insurance companies, especially between banks from the same banking group. These comprise a large share of credit volumes (about a third of short-term credit).

As per the French Law of Modernization of the Economy (LME) published in 2008, small and mediumsized enterprises (SMEs) are firms with fewer than 250 employees, with turnover of less than 50 million EUR or total assets less than 43 million EUR. Mid-tier enterprises (MTEs) are enterprises that are not in the small and medium-sized enterprise category, have fewer than 5,000 employees, turnover of less than 1.5 billion EUR or total assets of less than 2 billion EUR. All other enterprises are defined as large.

We replicate the analysis with deciles find our results are robust. We retain septiles throughout the paper as these imply more populated cells.

We ran logit specification with fixed effects and results were similar.

The one exception concerns dividends in the 20 percent sample when firms are constrained to borrow from either treated or untreated banks.

Appendix A1 Summary Statistics