Do credit market shocks drive output fluctuations? Evidence from corporate spreads and defaults Roland Meeks∗ First draft June 2009 Revised draft November 2011

Abstract Several recent papers have found that exogenous shocks to lending spreads in corporate credit markets are a substantial source of macroeconomic fluctuations. An alternative explanation of the data is that borrowing costs respond endogenously to expectations of future default, driven by macroeconomic shocks. We answer the title question by using a simple bond pricing model to impose restrictions on a VAR that isolate the influence of expected default on spreads. We find that adverse credit shocks have contributed to declining output in every post-1982 recession, and can account for three-fifths of the decline in output during the 2007-9 contraction. However, credit shocks account on average for only around a fifth of business cycle fluctuations. We further show that shocks in a theoretical economy with firm-side credit frictions imply restrictions that we assess against the data. Our findings lend support to quantitative-theoretic models that incorporate exogenous financial shocks as an independent source of fluctuations. But they also suggest that we should treat with caution findings that exogenous shocks arising from corporate credit markets are a major driver of the U.S. business cycle. Keywords: corporate bond spreads; default rates; sign restrictions; Bayesian vector autoregression. JEL classification: C32, E32, E43, E44.

∗

Corresponding author: This paper was written while the author was at the Research Department, Federal Reserve Bank of Dallas. Email address: [email protected].

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Do credit shocks drive output fluctuations? Recent experience during the financial crisis seems to show that the answer is a firm ’yes’: A graphic case was made for how a shock to money markets, especially if it affects highly levered financial firms with a lot of short-term funding, can precipitate financial distress which is quickly transmitted to the real economy. But is the story always that straightforward? For non-financial firms, which tend to carry less leverage, there is usually scope to offset shocks to market credit by drawing upon alternative sources of funds, such as bank credit lines (James, 2009) or retained earnings. Further, because most credit market borrowing by non-financial firms is long term in nature, a relatively small proportion of outstanding debt must be refinanced each month. Consequently a shock to the bond market might not be expected to have immediate effects on output. Moreover, shocks may be sufficiently infrequent that they play little role in the ‘normal’ ups and downs of the business cycle. Thus Bernanke and Gertler (1995, p. 43) argue that except in rare financial crises, credit is not a ‘primitive driving force’ of economic fluctuations1 . Changes in the spreads on corporate bonds are closely related to changes in the risk of borrower default. Figure 1 depicts the spread on a broad index of speculative-grade (synonymously, ‘high yield’) bonds alongside default rates2 . Periods of stress in the credit market, marked by higher default rates and wider spreads, are evident during recessions; for example, in the recent downturn the spread peaked at a little over two thousand basis points (hundredths of a percent), compared to six hundred basis points a year earlier. One hypothesis attributes a large portion of this increase to credit shocks. An alternative explanation of the data is that credit spreads responded endogenously to fundamental macroeconomic shocks that altered the expected likelihood of default. Understanding 1

Cochrane (1994) strikes a similarly skeptical note on the importance of credit shocks for output fluctuations, although he too makes an allowance for the negative impact of banking crises. There is evidence from non-crisis periods that bank loan supply shocks do have a systematic impact on at least some components of GDP (Peek and Rosengren, 2000), but nagging problems of identification and measurement often remain. 2 The spread is defined as the difference between the yield on a risky (defaultable) corporate bond, and the yield on a safe Treasury bond of equivalent time-to-maturity. Most high yield bonds are rated between BB and B, with the term ‘junk’ usually reserved for bonds rated CCC and below. Gertler and Lown (1999) argue that the speculative-grade bond spread is likely to proxy well for the cost of finance prevailing for more credit constrained firms in the economy, and thus is a good indicator of overall financial conditions.

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which view has the most merit is of clear practical importance, as policymakers pay close attention to developments in bond markets in the belief that they provide signals about future economic activity (reflected in numerous references to bond spreads in the minutes of FOMC meetings over the 2007-9 period). It also matters because results from a growing set of quantitative-theoretic models suggest that credit market shocks play an important role in U.S. macroeconomic fluctuations3 . This paper sets out to gauge the macroeconomic effects of shocks to corporate credit markets. To this end, we estimate a structural vector autoregression (VAR) that allows both for the direct effects of credit shocks on the macroeconomy, and for feedbacks from the macroeconomy to the credit market. The model has two central features. First, it augments the standard monetary policy VAR with key credit market indicators: the spread on a large portfolio of corporate bonds; and the realized default rate on a closely-matching bond portfolio. Second, it departs from past studies by motivating identification from explicit economic assumptions. The identification step has previously been left quite vague, with most researchers specifying a causal ordering of the variables in the VAR based on an assumption about the timing of shocks4 . The benefit of the new approach, which imposes no timing restrictions, is that we obtain a sharper characterization of the macroeconomic response to a credit shock, and a clearer understanding of what an exogenous shock to spreads represents, than in previous work. Our key findings are as follows. First, shocks in the corporate credit market lead to output recessions and slow recoveries, consistent with firms being subject to significant financial frictions. Historical decompositions show that the cumulative effect of credit shocks was a factor behind falling output in every recession since 1982. Credit shocks were a significant factor driving up bond spreads and driving down output both during the recent financial crisis, and importantly also in the run-up to the business cycle peak 3 See inter alia Nolan and Thoenissen (2009), Jermann and Quadrini (2009) and Gomes and Schmid (2010). These works all focus on (non-financial) corporate credit markets, rather than shocks to financial intermediaries. 4 See inter alia Balke (2000), Friedman and Kuttner (1998), Gertler and Lown (1999) and Gilchrist et al. (2009) for examples of VAR’s identified using timing assumptions.

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of December 2007. However, most of the increase in bond spreads seen in the crisis was an endogenous response to higher default risk. Variance decompositions show that, on average, about one fifth of the variance of output can be attributed to credit market shocks at one-to-two year horizons, and rather little of the variation in spreads. In sum, our main results show that credit shocks did play an independent role in the recent crisis, and they also appear to make a non-zero, albeit limited, contribution to average macroeconomic fluctuations. Second, robustness checks reveal that the estimated credit shocks are unrelated to a measure of exogenous changes in monetary policy constructed from external data on futures prices, which rules out a potentially confounding influence. Furthermore, the estimated macroeconomic responses, which are unrestricted in the baseline model, are shown to be robust to imposing restrictions that explicitly rule out the influence of fundamentals on the results. Third, several pieces of evidence are advanced for how credit shocks may be interpreted. A strong statistical association is found between credit shocks and shocks to the VIX index, a measure of expected equity volatility. This finding is taken as evidence of a time-varying risk premium. Further, it is demonstrated that a popular theoretical model of lending spreads has implications that can be imposed on the empirical model as a special case of the restrictions used to obtain the paper’s main results. We find that the results from the restrictive model offer some support for the theory, although not all of the variation that can be ascribed to credit shocks is captured by the mechanism described. The reader should be aware of what is not done in this paper. First, we do not claim to give a comprehensive account of credit market disruptions. The market for high yield bonds, although an important source of business finance, did not trigger the financial crisis which began in 2007. However, the deliberately narrow view of credit market disturbances adopted here has the advantage that it makes it possible to extract an exogenous component from spreads with little risk of confounding the effects of macroeconomic shocks. Second, a number of studies have examined credit market

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shocks resulting from financial deregulation, such as the removal of interest rate ceilings, on macroeconomic performance and monetary policy (Benk et al. (2005); Mertens (2008)). However, the long-term structural consequences of regulatory changes are not the main focus of this paper. Such changes are not likely to be unanticipated at monthly or quarterly frequencies, and indeed regulatory policy may be shaped in response to macroeconomic developments rather than being truly exogenous. The remainder of the paper is organized as follows. Section 1 motivates the approach to identification by outlining an economic model of the spread. Our data are discussed in section 2.1, with a discussion of the results of an impulse-response analysis in section 2.2. The importance of credit market shocks in past recessions is detailed in section 2.3, and their overall role in macroeconomic fluctuations is related in section 2.4. The robustness and interpretation of the results are dealt with in sections 3.1 and 3.2. Section 4 investigates the responses of a theoretical economy to credit shocks, and assesses its empirical relevance. Finally, section 5 concludes.

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Identifying credit market shocks

Our first task is to disentangle shocks that arise from the corporate bond market from fundamental macroeconomic shocks. The tool we will use is a structural VAR, identified using sign restrictions on the response functions of credit variables. Identifying the effects of individual macroeconomic shocks, although possible in this framework, is not necessary to achieve our particular aim. Thus we will concern ourselves only with how to split out credit shocks from all the rest5 . Structural identification requires that a stand be taken on the behavioral relationships between variables. Some assumption is needed because the same reduced form relationship can be generated by many different behavioral models, but naturally a poor choice can lead us to draw erroneous conclusions. The assumption that has been used in the 5 Section 3.1 identifies additional shocks as a check on model robustness. A detailed description of the sign restrictions approach to identification can be found in Canova and De Nicolo´ (2002) and Uhlig (2005). Peersman (2005) identifies all four structural macroeconomic shocks in a four-dimensional VAR.

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literature is that the variables in the VAR can be arranged in a Wold causal chain with bond spreads ordered last, meaning that other variables respond with a delay to orthogonalized innovations to the spread (Friedman and Kuttner (1998); Gertler and Lown (1999); Gilchrist et al. (2009)). A drawback of this approach is that economic theory does not usually deliver restrictions that take this form. Instead, we take our cue from a large literature that demonstrates the failure of standard ‘structural’ pricing models to reconcile observed spreads on corporate bonds with actual default rates. A robust finding is that observed variation in bond spreads cannot be explained by changes in the fundamental drivers of default (Collin-Dufresne et al. (2001); Elton et al. (2001)). Here, it is assumed that fundamental macroeconomic shocks cause movements in the spread solely by altering expected default rates. That assumption is consistent with the canonical dynamic macroeconomic model of firm-side financial frictions, in which lending spreads compensate investors for the expected deadweight costs incurred in the case of default (inter alia, Carlstrom and Fuerst (1997); Bernanke et al. (1999))6 . Innovations to the residual component of observed spreads, after purging the effect of expected default, are taken to be ‘purely financial’ in origin. We show that they can be separated from other disturbances by imposing restrictions on the impulseresponse functions of spreads and default rates in a VAR. Our baseline identification leaves agnostically open the responses of output, monetary policy and other asset prices. As in Uhlig (2005), this approach leaves the data free to speak on the question of interest. Later, the sensitivity of the results to imposing additional restrictions is assessed. 6 A important recent literature has sought to account for the credit spread puzzle with exogenous timevarying risk premiums or macro factors (see Chen et al. (2009), for example). But Gomes and Schmid (2010) offer a general equilibrium model in which a shock to total factor productivity has an endogenous impact on both default risk and risk premiums. It should be noted that some exogenous variation in risk premiums, and in the non-default component spreads more generally, is not ruled out by their model. However, their work has clear implications for the present paper, and accordingly the issues raised are addressed directly in section 3.1.

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1.1

The restrictions in detail This section describes how our identifying assumption maps into sign restrictions

on the impulse-response functions for the bond spread and default rate in a VAR. The intuition is fairly straightforward. At each point in time, the VAR gives us a projection for the path of future spreads and default rates. One way to think about the impulse-response function is as the revision made to this projection, conditional (in our case) on a credit market shock. Suppose the observed bond spread St increases. One component of St can be shown to depend on the cumulative likelihood of the bond defaulting over some horizon hd . Identification follows from the sign of the response of the residual non-default component of the spread, which is inferred from the responses of observed spreads and expected default rates: any increase in the non-default component is the result of a credit shock7 . The argument can be clarified using a simplified example, in which investors are assumed to be risk-neutral, defaulting bonds are assumed to have a zero recovery rate, and default and interest rate risk are independent. The difference in yield between a defaultable and a risk-free bond with identical promised cash-flows can then be thought of as the compensation investors demand to bear expected default losses over the lifetime or ‘tenor’ of the bond. Consider a zero-coupon bond that pays $1 with certainty in n periods’ time. Let its price at time t be Pnt , then its yield to maturity (the discount rate that equates the bond’s present value with its price) is Ynt , and the continuously compounded yield is defined by ynt := log[1+Ynt ] with ynt := −n−1 log[Pnt ]. Now consider the price of a risky claim to $1 in n periods, denoted Qnt . Given the probabilities of default {δt+j } j=1,2,...,n , and under our assumptions, Qnt is equal to the expected present value of the claim, as in: Qnt =

(1 − δt+1 )(1 − δt+2 ) · · · (1 − δt+n ) (1 + Ynt )n

(1)

7 A more restrictive identifying assumption is that the response of default likelihood be negative, i.e. that the credit shock only works through the non-default channel (see section 4.3). A related approach to the one we describe is the present value VAR model proposed in Campbell and Shiller (1987). Their method would be applicable if we were to model the level of corporate bond yields, rather than the spread, and if the yields were I(1), or integrated of order one.

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which implies that the yield to maturity on the risky bond rnt := −n−1 log[Qnt ] is given by rnt = −n−1 log{(1 − δt+1 )(1 − δt+2 ) · · · (1 − δt+n )} + ynt

(2)

When the δs are not too large, the risky yield is well approximated (up to a constant) by n

rnt ≈

1X δt+j + ynt n

(3)

j=1

In this model, the theoretical spread, denoted S˜ nt := rnt − ynt , reflects compensation for expected default. The difference between the observed spread Snt and this default component is the residual ‘non-default’ component, Snt − S˜ nt . This residual is unobserved, due to the unobservability of S˜ t . How are credit shocks estimated using the VAR? First, to construct S˜ t , the VAR includes an estimate Dt of the default probabilities appearing in (3), with the projections Dt+s from the VAR in place of the δt+s , for s = 0, . . . , hd . Next, suppose there is an orthogonal shock that increases the measured bond spread at time t. The impulse-response function for the default rate shows how Dt+s is revised following the shock, with all other shocks at all other dates set to zero. This tells us the size and sign of the impact of the shock on the latent S˜ t relative to the observed St , and so tells us the change in the non-default component of the spread. The final step is to determine whether the orthogonal shock just mentioned classifies as a credit shock, in our sense. A fundamental macroeconomic shock affects spreads only via expected default. In this case, the response of the default rate pushes up S˜ t relative to the increase in St . The non-default component St − S˜ t does not increase. On the other hand, a credit shock leads to a widening of measured spreads that is greater than warranted by the revision to expected defaults. The response of the non-default component St − S˜ t then has a positive sign. By searching for shocks which satisfy this sign restriction, we are able to split orthogonal innovations to credit from all the remaining, non-credit disturbances that also affect spreads8 . 8

To make the sign restriction operational in the following sections, it is necessary to make an appropriate choice of restriction horizon hd . How hd is chosen is specified in section 2.2 below. The sign restriction algorithm is discussed in Appendix A.

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1.2

Alternative approaches to identification We close the discussion of identification with a brief tour of some other approaches that

have been taken in the literature. Many studies have made use of an alternative estimate of default likelihood based on individual issuer characteristics, that is based on ‘structural’ or Merton-type models9 . A drawback of this approach is the need to infer unobserved firm-specific characteristics, such as the market value and volatility of assets, from equity prices or from infrequent balance sheet (book) data. Eom et al. (2004) test different implementations of the class of structural models against realized default rates, reporting widely-varying empirical performance. They conclude that default likelihood tends to be overstated for risky bonds such as those in our sample. Jarrow and Turnbull (2000) offer a detailed critique of the widely-used (but proprietary) MKMV model, arguing the likelihood of default during recessions tends to be understated. Market-based measures such as credit default swap (CDS) rates are available for only a limited number of the largest companies, and have a relatively short history (see Longstaff et al. (2005)). Our approach seeks to circumvent some of these drawbacks by focusing on a broad index of bonds, and on actual default experience.

2 2.1

Data and Results

Data Our data runs monthly from November 1982 to April 2009. These dates span a period

from the end of the Volker-era non-borrowed reserves targeting to the start of ‘credit easing’ (Bernanke, 2009). Where the underlying observations are at a daily frequency, data for the last day of the month are used. We turn first to our credit market variables. The bond spread (S) is measured as the difference between the yield to maturity on a value-weighted portfolio of cash-pay only corporate bonds and the yield to maturity on a closely-matching government bond. The 9

See inter alia Collin-Dufresne et al. (2001), Gilchrist et al. (2009) and Gilchrist and Zakrajˇsek (2010); Mueller (2009) adopts the alternative ‘reduced-form’ approach. A textbook exposition of workhorse models is given in Duffie and Singleton (2003).

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corporate bond index covers a broad segment of the U.S. high yield corporate market, so as to match as closely as possible the universe of bonds used in the default series described below10 . The average quality rating of the portfolio remains in the B1/B2 range, a category described by Moody’s as being ‘subject to high credit risk’. The maturity of the portfolio, measured by its Macaulay duration, varies over time between 6 years 1 month and 4 years 2 months. We ensure that the yield spread is calculated with respect to the Treasury bond of equivalent duration following each month’s portfolio re-balancing, to avoid conflating movements in the corporate bond spread with changes in term premiums. If the spread is calculated using a constant ten year maturity Treasury bond, it contains significant measurement error: For example, in late 2008 the discrepancy between the duration-adjusted and constant-maturity spreads exceeded 200bps, due to a rapid decline in the duration of the underlying corporate bond portfolio. Furthermore, as the measurement error is directly due to movements in the risk free term structure, it is strongly correlated with the business cycle11 . This fact is very likely to have contaminated the inferences previous research has drawn on the relationship between high yield spreads and economic activity12 . An estimate of default likelihood for the bond portfolio is given by the monthly default 10 The Merrill Lynch index is a widely-used benchmark for assessing portfolio performance. For inclusion in the index, bonds must be a year or more from maturity, be U.S. dollar denominated, and have at least $100 million face value outstanding. The ‘cash pay’ index excludes deferred interest and pay-in-kind issues. Full details of the calculations behind the index can be found in Galdi (1997). Because the bond index starts only in November 1984, we interpolate back an additional two years of data using a quarterly index from Gertler and Lown (1999) and a monthly index of Moodys Baa-rated bonds (none of the results are sensitive to excluding the interpolated data). 11 Information on the Macaulay duration of the Merrill Lynch bond index were obtained from Bloomberg. We calculated spreads against zero-coupon Treasury yields estimated from a Svensson yield curve from the Federal Reserve Board. This measure of the spread is not fully satisfactory as the returns on a coupon bearing bond and a zero coupon bond of identical Macaulay durations will be equal only up to a first-order, and only for a level shift in the yield curve. However, in the absence of information on coupon schedules it is likely to be a reasonable approximation, and it is widely used in the literature. 12 Gilchrist et al. (2009) investigated the properties of the Merrill Lynch index as a comparator to their self-constructed aggregate bond spread, but calculated the index spread relative to a 10-year government bond, rather than adjusting for duration each month as we do here. Gilchrist and Zakrajˇsek (2010) are careful to compute individual bond spreads with respect to the correct maturity Treasury bond, and so arguably obtain far more accurate tests of predictive power.

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rate (D) on the universe of Moody’s rated U.S. speculative-grade corporate bonds13 . Moody’s defines default events broadly to include any missed payments of interest or principal, the initiation of bankruptcy or other legal blocks to payments, and distressed exchanges which reduce the issuer’s financial obligations (for example, an exchange of a less senior for a more senior obligation). Denote the number of defaults in month t by dt , and the total number of rated issues outstanding by Nt . An estimate of the marginal default likelihood at time t attaching to a broad portfolio of speculative grade bonds is P constructed as the trailing 12-month cumulative default rate Dt = 11 s=0 dt−s /Nt−11 . It can be seen that Dt is the proportion of those issues outstanding 12 months ago that defaulted. The denominator N is adjusted for ratings withdrawals, due to scheduled repayments, calls, or mergers. The measure is issuer-based, meaning that the expected likelihood of default for a particular issue with a particular rating is expected to be the same regardless of its nominal size (see Hamilton and Cantor (2006) for details of Moody’s methodology). The remaining variables are reasonably standard for monetary economics. Output and prices are measured by the log industrial production (IP) index14 and the log core consumer price index (P) respectively, while policy is measured by the effective federal funds rate (FFR). There is a debate on whether money is a necessary component in a VAR model. Although often excluded, canonical models such as Christiano et al. (2005) and Uhlig (2005) choose to include some measure of money, with Nelson (2003) arguing that money usefully summarizes information on many asset prices relevant for determining aggregate demand. In this paper we chose to include the log of real M1 in the VAR, but for the purposes of identifying the credit shock, it made little difference to our conclusions if it were excluded, or if total and non-borrowed reserves were included instead of M1 (for the period November 1982 to December 2007). Last, we include the logarithm of an 13

Moody’s defines this universe as those senior unsecured bonds carrying a rating of Ba1 or lower (the Standard and Poor’s equivalent rating is BB+). The equivalent series of speculative-grade default rates produced by Standard and Poor’s has a correlation of .96 with the Moody’s series. 14 Other authors have favored monthly estimates of aggregate GDP over the IP index. The aggregate output measure that is most comparable is GDP for goods. It comprises durable and nondurable personal consumption expenditures, fixed investment, change in private inventories, and net exports (further explanation can be found on the BEA website).

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equity price index (EQ) for mid-sized stocks, the S&P MidCap 400, to capture linkages between asset markets (specifically, the well-known sensitivity of high yield bond yields to equity returns), and as a proxy for collateral values.

2.2

Impulse-responses The baseline statistical model is a Bayesian VAR(6) for yt = [ln(IPt ), ln(Pt ), FFRt ,

ln(M1/Pt ), ln(EQt ), Dt , St ]’ (details of our estimation methods can be found in Appendix A). The identifying sign restrictions imposed on the impulse-response functions of the VAR require us to specify how far ahead projected default rates matter for the current bond spread, as described in section 1.1. As a baseline assumption, spreads are taken to depend on defaults over a horizon of hd = 60 months. The results presented below were not sensitive to imposing the restriction for longer or shorter horizons, although in order for our identification to be sensible, it was thought that imposing the sign restriction for less than three years was undesirable as the average Macaulay duration of the bond portfolio is around six years. Imposing the restriction for more than five years has little effect since default risk at very long horizons is not greatly influenced by current macroeconomic conditions. The estimated responses to an adverse credit market shock (one that raises the credit spread by 50bps) are shown in figure 2. The solid line shows the median value of the impulse-response function distribution for each horizon h across all posterior draws. The dashed lines give the 16th and 84th percentiles of the impulse-response function distribution at each h. Output is estimated to drop by a little over a percentage point at a one year horizon, and is expected to remain low for a protracted period, beginning to recover only after two years. The error band indicates that with high probability, output remains below its baseline value for a full three years following the shock, indicating that credit-induced recessions may be followed by sluggish recoveries. The fall in output accords with the predictions of standard theory: when firms face a higher cost of market funds and thus higher effective input costs, they lower input demand

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and cut output. The responses are consistent with the presence of financial frictions, which imply alternative means of financing are imperfectly substitutable and dependent on borrower net worth, giving rise to financial accelerator effects (Bernanke and Gertler (1995); Gertler and Lown (1999)). The sluggish recovery in output is consistent with theories of debt overhang, where firms may pass up profitable expansion opportunities if new money would partly bail out existing debt holders. The responses of the federal funds rate and of money are consistent with a systematic easing of monetary policy in reaction to a combination of lower output and lower prices. Default rates have a roughly equal chance of rising or falling on impact, followed by a ‘hump-shaped’ increase in subsequent periods as defaults respond endogenously to lower real activity. The rate levels off after a year, when output begins to recover. There could be several reasons underlying initially lower default rates. Firstly, firms under financial stress are known to take a variety of steps to improve their creditworthiness. Asquith et al.’s (1994) study of junk bond issuers presents evidence that firms respond to a higher cost of funds by raising cash through asset sales, which reduce productive capacity but improve liquidity, and by outright mergers. On the other side of their balance sheets, firms make important changes to their private liabilities, which are designed to alleviate near-term stress and at the same time improve creditworthiness. These margins of adjustment can lead to fewer outright defaults, even as output is cut. Secondly, if firms respond to the credit shock by delaying new debt issues, lower aggregate default rates can be explained by the well-known aging effect (Helwege and Kleiman, 1996). Historically, more recently-issued bonds have experienced a higher frequency of default than seasoned bonds, so fewer new issues would mean lower average default rates15 . 15

As noted in the minutes of the October 2008 FOMC meeting, new issuance of speculative-grade bonds all but ceased in the fall of 2008. McDonald and Van de Gucht (1999) document that the default likelihood of a new issue increases sharply at two years and then steadily declines, such that an issue that has survived for five years is about half as likely to default as an issue that has survived only two years.

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2.3

Historical decomposition Further insight into the effects of credit market shocks can be gained by considering the

historical contributions they have made to fluctuations in output and spreads. Results are shown for the median model (Appendix A describes how the median model is selected). Panel (a) of figure 3 shows the deviation of (the logarithm of) actual industrial production from a projection based on pre-sample data, and the contribution of credit shocks to this deviation. Panel (b) of figure 3 shows the same information for the high-yield bond spread. The net contribution of all the other (unidentified) shocks is then the difference between the two lines in each of these figures. Naturally, without identifying the other shocks we are unable to say whether credit played the dominant role in a particular episode, but we can gauge its absolute importance. The recessions of the early 1990s, of 2001 and of 2007-9 are marked by clear declines in industrial output. In all cases, the cumulative effect of credit market shocks during these episodes was negative for industrial production. In the 1990-1 recession, about a third of the peak-to-trough decline in output, and about two fifths of the run-up in spreads, was due to credit shocks16 . Although spreads were higher than in the base projection, the model attributes most of the increase to higher expected defaults, defaults which did transpire (see figure 1). The 2001 recession was also caused in part by credit shocks. From the peak of the business cycle in February 2001, to the trough of the recession in November, industrial production contracted 6.1% (relative to a baseline projection) of which 2.1%, or roughly a third, was due to credit shocks. Spreads peaked in September 2001, at 2.3 percentage points (ppt) above pre-recession levels. Credit shocks made a 1.3ppt contribution, just over half of the total. The largest absolute effects, unsurprisingly, are seen during the 2007-9 recession. From the business cycle peak in November 2007 to the end of the first quarter of 2009, industrial production contracted 16.2%. Credit shocks account for a 9.2% decline, just under three fifths of the total. From the onset of the subprime crisis in June 2007, through to the start 16

By this it is meant that under a counterfactual scenario in which credit shocks were zero over the same period, but all other shocks took the same values, a third of the decline in output would not have occurred.

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of the recession in December 2007, credit shocks raised spreads by a cumulative 2.1ppt out of a total increase of 3ppt. This accords well with the pattern of falling default rates over that period, which hit an all time low of 1% in December, and with narrative accounts that show that over this period, the full extent of the crisis was hardly imagined. On the eve of the crisis, The Economist called corporate debt defaults ‘the mosquito that did not bite in the night’, and asked when the default cycle would turn, while S&P’s issued upgrades for a large number of junk bonds17 . Anecdotal evidence would seem to agree with what our model-based forecasts tell us, namely that in the earlier stages of the crisis spreads were driven higher by credit market shocks. Once the recession got underway, spreads peaked 13.8ppt above their November 2007 level, of which 3.8ppt was due to credit shocks. Almost three quarters of the increase in spreads over this period was an endogenous response to expected credit losses. To complete the discussion of the historical decompositions, we now scrutinize the direct impact of our estimated credit shocks on the federal funds rate, in panel (c) of figure 3, and (the logarithm of) equity prices in panel (d). The evidence from our VAR suggests that credit shocks have been an important driver of monetary policy, especially since the late 1990s. The time series pattern of the credit shocks’ contribution appears to be very similar to that for output, in panel (a), but with a delay of several months. This pattern indicates that much of the movement in the funds rate in response to credit shocks comes through the systematic policy response to changes in output. Turning last to equity prices, panel (d) indicates that the VAR picks up an interesting link between bond and equity markets. The contribution of credit shocks to equity prices appears similar, but inverse, to their contribution to spreads. To take a particular recent episode, the stock market peaked in the fourth quarter of 2007, and had fallen by around half by the first quarter of 2009. Credit shocks drive equity prices lower (relative to the base projection) by around 20% over this period, while at the same time driving up spreads, as discussed above. The equity price effect could be an additional factor behind 17

‘Unsinkable junk’, The Economist, June 24, 2007; ‘S&P upgrades 1,500 junk bonds and loans’, Financial Times, June 7, 2007.

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lower output, for example, by precipitating declines in aggregate demand through the wealth channel.

2.4

Variance decomposition In this section, variance decompositions for macroeconomic and credit variables are

reported. One should keep in mind when looking at these results that the particular type of credit disturbance we have identified; those which arise in corporate credit markets; may be only one of several ways in which credit shocks might impinge on the economy. There may well be other distinct, uncorrelated credit disturbances which are not measured here, the most obvious arising from the banking sector, or as recently, from markets for securitized credit products18 . For that reason, the results we obtain are best regarded as giving a lower bound for the contribution of credit market shocks, broadly understood, to the business cycle. Table 1 reports the percentage contribution of credit market shocks to the total mean square prediction error in output, default rates and spreads at various horizons. The top panel reports results under sign restrictions. The median proportion of output variation accounted for at the one-year horizon is 21%, which is comparable to the contribution of monetary policy shocks at the same horizon, reported for example in Christiano et al. (2005). As usual in this type of analysis, caution is required in assessing the magnitude of the contribution, which cannot be gauged with high precision. At the two-to-three year horizon, the contribution remains in the region of 20%, which is a little under typical estimates for monetary policy shocks at business cycle frequencies. Estimates for the contribution of credit market shocks to the variance of spreads are small: their average contribution is never more than 15% at any horizon. Spreads are highly volatile, and credit market shocks are small, thus the bulk of the variation in spreads is due to other disturbances19 . In line with previous studies, it appears that for high yield corporate 18

Spreads on speculative-grade bonds are not likely to be directly informative about the state of the banking sector. As of December 2008, none of the 50 largest bank holding companies had debt rated below Baa. 19 A one standard deviation credit shock raises spreads by 10-20bp.

16

bonds, ‘non-default’ shocks do not account for much of the variation in spreads. The estimated credit shocks unsurprisingly account for only a small part of the variation in default rates at business cycle frequencies. The results just outlined lend support to the view that credit market shocks do play a role, albeit a modest one, in business cycle fluctuations. As they are the source, on average, of about a fifth of output fluctuations at the one-to-two year horizon, it is the case that even in ‘normal’ times credit shocks do matter. But their contribution is below that reported in other recent VAR studies20 . Their contribution is also below that reported in some quantitative-theoretic studies. For example, Nolan and Thoenissen (2009) argue that credit shocks are a ‘key driver for output, investment, the external finance premium [spreads], the federal funds rate and hours worked’, concluding that credit shocks contribute as much to the volatility of output as do shocks to total factor productivity (about 45%, over a longer sample period). The findings in the factor VAR study of Gilchrist et al. (2009) also suggest that credit shocks are a significant cause of economic fluctuations, accounting for 30% of the variability of output, and a large fraction of the variability of spreads.

3

Robustness and Interpretation

In this section, the results presented in section 2 are put under close scrutiny. An important motivation for the approach taken to identification adopted in this paper was that it should not confound credit market and macroeconomic shocks. The first task is to establish that the estimated credit market shocks satisfy that basic assumption. Two pieces of empirical evidence are advanced to show that they do, putting on firm footing the claim that the credit shocks we identify are a ‘primitive driving force’ of fluctuations, rather than a manifestation of other fundamental macroeconomic shocks. The second task is to glean some insights into how the identified shocks may be interpreted, examining liquidity and risk compensation in turn. 20

Gilchrist and Zakrajˇsek (2010) estimate a similarly-sized contribution to output fluctuations from shocks to their measure of the excess bond premium.

17

3.1

Are the identified shocks reasonable? In this subsection, an empirical case is built for the plausibility of the identification

scheme outlined section 1. The first piece of evidence is a test against data that is strictly external to the VAR, in the spirit of Rudebusch (1998)21 . A test based on externally-measured shocks has high power to detect misspecification, if the external measure is good. The second piece of evidence is a demonstration that the results reported above are robust to the imposition of additional restrictions that rule out fundamentals as an underlying cause of the disturbances we have attributed to the corporate credit market. These results are important in the light of the theoretical mechanism laid out in Gomes and Schmid (2010), which permits the risk premium on defaultable bonds to move endogenously in response to macroeconomic shocks22 . Monetary Policy Shocks:

Surprise moves in monetary policy are often taken to be a

fundamental driver of macroeconomic fluctuations. They are also an obvious source of high-frequency variation in interest rates that should be unrelated to credit shocks. Further, although we were careful to eliminate maturity mismatch between our corporate bond yields and the risk free Treasury yields, it is still possible that monetary policyinduced shifts in the term structure confounded our inference. To explore potential misspecification and mismeasurement, an external measure of monetary policy shocks was calculated from movements in the Federal Funds Futures (FFF) rate around FOMC meeting days, following the approach in Faust et al. (2004)23 . We have approximately 16 years of data, starting in 1992, and after allowing for months in which there was no scheduled policy meeting are left with 131 data points. Figure 4 plots monetary policy shocks against the VAR-based credit market shocks (where the latter are rescaled so 21

Rudebusch provides a critique of the structural VAR method in the context of monetary policy shocks. Further robustness tests, not reported here, ruled out variation in the value of call options embedded in the bonds contained in the index used to construct our measure of yields as a contaminating influence on the results. 23 The change in the implied federal funds rate for the month of the meeting that occurs on the day policy decision is announced. Full details of how the policy shocks are constructed can be found in the cited work. Unfortunately, the match between our credit shocks, which correspond to end-of-month data, and the policy shocks, which correspond to meeting day data, is somewhat imperfect. 22

18

both series have the same variance). Bars join observations on a given date to make the association clearer. It does not appear to be a close one: for example, in February 1994 and December 1995 there were adverse credit shocks of roughly equal magnitude, but in first case the futures market was surprised by monetary policy being 11bp tighter than anticipated, and in the second, by it being roughly 10bp looser. To investigate further, the estimated credit shock vˆt was regressed on the monetary policy shock εˆFFF t , with the following results (robust t-statistics in parentheses): vˆt = −.153 + (1.37)

1.99

εˆFFF t ,

R2 = .006, N = 131

(.942)

The regression reveals no statistical association between our estimated credit market shocks, and the independently measured exogenous monetary policy shocks. This finding adds confidence to the identifying assumptions adopted in section 1, and also suggests that the degree of error in our measurement of the bond spread is not too large. Additional restrictions: It was argued above that external data on macroeconomic shocks provides a stiff test of a model’s validity. However, convenient external measures do not exist for many fundamental shocks, or where they do, that measure is observed at too low a frequency to be of great value in the present study. A different approach is to assess the robustness of the results to the imposition of further restrictions on the baseline VAR. The restrictions are chosen explicitly to rule out the potentially confounding influences of fundamental shocks to supply, demand, and monetary policy on our results. Fundamental shocks are identified using sign restrictions, following a similar strategy to Peersman (2005). Shocks to demand are identified by restricting output and prices to move in the same direction for a year, with monetary policy moving to offset price changes over the same period; shocks to supply are assumed to cause output and prices to move in opposite directions, with monetary policy again acting to offset price changes; and shocks to monetary policy act via the funds rate, inducing a liquidity effect, followed with a six month lag (since nominal rigidities are commonly assumed to preclude immediate responses) by conventionally-signed responses in output and prices. 19

We then proceed as follows. Two orthogonal shocks to credit and to fundamentals are jointly identified by imposing (respectively) the sign restrictions given in section 1, and one of those just outlined. The signs of the responses to the credit shock are then checked. If they also satisfy one of the additional restrictions that define a fundamental macroeconomic shock, then that identification is ruled inadmissible. For example, any candidate credit shock that induces the positive output-price comovement and countervailing monetary response typical of a ‘demand shock’ is discarded; any that induces a negative comovement or which does not induce the specified policy response is retained. Thus by assumption, the credit shocks that are retained are impossible to confuse with fundamental shocks. The resulting impulses may be compared to their unrestricted counterparts. If substantial differences were found, it would be evidence against the claimed identification. Median impulse-responses to a credit shock with and without excluding the various fundamental shocks are shown in figure 5. The responses of most variables are robust to imposing additional restrictions. Of particular relevance to the question posed by this paper is the response of output, which is quantitatively similar to the baseline in all cases. Ruling out the influence of disturbances to supply has virtually no effect, which suggests that endogenous movements in risk premia of the type suggested in the theoretical model of Gomes and Schmid (2010) cannot be driving our results24 . The only variables to show substantially different responses are prices and money under monetary policy shocks. However, as we were already able to establish that monetary policy shocks are not related to credit shocks, and given that the behavior of other variables is rather similar, we should not regard this result with too much concern. 24

This finding does not rule out Gomes and Schmid’s theoretical mechanism, however, as it is possible for additional shocks, not identified here, to cause endogenous movements in the non-default component of the bond spread.

20

3.2

How can the identified shocks be interpreted? In the previous sub-section, evidence was presented to establish that credit shocks

identified under the assumptions of section 1 are unlikely to be confounding fundamental macroeconomic shocks. That leaves open the question of how best to interpret them. Below, we look for correlations between credit shocks and external measures of liquidity and risk premium shocks. The results suggest that shocks to risk premiums are a partial explanation, but also that much exogenous variation in spreads remains unexplained. In section 4, a complementary theoretical mechanism is outlined. Liquidity Shocks: Corporate bonds are far less liquid than other types of debt instrument. Average daily trading volumes are roughly 5% of those in the Treasury market, and less than 10% of those in the agency MBS market (Bessembinder and Maxwell, 2008). Chen et al. (2007) investigate bond-specific liquidity effects using detailed quote data, which includes liquidity proxies such as the size of the bid-ask spread, and the occurrence of zero returns. They find that the liquidity of individual bond issues is a significant determinant of changes in their spreads, after controlling for ratings effects, firm-specific characteristics and certain key interest rates. Another possibility is that changes in the liquidity of the government bond market drive changes in the spread. Government bonds carry a significant liquidity premium, particularly on-the-run Treasury issues25 , a factor that gives rise to their ‘specialness’. However, Collin-Dufresne et al. (2001) report that aggregate liquidity proxies such as the on-the-run/off-the-run spread do not explain changes in corporate bond spreads. Lacking a measure of liquidity premiums in corporate bond markets, we examined premiums on government bonds. To arrive at a measure of liquidity shocks, we projected the on-the-run/off-the-run spread, denoted ONOFF, on six own lags and six lags of all the explanatory variables used in the VAR. We then ran an OLS regression of our credit market shocks on the liquidity shocks. The results were as 25 The most recently issued and so most liquid Treasury bond of a particular maturity. Secondary market ‘off-the-run’ Treasury bonds are less liquid.

21

follows: vˆt = −

.108

−

(1.56)

1.97

εˆONOFF , t

R2 = .003 1984 : 5 − 2009 : 4

(.998)

Liquidity shocks have no statistical association with credit shocks. Naturally, this result does not rule out an independent role for liquidity shocks as a driver of changes in the high yield bond spread, but it does indicate that the variation in spreads that we identify is not primarily liquidity-related. Risk premium shocks:

Changes in the non-default component of the spread may be

driven by shocks to risk premiums. Theoretically, even if diversification of risk means that investors’ risk-neutral assessment of default likelihood coincides with the actual (‘physical’) likelihood we model in the VAR, actual and risk-neutral bond prices need not coincide as pricing is done under the risk-neutral probability measure26 . This means that changes in risk premiums could be behind non-default moves in spreads. Elton et al. (2001) find that a significant portion of time series variation in spreads is due to variations in the compensation required for bearing systematic risk, by regressing the ‘residual’ spread, after accounting for default, on the Fama-French factors27 . Unfortunately, risk premiums are hard to measure, and no ready empirical proxy exists. One imperfect possibility is to use the CBOE’s VIX index, a measure of expected 30 day volatility in the S&P equity index based on index option prices. The VIX can be thought of as primarily reflecting the price of protecting investor portfolios against loss, and as such captures shifting demand for ‘insurance’ that is likely linked to risk premiums28 . To construct a ‘risk premium shock’, we projected the logarithm of the VIX index on six own lags and six lags of the other variables. We then ran an OLS regression of our credit market shocks 26

See Duffie and Singleton (2003) for a discussion of this point. These are returns on small versus large stocks, high versus low book-to-market stocks, and excess returns on the market. Elton et al. abstract from liquidity effects. 28 The S&P index option market is dominated by trading in index puts, see Whaley (2008). 27

22

on εˆVIX with the following results: t vˆt = −

.182 (2.33)

+

2.68

εˆVIX t

R2 = .070 1990 : 7 − 2009 : 4

(3.72)

The strong statistical association between VIX shocks and credit shocks is reminiscent of the results reported in Collin-Dufresne et al. (2001), who find that changes in VIX are statistically significant in regressions of changes in corporate bond spreads. Their interpretation of this result is that VIX proxies for firm-specific volatility, which according to the structural model is an important determinant of credit spreads. However, Schaefer and Strebulaev (2008) show that, contrary to the predictions of the structural model, the sensitivity of corporate bond spreads to VIX is unrelated to credit exposure. Our risk premium interpretation is a plausible alternative, but given the regression R2 of .07, much variation in the estimated credit shocks remains unexplained.

4

A theoretical examination of credit market shocks

The turmoil seen in financial markets in the 2007-9 recession have spurred interest in incorporating ‘non-standard’ credit market shocks into macroeconomic models. In this section, we analyze the effects of a credit shock in a model where financial frictions are the result of an underlying costly state verification (CSV) problem, as in the early contributions of Williamson (1987) and Bernanke and Gertler (1989) and much subsequent literature29 . Our purpose in doing this will be to show that a particular credit shock produces a characteristic pattern of co-movement between spreads and defaults. The restrictions implied by this pattern turn out to be a special case of the those given in section 1, and are therefore amenable to empirical assessment. 29 See inter alia Bernanke et al. (1999), Carlstrom and Fuerst (1997), Christiano et al. (2010), Covas and den Haan (2010), De Graeve (2008) and Nolan and Thoenissen (2009).

23

4.1

The CSV model We begin by describing the contracting problem faced borrowers and investors when

there is CSV. CSV has proved a useful and popular way to think about financial arrangements in macroeconomic models, as under a set of commonly-used assumptions, optimal contracts resemble standard debt30 . It has also been shown to provide a remarkably good characterization of the behavior of credit spreads in the context of business cycle models (De Graeve, 2008). For our purposes, the CSV model class is particularly useful as it allows default to occur in equilibrium, as well as generating quantitative predictions for spreads, defaults and recovery rates that are useful for calibration. A general equilibrium treatment of the CSV model class is available elsewhere (see e.g. Carlstrom and Fuerst (1997)), as are the model’s responses to various macroeconomic shocks, such as monetary policy or total factor productivity (see e.g. Christensen and Dib (2008)). Our goal here is to explore the properties of a financial shock on credit market equilibrium, and so to keep matters simple, we will outline the main results in a static partial equilibrium setting31 . The model economy is populated by a large number of ex ante identical, risk-neutral, and competitive firms. Firms produce a final output good using a linear technology that is subject to both idiosyncratic productivity shocks and aggregate shocks. The aggregate shock θ is observed prior to capital markets opening. The idiosyncratic shock ω is observed privately by the firm only at the production stage. It is taken to have unit expected value. As a further simplification, the input and the output good will be treated as identical, so their relative price is one. 30 A range of alternative approaches to financing frictions have be employed, for example by assuming that borrowers have private information about their individual productivities, leading to an adverse selection problem for lenders (House, 2006); or by introducing limited contract enforceability (Jermann and Quadrini, 2009). 31 In the cited papers and the subsequent literature (Carlstrom and Fuerst (1997); Bernanke et al. (1999)), it is assumed that the financing contracts are static or ‘one-shot’ arrangements, rather than the more realistic case of multi-period debt. For that reason, nothing is lost here by abstracting from dynamics. An explanation for this lacuna is the difficulties entailed in any extension of the CSV model to multi-period settings, as detailed in Monnet and Quintin (2005). As they show, optimal dynamic contracts no longer resemble standard debt. However, we can think of the static contracts as descriptive of observed debt arrangements without insisting that they represent optimal contracts, as in Covas and den Haan (2010), for example.

24

The firm optimally sinks its entire equity, or net worth n, into paying for its inputs y, but expects to earn higher profits by leveraging its returns with borrowings y − n from a risk-neutral, competitive intermediary or ‘investor’, which carry a gross loan rate of Rd . If the realized value of ω results in sufficient final output goods to repay the investor, the firm is solvent, otherwise it defaults on its debts and the investor pays a monitoring fee µ to recover any residual output. The break-even level of entrepreneurspecific productivity is implicitly defined by θωy ¯ = Rd [y − n], such that for realizations of the random idiosyncratic shock ω˜ < ω¯ the firm defaults and monitoring occurs32 . Adopting the commonly-used notation, f (ω) ¯ and g(ω) ¯ are the expected revenue shares accruing to the firm and investor respectively. Because of the deadweight losses connected with default, these revenue shares do not sum to one. The firm’s expected profit is the expected revenue earned and retained when solvent, less the expected loan repayment Z θ f (ω)y ¯ := θ ωydΦ(ω) − [1 − Φ(ω)]θ ¯ ωy ¯ (4) ω>ω ¯

where Φ(ω) ¯ := Pr[ω < ω] ¯ is the probability of default. The expected revenue to the investor is comprised of the expected value of assets recovered from a defaulting firm net of monitoring costs plus the expected loan repayment Z θg(ω)y ¯ := (1 − µ)θ ωydΦ(ω) + [1 − Φ(ω)]θ ¯ ωy ¯ ω<ω ¯

(5)

We can assume that investors’ opportunity cost of funds is zero without loss of generality (as we’re interested in the spread over a risk free rate, rather than an absolute level), and derive the optimal amount of borrowing (equivalently, demand for inputs y) and its cost (equivalently, the optimal threshold productivity level ω) ¯ by maximizing the firm’s expected profit from sale of final goods, taking the parameters θ, n and µ as given, and subject to the investor breaking even (she expects to break even when θg(ω)y ¯ = y − n). 32

Covas and den Haan (2010) have criticized the use of linear technologies in this context, as this implies that net worth scales the size of the firm’s project, without affecting the spread or default rate.

25

4.2

The comparative statics of spreads and defaults The effects of a change in the macro state θ on capital market equilibrium are formally

derived in equations (B.8) and (B.9) of Appendix B. The threshold level of idiosyncratic productivity ω ¯ is increasing in θ, and consequently so is default likelihood Φ(ω), ¯ the gross lending rate Rd and input demand y. This is because, other things equal, a higher θ leads the investor to expect that for any given initial level of lending, positive profits will be earned as a consequence of firms’ greater ability to repay. Investors are thus willing to extend more credit (and so take on more credit risk) until they expect to break even. From the firm’s point of view, the tradeoff between leverage and default improves, which raises their desired scale of operation, and for fixed net worth, their leverage. The final effect is to increase borrowing, the default rate and the spread. The key prediction from our point of view is that defaults and spreads move together in response to the macro shock, the usual ‘default channel’. The equilibrium effect of credit market disruptions on leverage, default likelihood and credit spreads may now be characterized. A useful way to formalize a credit market disruption is as an increase in the deadweight losses suffered upon default, parameterized by an increase in µ. Higher default costs can be thought of as a decrease in the efficiency of investors’ monitoring technology, and as such have a natural interpretation in our context. Furthermore, similar types of shock have been analyzed in related environments by Jermann and Quadrini (2009) and Gomes and Schmid (2010)33 . Higher default costs lead unambiguously to less borrowing and a lower probability of default in equilibrium, shown formally in equations (B.10) and (B.11) of Appendix B. The intuition for this result is that the increase in deadweight default losses requires that investors demand a higher payoff for any given size of loan in order to break even, as their income in the default state is directly reduced when a greater proportion of output is lost. As a consequence, firms face a worse tradeoff between leverage and default likelihood in equilibrium, and thus choose reduced leverage, and for fixed net worth, produce lower 33

In both the cited works, financial shocks are thought of as being related to variation in lenders’ recovery rates. A complete theory would supply micro-foundations for this type of variation.

26

output. To gain a little more insight, figure 6 depicts the firm’s iso-expected profit line bb along with the investor’s break-even constraint na. The vertical distance y − n gives borrowing. The firm’s expected profits increase with higher borrowing, and a lower repayment threshold ω. ¯ The investor expects to make profits below her break-even line, and losses above it. When default costs increase to µ0 , the break-even constraint rotates to na0 , and the investor makes losses at the initial equilibrium. Changes in µ do not affect the firm’s desired rate of substitution between leverage and default, so faced with a flatter constraint at µ0 , they reduce leverage and make lower profits. To analyze the response of the spread, it is convenient to rewrite the lending rate as Rd

= ω/g( ¯ ω), ¯ the ratio of the promised repayment rate to the investor’s share of total

project revenue (the spread, recall, is Rd − 1). The equilibrium effect of an increase in default costs on the credit spread cannot be pinned down analytically. There are two opposing effects. First, the fall in ω ¯ reduces Rd . Second, the direct negative effect on the investor’s share of revenues in the default state acts to increase Rd . The latter effect can be seen from the partial derivative gµ < 0 in gµ (ω) ¯ d ¯ dRd ∂Rd dω = − R . dµ g(ω) ¯ ∂ω ¯ dµ

(6)

To say more, it is necessary to specialize to a particular distribution for idiosyncratic risk, and investigate the quantitative predictions of the model through calibration. Accordingly, idiosyncratic risk is taken to be lognormal with variance σω , and the model is calibrated using data from the high yield bond market, which provide a natural counterpart to our theoretical quantities: The default rate Φ(ω) ¯ is matched to the default rate seen in the crisis, around 10 percent; {σω , µ} are matched to historic recovery rates (RR) and spreads. According to Moody’s, the average recovery rate on defaulted unsecured bonds has ranged from low double digits up to 32 per cent, depending on the lien position of the bond in question. The yield premium carried by speculative grade bonds over Treasuries has ranged from around 2 percent to more than 10 per cent. The orthogonality conditions required for the calibration are given in equations (B.12) and (B.13) in Appendix B. The sensitivity of Rd to µ given by equation (6) is shown in figure 7. The principal 27

result is that for most parameterizations the spread rises in response to higher default costs. The finding is robust, in the sense that a wide range of recovery rates and spreads are consistent with spreads rising in response to higher bankruptcy costs. Exceptions lie in a ‘knife-edge’ region. Second, Rd is most responsive to changes in µ when recovery rates are high, and spreads are low. Last, not all combinations of recovery rates and spreads are consistent with the model. However, high recovery rates are consistent with lower spreads, and low recovery rates with high spreads, as anticipated. To match the wide spreads occasionally seen on high yield bonds requires some combination of low recovery rates, and a high probability of default.

4.3

An empirical assessment In the previous sub-section, the signs of the responses of credit variables to a shock to

default costs in the CSV model were derived. The model’s key prediction is that, following an increase in costs, the likelihood of default falls, while borrowing spreads rise. This theoretically-motivated sign restriction can be imposed on the empirical model of section 2 in a straightforward way. It is sufficient only to impose that there be no increase in defaults following an adverse credit shock, nor a decrease following a favorable one34 . This restriction identifies a subset of models obtained under the more general assumption of section 1. To see this, note that if spreads widen while the default rate (and so the average default rate) falls, then recalling equation (3), there has been an increase in the non-default component of spreads. Consequently any shock that is identified as a credit shock in the CSV model of this section is a also credit shock under the identifying assumption of section 1. It is of interest to ask how important the sub-set of credit shocks consistent with the CSV model are for overall fluctuations. To answer this question, table 2 reports variance decompositions for output, spreads and defaults. Table 1, which reports the 34

It is still necessary to choose a value for hd , the horizon over which the restrictions apply; the same value as in section 2.2 was used, although naturally others are possible, in order that the identified shocks are a proper subset those found earlier.

28

same information for the general identification scheme, serves as a point of reference. As might be expected, the median contributions of credit shocks to output fluctuations are lower under the tighter restrictions: At one year the contribution is 9.1% versus 21.2%; and at two years it is 6% versus 21.4%. Furthermore, the restricted shocks explain less than 5% of the variance of spreads, versus 10%-15%. In sum, the theoretical mechanism described in this section can explain part, but not all, of the variation in the data we attribute to credit shocks.

5

Conclusion

The aim of this paper is to quantify the macroeconomic effects of shocks arising in corporate credit markets. The joint behavior of the macroeconomy and the credit market are modeled using a VAR, estimated on US data from 1982-2009. Unlike in previous studies, identification is motivated by explicit economic assumptions, rather than by an ad hoc timing assumption. Shocks to lending spreads in the market for long-term corporate debt are found to cause prolonged contractions in output. Historical decompositions show that credit market shocks had an adverse effect on output in every recession since 1982. In the recent recession, credit shocks reduced output by 9.2%, and drove bond spreads up by 3.2ppt, at their peak. However, most of the run-up in spreads seen during the financial crisis was due to higher expected defaults. Also, the average size of credit’s direct contribution to business cycle fluctuations is much more modest than several recent papers have estimated, at around 20% of the variance of output at the one-to-two year horizon. The results of this paper have implications for quantitative theoretical models too. They lend empirical support to a recent literature in which exogenous financial shocks are an independent source of business cycle fluctuations. They are also supportive of the existence of a financial propagation mechanism that theory models attribute to persistent frictions in credit markets. However, the evidence presented here also suggests that we should treat with caution findings that exogenous shocks arising from corporate credit markets are a major driver of the U.S. business cycle.

29

Acknowledgements I received valuable feedback and suggestions from two anonymous referees, Jens Chris` tensen, Ferre De Graeve, Liam Graham, Oscar Jord`a, John Muellbauer, Argia Sbordone and Egon Zakrajˇsek, and seminar participants at the Federal Reserve Bank of New York, the Riksbank, and the National Bank of Belgium, as well as participants at the 2011 Royal Economics Society Conference (Royal Holloway), and the 2011 Midwest Macroeconomics Meetings (Vanderbilt). My thanks also to the Research Department at the Federal Reserve Bank of San Francisco, and to Matt Harding at Stanford Economics Department for their hospitality while writing this paper. This paper is a revised version of the manuscript circulated under the title ‘Credit market shocks: Evidence from corporate spreads and defaults’, Federal Reserve Bank of Dallas Working Paper 0906. The views expressed herein are not necessarily those of the Federal Reserve Bank of Dallas or the Federal Reserve System.

30

Figure 1: High-Yield Bond Spread and Default Rate 20%

15%

10%

5%

0% Nov-82 Mar-85 Jul-87 Nov-89 Mar-92 Jul-94 Nov-96 Mar-99 Jul-01 Nov-03 Mar-06 Jul-08 NBER Recession

High yield default rate

High yield bond spread

Note: Spread is in annual percentage points; default rate is the percent of bonds outstanding 12 months earlier that subsequently defaulted, weighted by issuer. The shaded rectangles represent NBER defined recessions. See Section 2.1 for details of data construction.

31

32

40

0

1

0

10

20

30

40

50

60

10

20

10 20 Default Rate (ppt)

30

30

30

40

40

40

50

50

50

60

60

60

Note: Solid line is the posterior median of the impulse response function distribution at each horizon. Dashed lines are the 16th and 84th percentiles of the posterior distribution of the impulse response function at each horizon. Figure shows responses to a credit market shock that raises spreads by 50bps. Model is a VAR(6), sample is 1982:11 - 2009:4.

0

0

1

0

60

60

0

50

50

−2

0

0 10 20 Real M1 (%) 2

−1

10 20 30 40 High−Yield Bond Spread (ppt)

30

60

−10

0

0 10 20 Equity Prices (%) 10

−0.5

0

50

−1

−2 40

−0.5

−1

0 10 20 30 Fed Funds Rate (%) 0.5

0

0

Ind. Production (%)

Figure 2: Impulse-responses: Sign restrictions Core CPI (%)

h IP D S

Table 1: Forecast Error Variance Decomposition Sign Restrictions 3 6 12 24 36 60 16.7 19.9 21.2 21.4 20.3 20.0 (5 – 40)

(6 – 43)

(7 – 44)

(6 – 45)

(5 – 44)

7.3

8.3

11.3

10.2

10.8

(6 – 42)

14.0

(1 - 28)

(2 – 28)

(3 – 31)

(3 – 28)

(4 –26)

(6 – 29)

14.8

14.0

12.7

11.5

12.1

14.2

(5 – 36)

(4 – 34)

(4 – 32)

(4 – 29)

(5 – 27)

(6 – 27)

Note: Estimated median percentage share of total horizon-h forecast error variance attributed to credit market shocks under sign restrictions. The 16th and 84th percentiles of the distribution of the horizon h variance share in parentheses. IP industrial production, D default rate on high yield corporate bonds, S yield spread between high yield corporate bonds and Treasuries.

33

0.15

Figure 3: Historical contributions of credit market shocks (a) Industrial production

0.10

Log Deviation

0.05 0.00 -0.05 -0.10 -0.15 -0.20 Nov-83 Jan-87 Mar-90 May-93 NBER Recession

16

Jul-96

Sep-99 Nov-02 Jan-06 Mar-09

Deviation from Base Projection

Shock Contribution

(b) High-yield bond spread

14

Percentage Points

12 10 8 6 4 2 0 -2 -4 Nov-83 Jan-87

Mar-90 May-93

NBER Recession

Jul-96

Sep-99 Nov-02 Jan-06

Deviation from Base Projection

34

Mar-09

Shock Contribution

5

(c) Federal funds rate

4

Percentage Points

3 2 1 0 -1 -2 -3 -4 Nov-83

Jan-87

Mar-90 May-93

NBER Recession

0.4

Jul-96

Sep-99 Nov-02

Deviation from Base Projection

Jan-06

Mar-09

Shock Contribution

(d) Equity prices

0.2

Log Deviation

0 -0.2 -0.4 -0.6 -0.8 -1 -1.2 Nov-83 Jan-87

Mar-90 May-93

NBER Recession

Jul-96

Sep-99 Nov-02 Jan-06

Deviation from Base Projection

35

Mar-09

Shock Contribution

36 May-94

Sep-95

May-98

NBER Recession

Jan-97

Jan-01 Credit Shock

Sep-99

Sep-03

Jan-05 Monetary Policy Shock

May-02

Figure 4: Monetary policy shocks and estimated credit shocks

May-06

Sep-07

Jan-09

Note: Chart shows futures-derived monetary policy shocks for scheduled FOMC meetings calculated using the method of Faust et al. (2004), plotted against VAR-based credit shocks generated by the median model (described in Appendix A). For each month in which a monetary policy shock is observed, the corresponding credit shock is plotted. A bar connects shocks that occur in the same month. The vertical scale is in percentage points for the monetary policy shock, and the credit shocks have been rescaled so that both series have the same variance. Note that there are a large number of months in which monetary policy shocks were exactly zero.

-0.25 Jan-93

-0.2

-0.15

-0.1

-0 05 -0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

37

40

10

20

30

40

50

50

50

60

10 20 Real M1 (%)

0.0

0.2

10

20

0 10 20 Default Rate (ppt) 0.4

−0.2 60 0

60

0

Core CPI (%)

30

30

30

40

40

40

50

50

50

Note: Chart shows the median responses to an identified credit shock, after excluding any response that could be confounded with a shock to supply (+), demand (◦) or monetary policy (♦). The bold solid line is the median response under the baseline identification, as shown in figure 2.

0

0.0

0.2

0 10 20 30 40 High−Yield Bond Spread (ppt) 0.4

−1.0

0

1.0

30

−0.25

−0.2 0

10 20 Equity Prices (%)

0.00

−0.1

60 0.25

50

0.0

40

−0.2

0.0

0.50

Ind. Production (%)

0 10 20 30 Fed Funds Rate (ppt) 0.1

−0.4

−0.2

0.0

Figure 5: Robustness of identified credit shocks

60

60

60

Figure 6: The effect of an increase in µ on y and ω ¯ a

y 6 b b0

a0

r

n

b b0

r

ω(µ ¯ 0)

-

ω(µ) ¯

ω ¯

Note: The investor’s initial break-even constraint is labeled na, and the borrower’s initial iso-profit line is bb. With µ0 > µ, the break-even constraint rotates to na0 , and the borrower’s iso-profit line shifts down to b0 b0 .

Table 2: Forecast Error Variance Decomposition under CSV Restrictions h 3 6 12 24 36 60 IP 11.0 11.5 9.1 6.0 5.0 5.0 (3 – 30)

D S

(3 – 26)

(2 – 20)

(2 – 15)

(1 – 14)

(1 – 14)

15.4

11.2

5.2

2.8

3.2

3.5

(4 - 35)

(4 – 26)

(2 – 13)

(1 – 7)

(1 –7)

(1 – 8)

3.3

2.6

2.2

2.1

2.5

2.6

(1 – 8)

(1 – 6)

(1 – 5)

(1 – 4)

(1 – 5)

(1 – 6)

Note: Estimated median percentage share of total horizon-h forecast error variance attributed to credit market shocks under the costly state verification (CSV)-consistent identification scheme. The 16th and 84th percentiles of the distribution of the horizon h variance share in parentheses. IP industrial production, D default rate on high yield corporate bonds, S yield spread between high yield corporate bonds and Treasuries.

38

Figure 7: Sensitivity of dRd /dµ to assumptions on recovery rates and premia 35

Recovery Rate (ppt)

30

25

20

15

10

5

2

3

4

5 6 7 Annualized Spread (ppt)

8

9

10

Note: Surface plot of the value of the derivative in equation (6) given various combinations of recovery rates (B.12) and spreads (B.13). Contour lines join points of equal height, with lighter shading representing higher values. Points to the south-west indicate combinations of lending spreads and recovery rates that result in an increase in Rd in response to an increase in µ. The darker band to the north-east indicates combinations that result in a decrease in Rd . Spread is in annual percentage points, with taxation assumed to contribute .75ppt, and the assumed annual default rate is fixed to 10%. The missing values, represented by uncolored space, require inadmissible values of µ and σω (see Appendix B), or are not attainable.

39

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44

Online Appendices A

Estimation, Inference and Model Selection

This appendix outlines the specification and estimation of our baseline statistical model, and reviews the sign restriction approach to identification. We follow a conventional estimation strategy, choosing the familiar reduced-form linear VAR(p), written B(L)yt = ut

(A.1)

where yt is an n-vector of variables of interest, and B(L) is a lag polynomial of order p with B0 = In . We take a Bayesian perspective to inference, and do not include any deterministic components, such as a constant or trend. We adopt the uninformative priors for (B, Σ) described by Uhlig (2005, Appendix B). Lag length p was set to 6 months, although the choice of either 12 months or 3 months was not found to greatly affect the results. The solution to the VAR is the vector moving average process yt = C(L)ut

(A.2)

It is usual to transform the reduced form innovations ut to orthogonality to see the ‘distinct patterns of movement’ in the system. A common approach is to assume a contemporaneously recursive structure by using the lower triangular Choleski factor of the covariance matrix Σ, denoted A0 , which gives the transformation 0

ut = A0 v∗t

E[v∗t v∗t ] = I

(A.3)

where v∗t are the Choleski-orthogonalized residuals. It is straightforward to see that this factorization of Σ is not unique. For any nonsingular matrix Q, we can form a new impact matrix A = A0 Q and associated structural shocks vt = Q−1 v∗t such that the reduced form covariance structure is preserved. Supposing we choose Q to be an orthogonal matrix, such that Q−1 = Q0 , then we may write ut = Avt := A0 QQ0 v∗t

E[Avt v0t A0 ] = AA0 = Σ 1

(A.4)

There are many candidate structural VMA representations, each given by an A in yt = C(L)Avt

(A.5)

and we select amongst them according to prior sign restrictions placed on the impulseresponse functions. If the matrices Ci in the reduced form moving average representation are stacked, then the response vectors up to horizon h for a particular model given by A0 Q are straightforwardly found as the n(h + 1) × n matrix R(h) = [A00

A00 C01

A00 C02

...

A00 C0h ]0 Q

(A.6)

The sign restrictions that we will impose on the impulse responses are then restrictions on the columns of this matrix. Some blocks will be unrestricted; for example, if a set of sign restrictions hold only contemporaneously, then only columns of A0 Q need be considered. Similarly, if the sign of the response of variable i is free under every restriction vector, then rows (i, i + n, i + 2n, ..., i + hn) will be unrestricted. The advantage of the sign restrictions approach is that the tasks of orthogonalizing the VAR residuals and of ensuring that they obey theoretical priors are separated. The computational approach is described in Rubio-Ram´ırez et al. (2005, Algorithm 2): for each posterior draw of (B, Σ), we draw a Q matrix and check if our sign priors are satisfied for every shock that is to be identified; if they are not, we draw another Q and so on until a one is found that does. To obtain Q, we draw an (n × n) Gaussian matrix, and then compute the orthogonal-triangular or QR decomposition to obtain the orthonormal matrix Q. Because Q is orthonormal, each column satisfies ||qi || = 1 and q0i q j = 0 for all i , j. As there exists a Q such that ai = A0 qi , this method provides a constructive means to find a set of n impulse vectors A = [a1 , ..., an ]. Fry and Pagan (2007) have cautioned against certain innovation accounting methods that fail to preserve the orthogonality between structural shocks. Following their lead, the ‘median model’ mentioned in the text is found as follows. A single model from the posterior set is chosen that has an impulse-response function closest to the median response for each variable and at every horizon. Define the stacked and standardized 2

¯ impulse response function for model k by φ(k) = (vec[R(h)(k) − R(h)])/std[R(h)]. Then the model that generates the smallest deviation from the median response solves k(∞) = arg min{||φ(k) ||∞ }

(A.7)

k

where ||.||∞ denotes the uniform norm, and we set h = 48.

B

Comparative static results

This appendix provides comparative static results for the costly state verification model described in Section 4. We impose some standard, unrestrictive assumptions on the distribution of individual-level productivity in order to guarantee the Lagrangian for the optimization problem solved by the borrower is jointly strictly concave in (y, ω). ¯ We adopt the notation Φ(ω) for the distribution function, and φ(ω) for the density function of ω. It will be useful to collect the relevant partial derivatives for reference: f$ ($; σω ) = −[1 − Φ(ω)], ¯ g$ (ω) ¯ = 1 − Φ(ω) ¯ − µφ(ω) ¯ ω, ¯ g$µ (ω) ¯ = −ωφ( ¯ ω), ¯

f$$ (ω) ¯ = φ(ω) ¯ Z $ gµ (ω) ¯ =− ωφ(ω)dω 0

g$$ (ω) ¯ = −(1 + µ)φ(ω) ¯ − µφ0 (ω) ¯ ω ¯

The contracting problem discussed in the main text may be formally stated as max θ f (ω)y ¯ {y, ω} ¯

s.t. θg(ω)y ¯ = y−n

(B.1)

The first order condition for ω ¯ is λ(ω) ¯ =−

f$ (ω) ¯ g$ (ω) ¯

(B.2)

where λ is the Lagrange multiplier on the investor’s break-even constraint, and subscripts indicate partial derivatives. Other first order conditions include35 θ f (ω) ¯ + λ(θg(ω) ¯ − 1) = 0

(B.3)

θg(ω)y ¯ − (y − n) = 0

(B.4)

35

Incentive compatibility is always satisfied under the usual assumptions on the distribution of idiosyncratic risk, i.e. the firm always wishes to participate in the loan market.

3

Given the (positive) hazard function h(ω) ¯ = φ(ω)/[1 ¯ − Φ(ω)], ¯ Assumption 1 can be shown to be sufficient for a regular solution. Assumption 1. The hazard function satisfies h(ω)µ ¯ ω ¯ < 1 at the optimal cutoff ω. ¯ We can immediately state our first result. Result 1. The return on internal funds λ exceeds unity, the opportunity cost of funds. Proof. From the first order condition (B.2), we may obtain that: λ=

1 >1 1 − h(ω)µ ¯ ω ¯

from Assumption 1.



The second assumption is necessary because under general risk distributions, the problem is not necessarily regular enough to guarantee a local maximum. However, necessary and sufficient conditions can be checked. Assumption 2. The optimal (y, $) pair that solve first order conditions (B.2)-(B.4) are a local maximum. Necessary and sufficient conditions. The Hessian matrix of the Lagrangian with x = (y, $) is:   " #  0 θg − 1 θyg$    Lλλ Lλx  0 0 = θg − 1  Lxλ Lxx0  θyg$ 0 θy( f$$ + λg$$ ) A necessary and sufficient condition for a local maximum is the positivity of the determinant of this Hessian: ∆ = −(θg − 1)2 θy( f$$ + λg$$ ) > 0 To guarantee that condition is met we need that: f$$ + λg$$ = (1 − [1 + µ]λ)φ(ω) ¯ − µφ0 (ω) ¯ ω ¯ <0

(B.5)

The first term is clearly negative, since (1 + µ)λ > 1; the sign of the second term depends on φ0 . For the rectangular distribution, it would be zero, and we would be guaranteed a local maximum. For the lognormal, it is a condition that must be checked. 

4

Proof that Rd is increasing in ω. ¯ To see this, note that the investor’s break-even constraint may be used to write Rd = ω/g( ¯ ω), ¯ the ratio of the promised repayment to the investor’s share of total project revenue. It then follows that g(ω) ¯ − ωg ¯ $ (ω) ¯ ∂Rd = 2 ∂ω ¯ [g(ω)] ¯

(B.6)

The numerator is equal to $

Z g(ω) ¯ − ωg ¯ $ (ω) ¯ = (1 − µ)

ωdΦ(ω) + µφ($)$2 > 0

0

Thus a higher default threshold raises the lending rate.



Comparative statics. The basis of the comparative static analysis is the following fundamental differential of the Lagrangian:   0 θg − 1 θyg$   θg − 1 0 0    θyg 0 θy( f + λg $

$$

      dλ      yg θyg µ         dθ       dy  = −  f + λg λθgµ            dµ         0 λθyg$µ  $$ ) d$

(B.7)

We may now prove our main results. Aggregate macro shock. Macroeconomic shocks affect the economy through the parameter θ. Any fundamental shock can be represented in a reduced form way as a change in this parameter, but it may be useful to think of it as representing total factor productivity. It follows directly from (B.7) that the response of the shadow price on internal funds responds positively to productivity, with a larger response when leverage is higher: dλ λ y = >0 dθ θ n From this we can immediately find that the response of the default cutoff is  y  λg$ d$ =− >0 dθ f$$ + λg$$ nθ

(B.8)

and correspondingly that the response of borrowing (given fixed n) is dy yg θyg$ d$ = + >0 dθ 1 − θg 1 − θg dθ

(B.9)

It is immediate from (B.6) that spreads and defaults move together in response to a change in productivity.  5

Effects of a ‘financial shock’ µ. Financial shocks alter the deadweight losses associated with recovering the assets from firms in default. It follows directly from (B.7) that the return on internal funds is lower when µ is high since θgµ dλ =λ <0 dµ 1 − θg To show that the default cutoff is decreasing in bankruptcy costs, use this result to find ! θg$ gµ d$ −1 = −( f$$ + λg$$ ) λ g$µ + <0 (B.10) dµ 1 − θg Finally, we have that borrowing is decreasing in µ (firms delever), since ! dy θy d$ gµ + g$ <0 = dµ 1 − θg dµ The response of the spread is indeterminate without further assumptions, see (6).

(B.11) 

Calibration. We estimated the structural parameters of the model for various values expected recovery rates and spreads, using the sample orthogonality conditions ω ¯

Z (1 − µ) 0

ω dΦ(ω; σω ) − RR = 0 Φ(ω; ¯ σω ) ! ω ¯ −1 −S = 0 g(ω; ¯ µ, σω )

(B.12) (B.13)

With the resulting estimates for σω and µ in hand for each {RR, S} pair, the derivative in equation (6) is computed.

6