Theory Ahead of Measurement? Assessing the Nonlinear Effects of Financial Market Disruptions

Transcription

1 Theory Ahead of Measurement? Assessing the Nonlinear Effects of Financial Market Disruptions Regis Barnichon, Christian Matthes, and Alexander Ziegenbein July 1, 217 Abstract An important, yet untested, prediction of many macro models with financial frictions is that financial market disruptions can have highly nonlinear effects on economic activity. This paper presents empirical evidence supporting this prediction, and in particular that financial shocks have substantial (i) asymmetric and (ii) state dependent effects. First, negative shocks to credit supply have large and persistent effects on output, but positive shocks have no significant effect. Second, credit supply shocks have larger and more persistent effects in periods of weak economic growth. For helpful comments, we would like to thank Efrem Castelnuovo, Luca Fornaro, Jordi Gali, Guillaume Horny, Oscar Jorda, Giovanni Pellegrino, Ricardo Reis, and seminar participants at CREI- Universitat Pompeu Fabra, Banque de France and the 216 Norges Bank/HEC Montreal/LUISS conference on New Developments in Business Cycle Analysis. We gratefully acknowledge financial assistance from the Fondation Banque de France. We thank Jean-Paul Renne for sharing his KfW-Bund spread data and Annemarie Schweinert for excellent research assistance. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Banks of Richmond and San Francisco or the Federal Reserve System. Federal Reserve Bank of San Francisco, CREI, Universitat Pompeu Fabra, CEPR. Federal Reserve Bank of Richmond. Universitat Pompeu Fabra. 1

2 1 Introduction A large literature aims at better understanding the macroeconomic implications of financial frictions and the effects of financial shocks. Building on earlier theoretical contributions, 1 a set of recent papers shows that financial constraints can lead to highly nonlinear dynamics in the economy s response to shocks. 2 In particular, financial frictions can lead to (i) asymmetric impulse responses a positive shock triggering a different impulse response than a negative shock if the financial constraints are occasionally binding, and (ii) state dependent impulse responses as financial disruptions can have larger effects in recessions when firms have little net worth and are more sensitive to credit shortages. Surprisingly, while the existence of such non-linearities can provide an important diagnostic for models of financial frictions, these predictions have never been evaluated empirically. Instead, empirical studies have focused exclusively on the linear effects of financial market disruptions, whether credit shocks or financial crises. 3 This paper fills this gap by studying the nonlinear effects of shocks to the supply of credit. predictions. We find strong evidence of nonlinear dynamics consistent with theoretical First, contractionary shocks to credit supply have large and persistent adverse effects on output, but expansionary shocks have no significant effect, consistent with the presence of occasionally binding financial constraints. Remarkably, we find the same results using three independent sources of variations; credit shocks affecting the US, credit shocks affecting the UK and credit shocks affecting the Euro area. Second, negative shocks to credit supply have larger and more persistent adverse effects during recessions than during expansions, consistent with the idea that net worth influences the effect of a credit shock. Our main evidence is based on US data, where we follow Gilchrist and Zakrajsek (GZ, 212) and identify credit supply shocks from innovations to GZ s Excess Bond Premium (EBP), the component of credit spreads purged from the expected default risk of borrowers. However, we also consider other sources of variation, and we explore the presence of non-linear effects in the UK by exploiting an EBP measure Bleaney et al. (216). Despite the shorter sample size, we obtain very similar results: 1 In particular, Bernanke and Gertler (1989), Kiyotaki and Moore (1997), and Bernanke, Gertler and Gilchrist (1999) 2 See Mendoza (21), He and Krishnamurthy (213), and Brunnermeier and Sannikov (214), Guerrieri and Iacoviello (215). 3 For studies of the effects of credit supply shocks, see Helbling et al. (21), Gilchrist, Yankov, and Zakrajsek (29), Gilchrist and Zakrajsek (211, 212), and Boivin et al. (213). For studies of the effects of financial crises, see Cerra and Saxena (28), Reinhart and Rogoff (214), Jorda et al. (21), Bordo and Haubrich (212), Ball (214), Blanchard, Cerutti, and Summers (215), Krishnamurthy and Muir (215), Romer and Romer (215). 2

3 contractionary credit shocks have much stronger effects on output than expansionary shocks and credit shocks have their largest effects in recessions. Finally, we use a third source of variation movements in the KfW-Bund spread to identify shocks to financial constraints in the Euro area, and we again find that only contractionary shocks have large and persistent effects on output. An important reason for the lack of studies on the possibly asymmetric and state dependent nature of financial shocks is methodological. Standard techniques assume linearity and thus preclude the exploration of nonlinearities. In particular, VARs (or factor-augmented VARs), as used by Gilchrist and Zakrajsek (211, 212) and Boivin et al. (213), cannot allow the impulse response to depend on the sign of the shock. 4 The narrative approach, which isolates financial crisis episodes and studies the economy s behavior around these episodes, 5 is more flexible and could be extended to allow for nonlinearities using Autoregressive Distributed Lag models (ADL) or Local Projection (LP, Jorda, 25). However, it suffers from two limitations: (i) shock identification and (ii) low efficiency. First, the financial crisis dates isolated through the narrative approach need not identify shocks originating in the financial markets, so that the approach is mostly aimed at measuring correlations rather than at identifying the causal effect of a financial crisis on economic activity. 6 Second, because of their nonparametric nature, ADL and LP methods are limited by efficiency considerations, which makes inferences on a rich set of nonlinearities (e.g., asymmetry and state dependence) difficult. To overcome these technical challenges, we use a new method that combines the strength of the VAR for shock identification with the flexibility of ADL and LP models to allow for nonlinearities, in particular asymmetry and state dependence. The method consists in (i) directly estimating the impulse response function (i.e. the moving average representation) from the data while simultaneously identifying the structural shocks, and (ii) using Gaussian basis functions to approximate the impulse response functions, which offers efficiency gains and allows for the exploration of a rich set of nonlinearities. 4 Regime-switching VAR models can capture certain types of nonlinearities such as state dependence (whereby the value of some state variable affects the impulse response functions), but they cannot capture asymmetric effects of shocks (whereby the impulse response to a structural shock depends on the sign of that shock). With regime-switching VAR models, it is assumed that the economy can be in a finite number of regimes, and that each regime corresponds to a different set of VAR coefficients. However, if the true data-generating process features more general asymmetric impulse responses, a new set of VAR coefficients would be necessary each period, because the (nonlinear) behavior of the economy at any point in time can depend on all structural shocks up to that point. As a result, such asymmetric data-generating process cannot be well approximated by a small number of state variables such as in threshold VARs or Markov-switching models. 5 Reinhart and Rogoff (214) and all references in Footnote 3. 6 An exception is Romer and Romer (215), who use real-time narrative accounts to identify surprises originating in financial markets. 3

4 This method Functional Approximation of Impulse Responses (FAIR) builds on two premises: (i) any mean-reverting impulse response function can be modeled as a basis function expansion, and (ii) a small number (one or two) of Gaussian functions can already capture a large variety of impulse response functions, and notably the typical impulse responses to credit shocks found in empirical or theoretical studies. 7 Thanks to the small number of free parameters allowed by FAIR, it is then possible to directly estimate impulse response functions from the data using Maximum Likelihood or Bayesian methods. A more technical companion paper (Barnichon and Matthes, 216) provides details on the technical aspects of FAIR as well as Monte-Carlo simulations to assess its (good) performances in finite samples. The remainder of the paper is structured as follows. Section 2 presents our empirical model, our method to approximate impulse responses using Gaussian basis functions and our strategy to identify structural shocks to credit supply; Section 3 presents our results; Section 4 presents robustness checks using an alternative econometric technique. Section 5 presents additional evidence on the non-linear effects of credit supply shocks from the Euro Area and the UK. Section 6 concludes and lays out possible paths for future research. 2 The linear effects of credit market shocks As a preliminary to our analysis, we first reproduce Gilchrist and Zakrajsek (211, 212) evidence on the (linear) effects of credit shocks on macroeconomic variables. To measure conditions in financial markets, Gilchrist and Zakrajsek (212) focus on credit spreads and purge the spreads from expected defaults, liquidity risk, and prepayment risk to construct an Excess Bond Premium (EBP) measure. 8 The EBP is meant to capture the effective risk bearing capacity of the financial sector and hence credit supply. Then, Gilchrist and Zakrajsek (212) identify shocks to credit supply from innovations to the EBP in a structural VAR. We thus estimate a VAR (i) the log-difference of industrial production, (ii) CPI inflation, (iii) the excess bond premium, and (iv) the effective federal funds rate. y t = [ log(ip t ), log(cp I t ), EBP t, F F R t ] We use with twelve lags, and we identify credit supply shocks from the short-run 7 See e.g., Gilchrist and Zakrajsek (212) for empirical evidence or Bernanke, Gertler, and Gilchrist (1999), Gertler and Kiyotaki (21), Gertler and Karadi (211) for theoretical predictions. 8 See the appendix for more details. 4

5 restriction that macroeconomic variables can only react with a lag to credit supply shocks while the fed funds rate can react contemporaneously. To make use of post-28 data, we must address the fact that the federal funds rate is at the zero lower bound and therefore no longer captures variations in the stance of monetary policy. We address this issue in two ways. First, we use the shadow federal funds rate of Wu and Xia (214) as a measure of the monetary policy stance. 9 Second, we check the robustness of our results by estimating our specifications using only data from 1973 to 27 to avoid the zero lower bound period. Figure 2 plots the impulse responses to a 1 standard-deviation shock to the EBP - about.25 percentage point. As found by Gilchrist and Zakrajsek (211, 212), an unanticipated increase in the EBP leads to a substantial reduction in output growth, to a decline in inflation, and to a decline in the federal funds rate. In terms of dynamics, output growth bottoms out one year after the shock, then recovers and turns slightly positive after two years. After three years, the level of output (not shown) is no longer significantly different from zero. 3 Estimating the non-linear effects of credit shocks Our goal in this paper is to study to what extent the effects of a credit shock depend on the sign of the shock as well as on the state of the business cycle at the time of the shock. To capture these possibilities, we need a model that allows the impulse response functions to depend on the sign of the shock and on the state of the economy. 1 empirical model is thus a nonlinear Vector Moving-Average model, in which the behavior of a vector of macroeconomic variables is dictated by its response to past and present structural shocks. Specifically, denoting y t a vector of stationary macroeconomic variables, the economy is described by y t = Our K Ψ k (ε t k, z t k )ε t k, (1) k= where ε t is a vector of structural shocks with E(ε t ) =, E(ε t ε t ) = I, K is the number of lags, which can be finite or infinite, and z t is a stationary variable that can be a function 9 The shadow rate is the hypothetical level of a federal funds rate not constrained by the zero lower bound, given the level of asset purchases and forward guidance. Wu and Xia (214) construct an estimate of the shadow rate from the observed Treasury yield curve, i.e., by finding the level (positive or negative) of the policy rate that would generate the observed yield curve. See also Krippner (214). 1 As we argue in a few paragraphs, a VAR is ill-suited to capture such nonlinearities. 5

6 of past values of y t or of exogenous variables. Ψ k is the matrix of lag coefficients, i.e., the impulse response functions to shocks. Note that (1) is a nonlinear moving average model, because the coefficients of Ψ k can depend on the values of the structural innovations ε t k and on the value of the macroeconomic variable z t k. With Ψ k a function of ε t k, the impulse response functions to a given structural shock depend on the value of the shock at the time of shock. For instance, a positive shock may trigger a different impulse response than a negative shock. With Ψ k a function of z t k, the impulse response functions to a structural shock depend on the value of the macroeconomic variables z at the time of that shock. For instance, the response function may be different depending on the state of the business cycle (recession or expansion) at the time of the shock. Importantly, our empirical model is not a structural Vector AutoRegression (VAR). While the use of a VAR is a common way to estimate a moving-average model, it relies on the existence of a VAR representation. However, in a nonlinear world where Ψ k depends on the sign of the shocks ε as in (1), the existence of a VAR is compromised, because inverting (1) is generally not possible. Thus, in this paper, we work with an empirical method that side-steps the VAR and instead directly estimates the Vector Moving Average model (1). 3.1 Functional Approximations of Impulse Responses (FAIR) Estimating a moving-average model is notoriously difficult, because the number of free parameters {Ψ k } K k= in (1) is very large or possibly infinite. To address this issue, we use Functional Approximations of Impulse Responses, which consists in representing the impulse response functions as expansions in basis functions. As a first example to illustrate FAIR, consider a linear version of (1), i.e. y t = Ψ k ε t k. (2) k= Denote ψ(k) the representative element of matrix Ψ k, so that ψ(k) is the value of the impulse response function ψ at horizon k. If we parametrize the impulse response function ψ with one Gaussian function, we have that k b ψ(k) = ae ( c ) 2 k >, (3) 6

7 where a, b, and c are the parameters to be estimated. Note how a, b, and c have a direct interpretation in this simple case: a captures the peak response to the shock, b is the point in time when the peak effect occurs, and c captures the persistence of the effect. 11 For additional flexibility, we can let the contemporaneous impact coefficient ψ() be a free parameter. The parsimony of FAIR has two important advantages. First, it will allow us to directly estimate the impulse responses from the moving-average representation (2). Second, it will allow us to add more degrees of freedom and introduce (and estimate) possible asymmetric and/or state-dependent effects of shocks. In order to capture more complex shapes of impulse responses, one can approximate the impulse response functions with a sum of Gaussian basis functions. A FAIR of order N, or FAIR(N), is of the form ψ(k) = N n=1 ( ) 2 a n e k bn cn k >. (4) For instance, one might want to add a second Gaussian function in order to capture an oscillating impulse response function, such as the response of output growth to a credit shock (Figure 2). Figure 3 describes how the sum of Gaussian functions can be used to capture such a pattern. In this FAIR(2) example, the first Gaussian captures the firstround effect of the shock the initial decline in output growth, while the second Gaussian captures the second-round effect the later rebound in output growth. Similarly to the FAIR(1) case, the parameters a n, b n, and c n of the nth Gaussian basis function correspond to the magnitude, location and persistence of the nth effect of the shock. Allowing for asymmetric impulse responses To allow for asymmetries, we let Ψ k depend on the signs of the structural shocks, i.e., we let Ψ k take two possible values: Ψ + k asymmetric effects of shocks would be y t = K k= or Ψ k. Specifically, a model that allows for [ Ψ + k (ε t k 1 εt k >) + Ψ k (ε t k 1 εt k ) ] (5) with Ψ + k and Ψ k the lag matrices of coefficients for, respectively, positive and negative shocks and denoting element-wise multiplication. 11 The amount of time τ required for the effect of a shock to be 5% of its maximum value is given by τ = c ln 2. 7

8 In our case of interest, denoting ψ +, an impulse response function to a positive shock to credit supply and similarly for ψ, a FAIR(N) model of the impulse response function ψ + would write ψ + (k) = N n=1 ( ) k b( a + n e n 2 + c+ n, k > (6) with a + n, b + n, c + n some constants to be estimated. A similar expression would hold for ψ (k). Allowing for asymmetric and state dependent impulse responses With asymmetry and state dependence in response to credit shocks, the matrix Ψ + k becomes Ψ + k (z t k), i.e., the impulse response to a positive shock depends on some indicator variable z, capturing for instance the state of the business cycle at the time of the shock. And similarly for Ψ k. To construct a model that allows for both asymmetry and state dependence while preserving parsimony, we build on the asymmetric FAIR(N) model (6) and allow a + n, the loading on each Gaussian function, to be a linear function of the state, i.e. where now α n +, b + n, c + n, and β n + functional form holds for ψ. ( ) ψ + (k, z t k ) = N i=1 a+ n (z t k )e k b + 2 n c + n a + n (z t k ) = α + n + β + n z t k k >, (7) are the parameters to be estimated. An identical Note that in specification (7), the state of the cycle is allowed to expand/shrink the loading on each Gaussian basis function, but the Gaussian basis functions are themselves fixed (the b and c parameters do not depend of z t ). While one could allow for a more general model in which all parameters a, b and c depend on the indicator variable, specification (7), with limited sample size, it is necessary to impose some structure on the data. Imposing fixed basis functions is a reasonable and parsimonious starting point This assumption is easy to relax or to evaluate by model comparison using posterior odds ratios. 8

9 3.2 Estimation We now briefly describe how we use Bayesian methods to estimate a multivariate linear FAIR(N) model with a short-run restriction. relatively straightforward bar some technical details. 13 The extension to nonlinear models is The key to estimating a moving-average model (1) is the construction of the likelihood function p(y T θ, z T ) of a sample of size T for a moving-average model with parameter vector θ and where a variable with a superscript denotes the sample of that variable up to the date in the superscript. For the indicator vector z t, we will consider here that it is a function of lagged values of y t (as will be the case in the empirical application). We use the prediction error decomposition to break up the density p(y T θ, z T ) as follows: 14 p(y T θ) = T p(y t θ, y t 1 ). (8) t=1 Then, to calculate the one-step-ahead conditional likelihood function p(y t θ, y t 1 ), we assume that all innovations {ε t } are Gaussian with mean zero and variance one, and we note that the density p(y t y t 1, θ) can be re-written as p(y t θ, y t 1 ) = p(ψ ε t θ, y t 1 ) since y t = Ψ ε t + K Ψ k ε t k. (9) Since the contemporaneous impact matrix is a constant, p(ψ ε t θ, y t 1 ) is a straightforward function of the density of ε t. k=1 To recursively construct ε t as a function of θ and y t, we need to uniquely pin down the value of the components of ε t, that is we need that Ψ is invertible. We impose this restriction by only keeping parameter draws for which Ψ is invertible. It is also at this stage that we impose the identifying restriction: We order the variables in y such that the EBP is ordered third after output growth and inflation, but before the fed funds rate and we impose that for the last two columns of Ψ the elements above the diagonal are filled with zeros. Finally, to initialize the recursion, we set the first K values of ε to zero. 15,16 13 See Barnichon and Matthes (216). 14 To derive the conditional densities in decomposition (8), our parameter vector θ thus implicitly also includes the K initial values of the shocks: {ε K...ε }. We will keep those fixed throughout the estimation and discuss our initialization below. 15 Alternatively, we could use the first K values of the shocks recovered from a structural VAR. 16 When K, the lag length of the moving average (1), is infinite, we truncate the model at some horizon K, large enough to ensure that the lag matrix coefficients Ψ K are close to zero. Such a K exists since the variables are stationary. 9

10 We use flat (improper) priors, and to explore the posterior density, we use a Metropoliswithin-Gibbs algorithm (Robert and Casella, 24) with the blocks given by the different groups of parameters in our model; a, b, and c. Using a flat prior allows us to interpret our results as outcomes of a maximum likelihood estimation. To initialize the Metropolis-Hastings algorithm in an area of the parameter space that has substantial posterior probability, we follow a two-step procedure: first, we estimate a standard VAR using OLS on our data set, calculate the moving-average representation, and we use the impulse response functions implied by the VAR as our starting point. 17 In the nonlinear models, we initialize the parameters capturing asymmetry and state dependence at zero (i.e., no nonlinearity). This approach is consistent with the starting point (the null) of this paper: shocks have linear effects on the economy, and we are testing this null against the alternative that shocks have nonlinear effects. 4 Evidence from US data This section presents our empirical results using US data. We first allow for asymmetry and let credit supply shocks generate different impulse responses depending on the sign of the shock. We then add state dependence to the model and allow the effect of a credit supply shock to depend on the state of the business cycle at the time of the shock. Finally, we check the robustness of our results to using Jorda s (25) Local Projections as an (imperfect) alternative to FAIR. 4.1 Asymmetric Effects of Credit Shocks We first study whether credit supply contractions and expansions have asymmetric effects on the economy. We use a FAIR(2) model two Gaussian functions per impulse response as a likelihoodratio test favors a FAIR(2) over a FAIR(1) or a FAIR(3) (Table 1). A FAIR(2) is particularly relevant here, because it allows us to capture the mean-reverting pattern of output. As an illustration, Figure 4 shows that a FAIR(2) achieves a very good approximation of the linear VAR-based impulse responses, and the right panel also illustrates how the two Gaussian functions are combined to parametrize the impulse responses. This fit to the VAR-based impulse responses is then used as initial guess in our Metropolis-Hastings 17 Specifically, we set the parameters of our FAIR model (the a, b, and c coefficients) to minimize the discrepancy (sum of squared residuals) between the impulse responses implied by FAIR and those implied by the estimated VAR. 1

11 algorithm. We truncate the moving-average process after K = 1 months and use a recursive identification scheme as described in Section 2.2. Allowing for asymmetric effects of credit shocks leads to a large improvement in the goodness of fit of the model. Table 1 summarizes the log likelihood of alternative FAIR models, and we can see that allowing for asymmetric effects substantially increases the log likelihood (comparing columns (1) and (2)). Since the FAIR models are nested, we can compare them with likelihood-ratio tests, and we can reject the symmetric FAIR model in favor of the asymmetric FAIR model. Figure 5 presents the estimated impulse responses of credit supply shocks. The thick lines are posterior mode estimates and the shaded areas cover 9% of the posterior probability, and the thick dashed lines are the VAR-based impulse responses plotted as a benchmark. The left panel shows the impulse responses following a credit supply contraction (an increase in the EBP), and the right panel shows the impulse responses following a credit supply expansion (a decrease in the EBP). When comparing impulse responses to positive and negative shocks, it is important to keep in mind that the impulse responses to expansionary credit shocks (a decrease in the EBP) were multiplied by in order to ease comparison across impulse responses. With this convention, when there is no asymmetry, the impulse responses are identical in the left panel (responses to a contractionary credit shock) and in the right panel (responses to an expansionary credit shock). Credit supply shocks have strongly asymmetric effects. A ontractionary credit supply shock leads to a large decline in output growth while an expansionary shock generates little movements in output growth. Moreover, while the VAR estimate shows a rebound in output growth after two years, the rebound is weaker following a contractionary shock. As a result, the level of output appears to be persistently affected by a contractionary shock (Figure 6). Asymmetry is also present in the response of inflation with only contractionary shocks generating a significant disinflationary episode. Interestingly, the response of the fed funds rate cannot explain the asymmetric responses of output growth and inflation, because monetary policy is more accomodative following a contractionary shock, which should dampen the asymmetry. 4.2 Effects on Other Selected Variables To get a more nuanced perspective on the effects of credit supply shocks on the economy, we now explore the asymmetric impulse response functions of four additional macroeconomic variables: personal consumption expenditures (C), business fixed investment 11

12 (I), the unemployment rate (U), and business investment in research and development (R&D). 18 To study the effects of credit supply shocks on variables not included in y t, we proceed in two steps. First, we extract the structural shocks to credit supply, denoted {ˆε t }, that we identified from our baseline specification. 19 Second, we directly estimate a univariate model - a univariate FAIR - capturing the impulse response of our selected variables. Specifically, denoting y t a variable of interest, we estimate y t = K ψ(k)ˆε t k + u t, (1) k= where ψ captures the impulse response function to the credit supply shock and u t is the residual. Since the u t s are likely to be serially correlated, in order to improve efficiency, we will allow for serial correlation in u t by positing that u t follows an AR(1) process. Then, we use FAIR as in equation (4) to parametrize the impulse response ψ. estimate the model with y set to respectively C, I, R&D and U, and we use a FAIR(2) to have enough flexibility to capture the (potentially) mean-reverting pattern of our variables. We allow for asymmetric effects of credit shocks by estimating two impulse response functions ψ + and ψ, and we estimate a linear FAIR(2) model to use as a linear benchmark. Figure 7 summarizes our results and again shows very asymmetric impulse responses to credit supply shocks. The effect of a credit supply contraction on the levels of consumption, investment, R&D spending, and unemployment is larger than implied by the linear estimates. 2 It is also very persistent, with the responses of consumption, investment, and R&D spending displaying no mean-reverting pattern. In contrast, credit supply expansions have no significant effect on all four variables, and the response of consumption and investment display a mean-reverting pattern. The strong and persistent adverse effect of credit supply contractions on R&D spending is interesting and deserves further exploration. While the response of R&D spending could be driven solely by the strong decline in output, the behavior of R&D also provides a natural link from business cycle fluctuations to long-term economic performance. For 18 We use private domestic investment in research and development. 19 More specifically, the Bayesian estimation of the vector-fair model described by equation (5) and (6) delivers a posterior distribution of the credit shocks {ˆε t}. 2 We obtain the impulse responses of C, I, and R&D from the cumulative impulse responses of C, I, and R&D. We 12

13 instance, it has been argued that adverse transitory shocks that lower R&D spending can inhibit economic performance in the long run (see e.g. Comin and Gertler, 26; Bianchi and Kung, 215). In this context, a decline in R&D spending could cause a persistent decline in output. 4.3 Asymmetric and State Dependent effects of Credit Shocks We now extend our model by allowing the effect of credit supply shocks to also depend on the state of the business cycle. That is, we estimate the vector moving average (5) using a FAIR model with asymmetry and state dependence as in (7). For our cyclical indicator, z t, we use the 12-month centered moving average growth rate of industrial production (see Figure 8). 21 Table 1 shows that adding state dependence to the model significantly improves the goodness of fit, and a likelihood-ratio test favors the model featuring both asymmetry and state dependence against a model with asymmetry only. To visualize how the state of the business cycle affects the response of the economy to credit shocks, Figure 9 shows how the peak responses of output growth and inflation depend on the (annual) growth rate of Industrial Production (IP) at the time of the shock. 22 To better understand the effect captured by Figure 9, it is useful to go back to Figures 2 and 3 and the oscillating pattern of output growth. Following an adverse shock, output growth is initially negative, reaches a low point and then turns positive as output partially reverts to its pre-shock level. In the first row of Figure 9, we plot how that low point in output growth depends the state of the business cycle. The middle row plots a similar relation for the impulse response of inflation. The peak effects of contractionary credit shocks are plotted in the left panels and the peak effects of expansionary credit shocks in the right panels. In addition, the bottom panels of Figure 9 plot the histograms of the distributions of respectively contractionary shocks and expansionary shocks over the business cycle. This information is meant to get a sense of the range of our indicator variable (annual IP growth rate) over which we identify the coefficients capturing state dependence. Our main conclusion is that the the effect of a contractionary credit shocks on output is stronger in recessions, and (ii) contractionary credit shocks always have stronger effects than their expansionary counterparts. Regarding the response of inflation, we find no 21 In our sample, the mean growth rate of industrial production is 2.6% with a standard deviation of 4.1%. 22 To be specific, for a variable i with impulse response ψ i(k, z) at horizon k when the indicator variable takes the value z, we plot the function defined by f i(z) = max ψi(k, z). k [,K] 13

14 significant effect of the state of the cycle. Looking at the left upper panel of Figure 9, we can see that contractionary credit supply shocks have very severe effects on output growth during recessionary periods and milder effects during expansionary periods. The right upper panel shows that an expansionary credit supply shock has also somewhat larger effects in recessions, but the asymmetry between positive and negative shocks is still present and expansionary shocks always have smaller effects than their contractionary counterparts. To illustrate the effects of state dependence from a different angle, Figure 1 shows how the impulse response of output depends on the state of the business cycle. Compared to Figure 9 (focused on the first-round effect of the shock on output growth), Figure 1 plots the cumulative impulse response of output growth, so that we can also visualize how the longer-run effects of a credit shock depend on the state of the cycle. Again, the impulse responses to expansionary credit shocks (right-hand panels) were multiplied by in order to ease comparison across impulse responses. Our main conclusion is that contractionary credit shocks have strong and persistent effects on output during recessionary periods. The top panels show the impulse responses of output to a shock occurring during a recessionary period, i.e. when annual IP growth is -2%. During recessions, contractionary credit shocks have particularly large and persistent effects on output. The posterior probability bands comfortably exclude zero, indicating that output does not revert to its pre-crisis trend five years after the shock. The bottom panels show the impulse responses of output to a shock occurring during a large economic expansion, i.e. when annual IP growth is at 5%. The effects of the credit shock on output are now muted: Credit supply contractions only have a mild effect in the short-run and no longer have a significant adverse effect on output in the longer run. 4.4 Robustness Checks To verify the robustness of our results, we perform a number of checks. We first evaluate whether our results are sensitive to (i) excluding data from the global financial crisis and the period in which the nominal interest rate was at the zero lower bound, (ii) using alternative measures of economic activity, the price level and the stance of monetary policy, and (iii) using alternative identifying restrictions. Finally, we use Local Projections (Jorda, 25) to examine the robustness of our results to the parametrization imposed by the FAIR approach. 14

15 Sensitivity Analysis First, we re-estimate our model excluding data from the global financial crisis and the period in which the nominal interest rate was at the zero lower bound. That is, we estimate our same benchmark specification using data over only. 23 Our key results remain unchanged, and the impulse responses are very similar. The only quantitative difference (not shown) is that the decline in output following a credit supply contraction is somewhat smaller being about.2 percentage points lower in the linear model or in the asymmetric FAIR(2) model. Second, we evaluate whether our results are sensitive to using alternative measures of economic activity, the price level and the stance of monetary policy. To do so, we re-estimate our model replacing IP growth with the unemployment rate; CPI inflation with the GDP deflator, PCE inflation or core CPI inflation; the Wu-Xia shadow rate with the Fed funds rate. We also re-estimate our model using quarterly data in which case we use GDP growth instead of IP growth. We obtain very similar results using these alternative measures and conclude that all our findings are robust to these changes. Third, we test whether our timing assumption is crucial to obtain our results. Recall that to identify credit supply shocks as in Gilchrist and Zakrajsek (212), we assumed that macroeconomic variables react with a lag to credit supply disturbances while the federal funds rate can react contemporaneously, i.e. we ordered the EBP third in y t. We re-estimate our model using two alternative causal orderings: (i) EBP first, i.e. all variables can react contemporaneously to a credit supply shock, and, (ii) EPB last, i.e. all variables react with a lag to a credit supply shock. All results remain similar using these alternative identification assumptions. In particular, we find that even when the EBP is ordered first none of the other variables exhibits a significant contemporaneous response to a credit supply shock. Local Projections To the best of our knowledge, the FAIR approach used in this paper is the only operational way of identifying structural shocks when the Data Generating Process (DGP) is nonlinear with asymmetric impulse responses. However, since our approach relies on the parametrization of the impulse response 23 We do this for two reasons. First, the financial crisis constituted an exceptional disruption in the credit markets, which could be driving our results. Second, after December 28 the federal funds rate no longer captures the stance of monetary policy. While we addressed this problem using Wu and Xia s (214) shadow federal funds rate as our measure of the monetary policy stance, this approach has its own limitations (Krippner, 214). 15

16 functions with Gaussian basis functions, in this section, we examine the robustness of our results to this parametrization. The idea of the robustness check is to not rely on a FAIR but instead to use a nonparametric method Jorda s (25) Local Projections (LP) which imposes little structure on the Data-Generating Process (DGP) and is thus more robust to misspecification than a FAIR model (at the cost of efficiency). The drawback of this approach is that it requires a series of previously identified credit shocks. We thus use an VAR-LP procedure that proceeds in two steps: First, we estimate a standard structural VAR as described in Section 2 to identify structural shocks to the supply of credit, denoted { ε t }. Second, we estimate the dynamic effects of these shocks using Local Projections, possibly allowing for sign-dependence and state dependence. While such a hybrid VAR-LP procedure is flawed (in fact, not internally consistent since the VAR shocks are identified under the assumption that the DGP is linear), we see it as a useful robustness check of our results based on FAIRs. We come back to this point at the end of the section. To first have a linear benchmark for the effects of credit shocks, we run linear Local Projections, i.e. we estimate H + 1 equations y t+h = α h + β h ε t + γ x t + u t+h, h =, 1,..., H (11) where y t+h is the variable of interest, x t contains 12 lags of y t, and ε t is our VARbased estimate of the credit shock at time t. The impulse responses are then given by β, β 1,..., β H. We use an horizon of H = 6 months (or 5 years). We report Newey-West (1987) standard errors allowing for autocorrelation of order h in the error terms. To allow for asymmetric effects of credit shocks, we allow for sign dependence in β h, that is we estimate the H + 1 equations y t+h = α h + β + h ε+ t + β h ε t + γ x t + u t+h, h =, 1,..., H (12) where β + h is the response to a positive credit supply shock ε+ t, and β h is the response to a negative credit supply shock ε t at horizon h. We estimate (11) and (12) for output growth and inflation, and Figure 11 plots the impulse responses. Overall, the results are very similar to the results obtained with FAIR models: the effects of credit supply contractions are larger than implied by linear estimates and highly persistent. Credit supply expansions, on the other hand, have no significant effects on our variables. Quantitatively, we find that our results obtained with FAIR are the more conservative ones, since the hybrid VAR-Local Projection method 16

17 points to even stronger asymmetries. We can also allow for state dependence in the Local Projections. As a cyclical indicator we use NBER recession dates, 24 and we estimate the following H +1 equations: y t+h = α h + β +,R h ε +,R t + β,r h ε,r t + β +,B h ε +,B t + β,b h ε,b t + γ x t + u t+h, (13) h =, 1,..., H where B stands for boom and R for recession. As in Figure 1 with the state dependent FAIR model, Figure 12 summarizes our results by showing how the impulse response of output varies with the sign of the shock and the state of the cycle at the time of the shock. Again, we find that the results are very similar to the results from a FAIR model (Figure 1): the adverse effects of contractionary shocks are very pronounced during recessions but mild during expansions. We conclude from this robustness exercise that a) nonlinearities in the effects of credit supply shocks are important, and b) our previous conclusions on the asymmetric and state dependent effect of credit shocks do not seem to be driven by the parametric restrictions imposed by FAIR. As a final remark, note that while the hybrid VAR-LP approach is attractive because it relies only on standard linear regression techniques, it is flawed for two reasons. First, to perform the Local Projection exercise laid out above, one needs to know the structural shocks. Here, we take the shocks identified from the structural VAR as given. They are, however, the result of a first stage estimation and therefore the standard errors obtained from Local Projections are incorrect. Second, if the data are generated by a nonlinear process, a linear model to identify the structural shocks is misspecified and we cannot estimate consistently the true structural shocks. To do so, one should explicitly account for the nonlinearities in the data-generating process. These two drawbacks can however be overcome with FAIR. Despite its shortcomings, we think of the hybrid VAR-Local Projection approach as a useful tool. First, it can be used as a quick test for nonlinearities in the impulse response functions to shocks estimated from a linear VAR. Therefore, one might see it as (visual) test for misspecification in terms of omitted nonlinearities. Second, once structural shocks are estimated from any model (for instance from a VAR or FAIRs), Local Projections can be used to examine whether relaxing the dynamic structure (i.e., the parametric restrictions) imposed by the model alters the results substantially. 24 We use a binary indicator (instead of a continuous indicator as was the case with FAIRs) for efficiency reasons. 17

18 5 Evidence from Other Countries In this final section, we provide independent evidence that credit shocks have non-linear effects by using alternative sources of variations. Specifically, we study the effects of credit shocks in (i) the United Kingdom (UK) and (ii) the Euro Area (EA). 5.1 United Kingdom While the EBP measure was originally constructed for the US, Bleaney et al. (216) recently constructed EBP measures for some European countries. While the sample size is small for most countries (23Q2-21Q3 or even shorter), the EBP measure for the UK covers 1996Q1-21Q2, offering hope that there might be enough variation to detect non-linear effects of credit shocks. As with the US, our specification uses four endogenous variables: (i) GDP growth (ii) CPI inflation, (iii) the excess bond premium, and, (iv) the Official Bank Rate (OBR) of the Bank of England to measure the stance of monetary policy. y t = [ log(gdp t ), log(cp I t ), EBP t, OBR t ] We use the same identifying assumption as for the US and assume that macroeconomic variables react with a lag to credit supply shocks while the Bank of England s OBR can react contemporaneously. We first estimate an asymmetric FAIR(2) model, and Figure 13 plots our results. The output effects of credit supply shocks are very similar to the ones we obtained for the US: A credit supply contraction leads to a large and persistent reduction in output growth. Credit supply expansions, on the other hand, have no significant effect on GDP. The effect of credit supply shocks on UK inflation is smaller than in the US but the asymmetry goes in the same direction, with only contractionary shocks leading to a disinflationary episode. As with the US, the interest rate declines after an adverse credit supply shock, but not enough to offset the decline in output. Next, we estimate a model with asymmetry and state-dependence. In order to increase efficiency and in light of the small number of observations for the UK, we parametrize the impulse responses with a more parsimonious FAIR(1) model. For our cyclical indicator z t, we use the 4-quarter moving average of GDP growth. 25 Similarly to Figure 9 for the US, Figure 14 shows how the peak response of GDP growth depends on the state of the business cycle at the time of the shock. The results are again consistent 25 In our sample, the mean growth rate of UK GDP is 2.3% with a standard deviation of 2.%. 18

19 with our US evidence. The top left panel shows that contractionary credit supply shocks have a particularly severe effect during recessionary periods, while the effect is more mild during large expansions. In fact, our confidence bands do not exclude that credit supply contractions have no significant effect on GDP growth during large expansions. For expansionary shocks (top right panel), the evidence for state dependence is weak, although the effect seems again to be larger during recessions. Regarding inflation, we find no significant effect of the state of the business cycle (not shown). 5.2 Euro Area To obtain exogenous variations in financial conditions in the Euro Area (EA) over a longer sample than available from Bleaney et al. (216), we use an alternative to the EBP, and we measure credit supply from the spread between the KfW, a German Government-owned development bank whose debt is guaranteed by the Government, and the Bund. This proxy of changes in liquidity conditions was introduced by Monfort and Renne (214). The argument goes as follows: because bonds issued by the KfW have the same credit quality but are less liquid than the Bund, a rise in the KfW-Bund spread signals a rise in the liquidity premium. Monford and Renne (214) show that a rise in the liquidity premium (measured by the KfW-Bund spread) transmits to other EA bond market yields. Therefore, we can interpret a rise in the KfW-Bund spread as a tightening of financial constraints in the EA. Our specification uses four endogenous variables: (i) the KfW-Bund spread (ii) industrial production growth, (iii) CPI inflation, and, (iv) the Euro OverNight Index Average (EONIA). y t = [KfW Spread t, log(ip t ), log(cp I t ), EONIA t ] Similarly to Gilchrist and Mojon (216), we assume that the KfW-Bund spread is contemporaneously independent of changes in private sector credit risk, and we order it first in the system. For the EA, the data are monthly and cover 1997 to As with the US and the UK, we estimate an asymmetric FAIR(2), and Figure 15 plots the estimated impulse responses. In line with our US and UK results, a contractionary credit supply shock causes a significant decline in output growth but an expansionary shock has no sizeable effect. Regarding inflation, we find no significant effect of both contractionary and expansionary credit supply shocks. 26 The KfW-Bund spread data from 1997 to 21 are from Schuster and Uhrig-Homburg (212). We extent this time-series to 213 using data from Monfrot and Renne (214). 19

20 Finally, as for the UK, we estimate a FAIR(1) model with asymmetry and state dependence. For our cyclical indicator z t, we use the 12-month moving average of IP growth rate. 27 Similarly to Figure 9 for the US, Figure 16 shows how the peak response of GDP growth depends on the state of the business cycle at the time of the shock. This time however, we do not find strong evidence of state dependence. The effect of expansionary shock is again larger in recessions (although the credible bands are too large to be conclusive), but we do not detect that contractionary shocks have larger effects in recessions. That being said, most of the useful variation in our EA sample comes from an exceptional time period for the EA (post-27), so that our small-scale model may have a hard time accurately capturing the post-27 period, thereby making the detection of state dependence particularly difficult. With that observation mind, we find it all the more remarkable to be able to confirm the presence of asymmetric impulse responses in the EA data. 6 Conclusion We assess whether credit shocks have nonlinear effects, notably asymmetry and state dependence, that have been predicted theoretically but never considered empirically. We obtain two main results. First, negative shocks to credit supply have large and persistent effects on output, but positive shocks have no significant effect. Second, credit supply shocks have larger and more persistent effects in periods of weak economic growth. These findings are consistent with the presence of occasionally binding financial constraints and provide important empirical support for the predictions of mainstream models of financial constraints. With the existence of nonlinearities established from both a theoretical and an empirical perspective, an interesting avenue for future research is to explore the policy implications of such nonlinearities. For instance, as highlighted in a speech by Federal Reserve Governor Jeremy Stein (214), exploring the implications of the asymmetric effects of financial market disruptions for the conduct of monetary policy is an important goal for research. 27 In our sample, the mean growth rate of EA IP is.2% with a standard deviation of 4.1%. 2