The Macroeconomic Effects of Uncertainty Shocks: The Role of the Financial Channel

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1 The Macroeconomic Effects of Uncertainty Shocks: The Role of the Financial Channel Aaron Popp and Fang Zhang May 20, 2016 Abstract This paper studies the macroeconomic effects of uncertainty shocks with an emphasis on the interaction between elevated uncertainty and credit market conditions when the economy is in different regimes (recessions vs. non-recessions). We use a smooth-transition factor-augmented vector autoregression (ST-FAVAR) and a large monthly panel of U.S. macroeconomic and financial indicators in our estimation. Our findings are twofold. First, while an unanticipated increase in uncertainty has adverse effects on the real economy and financial markets, the effects are quantitatively larger during recessions. Second, the financial channel is important in the transmission of uncertainty shocks, with a greater role during recessions and in the short run. JEL Classifications: E32, E37, E44, C32, C53 Keywords: uncertainty shocks, credit spread, recessions, smooth-transition vector autoregression, dynamic factor analysis 1 Introduction Between 2007 and 2009, the U.S. economy experienced an elevation in uncertainty and one of the most tumultuous financial and economic periods since the Great Depression. It renewed interest Department of Economics, California State University, Fullerton. 800 N. State College Blvd., Fullerton, CA apopp@fullerton.edu. Corresponding author. Department of Economics, California State University, Fullerton. 800 N. State College Blvd., Fullerton, CA fazhang@fullerton.edu. 1

2 among economists in the connection between the real economy and financial markets, and there has been an increasing focus on uncertainty as an important driver of economic fluctuations. This paper investigates the macroeconomic effects of uncertainty shocks with emphasis on the interaction between elevated uncertainty and credit market conditions when the economy is in different regimes (recessions vs. non-recessions). The questions that we ask are: What are the macroeconomic effects of uncertainty shocks? How important is the financial channel in the transmission of uncertainty shocks? Do uncertainty shocks and the financial channel matter differently during recessions? We estimate the impact of uncertainty shocks and the role of the financial transmission channel using a smooth-transition factor-augmented vector-autoregression model (ST-FAVAR) and a large panel of U.S. monthly macroeconomic data. The method allows us to isolate recessions while comprehensively and coherently examining the effects of uncertainty shocks in a data-rich environment. We propose that the common fluctuations of macroeconomic variables can be explained by changes in uncertainty, credit conditions, and several unobservable factors, and that the dynamics of these factors and their influence on the macroeconomy transition smoothly across regimes. To study how important the financial channel is in the transmission of uncertainty shocks, we isolate the effect of uncertainty shocks transmitted through the financial channel using a counterfactual decomposition approach as in Bernanke et al. (1997), Sims and Zha (2006), Kilian and Lewis (2011), and Bachmann and Sims (2012). We have four main empirical findings. First, uncertainty shocks have overall contractionary effects on real economic activity, and they lower interest rates and inflation in the short run. A "bust-rebound-overshoot" is found in many real economic indicators. In particular, uncertainty shocks lead to a significant widening in credit spreads and declines in equity returns, suggesting an adverse effect of uncertainty on financial markets. Second, we find that the effects of uncertainty shocks appear to be quantitatively more important during recessions, suggesting a possible interaction between uncertainty and the state of the economy. Third, we find that the financial channel of uncertainty shocks is more important during recessions, accounting for a greater fraction of the shock s effects during recessions. Fourth, we find that the financial channel matters because the uncertainty shock changes the expected default risk of businesses and the excess premium of corporate bonds, both of which affect businesses decisions and credit conditions, leading to amplified effect on overall economic activity. A decomposition of the financial channel into expected default and excess bond premium reveals that the relative importance of the sub-channels differs in different time horizons. The results provide stylized facts on the regime-dependent ef- 2

3 fects of uncertainty shocks and the financial channel, as well as insights on how and why the financial channel matters for the transmission of uncertainty. Our ST-FAVAR model extends a standard VAR model in two dimensions. First, we incorporate a dynamic factor structure as in Stock and Watson (2002), Bernanke et al. (2005), and Boivin et al. (2009) into our model. As discussed in this literature, incorporating a factor structure into VARs has a number of advantages, including reducing the risk of omitted variable bias, lower sensitivity to the choice of specific data series, and better avoidance of the non-fundamentalness issue discussed in Forni et al. (2009). Second, we incorporate regime dependency in our model to allow the effect of uncertainty shocks to differ between recession and non-recession periods. We model regime dependency following Granger and Terasvirta (1993) and Auerbach and Gorodnichenko (2012), in which the transition across regimes is smooth. One main benefit of using smooth-transition regressions, relative to estimating a model separately for each regime, is that the estimation is less affected by the issue of lacking observations in one regime (e.g. recessions), as the method allows the estimation to be based on a large number of observations by exploiting variations in degree of being in a regime. To estimate the importance of the financial channel in the transmission of uncertainty shocks, we use a counter-factual decomposition approach similar to Bernanke et al. (1997), Sims and Zha (2006), Kilian and Lewis (2011), and Bachmann and Sims (2012). The impulse response of a macroeconomic variable to uncertainty shocks can be broken down into two effects. The first is a direct effect of uncertainty shocks, as uncertainty is proposed to be one of the macro factors that are linked directly to the variable. Second, there is an indirect effect in which uncertainty shocks affect credit conditions and other factors, which in turn influence on the macroeconomic variable of interest. To study the importance of the financial channel in the transmission of an uncertainty shock, we construct hypothetical responses in which the macroeconomic variables react to an uncertainty shock as they would with the indirect effect shut down. We then compare the hypothetical impulse response of the macroeconomic variable to the actual impulse response of the variable. We apply this method to examine the role of the financial channel in the transmission of uncertainty shocks during normal times and recessions. To show how and why the financial channel matters, we decompose the financial channel into the effects that are caused by endogenous change in firms expected default risk and those caused by other factors. Intuitively, an increase in uncertainty increases the perceived riskiness of firms and leads to higher expected loss for lenders. At the same time, higher uncertainty worsens the asymmetric information problem in financial markets, which leads to increase in liquidity 3

4 premium and higher compensation beyond expected loss asked by investors to bear credit risk. Both of the effects lead to worsened credit conditions for firms and subsequent responses of their activities. We study the relative importance of these sub-channels by decomposing the credit spreads and performing the counter-factual approach to isolate the importance of each channel. Our data set includes 141 monthly series of U.S. economic and financial indicators during the period of 1962M7-2014M12. We proxy uncertainty using the Chicago Board Options Exchange VXO index, a measure of implied volatility of stock returns, and we use the Baa corporate- Treasury spread as the measure for credit market conditions. We also consider the realized volatility of stock returns and an uncertainty indicator by Jurado et al. (2015) as two alternative proxies for uncertainty, and the Baa-Aaa corporate bond spread and a measure of credit spread by Gilchrist and Zakraj sek (2012) as alternative measurements for credit spread. The estimation follows a two-step procedure similar to Bernanke et al. (2005) and Boivin et al. (2009) with a recursive identification. Our findings are robust to different identification assumptions, different model specifications, different selections of the transition indicator, and a truncated sample excluding zero lower bound period in interest rates. Our findings are also qualitatively robust to different proxies for uncertainty and different measurements for credit spread. To the best of our knowledge, this is one of the first papers that provides a systematic analysis of the regime-dependent effects of uncertainty shocks and the first to study their regimedependent interactions with financial conditions. The paper is related to two strands of literature. First, it is related to the literature that studies the macroeconomic effects of uncertainty shocks. The existing theoretical literature suggests that uncertainty shocks can be an important source of economic fluctuations (e.g. Bloom (2009), Fernández-Villaverde et al. (2011), Bloom et al. (2012), Basu and Bundick (2012)). The existing empirical studies typically use a linear vectorautoregression (VAR) model, such as Leduc and Liu (2015), and find that uncertainty shocks generally increase unemployment and decrease inflation, acting as "demand shocks". Our first empirical finding corroborates with this literature. But our paper also explores the possibility that uncertainty shocks may have time-varying effects on economic activity, as the impact of uncertainty shocks may depend on the state of the financial market and the economy. Focusing on the labor market, a recent paper by Caggiano et al. (2014) uses a smooth-transition VAR and finds significantly more important effects of uncertainty shocks on unemployment during recessions. We consider a broader set of labor market indicators, along with indicators characterizing other aspects of the macroeconomy and the financial markets, to provide a more comprehensive picture of the regime-dependent dynamics following uncertainty shocks. We also explicitly consider the 4

5 interactions between financial conditions and uncertainty shocks, which Caggiano et al. (2014) do not consider. The paper is also related to the literature that focuses on the effects of financial shocks and the role of changing credit conditions in the transmission of other shocks in the economy. A large and growing literature suggests financial frictions are important in explaining business cycles and in the propagation of other shocks (e.g. Kiyotaki and Moore (1997), Bernanke et al. (1999), Boivin et al. (2013)). More specifically, studies of the impact of uncertainty in the presence of financial constraints suggest that the financial channel is likely to be important in the transmission of uncertainty shocks as changes in uncertainty can raise borrowing costs, which in turn affect real economic activity (Arellano et al. (2012), Gilchrist et al. (2014), Christiano et al. (2014)). The empirical literature that jointly studies uncertainty and financial shocks is relatively limited, but includes Popescu and Smets (2010) and Caldara et al. (2014). Both of the papers use a linear VAR model and do not explore cross-regime differences, consider a smaller set of economic indicators than we do, and use a different approach to quantify the importance of the financial channel. The remainder of the paper is organized as follows. Section 2 presents an overview of our empirical model, describes the data and measurements, and presents our estimation methodology. Section 3 reports our main empirical results. Section 4 performs robustness checks. Section 5 concludes. 2 Econometric Framework We now turn to a description of our econometric framework. Section 2.1 presents our econometric model. Section 2.2 describes the data and measurements. Section 2.3 provides details on the identification and estimation strategy. Section 2.4 presents the method to isolate the role of the financial channel in transmitting the uncertainty shocks. 2.1 Empirical Model We employ a smooth-transition factor-augmented vector-autoregression (ST-FAVAR) to analyze the regime-dependent effects of uncertainty shocks on the macroeconomy. We augment the smoothtransition vector autoregression (ST-VAR) by Auerbach and Gorodnichenko (2012) with a dynamic factor structure as in as in Stock and Watson (2002). This augmentation allows us to examine the regime-dependent dynamics of a large set of macroeconomic and financial variables, and 5

6 the estimates are less affected by omitted variable bias and dimensionality problem of standard regime-switching VARs. As discussed in Koop and Potter (1999) and many others, it is difficult for VARs to deliver stable estimates with a large number of endogenous variables, especially when there is time variation in the parameters. But low-dimensional VARs are less likely to consider full information and lead to contaminated measures for shocks and transmission mechanisms 1. Our model is specified as follows: X t = f (z t 1 )Λ R C t + (1 f (z t 1 ))Λ NR C t + e t, (1) C t = f (z t 1 )Π R (L)C t 1 + (1 f (z t 1 ))Π NR (L)C t 1 + u t, (2) u t N(0, Ω t ), (3) Ω t = f (z t 1 )Ω R + (1 f (z t ))Ω NR, (4) e t N(0, Σ), (5) f (z t ) = exp( γz t ) 1 + exp( γz t ), γ > 0, var(z t) = 1, E(z t ) = 0. (6) X t is a N 1 vector of macroeconomic variables entering the data set, where N is large. We assume that X t is affected by a (K + 2) 1 vector of macroeconomic factors C t and that the influence of factors is regime-dependent. As we will be interested in characterizing the effect of uncertainty shocks and the role of credit spread in the transmission of the shocks, we let C t include a measure of uncertainty, U, a measure of credit spread, Spd, and a K 1 vector of unobservable factors, F, that captures other macroeconomic dynamics, i.e. C t = [F t, Spd t, U t ] 0. z is a transition indicator. f (z t 1 ) is a logistic transition function that captures the probability of being in recessions (R) versus non-recessions (NR), whose smoothness is characterized by γ. Λ R and Λ NR are N (K + 2) matrices of factor loadings for regime R and NR. e is a N 1 series-specific error vector that has mean zero and is uncorrelated with C t. We allow e to be weakly correlated across series. Equations (2) - (4) characterize the dynamics of factors and resemble a smooth-transition vectorautoregression (ST-VAR) as in Auerbach and Gorodnichenko (2012) with the regressors being the factors. Π R (L) and Π NR (L) are regime-dependent lag polynomials of finite order d. u is a vector of reduced-form residuals with mean zero and time-varying, regime-dependent covariance matrix Ω t. Ω R and Ω NR are the covariance matrices of the residuals computed during recession and non-recessions respectively. 1 For a general discussion on this issue, see Boivin et al. (2009) and Forni et al. (2009). For an illustration of misidentification of uncertainty shocks in a small-scale VAR, see Knotek and Khan (2011), which shows that adding additional variables to VARs leads to a different effect of uncertainty shocks on household consumption from a bivariate VAR. 6

7 Intuitively, the model assumes that the dynamics of X can be described by a linear combination of two linear FAVARs: one suited to describe the dynamics during recessions, and the other suited to describe the dynamics during expansions. f (z), bounded between 0 and 1, characterizes the degree of economic contraction or simply the probability of being in the recession regime given observations of z. Small values of z during economic stress translate into large values of f (z) near 1, resulting in a heavier weight of the recession-regime FAVAR in the characterization of the data in these periods. The model nests a standard linear FAVAR in the limiting cases when f (z) = 0 or f (z) = 1. The model specified by equation (1) - (6) allows three ways for differences in the propagation of structural shocks across regimes to occur: contemporaneous difference via differences in covariances matrices Ω R and Ω NR, dynamic difference via differences in lag polynomials Π R (L) and Π NR (L), and difference via differences in factor loadings Λ R and Λ NR. Our baseline ST-FAVAR features five lags and five factors. Our results are robust to reasonable variations of the number of lags and the number of factors. We performed a similar test for nonlinearity as in Auerbach and Gorodnichenko (2012) that uses of a second order approximation to equation (1) - (6) using lags of C t, C t z t, and C t z 2 t. Akaike and Bayesian information criteria favor a nonlinear specification in describing the dynamics of X t Data and Measurement The data set used in our estimation is a panel of 141 monthly series for the period of 1962M7-2014M12. The data set extends the FRED-MD data set of McCracken and Ng (2015) by adding selected series of uncertainty proxies, credit spreads, and disaggregated personal consumption. The data set includes various measures of output, employment, consumption, prices, interest rates and other key macroeconomic and financial variables in the United States. We transform the data to induce stationarity. Appendix A provides details on the data and the transformation applied to each series. We follow Bloom (2009) and use the Chicago Board Options Exchange Market Volatility Index (VXO) as our measurement for uncertainty in the baseline analysis. The VXO index measures the implied volatility of the S&P 100 index options, reflecting market expectations of stock market volatility over the next 30-day period. The index is available 1986 onward. To obtain the pre AIC = and BIC=-3.82 for a nonlinear model with 5 lags and 5 factors, while AIC = and BIC=-3.68 for a linear model with equal number of lags and factors. The test, however, does not address a particular form of the nonlinear specification. 7

8 data, we compute the actual monthly standard deviation of the daily S&P 500 index normalized to the same mean and variance as the VXO index when they overlap from 1986 onward, a practice similar to Bloom (2009). There are, however, many alternative measures for uncertainty. The realized volatility of stock market returns is used as proxy for uncertainty in Leahy and Whited (1996). Jurado et al. (2015) (JLN) construct a measure of macroeconomic uncertainty by exploring the common variation in forecast errors of a large number of economic indicators. Bachmann et al. (2013) consider cross-sectional dispersion of survey-based forecasts (FDISP) constructed using the Federal Reserve Bank of Philadelphia s Business Outlook Survey. Baker et al. (2013) (BBD) develop a news-based economic policy uncertainty index. It should be noted, however, though these uncertainty measures are correlated with each other to various degrees, they are somewhat distinct measures and have diverse characterizations of uncertainty during non-recession periods. Figure 1 plots the VXO index along with other measures of uncertainty. Figure 1 goes here. From Figure 1, all measures of uncertainty increase significantly during major post-wwii recessions ( , , ), and have strong comovements in the same direction. However, NBER expansionary periods see a mix of behaviors among these uncertainty measures. For example, the measure by Jurado et al. (2015) has only three large spikes in uncertainty, all occur during recessions, and no major change in uncertainty occurs during expansions. The marketvolatility-based measures, however, document spikes in recessions as well as a few episodes of expansions when there was significant turbulence in the stock market caused by major political, financial and economic events (e.g. JFK assassination and "Black Monday" in 1987). As there is little consensus on which is the best measure of economic uncertainty, given the diverse characterizations of behavior among the uncertainty proxies and the possibility of having contaminated information about the effect of economic uncertainty during expansion periods, we focus our analysis on the effect of uncertainty shocks during recessions and contrast the results to those predicted by a linear model, which describes a mixed effect of uncertainty shocks during expansion and recessions. Focusing on recession periods makes the analysis less sensitive to the choice of uncertainty proxy. We use implied stock market volatility (VXO index) in the baseline analysis and consider the measure by Jurado et al. (2015) and the realized volatility of S&P 500 in the robustness checks. We use corporate bond credit spreads to measure strains in financial markets. A large litera- 8

9 ture suggests that credit spreads are a class of highly informative financial indicators about the tightness of credit conditions and future economic activity. 3 We use the monthly spread between Moody s 30-year Baa-rated corporate bond yield index over the 30-year Treasury bond yield in our baseline analysis 4. We also consider the credit spread measure by Gilchrist and Zakraj sek (2012) (1973M1-2012M12), which is constructed based on a broad set of individual corporations bond prices rather than on aggregate credit spread indices, and the monthly spread between Moody s 30-year Baa-rated and Aaa-rated corporate bond yield to check robustness of our results. Figure 2 plots the credit spread measures. Figure 2 goes here. The transition variable z and transition probability f (z) play a key role in the model. Auerbach and Gorodnichenko (2012) and Bachmann and Sims (2012) model z using a standardized backward-looking 7-quarter moving average of the growth rate of real GDP in their quarterly smooth-transition models. Similarly, we model z to be a 12-month moving average of the Industrial Production Index, normalized to have mean zero and rescaled to have unit variance. We calibrate γ = 2 so that the economy spends about 15 percent of the time in recessions, defined as periods when f (z) 0.8, same as the NBER business cycle dates in our sample period. Figure 3(a) plots f (z). It is clear that the values of f (z) are highly correlated with NBER business cycles and f (z) 0.8 roughly replicates NBER recession episodes. In a robustness check, we consider an alternative indicator that is constructed using 21-month moving average of Industrial Production with γ = 1.4 to produce same duration of recession periods, plotted in Figure 3(b). Figure 3(a) and Figure 3(b) go here. 2.3 Estimation and Identification We follow a two-step estimation method similar to Bernanke et al. (2005) and Boivin et al. (2009). In the first step, the macroeconomic factors C t are estimated using principal components. As 3 A large and growing empirical literature (e.g. Gertler and Lown (1999); Gilchrist et al. (2009); Gilchrist and Zakraj sek (2012); Boivin et al. (2013); Faust et al. (2013)) shows that corporate bond credit spreads form the most informative and reliable class of financial indicators for future economic activity and that changes in credit spreads have large and persistent macroeconomic effects. 4 Following Bachmann et al. (2013), in the months when 30-year Treasury bond yield is not available (prior to 1977M2 and between 2002M2 and 2006M2), we use the 20-year Treasury bond yield instead. There are minor differences between 20-year and 30-year Treasury yield in periods when both series are available, and none of the replacements occur in recession periods. 9

10 shown in Stock and Watson (2002), when N is large and the number of principal components used is at least as large as the true number of factors, the principal component estimates Ĉ t consistently recover the space spanned by C t, even with breaks or time variation in the coefficients. We propose uncertainty (U t ) and credit spread (Spd t ) as two observable factors, and the estimates of the unobservable factors ˆF t are obtained as the part of Ĉ t that is not covered by U t and Spd t. In the second step, equations (2) - (4) are estimated as a smooth-transition reduced form VAR, with F t replaced by ˆF t. Using the principal component estimates is computationally easier and does not require strong distributional assumptions as in the alternative likelihood-based procedures 5. We follow a similar procedure as in Bernanke et al. (2005) to account for the uncertainty in factor estimation arising from the generated regressors problem in the impulse responses. The identification of equation (1) follows similar practice as in Bernanke et al. (2005) s first step estimation. We restrict FF 0 /T = I and let ˆF = TẐ, where Ẑ are the eigenvectors corresponding to the K largest eigenvalues of XX 0. The identification of exogenous variations in uncertainty in equation (2) is obtained by imposing the Cholesky assumption. As we restrict the order of the variables in C t to be [F t, Spd t, U t ] in our baseline analysis, it is assumed that uncertainty shocks affect the unobservable macro factors and credit spread with a 1-month delay. The ordering allows us to examine the role of uncertainty shocks conditional on the current condition of the credit market. Though using a recursive assumption is common in the literature 6, there is little consensus on the ordering given the endogenous nature of the variables. Bloom (2009) assumes that uncertainty is a slow-moving variable compared to S&P 500 index but is fast-moving compared to interest rate, prices, employment, and production, while Caggiano et al. (2014) and Leduc and Liu (2015) assume uncertainty is slow-moving and can have contemporaneous effects on inflation, unemployment, and interest rates. Furthermore, the relative ordering between U t and Spd t is debatable. To address this concern, we favor data of higher frequency in our estimation and consider an alternative ordering of C t = [F t, U t, Spd t ] 0 and C t = [U t, F t, Spd t ] 0 in our robustness checks. We do not find our results qualitatively sensitive to alternative ordering and short-run timing assumption. Given the nonlinearity of the model, we estimate it using the Markov-Chain Monte-Carlo (MCMC) simulation method proposed by Chernozhukov and Hong (2003). Appendix B reports 5 Stock and Watson (2002) justify using ˆF t as regressor without adjustment when N and T are large. Bai and Ng (2006) show that when T and N are large but p T/N is small, using principal component estimators as generated regressors in dynamic factor models yields consistent estimates. Bernanke et al. (2005), which considers a linear FAVAR, show that a one-step Bayesian likelihood-based and two-step principal component procedures perform similarly in their estimation. 6 e.g. Bloom (2009), Caggiano et al. (2014), Leduc and Liu (2015). 10

11 the technical details of the estimation methodology. The method finds a global optimum for model fit under standard conditions and allows for straightforward computation of parameter estimates and confidence intervals. As the model is linear conditional on a regime, absent any feedback to z t, the impulse responses to an uncertainty shock can be computed by assuming a linear VAR conditional on regime-specific parameter estimates Isolating the Role of Financial Channel We study the importance of the financial channel in the transmission of uncertainty shocks. This section presents the methodology for isolating the role of the credit spread, an indicator of financial conditions and an observable factor in the transmission of shocks. In the model summarized by equations (1) - (6), uncertainty shocks affect X in two ways. First, uncertainty shocks directly affect X. As U is restricted to be one of the macroeconomic factors linked to X according to equation (1), a change in U leads to a direct change in X. Second, uncertainty shocks also have an indirect effect on X. Uncertainty shocks affect unobservable factors F and the credit spread Spd according to (2). As X is also affected by these factors, some effect of the shocks are transmitted indirectly to X. Spread matters here in the transmission of shocks. To study how important the systematic response of the credit spread is, we construct a hypothetical impulse responses of X in which X and F react to an uncertainty shock as they normally would with the endogenous response in credit spread shut down at all horizons. Intuitively, it can be thought of as considering a hypothetical economy with an identical underlying economic environment, except that the uncertainty shocks are restricted not to move the credit spread at any horizon. As the spread remains fixed in this hypothetical case, the shock does not transmit through the spread to F or X. The importance of the credit spread can thus be isolated by comparing the hypothetical impulse responses to the actual responses. The method is similar to the one used in Bernanke et al. (1997), Sims and Zha (2006), Kilian and Lewis (2011), and Bachmann and Sims (2012). Specifically, we consider the VAR system of our model, conditional on a particular 7 We perform a robustness check in Section 4 that accounts for the feedback effect by endogenizing z. 11

12 regime: A (s) F 1,t F 2,t F 3,t Spd t d = A (s) j j= F 1,t j F 2,t j F 3,t j Spd t j ε 1t ε 2t ε 3t ε 4t, s = NR, R (7) 7 5 U t U t j ε 5t where s = NR and s = R are regime indicators for non-recessions and recessions. Parameters with superscript (s) indicate the parameter estimates conditional on the regime. ε t = [ε 1t, ε 2t, ε 3t, ε 4t, ε 5t ] 0 is a vector of structural shocks and given by ε t = A (s) 0 u t where A (s) 0 is a lower-triangular regimedependent impact matrix. More compactly, equation (7) can be rewritten in companion matrix form as VAR(1) by defining Z t = [C t, C t 1,..., C t d 1 ] 0, where C t = [F 1t, F 2t, F 3t, Spd 0 t, U t] 0. Z t = Φ (s) Z t 1 + ψ (s) t, Φ (s) = (s) -1 A 0 A s 1 A (s) -1 0 A (s) A I (s) -1 0 A (s) d 0 I I , ψ (s) t = (s) -1 A 0 ε t Let e i be a 1 (K + 2) selection row vector with a one in the i th place and zeros elsewhere. Let (s) -1 A (s) -1 0 (q) be the q th column of A 0. The impulse response of factor i to a structural shock q at horizon h in regime s is δ (s) i,q,h = e iφ (s) h 1 (s) -1 A 0 (q). The construction of hypothetical impulse responses to fix the spread response at all horizons requires restricting δ (s) 4,5,h = 0, for any h = 1,..., H, where 4 is the position indicator of Spd t and 5 is the position indicator of U t. This is achieved by creating a sequence of hypothetical shocks to the spread f ε (s) 4,h g h=1,...,h so that δ (s) 4,5,h = 0 in response to a unit shock in ε 5,1 in all horizon. To shut down the contemporaneous effect of U on the spread on impact, ε (s) 4,1 must satisfy (s) -1 A (s) -1 0 (4, 5) + A 0 (4, 4) ε (s) = 0, or ε(s) 4,1 4,1 = A(s) -1 The subsequent credit spread shocks can be computed recursively as 0 (4, 5) (s) -1 A 0 (4, 4). ε (s) 4,h = δ (s) h 1 4,5,h + j=1 e 4 Φ (s) h j (s) -1 A 0 (4) ε (s) 4,j (s) -1 e 4 A 0 (4), h = 2,..., H. 12

13 Given ε 5,1 = 1 and f ε s 4,h g h=1,...,h, we can construct the hypothetical impulse responses of the factors in the VAR system to the uncertainty shock as δ (s) h i,5,h = δ(s) i,5,h + e i Φ (s) h j (s) -1 A 0 (4) ε (s) 4,j, i = 1, 2,..., K + 2. j=1 The response of the macroeconomic variables in this hypothetical case is thus given by δ (s) K+2 x,5,h = i=1 Λ (s) (i) δ (s) i,5,h. Comparing δ x,5,h to the baseline response of X to a one unit shock in U characterizes the importance of the credit spread in transmitting the effect of the uncertainty shock. 3 Results This section presents the main results from our baseline linear FAVAR and ST-FAVAR models conditional on recessions. Section 3.1 presents the results for the effects of uncertainty shocks, jointly with changes in credit conditions, during recessions and contrasts them with the predictions under a linear FAVAR model 8. The section also discusses the associated forecast error variance decompositions. Section 3.2 describes the results concerning the importance of the financial channel in the transmission of uncertainty shocks during recessions and normal times. The next section provides more robustness results from additional specifications and alternative measurements. We could in principle plot the impulse responses of all variables included in the panel of X t, but we will focus on a subset of economic and financial indicators of interest. In all cases, the impulse is a unit shock to uncertainty. 8 There are two reasons for this practice. First, comparing the results to those under a linear model allows us to directly infer the importance of nonlinearity. Second, we focus on recessions rather than expansions, because recession episodes carry cleaner information about uncertainty shocks, while expansion episodes are characterized by heterogenous signals and diverse behavior across different uncertainty proxies. As discussed in Jurado et al. (2015), spikes in market volatility-based uncertainty proxies during expansions possibly carry little information regarding changes in economic uncertainty. To avoid this possible issue, we report our results under recessions and compare them to those predicted by a linear model, which describes a mixed effect of uncertainty shocks during different phases. This practice is similar to Caggiano et al. (2014). 13

14 3.1 Uncertainty and Economic Activity Figure 4(a) and 4(b) report the impulse responses of 32 variables in the baseline linear FAVAR and ST-FAVAR conditional on the recession regime. 9 The solid lines show the median impulse responses of the variables in "normal" economic times, predicted in our linear FAVAR that does not distinguish the behavior between recession and non-recession periods. The red dashed lines show the median impulse responses of the variables in recessions. The shaded bands are one-standarddeviation confidence intervals of the impulse responses under the linear model and under the ST-VAR model conditional on recessions. Table 1 summarizes the maximum impact within 12 months and the cumulative impact of uncertainty shocks up to 6 months and 12 months on selected variables in the two baseline specifications. Table 1 goes here. An unanticipated increase in uncertainty induces adverse effects on real economic activity in general, with the effects much stronger in recessions. A "bust-rebound-overshoot" pattern is observed in many production, labor market, and consumption series. In addition, uncertainty shocks are associated with declining interest rates, increasing money growth, increasing credit spread, declining lending, and falling stock returns. Uncertainty shocks appear to have shortterm negative effects on inflation, but inflation increases and overshoots at longer horizon Output, Employment, Consumption and Order On the real side, output, employment, consumption, and orders change little on impact but then fall sharply in subsequent months. The maximum impact on real economic activity occurs within 12 months after the shock. A bust-rebound followed by an overshoot is found for many of the real variables in both recession and non-recession periods. Comparing the impulse responses across regimes, we find a greater real effect of uncertainty shocks in the short run and more rapid 9 The series are transformed according to the transformation code provided in Appendix A to ensure stationarity, then normalized to have zero mean and unit variance over the full sample, before entering the estimation. For the variables with transformation code 1-5, the reported responses are the responses of the transformed series without further adjustments. For example, the response of IP, with transformation code 5 (first order log difference), is reported in terms of the standard-deviation change of the first log difference of IP, and the response of the federal funds rate,with transformation code 2 (first difference), is reported in terms of the standard-deviation change of the level difference in the interest rate. For the variables with transformation code 6 (second order log difference), including hourly earnings, money supply, prices, and loans, the responses in second order log difference are transformed into the first order log difference responses of the variables to allow for more straightforward interpretations of the results. 14

15 recovery at longer horizons during recessions. The differences between regimes are statistically and quantitatively significant for the majority of the real series. Figure 4(a) goes here. Among the production series, industrial production (IP) growth responds quickly to the unanticipated increase in uncertainty in our linear model, with the maximum adverse impact of 0.20 standard-deviation (SD) below trend about 4 months after the shock before returning to its initial level. A statistically significant overshoot in IP occurs after 20 months. In recessions, IP growth responds with a larger magnitude of 0.26 SD, and an overshoot occurs 4 months earlier. A similar pattern, including the cross-regime differences, is found in other production and income series, including the production of durables, the production of business equipment, real personal income, and capacity utilization. For the labor market, uncertainty shocks that occur during recessions have overall greater but less persistent contractionary effects, and are associated with more prompt recoveries. In the short run, an unanticipated shock in uncertainty lowers the help-wanted index, labor force, employment, average weekly hours, and average hourly earnings, while it increases the unemployment rate and the median duration of unemployment, suggesting a weakened labor market overall. Overshoots are observed at a medium-long horizon for the help-wanted index, employment, unemployment rate, and hours, but uncertainty shocks do not appear to induce overshoots in the recovery of the labor force and unemployment duration. Average weekly hours decline sharply in the short run following an uncertainty shock, but the pattern differs qualitatively from other labor market indicators in the sense that the uncertainty shock has only a brief contractionary effect on hours followed by a long-lasting rebound and overshoot, especially during recessions. For average weekly hours and the unemployment rate, uncertainty shocks appear to have a similar peak effect but are more transient during recessions. The similar peak response of the unemployment rate but a greater peak response in employment during recessions can be reconciled by a proportionally larger effect of uncertainty shocks on employment and the labor force across regimes. The similar peak response of hours across regimes but a greater peak response in employment during recessions reveals that a fraction of firms may not change their workers hours significantly during recessions, in order to partially compensate for a significantly decreasing number of workers, suggesting a relatively larger impact of uncertainty shocks on the extensive margin than the intensive margin during recessions. 15

16 For the consumption and orders series, an uncertainty shock has adverse effects in the short run, especially during recessions. For example, real personal consumption expenditures growth falls about 0.12 SD maximum in the linear model and 0.21 SD maximum in recessions, with the maximum impact within 6 months in both regimes. The growth of housing starts falls by a maximum of 0.19 SD and 0.35 SD in normal and recession periods respectively. We also find that permits and real estate loans decline in the short run after the shock, which reflects a weaker housing market overall, especially in recessions. A statistically significant overshoot is also observed in real personal consumption expenditures, durable goods consumption, NAPM index, and new orders. Table 1 reports the maximum and cumulative response of the selected variables to the unit shock in uncertainty predicted by our baseline linear FAVAR and ST-FAVAR conditional on the recessions respectively. For many of the real variables, we find the uncertainty shock has a more than 30 percent greater maximum impact during the identified recession periods, and overshoots, when observed, occur a few months sooner during recession periods Money, Interest Rates, Prices, and Financial Markets On the nominal and financial side, a rise in uncertainty leads to a sharp decrease, 0.46 SD in the linear model and 0.53 SD in recessions, in the growth of S&P 500 returns on impact and a gradual recovery in subsequent months. The effect of uncertainty shocks on the stock market is greater on impact and shorter-lived in recessions than in normal times. It takes nearly 12 months for the S&P 500 to return to its trend in recessions but 20 months in normal times. The drop in the stock market implies a substantial decline in household wealth, which might partially contribute to the decline in overall consumption discussed above. The contractionary uncertainty shock appears to elicit an easing of monetary policy. The federal funds rate falls below trend for a duration exceeding 24 months while the growth rates of money stock M1 and M2 both increase persistently for more than 48 months. Recession periods see greater changes in interest rates and money supply elicited by the rise in uncertainty. Inflation falls initially in response to the unanticipated rise in uncertainty, but the disinflation effect is brief, lasting for less than 10 months in normal times and 20 months in recessions, which might be the result of the long-lasting offsetting monetary policy and the recovery of real economic activity in the medium run. The unanticipated rise in uncertainty also widens the credit spread. The spread between long- 16

17 term Baa-rated corporate bonds and Treasury bonds of similar maturity increases by a maximum size of 0.20 percent in normal times and 0.34 in recessions. Overshooting is observed for many series of spreads, including Baa-Treasury and Baa-Aaa, and it occurs earlier in recessions. An increase in credit spreads increases borrowing costs for firms and households, making investments and purchases more expensive, which also contributes to the decline in real economic activity. Figure 4(b) goes here Variance Decomposition To study the quantitative contribution of uncertainty shocks to macroeconomic fluctuations, Table 2 reports 48-months ahead forecast error variance decomposition for selected macroeconomic variables under ST-FAVAR conditional on recessions and compares them with the decompositions when we use a linear FAVAR 10. Table 2 also contains the fraction of the variability of the series explained by the common fluctuations, i.e., the R 2 result of equation (1) for the selected variable. Table 2 goes here. Under linear FAVAR, uncertainty shocks explain a moderate share of the fluctuations in macroeconomic variables. For example, uncertainty shocks are responsible for 3.2 percent of the fluctuations in industrial production, 6.1 percent in unemployment, 11.9 percent in unemployment duration, 9.9 percent in personal consumption, 3.5 percent in CPI inflation, and 8.0 percent in the Baa-Treasury spread. 11 But conditional on recessions, uncertainty shocks contribute much more in the fluctuations of some variables. In recessions, uncertainty shocks are responsible for 4.9 percent of the fluctuations in industrial production, 30.5 percent in unemployment duration, 10.7 percent in personal consumption, 6.5 percent in CPI inflation, and 11.5 percent in the Baa- Treasury spread. Out of the 28 variables reported in Table 2, uncertainty shocks account for a larger fraction of fluctuations in 24 variables during recessions. The cross-regime difference in our variance decomposition of unemployment is qualitatively similar to Caggiano et al. (2014), who uses a small-scale ST-VAR model to find that uncertainty shocks explain much more of the 10 The variance decompositions are computed for the transformed series. For example, the variance decomposition of IP is the variance decomposition of the first log difference of IP. 11 For reference, monetary shocks are estimated to be responsible for 7.6 percent fluctuations in industrial production, 5.4 percent in personal consumption, 12.6 percent fluctuations in unemployment, according to the linear FAVAR results by Bernanke et al. (2005). 17

18 fluctuations in unemployment during recessions. However, our estimations of the contribution of uncertainty shocks are significant lower than Caggiano et al. (2014). The quantitative difference is mainly explained by the difference in our methodology. Compared to a small-scale VAR, our factor-augmented approach is less likely to overestimate the importance of uncertainty shocks due to omitted variables Discussion Our findings from the linear FAVAR are in general consistent with the existing literature on the effect of uncertainty shocks. For example, Leahy and Whited (1996) considers a panel of individual US publicly listed firms and finds a strong relationship between uncertainty, proxied by stock-price volatility for the firm, and investment. Bloom (2009) uses a linear VAR and finds negative effects of uncertainty shocks (proxied by VXO) on industrial production and employment with the maximum impact occurring within 12 months. Leduc and Liu (2015) also uses a linear VAR but considers an alternative uncertainty proxy based on consumer perceived uncertainty from Thomson Reuters/University of Michigan Surveys of Consumers along with the VXO proxy. They find that uncertainty shocks act in a similar way as negative "demand shocks" that temporarily increase unemployment while decreasing inflation. By considering a more broad set of economic indicators, we find similar contractionary effects following an unanticipated increase in uncertainty, but among some economic indicators the effect differs qualitatively. In addition, by exploring the role of nonlinearity, we also document that such contractionary real effects are more important during recessions. Our results also shed light on why uncertainty shocks matter. First, the real option mechanism of uncertainty shocks proposed by Bloom (2009) is likely to explain a significant part of the real effects of uncertainty shocks. The idea of the real option mechanism is that when firms face nonconvex adjustment cost in investment and hiring, an increase in uncertainty increases the option value to delay making a decision on these activities. Firms want to avoid making mistakes that are expensive to reverse. Similarly, consumers may become more cautious in making big ticket item purchases during periods of high uncertainty and postpone their consumption. As a result, the reduction in consumption, investment, hiring, and productivity, caused by nonoptimal allocation of resources, provides an explanation for the negative impact of uncertainty shocks on real economic activity. Consistent with this intuition, we find larger declines in the consumption and pro- 12 As recognized by Caggiano et al. (2014), adding S&P 500 into their ST-VAR significantly reduces the importance of uncertainty shocks in explaining the fluctuations of unemployment. 18

19 duction of durables than nondurables, and in employment than hours. Unemployment duration also increases after the elevated uncertainty. The bust-rebound-overshoot dynamics are observed for many production, labor market, and consumption series, and appear stronger for series that feature greater adjustment frictions and irreversibility, such as the consumption of durables, purchase of business equipments, and employment. We also find greater effects of uncertainty shocks during recessions. Intuitively, the real option mechanism may be stronger during recessions when large uncertainty shocks may occur, along with lower sales, lower income and less job security, making firms and households even more cautious. Second, we also find the financial channel can be potentially important for the transmission of uncertainty shocks, consistent with the literature that includes Christiano et al. (2014) and Gilchrist et al. (2014). As shown in Stock and Watson (2003), Gilchrist et al. (2009), Boivin et al. (2013) and many others, changes in credit spreads lead to fluctuations in economic activity. Meanwhile, fluctuations in credit spreads can be attributed to changes in uncertainty. We find that credit spreads widen significantly following an uncertainty shock, suggesting a tightening of credit conditions. Tightening credit conditions then affect firms and households, postponing and/or reducing their investment and large expenditures, and reducing overall macroeconomic activity. As stress in the financial markets is likely to be more severe when the economy is in a recession, uncertainty shocks would have more significant macroeconomic effects if much of the effects are transmitted through the financial channel. Section 3.2 performs an exercise to examine the importance of the financial channel of uncertainty shocks. 3.2 The Financial Channel of Uncertainty Shocks The results from the previous section suggest that changes in credit conditions may play an important role in the transmission of uncertainty shocks. To quantify the importance of credit conditions, we use the method introduced in Section 2.4 to shut down the indirect effect on macroeconomic variables caused by changes in the credit spread as a result of the uncertainty shock Does the Financial Channel Matter and How Much Does It Matter? Figures 5(a) and 5(b) report the impulse responses of the macroeconomic variables after the financial channel is shut down, and compare them to the unrestricted impulse responses under a linear FAVAR specification. The solid black lines plot the actual impulse responses in an unrestricted linear FAVAR, and the dashed blue lines plot the responses after the indirect effect of credit spread 19

20 is removed, i.e. credit spread is restricted to be fixed at all horizons in response to the uncertainty shock. Figures 6(a) and 6(b) report the results under the ST-FAVAR specification conditional on recessions. The solid red lines plot the actual unrestricted impulse responses under recessions. The dashed green lines plot the impulse responses after we remove the indirect effects of the credit spread. The difference between the unrestricted response and restricted response provides a measure of the indirect effect on the variable transmitted through the financial channel. Table 3 presents the maximum and cumulative impacts of the impulse responses in the restricted case for both specifications. Table 3 goes here. Under the linear specification, the financial channel appears to have limited importance in the transmission of uncertainty shocks into many of the income, consumption, interest rate, and price indicators. Removing the indirect effect transmitted by credit spreads on these indicators has only a small effect, as the actual responses to an uncertainty shock are very similar to the ones when the credit spread is held fixed. Exceptions are durable goods production and purchase and a few labor market indicators for which the financial channel appears to matter more in the short run. For example, the 12-month maximum responses drop for the growths of IP business equipment, unemployment duration, and housing starts by percent after removing the indirect effect transmitted by changes in credit spread. Figure 5(a) and Figure 5(b) go here. Though the financial channel appears to play a limited role in normal economic times, it is more important during recessions. In Figures 6(a) and 6(b), the dynamic responses of a majority of the variables in recessions exhibit noticeable differences after the indirect effect caused by the endogenous response in the credit spread is removed. Though the qualitative impacts remain in most of the series, the magnitude is greatly reduced in the short run, and the response becomes more persistent at longer horizons. For example, removing the indirect effect of the credit spread leads to a 50 percent reduction in the maximum impact of uncertainty shocks and an overshoot that occurs 5 months later. The results have two implications. First, changes in credit market conditions greatly amplify the effect of uncertainty shocks in recessions and move much of the effect into the short-run, making the contractions sharp but brief. Second, though the financial channel is important in the transmission of uncertainty shocks during recessions, it is not the 20

21 exclusive channel for uncertainty shocks to matter. This result is somewhat different from Caldara et al. (2014) who find that financial shocks have significant adverse effects on economic activity after they control for uncertainty shocks, while uncertainty shocks have meaningful effects on economic activity only when including the financial channel. We find that uncertainty shocks have significant macroeconomic effects in both regimes after we restrict changes in credit spread, suggesting that other transmission mechanisms, along with the financial channel, are important to account for the significant macroeconomic effects of uncertainty shocks. The difference between our results and those of Caldara et al. (2014) may be caused by differences in our approach and differences in the proxy for uncertainty and credit spread. Once we use their measurements of credit spread and uncertainty proxy (spread constructed by Gilchrist and Zakraj sek (2012) and realized volatility of stock returns), the financial channel becomes more important, eliminating the effect of uncertainty shocks in the medium-long run, but uncertainty shocks remain important in the short run after the financial channel is removed. Figure 6(a) and Figure 6(b) go here. In Section 4, we use alternative measures of uncertainty, alternative measures for the credit spread, and alternative model specifications to examine the robustness of our results. Despite the large difference in the measurements and model assumptions, the predictions are qualitatively robust How does the Financial Channel Matter Credit spreads are used as a gauge of the degree of the stress in the financial system, and endogenous movements in credit spreads can propagate the effects of uncertainty shocks on macroeconomic variables. As discussed in the corporate finance literature, fluctuations in corporate bond credit spreads convey information on changes in many factors. Some fluctuations are related to issuer s financial health and their balance sheet quality, while others capture changes in the availability of credit by financial intermediaries, liquidity premium, required additional compensation by investors for bearing credit risk, and tax treatment. In this section, we decompose the financial channel to address how uncertainty shocks affect some of these factors and to address their individual importance to the transmission of uncertainty shocks. Following the literature, we decompose the movements in the corporate-treasury credit spread (BaaT30Y) into two components: a component that captures time-varying expected defaults of 21

22 corporations and their financial health, and a residual component that captures the combined effect of all other factors, the majority of which results from changes in liquidity premium, tax treatment, capital position in financial intermediaries, and compensation beyond the expected losses required by investors for bearing credit risk of corporate bonds. We measure corporations expected probability of default following Gilchrist and Zakraj sek (2012), which employs the distance-to-default framework by Merton (1974) to U.S. nonfinancial firms with senior unsecured issues and fixed coupon schedule, covered by the S&P Compustat and Center for Research in Security Prices (CRSP). We use the cross-sectional median of firms distance-to-default (DD) as the measurement for systematic expected defaults. The residual component, excess bond premium (EBP), is estimated by the difference between the credit spread and the fitted value from a linear model using DD. Figure 7 plots the Baa-rated Corporate - Treasury spread and the component explained by expected default. Figure 7 goes here. We then isolate the effect of each component separately to address their importance in transmitting the effect of uncertainty shocks. We impose DD and EBP as two observable factors, along with uncertainty, in the estimation, i.e. C t = [F t, DD t, EBP t, U t ] 0. The estimation is performed for the sample 1973M1-2010M9 due to data availability. To study the importance of expected default and the excess bond premium in explaining the financial channel of uncertainty shocks, we remove the indirect effect of expected default and the excess bond premium one at a time using the counterfactual decomposition approach described in Section 2.4. That is, we restrict DD not to move in response to uncertainty shocks to get the hypothetical impulse responses of variable x, δ x,6,h,dd, where 6 is the position indicator for uncertainty shock and h is the time horizon. The effect channeled through expected default can be estimated by the difference of the actual responses δ x,6,h and hypothetical impulse responses δ (s) x,6,h,dd of variable x, i.e. ρ x,h,dd = δ x,6,h δ x,6,h,dd. We then use the same method and estimate the hypothetical responses δ x,6,h,ebp when we restrict EBP to be fixed in response to uncertainty shocks, and quantify the effect channeled through excess bond premium by ρ x,h,ebp = δ x,6,h δ x,6,h,ebp. 22

23 Figure 8 and Figure 9 plots ρ (s) x,h,dd and ρ(s) x,h,ebp for a set of 16 variables13. The maximum afterimpact responses to uncertainty shocks channeled through expected default and the excess bond premium, and the month that the maximum responses occur are reported in Table The decomposition of the financial channel leads to two main results. First, both the expected default and the excess bond premium channel appear more important during recessions. According to Table 4, the endogenous increase of expected default during recessions is responsible for a maximum of 0.51 SD decrease in IP and a maximum of 0.58 SD decrease in employment following a SD uncertainty shock, while the maximum effect channeled through expected default is SD and SD for IP and employment in the linear model. For the excess bond premium, Table 4 reports a maximum of SD and a maximum of SD decrease in IP and employment channeled through the endogenous response of excess bond premium after the uncertainty shock during recessions, compared to a SD and a SD in the linear model. Comparing Figure 8 and Figure 9 also suggests that the effects channeled through the endogenous response of the expected default and the excess bond premium are larger in magnitude during recessions for all reported real and nominal economic variables, suggesting an overall higher importance of the financial channel during recessions. Second, comparing the excess premium and the expected default channels shows that relative importance of the two channels varies over the forecast horizons. In the short run, the excess bond premium channel is more important for the transmission of the uncertainty shocks, while the expected default channel is more important at longer horizons. As shown in Table 4, the maximum effects channeled through the excess bond premium occur within 5 months after the shock, while the maximum effects through expected default occur after 5 months for most series. As shown in Figure 9, the endogenous response of the excess bond premium leads to a sharp decline in overall real economic activity within 6 months after an expected rise in uncertainty, followed by quick recoveries and overshooting after 12 months. Changes in firms expected defaults cause a slower and more moderate decline of real activity with the peak effects occurring after 12 months, followed by smaller and more delayed overshoots. Figure 8 and Figure 9 go here. 13 As documented in Section 3.2.1, the financial channel appears important mainly for the production, income, consumption, labor market, interest rates, and credit spread series. Figure 8 and 9 select 16 series representing these categories. The full set of results are available upon request. 14 Numbers are reported in the maximum absolute values. 23

24 Table 4 goes here. Our results from the decomposition provided evidence for how and why the financial channel matters for uncertainty shocks. An unexpected elevation in uncertainty leads to a subsequent perceived increase in the probability of default, which contracts real economic activity through a few possible mechanisms. To avoid default, firms may contract the size of their investments and hiring 15, or simply postpone these activities to improve their financial positions. Furthermore, higher perceived riskiness of firms also leads to higher expected loss for lenders, making borrowing more difficult and costly. Tighter credit conditions amplify the real economic effects of uncertainty shocks. During deep recessions, lenders may be even more reluctant to lend, and businesses may be more likely to contract their real activities further due to lower sales, worsened balance sheet positions, and a lower probability of obtaining external funds, all of which can result in more significant effects of the uncertainty shock and a more important expected default channel during recessions. We show that the increase in expected defaults is more relevant in the medium-long run. An increase in uncertainty also leads to a higher liquidity premium and higher additional compensation to investors for bearing the risk of corporate bonds, beyond the expected loss, caused by lenders worsened financial conditions, lowered investor confidence, and asymmetric information in the financial markets. Elevated uncertainty leads to larger expected dispersion of firms quality and makes it more difficult to learn information, both of which exacerbate the adverse selection problem, making external financing more costly for firms and corporate bonds more difficult to trade. During recessions, such effects are likely to be larger as a result of flight to quality by lenders and more pessimism from the market as a whole. In addition, financial intermediaries capital condition often worsens during recessions, which constrains the availability of funds that they can lend to businesses. We show that the increase in the required liquidity premium, risk compensation, and changes in capital condition of financial intermediaries are responsible for a sharp short-run increase in firms cost of borrowing, which leads to a short-run contraction in real economic activity. The overshooting behavior in the medium horizon can be caused by restoration of market confidence and reallocation of funds to higher return assets by investors. 15 The contractionary effect on the labor market is mainly through the external margin. As shown in Figure 8 and 9, increasing expected default caused by an uncertainty shock appears to lower employment and increase unemployment duration, while moderately increases hours, suggesting that some firms choose to increase their workers hours to partially offset the lowered hiring. 24

25 4 Robustness To provide a robustness analysis of the results described above, we examine other model specifications, and estimate the model under alternative measurements for uncertainty and credit spreads. For the sake of brevity, we report the impulse responses of a few selected series representative of economic activity from those reported in the previous section. The series reported are a proxy for uncertainty, industrial production, real personal consumption expenditures, employment, and a measure of credit spreads. 4.1 Alternative Proxy for Uncertainty One difficulty with empirically examining the effect of uncertainty is the measurement. No direct measurement for uncertainty exists, and the literature has mainly relied on proxies or indicators of uncertainty, such as the implied volatility of stock returns (VXO) used in Bloom (2009) and this paper. There are, however, some potential concerns regarding this proxy. First, the pre-1986 index is not available and thus replaced by realized stock return volatility, normalized to have the same mean and variance as VXO from 1986 onward. To show the robustness of our results, we also report the results using the realized volatility of S&P 500 returns for the full sample. Some literature, including Caldara et al. (2014), use the realized stock market volatility as proxy for uncertainty. The cross-regime impulse responses of industrial production, employment, personal consumption, and the Baa-Treasury spread are reported in the second column of Figure A1(a). The second columns of Figure A2(a) and Figure A3(a) report the restricted impulse responses of these series when the credit spread is held fixed and contrast them with the actual responses in normal and recession periods respectively. Our main results are robust to this alternative proxy for uncertainty. Another issue, as discussed in Jurado et al. (2015), is that implied and realized stock market volatilities may be contaminated by leverage and investor sentiment, so the changes in these proxies might not necessarily reflect changes in uncertainty about economic fundamentals. Jurado et al. (2015) constructs a new proxy for uncertainty (JLN) that is more closely related to macroeconomic activity, which we also use to check the robustness of our results. It should be noted, however, that the JLN measurement only weak correlates with VXO (correlation coefficient = 0.43) and is more persistent (first-order autocorrelation coefficient = 0.99 over the full sample). A unit shock to JLN thus will have more persistent macroeconomic effects compared to the VXO proxy. 25

26 In addition, a unit SD shock to JLN leads to responses with a greater magnitude than a unit SD shock to VXO, possibly because JLN measured uncertainty, by construction, are more closely related to macroeconomic fundamentals. The overshooting behavior is not observed when JLN is used as uncertainty measures 16. Despite the difference, we find qualitatively consistent main results: (1) an increase in uncertainty leads to larger and less persistent responses in recessions than normal times (see the first column of Figure A1(a)); (2) the contribution of the financial channel is significantly larger in recessions (compare the first columns of Figure A2(a) and Figure A3(a)); (3) the financial channel primarily amplifies the effects of the uncertainty shocks in the short run and reduces the persistence of the effect in the long run (see the first columns of Figure A2(a) and Figure A3(a)). 4.2 Alternative Measurement for Credit Spread There are also many measures of credit spreads. As we have to select one measure of credit spread as an observable factor in our analysis, we should also consider alternative measurements for robustness. First, we consider the difference between Moody s Aaa-rated and Baa-rated corporate bond yields, another common indicator of financial stress in the literature. Second, we consider the credit spread by Gilchrist and Zakraj sek (2012) (GZspread, 1973M1-2012M12), which is constructed from secondary bond prices on outstanding senior unsecured debt by a large panel of individual nonfinancial firms using a "ground-up approach. These authors have shown that GZspread has better predictive power for economic activity than some other spread measurements. The third and fourth columns of Figure A1(a), Figure A2(a), and Figure A3(a) report the results under these two measurements. We found similar cross-regime differences in the impulse responses as our baseline analysis for both of the measures. It also appears that the results under Baa-Aaa credit spread regarding the importance of financial channels are similar to those in the baseline analysis. When GZspread is used, we find only a moderate difference between the actual and hypothetical responses in the short run, but the effects of the uncertainty shock appear to be greatly reduced in the medium-long run when GZspread is held fixed, suggesting a similar importance of the financial channel in the transmission of uncertainty shocks at longer horizons for this alternative measure. In addition, after we restrict the endogenous response of GZspread, uncertainty shocks seem to have more 16 This finding is consistent to Jurado et al. (2015). They use a linear VAR and the JLN measure for uncertainty, and find no overshooting behavior that is typically found when stock market volatilities are used to proxy for uncertainty. 26

27 transient effects lasting less than 12 months, and overshoots disappear. It could be caused by the fact that fluctuations in GZspread have greater predictive power in changes of economic fundamentals in the medium-long run and are more closely correlated with fluctuations in VXO (correlation coefficient = 0.695) than the Baa-Treasury spread (0.581) and the Baa-Aaa spread (0.443). Removing the effect of GZspread is likely to remove a greater amount of the uncertainty shock s effects from the responses of macroeconomic variables. 4.3 Alternative Ordering of Factors Our identification strategy is based on a recursive assumption, with U ordered last and Spd ordered after the macroeconomic unobservable factors and before U. By assumption, uncertainty shocks affect credit spreads and the unobservable factors with delay. Meanwhile, changes in credit spreads have immediate effects on uncertainty but not on the unobservable factors. The baseline ordering allows us to examine the role of uncertainty shocks conditional on the current credit market conditions. However, a possible issue could be the relative ordering between uncertainty and credit spread, as both variables can be fast-moving and possibly affect each other with little delay. To address this concern, we reverse the order of the uncertainty and credit spread, which allows us to examine the role of uncertainty shocks conditional on the current condition of the credit market. The results are reported in the fifth columns of Figure A1(a), Figure A2(a), and Figure A3(a). Another possible issue is the order of uncertainty relative to unobservable macro factors. The unobservable factors, by construction, capture the common movements in all macroeconomic series, which include slow-moving variables such as prices and employment, and fast-moving variables such as S&P 500 and the federal funds rate. To address this concern, we also consider reversing the order of the uncertainty and unobservable factors. Results are reported in the first columns of Figure A1(b), Figure A2(b), and Figure A3(b). Both alternative identifications produce similar impulse responses as the baseline specification. 4.4 Alternative Transition Indicator We model the transition indicator z using a standardized backward-looking 12-month moving average of the growth rate of Industrial Production Index, normalized to have mean zero and rescaled to have unit variance. Though the approach is consistent with the literature including 27

28 Auerbach and Gorodnichenko (2012), we use a 12 month moving average of IP rather than the 7-quarter moving average of real GDP that this literature uses. The reason is that we use monthly data and measure real economic activity using industrial production. By carefully examining the behavior of the transition probability f (z) constructed using industrial production, we find a 12-month moving average better replicates the dates of NBER business cycles than a 21-month moving average, though there are more "flips" when z is constructed based on a 12-month average. To be consistent with the literature, we also consider 21-month moving average in our robustness check. The results are reported in the second columns of Figure A1(b), Figure A2(b), and Figure A3(b). Our results do not appear to be sensitive to the alternative identification of transition indicator. 4.5 Alternative Specification of the Number of Factors We use three unobservable factors and two observable factors in our baseline analysis. Including more factors may better capture the common movements of the macroeconomic variables in the data set, but it also expands the parameter space, making it difficult to obtain stable and credible estimates. We find our results are not sensitive to reasonable increases in the number of factors. The third columns of Figure A1(b), Figure A2(b), and Figure A3(b) report the cross-regime impulse responses and the responses without the financial channel when we use a six factor model with four unobservable factors. 4.6 Generalized Impulse Responses Following Auerbach and Gorodnichenko (2012), Bachmann and Sims (2012), and Caggiano et al. (2014), we construct the impulse responses in our regime-dependent model, assuming that the current regime is fixed during our horizon of forecasting. The assumption makes the model linear conditional on a fixed regime and the responses independent of history, but ignore possible feedback from changes in the dynamics of macroeconomic variables to the probability of being in a regime 17. To address this concern, we compute the generalized impulse responses (GIRF) as in Koop et al. (1996) and Caggiano et al. (2014) by including the regime-transition indicator z as an endogenous variable in the vector, with z ordered first, and accounting for the feedback between the variables and the regime. We estimate the GIRF with 3 lags and report our results 17 Ramey and Zubairy (2014) criticize Auerbach and Gorodnichenko (2012), which studies regime-dependent effect of fiscal shocks, for ignoring the possibility that an expansionary fiscal shock can help the economy out of a recession. 28

29 in the fourth columns of Figure A1(b), Figure A2(b), and Figure A3(b). The contractionary effects of an uncertainty shock in the short-run and the overshooting behavior at longer horizons appear qualitatively similar to those under the baseline model. Removing the endogenous responses of the credit spread also lead to dampened responses, similar to our baseline results. 4.7 Truncated Sample The federal funds rate hit an effective zero lower bound (ZLB) in December 2008 and has been maintained near zero since. A concern might be that passive monetary policy might affect the manner in which shocks affect the economy, including uncertainty shocks. Due to unresponsive policy at the ZLB, uncertainly shocks are likely to have greater effects on economic variables, which might contaminate our results regarding the comparison of shock dynamics across regimes. Another concern might be that our findings regarding the higher importance of the financial channel during recessions could be driven by including the severe financial crisis that precipitated the Great Recession in our sample, and whether our results are robust in situations that are not accompanied by such large financial disruptions. To address these concerns, we re-estimate the model using a truncated sample from 1962M7 to 2007M6, which excludes the major disruptive events such as the collapse of Bear Stearns and the bankruptcy of Lehman Brothers, as well as the post-2008 period with ZLB 18. Our results are reported in the last columns of Figure A1(b), Figure A2(b), and Figure A3(b). We find that uncertainty shocks have weaker and shorter-lived contractionary effects in the truncated sample, but the results regarding the state-dependent impulse responses remain robust. The peak effect on IP during normal and recession times are 0.20 SD and 0.26 SD respectively in the full subsample, while 0.09 SD and 0.17 SD in the subsample. IP returns to the pre-shock level around 20 months after the shock in the full sample estimation, while around 12 months in the truncated sample. Despite of these differences, we have consistent qualitative findings to our baseline results. When the ZLB is absent, uncertainty shocks still lead to stronger responses in real economic activity in the short-run during recession phases, and the overshooting behavior is observed for many variables during the medium-long run 19. We also find that the financial channel remains more important during recessions in the trun- 18 Removing the post-2007m6 sample help eliminating the bias caused by the ZLB and the financial crisis, but also excludes some valuable information regarding the effect of uncertainty shocks and the financial channels during the Great Recession. 19 For brevity, we report the responses of IP, employment, consumption, and credit spread in the truncated sample, similar to other robustness checks. The full set of results for this robustness check is available upon request. 29

30 cated sample. Removing the indirect effect channeled by the financial channel leads to a 41 percent reduction in the peak response of IP (from 0.17 SD to 0.10 SD) during recessions, while a 23 percent reduction (from 0.09 SD to 0.07 SD) in the linear model. Compared to the full sample, though the overall importance of the financial channel is reduced 20, the findings that the financial channel is more important during recessions and in the short run remain qualitatively robust. 4.8 ST-VAR vs. ST-FAVAR ST-VAR models are used to study the regime-dependent dynamics in a number of studies. For example, they are used in Auerbach and Gorodnichenko (2012) and Bachmann and Sims (2012) to study the regime-dependent effects of fiscal shocks, and in Caggiano et al. (2014) to study the effects of uncertainty shocks on unemployment during U.S. recessions. A question might be whether it would be necessary to augment the ST-VAR with a factor structure in our study. First, ST-VAR can be viewed as a special case of ST-FAVAR, when factors are restricted to be the selected economic series. It is a well-known problem that VARs can possibly lead to misidentification of shocks and shock dynamics due to omitted information, especially for regime-dependent VARs that usually include a small number of variables. By imposing a factor structure, we can utilize information from a larger set of macroeconomic and financial indicators and statistically extract the factors that best capture the common movements of these indicators. The factoraugmented approach reduces the risk of misidentification due to omitted information, reduces the sensitivity to the choice of specific data series, and better avoids the non-fundamentalness issue. Second, the ST-FAVAR framework allows us to consistently study the effect of uncertainty shocks on a large set of economic and financial indicators within the model. VARs include a small number of variables, and only the dynamics of these variables can be examined. If one would like to know the dynamics of different variables, then different VARs will have to be estimated. Third, and more specific for our study, incorporating a dynamic factor structure not only leads to more accurate identification of the uncertainty shocks, it also allows a more precise estimation on the importance of the financial channel. As the method described in Section 2.4, the importance of the financial channel is quantified by shutting down the endogenous responses of the credit spread following the uncertainty shock. In a small-scale VAR with possible omitted variables, 20 Removing the indirect effect channeled by movements of the credit spread leads to a 50 percent and a 35 percent reduction in IP responses during recessions and normal times in the full sample. 30

31 removing the credit spread in the estimation removes not only the endogenous changes in the credit spread, but also the changes in the omitted variables that are captured by the movements in the credit spread, which may lead to an over-estimation of the importance of financial channels. We conduct an experiment using a ST-VAR model with 4 variables and 3 lags. We select IP and employment as measures of real economic activity, Baa-Treasury spread as a measure of credit spread, and VXO as a measure of uncertainty. The variables are ordered as [IP t, Employment t, Spd t, VXO t ] 0 in the estimation. The results are reported in Figure A4 and Figure A5. Uncertainty shocks have greater effects in the short run on IP and employment under the VAR specification than the FAVAR specification. According to Figure A4, the maximum response of IP is 0.26 SD and 0.49 SD during normal and recession times, compared to 0.20 and 0.26 SD in our baseline FAVAR. An increase in uncertainty has a longer contractionary effect on IP and employment, and overshooting in the first log difference responses of IP and employment are not observed under the VAR specification. Meanwhile, the financial channel appears more important in the VAR specification. Removing the endogenous response of the credit spread leads to a 54 percent reduction (from 0.26 SD to 0.12 SD) and 58 percent reduction (from 0.49 SD to 0.21 SD) in IP during normal and recession times under the VAR specification. We find a similar pattern when we look at the contribution of the expected default and excess bond premiums separately in Figure A5. These differences are consistent with the intuition of using this alternative specification. Despite these differences, we find that most of our qualitative results are robust in the VAR specification. Uncertainty shocks continue to have greater effects on real economic activity during recessions, and removing the indirect responses of the credit spread leads to more dampened responses during recessions and in the short run. 5 Conclusion This paper focuses on two aspects of the macroeconomic effects of uncertainty shocks. First, we examine the possible differences in effects of uncertainty shocks between recessions and nonrecessions. Second, using the results from the previous part as a benchmark, we examine the importance of the financial channel in the transmission of uncertainty shocks in the two regimes. To study the cross-regime dynamics, we augment a smooth-transition VAR with a dynamic factor structure that is estimated using a large panel of U.S. economic and financial indicators. This method allows us to get a comprehensive picture of the effects of uncertainty shocks across 31

32 regimes without imposing many theoretical restrictions, while better addressing the omittedvariable and non-fundamentalness issue of standard VARs. We use a counterfactual decomposition approach to isolate the importance of the financial channel. Intuitively, we remove the indirect effect of uncertainty shocks caused by the endogenous response in the financial conditions, and compare the impulse responses to the benchmark responses where the role of financial channel is not restricted. We have four main empirical findings. First, uncertainty shocks have significant effects on many economic and financial indicators and explain a moderate share of fluctuations in these indicators. Overall, an uncertainty shock contracts real economic activity and lowers inflation, while tightening financial conditions in the short run. A "bust-rebound-overshoot" is found in some real economic and financial indicators. Second, we find that the effects of uncertainty shocks appear to be quantitatively larger during recessions. The response of many indicators have greater magnitude and are more front-loaded during recession periods. Third, we find that the financial channel is important in the transmission of uncertainty shocks, especially during recessions and in the short-run, though it is not the exclusive channel through which uncertainty shocks matter. Removing the indirect effect transmitted through the financial channel greatly reduces the overall effect of uncertainty shocks during recessions. Meanwhile, other transmission channels, such as the real-option mechanism, consumer and business confidence, and precautionary saving, are also likely to be important to explain the macroeconomic effects of uncertainty shocks. Fourth, the financial channel matters for uncertainty shocks because an uncertainty shock changes businesses expected default risk and excess premium of corporate bonds, both of which affect businesses decisions and financial market conditions, leading to an amplified effect on overall economic activity. A decomposition of the financial channel into the expected default and excess bond premium effects reveals that the relative importance of the sub-channels differs in different time horizons. Our results provide stylized facts for future studies of uncertainty shocks and their transmission channels. Bibliography Arellano, C., Y. Bai, and P. J. Kehoe (2012). Financial frictions and fluctuations in volatility. Staff Report 466, Federal Reserve Bank of Minneapolis. Auerbach, A. J. and Y. Gorodnichenko (2012). Measuring the output responses to fiscal policy. 32

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36 Stock, J. H. and M. W. Watson (2002). Macroeconomic forecasting using diffusion indexes. Journal of Business & Economic Statistics 20(2), Stock, J. H. and M. W. Watson (2003). Forecasting output and inflation: The role of asset prices. Journal of Economic Literature 41(3),

37 6 Appendix A Data Appendix The data set is based on FRED-MD, a collection of publicly available U.S. monthly data series described in McCracken and Ng (2015). Series that are available over the full 1962M7 to 2014M12 time period are included. The series are sorted below by type and are listed with an abbreviation (FRED code when available), brief description, and transformation code (TC). The transformation code indicates how the series was transformed to ensure stationarity. With the untransformed series at time t denoted X t, the transformation codes are as follows: (1) no transformation (X t ); (2) difference (4X t ); (3) 2nd difference (4 2 X t ) ; (4) logged (log(x t )); (5) log difference (4log(X t )); (6) 2nd log difference (4 2 log(x t )); (7) 1st difference of percentage change ( 4X t X t 1 4X t 1 X t 2 ). Series that are not in FRED-MD are marked with an asterisk. Table A1: Output and Income Series ID Abbreviation TC Description 1 RPI 5 Real Personal Income 2 W875RX1 5 Real Personal Income Excluding Transfer Receipts 4 CMRMTSPLx 5 Real Manufacturing and Trade Sales 5 RETAILx 5 Retail and Food Service Sales 6 INDPRO 5 Industrial Production (IP) Index 7 IPFPNSS 5 IP: Final Products and Nonindustrial Supplies 8 IPFINAL 5 IP: Final Products (Market Group) 9 IPCONGD 5 IP: Consumer Goods 10 IPDCONGD 5 IP: Durable Consumer Goods 11 IPNCONGD 5 IP: Nondurable Consumer Goods 12 IPBUSEQ 5 IP: Business Equipment 13 IPMAT 5 IP: Materials 14 IPDMAT 5 IP: Durable Materials 15 IPNMAT 5 IP: Nondurable Materials 16 IPMANSICS 5 IP: Manufacturing, Standard Industrial Classification (SIC) 17 IPB51222S 5 IP: Residential Utilities 18 IPFUELS 5 IP: Fuels 19 NAPMPI 1 Institute for Supply Management (ISM) Manufacturing: Production Index 20 CUMFNS 2 Capacity Utilitization in Manufacturing 37

38 Table A2: Labor Market Series ID Abbreviation TC Description 21 HWI 2 Barnichon (2010) Help-Wanted Index 22 HWIURATIO 2 Ratio of Help Wanted to Number of Unemployed (Labor Market Tightness) 23 CLF16OV 5 Civilian Labor Force 24 CE16OV 5 Civilian Employment 25 UNRATE 2 Civilian Unemployment Rate 26 UEMPMEAN 2 Mean Duration of Unemployment in Weeks 27 UEMPLT5 5 Number of Civilians Unemployed Less than 5 Weeks 28 UEMP5TO14 5 Number of Civilians Unemployed 5-14 Weeks 29 UEMP15OV 5 Number of Civilians Unemployed 15 Weeks and Over 30 UEMP15T26 5 Number of Civilians Unemployed Weeks 31 UEMP27OV 5 Number of Civilians Unemployed 27 Weeks and Over 32 CLAIMSx 5 Initial Unemployment Insurance Claims 33 PAYEMS 5 All Employees: Total Nonfarm 34 USGOOD 5 All Employees: Goods-Producing 35 CES All Employees: Mining and Logging 36 USCONS 5 All Employees: Construction 37 MANEMP 5 All Employees: Manufacturing 38 DMANEMP 5 All Employees: Durable Goods 39 NDMANEMP 5 All Employees: Nondurable Goods 40 SRVPRD 5 All Employees: Service Providers 41 USTPU 5 All Employees: Trade, Transportation, and Utilities 42 USWTRADE 5 All Employees: Wholesale Trade 43 USTRADE 5 All Employees: Retail Trade 44 USFIRE 5 All Employees: Financial Activities 45 USGOVT 5 All Employees: Government 46 CES Average Weekly Hours of Production and Nonsupervisory Employees: Goods-Producing 47 AWOTMAN 2 Average Weekly Overtime Hours of Production and Nonsupervisory Employees: Goods-Producing 48 AWHMAN 1 Average Weekly Hours of Production and Nonsupervisory Employees: Manufacturing 49 NAPMEI 1 ISM Manufacturing: Employment Index 128 CES Average Hourly Earnings of Production and Nonsupervisory Employees: Goods-Producing 129 CES Average Hourly Earnings of Production and Nonsupervisory Employees: Construction 130 CES Average Hourly Earnings of Production and Nonsupervisory Employees: Manufacturing 38

39 Table A3: Consumption and Housing ID Abbreviation TC Description 3 DPCERA3M086SBEA 5 Real Personal Consumption Expenditures (PCE) 135 DSERRA3M086SBEA* 5 Real PCE: Services 136 DNDGRA3M086SBEA* 5 Real PCE: Nondurables 137 DDURRA3M086SBEA* 5 Real PCE: Durables 50 HOUST 4 New Privately Owned Housing Units Started 51 HOUSTNE 4 New Privately Owned Housing Units Started: Northeast 52 HOUSTMW 4 New Privately Owned Housing Units Started: Midwest 53 HOUSTS 4 New Privately Owned Housing Units Started: South 54 HOUSTW 4 New Privately Owned Housing Units Started: West 55 PERMIT 4 New Private Housing Units Authorized by Building Permits 56 PERMITNE 4 New Private Housing Units Authorized by Building Permits: Northeast 57 PERMITMW 4 New Private Housing Units Authorized by Building Permits: Midwest 58 PERMITS 4 New Private Housing Units Authorized by Building Permits: South 59 PERMITW 4 New Private Housing Units Authorized by Building Permits: West Table A4: Orders and Inventories ID Abbreviation TC Description 60 NAPM 1 ISM Manufacturing: PMI Composite Index 61 NAPMNOI 1 ISM Manufacturing: New Orders Index 62 NAPMSDI 1 ISM Manufacturing: Suppliers Deliveries Index 63 NAPMII 1 ISM Manufacturing: Inventories Index 64 AMDMNOx 5 Value of Manufacturers New Orders for Consumer Goods Industries 65 AMDMUOx 5 Value of Manufacturers New Orders for Durable Consumer Goods Industries 66 BUSINVx 5 Value of Manufacturers New Orders for Nondurable Consumer Goods Industries 67 ISRATIOx 2 Inventory to Sales Ratio 39

40 Table A5: Money and Credit ID Abbreviation TC Description 68 M1SL 6 Money Stock: M1 69 M2SL 6 Money Stock: M2 70 M2REAL 5 Money Stock: Real M2 71 AMBSL 6 St. Louis Adjusted Monetary Base 72 TOTRESNS 6 Total Reserves 73 NONBORRES 7 Nonborrowed Reserves 74 BUSLOANS 6 Commerical and Industrial Loans 75 REALLN 6 Real Estate Loans 76 NONREVSL 6 Total Nonrevolving Credit 77 CONSPI 2 Credit to PI Ratio 131 MZMSL 6 Money Stock: MZM 132 DTCOLNVHFNM 6 Consumer Motor Vehicle Loans Owned By Finance Companies, Outstanding 133 DTCTHFNM 6 Total Consumer Loans and Leases Owned and Securitized by Finance Companies, Outstanding 134 INVEST 6 Securities in Bank Credit at All Commercial Banks Table A6: Interest Rates ID Abbreviation TC Description 82 FEDFUNDS 2 Effective Fed Funds Rate 83 CP3Mx 2 3-Month AA Commerical Paper Rate 84 TB3MS 2 T-Bill: 3 Month 85 TB6MS 2 T-Bill: 6 Month 86 GS1 2 T-Bond: 1 Year 87 GS5 2 T-Bond: 5 Year 88 GS10 2 T-Bond: 10 Year 89 AAA 2 Moody s Seasoned Aaa Corporate Bond Yield 90 BAA 2 Moody s Seasoned Baa Corporate Bond Yield 91 COMPAPFFx 1 Commerical Paper - Fed Funds Rate Spread 92 TB3SMFFM 1 3 Month Treasury - Fed Funds Rate Spread 93 TB6SMFFM 1 6 Month Treasury - Fed Funds Rate Spread 94 T1YFFM 1 1 Year Treasury - Fed Funds Rate Spread 95 T5YFFM 1 5 Year Treasury - Fed Funds Rate Spread 96 T10YFFM 1 10 Year Treasury - Fed Funds Rate Spread 97 AAAFFM 1 Aaa Corporate Bond - Fed Funds Rate Spread 98 BAAFFM 1 Baa Corporate Bond - Fed Funds Rate Spread 99 BaaT10Y* 1 Baa Corporate Bond - 10 Year Treasury Spread 100 BaaT30Y* 1 Baa Corporate Bond - 30 Year Treasury Spread 101 BaaAaa* 1 Baa Corporate Bond - Aaa Corporate Bond Spread 102 3mCPT3m* 1 3 Month Commercial Paper - 3 Month Treasury Spread 141 GZspread* 1 Corporate Bond Spread by Gilchrist et al. (2012) 40

41 Table A7: Exchange Rates ID Abbreviation TC Description 103 EXSZUSx 5 Switerzerland/US Exchange Rate 104 EXJPUSx 5 Japan/US Exchange Rate 105 EXUSUKx 5 US/United Kingdom Exchange Rate 106 EXCAUSx 5 Canada/US Exchange Rate Table A8: Prices ID Abbreviation TC Description 107 PPIFGS 6 Producer Price Index (PPI): Finished Goods 108 PPIFCG 6 PPI: Finished Consumer Goods 109 PPIITM 6 PPI: Intermediate Materials 110 PPICRM 6 PPI: Crude Materials 111 OILPRICEx 6 Crude Oil Price: West Texas Intermediate 112 PPICMM 6 PPI: Commodities 113 NAPMPRI 1 ISM Manufacturing: Prices 114 CPIAUCSL 6 Consumer Price Index (CPI): All Items 115 CPIAPPSL 6 CPI: Apparel 116 CPITRNSL 6 CPI: Transportation 117 CPIMEDSL 6 CPI: Medical Care 118 CUSR0000SAC 6 CPI: Commodities 119 CUUR0000SAD 6 CPI: Durables 120 CUSR0000SAS 6 CPI: Services 121 CPIULFSL 6 CPI: All Items Less Food 122 CUUR0000SA0L2 6 CPI: All Items Less Shelter 123 CUSR0000SA0L5 6 CPI: All Items Less Medical Care 124 PCEPI 6 Personal Consumption Expenditures (PCE) Price Index 125 DDURRG3M086SBEA 6 PCE Price Index: Durable Goods 126 DNDGRG3M086SBEA 6 PCE Price Index: Nondurable Goods 127 DSERRG3M086SBEA 6 PCE Price Index: Services Table A9: Stock Market ID Abbreviation TC Description 78 S&P S&P 500 Return 79 S&P: indust 5 S&P: Industrial Index 80 S&P div yield 2 S&P Dividend Yield 81 S&P PE ratio 5 S&P Price-Earnings Ratio Table A10: Uncertainty ID Abbreviation TC Description 138 VXO* 1 Chicago Board Options Exchange Market Volatility Index 139 StockVol* 1 Monthly Standard Deviation of Daily S&P 500 Index 140 UncertaintyJLN* 1 JLN Uncertainty Measure by Jurado et al. (2015) 41

42 B Estimation of the Smooth-Transition FAVAR This section discusses the estimation procedure for our model (1) - (6). As previously introduced, we use a two-step estimation method. We first estimate the macroeconomic factors using principal components, and use the estimates as regressors in the second step. γ is fixed in the estimation of the remaining parameters. Given the probability indicators and factor estimates, regime-dependent factor loadings and the covariance matrix in the measurement equation (1) and (5) can be estimated as a normal linear model with extended regressors. Conditional on the factors estimates, transition equation (2) - (4) resembles a smooth-transition reduced form VAR. We estimate the regime-dependent coefficients and covariance matrices in VAR using similar approach as in Auerbach and Gorodnichenko (2012). Due to the nonlinearity of the problem and the dimension of parameters, we use a Markov Chain Monte Carlo (MCMC) algorithm in the estimation and the construction of confidence intervals. The parameters that need to be estimated are fλ R, Λ NR, Σ, Π R (L), Π NR (L), Ω R, Ω NR g. Note that the parameters in the measurement equations, = fλ R, Λ NR, Σg, and those in the transition equation, Ψ = fπ R (L), Π NR (L), Ω R, Ω NR g, can be estimated separately once the principal component estimates are used as data in the transition equation. Also note that conditional on {Ω R, Ω NR }, the transition equation becomes linear in lag polynomials fπ R (L), Π NR (L)g. Thus we can separate the parameters into three blocks in the estimation. Conditional on the factor estimates and factor loadings, the log likelihood for model (2) - (4) is given by log L(ΨjΛ R, Λ NR, C) = const T 1 2 log jω t j t=1 T 1 2 u 0 tωt 1 u t, (8) t=1 where u t = C t (1 F(z t 1 ))Π NR (L)C t 1 F(z t 1 )Π R (L)C t 1 and Ω t = F(z t 1 )Ω R + (1 F(z t ))Ω NR. More compactly, we can write u t = C t ΠW 0 t, where Π = [Π R(L) Π NR (L)] and W t = [F(z t 1 )C t 1 (1 F(z t 1 ))C t 1... F(z t p )C t p (1 F(z t p ))C t p ]. Conditional on {Ω R, Ω NR }, the model is then linear in fπ R (L), Π NR (L)g. For a given value of {Ω R, Ω NR }, we obtain estimate of fπ R (L), Π NR (L)g by minimizing 1 2 T u 0 tωt 1 u t = 1 2 t=1 T t=1 (C t ΠWt) 0 0 Ωt 1 (C t ΠWt). 0 The first order condition with respect to Π is t=1(w T 0 t C tωt 1 W 0 t W tπ 0 Ωt 1 ) = 0, which gives the estimate vec(π) 0 = ( T t=1 Ω 1 t W 0 tw t ) 1 vec( T t=1 W 0 tc t Ω 1 t ). 21 (9) The procedure iterates over different sets of values of fω R, Ω NR g until a maximum is reached for (8). To ensure {Ω R, Ω NR g are positive definite, we use Ψ = fπ R (L), Π NR (L), chol(ω R ), chol(ω NR )g in the iteration, where chol is the operator for Cholesky decomposition. Following Auerbach and Gorodnichenko (2012), we use Metropolis-Hastings algorithm to implement the MCMC estima- 21 See Auerbach and Gorodnichenko (2012) for more details of the derivation. 42

43 tion. The method delivers a global optimum and posterior distributions of parameter estimates. The chains are constructed in the following steps: 1. Draw a candidate vector of parameter values Θ (n) = Ψ (n) + ψ (n) for the chain s n + 1 state, where Ψ (n) is current state, ψ (n) is a vector of i.i.d. shocks draw from N(0, Ω ψ ). Ω ψ is diagonal. 2. Take the n + 1 state of the chain as Ψ (n+1) = ( Θ (n) with probability minf1, exp[log L(Θ (n) ) log L(Ψ (n) )]g Ψ (n) otherwise. The starting value Ψ (0) is computed using maximum likelihood to estimate fchol(ω R ), chol(ω NR )g from the residuals of a second order approximation to equation (2) - (4) using lags of C t, C t z t, and C t z 2 t, and then estimating fπ R(L), Π NR (L)g using equation (9). The initial Ω ψ is chosen to be three percent of the parameter values and later adjusted on the fly for the first 5,000 draws to generate a 0.35 acceptance rates of candidate draws. We employ 30,000 draws and drop the first 5,000 draws. Conditional on the factors and transition probability, the measurement equation (1) is a system of linear regression models with extended regressors [F(z t 1 )C t (1 F(z t 1 ))C t ]. Estimates for can be obtained using standard procedures by imposing natural conjugate priors. That is, ΛjΣ N(λ, ΣV), Σ 1 W(S 1, v), which implies the posterior to be ΛjΣ, X, C N( λ, Σ V), Σ 1 jx, C W( S 1, v), where Λ = [Λ R Λ NR ], V = [V 1 + C 0 C] 1, λ = V[V 1 λ + C 0 C ˆλ], S = S + S + ˆλ 0 C 0 C ˆλ + λ 0 V 1 λ λ 0 (V 1 + C 0 C) λ, v = T + v. ˆλ and S are maximum likelihood estimates of Λ and Σ respectively. The hyperparameters λ and V are set so that ΛjΣ has a normal distribution with mean zero and 10 times of the variation of Σ. S is set to be the identity matrix, and v equals the number of variables. Chains of = fλ, Σg are generated from the posterior distributions. We can construct the confidence intervals of the impulse responses using the generated chain of parameter values of fψ (n) } n=1 N and f (n) gn=1 N. We draw the covariance of matrices following Auerbach and Gorodnichenko (2012) to avoid wide confidence bands caused by taking the inverse of near-zero entries in the computation. We implement a similar bootstrap procedure as in Bernanke et al. (2005) to account for uncertainty in the factor estimation. We take 5,000 draws from fψ (n) gn=1 N and f (n) gn=1 N, and for each draw we compute an impulse response. The onestandard-deviation confidence bands are computed as the 16th and 84th percentiles of the generated impulse responses. 43

44 C Tables and Figures Table 1 Effect of Uncertainty Shocks Linear Recession Variable Max Resp. Cum.6m Cum.12m Max Resp. Cum.6m Cum.12m VXO Personal Income IP IP Equipment Capacity Utilization Help-wanted Labor Force Employment Unemployment Rate Unemploy. Duration Avg. Weekly Hours Real PCE Real PCE: Durables Housing Starts NAPM Production NAPM: New Orders M M S&P S&P P/E Ratio Federal Funds Rate m Treasury Bill Rate y Treasury Note Rate Spread: Baa-Treasury Spread: Baa-Aaa PPI: Finished Goods CPI: All Items PCE: Chain Index

45 Table 2 Variance Decomposition Linear Recession Variable Var. Decomposition R 2 Var. Decomposition R 2 VXO Real Personal Income Industrial Production IP Equipment Capacity Utilization Help-wanted Labor Force Employment Unemployment Rate Avg. Unemployment Duration Ave. Weekly Hours Real PCE Real PCE: Durables Housing Starts NAPM Production NAPM: New Orders M M S&P S&P P/E Ratio Federal Funds Rate m Treasury Bill Rate y Treasury Note Rate Spread: Baa-Treasury Spread: Baa-Aaa PPI: Finished Goods CPI: All Items PCE: Chain Index

46 Table 3 Effect of Uncertainty Shocks without Financial Channel Linear w/o Spread Recession w/o Spread Variable Max Resp. Cum.6m Cum.12m Max Resp. Cum.6m Cum.12m VXO Personal Income IP IP Equipment Capacity Utilization Help-wanted Labor Force Employment Unemployment Rate Unemploy. Duration Avg. Weekly Hours Real PCE Real PCE: Durables Housing Starts NAPM Production NAPM: New Orders M M S&P S&P P/E Ratio Federal Funds Rate m Treasury Bill Rate y Treasury Note Rate Spread: Baa-Treasury Spread: Baa-Aaa PPI: Finished Goods CPI: All Items PCE: Chain Index

47 Table 4 Maximum Effect Channeled Through DD and EBP Linear Recession Variable DD Month EBP Month DD Month EBP Month VXO Personal Income IP IP Equipment Help-Wanted Employment Unemployment Rate Unemploy. Duration Hours Real PCE Real PCE: Durables NAPM New Orders Federal Funds Rate y Treasury Note Rate Spread: Baa-Treasury

48 Figure 1 Uncertainty Indicators 48

49 Figure 2 Measurements of Credit Spread 49

50 Figure 3(a) Transition Probability f (z) (12m MA) - Baseline Figure 3(b) Transition Probability f (z) (21m MA) 50

51 Figure 4(a) Effect of Uncertainty Shock: Linear vs. Recession 51

52 Figure 4(b) Effect of Uncertainty Shock: Linear vs. Recession, continued 52

53 Figure 5(a) Uncertainty Shocks and Credit Spread: Linear 53

54 Figure 5(b) Uncertainty Shocks and Credit Spread: Linear, continued 54

55 Figure 6(a) Uncertainty Shocks and Credit Spread: Recession 55

56 Figure 6(b) Uncertainty Shocks and Credit Spread: Recession, continued 56

57 Figure 7 Credit Spread: Actual vs. Predicted by Default 57