Endogenous Uncertainty

We show that macroeconomic uncertainty can be considered as exogenous when assessing its e¤ects on the U.S. economy. Instead, …nancial uncertainty can at least in part arise as an endogenous response to some macroeconomic developments, and overlooking this channel leads to distortions in the estimated e¤ects of …nancial uncertainty shocks on the economy. We obtain these empirical …ndings with an econometric model which simultaneously allows for contemporaneous e¤ects of both uncertainty shocks on economic variables, and of economic shocks on uncertainty. While the traditional econometric approaches do not allow to simultaneously identify both of these transmission channels, we achieve identi…cation by exploiting the heteroskedasticity of macroeconomic data. Methodologically, we develop a structural VAR with time-varying volatility in which one of the variables (the uncertainty measure) impacts both the mean and the variance of the other variables. We provide conditional posterior distributions for this model, which is a substantial extension of the popular leverage model of Jacquier, Polson, and Rossi (2004), and provide an MCMC algorithm for estimation. J.E.L. Classi…cation: C11, C32, D81, E32. Keywords: Uncertainty, Endogeneity, Identi…cation, Stochastic Volatility, Bayesian Methods We gratefully acknowledge comments from Daniel Lewis, Helmut Lütkepohl, Davide Pettenuzzo, Giorgio Primiceri, Harald Uhlig, Molin Zhong, and seminar participants at the Federal Reserve Board. The views expressed herein are solely those of the authors and do not necessarily re‡ect the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System. 1 Introduction Starting from the seminal work of Bloom (2009), the business cycle relationship between uncertainty and output growth and the transmission mechanism from one to the other have received substantial attention in the literature; see Bloom (2014) for an exhaustive survey. Various measures of uncertainty have been put forward, and several e¤orts have been made to study the macroeconomic e¤ects and broader importance of uncertainty shocks. A nonexhaustive list of studies in this area includes Bloom (2009), Bloom, et al. (2012), Bachmann, Elstner, and Sims (2013), Caggiano, Castelnuovo, and Groshenny (2014), Jurado, Ludvigson, and Ng (2015, JLN), Rossi and Sekhposyan (2015), Baker, Bloom, and Davis (2016), Shin and Zhong (2018), Basu and Bundick (2017), Carriero, Clark, and Marcellino (2017a, CCM), Cesa-Bianchi, Pesaran, and Rebucci (2017), and Caldara, et al. (2018). While the de…nitions and measurements of uncertainty di¤er in all these contributions, the common denominator in this line of research is the way in which the e¤ects of uncertainty shocks are identi…ed and assessed. Speci…cally, most econometric studies typically estimate the e¤ects of uncertainty on economic variables by using structural VARs with some recursive identi…cation scheme, which all inevitably assume some type of causal direction between uncertainty and economic variables. The assumption typically made is that uncertainty (be it macroeconomic or …nancial) is exogenous; i.e., it does not react contemporaneously to economic variables, while economic variables react contemporaneously to uncertainty.1 However, as is well known in the profession, recursive schemes have the advantage of simplicity of implementation and interpretation, but in some cases they can be hard to defend as a credible identi…cation strategy. This is particularly true when economists have very little a priori, generally accepted, and theoretically grounded reasons to believe a speci…c recursive ordering is valid. The study of uncertainty shocks is such a case, since the existing evidence and economic wisdom makes us unable to take a stand on the direction of the causality between uncertainty and economic variables such as GDP growth. In line with this reasoning, Ludvigson, Ma, and Ng (2018, LMN) pointed out that most of these previous results could be biased by an endogeneity problem, and using an identi…cation procedure based on external information concluded that macro uncertainty is mostly endogenous, i.e. it mainly reacts to growth conditions rather than being an exogenous source of business cycle ‡uctuations, while …nancial uncertainty is mostly exogenous. In this paper we show that macroeconomic uncertainty can be considered as mostly exogenous when assessing its e¤ects on the U.S. economy. Instead, …nancial uncertainty can at least in part arise as an endogenous response to some macroeconomic developments, and Exogenous as used here and in the rest of the paper is not meant to mean strict exogeneity. Rather, we use it as short-hand for uncertainty being predetermined within the period. 1 overlooking this channel leads to a distorted estimate of the e¤ects of …nancial uncertainty shocks on the economy. We obtain these empirical …ndings with an econometric model in which current and past values of uncertainty a¤ect the current levels of economic variables, and uncertainty is in turn also a¤ected by them contemporaneously. We achieve identi…cation by means of a novel procedure hinging on time-varying volatility of macroeconomic variables. Di¤erently from the approaches based on recursive schemes, our identi…cation strategy allows us to leave the causal channel going from uncertainty to the macroeconomy and the opposite causal channel going from the macroeconomy to uncertainty (which we will refer to as the “feedback channel”) to be both potentially relevant and quanti…able. The existing literature has indeed shown that both these channels can be relevant. For example, the case has been made that uncertainty has e¤ects on the economy through the …rms’behavior. Firms’behavior can be in‡uenced by uncertainty for several reasons, e.g. because of the real option value of waiting before taking investment decisions (e.g., Bernanke (1983), McDonald and Siegel (1986)); because of the postponement of hiring and capital investment decisions (e.g., Leduc and Liu (2012), Bloom (2009), Bloom, et al. (2012)); and because of the interaction with …nancial frictions constraining …rms’decisions (e.g., Arellano, Bai, and Kehoe (2011), Gilchrist, Sim, and Zakrajsek (2014)). From the consumers’side, the e¤ects of uncertainty on the macroeconomy are possible via precautionary savings (e.g., Basu and Bundick (2017) and Fernandez-Villaverde, et al. (2011)). Equivalently, it is reasonable to conjecture that lower growth, typically associated with higher unemployment, tighter credit conditions, and larger volatility in …nancial markets, in turn can increase uncertainty. One of the …rst papers to stress possible endogeneity of uncertainty is Bachmann, Elstner, and Sims (2013). Using an identi…cation strategy in which uncertainty shocks have no long-run e¤ects on aggregate economic activity, they …nd that the uncertainty shocks then have also no e¤ects in the short run. Instead, various measures of uncertainty substantially increase after a negative shock to aggregate economic activity (see e.g. Bachmann and Moscarini (2011) and Fajgelbaum, Schaal, and Taschereau-Dumouchel (2014)). In our framework, identi…cation is obtained by a particular heteroskedasticity structure in which the time-varying conditional variances of the variables are driven by an uncertainty measure plus a stochastic idiosyncratic component. In this sense, our identi…cation method belongs to the heteroskedasticity-based identi…cation tradition (see for example Rigobon (2003), Sentana, and Fiorentini (2001), and the review in Kilian and Lütkepohl (2017, chapter 14)). However di¤erently from this tradition, our methodology is based on modeling the conditional variances via stochastic volatility. This di¤erence is non-trivial, because it allows much more ‡exibility in the evolution of the conditional variances than regime 2 switching or GARCH speci…cations, since the time-varying volatilities have their own shocks which are independent from the shocks hitting the level of the variables. As we shall see, the use of stochastic volatility also impacts the type and number of identifying restrictions, which are di¤erent from those implied by other heteroskedasticity-based identi…cation methods. It is also worth mentioning that the presence of stochastic volatility makes the errors of our model non-Gaussian, so that another way to interpret our identi…cation procedure is that it exploits the information in higher order moments, rather than only in the second moments as in traditional Gaussian VARs. In this sense, our approach also belongs to the strand of the literature on identi…cation in non-Gaussian models; see, for example, Lanne, Meitz, and Saikkonen (2017). Methodologically, the model developed in this paper is a structural VAR with timevarying volatility in which one of the variables (the uncertainty measure) impacts both the mean and the variance of the other variables. We provide conditional posterior distributions for this model, which is a substantial extension of the leverage model of Jacquier, Polson, and Rossi (2004), a widely used model in the …nance literature. These distributions are nontrivial because, with respect to the model of Jacquier, Polson, and Rossi (2004), our model entails an additional layer of complication insofar as the stochastic volatility factor also enters the conditional mean of the process. The e¢ ciency and reliability of the algorithm are established in Monte Carlo experiments with simulated data, prior to use with monthly and quarterly U.S. datasets. Our empirical application, based on both monthly and quarterly U.S. data over the period 1960-2017, leads to three main …ndings. First, when allowing for the simultaneous feedback e¤ect, shocks to macro and …nancial uncertainty have a depressive e¤ect on output growth, investment, and consumption, in line with previous empirical studies such as JLN and CCM and the theoretical contributions mentioned above. Second, when looking at macro uncertainty, we …nd strong evidence that coe¢ cients related to the feedback channel are close to zero, which means that treating macroeconomic uncertainty as exogenous is likely harmless. Third, we …nd that some of the coe¢ cients measuring the feedback e¤ect of macroeconomic variables on …nancial uncertainty are signi…cantly di¤erent from zero, thereby indicating that …nancial uncertainty can be endogenous to some extent. This pattern is particularly evident in the monthly dataset, with variables such as consumer spending, in‡ation, industrial production, and the federal funds rate all featuring negative feedback coe¢ cients, implying that an increase in these indicators leads to a reduction in …nancial uncertainty. Endogeneity of …nancial uncertainty is in contrast with the …ndings of LMN, who …nd less endogeneity in …nancial uncertainty with respect to macro uncertainty, but more in line with the treatment of …nancial indicators as “fast” variables that can react 3 contemporaneously to macroeconomic shocks; see, e.g., Bernanke, Boivin, and Eliasz (2005). The paper is structured as follows. Section 2 presents the model and the identi…cation approach. Section 3 develops the estimation algorithm. Section 4 provides an illustrative application and Monte Carlo experiments based on a small scale version of the model. Section 5 presents the main empirical results. Section 6 summarizes our main …ndings and concludes. The Appendix contains derivations and algorithm diagnostics. 2 A model of endogenous uncertainty 2.1 Model speci…cation Our interest is in modeling the relationship between a set of economic variables, which we collect in the n-dimensional vector process yt, and an observable scalar measure of uncertainty, which we label mt. We specify the following model: yt = 0 + y(L)yt 1 + m(L) lnmt 1 + lnmt +A 1 0:5 t t (1) lnmt = + y(L)yt 1 + m(L) lnmt 1 + t + ~ ut; (2) where y(L) is a n n matrix polynomial, m(L) is a n 1 vector polynomial, 0 and are n 1 vectors, y(L) and m(L) are 1 n vector polynomials, is a 1 n vector, and is a scalar. The matrix A 1 is a lower triangular n n matrix with ones on the main diagonal, which describes the contemporaneous relationships across the economic variables, and t is an n n diagonal matrix. The shocks are t iid N(0; In), ~ ut iid N(0; ~ u), and are mutually independent. The model (1)-(2) is a structural VAR for the (n + 1)-dimensional vector (y0 t lnmt) 0. There are three features that di¤erentiate this model from the VARs typically used in the uncertainty literature (e.g., in studies such as Bloom (2009) and JLN). The …rst major feature is that the model allows for bilateral simultaneity between economic variables and uncertainty. Speci…cally, the model allows for both i) contemporaneous e¤ects of a shock to uncertainty on the economic variables, as measured by @yt=@~ ut = , and ii) contemporaneous e¤ect of a shock to economic variables on uncertainty, as measured by @ lnmt=@ t = (we will refer to this as the “feedback e¤ect”). This bilateral simultaneity is typically not present in the traditional implementations of uncertainty VARs, and is in The uncertainty measure could be also treated as unobservable. In this case, an additional step in the MCMC sampler would be needed in order to draw from its conditional posterior distribution. For an example of this approach in a model which does not allow for endogenous uncertainty see Carriero, Clark, and Marcellino (2017a).