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Fundamental Economic Shocks and the Macroeconomy Charles L. Evans and David A. Marshall Federal Reserve Bank of Chicago April 10, 2007 Abstract This paper asks how macroeconomic and …nancial variables respond to economic impulses. We identify structural economic shocks using a strategy that utilizes measures of economic shocks explicitly derived from economic models. We use this approach to identify technology shocks, marginal-rate-of-substitution (labor supply) shocks, and monetary policy shocks in the context of a Factor Augmented VAR similar to that developed by Bernanke, Boivin, and Eliasz (2005). We then examine the Bayesian posterior distribution for the responses of a large number of endogenous macroeconomic and …nancial variables to these three shocks. These shocks account for the preponderance of output, productivity and price ‡ uctuations. We …nd that technology shocks have a permanent impact on measures of economic activity, even though this characteristic of technology shocks is not imposed as an identifying restriction. In contrast, the other shocks have a more transitory impact. Labor inputs have little initial response to technology shocks; the response builds steadily over the …ve year period. Consumption has a sluggish response to the technology shock, consistent with a model of habit formation. Monetary policy has a small response to technology shocks, but “leans against the wind” in response to the more cyclical labor supply shock. This shock has the biggest impact on interest rates. Stock prices respond to all three shocks. A number of other empirical implications of our approach are discussed. Corresponding Author. Address: Federal Reserve Bank of Chicago, 230 South LaSalle St., Chicago, IL 60604-1413. Telephone: (312) 322-5102. e-mail: david.marshall@chi.frb.org. We are grateful to Frank Schorfheide, Mark Watson, and Tao Zha for helpful comments. The opinions in this paper are those of the authors, and do not re‡ the views of the Federal Reserve Bank of Chicago or the Federal Reserve System. ect 1. Introduction This paper investigates how macroeconomic and …nancial variables respond to structural economic shocks. We use a relatively new and unexplored identi…cation strategy that simultaneously identi…es multiple impulses. Our strategy is linked to economic theory without being tied rigidly to a particular theoretical model. Furthermore, it minimizes dependence on arbitrary choices, such as the choice of variables to be included in a vector autoregression (VAR). Current methods for identifying and estimating economic shocks have been well-studied since Sims’ (1980) important contribution. See Stock and Watson (2001) and Christiano, s Eichenbaum, and Evans (1999) for recent surveys. A stalwart identi…cation method is to place zero restrictions on a matrix of contemporaneous impact multipliers in a VAR. Although much has been learned through these methods, such zero restrictions rarely conform precisely to the equilibrium decision rules of any dynamic stochastic general equilibrium model (DSGE), a point made by Lucas and Stokey (1987) in response to Litterman and Weiss (1985). Long-run restrictions are more likely to be compatible with a set of DSGE models, although subtle changes in model trending details can make these implications fragile, as King and Watson (1997) have discussed relative to Lucas’ theory of the natural rate s (1972). Furthermore, economic shocks are often identi…ed one at a time, ignoring potential correlations across shocks. We propose an identi…cation strategy that is more closely motivated by the insights of economic theory without imposing all the restrictions of a particular economic model. Furthermore, we seek to identify multiple shocks simultaneously, imposing orthogonality across these shocks.1 Our approach is to use measures of fundamental shocks that are derived from economic models developed in antecedent literature. We call these“modelbased measures” . In particular, we measure technology shocks as Solow residuals and monetary policy shocks from a Taylor rule speci…cation. In addition, we construct a measure of shocks to the marginal rate of substitution (MRS) between consumption and leisure using a procedure similar to Hall (1997). As Hall notes, these shocks can be interpreted as labor supply shocks. These measures are potentially noisy. Speci…cally, since they are mutually correlated it is problematic for our purposes to treat these as clean measures of the true underlying structural impulses. Instead, we follow the structural VAR (SVAR) literature in assuming that all structural shocks are mutually orthogonal. We use our model-based shock measures 1 Important recent papers in the literature that identify multiple structural shocks include Gali (1992), Leeper, Sims, and Zha (1996), and Del Negro, Shorfheide, Smets, and Wouters (2005). 1 to derive the linear combination of VAR innovations that best replicates each structural impulse. This allows us to compute identi…ed impulse response functions, and relate the evidence to important macroeconomic questions and alternative models. In using shock measures derived from economic models, our identi…cation strategy exploits the restrictions implied by economic theory more directly than the typical identifying strategies used in VAR analysis. However, we do not impose all of the restrictions implied by these economic models. (For example, we leave the dynamics unrestricted.) In this sense, our approach is midway between the standard SVAR approach and a fully-articulated DSGE model. Our approach does require strong assumptions, and we do not assert that it pointwise dominates other approaches. Nonetheless, it is a plausible approach that di¤ers from others currently in use, so it could o¤er a di¤erent perspective on economic issues of interest.2 Evans and Marshall (2003) used a variant of this method to examine a variety of term structure responses. This paper advances that work along a number of dimensions. First, we use an alternative, and arguably more robust, set of identifying restrictions. Second, rather than restricting our information set to a small number of macroeconomic variables, we incorporate a much larger data set by using the Factor Augmented VAR (FAVAR) approach of Bernanke, Boivin, and Eliasz (2005). This approach allows us to incorporate enough information in the VAR residuals to span the true shocks without exhausting our degrees of freedom. In addition, the approach limits the e¤ect of arbitrary choices regarding which variables to include in the SVAR. Finally, we move from Evans and Marshall’ (2003) focus s on interest rate responses to examine the responses of a wide range of macroeconomic and …nancial data. This enables us to explore a number of substantive questions that clearly can bene…t from a multi-shock context. Speci…c questions we address include the following: Can a small number of shocks account for most output ‡ uctuation? How realistic is the traditional focus on technology shocks as drivers of business cycle variation in output, investment, and labor inputs? (Kydland and Prescott, 1982, and subsequent RBC literature) Is it reasonable to associate technology shocks with permanent shocks to output (Blanchard and Quah, 1989; Gali, 1992) or to labor productivity (Gali, 1999; Christiano, 2 In linking identi…cation to the insights of economic theory without tying the identi…cation too tightly to any single economic model, our approach is related to Del Negro, Shorfheide, Smets, and Wouters (2005). They use a Bayesian approach to identify a VAR in which the prior distribution is derived from a particular dynamic general equilibrium model. The strength of the prior determines how tightly the identi…cation is linked to the underlying model. 2 Eichenbaum, and Vigfuson, 2003), with other shocks (such as “aggregate demand” shocks) having only transient e¤ects on these variables? What drives procyclical labor productivity: technology shocks or demand shocks (“labor hoarding” )? Are technology shocks contractionary for labor hours and employment (as argued by Basu, Fernald, and Kimball, 2004, and Gali, 1999), or do these measures of labor inputs rise contemporaneously with an expansionary technology shock (as argued by Christiano, Eichenbaum, and Vigfuson, 2003)? What is the role of monetary policy in aggregate ‡ uctuations? Is monetary policy driven largely by responses to economic conditions, or is there an important role for exogenous monetary policy shocks? Does monetary policy respond di¤erently to technology (“supply” shocks than to labor supply (“demand” shocks? Are monetary ) ) policy shocks an important source of business cycle variation (as implied by the estimates of Strongin, 1995) or are they rather minor contributors (as discussed by Sims and Zha, 1998, and Christiano, Eichenbaum, and Evans, 1999)? What drives ‡ uctuations in the price level and in‡ ation? In particular, what is the role of real side impulses (such as Phillips curve e¤ects or shocks to marginal costs)? Are movements in asset prices driven to a signi…cant extent by macroeconomic impulses? Or are asset prices primarily driven by dynamics internal to the …nancial markets that are largely orthogonal to the macroeconomy? If macro impulses have a signi…cant role in …nancial markets, which speci…c impulses are most important? Our results shed light on these questions. We …nd that the three shocks we identify account for around 72% of the short-run variation in output and over 84% of the variation in output at longer horizons. In addition, these shocks account for more than 50% of the long-run variation in in‡ ation, although they account for only about 20% of in‡ ation variation at the 3-month horizon. The MRS shock is an important driver of short-run output variation, but the e¤ect of the technology shock is much longer-lived. Thus, our evidence favors the permanent vs. transitory distinction between technology shocks and other shocks, even though we do not impose this distinction as an identifying restriction. We …nd that the procyclical response of labor productivity is due almost entirely to procyclical technology shocks. Labor input measures display almost no contemporary response to technology shocks, but rise gradually in the years following the shock. 3 Similarly, wages have only a small initial response to technology shocks, even though the technology shocks boost labor’ s marginal product. Wages then rise monotonically over the next four years. Monetary policy shocks have a very small impact on real economic activity. While these shocks do account for a good deal of the short-run variation in the fed funds rate, their impact is extremely short-lived. Longer-lived policy actions are mostly endogenous responses of the Fed to other shocks. In particular, the Fed displays a rather small response to technology shocks, but strongly “leans against the wind” in response to the more cyclical MRS shock. Finally, while most variation in stock prices is accounted for by sources other than our three identi…ed shocks, there are a number of intriguing patterns that point to linkages between …nancial markets and the macroeconomy. In particular: the MRS shock accounts for most variation in Treasury yields, and all three shocks have signi…cant impacts on stock prices. The paper is organized as follows. Section 2 describes the basic framework we use. Section 3 discusses our Bayesian approach to statistical inference. Section 4 describes the construction of our three model-based shock measures and discusses our FAVAR speci…cation. Section 5 describes our empirical results, and section 6 concludes. 2. Identifying a Structural VAR using Model-Based Shock Measures 2.1. Basic Framework We study the responses of macroeconomic and …nancial variables to a set of m fundamental shocks. Let "t denote the m 1 vector of shocks we wish to identify. It is assumed that "t is serially uncorrelated, with E"t = 0 and E"t "0t = I (2.1) A key assumption in our approach is that the econometrician observes a m 1 vector t of model-based measures of these processes. For example, if one element of the "t vector is an exogenous technology shock, the corresponding observable model-based measure might be a data series consisting of Solow residuals. Or, if another element of "t were a monetary policy shock, the corresponding model-based measure might be the residual from an empirical Taylor rule. These model-based measures may be serially correlated and contaminated with measurement error. Furthermore, they may not be clean, in the sense that a given element of t may be a function of all of the "t ’ For example, the measured Solow residual series s. may be contaminated with monetary policy shocks, as argued by Evans (1992). To capture these possibilities, we assume that the t vector of model-based shocks is related to the true, 4 unobserved shock vector process "t by t = D0 "t + D1 "t where Dk ; k = 0; :::; K; are m 1 + ::: + DK "t K (2.2) + wt m matrices of parameters and wt is an m random measurement errors with covariance matrix E"t wt j 1 vector of for which w = 0; 8j = 0; 1; 2; ::: (2.3) We assume that D0 is nonsingular. If D0 is diagonal, then the innovation to a given modelbased shock i;t is a function only of its own fundamental shock "i;t (plus the measurement error wt ). However, if the ith row of D0 is non-diagonal, then the innovation to the shock i;t is a function of two or more elements of "t . In addition to the t vector, the econometrician also observes an n economic variables, where n 1 vector Yt of The law of motion for Yt has the following structural m. representation: b AYt = B(L)Yt 1 "t + (2.4) t b where A is an n n nonsingular matrix of parameters, B(L) is an n n matrix of polynomials in the lag operator, and t is an (n orthogonal to "t . In particular, E 1 vector of additional i.i.d. structural shocks m) "t "0t t 00 t (2.5) =I In the general case, representation (2.4) could be the reduced form of some linearized or loglinearized DSGE model. Alternatively, it could be an atheoretic forecasting model. From the standpoint of our investigation, t are “nuisance shocks”that we do not seek to identify. Equation (2.4) can be written as a VAR: Yt = B(L)Yt where ut is an n and 1 (2.6) + ut 1 vector of VAR residuals with covariance matrix u, b B (L) = A 1 B(L) "t = Aut t It is convenient to partition the rows of A as follows: A" A A= 5 (2.7) where the m n matrix A" consists of the …rst m rows of A. Notice that (2.8) " t = A" u t : According to equation (2.8), we can recover the structural shocks "t from the VAR residuals if we can identify the mn elements of the matrix A" . To that end, note that we can combine equations (2.2) and (2.8) to get t where the n = C0 ut + C1 ut 1 + ::: + CK ut K + wt (2.9) m matrices Ck ; k = 0; :::; K; are de…ned by Ck (2.10) Dk A" ; k = 1; :::; K: Equation (2.10) with k = 0 means that matrix A" is identi…ed if we can identify the matrices C0 and D0 . In the next subsection we turn to this task. 2.2. Identi…cation of A" First, note that equations (2.1) and (2.8) imply that I = A" 0 u A" : (2.11) Equations (2.10) and (2.11) in turn imply 0 D0 D0 = C0 0 u C0 0 u C0 . 0 C0 u C0 which says that D0 is a decomposition of C0 (2.12) To identify D0 from data, we …rst impose restrictions su¢ cient to ensure that can be estimated from the data. We then impose additional assumptions to ensure that the decomposition in equation (2.12) is unique. Let us turn …rst to the estimation of C0 0 u C0 . Matrix u can be estimated in the usual way from the variance-covariance matrix of the VAR residuals. Estimation of C0 requires an additional assumption: E t wt = 0 (2.13) 0 Together, equations (2.3), (2.7), and (2.13) ensure that Eut wt = 0, so we can estimate Ck ; k = 0; :::; K by regressing t on ut .3 3 OLS estimation of equation (2.9) is consistent, but not e¢ cient. However, using OLS estimation simpli…es computation of the Bayesian posterior distribution of the model parameters, which we use for inference. See the appendix for details. 6 While equation (2.13) is a strong restriction, some form of strong exclusion restrictions must be imposed in virtually any procedure that seeks to identify a small number of shocks using a large data set. For example, index model approaches, such as Sargent and Sims (1977) or Stock and Watson (1989), are typically implemented by strongly restricting the covariances among fundamental shocks and measurement disturbances. Given the estimates of C0 and u , equation (2.12) represents m(m + 1)=2 restrictions on the m2 elements of D0 . We can identify D0 if we impose another m(m 1)=2 restrictions on ~ D0 . It is useful to formalize these restrictions by specifying m (m 1) =2 free parameters, d, n o 2 ~ along with a mapping d : Rm ! Rm(m 1)=2 such that, given d; C0 ; u ; D0 is the solution to the following system of n2 equations: ~ d (D0 ) = d (2.14) 0 D0 D0 = C0 0 u C0 For example, one possible set of identifying restrictions could be to require that D0 be lowertriangular.4 These restrictions would be represented in system (2.14) by having the mapping ~ d ( ) pick out the m (m 1) =2 upper triangular elements of D0 , and then setting d equal to ~ a vector of zeros. (In section 4.2, below, we discuss the speci…cation of d ( ) and d that we actually use in the empirical part of this paper.) Having estimated C0 and identi…ed D0 , we can then identify A" using equation (2.10), which implies that A" = D0 1 C0 . The structural shock vector "t can then be identi…ed using equation (2.8). To compute impulse responses of Yt to "t , rewrite the reduced form (2.6) as Yt = B(L)Yt 1 +A 1 "t (2.15) : t Computing impulse responses to "t requires that we know the …rst m columns of A 1 , which we can denote “[A 1 ]" ” This submatrix can be computed from knowledge of A" using the . relation A 1 " = 0 u A" (2.16) which follows directly from equation (2.11). Once [A 1 ]" is identi…ed, we can compute the response of any variable zt , even one not included in the vector Yt . To do so, we augment system (2.6) and (2.7) with another equation in zt : Yt zt 4 = B(L) (L) 0 (L) Yt zt 1 1 + A F 1 0 G 2 4 "t t t 3 5: (2.17) Evans and Marshall (2003) pursue this strategy after rejecting the testable hypothesis that D is diagonal. 7 In equation (2.17), (L) and (L) are respectively 1 n and 1 1 vector polynomials in the lag operator, F and G are 1 n and 1 1 parameter vectors, and t is a serially uncorrelated disturbance that is also uncorrelated with "t and t . The zero restrictions in equation (2.17) ensure that, given knowledge of Yt 1 and its lags along with "t and t, neither t, zt , nor its lags are needed to determine Yt . 2.3. Expanding the Information Set As with any structural VAR, a key requirement of our approach is that the true fundamental shocks "t are spanned by the VAR residuals ut . To ensure that this is indeed the case, one would want to incorporate a large number of data series in the VAR. However, to do so directly would quickly lead to degrees-of-freedom problems. As discussed in Bernanke, Boivin, and Eliasz (2005), VARs typically used in the literature incorporate no more than 6 to 8 variables.5 To address this problem, we follow Bernanke Boivin, and Eliasz (2005) and implement equation (2.4) as a Factor Augmented Vector Autoregression (FAVAR). Speci…cally, we use a set Xt of p observable data series (where p is large), and we assume that Xt is a function b of n factors Yt , where n is much smaller than p: b Xt = Yt + et : (2.18) We assume that et displays weak cross-correlation in the sense of Stock and Watson (1998). As in Stock and Watson (1998, 2002) and Bernanke Boivin, and Eliasz (2005), we estimate b b Yt as the …rst n principal components of Xt . We then use Yt in equation (2.4) in place of Yt . b Note that this is a two-step procedure: …rst we estimate equation (2.18) to generate Yt , and then we estimate equation (2.4) and impose the strategy of section 2.2 to identify the shocks "t . In using this two-step approach we follow Stock and Watson (1998, 2002). In principle, one could combine these two steps. However, Bernanke Boivin, and Eliasz (2005) argue that the gains from doing so appear to be rather small, while the computational burden increases substantially.6 5 These degrees-of-freedom problems can be mitigated to some extent by imposing a Bayesian prior. For example, Leeper, Sims and Zha (1996) use this approach to estimate a VAR with 18 variables. 6 b There is a technical issue in using Yt in place of Yt in equation (2.17): if zt is one of the elements of the information vector Xt , then it is not clear that the zero restrictions in equation (2.17) will hold. In their treatment of dynamic factor models, Stock and Watson (2005) test a variety of restrictions of this form. While they often reject the zero restrictions in a statistical sense, they …nd that the deviations from the zero restrictions are of no economic signi…cance in virtually all cases. We will continue to impose the zero restrictions in equation (2.17) as a maintained assumption 8 3. Bayesian Inference b Given the Yt series n estimated in theo …rst step, the remaining parameters to be determined in ~ the second step are B; u ; C; w ; d , where B contains the coe¢ cients of the lag polynomial ~ B (L) ; C fCk gK ; and d is the vector of free parameters that identi…es the elements of k=0 matrix D0 in equation (2.14). A joint prior distribution can be imposed on these parameters, and the posterior distribution can then be computed. In doing so, we are explicitly treating b the generated series Yt as known data. 7 ~ Note that the parameter vector d di¤ers from the other parameters. Since m (m 1) =2 restrictions have been imposed on the D0 matrix, the model is exactly identi…ed. Therefore, the parameters fB; u ; C; w g exhaust the information in the data, so any speci…cation of ~ ~ the m (m 1) =2 elements of d is equally likely. Thus the prior on d equals the posterior, so this prior acts as a way of specifying soft restrictions on the D0 matrix. The appendix contains a detailed description of how one computes the posterior distribution for fB; u ; C; w g given an uninformative prior on these four parameter elements. This paper only explores the implications of this uninformative prior. It is straightforward to amend this procedure for an informative prior. 4. Empirical Implementation 4.1. Model-Based Shock Measures In our empirical application of the identifying strategy of section 2, we seek to identify three shocks: a technology shock, a marginal-rate-of-substitution shock that can be interpreted as a labor supply shock, and a monetary policy shock. To implement the model-based identi…cation strategy, we need model-based measures of these three shocks. In this section we describe how we construct these measures. 4.1.1. Technology Shocks Since Prescott (1986), the driving process for aggregate technology shocks in real business cycle models has been calibrated to empirical measures of Solow residuals. A large literature, including Prescott (1986), has noted that a portion of the ‡ uctuations in standard Solow 7 Note, in addition, we are treating the model-based measures t as known, even though, in some cases, these measures may involve estimated parameters. An alternative procedure would be to impose a prior on parameter matrices f ; g in equation (2.18), and then compute the joint posterior over all the parameters. However, these matrices are extremely large. In our empirical application, is 190 6 and , the covariance matrix of t , is 190 190. As a result, this alternative procedure borders on the infeasible. 9 residual measures is endogenous, responding to macro shocks.8 Basu, Fernald, and Shapiro (2001b) provide a recent estimate of technology innovations that attempts to reduce these in‡ uences. Ignoring industry composition e¤ects, their aggregate analysis speci…es production as follows: Yt = zt gt F (vt Kt ; et Nt ) ln zt = + ln zt 1 + (4.1) T ech;t where Y , z, v, K; e, and N are the levels of output, technology, capital utilization rate, capital stock, labor e¤ort, and labor hours.9 The object gt represents costs of adjusting employment and the capital stock. It is an explicit function of observable data, and is calibrated from econometric estimates in the literature (see Shapiro (1986) and Basu, Fernald, and Shapiro (2001a,b)). F is a production function that is homogeneous of degree 1, allowing for the possibility of increasing returns. Basu, Fernald, and Shapiro (2001a,b)) specify an economic environment where the unobserved variables v and e can be measured as proportional to the workweek of labor and capital. Assuming = 1 — constant-returns-to-scale — Basu, Fernald, and Shapiro (2001b) use time-varying cost shares to compute a quarterly, aggregate measure of the technology innovation, T ech;t . We use Basu, Fernald, and Shapiro’ (2001b) quarterly, aggregate measure of technology s for our model-based empirical measure T ech of the aggregate technology shock.10 Although this quarterly measure includes controls for many latent, endogenous features, data limitations prevent controlling for industry compositional e¤ects. This potentially introduces measurement error into this series. The data begin in 1965:II and end in 2000:IV. 4.1.2. Marginal-Rate-Of-Substitution Shocks A shock to the marginal rate of substitution (MRS) between consumption and leisure can potentially shift aggregate demand for goods and services. Hall (1997), Shapiro and Watson (1988), and Baxter and King (1990) …nd substantial business cycle e¤ects from empirical measures of intratemporal marginal rates of substitution between consumption and leisure. To generate a model-based empirical measure of an MRS shock, we generalize Hall’ (1997) s procedure to allow for time-nonseparable preferences.11 Consider a representative consumer with the following utility speci…cation: U (Ct ; Nt ) = Ct t bC t 1 8 1 1 Nt1+ 1+ For example, see Burnside, Eichenbaum and Rebelo (1993) and Braun and Evans (1998). Throughout this paper, we omit the time subscript t if no ambiguity is implied. 10 We thank John Fernald for providing us with this time series on technology shocks. 11 Holland and Scott (1998) study a similar MRS shock for the United Kingdom economy. 9 10 ln t = (L) ln t 1 + (4.2) M RS;t where C is the consumption by the representative agent, C represents the per-capita aggregate consumption level, N is labor hours, M RS is a serially correlated preference shifter, and is a serially independent shock. The …rst-order conditions for consumption and labor hours lead to the following intratemporal Euler equation (or MRS relationship) Ct t bC t 1 = Nt where Wt is the real wage and ln t = t ln Nt 1 Wt (1 (4.3) t) is the labor tax rate. Taking logs, we obtain lnWt ln (1 t) + ln Ct bC t 1 : (4.4) In equilibrium, the per-capita aggregate consumption equals the consumption levels of the representative agent, so C = C: We use equation (4.4) to obtain an empirical measure of ln t . We then compute our model-based empirical measure M RS;t of the MRS shock as the residual from the OLS estimate of equation (4:2) : Our data are quarterly and extend from 1964:I to 2000:IV. Consumption is measured by per capita nondurables and services expenditures in chain-weighted 1996 dollars. Labor hours correspond to hours worked in the business sector per capita. The real wage corresponds to nominal compensation per labor hour worked in the business sector de‡ ated by the personal consumption expenditure chain price index. The hours and compensation data are reported in the BLS productivity release. Finally, our measure of the labor tax rate is a quarterly interpolation of the annual labor tax series used in Mulligan (2002).12 We calibrate the utility function parameters as follows. First, to ensure balanced growth we set = 1; corresponding to log utility for consumption services. Second, we use Hall’ (1997) value for s = 1:7, corresponding to a compensated elasticity of labor supply of 0.6. Finally, we set the habit persistence parameter b = 0:73 as estimated by Boldrin, Christiano and Fisher (2001). We measure M RS as the residual in equation (4.2). We estimate a sixth-order polynomial for (L). In addition, the M RS measure exhibits noticeable low frequency variation, so we also include a linear time trend in the regression to account for demographic factors that are beyond the scope of this analysis. If the theoretical variables and data series coincide and our estimate of (L) is correct, then our measure of M RS would equal "M RS : If, however, our measures of consumption, labor hours, and the spot real wage di¤er from the theory, then 12 M RS would represent a noisy measure of "M RS . In order to allow for serially-correlated We would like to thank Casey Mulligan for providing us with his labor tax rate data. 11 measurement errors in t, we use an instrumental variables estimator to estimate (L).13 If our model-based measure M RS were a clean measure of the true structural shock "M RS , it should be causally prior to any endogenous variables. While we do not use the model-based measure directly as the structural shock, clearly causal priority is a desirable characteristic for our M RS measure. Gali, Gertler, and Lopez-Salido (2001) speci…cally raise this issue with regard to a series similar to our M RS measure, questioning whether it was Granger-causally prior to output, the short-term interest rate, and the term spread. When we replicate the Gali, Gertler, and Lopez-Salido (2001) causality tests for our M RS measure, we …nd no evidence that M RS is Granger-caused by the variables they consider (detrended GDP, the federal funds rate, and the term spread). Details of these causality tests are displayed in Table 1. Derived this way, our MRS shock has a clear interpretation as a preference shifter. However, macroeconomic researchers have o¤ered several alternative interpretations for the random marginal rate of substitution shifter t in equation (4:3).14 First, the home production literature due to Benhabib, Rogerson, and Wright (1991), Greenwood and Hercowitz (1991), and Chang and Shorfheide (2003), among others, suggests that t could be a productivity shock to the production of home goods. Second, inertial wage and price contracts will distort the simple intratemporal Euler equation as it is speci…ed in (4:3) : In particular, in the Calvo pricing environments considered by Christiano, Eichenbaum, and Evans (2005) and Galí, Gertler, Lopez-Salido (2001), alternative versions of (4:3) hold. Third, Mulligan (2002) interprets t as re‡ ecting labor market distortions, such as changes in tax rates or union bargaining power. To the extent that these alternative explanations have di¤erent theoretical implications for impulse response functions, an empirical analysis of our MRS shock can help shed light on which explanation seems to be consistent with the aggregate data. 4.1.3. Monetary Policy Shocks Unlike the previous two shock measures, there is no well-developed theory that derives monetary policy shocks from an optimizing framework. However, many theoretical models assume that the monetary authority sets monetary policy via some variant of a Taylor (1993) rule. That is, the short-term interest rate is set as an increasing function of both in‡ ation and the output gap (a measure of the shortfall in economic activity compared to its 13 Our shock identi…cation strategy assumes that the measurement errors in our model-based shocks are independent of the VAR innovations. Consequently, we use real GDP, the GDP price index, and commodity prices as instruments. 14 As Hall (1997) pointed out, the greatest amount of evidence against Eichenbaum, Hansen, and Singleton’ s (1988) preference speci…cations surrounded the intratemporal Euler equation for consumption and leisure. 12 potential). In some speci…cations, lags of the short-term interest rate are included in order to capture the desire of the monetary authority to smooth changes in the interest rate.15 In these models, the natural speci…cation for monetary policy shocks is the disturbance to the short-term interest rate that is orthogonal to these systematic components of the Taylor Rule. We adopt this approach for our model-based measure of the monetary policy shock MP . The particular approach we use is to specify a backward-looking Taylor rule, so the interest rate is a function of current and lagged in‡ ation, as opposed to expected future in‡ ation. In addition, the output gap is not observed, so some empirical proxy for this gap variable must be used. In the spirit of taking our model-based measures from approaches proposed in antecedent literature, we use a gap measure derived from work by Staiger, Stock, and Watson (1997). In particular, we measure the gap as the di¤erence between the current unemployment rate and the Staiger-Stock-Watson measure of the natural rate of unemployment.16 In addition, we allow the coe¢ cients on in‡ ation and on the gap variable to be regime dependent. Speci…cally, we allow for three regimes: before 1979:Q4, 1979:Q4 - 1982:Q4, and after 1982:Q4. The speci…c model is as follows: rf ft = 4 X j rf ft j + j=1 3 X [ k (Ik ugapt ) + k (Ik t )] + (4.5) M P;t k=1 where rf ft denotes the fed funds rate, ugapt denotes the gap between current unemployment and the Staiger-Stock-Watson measure of the natural unemployment rate,17 t denotes the log change in the GDP de‡ ator, and Ik is an indicator variable for the three regimes. The data run from 1959:I through 2000:IV. 4.1.4. Correlations among model-based measures Table 2 displays the correlations among our three model-based measures f T ech ; M RS ; M P g. As can be seen, the correlations are small but non-zero. As a result, we are reluctant to use them as clean measures of the true structural shocks "t . Instead, we use them as inputs into the identi…cation strategy described above in section 2.18 In section 5.8, below, we consider some interpretive problems that would arise if we were to treat the model-based measures as error-free measures of the structural shocks. 15 A time-varying in‡ ation target is also sometimes included. See, e.g., Kozicki and Tinsley (2001). We have experimented with several other speci…cations for the Taylor Rule, including measuring the gap as detrended output, and using real-time data. The results are very close to those in our baseline speci…cation, except the error bands are somewhat tighter when we use the Staiger-Stock-Watson gap measure. 17 We obtained data on ugapt from Mark Watson’ website. s 18 Boivin and Giannoni (2006) develop an alternative approach to handling potential mismeasurement of structural shocks within a fully speci…ed DSGE model. 16 13 4.2. Identifying restrictions To identify the model, we must impose m (m 1) =2 restrictions on matrix D0 . Since m = 3, we need 3 restrictions. To motivate the restrictions we impose, note that our procedure is only likely to be informative if the model-based measures contain a good deal of information about the shocks they seek to identify. Speci…cally, a shock measure "i only if most of the variation in i, i is informative about after controlling for measurement error wt , is accounted for by "i : Equations (2.2) and (2.1) imply that vart 1 i;t wi;t = m X 2 D0;ij (4.6) j=1 where D0;ij = (i; j)th element of matrix D. We will refer to the left-hand side of equation (4.6) as the “non-noise variance” of i;t . To ensure that most of this variance is driven by the own shock "i , we need the fraction of this variance associated with the diagonal element D0 ;ii to be fairly large. Our restrictions on D0 are motivated by this consideration. In particular, we restrict the three diagonal elements such that D ;2 ~ Pm 0 ii 2 = di ; i = 1; 2; 3 D0 ;ij j=1 (4.7) ~ where di is drawn from a uniform distribution with support [:80; :95]: This ensures that between 80% and 95% of the non-noise variance of each model-based measure i is due to 19 its own shock "i . 4.3. FAVAR Speci…cation In order to ensure that our information set Xt in equation (2.18) is big enough to span the space of the shocks "t we seek to identify, we use 190 data series in Xt . Thirty-six of these are quarterly data, while 154 are monthly series that have been quarterly averaged. The data sample is from 1967:Q2 through 2000:Q4. The data series used are listed in Table 1A in the Data Appendix, along with the transformations used to induce stationarity.20 We set n = 6, b and we compute Yt in equation (2.18) as the …rst six principal components of Xt .21 Four 19 Restrictions (2.12) and (4.7) constitute a system of nine equations in the nine unknown elements of D0 . However, these equations are nonlinear, so there is no guarantee that a solution to this system exists. In 0 practice, for the estimated matrix C0 u C0 (or for the draws of this matrix from its postierior distribution), ~ ~ we …nd no di¢ culties solving the system as long as di < 0:95. When di is very near unity for i = 1; 2; 3, ~ however, we …nd that no solution exists. Perhaps this is not surprising, since di = 1, 8i, cannot be a solution 0 to the system if C0 u C0 is non-diagonal. 20 We control for outliers by replacing any data point more than six times the interquartile range (IQR) above the series median with median + 6 IQR (and analogously for data points more than 6 IQR below the IQR). All transformed series are then de-meaned and standardized. 21 When we increase the number of principal components to eight, the results are almost identical to those when six principal components are used. In no case are the substantive implications changed. 14 quarterly lags of each principal component are used in the VAR, equation (2.4). We then use b equation (2.17) (substituting Yt for Yt ) to compute the responses to f"T ECH ; "M RS ; "M P g of a number macroeconomic and …nancial market variables, using the approach of Zha (1999). The model-based measures only provide useful information for identifying A if they are correlated with the VAR residuals ut . Table 3 provides evidence on these correlations in the data we use. It displays the R2 s for the OLS regressions in system (2.9) using our measures of t . These R2 s show that over 50% of the variation in each model-based measure is accounted for by the VAR residuals. In addition, the F -statistics testing the hypotheses that the VAR residuals are uninformative for the t measures reject these hypotheses at any desired signi…cance level. Under our identifying restrictions, these statistics imply that our measures are potentially informative for the true structural shock vector "t . 5. Empirical Results The data we use are described in the Data Appendix. Our empirical results are displayed in Table 4 and Figures 1 - 7. For each endogenous variable listed, Table 4 gives the median fraction of 3-, 12-, and 60-month ahead forecast variance accounted for by the three identi…ed shocks, f"M P ; "M RS ; "T ECH g, according to the posterior distribution. The fourth line in each panel gives the median fraction of each forecast variance accounted for by the three shocks collectively. The two numbers in parentheses following each median statistic give the 95% and 5% quantiles of the posterior distribution for each forecast variance fraction. Figures 1 - 7 display the median impulse responses of selected endogenous variables. The upper and lower dashed lines give the 95% and 5% quantiles of the response distribution, respectively. All of these statistics were computed using 500 draws from the posterior distribution of the model’ parameters. s 5.1. Long Run Behavior of the Economy Figure 1 displays the responses of GDP and labor productivity to our three identi…ed shocks over an 80 quarter horizon. There is clear evidence that technology shocks induce permanent shifts in the level of GDP and productivity. In contrast, the responses to the MRS shock and the monetary policy shock appear to display mean reversion, with little evidence of a permanent level shift for GDP or productivity. An alternative way of describing the posterior distribution of these long run responses is in Table 5, which gives the probability that the 80-quarter ahead response exceeds zero. For the technology shock, we estimate these probabilities at 100% and 99% for GDP and labor productivity respectively. In contrast, the probability that the 80-quarter ahead responses 15 to "M RS exceeds zero is only 61% for GDP and 19% for productivity; the corresponding probabilities for "M P are 53% for GDP and 73% for productivity. These results support the identifying assumption, used by Gali (1992, 1999) and Christiano, Eichenbaum, and Vigfuson (2003), that only technology shocks induce permanent shifts in output and/or productivity. 5.2. Cyclical Behavior of GDP and its Components According to Table 4, about 72% of the variance of the 3-month ahead forecast error of GDP is explained by our three identi…ed shocks. This fraction rises to 84% for the 60-month ahead forecast error. Recall that there are a total of six VAR innovations, so there are three remaining sources of variation (the t vector) in system (2.4). Thus, our identi…ed shocks do a reasonable job of accounting for output movements. The technology shock and the MRS shock are about equally important at the twelve-month horizon. However, at the 5-year horizon, the technology shock is the predominant driver of output variation. In contrast, the monetary policy shock accounts for a very small fraction of output variation at all horizons. This result supports results in Sims and Zha (1998) and Christiano, Eichenbaum, and Evans (1999) that monetary policy shocks account for, at best, only a small fraction of output ‡ uctuation. These patterns can also be seen in the GDP responses displayed in Figure 2, which displays impulse responses over a 20 quarter horizon. Note that the initial responses of GDP to "T ECH and "M RS are similar in magnitude. However, the response to the technology shock persists, whereas the response to the MRS shock mean-reverts in 1-1/2 to 2 years. Finally, a contractionary monetary policy shock dampens GDP, although the posterior distribution of this response is quite spread out. Turning to the key components of GDP, Table 4 shows that our three identi…ed shocks account for over 70% of business …xed investment (equipment and software, investment structures) variation at the 5-year horizon, and over 60% of the corresponding variation in total consumption expenditures. Figure 2 shows that the responses of these GDP components look similar to the GDP responses: permanent response to "T ECH , transient response to "M RS , negative but relatively small response to contractionary "M P . In contrast, the response of residential investment to both "T ECH and "M RS mean-revert rather quickly after an initial positive response. In addition, residential investment displays a more pronounced response to the contractionary monetary policy shock. These responses re‡ the high interest rate ect sensitivity of residential investment. As we shall discuss in section 5.5, below, monetary policy contracts in response to both an MRS shock and a technology shock, although the 16 second response is with a delay of four to six quarters. These interest rate increases reverse the initially positive responses of residential investment to "T ECH and "M RS . One additional noteworthy result from Figure 2 is the gradual, hump-shaped response of consumption to permanent income drivers. In particular, real compensation has a gradual but permanent response to the technology shock, implying an substantial increase in permanent income. Thus, it is noteworthy that consumption expenditure has a rather small response to the technology shock on impact. Thereafter, consumption rises. This sluggish response of consumption to the technology shock would seem inconsistent with a simple formulation of the permanent income hypothesis, but would be consistent with the models of habit formation that are increasingly used in macroeconomic models. (See, for example, Boldrin, Christiano, and Fisher, 2001; and Fuhrer, 2000.) 5.3. Labor Markets Figure 3 displays the responses of hours worked, payroll employment, and labor productivity to our three identi…ed shocks. Note …rst that the MRS shock elicits an immediate rise in both hours and employment on impact. This e¤ect, however appears to be transient, dissipating in about two years. In contrast there is virtually no response of hours or employment to a technology shock on impact. Thereafter, these measures of labor inputs rise steadily, reaching a new steady state in about 2 to 2-1/2 years. On the face of it, the permanent response of hours to the technology shock contradicts the theoretical premise that hours per capita should be stationary. This problem is not unique to our identi…cation strategy, but generally arises in studies that use unadjusted hours data computed by the Bureau of Labor Statistics. Per-capita hours derived from these data are non-stationary, displaying a trend of about 0.6% per year.22 The initial response of labor inputs to technology shocks is a matter of some controversy in the literature. Basu, Fernald, and Kimball (2004) estimate that hours and payrolls fall with a technology shock on impact. Intuitively, higher productivity enables …rms to meet demand with less labor. In contrast, Christiano, Eichenbaum and Vigfuson (2003) estimate a contemporaneous rise in labor inputs in response to a technology shock. Both of these papers identify the technology shock using long run restrictions, although the way these restrictions are implemented di¤ers between the two papers. Our identi…cation strategy does not impose long run restrictions, and our results are intermediate between these two earlier papers. 22 Ramey and Francis (2006) construct a measure of per capita hours that adjusts for home production hours, hours spent in school, and other factors. In contrast with the unadjusted BLS data, their measure appears to be stationary. 17 Another question addressed by Figure 3 is whether the observed procyclicality of labor productivity is due to “labor hoarding” (a sluggish response of labor demand to cyclical movements in product demand) or simply due to procyclical technology shocks that directly drive productivity and output in the same direction. The impulse responses in Figure 3 tend to support the second explanation. They imply that labor productivity is driven almost exclusively by technology shocks. In particular, the productivity response to "T ECH is positive over the …rst year with virtually 100% probability. In contrast, the responses of productivity to the MRS and monetary policy shocks are small and dissipate quickly. If labor hoarding were an important factor in explaining procyclical labor productivity, we would expect to see signi…cant responses of productivity to these non-technology shocks. Thus, the small responses of productivity to "M RS and "M P provide little support for the labor hoarding story. 5.4. In‡ ation According to Table 4, about 60% of the 5-year ahead variation in in‡ ation is explained by our three identi…ed shocks. The top row of Figure 4, which displays the responses of in‡ ation to these three shocks, shows that both nominal and real shocks are important for in‡ ation. In‡ ation rises strongly in response to "M RS . The in‡ ationary response dissipates in two to three years. As a shock that induces short-term positive responses of both economic activity and prices, "M RS behaves as what Blanchard (1989) would call an aggregate demand shock. An expansionary technology shock induces a fall in in‡ ation for about a year and a half. This would be consistent with a model of monopolistically competitive …rms that set prices as a markup over marginal cost. After the …rst 6 quarters or so, in‡ ation appears to rise, and monetary policy responds by contracting. What appears to be driving this in‡ ation increase is the delayed response of consumption and business investment demand to the technology shock, discussed above in Section 5.2. In particular, while the technology shock induces an increase in productive capacity (both directly and as a result of the investment response), it also induces a rise in demand that exceeds the rise in capacity over the 5 year horizon displayed in the impulse responses. This results in an increasing output gap, de…ned as the di¤erence between the actual output and the long-run sustainable level of output, given current productive capacity. The second row in Figure 4 displays the response of the output gap (measured as the di¤erence between GDP and the Congressional Budget O¢ ce’ measure of potential GDP). According to the …gure, s the output gap rises steadily for the two years following a technology shock, and remains elevated for at least another two years. Standard policy analysis would associate this sort of sustained output gap with in‡ ationary pressures. This sort of association can be justi…ed 18 theoretically in models that generate a New Keynesian Phillips Curve (such as Gali and Gertler, 1999, and Eichenbaum and Fisher 2004).23 Finally, a notable result in Figure 4 is that a contractionary monetary policy shock is clearly de‡ ationary, as theory would predict. That is, our identi…cation approach shows no evidence of Sims’ (1992) “price puzzle” An identi…cation procedure for monetary policy s . shocks is said to display a price puzzle if it implies a pronounced and sustained in‡ ationary response to a contractionary policy shock. Many procedures used in the literature to identify monetary policy shocks have this problem. The typical way to avoid a price puzzle is to include commodity prices, or some other forecaster of in‡ ation, in the VAR. Our procedure avoids a price puzzle without explicitly including commodity prices. However, the principal components used in our FAVAR speci…cation may span the information needed to forecast in‡ ation. 5.5. Monetary Policy As is common practice, we view the federal funds rate as the indicator of monetary policy. At short horizons, the most important of our three identi…ed shocks for the federal funds rate is "M P . Speci…cally, "M P accounts for 34% of the 3-month ahead forecast variance of the federal funds rate at the median of the posterior distribution. (See Table 4.) By way of comparison, "T ECH and "M RS account for just 7% and 14% of this variance, respectively. Figure 5 displays the responses of the funds rate to our three identi…ed shocks. It shows that the response of the funds rate to the monetary policy shock is extremely short-lived, fully dissipating in about two quarters. At longer horizons, the MRS shock is by far the most important determinant of the stance of monetary policy, accounting for 59% of the 5-year ahead forecast variance of the funds rate (again, at the median of the posterior distribution). At this 5-year horizon, the corresponding variance percentage attributable to the technology shock falls to 9%, and the variance percentage of the monetary policy shock declines to 7%. The response of the funds rate to "M RS follows the qualitative patterns predicted by a Taylor rule. In particular, the MRS shock induces a rise in both in‡ ation and output without a concomitant increase in potential output. As a result, a Taylor Rule would predict monetary tightening. This is precisely what we …nd. In response to an "M RS impulse, the federal funds rate rises by over 100 basis points over four quarters. This response by the monetary authority is quite long-lived: the median funds rate remains about 70 basis points above its starting value even after …ve years. By all appearances, this looks like a classic 23 While Gali and Gertler (1999) and Eichenbaum and Fisher (2004) associate in‡ ationary pressures with increasing marginal costs, Gali and Gertler (1999) note that there is an approximate log-linear relationship between marginal costs and the output gap. 19 countercyclical response to a demand shock. What is puzzling about this result is that the policy response to "M RS is far longer-lived than the corresponding responses of either in‡ ation or the output gap. This could be interpreted as evidence of policy inertia in the Fed’ response to in‡ s ationary pressures. Finally, Figure 5 shows that monetary policy becomes slightly accommodative on impact in response to an expansionary technology shock. In particular, the median response of the federal funds rate to "T ech is a 30 basis point decline. This is not surprising, given the de‡ ationary impact of "T ech that we saw in Figure 4. Policy does not reliably turn restrictive until the in‡ ation response turns positive, as described above in section 5.4. 5.6. Treasury Yields We consider the one-, twelve-, and sixty-month zero-coupon U.S. Treasury yields as computed in the Fama-Bliss data base from CRSP. According to Table 4, between 66% and 75% of Treasury yield variation at the …ve-year horizon is explained jointly by our three identi…ed shocks. The MRS shock is clearly the most important beyond the initial quarters. The last three rows of Figure 5 give the responses of these yields to the three identi…ed shocks. Notice that the responses of the intermediate and long rates are similar both in shape and magnitude to the response of the short rate. As a result, the MRS shock induces approximately a parallel shift in the yield curve level. The monetary policy shock is only important at the very shortest horizon for shortest-term rates (the fed funds rate and the one-month yield) becoming less important for the longer-term rates. Hence, the monetary policy shock shifts the yield curve slope. The yield responses to the technology shock are small and the distribution is spread around zero. For example, the probability that the one-month yield has a positive average response over the …rst year is 61%. (The corresponding probability for the 12- and 60month yields are 66% and 53%, respectively.) So it would seem that treasury yields could easily respond in either direction. Perhaps this is not surprising. As noted by Evans and Marshall (2003), a technology shock moves real rates and expected in‡ ation in opposite directions, so the theoretical predictions for nominal yields’ responses are ambiguous. In Evans and Marshall (2003), the expected in‡ ation e¤ect tended to dominate, so technology shocks induced a fall in yields. In this study, however, we …nd that these two e¤ects are of approximately the same magnitude, at least over the …rst year or so. technology shock has a small e¤ect on nominal yields. 20 As a result, the 5.7. Equity Markets Our three identi…ed shocks have relatively little explanatory power for stock prices. As shown in Table 4, they jointly explain only 26% of stock price variation at the …ve-year horizon (according to the median of the posterior distribution). They explain even less at shorter horizons: the corresponding variance fraction explained for the three month forecast error is only 9%. Thus, most variation in stock prices and returns are driven by factors other than our three identi…ed impulses. Having said this, the stock market does display signi…cant responses to all three shocks. Figure 6 displays the responses of the S&P 500 index, the excess return to the market, and corporate pro…ts. The stock market displays a pronounced positive response to an expansionary technology shock for about a year and a half. In particular, the median response of the level of the S&P 500 index over the four quarters averages a bit over one percentage point, rising to an average of 1.3 percentage points over the …fth through eighth quarters. The probability that these responses are positive is 96% and 88%, respectively. This response of the stock price index dissipates in 6 to 8 quarters, perhaps due to the contractionary response of monetary policy. The mechanism underlying this stock price response is clear if we regard stock prices as discounted cash ‡ ows. In response to the technology shock, Figure 6 shows a positive response of pro…ts (a proxy for cash ‡ ows), while Figure 5 shows a negligible response of long-term interest rates (a proxy for the discount factor). It follows that the discounted present value of the cash ‡ to equity holders must rise. ow The response of the stock market to an expansionary MRS shock is rather di¤erent than the response to a technology shock. There may be a small initial rise in the stock market upon impact (the error bands are quite wide), but this response is immediately reversed. The subsequent movement of the stock market is negative, and the market fails to recover its pre-shock level even after …ve years. This negative outcome for equity markets appears to be driven by the strong contractionary response of monetary policy along with the concomitant increase in longer-term interest rates. In particular, while Figure 6 does show a positive response of pro…ts to the MRS shock, the response of interest rates is much bigger. The resulting e¤ect is to decrease the present value of cash ‡ ows to the equity holder. One might say that while “good news is good news”when the good news is an expansionary technology shock, “good news is bad news” for the market when the news is an expansionary MRS shock.24 24 Contrast this result with that in Boyd, Hu, and Jagannathan (2005), where the market responds positively to good economic news in recessions, but tends to respond negatively to good economic news in expansions. 21 Finally, Figure 6 shows a substantial and fairly long-lived negative response of stock prices to a contractionary "M P shock. In particular, the median response of the S&P500 index in the eight quarters following the shock is a decline of over 2 percent. The probability of a negative response over this period is greater than 98%. The excess return to the market portfolio declines by about 70 basis points on impact with negative excess returns persisting for at least two quarters. These responses are pure discount-rate e¤ects. (The response of pro…ts to "M P is small and insigni…cant.) All this conforms roughly to the conventional wisdom that monetary contraction is bad for the stock market. 5.8. Univariate responses to model-based shock measures A focus of this paper is to use our model-based shock measures t to simultaneously identify all three shocks "t , imposing the restriction that the elements of "t are mutually orthogonal. An alternative, and simpler, approach would be to compute the responses of macroeconomic variables directly to the innovation to each element of t individually. We call this the “single- approach” This simpler approach ignores the correlations among the elements . of t that are documented in Table 2. It also ignores possible contamination of i;t by "j;t , j 6= i, and ignores possible measurement error wi;t . In this section, we brie‡ discuss y the implications of the single- approach, and contrast its implications with the baseline approach of Section 2. To implement the single- approach, we estimate bivariate recursive VARs of the form i;t zt where i;t = i;t 1 (L) zt 1 + t; E 0 t t (5.1) =I is one of our three model-based shock measures, zt is an endogenous variables whose responses we wish to explore, t is a bivariate i.i.d. disturbance, and triangular matrix. In this structure, 1;t is interpreted as the shock to i;t . is a lower We use four quarterly lags in this VAR. Figure 7 presents selected responses from the single- approach, and contrasts them with the corresponding responses using the baseline approach described in sections 2 through 4, above. While most of the responses to the model-based shock measures in framework (5.1) are qualitatively the same as in our baseline approach, there are several di¤erences worthy of note. First, and most notably, the in‡ ation response to the shock to M P in framework (5.1) displays a huge price puzzle. As shown in Figure 7, a contractionary shock to MP (“Single-Eta MP shock” induces a signi…cant positive response to both the price level and ) the in‡ ation rate. In‡ ation remains elevated for at least …ve years after the initial impulse. 22 This contrasts with the negative response to a contractionary "M P in both the price level and the in‡ ation rate (also displayed in Figure 7). Second, measures of consumption and investment appear to display permanent responses to MP in framework (5.1), which would seem to violate long run neutrality. Again, these di¤er from the response patterns to "M P . (Both are displayed in Figure 7.) Third, the federal funds rate displays essentially no response to T ech , the Basu-Fernald-Shapiro technology measure (“Single-Eta Tech shock”in Figure 7). If one believes that an expansionary technology shock ought to elicit an accommodative policy response, this …nding would be puzzling. More generally, if these anomalous responses are interpreted as evidence of misspeci…cation, then one would not want to use the innovations to t as empirical counterparts to the structural shocks. Our baseline procedure would provide a more satisfactory alternative. 6. Conclusions In this paper, we have proposed an approach to identifying multiple fundamental macroeconomic shocks. In the introduction, we listed a number of questions that could be fruitfully addressed by a multiple-shock approach. We …nd that the preponderance of variation in measures of economic activity can be explained as responses to the three shocks we identify: technology shocks, shocks to the marginal rate of substitution between consumption and leisure, and monetary policy shocks. In particular, these three shocks explain over 80% of the long-run variability in GDP and labor inputs, over 70% of the corresponding variability in the components of business …xed investment, and over 55% of the variability in the components of consumption and housing. The traditional emphasis on technology shocks in macroeconomic modelling seems warranted if the focus is on the determinants of long-horizon variability in economic activity. In the shorter run, a more cyclical driver (here identi…ed as our MRS shock) also needs to be considered. The association of technology shocks with permanent shocks to output and productivity is borne out by our analysis. More transitory responses are associated with our MRS shock, which is orthogonal to the technology shock. We …nd no evidence that procyclical labor productivity is driven by “labor hoarding” . Such an explanation would imply signi…cant responses of productivity to non-technology shocks such as our MRS shock. In our results however, the only important driver of productivity is the technology shock. Furthermore, technology shocks are neither expansionary nor contractionary on impact for labor inputs. Rather, inputs have a negligible contemporaneous response to "T ECH . This result is midway between that found by Basu, Fernald, 23 and Kimball (2004) and that reported by Christiano, Eichenbaum, and Vigfuson (2003). Monetary policy shocks account for a rather small fraction of output variation. Furthermore, these shocks are important for monetary policy itself only in the short run. Over a longer horizon, most variation in the federal funds rate is due to the endogenous response of monetary policy to an MRS shock. The central bank “leans against the wind” in response to aggregate demand shocks. About 60% of long-run variation in in‡ ation is explained by our three identi…ed shocks. Both nominal shocks ("M P ) and real shocks ("T ECH and "M RS ) are important determinants of price level and in‡ ation. The preponderance of variation in Treasury yields at all maturities is explained by our three shocks, with the MRS shock (which we think of as analogous to an “aggregate demand”shock) most important. In contrast, most variation in stock prices and returns is driven by factors other than those identi…ed in this study. Nonetheless, there is evidence that the stock market displays signi…cant responses to all three shocks. As expected, expansionary technology shocks induce increases in stock prices while contractionary monetary policy shocks are bad for the market. The market reacts negatively to the “good news”of an expansionary MRS shock (after 2-3 quarters). While the results of this paper are intriguing, they raise as many questions as they answer. Would the results change if more fundamental shocks were added (for example, …scal policy shocks or investment-speci…c technology shocks)? What is the interpretation of the MRS shock? We …nd that it behaves rather di¤erently than the technology shock, suggesting that it probably is not simply a shock to home production technology. But is it best interpreted as a preference shock (as argued by Hall, 1997), or as a shock to implicit labor taxes or labor market frictions? Are there other fundamental shocks that can explain the remaining stock return variation, or does the stock market largely follow its own dynamic, with most of its volatility orthogonal to the macroeconomy? All of these questions await future work. 24 7. Appendix: Estimation of the Posterior Distribution Assuming an Uninformative Prior In this appendix, we construct the posterior distribution for the model parameters f u ; B; w ; Cg ; b assuming an uninformative prior. As discussed in Section 3, we treat Yt and t as known data. e It is …rst useful to …x some notation. Let Y ([T + l] n) denote a matrix containing b the factor series Yt used in the VAR. (Here, T denotes the number of usable observations, l denotes the number of lags in the VAR, and n denotes the number of factors in the VAR.) To write the VAR in regression notation, let q let the (T n) matrix of dependent variables in the VAR be denoted Y; Y let the (T 2 1 6 6 1 6 6 X 6 6 6 4 1 nl + 1, the number of regressors per equation, 2 6 6 6 6 4 e Yl+1;1 e Yl+T;1 3 e Yl+1;n e Yl+T;n 7 7 7 7 5 q) matrix of VAR regressors be denoted X; e Yl;1 e Yl+1;1 e Yl+T and let the (T 1;1 e Yl 1;1 e Yl;1 e Yl+T e Y1;1 e Y2;1 e Yl;2 e Yl+1;2 e e YT;1 Yl+T 2;1 1;2 e Yl 1;2 e Yl;2 e Yl+T e Y1;2 e Y2;2 e e YT;2 Yl+T 2;2 m) matrix of model-based shocks be denoted H; 2 3 H 6 6 6 6 4 1;1 1;m T;1 T;m w ; B; u) = p (Cj w ; B; u) p ( 25 w jB; w ; B; u) ; u ) p (Bj All densities in equation (7.1) are conditional on the data fY; X; Hg. explicitly. 25 1;3 3 e Y1;n e 7 Y2;n 7 7 7 7; 7 7 5 e YT;N 7 7 7: 7 5 Our goal is to compute the joint posterior density p (C; as follows:25 p (C; e Yl;3 e Yl+1;3 which can be written u) p ( u) (7.1) This dependency is not noted We assume uninformative priors in the usual way: prior ( u) /j uj (n+1)=2 (7.2) prior(B) = constant prior ( w) /j wj (7.3) (m+1)=2 (7.4) prior(C) = constant (7.5) The reduced form of the VAR is given by the regression equation (7.6) Y = XB + U where matrix U contains the n 1 i.i.d. error process ut as U = (u1 ; u2 ; ; uT )0 , and it is assumed that ut N (0; (7.7) u) : In equation (7.6), the coe¢ cient matrix B has dimension (q n). The rows of B correspond b to the regressors X; the columns correspond to the n equations. Let B denotes the matrix of OLS estimates of the VAR slope coe¢ cients b B (X 0 X) Y b XB 1 X 0Y (7.8) and let S denotes T times the sample covariance matrix of the VAR disturbances S 0 Y b XB : b b Finally, let Bs and Bs denote the vectors formed by stacking the columns of B and B, respectively. Zellner (1971) shows that, given the priors (7.2) and (7.3), the posterior distribution is inverted Wishart with parameter S. He also shows that, conditional on u , the b posterior distribution p (Bs j u ) is multivariate normal with mean Bs and variance-covariance p( u) matrix u (X 0 X) 1 . We can use Zellner’ (1971) logic to derive the remaining components of the joint posterior s distribution (7.1). Equation (2.2) can be written e H = U C + W: (7.9) e In equation (7.9), U is a matrix whose columns contain contemporaneous and K lags of U , W stacks the m 1 i.i.d. measurement error process wt as W = (w1 ; w2 ; ; wT )0 , and it is assumed that W N (0; 26 w) : (7.10) We follow the same steps as we used to derive p ( u) and p (Bj u ), except that we condition on B. (It turns out that u does not directly a¤ect the conditional distribution of C and w .) For a given B, let us write U (B) and V (B) b C (B) H Y XB e e U (B)0 U (B) e b U (B)C (B) 0 1 H e U (B)0 H e b U (B)C (B) e (where U (B) contains the contemporaneous and K lags of U (B)). The interpretation of these objects is as follows: U (B) is the matrix of residuals implied by equation (7.6) given b the observed data fY; Xg and a particular choice of B; C (B) is the estimate of C that one would obtain from U (B) and H if one estimated equation (7.9) via OLS; V (B) is the moment matrix of n residuals from this OLS estimation of equation (7.9). Conditional the o b on B, the objects U (B); C (B) ; V (B) are functions of the data, so can be treated as known quantities. Therefore, by logic analogous to Zellner (1971), posterior distribution w jB) is inverted Wishart with parameter V (B), and posterior distribution p(Cs j w ; B) is 1 b e e multivariate normal with mean C (B) and variance-covariance matrix w U (B)0 U (B) : p( s One draws from the posterior distribution for fC; 1. Draw u w ; B; ug as follows: from the inverted Wishart density with parameter S, which is a function of data. 2. Given this draw of u ; draw Bs from the multivariate normal distribution with mean b Bs and variance-covariance matrix u (X 0 X) 1 . 3. Given this draw of B, draw w from the inverted Wishart density with parameter V (B). 4. Given these draws of B and w , draw Cs from the multivariate normal distribution 1 b e e U (B)0 U (B) : with mean C (B)s and variance-covariance matrix w 8. Data Appendix We use quarterly data from 1967:Q1 through 2000:Q4.26 As described in the text, we use two (overlapping) data sets. The …rst data set consists of the 190 series used to construct the 26 We start in 1967 because many of the series used to generate the principal components used in the FAVAR speci…cation are available only from 1967 onward. 27 b factors in the FAVAR model. Speci…cally, the six factors comprising vector Yt in equation (2.18) are the …rst six principal components of these 190 data series. 154 of these series are monthly, and the remaining 36 are quarterly. To facilitate computation of principal components, each of these data series is rendered stationary. Table 1A lists these data in detail, along with the stationarity-inducing transformations used. The second data set is used to construct the series zt (in equation (2.17), whose impulse responses are to be computed. The data used are as follows: Data on real GDP and its components (total consumption expenditure, investment in equipment and software, investment in structures, residential investment) are quarterly data (seasonally adjusted in chained 2000 dollars) from the Bureau of Economic Analysis (BEA). The output gap is the log of real GDP minus the log of the Congressional Budget O¢ ce’ measure of potential GDP. s Our measure of the price level is the GDP chain-type price index from BEA. The 3 month in‡ ation rate is the log di¤erence of the price level. Labor productivity is seasonally adjusted business sector output per hour of all persons (seasonally adjusted) from the Bureau of Labor Statistics (BLS) Employment is total nonfarm employment, and payroll hours series is the aggregate total private hours per week index. Both of these are seasonally adjusted data from the BLS establishment survey. The real compensation series is business sector real compensation per hour from the BEA, de‡ ated by the GDP chain-type price index. The Federal Funds Rate is the e¤ective funds rate from the Federal Reserve Bank of New York. The 1- 12- and 60-month zero coupon Treasury yields are from the FamaBliss zero coupon bond …les in the CRSP database. The S&P500 Stock Index is from Standard and Poor’ All of these …nancial data series are converted to quarterly series s. by sampling the last business day of each quarter. Our measure of the excess stock market return is the …rst Fama-French factor from Kenneth French’ web page s http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html These data are rendered quarterly by sampling the last month of quarter. 28 Pro…ts is the BEA measure of corporate pro…ts (pre-tax) from current production, seasonally adjusted. For all series other than the in‡ ation rate, interest rates, and excess stock returns, we estimate the VAR in log-di¤erences, and then we cumulated the impulse responses to display the responses of log-levels. 29 References [1] Basu, S., Fernald, J., and M. Kimball. (2004) Are Technology Improvements Contractionary? Forthcoming in the American Economic Review. [2] Basu, S., Fernald, J., and Shapiro, M. (2001a) Productivity Growth in the 1990s: Technology, Utilization, or Adjustment? Carnegie-Rochester Conference Series on Public Policy, December 2001, v. 55, iss. 0, pp. 117-65 [3] Basu, S., Fernald, J. and M. Shapiro. 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(1999) Block Recursion and Structural Vector Autoregressions, Journal of Econometrics, 90, 290-316. 34 Table 1: Granger-Causality Tests for MRS Measure Explanatory # Lags Marginal Signi…cance Variable of F-test Detrended GDP 4 5 6 4 5 6 4 5 6 Fed Funds Rate Term Spread Notes: 0.742 0.891 0.715 0.356 0.582 0.510 0.199 0.165 0.202 This table displays the marginal signi…cance of exclusion F-statistics for the following Granger-Causality regressions M RS;t = N X j M RS;t j + j Xt j + wi;t ; j=1 where N = 4; 5; or 6; the explanatory variable X is either detrended GDP, the federal funds rate, or the term spread (de…ned as the di¤erence between the 5-year Treasury Yield and the federal funds rate); and the F-statistic tests the hypothesis j = 0; 8j = 1; :::; N: Table 2: Correlation Matrix of the Model-Based Shock Measures M RS MP MP M RS T ECH 1.0 0.11 1.0 -0.037 0.062 35 T ECH 1.0 Table 3: R2 s For Regression of Model-Based Shock Measures on VAR Residuals Shock Measure R2 when regressed on VAR residuals F -test 54.1% 29.7 MP (0.000) 53.6% 61.2 M RS (0.000) 52.3% 140.7 T ECH (0.000) Notes: The second column displays the R2 s for the regressions C4 ut 4 + wt (equation (2.9)), where t denotes the 3 t = C0 ut +C1 ut 1 +:::+ 1 vector of model-based measures, ut denotes the 6 1 vector of VAR residuals, and wt denotes the 3 1 vector of residuals.. The third column displays the F-statistic testing the hypothesis that the given row of C0 = 0. 36 Table 4 Fraction of Variance of Endogenous Variables Accounted for by the Three Identified Shocks Notes: For each of the variables listed, the table gives the median fraction of 3-, 12, and 60-month ahead forecast variance accounted for by the three identified shocks, εMP , εMRS , and εTECH, according to the posterior distribution. The fourth line in each panel gives the median fraction of each forecast variance accounted for by the three shocks collectively. The two numbers in parentheses following each median statistic give the 95% and 5% quantiles of the posterior distribution for each forecast variance fraction. These statistics were computed using 500 draws from the posterior distribution of the model’s parameters. Real GDP Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.049 0.282 0.344 0.721 0.064 0.328 0.422 0.861 0.124 0.107 0.527 0.844 to MP to MRS to Tech of 3 Shocks (0.233,0.001) (0.514,0.088) (0.573,0.151) (0.779,0.632) (0.224,0.021) (0.609,0.087) (0.702,0.176) (0.909,0.763) (0.433,0.014) (0.411,0.024) (0.774,0.208) (0.928,0.648) Total Consumption Expenditures Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.112 0.137 0.372 0.661 0.081 0.060 0.399 0.617 to MP to MRS to Tech of 3 Shocks 0.009 0.305 0.156 0.492 (0.076,0.000) (0.478,0.121) (0.332,0.033) (0.598,0.365) (0.322,0.014) (0.369,0.029) (0.593,0.134) (0.768,0.497) (0.330,0.013) (0.284,0.011) (0.650,0.162) (0.791,0.400) Investment Equip & Software Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.027 0.535 0.128 0.721 0.058 0.289 0.303 0.712 to MP to MRS to Tech of 3 Shocks 0.027 0.339 0.015 0.404 (0.116,0.001) (0.430,0.221) (0.095,0.000) (0.488,0.307) (0.136,0.008) (0.702,0.307) (0.357,0.014) (0.801,0.602) (0.274,0.011) (0.576,0.074) (0.606,0.070) (0.864,0.490) Investment Structures Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.034 0.346 0.074 0.497 0.030 0.461 0.179 0.735 to MP to MRS to Tech of 3 Shocks 0.031 0.074 0.020 0.138 (0.095,0.001) (0.137,0.028) (0.061,0.001) (0.201,0.089) (0.186,0.002) (0.512,0.186) (0.246,0.005) (0.626,0.361) (0.229,0.003) (0.717,0.185) (0.488,0.016) (0.861,0.548) Residential Investment Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.232 0.104 0.225 0.591 0.164 0.240 0.147 0.605 to MP to MRS to Tech of 3 Shocks 0.005 0.245 0.061 0.328 (0.048,0.000) (0.336,0.133) (0.179,0.004) (0.399,0.257) (0.419,0.086) (0.233,0.052) (0.412,0.050) (0.698,0.459) (0.340,0.058) (0.513,0.036) (0.313,0.039) (0.808,0.316) Table 4 (continued) Labor Productivity Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.019 0.019 0.464 0.530 0.041 0.025 0.435 0.536 0.044 0.045 0.337 0.472 to MP to MRS to Tech of 3 Shocks (0.099,0.000) (0.118,0.000) (0.552,0.347) (0.600,0.446) (0.190,0.012) (0.104,0.005) (0.569,0.289) (0.652,0.413) (0.207,0.007) (0.209,0.008) (0.537,0.156) (0.656,0.299) Payroll Employment Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.098 0.522 0.028 0.688 0.031 0.592 0.161 0.821 0.085 0.212 0.440 0.831 to MP to MRS to Tech of 3 Shocks (0.290,0.007) (0.655,0.360) (0.186,0.000) (0.755,0.601) (0.139,0.010) (0.764,0.319) (0.422,0.029) (0.882,0.702) (0.369,0.010) (0.545,0.050) (0.741,0.158) (0.912,0.639) Payroll Hours Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.094 0.537 0.016 0.690 0.040 0.595 0.139 0.816 0.072 0.247 0.405 0.803 to MP to MRS to Tech of 3 Shocks (0.282,0.007) (0.673,0.373) (0.140,0.000) (0.764,0.583) (0.147,0.012) (0.768,0.347) (0.391,0.026) (0.884,0.679) (0.314,0.013) (0.552,0.068) (0.715,0.137) (0.902,0.621) Real Wage Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.046 0.002 0.003 0.055 0.050 0.044 0.013 0.120 0.109 0.167 0.095 0.460 to MP to MRS to Tech of 3 Shocks (0.094,0.008) (0.016,0.000) (0.024,0.000) (0.106,0.018) (0.141,0.006) (0.122,0.009) (0.042,0.004) (0.226,0.040) (0.373,0.006) (0.443,0.011) (0.334,0.005) (0.691,0.198) Inflation Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.045 0.007 0.130 0.199 0.037 0.095 0.194 0.362 0.216 0.164 0.171 0.596 to MP to MRS to Tech of 3 Shocks (0.162,0.001) (0.061,0.000) (0.229,0.035) (0.307,0.108) (0.117,0.008) (0.260,0.022) (0.356,0.070) (0.502,0.210) (0.419,0.067) (0.370,0.054) (0.341,0.060) (0.774,0.390) Federal Funds Rate Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.342 0.141 0.068 0.577 0.147 0.511 0.047 0.726 0.074 0.594 0.090 0.803 to MP to MRS to Tech of 3 Shocks (0.485,0.186) (0.329,0.032) (0.194,0.002) (0.648,0.498) (0.302,0.066) (0.647,0.345) (0.146,0.010) (0.795,0.628) (0.227,0.024) (0.761,0.302) (0.351,0.013) (0.891,0.617) 1-month Treasury Yield Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.114 0.378 0.032 0.552 0.071 0.540 0.108 0.751 to MP to MRS to Tech of 3 Shocks 0.164 0.087 0.015 0.281 (0.254,0.084) (0.189,0.025) (0.064,0.000) (0.357,0.211) (0.248,0.047) (0.511,0.251) (0.123,0.009) (0.641,0.449) (0.203,0.023) (0.725,0.262) (0.376,0.011) (0.860,0.575) Table 4 (continued) 12- month Treasury Yield Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.150 0.421 0.021 0.624 0.079 0.546 0.077 0.746 to MP to MRS to Tech of 3 Shocks 0.247 0.152 0.008 0.422 (0.373,0.122) (0.288,0.052) (0.055,0.000) (0.504,0.334) (0.337,0.048) (0.569,0.251) (0.128,0.004) (0.715,0.513) (0.214,0.026) (0.741,0.294) (0.336,0.008) (0.867,0.570) 60- month Treasury Yield Steps ahead: 3-month 12-months 60-months Shock to Shock to Shock to 0.121 (0.235,0.084) 0.137 (0.245,0.025) 0.005 (0.047,0.000) 0.133 (0.314,0.026) 0.339 (0.505,0.192) 0.015 (0.088,0.002) 0.076 (0.221,0.023) 0.511 (0.709,0.277) 0.038 (0.210,0.006) Total of 3 Shocks 0.287 (0.363,0.196) 0.522 (0.628,0.394) 0.662 (0.823,0.467) S&P500 Stock Index Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.040 0.010 0.033 0.094 0.081 0.059 0.049 0.199 0.086 0.092 0.074 0.262 MP MRS Tech to MP to MRS to Tech of 3 Shocks (0.101,0.008) (0.046,0.000) (0.095,0.003) (0.176,0.047) (0.172,0.026) (0.118,0.028) (0.097,0.019) (0.334,0.117) (0.162,0.038) (0.152,0.040) (0.138,0.024) (0.355,0.181) Excess Stock Market Return Steps ahead: 3-month 12-months 60-months Shock Shock Shock Total 0.078 0.043 0.067 0.193 0.081 0.065 0.079 0.233 to MP to MRS to Tech of 3 Shocks 0.066 0.006 0.047 0.132 (0.141,0.017) (0.044,0.000) (0.100,0.007) (0.194,0.076) (0.143,0.031) (0.087,0.017) (0.116,0.025) (0.266,0.128) (0.144,0.036) (0.112,0.033) (0.134,0.038) (0.311,0.162) Table 5: Long-Run Responses to 1 SD Shock GDP Productivity Technology Shock 58 bps (1.00) 31 bps (0.99) 7 bps (0.61) -15 bps (0.19) MRS Shock MP Shock 3 bps (0.53) 12 bps (0.73) Notes: This table gives the median 80-quarter ahead responses of GDP and labor productivity to a one standard deviation impulse to each of the three shocks listed in the left-most column. The numbers in parenthesis give the probability that this 80-quarter ahead response is positive according to the Bayesian posterior distribution. 37 Table 1A: Data Used in Constructing FAVAR Factors Panel A: Monthly Data Series Data Description Transformation Personal Consumption Expenditures (SAAR, Bil.Chn.2000$) log 1st diff Personal Consumption Expenditures: Durable Goods (SAAR, Bil.Chn.2000$) log 1st diff Personal Consumption Expenditures: Nondurable Goods (SAAR,Bil.Chn.2000$) log 1st diff Personal Consumption Expenditures: Services (SAAR, Bil.Chn.2000$) log 1st diff Real Disposable Personal Income (SAAR, Bil.Chn.2000$) log 1st diff Value of Public Construction Put in Place (SAAR, Mil.Chn. $) log 1st diff Value of Private Construction Put in Place (SAAR, Mil. Chn. $) log 1st diff Manufacturers' Shipments of Mobile Homes (SAAR, Thous.Units) log Housing Starts (SAAR, Thous.Units) log Housing Starts: Midwest (SAAR, Thous.Units) log Housing Starts: Northeast (SAAR, Thous.Units) log Housing Starts: South (SAAR, Thous.Units) log Housing Starts: West (SAAR, Thous.Units) log Industrial Production Index (SA, 1997=100) log 1st diff Industrial Production: Consumer Goods (SA, 1997=100) log 1st diff Industrial Production: Durable Consumer Goods (SA, 1997=100) log 1st diff Industrial Production: Nondurable Consumer Goods (SA, 1997=100) log 1st diff Industrial Production: Business Equipment (SA, 1997=100) log 1st diff Industrial Production: Materials (SA, 1997=100) log 1st diff Industrial Production: Durable Goods Materials (SA, 1997=100) log 1st diff Industrial Production: Nondurable Goods Materials (SA, 1997=100) log 1st diff Industrial Production: Nonindustrial Supplies (SA, 1997=100) log 1st diff Industrial Production: Mining (SA, 1997=100) log 1st diff Industrial Production: Final Products (SA, 1997=100) log 1st diff Industrial Production: Durable Goods [NAICS] (SA, 1997=100) log 1st diff Industrial Production: Manufacturing [SIC] (SA, 1997=100) log 1st diff Industrial Production: Nondurable Manufacturing (SA, 1997=100) log 1st diff Industrial Production: Final Products and Nonindustrial Supplies (SA, 1997=100) log 1st diff Industrial Production: Electric and Gas Utilities (SA, 1997=100) log 1st diff All Employees: Construction (SA, Thous) log 1st diff All Employees: Durable Goods Manufacturing (SA, Thous) log 1st diff All Employees: Financial Activities (SA, Thous) log 1st diff All Employees: Goods-producing Industries (SA, Thous) log 1st diff All Employees: Government (SA, Thous) log 1st diff All Employees: Manufacturing (SA, Thous) log 1st diff All Employees: Mining (SA, Thous) log 1st diff All Employees: Total Nonfarm (SA, Thous) log 1st diff All Employees: Nondurable Goods Manufacturing (SA, Thous) log 1st diff All Employees: Total Private Industries (SA, Thous) log 1st diff All Employees: Retail Trade (SA, Thous) log 1st diff All Employees: Service-providing Industries (SA, Thous) log 1st diff All Employees: Aggregate of categories log 1st diff Civilian Employment: Nonagricultural Industries: 16 yr + (SA, Thous) log 1st diff Ratio: Help-Wanted Advertising in Newspapers/Number Unemployed (SA) log 1st diff Average Weekly Hours: Overtime: Manufacturing (SA, Hrs) 1st diff Average Weekly Hours: Manufacturing (SA, Hrs) 1st diff ISM Mfg: PMI Composite Index (SA, 50+ = Econ Expand) level ISM Mfg: Employment Index (SA, 50+ = Econ Expand) level ISM Mfg: Inventories Index (SA, 50+ = Econ Expand) level ISM Mfg: New Orders Index (SA, 50+ = Econ Expand) level ISM Mfg: Production Index (SA, 50+ = Econ Expand) level Real Retail Sales: Durable Goods (SA, Mil.Chain.2000$) log 1st diff Retail Sales: Retail Trade (SA, Spliced, Mil.Chn 2000$) log 1st diff Real Retail Sales: Nondurable Goods (SA, Mil.Chain.2000$) log 1st diff Real Inventories: Mfg: Durable Goods Industries (SA, EOP, Spliced, Mil Chn 2000$) log 1st diff Real Manufacturing & Trade Inventories: Mfg Industries (SA, EOP, Spliced, Mil.Chn 2000$) log 1st diff Real Mfg Inventories: Nondurable Goods Industries (SA, EOP, Spliced, Mil.Chn 2000$) log 1st diff Real Inventories: Retail Trade Industries (SA, EOP, Spliced, Mil.Chn 2000$) log 1st diff Real Manufacturing & Trade Inventories: Industries (SA, EOP, Spliced, Mil.Chn 2000$) log 1st diff Real Inventories: Merchant Wholesale Trade Industries (SA, EOP, Spliced, Mil.Chn 2000$) log 1st diff Real Inventories/Sales Ratio: Manufacturing Industries (SA, Spliced, Chained 2000$) 1st diff Inventories/Sales Ratio: Retail Trade Industries (SA, Spliced, Chained 2000$) 1st diff Real Manufacturing & Trade: Inventories/Sales Ratio (SA, Spliced, Chained 2000$) 1st diff Inventories/Sales Ratio: Merchant Wholesale Trade Industries(SA, Chained 2000$) 1st diff Real Sales: Mfg: Durable Goods Industries(SA, Spliced, Mil.Chn 2000$) log 1st diff Real Sales: Manufacturing Industries (SA, Spliced, Mil.Chn 2000$) log 1st diff Real Sales: Mfg: Nondurable Goods Industries (SA, Spliced, Mil.Chn 2000$) log 1st diff Real Manufacturing & Trade Sales: All Industries (SA, Spliced, Mil.Chn 2000$) log 1st diff Real Sales: Merchant Wholesalers: Durable Gds Industrs (SA, Spliced, Mil.Chn 2000$) log 1st diff Real Sales: Merchant Wholesale Trade Industries (SA, Spliced, Mil.Chn 2000$) log 1st diff Real Sales: Merch Wholesale: Nondurable Goods Industries (SA, Mil.Chn 2000$) log 1st diff Real Personal Income Less Transfer Payments (SAAR, Bil.Chn.2000$) log 1st diff PCE: Durable Goods: Motor Vehicles and Parts (SAAR, Mil.Chn.2000$) log 1st diff Mfrs New Orders: Durable Goods (SA, Mil.Chn.2000.$) log 1st diff Manufacturers New Orders: Consumer Goods & Materials (SA, Mil. 1982$) log 1st diff Manufacturers New Orders: Nondefense Capital Goods (SA, Mil. 1982$) log 1st diff New Pvt Housing Units Authorized by Building Permit (SAAR, Thous.Units) log Capacity Utilization: Manufacturing [SIC] (SA, Percent of Capacity) 1st diff Index of Help-Wanted Advertising in Newspapers (SA,1987=100) log 1st diff Civilian Unemployment Rate: 16 yr + (SA, %) 1st diff University of Michigan: Consumer Expectations (NSA, 66Q1=100) level Civilians Unemployed for Less Than 5 Weeks (SA, Thous.) level Civilians Unemployed for 15-26 Weeks (SA, Thous.) level Civilians Unemployed for 5-14 Weeks (SA, Thous.) level Average {Mean} Duration of Unemployment (SA, Weeks) level Civilians Unemployed for 15 Weeks and Over (SA, Thous.) level Civilians Unemployed for 27 Weeks and Over (SA, Thous.) level Adjusted Monetary Base (SA, Mil.$) log 2nd diff Adjusted Nonborrowed Reserves of Depository Institutions (SA, Mil.$) log 2nd diff Adjusted Nonborrowed Reserves Plus Extended Credit (SA, Mil.$) log 2nd diff Adjusted Reserves of Depository Institutions (SA, Mil.$) log 2nd diff Adj Monetary Base inc Deposits to Satisfy Clearing Bal Contracts (SA, Bil.$) log 2nd diff Money Stock: M1 (SA, Bil.$) log 2nd diff Real Money Stock: M2 (SA, Bil.Chn.2000$) log 1st diff Money Stock: M3 (SA, Bil.$) log 2nd diff Nominal Broad Trade-Weighted Exchange Value of the US$ (JAN 97=100) log 1st diff Foreign Exchange Rate: United Kingdom (US$/Pound) log 1st diff Moody's Seasoned Aaa Corporate Bond Yield (% p.a.) 1st diff Moody's Seasoned Baa Corporate Bond Yield (% p.a.) 1st diff Moody's Seasoned Aaa Corporate Bond Yield - Federal Funds Rate(% p.a.) level Moody's Seasoned Baa Corporate Bond Yield - Federal Funds Rate (% p.a.) level S&P: Composite 500, Dividend Yield (%) level Stock Price Index: Standard & Poor's 500 Composite (1941-43=10) log 1st diff S&P: 500 Composite, P/E Ratio, 4-Qtr Trailing Earnings level Stock Price Index: NYSE Composite (Avg, Dec. 31, 2002=5000) log 1st diff Stock Price Index: Standard & Poor's 400 Industrials (1941-43=10) log 1st diff 3-Month Treasury Bills, Secondary Market (% p.a.) 1st diff 6-Month Treasury Bills, Secondary Market (% p.a.) 1st diff 3-Month Treasury Bills - Federal Funds Rate, (% p.a.) level 6-Month Treasury Bills - Federal Funds Rate (% p.a.) level 1-Year Treasury Bill Yield at Constant Maturity (% p.a.) 1st diff 5-Year Treasury Note Yield at Constant Maturity (% p.a.) 1st diff 1-Year Treasury Bill Yield at Constant Maturity - Federal Funds Rate (% p.a.) level 5-Year Treasury Note Yield at Constant Maturity - Federal Funds Rate (% p.a.) level 10-Year Treasury Note Yield at Constant Maturity - Federal Funds Rate (% p.a.) level PPI: Crude Materials for Further Processing (SA, 1982=100) log 2nd diff PPI: Finished Consumer Goods (SA, 1982=100) log 2nd diff CPI-U: Apparel (SA, 1982-84=100) log 2nd diff CPI-U: Commodities (SA, 1982-84=100) log 2nd diff CPI-U: Durables (SA, 1982-84=100) log 2nd diff CPI-U: Services (SA, 1982-84=100) log 2nd diff CPI-U: Medical Care (SA, 1982-84=100) log 2nd diff CPI-U: All Items Less Food (SA, 1982-84=100) log 2nd diff CPI-U: All Items Less Medical Care (SA, 1982-84=100) log 2nd diff CPI-U: All Items Less Shelter (SA, 1982-84=100) log 2nd diff CPI-U: Transportation (SA, 1982-84=100) log 2nd diff PCE: Durable Goods: Chain Price Index (SA, 2000=100) log 2nd diff PCE: Personal Consumption Expenditures: Chain Price Index (SA, 2000=100) log 2nd diff PCE: Nondurable Goods: Chain Price Index (SA, 2000=100) log 2nd diff PCE: Services: Chain Price Index (SA, 2000=100) log 2nd diff Avg Hourly Earnings: Construction (SA, $/Hr) log 2nd diff Avg Hourly Earnings: Manufacturing (SA, $/Hr) log 2nd diff Commercial & Industrial Loans Outstanding (EOP, SA, Mil.Chn.2000 $) 1st diff Money Stock: M2 (SA, Bil.$) log 2nd diff 10-Year Treasury Note Yield at Constant Maturity (% p.a.) 1st diff Federal Funds [effective] Rate (% p.a.) 1st diff PPI: Intermediate Materials, Supplies and Components (SA, 1982=100) log 2nd diff PPI: Finished Goods (SA, 1982=100) log 2nd diff ISM: Mfg: Prices Index (NSA, 50+ = Econ Expand) level CPI-U: All Items (SA, 1982-84=100) log 1st diff Mfrs' New Orders:Durable Goods Industries With Unfilled Orders (SA,Mil$) log 1st diff Manufacturers' New Orders (SA, Mil.$) log 1st diff Manufacturers' New Orders: Nondurable Goods Industries (SA, Mil.$) log 1st diff Mfrs' New Orders:Nondurable Goods Industries W/Unfilled Orders (SA,Mil$) log 1st diff Manufacturers' Unfilled Orders: Durable Goods Industries (EOP,SA,Mil.$) log 1st diff Manufacturers' Unfilled Orders (EOP, SA, Mil.$) log 1st diff Manufacturers' Unfilled Orders:Nondurable Goods Industries (EOP,SA,Mil$) log 1st diff Foreign Exchange Rate: Canada (C$/US$) log 1st diff Foreign Exchange Rate: Germany (D. Mark/US$) log 1st diff Foreign Exchange Rate: Japan (Yen/US$) log 1st diff Foreign Exchange Rate: Switzerland (Franc/US$) log 1st diff Contracts & Orders: Plant & Equipment (SA, Mil.$) log 1st diff Panel B: Quarterly Data Data Description Transformation Business Sector: Compensation per Hour of all Persons (SA,1992=100) log 1st diff Business Sector: Real Compensation per Hour of all Persons (SA,1992=100) log 1st diff Business Sector: Unit Labor Costs (SA,1992=100) log 1st diff Business Sector: Unit Non-Labor Payments (SA,1992=100) log 1st diff Non-farm Business Sector: Unit Non-Labor Payments (SA,1992=100) log 1st diff Non-financial Corporations: Output per Hour, All employees (SA, 1992=100) log 1st diff Non-financial Corporations: Compensation per Hour, All employees (SA, 1992=100) log 1st diff Non-financial Corporations: Real Compensation per Hour, All employees (SA, 1992=100) log 1st diff Non-financial Corporations: Unit Labor Costs, All employees (SA, 1992=100) log 1st diff Non-financial Corporations: Unit Non-Labor Costs, All employees (SA, 1992=100) log 1st diff Non-financial Corporations: Total Unit Costs, All employees (SA, 1992=100) log 1st diff Business Sector: Real Unit Labor Costs (SA,1992=100) log 1st diff Non-financial Corporations: Real Unit Labor Costs, All employees (SA, 1992=100) log 1st diff Business Sector: Real Unit Non-Labor Payments (SA,1992=100) log 1st diff Non-farm Business Sector: Real Unit Non-Labor Payments (SA,1992=100) log 1st diff Non-financial Corporations: Real Unit Non-Labor Costs, All employees (SA, 1992=100) log 1st diff Non-financial Corporations: Real Total Unit Costs, All employees (SA, 1992=100) log 1st diff Government Total Receipts (SAAR, Bil. $) log 1st diff Government Total Expenditures (SAAR, Bil. $) log 1st diff Government Net Lending or Net Borrowing (SAAR, Bil. $) 1st diff GDP Deflator log 1st diff Gross Private Domestic Investment: Implicit Price Deflator (SA, 2000=100) log 1st diff Private Fixed Investment: Implicit Price Deflator (SA, 2000=100) log 1st diff Private Non-residential Fixed Investment: Implicit Price Deflator (SA, 2000=100) log 1st diff Private Non-residential Structures: Implicit Price Deflator (SA, 2000=100) log 1st diff Private Non-residential Equipment/Software: Implicit Price Deflator (SA, 2000=100) log 1st diff Private Residential Investment: Implicit Price Deflator (SA, 2000=100) log 1st diff Government Consumption/Gross Investment: Implicit Price Deflator (SA, 2000=100) log 1st diff Federal Non-Defense Consumption/Investment: Implicit Price Deflator (SA, 2000=100) log 1st diff Imports of Goods & Services: Implicit Price Deflator (SA, 2000=100) log 1st diff Exports of Goods & Services: Implicit Price Deflator (SA, 2000=100) log 1st diff Non-farm Business Sector: Output per Hour of all Persons (SA,1992=100) log 1st diff Non-farm Business Sector: Compensation per Hour of all Persons (SA,1992=100) log 1st diff Non-farm Business Sector: Real Compensation per Hour of all Persons (SA,1992=100) log 1st diff Non-farm Business Sector: Unit Labor Costs (SA,1992=100) log 1st diff Non-farm Business Sector: Real Unit Labor Costs (SA,1992=100) log 1st diff Figure 1: Long Horizon Responses Tech Shock --> GDP MRS Shock --> GDP MP Shock --> GDP 1.8 1.8 1.8 1.2 1.2 1.2 0.6 0.6 0.6 0.0 0.0 0.0 -0.6 -0.6 -0.6 -1.2 -1.2 -1.2 3 19 35 51 67 Tech Shock --> Productivity 3 19 35 51 67 MRS Shock --> Productivity 3 19 35 51 67 MP Shock --> Productivity 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 -1.0 3 19 35 51 67 3 19 35 51 67 3 19 35 51 67 Figure 2: Cyclical Responses Tech Shock --> GDP MRS Shock --> GDP MP Shock --> GDP 1.8 1.8 1.8 1.2 1.2 1.2 0.6 0.6 0.6 0.0 0.0 0.0 -0.6 -0.6 -0.6 -1.2 1 5 9 13 17 -1.2 Tech Shock --> CONS 1 5 9 13 17 -1.2 MRS Shock --> CONS 1 5 9 13 17 MP Shock --> CONS 1.2 1.2 1.2 0.8 0.8 0.8 0.4 0.4 0.4 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.8 1 5 9 13 17 -0.8 1 Tech Shock --> BFI 5 9 13 17 -0.8 1 MRS Shock --> BFI 5 9 13 17 MP Shock --> BFI 5.0 5.0 5.0 2.5 2.5 2.5 0.0 0.0 0.0 -2.5 1 5 9 13 17 -2.5 Tech Shock --> RES 1 5 9 13 17 -2.5 1 MRS Shock --> RES 5 9 13 17 MP Shock --> RES 5.0 5.0 5.0 2.5 2.5 2.5 0.0 0.0 0.0 -2.5 -2.5 -2.5 -5.0 -5.0 -5.0 -7.5 1 5 9 13 17 Tech Shock --> Real Compensation -7.5 1 5 9 13 17 MRS Shock --> Real Compensation -7.5 1 5 9 13 17 MP Shock --> Real Compensation 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 1 5 9 13 17 -1.0 1 5 9 13 17 -1.0 1 5 9 13 17 Figure 3: Responses of Labor Inputs and Productivity Tech Shock --> Hours MRS Shock --> Hours MP Shock --> Hours 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 1 5 9 13 17 Tech Shock --> Employment -1.0 1 5 9 13 17 MRS Shock --> Employment 1 5 9 13 17 MP Shock --> Employment 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 1 5 9 13 17 Tech Shock --> Productivity -1.0 1 5 9 13 17 MRS Shock --> Productivity 1 5 9 13 17 MP Shock --> Productivity 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 1 5 9 13 17 -1.0 1 5 9 13 17 1 5 9 13 17 Figure 4: Responses of Inflation and Output Gap Tech Shock --> Inflation MRS Shock --> Inflation MP Shock --> Inflation 0.50 0.50 0.50 0.25 0.25 0.25 0.00 0.00 0.00 -0.25 -0.25 -0.25 -0.50 -0.50 -0.50 -0.75 -0.75 -0.75 1 6 11 16 1 Tech Shock --> Output Gap 6 11 16 1 MRS Shock --> Output Gap 6 11 16 MP Shock --> Output Gap 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 -1.0 1 5 9 13 17 1 5 9 13 17 1 5 9 13 17 Figure 5: Responses of Interest Rates Tech Shock --> Fed Funds Rate MRS Shock --> Fed Funds Rate MP Shock --> Fed Funds Rate 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 1 5 9 13 17 -1.0 1 5 9 13 17 1 Tech Shock --> 1 Month Treasury Yield MRS Shock --> 1 Month Treasury Yield 1.0 1.0 0.5 0.0 -0.5 17 0.0 -0.5 13 0.5 0.0 9 1.0 0.5 5 -0.5 -1.0 -1.0 1 5 9 13 17 Tech Shock --> 12 Month Treasury Yield MP Shock --> 1 Month Treasury Yield -1.0 1 5 9 13 17 MRS Shock --> 12 Month Treasury Yield 1 5 9 13 17 MP Shock --> 12 Month Treasury Yield 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 -0.5 -0.5 -0.5 -1.0 -1.0 1 5 9 13 17 -1.0 1 5 9 13 17 1 Tech Shock --> 5 Year Treasury Yield MRS Shock --> 5 Year Treasury Yield 0.75 0.75 0.50 0.25 0.00 0.00 -0.25 -0.25 17 0.25 0.00 13 0.50 0.25 9 0.75 0.50 5 -0.25 -0.50 -0.50 1 6 11 16 MP Shock --> 5 Year Treasury Yield -0.50 1 6 11 16 1 6 11 16 Figure 6: Responses of Equity Markets Tech Shock --> S&P 500 MRS Shock --> S&P 500 MP Shock --> S&P 500 18 18 18 9 9 9 0 0 0 -9 -9 -9 -18 -18 1 5 9 13 -18 17 Tech Shock --> Excess Stock Return 1 5 9 13 17 1 MRS Shock --> Excess Stock Return 5 9 13 17 MP Shock --> Excess Stock Return 0.90 0.90 0.90 0.45 0.45 0.45 -0.00 -0.00 -0.00 -0.45 -0.45 -0.45 -0.90 -0.90 -0.90 -1.35 -1.35 1 6 11 -1.35 16 1 Tech Shock --> Profits 6 11 16 1 MRS Shock --> Profits 6 11 16 MP Shock --> Profits 5.0 5.0 5.0 2.5 2.5 2.5 0.0 0.0 0.0 -2.5 -2.5 -2.5 -5.0 -5.0 1 5 9 13 17 -5.0 1 5 9 13 17 1 5 9 13 17 Figure 7 Baseline Shocks vs. Single-Eta Shocks Baseline MP Shock --> Price Single-Eta MP Shock --> Price Baseline MP Shock --> Durable Cons. Single-Eta MP Shock --> Durable Cons. 0.5 0.5 1.8 1.8 0.0 0.0 0.9 0.9 -0.5 -0.5 -0.0 -0.0 -1.0 -1.0 -0.9 -0.9 -1.5 -1.5 -1.8 -1.8 -2.0 -2.0 1 5 9 13 17 Baseline MP Shock --> Inflation -2.7 1 5 9 13 -2.7 17 Single-Eta MP Shock --> Inflation 1 5 9 13 17 Baseline MP Shock --> Investment E&S 1 5 9 13 17 Single-Eta MP Shock --> Investment E&S 0.4 0.4 2 2 0.2 0.2 1 1 -0.0 -0.0 0 0 -0.2 -0.2 -1 -1 -0.4 -0.4 -2 -2 -0.6 -0.6 1 5 9 13 17 Baseline MP Shock --> Total Cons. -3 1 5 9 13 17 Single-Eta MP Shock --> Total Cons. 0.4 0.4 -0.0 -3 1 5 9 13 17 1 5 9 13 17 Baseline Tech Shock --> Fed Funds Rate Single-Eta Tech Shock --> Fed Funds Rate -0.0 0.6 0.0 0.0 -0.4 -0.8 1.2 0.6 -0.4 1.2 -0.8 -1.2 -1.2 1 5 9 13 17 -0.6 1 5 9 13 17 -0.6 1 5 9 13 17 1 5 9 13 17