The Quantitative Importance of News Shocks in Estimated DSGE Models

The Quantitative Importance of News Shocks in Estimated DSGE Models Hashmat Khan John Tsoukalas Carleton University University of Nottingham February 15, 2009 Abstract We estimate dynamic stochastic general equilibrium (DSGE) models with several frictions and shocks, including news shocks to total factor productivity (TFP) and investmentspecific (IS) technology, using quarterly US data from 1954-2004 and Bayesian methods. When all types of shocks are considered, TFP news and IS news compete with other atemporal and intertemporal shocks, respectively, and get a small role in accounting for fluctuations. Unanticipated IS shocks account for the bulk of the fluctuations. In a flexible price environment, however, both unanticipated TFP and TFP news shocks dominate and account for over 80% of unconditional variance in output growth, consumption growth, investment growth, and hours. In an environment with nominal frictions, IS news is the most important driver of fluctuations in these variables when (a) data on S&P 500 stock returns is included as an observable in the estimation or (b) another intertemporal shock, namely the preference shock, is absent. Our findings help shed light on why the recent work on news shocks in estimated DSGE models might have reached sharply different conclusions regarding their quantitative importance. More generally, given the sensitivity to model structure, shocks, and the data used, they suggest that estimated DSGE models may be limited in helping resolve the debate on the sources of business cycles. JEL classification: E2, E3 Key words: News shocks, Business cycles, DSGE models Department of Economics, D891 Loeb, 1125 Colonel By Drive, Ottawa, K1S 5B6, Canada, tel: +1 613 520 2600 (Ext. 1561). E-mail: Hashmat Khan@carleton.ca. Khan acknowledges support of the SSHRC Research Grant. School of Economics, University of Nottingham, University Park, Nottingham NG7 2RD tel: +44 (0) 115 846 7057. E-mail: John.Tsoukalas@nottingham.ac.uk. Tsoukalas acknowledges support of a British Acedemy Research Grant.

1. Introduction The quantitative importance of the various sources of business cycles has remained a subject of much debate among macroeconomists. Cochrane (1994) wrote What shocks are responsible for economic fluctuations? Despite at least two hundred years in which economists have observed fluctuations in economic activity, we are still not sure. The empirical findings of Galí (1999) suggest that shocks to disembodied technology (or, total factor productivity, TFP), as emphasized in the real business cycle literature, have not played a major role in US business cycles. On the other hand, Fisher (2006) finds that once the scope of technology includes embodied (or, investment-specific, IS) technology then technology shocks matter a lot. Beaudry and Portier (2006) have, however, suggested that an important fraction of business cycle fluctuations may be driven by shocks to anticipated future changes in technology, or news shocks. of business cycles. 1 This possibility is interesting as it brings to the stage an alternative source More recently, Beaudry and Lucke (2008) consider a structural vector error correction model (SVECM) and identify five shocks, namely, unanticipated TFP, anticipated TFP or news, unanticipated IS, preference, and monetary. They find that TFP news shocks are by far the most important and account for approximately 50% of the forecast error variance of economic activity at business cycle horizons. By contrast, the combined contribution of unanticipated TFP and IS shocks is approximately 20%. In this paper, we build on the work of Beaudry and Lucke (2008) but use the framework of estimated dynamic stochastic general equilibrium (DSGE) model instead. The main question that we seek to answer is as follows: When news shocks compete with a variety of other shocks in an estimated DSGE model, which shock dominates? So far the investigation of news shocks as 1 In early work Barro and King (1984) pointed out that changes in beliefs about the future cannot generate empirically recognizable business cycles within the standard real business cycle models. One strand of recent theoretical literature develops models with and without market frictions which overcome this challenge in response to news shocks. See, for example, Beaudry and Portier (2007), Jaimovich and Rebelo (2009), Christiano et al. (2007), Karnizova (2008), Kobayashi et al. (2007), Kobayashi and Nutahara (2008), Denhaan and Kattenbrunner (2008), and Guo (2008b). A related empirical literature cautions against the identification of news shocks using structural vector autoregressions. See, for example, Fève et al. (2008) and Choi (2008). 1

a source of business cycles using estimated models along the lines of Christiano et al. (2005) and Smets and Wouters (2003) has been somewhat limited. Moreover, a small set of papers which have estimated DSGE models, with both unanticipated and anticipated shocks, for the US data have reached sharply different conclusions about the relative importance of the type of the news shock. Davis (2007) introduces anticipated shocks in the Christiano et al. (2005) model and finds that IS news shocks account for about 52% of the variation in output growth. By contrast, Schmitt-Grohé and Uribe (2008), consider a DSGE model without nominal frictions, and find that TFP news shocks accounts for approximately two-thirds of the variation in output growth. Fujiwara et al. (2008) estimate a variant of Smets and Wouters (2007) model incorporating TFP news shocks and find that it accounts for approximately 12% of variation in output. These different conclusions about the relative contributions of the type of news shock suggests that some aspects of the model structure or shocks may itself affect the quantitative assessments. It would be of interest to help understand which elements influence the quantitative assessments the most and why. Our paper takes a step in this direction. We use the Smets and Wouters (2007) model and augment it to include up to six-quarter ahead news shocks to future TFP and IS technology. The Smets and Wouters (2007) model is a natural benchmark as it contains a variety of real and nominal frictions that are helpful in accounting for the conditional responses of macroeconomic variables to unanticipated shocks. The list of shocks we consider is, TFP (unanticipated and news), IS (unanticipated and news), preference, government spending, monetary, price markup, and wage markup. Following Jaimovich and Rebelo (2009), we introduce preferences which can, in theory, mitigate the strong wealth effects of anticipated shocks. Thus, the benchmark DSGE model we use in our analysis is equipped to produce co-movement among macroeconomic variables in response to news shocks. We estimate the model using Bayesian methods and US data on seven observables from 1954:Q3 to 2004:Q4. These variables are log difference of real GDP, real consumption, real investment, and GDP deflator, the real wage, log hours worked, and the federal funds rate. We find that when all types of shocks are considered in a sticky price-wage environment, unanticipated IS shocks account for the bulk of the fluctuations. Specifically, IS shocks account for 62% of the unconditional variance in output growth, 92% in investment growth, and 37% in hours. The 2

large role for IS shocks even in the presence of TFP and IS news shocks corroborates the findings of Justiniano et al. (2008). Preference and unanticipated TFP shocks account for approximately 50% of the fluctuation in consumption growth, followed by unanticipated IS shocks (approximately 18%). Unanticipated TFP shocks account for about 13% of variation in output growth. Monetary shocks account for 10% of the variation in output growth and about 17% in consumption growth. The wage markup shock accounts for 34% of the unconditional variance in hours worked. Quite surprisingly, when all shocks compete, both TFP news and IS news get an almost negligible role in accounting for fluctuations in macroeconomic variables. The quantitative findings, however, change dramatically in a flexible price-wage environment. We estimate a version of the DSGE model with nearly flexible prices and wages and no price markup shocks. In this environment, both TFP and TFP news shocks dominate and account for over 80% of unconditional variance in output growth, consumption growth, investment growth, and hours. The important role of TFP news in the flexible price-wage environment confirms the findings reported in Schmitt-Grohé and Uribe (2008). In the benchmark model, if we exclude only the preference shock, then the role for IS news shocks in accounting for fluctuations rises sharply. These shocks account for over 70% of the variation in output and investment, 32% in consumption, and 44% in hours. The unanticipated IS is the second most important shock in this environment. Fujiwara et al. (2008), for example, consider the Smets and Wouters (2007) model but without preference and IS news shocks. They find a limited role for TFP news in output fluctuations. Our findings, however, indicate that the quantitative conclusions about the importance of news shocks can be very sensitive to the inclusion and/or exclusion of other shocks. Finally, we investigate the sensitivity of quantitative assessments regarding news shocks to incorporating data on S&P 500 return, as an observable in the estimation, as in Davis (2007). We equate the unobservable real return on capital in the model to the observable real return on the S&P 500 index and estimate the benchmark model with nominal rigidities. There is a sharp rise in the role of IS news shocks consistent with the findings in Davis (2007). It accounts for approximately 70% of the fluctuations in output growth, 82% in investment growth and 42% in hours growth. Again, these findings are in sharp contrast to those from the benchmark model where IS news (and 3

TPP news) do not appear to play a quantitatively important role. To help understand the reason behind these findings and to contrast our results with those in the recent literature mentioned above, we adopt the distinction between intertemporal and intratemporal shocks as discussed in Primiceri et al. (2006). Intertemporal shocks are disturbances which affect trade-offs across periods in agents optimization problems whereas intratemporal shocks are disturbances which affect trade-offs within a period in agents optimization problems. We apply this distinction to news shocks. IS news shocks are intertemporal shocks as they directly influence the Euler condition for the optimal capital-investment decision whereas TFP news shocks do not. Thus, not only do all shocks compete with each other but also IS news shocks compete with the other intertemporal shocks, namely the unanticipated IS shock and the preference shock when fitting the data. And TFP news competes with other atemporal shocks such as unanticipated TFP, the price markup and the wage markup shocks. In a flexible price-wage environment and without the price-markup shock, the major source of fluctuations shifts from intertemporal to atemporal shocks, namely, from unanticipated IS to unanticipated TFP and TFP news shocks. Whereas, in the benchmark model without the preference shock - an intertemporal shock - the role of IS news shock rises sharply. We provide evidence for this shifting of the sources of shocks. When S&P returns data are included as an observable, we find that IS and IS news shocks compete to fit the large variation in stock returns, and the latter help to better account for the limited degree of comovement between consumption growth and the return to capital. The quantitative importance of news shocks in estimated DSGE models appears to be quite sensitive to the details of the model structure and shocks that are considered in the analysis. Our findings indicate that this is indeed the case and help shed light on why the recent work on news shocks in estimated DSGE models might have reached sharply different conclusions regarding their quantitative importance. More generally, they suggest that estimated DSGE models may be limited in helping resolve the debate on the sources of business cycles. The rest of the paper is structured as follows. Section 2 describes the model set-up, section 3 presents the estimation methodology, while section 4 presents estimation results and section 5 concludes. 4

2. The model Our objective is to estimate a DSGE model with real and nominal frictions which have been shown in the literature to help account for the variation in aggregate data. Prominent examples of such models are Christiano et al. (2005), Smets and Wouters (2003), and Smets and Wouters (2007). We consider the Smets and Wouters (2007) model as the starting point and consider two modifications: First, we introduce anticipated (or news) shocks to future total factor productivity (TFP) and investment-specific (IS) technology shock processes. Second, we consider the preferences suggested by Jaimovich and Rebelo (2009) which can help mitigate the strong wealth effects of news shocks on labour supply thereby helping to generate co-movement among key macroeconomic variables. The model has households that consume goods and services, supply specialized labor on a monopolistically competitive labor market, rent capital services to firms and make investment decisions. Firms choose the optimal level of labor and capital and supply differentiated products on a monopolistically competitive goods market. Prices and wages are re-optimized at random intervals as in Calvo (1983) and Erceg et al. (2000). When they are not re-optimized, prices and wages are partially indexed to past inflation rates. There are seven types of orthogonal structural shocks: TFP (including TFP news shocks), investment-specific technology (including IS news shocks), price and wage mark-ups, government spending, monetary policy, and preference shocks. 2 Using the same notation as in Smets and Wouters (2007), we present the log-linearized equations of the model here where lower case letters denote log deviations from steady state values, and the latter are denoted by a. The aggregate resource constraint is given by, y t = c y c t + i y i t + z y z t + ε g t (1) Output, y t, is the sum of consumption, c t, investment, i t, capital utilization costs, z y z t, and an exogenous spending disturbance, ε g t. The coefficient c y = 1 g y i y is the steady state share of consumption in output. The coefficients g y and i y are the steady state shares of government 2 We consider preference shocks as in Smets and Wouters (2003) instead of risk-premium shocks as in Smets and Wouters (2007). For our quantitative results and conclusions, it makes little difference if we use risk-premium shocks instead. 5

spending and investment in output, respectively. These steady state shares are linked to other model parameters, which are shown in Table 1. The government spending disturbance is assumed to follow a first-order autoregressive (AR (1)) process with a mean zero IID normal error term, η g N(0, σ g ) ε g t = ρ gε g t 1 + ηg t (2) We consider the preferences of household j [0, 1] of the type suggested by Jaimovich and Rebelo (2009) and described by the utility function where E 0 t=0 β t εb t ( C t χl 1+σ l t X t ) 1 σc 1 1 σ c (3) X t = C ω t X 1 ω t 1 is a geometric average of current and past consumption levels, E 0 denotes expectation conditional on the information available at time 0, 0 < β < 1, σ l > 0, χ > 0, σ c > 0, 0 ω 1 and ε b t is the preference shock assumed to follow an AR(1) process with mean zero IID normal error term η b t N(0, σ b ) ε b t = ρ b ε b t 1 + η b t (4) The preference structure in (3) nests two special cases: when ω = 1 the preferences are the same as in King et al. (1988) and when ω = 0 the preferences are the same as in Greenwood et al. (1988). Household j maximizes (3) subject to the budget constraint. 3 The log-linearized first-order condition for consumption is c t = E t c t+1 + c 1 (r t E t π t+1 ) + c 2 E t (l t+1 l t ) + c 3 E t (x t+1 x t ) + c 1 (E t ε b t+1 ε b t) (5) where the coefficients c 1 and c 2 depend on the underlying model parameters and the steady state level of hours worked, and c 3 = c 2 (1+σ l ) 1. The expressions for c 1 and c 2 are given in the Appendix. In the equation above, current consumption depends on future expected and past consumption (through the x t variable), expected hours growth, the real interest rate and the preference shock. 3 The details are presented in the Appendix. 6

Investment is described by the Euler equation ( 1 i t = i t 1 + βγ 1 σc E t i t+1 + 1 ) 1 + βγ 1 σc γ 2 ϕ (q t + ε i t) (6) where in the above equation, ϕ is second derivative of the investment adjustment cost function, S ( It I t 1 ), evaluated at the steady state (as in Christiano et al. (2005)). I t is the level of investment at time t. The parameter γ is the common, deterministic, growth rate of output, consumption investment and wages. The shock to investment-specific technology is ε i t and we specify its process in Section 2.1. The dynamics of the value of capital, q t, are described by q t = (r t E t π t+1 ) + r k (r k + (1 δ)) E trt+1 k (1 δ) + (r k + (1 δ)) E tq t+1 (7) where r k t denotes the rental rate on capital and δ is the depreciation rate. The aggregate production function is given by y t = φ p (αk s t + (1 α)l t + ε a t ) (8) That is, output is produced using capital (k s t ) and labor services (l t ). The parameter φ p is one plus the share of fixed costs in production. The variable ε a t is the total factor productivity shock and we describe its process in Section 2.1 Capital services used in production are a function of capital installed in the previous period, k t 1, and capital utilization, z t, and given as where capital utilization is a function of the rental rate of capital, k s t = k t 1 + z t (9) z t = 1 ψ ψ rk t (10) and 0 < ψ < 1 is a positive function of the elasticity of the capital utilization adjustment cost function with respect to utilization. The capital accumulation equation is given as ( k t = 1 (1 δ) k t 1 + γ (1 δ) γ 7 ) ( i t + 1 ) (1 δ) ε i t (11) γ

In the goods market, we can define the price mark-up as, µ p t = mpl t w t = α(k s t l t ) + ɛ a t w t (12) where mpl t is the marginal product of labour, and w t is the real wage. Inflation dynamics are described by the New-Keynesian Phillips curve π t = π 1 π t 1 + +π 2 E t π t+1 π 3 µ p t + εp t (13) where π 1 = ι p /(1+βγ 1 σc ι p ), π 2 = βγ 1 σc /(1+βγ 1 σc ι p ), π 3 = 1/(1+βγ 1 σc ι p )[(1 βγ 1 σc ξ p )(1 ξ p )/ξ p ((φ p 1)ε p + 1)]. In the notation above 1 ξ p denotes the probability that a given firm will be able to reset its price and ι p denotes the degree of indexation to past inflation by firms who do not optimally adjust prices. Finally, ε p is a parameter that governs the curvature of the Kimball goods market aggregator, and (φ p 1) denotes the share of fixed costs in production. 4 The price mark-up disturbance follows an ARMA(1,1) process with a mean zero IID normal error term ε p t = ρ pε p t 1 + ηp t µ pη p t 1 (14) Cost minimization by firms implies that the capital-labor ratio is inversely related to the rental rate of capital and positively related to the wage rate. r k t = (k t l t ) + w t (15) Similar to the goods market, in the labour market the wage markup is given by µ w t = w t mrs t = w t (1 χωl (1+σ l) γ (ω 1)/ω ) 1 ( (1 χωl (1+σ l) γ (ω 1)/ω σ l + χωl (1+σ l) γ (ω 1)/ω )l t ) + (1 χωl (1+σ l) γ (ω 1)/ω ) 1 ( (1 χωl (1+σ l) γ (ω 1)/ω + χωl (1+σ l) γ (ω 1)/ω )x t ) (1 χωl (1+σ l) γ (ω 1)/ω ) 1 ( χωl (1+σ l) γ (ω 1)/ω c t ) (16) Note that the mrs t expression is implied by the preferences in (3). 4 The Kimball goods (and labour) market aggregator implies that the demand elasticity of differentiated goods under monopolistic competition depends on their relative price (see Kimball (1995)). This helps obtain plausible duration of price and wage contracts. 8

The wage inflation dynamics are described by w t = w 1 w t 1 + (1 w 1 )(E t w t+1 + E t π t+1 ) w 2 π t + w 3 π t 1 w 4 µ w t + ε w t (17) where w 1 = 1 1+βγ 1 σc w 2 = 1+βγ1 σc ι w 1+βγ 1 σc, w 3 = ι w 1+βγ 1 σc, and w 4 = (1 ξ w)(1 βγ 1 σc ξ w) ((1+βγ 1 σc )ξ w)(1/((φ w 1)ε w+1)) The parameters (1 ξ w ) and ι w denote the probability of resetting wages and the degree of indexation to past wages, respectively. σ l is the elasticity of labor supply with respect to the real wage, and (φ w 1) denotes the steady state labor market markup. Similar to the goods market formulation ε w denotes the curvature parameter for the Kimball labor market aggregator. The wage mark up disturbance is assumed to follow an ARMA(1,1) process ε w t = ρ w ε w t 1 + η w t µ w η w t 1 (18) where η w is a mean zero IID normal error term. The monetary authority follows a generalized Taylor rule, r t = ρr t 1 + (1 ρ)[r π π t + r y (y t y f t )] + r y[(y t y f t ) (y t 1 y f t 1 )] + εr t (19) The policy instrument is the nominal interest rate, r t, which is adjusted gradually in response to inflation and the output gap, (y t y f t ), defined as the difference between actual and potential output, y f t, where the latter is the level of output that would prevail in equilibrium with flexible prices and in the absence of the two mark-up shocks. In addition, policy responds to the growth of the output gap. The parameter ρ captures the degree of interest rate smoothing. The disturbance ε r t is the monetary policy shock and is assumed to follow an AR(1) process with a mean zero IID normal error term: ε r t = ρ r ε r t 1 + ηt r (20) 2.1 News shocks We introduce news shocks in the model in the same way as in Davis (2007), Schmitt-Grohé and Uribe (2008), and Fujiwara et al. (2008). We write the TFP shock process as ε a t = ρ a ε a t 1 + η a t (21) 9

where the innovation, ηt a, is split into two components. An anticipated component, η a,0 t, and an unanticipated component, η a,news t, written as where η a,news t H h ηa,h t h and ηa,h t h η a t = η a,0 t + η a,news t (22) is the h-period ahead news about total factor productivity anticipated by the agents at period t h and H is the longest horizon over which the shocks are anticipated by the agents. The innovations to ε a t, η a,h t h, are IID normal with variance σ2 a,h, for h = 0, 1,..., H. A similar structure applies to the investment-specific shock process ε i t = ρ i ε i t 1 + η i t (23) where the innovation ηt i is split into two components. An anticipated component, η i,0 t, and an unanticipated component, η i,news t, and written as where η a,news t H h ηi,h t h and ηi,h t h η i t = η i,0 t + η a,news t (24) is the h-period ahead news about total factor productivity anticipated by the agents at period t h. The innovations to ε i t, η i,h t h, are IID normal with variance σi,h 2, for h = 0, 1,..., H. 3 Estimation methodology and data In this section we describe the Bayesian estimation methodology and the data used in the empirical analysis. 3.1 Bayesian methodology We use the Bayesian methodology to estimate a subset of model parameters. This methodology is now extensively used in estimating DSGE models (see Schorfheide (2000), Smets and Wouters (2003), and Lubik and Schorfheide (2004) for early examples). Recent overviews are presented in An and Schorfheide (2007) and Fernández-Villaverde (2009). The key steps in this methodology are as follows. The model presented in the previous sections is solved using standard numerical techniques and the solution is expressed in state-space form as follows: x t = Ax t 1 + Bε t 10

Y t = Cx t where A, B and C denotes matrices of reduced form coefficients that are non-linear functions of the structural parameters. x t denotes the vector of model variables, and Y t the vector of observable variables at time t to be used in the estimation below. Let Θ denote the vector that contains all the structural parameters of the model. The non-sample information is summarized with a prior distribution with density p(θ). 5 The sample information (conditional on model M i ) is contained in the likelihood function, L(Θ Y T, M i ), where Y T = [Y 1,..., Y T ] contains the data. The likelihood function allows one to update the prior distribution of Θ. Let p(y T Θ, M i ) = L(Θ Y T, M i ) denote the likelihood function of version M i of the DSGE model. Then, using Bayes theorem, we can express the posterior distribution of the parameters as p(θ Y T, M i ) = p(y T Θ, M i )p(θ) p(y T M i ) (25) where the denominator, p(y T M i ) = p(θ, Y T M i )dθ, in (25) is the marginal data density conditional on model M i. In Bayesian analysis the marginal data density constitutes a measure of model fit with two dimensions: goodness of in-sample fit and a penalty for model complexity. The posterior distribution of parameters is evaluated numerically using the random walk Metropolis- Hastings algorithm. We obtained a sample of 100,000 draws (after dropping the first 20,000 draws) and use this to (i) report the mean, and the 5 and 95 percentiles of the posterior distribution of the estimated parameters and (ii) evaluate the marginal likelihood of the model. 6 All estimations are done using DYNARE. 7 3.2 Data We estimate the model using quarterly US data (1954:Q3-2004:Q4) on output, consumption, inflation, investment, hours worked, wages and the nominal interest rate. All nominal series are expressed in real terms by dividing with the GDP deflator. Moreover, output, consumption, investment and hours worked are expressed in per capita terms by dividing with civilian non-institutional 5 We assume that parameters are a priori independent from each other. This is a widely used assumption in the applied DSGE literature and implies the joint prior distribution equals the product of marginal priors. 6 We also calculate convergence diagnostics in order to check and ensure the stability of the posterior distributions of parameters as described in Brooks and Gelman (1998). 7 http://www.cepremap.cnrs.fr/dynare/. The replication files are available upon request. 11

population between 16 and 65. We define nominal consumption as the sum of personal consumption expenditures on nondurable goods and services. As in Justiniano et al. (2008), we define nominal gross investment is the sum of personal consumption expenditures on durable goods and gross private domestic investment. Real wages are defined as compensation per hour in the non-farm business sector divided by the GDP deflator. Hours worked is the log of hours of all persons in the non-farm business sector, divided by the population. Inflation is measured as the quarterly log difference in the GDP deflator. Nominal interest rate series is the effective Federal Funds rate. All data except the interest rate are in logs and seasonally adjusted. Notice that we do not demean or de-trend the data. 3.3 Prior distribution We use prior distributions that conform to the assumptions used in Smets and Wouters (2007) and Justiniano et al. (2008). Table 1 lists the choice of priors. The first four columns in Table 1 list the parameters and the assumptions on the prior distributions. The remaining columns of Table 1 report the mean and 90 percent probability intervals for the structural parameters. A number of parameters is held fixed prior to estimation. We set the depreciation rate for capital, δ, equal to 0.025 a value conventional at the quarterly frequency. The curvature parameters for the Kimball goods and labor market aggregators, ε p, and ε w are both set equal to 10 and the steady state labor market markup, φ w, is set at 1.5 as in Smets and Wouters (2007). We set the capital share parameter in production, α, equal to 0.3, and the steady state government spending to output ratio equal to 0.22, the average value in the data. Finally, we normalize χ in the utility function equal to one, and set the steady state hours worked, L equal to 0.3. Given our focus on the importance of news shocks in generating business cycles we briefly discuss the choice of priors for the standard deviations of the TFP and IS news shocks. We choose a prior mean for each news component such that the variance of the unanticipated component of TFP and IS equals the sum of the variances of the associated anticipated components. Our choice of prior for the news disturbances is guided by the findings of Beaudry and Portier (2006) and Beaudry and Lucke (2008) who estimate that news shocks account for around 50% of macroeconomic fluctuations. 12

4. Results In this section we present the parameter estimates and variance decompositions of the benchmark model. Following that, we present estimates from other versions of the model and discuss why the quantitative assessments of news shocks differ across the environments we examine. 4.1 Parameter estimates Table 1 reports the estimated values for the structural parameters and standard deviations for the shocks of the benchmark model using the seven macroeconomic time series as described in section 3.2. Our estimates are in line with previous studies that have estimated similar specifications of the sticky price-wage framework we adopt here. We estimate a substantial degree of price and wage stickiness and a moderate degree of wage and price indexation as in Smets and Wouters (2007) and Justiniano et al. (2008). Similarly, our estimate of the investment adjustment cost parameter is within the values reported by the above studies and so are the Taylor rule coefficients for inflation, output gap, the growth in output gap and the interest rate smoothing parameter. The standard deviations of the seven unanticipated disturbances are also in line with values reported by those studies. A new parameter which we estimate is, ω. This parameter controls the wealth elasticity of labor supply and is estimated to be close to 1, a value that implies preferences that are close to those proposed by King et al. (1988). This estimate for ω implies a relatively high wealth elasticity of labor supply. By contrast, Schmitt-Grohé and Uribe (2008) estimate a flexible price-wage DSGE model and obtain a sharply different value for ω. According to their estimates, ω is very close to zero, consistent with the specification of preferences by Greenwood et al. (1988). Our model has more parameters, frictions, and shocks compared to the one considered in Schmitt-Grohé and Uribe (2008). In the larger model we consider, the estimate of ω parameter comes out to be close to one, implying preferences are close to King et al. (1988) preferences. 4.2 Variance decompositions To assess the driving forces behind macroeconomic fluctuations we examine the contribution of each shock to the unconditional variance of the variables. Although we used seven variables in 13

the estimation, we report here the results only for four real variables (quantities), namely, output growth, consumption growth, investment growth, and hours to highlight our key findings and to contrast the results with related literature. 8 4.3 Benchmark model Table 2 (Panel A) presents the variance decompositions for our benchmark model. We find that when all types of shocks are considered in a sticky price-wage environment, unanticipated IS shocks account for the bulk of the fluctuations. Specifically, IS shocks account for 62% of the unconditional variance in output growth, 92% in investment growth, and 37% in hours. The large role for IS shocks even in the presence of TFP and IS news shocks corroborates the findings of Justiniano et al. (2008), who do not consider news shocks. Preference and unanticipated TFP shocks account for approximately 50% of the fluctuation in consumption growth, followed by unanticipated IS shocks (approximately 18%). Unanticipated TFP shocks account for about 13% of variation in output growth. Monetary shocks account for 10% of the variation in output growth and about 17% in consumption growth. The wage markup shock accounts for around 35% of the unconditional variance in hours worked. Quite surprisingly, when all shocks compete, both TFP news and IS news get an almost negligible role in accounting for fluctuations in macroeconomic variables. This finding is in sharp contrast to those reported in recent literature, in particular, Schmitt-Grohé and Uribe (2008), Fujiwara et al. (2008), and Davis (2007). To help understand what drives the differences, we estimate different versions of the benchmark model and discuss the potential underlying reasons. Two other recent papers Guo (2008a) and Comin et al. (2008), have estimated DSGE models with news shocks. Guo (2008a) estimates a two-sector model but with a limited number of shocks, and finds that news shocks in the investment sector are relatively more important than news shocks in the consumption sector. Comin et al. (2008) propose a model in which there is endogenous technological change and shocks to the growth potential, similar to Beaudry and Portier (2007). Agents expectations are linked to the underlying drivers of the technology frontier, and thus interpret innovations shock to technology as news shocks. Comin et al. (2008) estimate a DSGE version of their model, where investment is split into equipment and structures, and with no wage 8 The variance decompositions for other variables are available upon request. 14

rigidities, they find, for example, that unanticipated TFP is the dominant source of fluctuations in output growth followed by the innovation/news shock. Since the model we considered in this paper is not a multi-sector model and does not have endogenous technological change, we restrict our comparison the findings of Schmitt-Grohé and Uribe (2008), Fujiwara et al. (2008), and Davis (2007). 4.3.1 Near flexible prices and wages with no markup shock Schmitt-Grohé and Uribe (2008) consider a flexible-price real business cycle model with real rigidities (investment adjustment costs, variable capacity utilization, habit formation in consumption, and habit formation in leisure). They allow for permanent and stationary TFP shocks, permanent IS shocks and government spending shocks. The innovations to the shock processes have both unanticipated and anticipated components. The main findings are that TFP news shocks account for the bulk of aggregate fluctuations. In particular, they account for 70% of the share of variance in output growth, 85% for consumption growth, 58% for investment growth, and 68% for hours growth. As shown in Table 2 (Panel A), however, when nominal frictions and price-wage markup shocks are present, the role of TFP news shocks becomes unimportant. Indeed, when we consider an environment with nearly flexible prices and wages, and shut down the price markup shock alone, TFP news shocks become substantially important, consistent with the Schmitt-Grohé and Uribe (2008) finding. 9 Table 2 (Panel B) shows the result for this case. TFP news shocks account for over 40% of the variance in output, consumption, and investment growth. TFP shocks, however, remain almost as important as TFP news shocks. For hours, TPF news shocks account for 39% of the unconditional variance whereas TFP shocks account for about 44% of the variance. In this environment, IS shocks are third most important for accounting for fluctuations in investment growth. As in the benchmark model, IS news shocks remain unimportant. 4.3.2 Excluding preference shock In the benchmark model, if we exclude only the preference shock, then the role for IS news shocks in accounting for fluctuations rises sharply. These shocks account for over 70% of the variation 9 A similar conclusion is reached if we shut down the wage markup shock. 15

in output and investment, 32% in consumption, and 44% in hours. The unanticipated IS is the second most important shock in this environment. Fujiwara et al. (2008), for example, consider the Smets and Wouters (2007) model but without preference and IS news shocks. They find that TFP news accounts for approximately 12% of the fluctuations in output growth. As shown in Table 2 (Panel C), when we exclude the preference shock alone, the role for IS news shocks in accounting for fluctuations in output growth, consumption growth, investment growth, and hours rises sharply. TFP news shocks turn out to be unimportant. Our findings, therefore indicate that the quantitative conclusions about the importance of news shocks can be very sensitive to the inclusion and/or exclusion of other shocks. 4.3.3 Including S&P 500 returns as an observable variable Davis (2007) considers a DSGE model with real and nominal rigidities. He builds on the Beaudry and Portier (2006) finding that stock market data can be useful in identifying news shocks and exploits information in the S&P 500 stock returns and also in the term structure (yields on zero coupon bonds maturing in one to five years) by including them as observables in the model estimation. When both the S&P 500 returns and the yields are included, IS news shocks account for 52% of the unconditional forecast error variance of output growth. We use the same methodology and link the model s real return on capital to the inflation adjusted return on S&P 500 index. 10 To highlight our point, we included on the S&P 500 returns alone as the additional observable relative to the benchmark. 11 Specifically, real return on capital t = r k (1 δ) r k + (1 δ) rk t + r k + (1 δ) q t q t 1 (26) Table 3 reports the parameter estimates of the benchmark model with (26) included. That is, with the addition of the return to capital in the vector of observables. The behavioral parameters are broadly similar to those in Table 1. The main difference arises in the estimated standard deviations of the IS news four and five quarters ahead. When we include stock returns in the estimation, the estimated standard deviations become very large compared to the values reported in Table 1. This point and the fact that the persistence parameter for the IS process, ρ I is estimated 10 The data were obtained from Robert Shiller s website 11 Note that Davis (2007) does not consider S&P 500 returns alone in the estimation. 16

close to one implies that IS news shocks will most likely be important for the unconditional variance of the macroeconomic variables in the presence of the stock return data. Table 2 (Panel D) presents the results for this case. Note that IS news shocks become quantitatively the most important in accounting for the variance of output growth and investment growth. They account for approximately 62% of the unconditional forecast variance of output growth, over 80% for investment growth. For hours, unanticipated IS continues to be the dominant shock although IS news shocks account for over 40% of the variance. Thus we find IS news shocks to be even more important than emphasized in Davis (2007). 12 They account for approximately 27% of the unconditional variance in consumption growth. Unanticipated IS accounts for approximately 15% and the preference shock for around 13% of consumption growth. 4.4 Discussion Why do the results on the importance of news shocks as sources of business cycle differ across the estimated DSGE models? Specifically, relative to the benchmark model in which all shocks compete, why does the assessment of news shocks change when (a) only a limited set of shocks is considered and (b) additional data is included as an observable? To help understand the reason behind our findings, we adopt the distinction between intertemporal and intratemporal shocks as discussed in Primiceri et al. (2006). Intertemporal shocks are disturbances which affect trade-offs across periods in agents optimization problems whereas intratemporal shocks are disturbances with affect trade-offs within a period in agent s optimization problems. We apply this distinction to news shocks. Like unanticipated IS and preference shocks, the IS news shocks are intertemporal shocks as they directly influence the Euler condition of the optimal capital-investment decision in (6). Like unanticipated TFP, price-wage markup shocks, the TFP news shocks are atemporal shocks. As such, not only do all shocks compete with each other but also IS news competes with the other intertemporal shocks, namely the unanticipated IS shock and the preference shock when fitting the data. And TFP news competes with other atemporal shocks such as the price markup and wage 12 Note three differences in details in contrast to Davis (2007). First, we consider Jaimovich and Rebelo (2009) preferences while Davis (2007) considers the KPR preferences with habits. Second, we do not consider news shocks to government spending while he does. Third, we include consumption durables in the measure of investment. Evidently, these differences account for an even greater role for IS news shocks which we find relative to Davis (2007). 17

markup shocks when fitting the data. It turns out that in the benchmark case, the unanticipated IS and preference shocks are the two most important intertemporal shocks. Interestingly, this finding corroborates those in Justiniano et al. (2008) who consider a model similar to the benchmark model here but do not allow for news shocks. In the (near) flexible price-wage environment, and without the atemporal price-markup shock, the major source of fluctuations shifts from intertemporal to atemporal shocks, namely, from unanticipated IS to unanticipated TFP and TFP news shocks. Thus, without (significant) nominal frictions, TFP news starts to play a larger role in fluctuations. This finding is consistent with Schmitt-Grohé and Uribe (2008) who consider a flexible price environment and find that TFP news is the dominant source of macroeconomic fluctuations. Unanticipated IS plays a limited role in accounting for fluctuations in investment growth and hours. Another point which we highlight here is that nominal frictions are necessary for obtaining quantitatively important role for unanticipated IS shocks. This finding is consistent with Primiceri et al. (2006) and Justiniano et al. (2008). In the benchmark model without the preference shock, the reason for the emergence of IS news shocks as the dominant source of fluctuations in the macroeconomic variables is as follows. When the preference shock is excluded, the model looses a degree of freedom in explaining consumption growth. Note from Table 2 (Panel A) that the preference shock explains around a quarter in the variation of consumption growth. The role of the preference shock in this case an intertemporal shock is taken by unanticipated IS and IS news shocks which are also intertemporal shocks. From the smoothed estimates of the shocks in the model we find that unanticipated IS shocks are needed to capture the discrepancy between consumption growth and real interest rate in this case (this discrepancy is explained by preference shocks in the benchmark model). But then this same shock cannot generate comovement between consumption, output, investment, and hours, a salient feature of the data. Thus, to compensate for the lack of comovement due to unanticipated IS shocks, the model now assigns a significant role to IS news, another intertemporal shock. Indeed a formal examination of the smoothed shock estimates (preference shock) from the benchmark model (Panel A) and unanticipated IS and sum of IS news shocks (Panel C) shows that the preference shock is largely projected onto IS and IS news. A simple OLS regression of the preference shock on unanticipated IS and IS news has an R 2 of 0.94. 18

Why does the inclusion of stock market data raises the significance of IS news shocks compared for example with the benchmark model (Table 2, Panel A)? The reason is as follows. Once the model s return on capital is linked to the real S&P 500 return, the large volatility in the stock return requires a large intertemporal shock. In principle this shock could be the unanticipated IS shock. However, unanticipated IS shock implies strong comovement between consumption growth and the return to capital (model implied correlation equal to 0.53) which is not consistent with the data, where this comovement is at best very limited (data correlation equal to 0.28). The large estimated standard deviation of the 4 and 5 quarters ahead IS news and the large share of the variance it implies reflects the model s attempt to minimize this discrepancy by assigning a large role to IS news shocks since the latter imply a negative comovement between these two variables. IS news shocks, therefore, help bring the model s correlation closer with the data. 4.5 Model fit We can compare fit of the benchmark model (in Table 2, Panel A) with the flexible price model (Table 2, Panel B) and the version without the preference shock (Table 2, Panel C) using the log marginal densities, ln(p(y T M i )), i = A, B, C. All three models are estimated with the same data. We find that for the benchmark model ln(p(y T M A )) = -2199.28, for the (near) flexible price-wage model ln(p(y T M B )) = -2595.0, and the version without the preference shock ln(p(y T M C )) = -2253.10. These values imply a very large Bayes factor in favour of the benchmark model. The implication is that, of the three models, the benchmark model fits the data the best. 4.6 Comparison with SVAR-SVECM findings Finally, we note that the findings on the quantitative importance of news shocks based on estimated DSGE models are less robust relative to those from the SVECM methodology in Beaudry and Lucke (2008). Although we cannot directly compare the results, our findings suggest that only in flexible price-wage environments with a limited set of shocks (Table 2, Panel B), do the results corroborate with the SVECM findings. The findings from the benchmark model where unanticipated IS shocks play a large role are consistent with Fisher (2006). 19

5. Conclusion We undertook a quantitative exploration into the role of news shocks in generating macroeconomic fluctuations using estimated DSGE models. Our benchmark model is the Smets and Wouters (2007) augmented to include news shocks to TFP and IS technology, and Jaimovich and Rebelo (2009) preferences. We let news shocks to TFP and IS technology compete with other sources of business cycles which have been extensively considered in the literature. Three sets of results stand out. First, when all shocks compete in a sticky price-wage environment, both TFP news and IS news get an almost negligible role in accounting for fluctuations in macroeconomic variables. Second, results change sharply in a flexible price-wage environment. Here unanticipated TFP and TFP news shocks account for the bulk of fluctuations in output growth, consumption growth, investment growth, and hours. Third, in a sticky price-wage environment, IS news shock is the most important driver of fluctuations in these variables when (a) data on the S&P 500 stock returns in included as an observable in the estimation or (b) another intertemporal shock, namely the preference shock, is absent. When high volatility stock returns are incorporated, IS news shocks become substantially important in fitting the data. Extending the useful distinction between intertemporal and intratemporal shocks in Primiceri et al. (2006) to IS and TFP news shocks, respectively, is helpful in understanding the quantitative results. Our findings help shed light on why might recent work on news shocks in estimated DSGE models has reached sharply different conclusions regarding their quantitative importance. More generally, given the sensitivity to model structure, shocks, and the data used, they suggest that estimated DSGE models may be limited in helping resolve the debate on the sources of business cycles. 20

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