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 Galı́ (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’. This possibility is interesting as it brings to the stage an alternative source
of business cycles.1 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,
yt = cy ct + iy it + zy zt + εgt
(1)
Output, yt , is the sum of consumption, ct , investment, it , capital utilization costs, zy zt , and an
exogenous spending disturbance, εgt . The coefficient cy = 1 − gy − iy is the steady state share
of consumption in output. The coefficients gy and iy 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, σg )
εgt = ρg εgt−1 + ηtg
(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
1−σc
1+σl
b
∞
−1
X εt Ct − χLt Xt
E0
βt
1 − σc
(3)
t=0
where
1−ω
Xt = Ctω Xt−1
is a geometric average of current and past consumption levels, E0 denotes expectation conditional
on the information available at time 0, 0 < β < 1, σl > 0, χ > 0, σc > 0, 0 ≤ ω ≤ 1 and εbt is
the preference shock assumed to follow an AR(1) process with mean zero IID normal error term
ηtb ∼ N (0, σb )
εbt = ρb εbt−1 + ηtb
(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
ct = Et ct+1 + c1 (rt − Et πt+1 ) + c2 Et (lt+1 − lt ) + c3 Et (xt+1 − xt ) + c1 (Et εbt+1 − εbt )
(5)
where the coefficients c1 and c2 depend on the underlying model parameters and the steady state
level of hours worked, and c3 = c2 (1+σl )−1 . The expressions for c1 and c2 are given in the Appendix.
In the equation above, current consumption depends on future expected and past consumption
(through the xt 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
1
i
1−σc
it−1 + βγ
Et it+1 + 2 (qt + εt )
it =
1 + βγ 1−σc
γ ϕ
(6)
where in the above equation, ϕ is second derivative of the investment adjustment cost function,
It
S It−1
, evaluated at the steady state (as in Christiano et al. (2005)). It 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 εit and we specify its process
in Section 2.1.
The dynamics of the value of capital, qt , are described by
qt = −(rt − Et πt+1 ) +
r∗k
(1 − δ)
k
Et rt+1
+ k
Et qt+1
k
(r∗ + (1 − δ))
(r∗ + (1 − δ))
(7)
where rtk denotes the rental rate on capital and δ is the depreciation rate.
The aggregate production function is given by
yt = φp (αkts + (1 − α)lt + εat )
(8)
That is, output is produced using capital (kts ) and labor services (lt ). The parameter φp is one plus
the share of fixed costs in production. The variable εat 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,
kt−1 , and capital utilization, zt , and given as
kts = kt−1 + zt
(9)
where capital utilization is a function of the rental rate of capital,
zt =
1−ψ k
r
ψ 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
(1 − δ)
(1 − δ)
(1 − δ) i
kt =
kt−1 + 1 −
it + 1 −
εt
γ
γ
γ
7
(11)
In the goods market, we can define the price mark-up as,
µpt = mplt − wt = α(kts − lt ) + at − wt
(12)
where mplt is the marginal product of labour, and wt is the real wage.
Inflation dynamics are described by the New-Keynesian Phillips curve
πt = π1 πt−1 + +π2 Et πt+1 − π3 µpt + εpt
(13)
where π1 = ιp /(1+βγ 1−σc ιp ), π2 = βγ 1−σc /(1+βγ 1−σc ιp ), π3 = 1/(1+βγ 1−σc ιp )[(1−βγ 1−σc ξp )(1−
ξp )/ξp ((φp − 1)εp + 1)]. In the notation above 1 − ξp denotes the probability that a given firm will
be able to reset its price and ιp denotes the degree of indexation to past inflation by firms who do
not optimally adjust prices. Finally, εp is a parameter that governs the curvature of the Kimball
goods market aggregator, and (φp − 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
p
εpt = ρp εpt−1 + ηtp − µp ηt−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.
rtk = −(kt − lt ) + wt
(15)
Similar to the goods market, in the labour market the wage markup is given by
µw
= wt − mrst
t
(1+σl ) (ω−1)/ω −1
= wt − (1 − χωL∗
+ (1 −
γ
)
(1+σ )
χωL∗ l γ (ω−1)/ω )−1
(1+σl ) (ω−1)/ω −1
− (1 − χωL∗
γ
)
(1 −
(1+σl ) (ω−1)/ω
(1 − χωL∗
γ
(1+σ )
χωL∗ l γ (ω−1)/ω
(1+σl ) (ω−1)/ω
χωL∗
γ
ct
+
(1+σl ) (ω−1)/ω
σl + χωL∗
γ
(1+σ )
χωL∗ l γ (ω−1)/ω )xt
)lt
(16)
Note that the mrst 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
wt = w1 wt−1 + (1 − w1 )(Et wt+1 + Et πt+1 ) − w2 πt + w3 πt−1 − w4 µw
t + εt
where w1 =
1
1+βγ 1−σc
w2 =
1+βγ 1−σc ιw
,
1+βγ 1−σc
w3 =
ιw
,
1+βγ 1−σc
and w4 =
(1−ξw )(1−βγ 1−σc ξw )
((1+βγ 1−σc )ξw )(1/((φw −1)εw +1))
(17)
The
parameters (1 − ξw ) and ιw denote the probability of resetting wages and the degree of indexation
to past wages, respectively. σl is the elasticity of labor supply with respect to the real wage, and
(φw − 1) denotes the steady state labor market markup. Similar to the goods market formulation
εw denotes the curvature parameter for the Kimball labor market aggregator. The wage mark up
disturbance is assumed to follow an ARMA(1,1) process
w
w
w
εw
t = ρw εt−1 + ηt − µw ηt−1
(18)
where η w is a mean zero IID normal error term.
The monetary authority follows a generalized Taylor rule,
f
rt = ρrt−1 + (1 − ρ)[rπ πt + ry (yt − ytf )] + r∆y [(yt − ytf ) − (yt−1 − yt−1
)] + εrt
(19)
The policy instrument is the nominal interest rate, rt , which is adjusted gradually in response
to inflation and the output gap, (yt − ytf ), defined as the difference between actual and potential
output, ytf , 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
εrt is the monetary policy shock and is assumed to follow an AR(1) process with a mean zero IID
normal error term:
εrt = ρr εrt−1 + ηtr
2.1
(20)
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
εat = ρa εat−1 + ηta
9
(21)
where the innovation, ηta , is split into two components. An anticipated component, ηta,0 , and an
unanticipated component, η a,news , written as
t
ηta = ηta,0 + ηta,news
where ηta,news ≡
PH
h
(22)
a,h
a,h
ηt−h
and ηt−h
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
a,h
2 , for
anticipated by the agents. The innovations to εat , ηt−h
, are IID normal with variance σa,h
h = 0, 1, ..., H. A similar structure applies to the investment-specific shock process
εit = ρi εit−1 + ηti
(23)
where the innovation ηti is split into two components. An anticipated component, ηti,0 , and an
unanticipated component, η i,news , and written as
t
ηti = ηti,0 + ηta,news
where ηta,news ≡
PH
h
(24)
i,h
i,h
is the h-period ahead news about total factor productivity
and ηt−h
ηt−h
i,h
, are IID normal with variance
anticipated by the agents at period t − h. The innovations to εit , ηt−h
2 , for h = 0, 1, ..., H.
σi,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:
xt = Axt−1 + Bεt
10
Yt = Cxt
where A, B and C denotes matrices of reduced form coefficients that are non-linear functions of the
structural parameters. xt denotes the vector of model variables, and Yt 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 Mi ) is contained
in the likelihood function, L(Θ|YT , Mi ), where YT = [Y1 , ..., YT ]0 contains the data. The likelihood
function allows one to update the prior distribution of Θ. Let p(YT |Θ, Mi ) = L(Θ|YT , Mi ) denote
the likelihood function of version Mi of the DSGE model. Then, using Bayes’ theorem, we can
express the posterior distribution of the parameters as
p(Θ|YT , Mi ) =
where the denominator, p(YT |Mi ) =
R
p(YT |Θ, Mi )p(Θ)
p(YT |Mi )
(25)
p(Θ, YT |Mi )dΘ, in (25) is the marginal data density
conditional on model Mi . 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 MetropolisHastings 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, εp , and εw are both set equal to 10 and the
steady state labor market markup, φw , 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 capitalt =
r∗k
(1 − δ)
rtk + k
qt − qt−1
k
r∗ + (1 − δ)
r∗ + (1 − δ)
(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, ρI is estimated
10
11
The data were obtained from Robert Shiller’s website
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 R2 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(YT |Mi )), i = A, B, C. All three models are estimated with the same data.
We find that for the benchmark model ln(p(YT |MA )) = -2199.28, for the (near) flexible price-wage
model ln(p(YT |MB )) = -2595.0, and the version without the preference shock ln(p(YT |MC )) =
-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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24
A. Appendix
We present the household’s problem in the benchmark model of Section 2 under Jaimovich and
Rebelo (2009) preferences.
Household j maximizes the following objective function
E0
∞
X
βt
1−σc
εbt Ct − χLt1+σl Xt
−1
1 − σc
t=0
1−ω
with Xt = Ctω Xt−1
, subject to the budget constraint, and the capital accumulation equation,
Ct (j) + It (j) +
Bt (j)
Bt−1 (j) Wth (j)Lt (j) Rtk Zt (j)Kt−1 (j)
Divt
− Tt ≤
+
+
− a(Zt (j))Kt−1 (j) +
(A.1)
Rt Pt
Pt
Pt
Pt
Pt
Kt (j) = (1 − δ)Kt−1 (j) +
εit
It (j)
1 − S(
) It (j)
It−1 (j)
(A.2)
where Ct is consumption, It is investment, Bt are nominal government bonds, Rt is the gross nominal
interest rate, Tt is lump-sum taxes, Rtk is the rental rate on capital, Zt is the utilization rate of
capital, a(Zt (j)) is a convex function of the utilization rate and Divt the dividends distributed to
It (j)
the households from labour unions. S( It−1
(j) ) is a convex investment adjustment cost function.
In the steady state it is assumed that, S = S 0 = 0 and S 00 > 0. Let λt , υt denote the lagrange
multipliers associated with (A.1) and (A.2) respectively. The FOCs for this problem (dropping the
index j) are given by,
−σc 1+σl ω−1 1−ω
l
λt = Ct − χL1+σ
X
1
−
χωL
εbt
C
X
t
t
t
t
t−1
λt
−σc
Wth = Ct − χLt1+σl Xt
χ(1 + σl )Lσt l Xt εbt
Pt
λt = βRt Et
λt =
υt εit
λt+1
πt+1
(A.4)
It
It
It+1 2
It
0
0 It+1
i
1 − S(
)−S (
)
+ βEt υt+1 εt+1 S (
)(
)
It−1
It−1 It−1
It
It
25
(A.3)
(A.5)
(A.6)
υt = βEt
λt+1
k
Rt+1
Zt+1 − a(Zt+1 )
Pt+1
!
!
+ υt+1 (1 − δ)
(A.7)
Rtk
0
= a (Zt )
Pt
(A.8)
Using (A.3) in (A.5), and log-linearizing around the steady state, we obtain
ct = Et ct+1 + c1 (rt − Et πt+1 ) + c2 Et (lt+1 − lt ) + c3 Et (xt+1 − xt ) + c1 (Et εbt+1 − εbt )
where the expressions for coefficients c1 and c2 in (A.9) are given as
(1+σl ) (ω−1)/ω
1−χωL∗
γ
−1
1+σl (ω−1)/ω −1
1+σl
1+σ
1+σ
−σc (1−χL∗
γ
) +χωL∗
σc γ (ω−1)/ω (1−χL∗ l γ (ω−1)/ω ) +χωL∗ l γ (ω−1)/ω
−1
1+σl
1+σ
1+σ
χL∗
σc (1+σl )γ (ω−1)/ω (1−χL∗ l γ (ω−1)/ω ) −χω(1+σl )L∗ l γ (ω−1)/ω
2
−1
1+σl (ω−1)/ω −1
1+σ
1+σ
1+σ
−σc (1−χL∗
γ
) +χωL∗ l σc γ (ω−1)/ω (1−χL∗ l γ (ω−1)/ω ) +χωL∗ l γ (ω−1)/ω
−1
2(1+σ
)
1+σ
l σ (1+σ )γ 2(ω−1)/ω (1−χL
l γ (ω−1)/ω )
χ2 ωL∗
c
l
∗
1+σ
1+σl (ω−1)/ω −1
1+σl
1+σl (ω−1)/ω −1
(ω−1)/ω
γ
) +χωL∗ l γ (ω−1)/ω
σc γ
(1−χL∗
γ
) +χωL∗
−σc (1−χL∗
c1 =
c =
−
,
and
c3 = c2 (1 + σl )−1 .
26
and
−
(A.9)
Table 1: Prior and Posterior distributions: Smets and
Wouters (2007) model with Jaimovich-Rebelo (2009) preferences and news shocks
Prior distribution
Posterior distribution
Distr.
Mean
Std.dev.
Mean
5%
95%
σc
Normal
1.0
0.37
1.05
0.35
1.66
ω
Beta
0.5
0.20
0.86
0.76
0.97
ξw
Beta
0.66
0.10
0.76
0.70
0.83
σl
Gamma
2.00
0.75
1.38
0.64
2.52
ξp
Beta
0.66
0.10
0.68
0.63
0.75
ιw
Beta
0.50
0.15
0.47
0.25
0.70
ιp
Beta
0.50
0.15
0.20
0.09
0.33
ψ
Beta
0.50
0.15
0.87
0.80
0.94
Φ
Normal
1.25
0.12
1.37
1.24
1.48
rπ
Normal
1.70
0.30
1.83
1.61
2.07
ρ
Beta
0.60
0.20
0.76
0.71
0.81
ry
Normal
0.12
0.05
0.08
0.05
0.11
r∆y
Normal
0.12
0.05
0.30
0.25
0.34
ϕ
Gamma
4.00
1.0
2.29
1.49
3.01
π
Normal
0.5
0.10
0.58
0.50
0.68
L
Normal
396.83
0.5
397.14
396.45
397.93
γ
Normal
0.5
0.03
0.48
0.45
0.51
Gamma
0.25
0.10
0.23
0.10
0.38
ρa
Beta
0.60
0.20
0.97
0.96
0.98
ρb
Beta
0.60
0.20
0.89
0.85
0.96
ρg
Beta
0.60
0.20
0.98
0.97
0.99
ρI
Beta
0.60
0.20
0.57
0.49
0.65
ρr
Beta
0.40
0.20
0.05
0.00
0.09
ρp
Beta
0.60
0.20
0.96
0.94
0.99
ρw
Beta
0.60
0.20
0.98
0.97
0.99
µp
Beta
0.50
0.20
0.82
0.73
0.91
µw
Beta
0.50
0.20
0.94
0.90
0.96
σa
InvGamma
0.5
2.0
0.49
0.43
0.55
σg
InvGamma
0.5
2.0
0.45
0.42
0.48
100(β −1
− 1)
Continued on next page
27
Table 1 – continued from previous page
Prior distribution
Posterior distribution
σb
InvGamma
0.5
2.0
1.25
1.00
1.63
σI
InvGamma
0.5
2.0
6.18
4.49
8.01
σr
InvGamma
0.5
2.0
0.25
0.22
0.27
σp
InvGamma
0.5
2.0
0.14
0.12
0.16
σw
InvGamma
0.5
2.0
0.26
0.23
0.29
News shocks
σa1
InvGamma
0.20
2.0
0.10
0.05
0.14
σa2
InvGamma
0.20
2.0
0.09
0.05
0.13
σa3
InvGamma
0.20
2.0
0.09
0.05
0.12
σa4
InvGamma
0.20
2.0
0.09
0.05
0.13
σa5
InvGamma
0.20
2.0
0.09
0.05
0.13
σa6
InvGamma
0.20
2.0
0.10
0.05
0.14
σI1
InvGamma
0.20
2.0
0.14
0.04
0.24
σI2
InvGamma
0.20
2.0
0.13
0.05
0.20
σI3
InvGamma
0.20
2.0
0.18
0.05
0.23
σI4
InvGamma
0.20
2.0
0.15
0.05
0.27
σI5
InvGamma
0.20
2.0
0.19
0.06
0.23
σI6
InvGamma
0.20
2.0
0.14
0.05
0.19
Notes. Posterior distributions are obtained via the Metropolis-Hastings algorithm using 100,000 draws.
28
Table 2: Contribution of each shock to the unconditional variance of variables ( in %)
Variable
TFP
T F Pnews
IS
ISnews
εb
εg
εr
εp
εw
A. Benchmark model
Output growth
12.95
1.21
62.41
0.14
3.78
5.11
10.25
2.23
1.86
Consumption growth
26.17
1.69
17.78
0.05
23.63
7.35
17.22
0.54
5.51
Investment growth
2.13
0.35
91.94
0.16
1.73
0.01
1.78
1.31
0.56
Hours
3.72
0.87
36.89
0.10
0.68
9.49
4.18
9.42
34.61
B. Near flexible prices and wages with no price markup shock
Output growth
55.47
44.09
0.31
0.00
0.02
0.02
0.00
-
0.07
Consumption growth
56.12
43.75
0.04
0.00
0.00
0.00
0.00
-
0.07
Investment growth
33.63
45.00
19.68
0.03
1.52
0.00
0.00
-
0.09
Hours
44.10
39.00
13.38
0.03
1.30
0.61
0.00
-
1.66
C. Excluding preference shock
Output growth
8.23
0.81
7.69
71.76
-
2.25
5.70
1.62
1.92
Consumption growth
15.31
0.96
33.07
32.62
-
5.76
8.31
0.22
3.72
Investment growth
2.00
0.33
19.41
74.84
-
0.33
1.42
1.08
0.81
Hours
1.43
0.36
18.86
44.73
-
2.39
2.34
9.96
19.88
D. Including S&P 500 returns as an observable
Output growth
7.37
0.57
10.36
62.29
2.33
2.44
4.41
1.24
1.94
Consumption growth
24.52
1.71
14.73
26.88
12.77
2.99
10.61
0.91
4.83
Investment growth
0.44
0.09
12.29
82.73
2.76
0.00
0.60
0.55
0.53
Hours
0.40
0.07
56.28 42.43
0.10 0.10 0.02 0.23 0.33
Notes. T F Pnews and ISnews are six-quarter sum of T F P and IS news shocks, respectively.
εb = preference shock, εg = government spending shock, εr = monetary policy shock,
εp =price mark-up shock, εw =wage mark-up shock. Entries decompose the forecast error
variance in each variable into percentages due to each shock.
29
Table 3: Prior and Posterior distributions: Smets and
Wouters (2007) model with Jaimovich-Rebelo (2009) preferences and news shocks (with stock market data)
Prior distribution
Posterior distribution
Distr.
Mean
Std.dev.
Mean
5%
95%
σc
Normal
1.0
0.37
1.0
0.43
1.66
ω
Beta
0.5
0.20
0.88
0.81
0.98
ξw
Beta
0.66
0.10
0.64
0.55
0.72
σl
Gamma
2.00
0.75
0.70
0.41
1.01
ξp
Beta
0.66
0.10
0.64
0.58
0.69
ιw
Beta
0.50
0.15
0.51
0.29
0.71
ιp
Beta
0.50
0.15
0.24
0.12
0.38
ψ
Beta
0.50
0.15
0.94
0.90
0.98
Φ
Normal
1.25
0.12
1.46
1.36
1.55
rπ
Normal
1.70
0.30
2.29
2.06
2.50
ρ
Beta
0.60
0.20
0.80
0.76
0.83
ry
Normal
0.12
0.05
0.03
0.00
0.05
r∆y
Normal
0.12
0.05
0.32
0.28
0.35
ϕ
Gamma
4.00
1.0
2.70
2.17
3.20
π
Normal
0.5
0.10
0.78
0.70
0.86
L
Normal
396.83
0.5
396.40
395.56
397.21
γ
Normal
0.5
0.03
0.46
0.41
0.51
100(β −1 − 1)
Gamma
0.25
0.10
0.26
0.10
0.40
ρa
Beta
0.60
0.20
0.99
0.98
0.99
ρb
Beta
0.60
0.20
0.97
0.96
0.99
ρg
Beta
0.60
0.20
0.98
0.97
0.99
ρI
Beta
0.60
0.20
0.99
0.99
0.99
ρr
Beta
0.40
0.20
0.05
0.00
0.09
ρp
Beta
0.60
0.20
0.99
0.98
0.99
ρw
Beta
0.60
0.20
0.96
0.94
0.98
µp
Beta
0.50
0.20
0.88
0.82
0.93
µw
Beta
0.50
0.20
0.81
0.74
0.88
σa
InvGamma
0.5
2.0
0.53
0.46
0.61
σg
InvGamma
0.5
2.0
0.44
0.41
0.48
Continued on next page
30
Table 3 – continued from previous page
Prior distribution
Posterior distribution
σb
InvGamma
0.5
2.0
3.01
2.06
4.12
σI
InvGamma
0.5
2.0
7.04
6.45
7.67
σr
InvGamma
0.5
2.0
0.24
0.22
0.27
σp
InvGamma
0.5
2.0
0.15
0.13
0.17
σw
InvGamma
0.5
2.0
0.25
0.22
0.29
σa1
InvGamma
0.20
2.0
0.10
0.05
0.15
σa2
InvGamma
0.20
2.0
0.11
0.05
0.17
σa3
InvGamma
0.20
2.0
0.10
0.05
0.15
σa4
InvGamma
0.20
2.0
0.12
0.06
0.18
σa5
InvGamma
0.20
2.0
0.12
0.05
0.18
σa6
InvGamma
0.20
2.0
0.14
0.06
0.22
σI1
InvGamma
0.20
2.0
0.20
0.05
0.45
σI2
InvGamma
0.20
2.0
0.14
0.04
0.24
σI3
InvGamma
0.20
2.0
0.19
0.05
0.41
σI4
InvGamma
0.20
2.0
4.55
3.42
5.73
σI5
InvGamma
0.20
2.0
4.15
2.90
5.46
σI6
InvGamma
0.20
2.0
0.29
0.05
0.23
News shocks
Notes. Posterior distributions are obtained via the Metropolis-Hastings algorithm using 100,000 draws.
31