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BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM
Division of Monetary Affairs
FOMC SECRETARIAT
Date:
October 25, 2011
To:
Research Directors
From:
Deborah J. Danker
Subject: Supporting Document for DSGE Models Update
The attached document supports the update on the projections of the
DSGE models that was distributed in yesterday’s memo, “DSGE Models
Update.”
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System DSGE Project: Research Directors Drafts
October 24, 2011
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Projections from EDO: Current Outlook
November FOMC Meeting
Hess Chung, Michael T. Kiley, and Jean-Philippe Laforte∗
October 18, 2011
1
The Outlook for 2011 to 2014
The EDO model projects economic growth a touch above trend and low inflation
while the policy rate is pegged to its effective lower bound until the second half of
2013, in line with the latest FOMC statement.
The normalization of the model’s risk premia from their elevated levels immediately following the crisis has thus far been unusually slow and households and firms
now anticipate that this pattern of slow normalization will persist for the near-term as
well. Consequently, the current sizeable gap between actual production and its longterm trend closely only modestly over the projection. Inflation remains low as wage
pressures are weak relative to labor productivity, reflecting the declines in household
wealth over the past several years, low level of hours worked anticipated over the next
few years, and the rapid increases in productivity seen in 2009.
This model forecast takes as data market expectations as of 2011:Q3 that the policy rate will remain at its effective lower bound until 2013Q3, followed by a gradual rise
thereafter. Conditional on these expectations and its usual observables, EDO projects
that real GDP will advance at a pace modestly above trend going forward– about 2
1/2 percent, on average, over 2012-2014, as shown in figure 1. The above-trend pace
∗
Hess Chung (hess.t.chung@frb.gov), Michael T. Kiley (michael.t.kiley@frb.gov), and JeanPhilippe Laforte (jean-philippe.laforte@frb.gov) are affiliated with the Division of Research and
Statistics of the Federal Reserve Board.
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of growth is accompanied by inflation around 1.5 percent per year, noticeably below
the target of 2 percent, as a consequence of labor market slack.1
Figure 1: Recent History and Forecasts
EDO Projection Summary
Real GDP
Core PCE price index
Percent change, a.r.
6
4
6
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
2009
2010
2011
2012
2013
2014
Percent change, a.r.
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
-2.0
-2.0
-2.5
2009
2010
2011
2012
2013
2014
-2.5
Federal Funds Rate
Percent
5
5
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-4
-4
2009
2010
2011
2012
2013
2014
2011
Q4/Q4
Real GDP (a)
Credible set (c)
Federal Funds Rate (b)
Credible set (c)
2013
Q4/Q4
2014
Q4/Q4
1.9
2.7
2.8
2.7
.1-3.4
-.1-3.9
.9-4.5
1.3-4.8
Core PCE Price index (a) 1.9
Credible set (c)
2012
Q4/Q4
1.5
1.5
1.5
1.7-2.1
.8-2.1
.7-2.1
.7-2.1
0.1
0.1
0.5
1.8
.0-.7
.0-1.9
.0-2.3
.6-3.6
(a) Q4/Q4 percent change, (b) Q4 level, (c) 68 percent
Black, solid line -- Data (through 2010Q4) and projections; Black, dashed line -- Steady-state or trend values
Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Green -- Other
The decomposition of the projections for these variables shown in figure 1 highlights the important role that the adverse shocks to financial conditions in 2008 and
early 2009 play in shaping the recession in that period and the projected recovery,
1
The EDO model has been shown to forecast as well as, or better than, alternatives in a number of
papers (e.g., Edge, Kiley, and Laforte (2010) and Wieland and Wolters (2010); however, forecasting
is very challenging, and models generally perform similar to, but not better than, simple time series
alternatives, or consensus forecasts.
2
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especially in the later years. Specifically, the figures decompose the movements in real
GDP, the federal funds rate, and core inflation into the contributions from financial
(risk premium) shocks, monetary policy shocks, productivity movements, and other
disturbances (largely markup, or Phillips-curve, shocks); the first two are traditional
“demand” shocks, and the latter two are traditional “supply” shocks.2 As shown
in the federal funds rate chart, the need to accommodate the adverse impact of the
strain in the financial conditions (the red bars) is the most largest factor holding
the federal funds rate at its affective lower bound throughout most of the projection.
The recovery in real GDP projected for 2012-14 is essentially entirely the result of
the projected gradual step-up in demand that should accompany lower risk premia,
again illustrated by the contribution of the red bars in the GDP chart. The easing
provided by forward guidance boosts real GDP growth in the early quarters of the
projection.
As mentioned previously, the forecast conditions on (rational) private-sector expectations of a policy rate path consistent with the latest statement of the FOMC.
This anticipated path is rationalized by augmenting the model’s usual exogenous
shock processes to include eight quarters of anticipated shocks to both the monetary
policy reaction function and the household’s Euler equation for nominal risk-free assets. Interestingly, these additional observables do little to change the EDO forecasts
for output and inflation estimated from the model’s usual information set, since the
two classes of anticipated shocks are estimated to have largely offsetting effects on
most variables other than the federal funds rate. On the one hand, the model explains the expected policy rate path as a response to continued strains from financial
conditions going forward. Indeed, the economy-wide risk premium remains at its
current level for the first two years of the projection instead of gradually falling as
its pre-crisis dynamics would have implied. On the other hand, however, even given
this additional weakness in the forecast, the stance of monetary policy appears very
accommodative, essentially offsetting the impact of higher risk-premia.
2
The contributions of the demand shocks now incorporate the effects of their anticipated counterparts.
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2
The Dynamics of the Model to Anticipated Shocks
This section explores the response of key economic aggregates to the aforementioned
anticipated monetary policy and economy-wide risk premium shocks to better understand their contribution to the projection. Figure 2 displays the dynamics of real
GDP growth in response to the anticipated shocks for eight different horizons. As expected, the anticipation of future contractionary policy shock or higher risk premium
depress real activity. The later positive contributions to real GDP growth results from
output eventually returning to the steady-state from its lower levels. We note the
broad symmetry of the responses across the two types of shock. This symmetry reflects the fact that both shocks essentially affect the economy through the willingness
of households to hold the risk-free nominal asset. As far as this arbitrage condition is
concerned, however, a one-off anticipated increase in the level of the federal funds rate
can be perfectly offset by corresponding one-off anticipated decrease in the premium
on holding that asset.
Figure 2: Impulse Responses – Real GDP Growth
1
1
Monetary Policy
0.5
0.5
0
−0.5
0
−1
−0.5
−1.5
−1
−2
−2.5
0
5
10
15
20
−1.5
0.5
0
5
10
15
20
0.6
0.4
Risk Premium
0
0.2
0
−0.5
−0.2
+1
+2
+3
+4
−1
−1.5
0
5
10
15
+5
+6
+7
+8
−0.4
−0.6
20
−0.8
0
5
10
15
20
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Figure 3: Impulse Responses – Core PCE Inflation
0
0
−0.05
Monetary Policy
−0.05
−0.1
−0.1
−0.15
−0.2
−0.15
−0.25
−0.2
Risk Premium
−0.25
−0.3
0
5
10
15
20
−0.35
0
−0.02
−0.02
−0.04
−0.04
0
5
10
15
20
−0.06
−0.06
−0.1
−0.12
−0.08
+1
+2
+3
+4
−0.08
0
5
10
15
+5
+6
+7
+8
−0.1
20
−0.12
0
5
10
15
20
An anticipated positive shock to the monetary policy rule gives private agents
an incentive to tilt their portfolios in favor of the nominal risk-free asset. Because
that asset is in fixed nominal supply, inflation falls in advance of the realization of the
shock, as shown in figure 3. Production falls, due to the presence of nominal rigidities.
As seen in figure 4, the fed funds rate actually declines as well in anticipation of the
future realization of a positive (hence contractionary) monetary policy shock as the
interest rate endogeneously adjusts to the declines in output and prices. It is only
upon or after (for the most distant horizons) its realization that the interest rate
becomes positive – albeit not by as much as the size of the shock. This dynamic
explains the positive contributions observed (see the gray bars in the lower left panel
of figure 1) early on in the projection from (anticipated) monetary policy shocks to
the fed funds rate. They correspond to the anticipated movements in the fed funds
rate that lead the realization of the furthest negative shocks used to impose the ZLB
in anticipation until 2013Q2.
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Figure 4: Impulse Responses – Fed Funds Rate
Monetary Policy
1
0.5
0
0
+5
+6
+7
+8
−0.5
−0.5
−1
Risk Premium
0.5
0
5
10
15
−1
20
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.5
3
0
5
10
15
5
10
15
20
0
5
10
15
20
−0.3
+1
+2
+3
+4
−0.4
0
−0.4
20
−0.5
An Overview of Key Model Features
Figure 5 provides a graphical overview of the model. While similar to most related
models, EDO has a more detailed description of production and expenditure than
most other models.3
Specifically, the model possesses two final good sectors in order to capture key
long-run growth facts and to differentiate between the cyclical properties of different
categories of durable expenditure (e.g., housing, consumer durables, and nonresidential investment). For example, technological progress has been faster in the production
of business capital and consumer durables (such as computers and electronics).
The disaggregation of production (aggregate supply) leads naturally to some disaggregation of expenditures (aggregate demand). We move beyond the typical model
with just two categories of (private domestic) demand (consumption and investment)
and distinguish between four categories of private demand: consumer non-durable
goods and non-housing services, consumer durable goods, residential investment, and
3
Chung, Kiley, and Laforte (2011) provide much more detail regarding the model specification,
estimated parameters, and model propeties.
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Figure 5: Model Overview
non-residential investment. The boxes surrounding the producers in the figure illustrate how we structure the sources of each demand category. Consumer non-durable
goods and services are sold directly to households; consumer durable goods, residential capital goods, and non-residential capital goods are intermediated through
capital-goods intermediaries (owned by the households), who then rent these capital stocks to households. Consumer non-durable goods and services and residential
capital goods are purchased (by households and residential capital goods owners,
respectively) from the first of economy’s two final goods producing sectors, while consumer durable goods and non-residential capital goods are purchased (by consumer
durable and residential capital goods owners, respectively) from the second sector.
In addition to consuming the non-durable goods and services that they purchase,
households supply labor to the intermediate goods-producing firms in both sectors of
the economy.
This remainder of this section provides an overview of the key properties of the
model. In particular, the model has five key features:
• Production of goods and services occurs in two sectors, with differential rates
of technological progress across sectors.
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• A disaggregated specification of household preferences and firm production processes that leads to separate modeling of nondurables and services consumption,
durables consumption, residential investment, and business investment.
• Risk premia associated with different investment decisions play a central role
in the model. These include A) an aggregate risk-premium, or natural rate of
interest, shock driving a wedge between the short-term policy rate and the interest rate facing private decisionmakers (as in Smets and Wouters (2007)) and
B) fluctuations in the discount factor/risk premia facing the intermediaries financing household (residential and consumer durable) and business investment.
• A new-Keynesian structure for price and wage dynamics.
• A monetary policy that reacts to inflation and a measure of resource utilization.
3.1
Two-sector production structure
It is well known (e.g., Edge, Kiley, and Laforte (2010)) that real outlays for business
investment and consumer durables have substantially outpaced those on other goods
and services, while the prices of these goods (relative to others) has fallen. For example, real outlays on consumer durables have far outpaced those on other consumption,
while prices for consumer durables have been flat and those for other consumption
have risen substantially; as a result, the ratio of nominal outlays in the two categories
has been much more stable, although consumer durable outlays plummeted in the
Great Recession. Many models fail to account for this fact.
EDO accounts for this development by assuming that business investment and
consumer durables are produced in one sector and other goods and services in another
sector. Specifically, production by firm j in each sector s (where s equals kb for the
sector producing business investment and consumer durables sector and cbi for the
sector producing other goods and services) is governed by a Cobb-Douglas production
function with sector-specific technologies:
α
Xts (j) = (Ztm Zts Lst (j))1−α (Ktu,nr,s (j)) , for s = cbi, kb.
(1)
In 1, Z m represents (labor-augmenting) aggregate technology, while Z s represents
(labor-augmenting) sector-specific technology; we assume that sector-specific techno8
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logical change affects the business investment and consumer durables sector only; Ls is
labor input and K u,nr,s is capital input (that is, utilized non-residential business capital (and hence the nr and u terms in the superscript). Growth in this sector-specific
technology accounts for the long-run trends, while high-frequency fluctuations allow
the possibility that investment-specific technological change is an important source
of business cycle fluctuations.
3.2
The structure of demand
EDO differentiates between several categories of expenditure. Specifically, business investment spending determines non-residential capital used in production, and households value consumer nondurables goods and services, consumer durable goods, and
residential capital (e.g., housing). Differentiation across these categories is important,
as fluctuations in these categories of expenditure can differ notably, with the cycles
in housing and business investment, for example, occurring at different points over
the last three decades.
Valuations of these goods and services, in terms of household utility, is given by
the following utility function:
∞
cnn
(i))+ς cd ln(Ktcd (i))
E0 β t ς cnn ln(Etcnn (i)−hEt−1
t=0
+ς
r
ln(Ktr (i))
−ς
cbi
kb
1+ν
l (Lt (i)+Lt (i))
1+ν
,
(2)
where E cnn represents expenditures on consumption of nondurable goods and services, K cd and K r represent the stocks of consumer durables and residential capital
(housing), Lcbi + Lkb represents the sum of labor supplied to each productive sector
(with hours worked causing disutility), and the remaining terms represent parameters (such as the discount factor, relative value in utility of each service flow, and the
elasticity of labor supply).
By modeling preferences over these disaggregated categories of expenditure, EDO
attempts to account for the disparate forces driving consumption of nondurables and
durables, residential investment, and business investment – thereby speaking to issues
such as the surge in business investment in the second half of the 1990s or the housing
cycle the early 2000s recession and the most recent downturn. Many other models do
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not distinguish between developments across these categories of spending.
3.3
Risk premia, financial shocks, and economic fluctuations
The structure of the EDO model implies that households value durable stocks according to their expected returns, including any expected service flows, and according to
their risk characteristics, with a premium on assets which have high expected returns in adverse states of the world. However, the behaviour of models such as EDO
is conventionally characterized under the assumption that this second component
is negligible. In the absence of risk adjustment, the model would then imply that
households adjust their portfolios until expected returns on all assets are equal.
Empirically, however, this risk adjustment may not be negligible and, moreover,
there may be a variety of factors, not explicitly modelled in EDO, which limit the
ability of households to arbitrage away expected return differentials across different
assets. To account for this possibility, EDO features several exogenous shocks to the
rates of return required by the household to hold the assets in question. Following
such a shock – an increase in the premium on a given asset, for example– households
will wish to alter their portfolio composition to favor the affected asset, leading to
changes in the prices of all assets and, ultimately, to changes in the expected path of
production underlying these claims.
The “sector-specific” risk shocks affect the composition of spending more than the
path of GDP itself. This occurs because a shock to these premia leads to sizable substitution across residential, consumer durable, and business investment; for example,
an increase in the risk premia on business investment leads households to shift away
from business investment and towards residential investment and consumer durables.
Consequently, it is intuitive that a large fraction of the non-cyclical, or idiosyncratic,
component of investment flows to physical stocks will be accounted for by movements
in the associated premia.
Shocks to the required rate of return on the nominal risk-free asset play an especially large role in EDO. Following an increase in the premium, in the absence of
nominal rigidities, the households’ desire for higher real holdings of the risk-free asset
would be satisfied entirely by a fall in prices, i.e., the premium is a shock to the
natural rate of interest. Given nominal rigidities, however, the desire for higher riskfree savings must be off-set, in part, through a fall in real income, a decline which
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is distributed across all spending components. Because this response is capable of
generating comovement across spending categories, the model naturally exploits such
shocks to explain the business cycle. Reflecting this role, we denote this shock as the
“aggregate risk-premium”.
3.4
New-Keynesian Price and Wage Phillips Curves
As in most of the related literature, nominal prices and wages are both “sticky” in
EDO. This friction implies that nominal disturbances – that is, changes in monetary
policy – have effects on real economic activity. In addition, the presence of both
price and wage rigidities implies that stabilization of inflation is not, in general, the
best possible policy objective (although a primary role for price stability in policy
objectives remains).
Given the widespread use of the New-Keynesian Phillips curve, it is perhaps easiest
to consider the form of the price and wage Phillips curves in EDO at the estimated
parameters. The price Phillips curve (governing price adjustment in both productive
sectors) has the form:
p,s
p,s
+ 0.76Et πt+1
+ .017mcst + θts
πtp,s = 0.22πt−1
(3)
where mc is marginal cost and θ is a markup shock. As the parameters indicate,
inflation is primarily forward-looking in EDO.
The wage (w) Phillips curve for each sector has the form:
s
s
s
w
+ 0.95Et wt+1
+ .012 mrsc,l
−
w
wts = 0.01wt−1
t
t + θt + adj. costs.
(4)
where mrs represents the marginal rate of substitution between consumption and
leisure. Wages are primarily forward looking and relatively insensitive to the gap
between households’ valuation of time spent working and the wage.
3.5
The Monetary Policy Rule
The estimated monetary policy rule has standard features – the policy interest rate
responds inertially to inflation and a deviation of output from a trend level:
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rt = 0.76rt−1 + (1 − 0.76) 1.50PtP CE + 1.20 (yt − trend) + δtRshock .
Rshock
+
δtRshock = ρRshock δt−1
R
t
(5)
(6)
The long-run responses to the output gap and inflation are very similar to those
in the literature. The measure of trend output is based on a production-function
concept – that is, trend output is the level of output consistent with labor input
and the utilization of capital at long-run levels, given the current level of productive
capital; this output concept is a Divisia aggregate of production in the two sectors
discussed earlier.
3.6
Summary of Model Specification
To summarize, fluctuations in all economic variables are driven by eleven structural
shocks. It is most convenient to summarize these shocks into four broad categories:
• Permanent technology shocks: This category consists of shocks to aggregate
and investment-specific (or fast-growing sector) technology.
• Financial, or intertemporal, shocks: This category consists of shocks to risk
premia. In EDO, variation in risk premia – both the premium households’
receive relative to the federal funds rate on nominal bond holdings and the
additional variation in discount rates applied to the investment decisions of
capital intermediaries – are purely exogenous. Nonetheless, the specification
captures aspects of related models with more explicit financial sectors (e.g.,
Bernanke, Gertler, and Gilchrist (1999)).
• Monetary policy shocks.
• Other shocks: This category is dominated by shocks to price and wage markups,
or Phillips curve shock; it als includes the shock to autonomous demand, which
is quantitatively not important in EDO.
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4
Estimation: Data and Properties
4.1
Data
The empirical implementation of the model takes a log-linear approximation to the
first-order conditions and constraints that describe the economy’s equilibrium, casts
this resulting system in its state-space representation for the set of (in our case 12)
observable variables, uses the Kalman filter to evaluate the likelihood of the observed
variables, and forms the posterior distribution of the parameters of interest by combining the likelihood function with a joint density characterizing some prior beliefs.
Since we do not have a closed-form solution of the posterior, we rely on Markov-Chain
Monte Carlo (MCMC) methods.
Because of the detailed modeling of demand, EDO can consider more data on
expenditure than other related models to inform its parameter estimates and projections. The model is estimated using 12 data series over the sample period from
1984:Q4 to 2011:Q1. The series are:
1. The growth rate of real gross domestic product (ΔGDP );
2. The growth rate of real consumption expenditure on non-durables and services
(ΔC);
3. The growth rate of real consumption expenditure on durables (ΔCD);
4. The growth rate of real residential investment expenditure (ΔRes);
5. The growth rate of real business investment expenditure (ΔI);
6. Consumer price inflation, as measured by the growth rate of the Personal Consumption Expenditure (PCE) price index (ΔPC,total );
7. Consumer price inflation, as measured by the growth rate of the PCE price
index excluding food and energy prices (ΔPC,core );
8. Inflation for consumer durable goods, as measured by the growth rate of the
PCE price index for durable goods (ΔPcd );
9. Hours, which equals hours of all persons in the non-farm business sector from
the Bureau of Labor Statistics (H);4
4
We remove a low-frequency trend from hours via the Hodrick-Prescott filter with a smoothing
parameter of 128000; our model is not designed to capture low frequency trends in population growth
or labor force participation.
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10. The growth rate of real wages, as given by compensation per hour in the nonfarm business sector from the Bureau of Labor Statistics divided by the GDP
price index (ΔRW );
11. The federal funds rate (R).
12. The yield on the 2-yr. U.S. Treasury security (RL).
Our implementation adds measurement error processes to the likelihood implied
by the model for all of the observed series used in estimation except the short-term
nominal interest rate series.
Figure 6 presents the observed data (in blue) and the observable data net of
the model’s estimated measurement error (in black), along 95 percent confidence
intervals. For series other than overall PCE price inflation, measurement error is a
moderate portion of movements in the series. The larger role for measurement error
in accounting for the path of PCE price inflation reflects the absence of separate
sectors for food and energy in the model.
4.2
Estimates of shocks and exogenous fundamentals
Figures 7 and 8 report modal estimates of the model’s structural shocks and the persistent exogenous fundamentals (i.e., risk premia and autonomous demand). These
series have recognizable patterns for those familiar with U.S. economic fluctuations.
For example, the risk premia jump at the end of the sample, reflecting the financial crisis and the model’s identification of risk premia, both economy-wide and for
housing, as key drivers.
Of course, these stories from a glance at the exogenous drivers yield applications
for alternative versions of the EDO model and future model enhancements. For example, the exogenous risk premia can easily be made to have an endogenous component
following the approach of Bernanke, Gertler, and Gilchrist (1999) (and indeed we
have considered models of that type). At this point we view incorporation of such
mechanisms in our baseline approach as premature, pending ongoing research on financial frictions, banking, and intermediation in dynamic general equilibrium models.
Nonetheless, the EDO model captured the key financial disturbances during the last
several years in its current specification, and examining the endogenous factors that
explain these developments will be a topic of further study.
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−1
−2
0
−5
−1
2010
1990
−5
1990
2000
−5
−10
1990
2000
Two−Year Treasury
1
0.5
0
−0.5
−1
1990
2000
2010
2000
2010
1990
2000
2010
1990
2000
2010
1
0
−1
2010
0
−1
2010
1990
2
1
0
−10
2010
0
5
4.3
2000
0
5
PCE Inflation
Aggregate Hours
2000
−0.5
2010
5
1990
Investment Inflation
2000
0
Core Inflation
Real Durables
1990
10
0.5
Real Wage
0
Real Housing Expenditures
Real GDP
1
Real Investment
Real Non−Durables
Figure 6: Smoothed Observables and Data
1990
2000
2010
1990
2000
2010
0.8
0.6
0.4
0.2
0
−0.2
−0.4
1
0
−1
Variance Decompositions and impulse responses
We provide detailed variance decompositions and impulse response in Chung, Kiley,
and Laforte (2011), and only highlight the key results here.
Volatility in hours per capita is accounted for primarily by the economy-wide
risk premium and business investment risk premium shocks at horizons between one
and sixteen quarters. The large role for risk premia shocks in the forecast error
decomposition at business cycle horizons illustrates the importance of this type of
“demand” shock for volatility in the labor market. This result is notable, as hours
per capita is the series most like a “gap” variable in the model – that is, house per
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2010
1990
Overall TFP
2
1
0
−1
−2
1990
2000
1
0
−1
−2
2000
2010
2000
0
−1
1990
2000
2010
2
1
0
−1
1990
2000
0
−0.2
2010
1
2010
2
1990
2010
1990
2000
2010
1990
2000
2010
1990
2000
2010
1990
2000
2010
1
0
−1
−2
20
0
−20
−40
0.2
Risk−premium
Capital Risk−Premium
2000
−10
1
0
−1
1990
2000
2010
1
Term Premium
Invest. Price Markup
Capital Goods Technology
1990
Funds Rate Shock
−1
0
0.2
Non−Invest. Price Markup
0
10
Durables Risk−Premium
Wage Markup
20
1
Housing Risk−Premium
Exog. Demand
Figure 7: Innovations to Exogenous Processes
0.5
0
−0.5
−1
1990
2000
2010
0.1
0
−0.1
−0.2
capita shows persistent cyclical fluctuations about its trend value.
Volatility in aggregate GDP growth is accounted for primarily by the technology shocks in each sector, although the economy-wide risk premium shock contributes
non-negligibly to the unconditional variance of GDP growth.
Volatility in core inflation is accounted for primarily by the markup shocks in
the short run and technology shocks in the long run.
Volatility in the federal funds rate is accounted for primarily by the economywide risk premium.
Volatility in expenditures on consumer non-durables and non-housing
services is, in the near horizon, accounted for predominantly by economy-wide and
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1
0
−1
2000
2005
2010
0
−1
1990
1995
2000
2005
2010
2
0
−2
1990
1995
2000
2005
2010
2
0
−2
1985
1990
1995
2000
2005
0
−2
2010
1990
1995
2000
2005
2010
1990
1995
2000
2005
2010
1990
1995
2000
2005
2010
1990
1995
2000
2005
2010
2
1
0
−1
−2
1985
4
−4
1985
2
1985
Capital−specific Tech.
1995
1
1985
Housing Risk−Premium
1990
Durables Risk−Premium
TFP Tech.
−2
1985
Capital Risk−Premium
Exog. Demand
2
2−y Term premium
Risk−premium
Figure 8: Exogenous Drivers
20
0
−20
−40
1985
1
0.5
0
1985
non-residential investment specific risk-premia shocks.
Volatilities in expenditures on consumer durables, residential investment, and non-residential investment are, in the near horizon, accounted for
predominantly by their own sector specific risk-premium shocks.
With regard to impulse responses, we previously highlight the responses to the
most important shock, the aggregate risk premium, in figure ??. As we noted, this
shock looks like a traditional demand shock, with an increase in the risk premium
lowering real GDP, hours worked, and inflation; monetary policy offsets these negative effects somewhat by becoming more accommodative. As for responses to other
disturbances, the impulse responses to a monetary policy innovation captures the con17
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ventional wisdom regarding the effects of such shocks. In particular, both household
and business expenditures on durables (consumer durables, residential investment,
and nonresidential investment) respond strongly (and with a hump-shape) to a contractionary policy shock, with more muted responses by nondurables and services
consumption; each measure of inflation responds gradually, albeit more quickly than
in some analyses based on vector autoregressions (VARs).5
Shocks to sectoral risk premia principally depress spending in the associated category of expenditure (e.g., an increase in the residential risk premium lowers residential
investment), with offsetting positive effects on other spending (which is “crowded in”).
Following an economy-wide technology shock, output rises gradually to its longrun level; hours respond relatively little to the shock (in comparison to, for example,
output), reflecting both the influence of stick prices and wages and the offsetting
income and substitution effects of such a shock on households willingness to supply
labor.
References
Bernanke, B., M. Gertler, and S. Gilchrist. 1999. The financial accelerator in a quantitative business cycle framework, In: John B. Taylor and Michael Woodford, Editor(s), Handbook of Macroeconomics, Elsevier, 1999, Volume 1, Part 3, Pages
1341-1393.
Boivin, J., M. Kiley, and F.S. Mishkin. 2010. How Has the Monetary Transmission
Mechanism Evolved Over Time? In B. Friedman and M. Woodford, eds., The
Handbook of Monetary Economics, Elsevier.
Edge, R., Kiley, M., Laforte, J.P., 2010. A comparison of forecast performance between Federal Reserve staff forecasts, simple reduced-form models, and a DSGE
model. Journal of Applied Econometrics.
Chung H., Kiley, M., Laforte, J.P., 2011. Using the Great Recession to Understand
the EDO Model of the U.S. Economy: Documentation of the 2011 Model Version.
Forthcoming in Federal Reserve Board Finance and Economics Discussion Paper
Series.
5
This difference between VAR-based and DSGE-model based impulse responses has been highlighted elsewhere – for example, in the survey of Boivin, Kiley, and Mishkin (2010).
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Hall, Robert E., 2010. Why Does the Economy Fall to Pieces after a Financial Crisis?
Journal of Economic Perspectives 24 4 3-20
http://www.aeaweb.org/articles.php?doi=10.1257/jep.24.4.3
Smets, F., Wouters, R., 2007. Shocks and Frictions in the US Busines Cycles: A
Bayesian DSGE Approach. American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
Wieland, Volker and Wolters, Maik H, 2010. ”The Diversity of Forecasts from Macroeconomic Models of the U.S. Economy,” CEPR Discussion Papers 7870, C.E.P.R.
Discussion Papers.
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FRBNY DSGE Model: Research Directors Draft
October 19, 2011
Overview
The FRBNY DSGE model forecast is obtained using data released through 2011Q2 augmented, for 2011Q3, with observations on the federal funds rate and the Baa corporate bond
spread, as well as the NY Fed staff forecast for real GDP growth, Core PCE inflation and
hours. The projections are conditional on the federal funds rate being 25bp through 2013Q2,
in line with the current FOMC statement.
The model projects weak growth in economic activity, as it did in June. Real growth
is 1.8% in 2011 (Q4/Q4), picks up in 2012 (Q4/Q4) to 2.6%, and returns to slightly below
2% in 2013-2014. Core inflation is 1.8% in 2011 (Q4/Q4), notably higher than in the June
projections, due to recent strong readings. In spite of this, inflation forecasts from 2012
onwards are actually lower than in June, due to the projected weakness in economic activity.
There is significant uncertainty around the real GDP forecasts, with a non negligible risk of
recession.
The main drivers of the subdued real GDP and inflation outlook are the same forces
behind the Great Recession, namely the two shocks associated with frictions in the financial
system: spread and MEI (marginal efficiency of investment) shocks, whose impact is longlasting.
General Features of the Model
The FRBNY DSGE model is a medium-scale, one-sector, dynamic stochastic general equilibrium model. It builds on the neoclassical growth model by adding nominal wage and price
rigidities, variable capital utilization, costs of adjusting investment, and habit formation in
consumption. The model follows the work of Christiano, Eichenbaum, and Evans (2005) and
Smets and Wouters (2007), but also includes credit frictions, as in the financial accelerator
model developed by Bernanke, Gertler, and Gilchrist (1999). The actual implementation of
the credit frictions closely follows Christiano, Motto, and Rostagno (2009).
In this section, we briefly describe the microfoundations of the model, including the optimization problem of the economic agents and the nature of the exogenous processes. The
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innovations to these processes, which we refer to as “shocks,” are the drivers of macroeconomic fluctuations. The model identifies these shocks by matching the model dynamics with
six quarterly data series: real GDP growth, core PCE inflation, the labor share, aggregate
hours worked, the effective federal funds rate (FFR), and the spread between Baa corporate bonds and 10-year Treasury yields. Model parameters are estimated from 1984Q1 to
the present using Bayesian methods. Details on the structure of the model, data sources,
and results of the estimation procedure can be found in the accompanying “FRBNY DSGE
Model Documentation” note.
The economic units in the model are households, firms, banks, entrepreneurs, and the
government. (Figure 1 describes the interactions among the various agents, the frictions and
the shocks that affect the dynamics of this economy.)
Households supply labor services to firms. The utility they derive from leisure is subject
to a random disturbance, which we call “labor supply” shocks (this shock is sometimes also
referred to as a “leisure” shock). Labor supply shocks capture exogenous movements in labor supply due to such factors as demographics and labor market imperfections. The labor
market is also subject to frictions because of nominal wage rigidities. These frictions play an
important role in the extent to which various shocks affect hours worked. Households also
have to choose the amount to consume and save. Their savings take the form of deposits
to banks and purchases of government bills. Household preferences take into account habit
persistence, a characteristic that affects their consumption smoothing decisions.
Monopolistically competitive firms produce intermediate goods, which a competitive firm
aggregates into the single final good that is used for both consumption and investment.
The production function of intermediate producers is subject to “total factor productivity”
(TFP) shocks. Intermediate goods markets are subject to price rigidities. Together with
wage rigidities, this friction is quite important in allowing demand shocks to be a source of
business cycle fluctuations, as countercyclical mark-ups induce firms to produce less when
demand is low. Inflation evolves in the model according to a standard, forward-looking New
Keynesian Phillips curve, which determines inflation as a function of marginal costs, expected future inflation, and “mark-up” shocks. Mark-up shocks capture exogenous changes
in the degree of competitiveness in the intermediate goods market. In practice, these shocks
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capture unmodeled inflation pressures, such as those arising from fluctuations in commodity
prices.
Financial intermediation involves two actors, banks and entrepreneurs, whose interaction
captures imperfections in financial markets. These actors should not be interpreted in a
literal sense, but rather as a device for modeling credit frictions. Banks take deposits from
households and lend them to entrepreneurs. Entrepreneurs use their own wealth and the
loans from banks to acquire capital. They then choose the utilization level of capital and
rent the capital to intermediate good producers. Entrepreneurs are subject to idiosyncratic
disturbances in their ability to manage the capital. Consequently, entrepreneurs’ revenue
may not be enough to repay their loans, in which case they default. Banks protect against
default risk by pooling loans to all entrepreneurs and charging a spread over the deposit rate.
Such spreads vary endogenously as a function of the entrepreneurs’ leverage, but also exogenously depending on the entrepreneurs’ riskiness. Specifically, mean-preserving changes
in the volatility of entrepreneurs’ idiosyncratic shocks lead to variations in the spread (to
compensate banks for changes in expected losses from individual defaults). We refer to these
exogenous movements as “spread” shocks. Spread shocks capture financial intermediation
disturbances that affect entrepreneurs’ borrowing costs. Faced with higher borrowing costs,
entrepreneurs reduce their demand for capital, and investment drops. With lower aggregate
demand, there is a contraction in hours worked and real wages. Wage rigidities imply that
hours worked fall even more (because nominal wages do not fall enough). Price rigidities
mitigate price contraction, further depressing aggregate demand.
Capital producers transform general output into capital goods, which they sell to the entrepreneurs. Their production function is subject to investment adjustment costs: producing
capital goods is more costly in periods of rapid investment growth. It is also subject to exogenous changes in the “marginal efficiency of investment” (MEI). These MEI shocks capture
exogenous movements in the productivity of new investments in generating new capital. A
positive MEI shock implies that fewer resources are needed to build new capital, leading to
higher real activity and inflation, with an effect that persists over time. Such MEI shocks
reflect both changes in the relative price of investment versus that of consumption goods
(although the literature has shown the effect of these relative price changes to be small), and
most importantly financial market imperfections that are not reflected in movements of the
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spread.
Finally, the government sector comprises a monetary authority that sets short-term interest rates according to a Taylor-type rule and a fiscal authority that sets public spending and
collects lump-sum taxes to balance the budget. Exogenous changes in government spending
are called “government” shocks (more generally, these shocks capture exogenous movements
in aggregate demand). All exogenous processes are assumed to follow independent AR(1)
processes with different degrees of persistence, except for i.i.d. “policy” shocks, which are
exogenous disturbances to the monetary policy rule.
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Figure 1: Model Structure
productivity shocks
Figure 1:
Firms
wage
rigidities
utilization
capital
labor supply
shocks
intermediate goods
price
rigidities
mark-up
shocks
labor
MEI
shocks
Capital
Producers
investment
adjustment
costs
Final Goods
Producers
investment
Entrepreneurs
consumption
Banks
Households
loans
credit
frictions
spread shocks
deposits
bills
habit
persistence
Government
interest rate
policy
policy
shocks
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shocks
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The Model’s Transmission Mechanism
In this section, we illustrate some of the key economic mechanisms at work in the model’s
equilibrium. We do so with the aid of the impulse reponse functions to the main shocks
hitting the economy, which we report in figures 7 to 13.
We start with the shock most closely associated with the Great Recession and the severe financial crisis that characterized it: the spread shock. As discussed above, this shock
stems from an increase in the perceived riskiness of borrowers, which induces banks to charge
higher interest rates for loans, thereby widening credit spreads. As a result of this increase in
the expected cost of capital, entrepreneurs’ borrowing falls, hindering their ability to channel resources to the productive sector via capital accumulation. The model identifies this
shock by matching the behavior of the Baa corporate bond rate over 10-year Treasuries, and
the spread’s comovement with output growth, inflation, and the other observables. Figure
7 shows the impulse responses of the variables used in the estimation to a one-standarddeviation innovation in the spread shock. An innovation of this size increases the observed
spread by roughly 35 basis points (bottom right panel). This leads to a reduction in investment and consequently to a reduction in output growth (top left panel) and hours worked
(top right panel). The fall in the level of hours is fairly sharp in the first year and persists
for many quarters afterwards, leaving the labor input not much higher than at the trough
five years after the impulse. Of course, the effects of this same shock on GDP growth, which
roughly mirrors the change in the level of hours, are much more short-lived. Output growth
returns to its steady state level about two years after the shock hits, but it barely moves
above it after that, implying no catch up of the level of GDP towards its previous trend.
The persistent drop in the level of economic activity due to the spread shock also leads to a
prolonged decline in real marginal costs - which in this model map one-to-one into the labor
share (middle left panel)- and, via the New Keynesian Phillips curve, in inflation (middle
right panel). Finally, policymakers endogenously respond to the change in the inflation and
real activity outlook by cutting the federal funds rate (bottom left panel).
Very similar considerations hold for the MEI shock, which represents a direct hit to
the “technological” ability of entrepreneurs to transform investment goods into productive
capital, rather than an increase in their funding cost. Although the origins of these two
shocks are different, the fact that they both affect the creation of new capital implies very
similar effects on the observable variables, as shown by the impulse responses in figure 8. In
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particular, a positive MEI shock also implies a very persistent increase in investment, output
and hours worked, as well as in the labor share and hence inflation. The key difference
between the two impulses, which is also what allows us to tell them apart empirically, is that
the MEI shock leaves spreads virtually unchanged (bottom right panel).
Another shock that plays an important role in the model, and whose estimated contribution to the Great Recession and its aftermath increased in light of the latest data revisions,
is the TFP shock. As shown in figure 9, a positive TFP shock has a large and persistent
effect on output growth, even if the reponse of hours is muted in the first few quarters (and
slightly negative on impact). This muted response of hours is due to the presence of nominal
rigidities, which prevent an expansion of aggregate demand sufficient to absorb the increased
ability of the economy to supply output. With higher productivity, marginal costs and thus
the labor share fall, leading to lower inflation. The policy rule specification implies that this
negative correlation between inflation and real activity, which is typical of supply shocks,
produces countervailing forces on the interest rate, which as a result moves little. These
dynamics make the TFP shock particularly suitable to account for the first phase of the
recovery, in which GDP growth was above trend, but hours and inflation remained weak.
With the recent softening of the expansion, though, the role of TFP shocks is fading.
The last shock that plays a relevant role in the current economic environment is the
mark-up shock, whose impulse response is depicted in figure 10. This shock is an exogenous
source of inflationary pressures, stemming from changes in the market power of intermediate
goods producers. As such, it leads to higher inflation and lower real activity, as producers
reduce supply to increase their desired markup. Compared to those of the other prominent
supply shock in the model, the TFP shock, the effects of markup-shocks feature significantly
less persistence. GDP growth falls on impact after mark-ups increase, but returns above
average after about one year. Inflation is sharply higher, but only for a couple of quarters,
leading to a temporary spike in the nominal interest rate, as monetary policy tries to limit
the pass-through of the shock to inflation. Unlike in the case of TFP shocks, however, hours
fall immediately, mirroring the behavior of output.
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Forecasts
Core PCE
Inflation
2011 (Q4/Q4)
Oct
June
1.5
0.8
(1.3,1.7) (0.2,1.4)
Unconditional Forecast
2012 (Q4/Q4)
2013 (Q4/Q4)
Oct
June
Oct
June
1.0
1.2
1.3
1.5
(0.2,1.6)
(0.3,1.9)
(0.4,2.0)
(0.6,2.4)
2014 (Q4/Q4)
Oct
June
1.6
1.8
(0.6,2.4)
(0.8,2.6)
Real GDP
Growth
0.9
(0.2,1.5)
1.7
(-1.6,4.2)
1.8
(-1.6,5.1)
Core PCE
Inflation
2011 (Q4/Q4)
Oct
June
1.8
1.4
(1.6,2.0) (1.0,1.7)
Conditional Forecast*
2012 (Q4/Q4)
2013 (Q4/Q4)
Oct
June
Oct
June
1.0
1.1
1.3
1.5
(0.3,1.7)
(0.3,1.8)
(0.4,2.0)
(0.6,2.3)
2014 (Q4/Q4)
Oct
June
1.6
1.7
(0.7,2.4)
(0.8,2.6)
Real GDP
Growth
1.8
(1.1,2.4)
2.6
(-0.8,5.0)
1.8
(-1.5,5.1)
2.7
(-0.2,4.8)
2.1
(0.7,3.2)
2.1
(-1.3,5.0)
2.0
(-1.3,4.6)
1.6
(-2.1,4.5)
1.8
(-1.8,4.8)
2.0
(-1.2,5.4)
1.9
(-1.2,5.2)
2.2
(-0.9,5.7)
2.2
(-1.0,5.6)
*The unconditional forecasts use data up to 2011Q2, the quarter for which we have the most recent GDP release, as well as
the federal funds rate and spreads data for 2011Q3. In the conditional forecasts, we further include the 2011Q3 FRBNY staff
projections for GDP growth, core PCE inflation, and hours worked as additional data points. Numbers in parentheses indicate
68 percent probability intervals.
We detail the forecast of three main variables over the horizon 2011-2014: real GDP
growth, core PCE inflation and the federal funds rate. The federal funds rate expectations
are constrained to be 25bp through 2013Q2. We capture policy anticipation by adding anticipated monetary policy shocks to the central bank’s reaction function, following Laseen
and Svensson (2009).
The table above presents Q4/Q4 forecasts for real GDP growth and inflation for 20112014, with 68 percent probability intervals. We include two sets of forecasts. The unconditional forecasts use data up to 2011Q2, the quarter for which we have the most recent GDP
release, as well as the federal funds rate and spreads data for 2011Q3, which are currently
available. In the conditional forecasts, we further include the 2011Q3 FRBNY staff projections for GDP growth, core PCE inflation, and hours worked as additional data points (as of
October 19, the staff projections for 2011Q3 are 2.8% for output growth, 2.1% for core PCE
inflation, and 0.1% growth for hours worked). Treating the staff forecasts as data allows us
to incorporate into the DSGE forecasts information about the current quarter that is not
yet available in the data. In addition to providing the current forecasts, for comparison we
report the forecasts included in the memo discussed at the June FOMC meeting (we did not
report forecasts for 2014 in that memo).
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Figure 2 presents quarterly forecasts, both unconditional (left panels) and conditional
(right panels). In the graphs, the black line represents data, the red line indicates the mean
forecast, and the shaded areas mark the uncertainty associated with our forecast as 50, 60,
70, 80 and 90 percent probability intervals. Output growth and inflation are expressed in
terms of percent annualized rates, quarter to quarter. The interest rate is the annualized
quarterly average. The bands reflect both parameter uncertainty and shock uncertainty.
Figure 3 compares the current forecasts with those produced for the June FOMC meeting.
Our inflation forecasts are notably higher for 2011 than they were in June, as the FRBNY
DSGE model was surprised by the strong readings for core PCE inflation in 2011. In spite
of this, inflation forecasts from 2012 onwards are actually lower than in June. This is due
to the weaker forecasts for economic activity, as discussed below. For both the 2012 and
2013 forecast horizons the 68% confidence bands for Q4/Q4 inflation are within the 0-2%
interval, implying that the model places great probability on the event that inflation is below
the implicit FOMC target at least through 2013. In 2014 the expected inflation (Q4/Q4) is
1.6%, and the 68% bands are between 0.7 and 2.4%.
The FRBNY DSGE forecasts for real output growth in June were already fairly weak,
as they projected growth between 2 and 3% for the remainder of 2011 and around 2% in
2012 and 2013. Current forecasts are even weaker in 2011 as a result of NIPA revisions and
weak new data. The mean projections for output growth in 2011 (Q4/Q4) are 0.9% and
1.8% for the unconditional and conditional forecasts, respectively. Note from Figure 2 that
the FRBNY staff projection for 2011Q3 is about 2% higher than the model’s unconditional
forecast. This relatively more upbeat assessment of current conditions carries over to 2011Q4
and to the end of 2012, explaining the difference in Q4/Q4 forecasts for 2012 (2.6 versus
1.7% for the conditional and unconditional forecast, respectively). In 2013 and 2014 the
two forecasts are quite similar, and envision growth slightly below 2% in both years. There
is significant uncertainty around the forecasts: the 25th percentile of the output growth
forecast distribution is below zero throughout the forecast distribution, implying that the
chance of negative readings for growth is larger than 1/4 in any given quarter. The 75th
percentile is between 3.5 and 5.0%.
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Figure 2: Forecasts
Unconditional
Conditional
2008
2009
2010
2011
2012
11
Figure
2:
10
2013
2014
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2015
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Output Growth
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
Output Growth
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
2008
Core PCE Inflation
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
−1.5
2009
2010
2011
2012
2013
2012
2013
2014
2014
5
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
−2
2015
−2
2007
−1.5
2008
2009
Interest Rate
2010
2011
2012
2013
2014
−2
2015
Interest Rate
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
2007
2008
2009
2010
2011
2012
2013
2014
0
2015
Percent Annualized
Percent Annualized
2011
5
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
5
2008
2010
Core PCE Inflation
5
−2
2007
2009
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2015
0
2007
2008
2009
2010
2011
2012
2013
2014
0
2015
Black lines indicate data, red lines indicate mean forecasts, and shaded areas mark the uncertainty associated with our forecast
as 50, 60, 70, 80, and 90 percent probability intervals.
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Figure 3: Change in Forecasts
Unconditional
Conditional
2008
2009
2010
2011
2012
Figure
3:
11
2013
2014
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2015
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Output Growth
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
Output Growth
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
2008
Core PCE Inflation
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
−1.5
2009
2010
2011
2012
2013
2012
2013
2014
2014
5
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
−2
2015
−2
2007
−1.5
2008
2009
Interest Rate
2010
2011
2012
2013
2014
−2
2015
Interest Rate
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
2007
2008
2009
2010
2011
2012
2013
2014
0
2015
Percent Annualized
Percent Annualized
2011
5
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
5
2008
2010
Core PCE Inflation
5
−2
2007
2009
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2015
0
2007
2008
2009
2010
2011
2012
2013
2014
0
2015
Solid and dashed red lines represent the mean for current and June’s forecast, respectively. Solid and dashed blue lines represent
90 percent probability intervals.
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Interpreting the Forecasts
To understand the forecasts, we use the shock decomposition shown in Figure 4. This figure
quantifies the importance of each shock for output growth, core PCE inflation, and the federal funds rate (FFR) from 2007 on, by showing the extent to which each of the disturbances
contributes to keeping the variables from reaching their long-run values. Specifically, in each
of the three panels the solid line (black for realized data, red for mean forecast) shows the
variable in deviation from its steady state (for output, the numbers are per capita, as the
model takes population growth as exogenous; for both output and inflation, the numbers are
quarter-to-quarter annualized). The bars represent the contribution of each shock to the deviation of the variable from steady state, that is, the counterfactual values of output growth,
inflation, and the federal funds rate (in deviations from the mean) obtained by setting all
other shocks to zero. By construction, for each observation the bars sum to the value on the
solid line.
The figure shows that all three variables of interest are currently below their steady-state
values, and are forecast to stay so through the end of the forecast horizon. Two of the shocks
most responsible for the Great Recession, the so-called “financial” shocks (Spread and MEI),
are still the main drivers of the outlook a few years after the end of the recession. This is
quite evident for inflation and interest rates, where it is clear that MEI and Spread shocks
(azure and purple bars, respectively) play a key role in keeping these two variables below
steady state.
This feature of the DSGE forecast is less evident for real output growth, as the contribution of MEI shocks seems small, particularly toward the end of the forecast horizon,
and the contribution of Spread shocks is negligible (and positive). However, recall that a
small, but still negative, effect on output growth implies that the effect of the MEI shocks on
the level of output is getting larger, even several quarters after the occurrence of the shock.
Similarly, the fact that the growth impact of Spread shock is positive but very small implies
that the level of output is very slowly returning to trend. This is evident in the protracted
effect of Spreads and MEI shocks on aggregate hours, shown in the impulse responses of
Figures 7 and 8, respectively, and discussed above. In turn, the fact that economic activity
is well below trend pushes inflation and consequently interest rates (given the Fed’s reaction
function) below steady state.
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Some more insight about the interpretation of the “financial” shocks – MEI and Spread
shocks – can be obtained from Figure 5. This figure shows the recent history of the shocks,
expressed in standard deviation units. The panel labeled “Spread” shows that during the
Great Recession there were two large Spread shocks, one in 2007 and one in concurrence with
the Lehman Brothers default (recall from Figure 7 that positive Spread shocks raise spreads
and have negative impact on economic activity). The panel labeled “MEI” shows that MEI
shocks were mostly negative from 2009 onwards, that is, after the end of the recession (recall
from Figure 8 that negative MEI shocks have negative impact on economic activity). These
shocks therefore seem to capture the headwinds from the financial crisis. (The Spread shocks
capture headwinds associated with a large spread while the MEI shocks capture financial
headwinds that are not reflected necessarily in the spread.)
In discussing the weak outlook for real activity we emphasized so far the impact of shocks
on deviations of the level of output from trend. But the trend may also shift, as pointed
out by the literature on unit roots. The FRBNY DSGE model allows for a stochastic trend
in total factor productivity, hence in output, and shifts in the trend can obviously have a
significant impact on the outlook. Is there evidence of any such shifts? Figure 6 addresses
this question. The figure shows the stochastic trend in TFP (solid lines) together with the
deterministic component of that trend (dashed blue lines), both expressed in logarithms and
normalized to zero at the beginning of 2007Q1. Deviations of the solid from the dashed line
represent shifts in the trend. Because of the decline in productivity during the recession,
by 2009 the trend had shifted down by about 6% relative to the deterministic drift. The
pick-up in productivity in the second half of 2009, however, almost completely erased that
gap, which now stands at about 0.5%. That shows that there is little evidence that shifts in
the trend are responsible for the bleak outlook.
Other shocks, beside the “financial” shocks, play an important role in explaining the
forecasts. For instance, the model attributes much of the rise in core inflation in 2011 to
price mark-up shocks. By assumption these shocks push inflation above marginal costs. Figure 10 shows that mark-up shocks capture large but transitory movements in inflation, such
as those due to oil price fluctuations. As a result, the large positive mark-up shock behind
the up-tick in inflation in recent quarters has almost no effect on the inflation forecasts.
Mark-up shocks also appear to sustain output growth in 2012 and 2013. This is due to the
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fact that the effect of mark-up shocks on the level of output, while negative, vanishes over
time, producing a positive effect in terms of growth rates.
Finally, according to the model, monetary policy shocks were largely expansionary in
recent history, and especially in 2008. These shocks include both contemporaneous and
anticipated deviations from the feedback rule, which we use to implement the lower bound
through 2013Q2. Notably, the impact of policy shocks on the interest rate is currently very
small, implying that the level of the interest rate is not too far from that implied by the
estimated policy rule. In 2013 and 2014 the impact of these shocks becomes larger: the
impact of the forward guidance, combined with the interest rates smoothing component of
the policy which limits quarter-to-quarter adjustments, implies that the renormalization path
is lower than that implied by the estimated rule. (Note however that this path is associated
with a rather dim outlook for output and inflation, indicating that the estimated interest
rate rule may be far from optimal under current circumstances.)
Policy shocks play an important role in pushing inflation upward in the aftermath of the
recession. Interestingly, while policy shocks have a positive impact on current output growth,
they have a negative impact on growth from 2012 onward. As much as this result may seem
counter-intuitive at first, it is actually the natural consequence of the fact that the impact of
expansionary monetary policy on the level of output, while still positive, is fading, implying
that the effect on the growth rate is currently negative (as the level of output returns to its
trend from below). This is partly because the stimulative effect of the “extended period”
language is front-loaded, and hence had most impact in the current quarter.
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Figure 4: Shock Decomposition
Output Growth
(deviations from mean)
Figure 4:
Percent Annualized
6
6
4
4
2
2
0
0
−2
−2
−4
−4
−6
−6
−8
−8
−10
−12
2007
−10
2008
2009
2010
2011
2012
2013
2014
−12
2015
Percent Annualized
Core PCE Inflation
(deviations from mean)
2
2
1
1
0
0
−1
−1
−2
−2
−3
2007
2008
2009
2010
2011
2012
2013
2014
−3
2015
Percent Annualized
Interest Rate
(deviations from mean)
2
2
1
1
0
0
−1
−1
−2
−2
−3
−3
−4
−4
−5
2007
2008
Spread
2009
2010
MEI
TFP
2011
Policy
2012
2013
Mark−Up
2014
Gov’t
−5
2015
Labor
]
The shock decomposition is presented for the conditional forecast. The solid lines (black for realized data, red for mean forecast)
show each variable in deviation from its steady state. The bars represent the shock contributions; specifically, the bars for each
shock represent the counterfactual values for the observables (in deviations from the mean) obtained by setting all other shocks
to zero.
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Figure 5: Shock Histories
TFP
Labor
4
4
Standard Deviations
3
2
2
1
1
0
0
Standard Deviations
Figure
5:
3
4
4
3
3
2
2
1
1
0
0
−1
−1
−2
−2
−3
−3
−4
2007−1
−4
−4
2007−1
2008−1
2009−1
2010−1
2011−1
−1
−1
−2
−2
−3
−3
2008−1
2011−1
−4
Demand
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
0
0
−1
−1
−1
−2
−2
−1
−2
−2
−3
−4
2007−1
−3
−3
−3
−4
−4
2007−1
4
4
3
3
2
2
1
1
0
0
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
2007−1
2008−1
2009−1
2010−1
2011−1
2008−1
−1
−1
−2
−2
−3
−3
−4
2007−1
2008−1
2009−1
2009−1
2010−1
2011−1
−4
Spread
2010−1
2011−1
−4
Standard Deviations
Mark−Up
Standard Deviations
2010−1
4
Standard Deviations
Standard Deviations
MEI
2009−1
2008−1
2009−1
2010−1
2011−1
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
Standard Deviations
Money
4
4
3
3
2
2
1
1
0
0
−1
−1
−2
−2
−3
−3
−4
2007−1
2008−1
2009−1
2010−1
2011−1
−4
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Figure 6: Trend Components of Productivity
Figure 6:
Level
17
17
16
16
15
15
14
14
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
−1
−1
−2
−2
−3
−3
−4
2007
2008
2009
2010
2011
2012
−4
2013
The trend in productivity is decomposed as the sum of a deterministic component (dotted blue line) and a stochastic component
(solid line; black for realized data and red for forecast). Shaded areas mark the uncertainty associated with our estimate as 50,
60, 70, 80, and 90 percent probability intervals.
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Figure 7: Responses to a Spread Shock
Output Growth
0
Percent Annualized
Percent Annualized
0
−0.5
−1
Aggregate Hours
Figure 7:
0.5
0
4
8
−0.2
−0.4
−0.6
−0.8
−1
12
0
Labor Share
Percent Annualized
Percent
−0.1
−0.15
0
4
8
12
0
−0.05
−0.1
−0.15
−0.2
0
4
Interest Rate
8
12
Spread
0.4
Percent Annualized
0
Percent Annualized
12
0.05
−0.05
−0.1
−0.2
−0.3
−0.4
8
Core PCE Inflation
0
−0.2
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
0.3
0.2
0.1
0
0
4
8
12
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Figure 8: Responses to an MEI Shock
Output Growth
1
Percent Annualized
Percent Annualized
0.8
0.6
0.4
0.2
0
Aggregate Hours
Figure 8:
1
0
4
8
0.8
0.6
0.4
0.2
0
12
0
Labor Share
Percent Annualized
Percent
0.1
0.05
0
4
8
0.2
0.15
0.1
0.05
0
12
0
4
Interest Rate
8
12
Spread
0.2
Percent Annualized
0.4
Percent Annualized
12
0.25
0.15
0.3
0.2
0.1
0
8
Core PCE Inflation
0.2
0
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
0.15
0.1
0.05
0
0
4
8
12
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Figure 9: Responses to a TFP Shock
Output Growth
Figure 9:
Percent Annualized
Percent Annualized
2
1.5
1
0.5
0
−0.5
0
4
8
Aggregate Hours
1.5
1
0.5
0
−0.5
12
0
Labor Share
Percent Annualized
Percent
−0.2
−0.4
0
4
8
0
−0.1
−0.2
−0.3
12
0
4
Interest Rate
8
12
Spread
0.08
Percent Annualized
0.15
Percent Annualized
12
0.1
0
0.1
0.05
0
−0.05
8
Core PCE Inflation
0.2
−0.6
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
0.06
0.04
0.02
0
0
4
8
12
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Figure 10: Responses to a Mark-up Shock
Output Growth
Percent Annualized
Percent Annualized
0
−0.5
−1
0
4
8
Aggregate Hours
Figure 10: 0.2
0.5
0
−0.2
−0.4
−0.6
12
0
Labor Share
Percent Annualized
Percent
−0.2
−0.3
0
4
8
0.6
0.4
0.2
0
−0.2
12
0
4
Interest Rate
8
12
Spread
0.01
Percent Annualized
0.3
Percent Annualized
12
0.8
−0.1
0.2
0.1
0
−0.1
8
Core PCE Inflation
0
−0.4
4
0
4
8
12
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0
−0.01
−0.02
0
4
8
12
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Figure 11: Responses to a Monetary Policy Shock
Output Growth
0
Percent Annualized
Percent Annualized
0
−0.5
−1
Aggregate Hours
Figure 11:
0.5
0
4
8
−0.2
−0.4
−0.6
−0.8
12
0
Labor Share
Percent Annualized
Percent
−0.1
−0.15
0
4
8
0.05
0
−0.05
−0.1
12
0
4
Interest Rate
8
12
Spread
0.02
Percent Annualized
0.8
Percent Annualized
12
0.1
−0.05
0.6
0.4
0.2
0
−0.2
8
Core PCE Inflation
0
−0.2
4
0
4
8
12
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0.01
0
−0.01
−0.02
0
4
8
12
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Figure 12: Responses to a Labor Supply Shock
Output Growth
Figure 12:
Percent Annualized
Percent Annualized
0.5
0
−0.5
−1
0
4
8
Aggregate Hours
0
−0.5
−1
−1.5
12
0
Labor Share
Percent Annualized
Percent
0.2
0
0
4
8
0.2
0.15
0.1
0.05
0
12
0
4
Interest Rate
8
12
Spread
0
Percent Annualized
0.2
Percent Annualized
12
0.25
0.4
0.15
0.1
0.05
0
8
Core PCE Inflation
0.6
−0.2
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
−0.02
−0.04
−0.06
−0.08
0
4
8
12
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Figure 13: Responses to a Government Spending Shock
Output Growth
Percent Annualized
Percent Annualized
1
0.5
0
−0.5
0
4
8
Aggregate Hours
Figure 13: 0.4
1.5
0.3
0.2
0.1
0
12
0
Labor Share
Percent Annualized
Percent
0.1
0.05
0
4
8
0.04
0.02
0
12
0
4
Interest Rate
8
12
Spread
0
Percent Annualized
0.08
Percent Annualized
12
0.06
0.15
0.06
0.04
0.02
0
8
Core PCE Inflation
0.2
0
4
0
4
8
12
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−0.005
−0.01
−0.015
−0.02
0
4
8
12
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References
[1] Bernanke, Ben, Mark Gertler and Simon Gilchrist, “The Financial Accelerator in a Quantitative Business Cycle Framework,” in J.B. Taylor and M. Woodford, eds., Handbook of Macroeconomics, vol. 1C, Amsterdam: North-Holland,
1999.
[2] Calvo, Guillermo, “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics, 1983, 12, 383–398.
[3] Christiano, Lawrence, Martin Eichenbaum, and Charles Evans, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal
of Political Economy, 2005, 113, 1–45.
[4] Christiano, Lawrence, Roberto Motto, and Massimo Rostagno, “Financial Factors in Economic Fluctuations,” Unpublished, 2009.
[5] Laseen, Stefan and Lars E. O. Svensson, “Anticipated Alternative
Instrument-Rate Paths in Policy Simulations,” NBER Working Paper No. w14902,
2009.
[6] Smets, Frank and Raphael Wouters, “Shocks and Frictions in US Business
Cycles: A Bayesian DSGE Approach,” American Economic Review, 2007, 97 (3),
586 – 606.
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Detailed Philadelphia (PRISM) Forecast Overview
October 2011
Keith Sill
Forecast Summary
The FRB Philadelphia DSGE model denoted PRISM, projects that real GDP growth will
rebound fairly strongly over the forecast horizon with real output growth approaching 5 percent
by mid 2012. Inflation is projected to be well contained at 1.5 percent through 2011, even with
significantly above-trend output growth. For this forecast round, we have implemented the
assumption that the federal funds rate remains in a range of 0 to 0.25 percent through mid-2013.
Monetary policy begins to tighten by the third quarter of 2013 in accord with the estimated
monetary policy rule, and reaches a bit over 2 percent in 2014Q4. Currently, many of the
model’s state variables are well below their steady-state values. In particular, consumption,
investment, and the capital stock are low relative to steady state, and absent any shocks, the
model would predict a rapid recovery. These state variables have been below steady state since
the end of the recession. The relatively slow recovery to date and the low inflation that has
recently characterized U.S. economic activity require the presence of shocks to offset the
strength of the model’s internal propagation channels.
The Current Forecast and Shock Identification
The PRISM model is an estimated New Keynesian DSGE model with sticky wages,
sticky prices, investment adjustment costs, and habit persistence. The model is similar to the
Smets & Wouters 2007 model and is described more fully in Schorfheide, Sill, and Kryshko
2010. Unlike in that paper though, we estimate PRISM directly on core PCE inflation rather
than projecting core inflation as a non-modeled variable. Details on the model and its estimation
are available in a Technical Appendix that was distributed for the June FOMC meeting or is
available on request.
The current forecasts for real GDP growth, core PCE inflation, and the federal funds rate
are shown in Figures 1a-1c along with the 68 percent probability coverage intervals. The
forecast uses data through 2011Q2 supplemented by observations on 2011Q3 from the most
recent Macroadvisers forecast. The model takes third quarter output growth of 2.4 percent as
given and the projection begins with 2011Q4. PRISM sees a strong rebound in real GDP
growth, which rises to about 5 percent by mid 2012. Output growth begins to taper off a bit in
2013, and falls to a 4 percent pace by 2014Q4. While output growth is fairly robust, core PCE
inflation stays moderate, dropping from a bit over 2 percent in mid 2011to 1.5 percent through
most of the forecast horizon. Based on the 68 percent coverage interval, the model sees little
chance of deflation over the next 3 years and almost no chance of recession. The federal funds
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rate is constrained at the zero bound through mid-2013. Thereafter, the model dynamics take
over and the funds rate rises to a bit over 2 percent in 2014Q4.
The key factors driving the projection are shown in the forecast shock decompositions
(shown in Figures 2a-2c) and the smoothed estimates of the model’s primary shocks (shown in
Figure 3, where they are normalized by standard deviation). The primary shocks driving abovetrend real output growth over the next 3 years are financial shocks in the form of discount factor
shocks (labeled Fin) and labor supply shocks (labeled Labor). PRISM estimates a long series of
largely negative shocks to labor supply since 2008. These shocks have a persistent negative
effect on hours worked and so account for a large share of the decline in output in 2009 and
2010. These shocks have pushed hours worked well below steady state, and as they unwind over
the projection period the labor market recovers and output growth is pushed above trend.
The model also estimates a sequence of largely negative discount factor shocks since
2008. All else equal, these shocks push down current consumption and push up investment, with
the effect being very persistent. Consequently, consumption (nondurables + services) is well
below the model’s estimated steady state at this point. As these shocks wane over the projection
period, consumption growth picks up to an above-4 percent pace over most of the next three
years. The negative discount factor shocks worked to push investment growth above steady state
since 2009, but the effects were to some extent offset by negative shocks to the marginal
efficiency of investment. As these MEI shocks unwind, they give a strong upward impetus to
investment growth over 2012-2014. But this effect is offset in part from the waning of discount
factor shocks that are putting downward pressure on investment growth. All told though,
investment growth runs at about a 7 percent pace in 2012, falling back to about 3 percent growth
by the end of the forecast horizon.
The forecast for core PCE inflation is largely a story of upward pressure from the
unwinding of labor supply shocks being offset by downward pressure from the waning of
discount factor shocks. Negative discount factor shocks have a strong and persistent negative
effect on marginal cost and inflation in the estimated model. Compared, for example, to a
negative MEI shock that lowers real output growth by 1 percent, a negative discount factor shock
that lower real output growth by 1 percent leads to a 3 times larger drop in inflation that is more
persistent (see the impulse responses in Figures 6a and 6b). The negative discount factor shock
leads to capital deepening and higher labor productivity. Consequently, marginal cost and
inflation fall. The negative effect of discount factor shocks on inflation is estimated to have been
quite significant since the end of 2008. As these shocks unwind over the projection period there
is a decreasing, but still substantial, downward effect on inflation over the next three years.
Shocks to price markups also help explain the recent strength of core PCE inflation, but their
effects are not very persistent so that inflation is projected to decline in the near-term.
Partly offsetting the downward pressure on inflation from discount factor shocks is the
upward pressure coming from labor supply shocks. Labor supply shocks that push down
aggregate hours also serve to put upward pressure on the real wage and hence marginal cost. The
effect is persistent, so as the labor supply shocks unwind over the forecast horizon they exert a
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strong, but waning, negative pull on inflation. On balance the effect of these opposing forces is
to keep inflation below 2 percent through the forecast horizon.
The Unconditional Forecast
Pinning down the federal funds rate at the zero lower bound through mid-2013 (using
fully anticipated monetary policy shocks) has a significant impact on the PRISM forecast.
Figures 4a-c show the forecast and shock decompositions for the unconditional forecast (ie, a
forecast that does not constrain the funds rate path). The forecasted path for real GDP growth is
about 1 percentage point higher over the next 3 years. The projection for core PCE inflation is
above 2 percent over the forecast horizon and the federal funds rate begins to rise immediately,
reaching nearly 4 percent by 2012Q4. Thus, the forecast is considerably stronger if the funds
rate is not constrained at the ZLB through mid-2013.
The shock decompositions provide guidance on the difference between the two forecasts.
When the federal funds rate is constrained at the ZLB through mid-2013, it has a strong effect on
expected inflation through the monetary policy reaction function (which puts little estimated
weight on the output gap). Agents in the model fully anticipate that the funds rate will be low
and with policy completely credible, expect that future inflation will be low given the policy
reaction function relationship between interest rates and inflation. This feedback has an effect on
the estimated current state of the economy and on how historical shocks get allocated by the
Kalman filter. In particular, absent constraining the federal funds rate, discount factor shocks
play a smaller role in the shock decompositions for inflation and output growth and MEI shocks
play a larger role in order for history to be consistent with the higher inflation projection (see
Figure 5). Indeed, the smoothed shock estimates show smaller estimated shocks for the discount
factor and larger estimated shocks for the marginal efficiency of investment in the case where the
funds rate is unconstrained. Consequently, there is less upward impetus on consumption over the
forecast horizon and more upward pressure on investment growth. Since discount factor shocks
play a smaller role in the historical shock decomposition, there is less downward pressure on
inflation over the forecast horizon as the shocks unwind. On the other hand, the larger role for
MEI shocks in the historical decomposition implies upward pressure on inflation in 2013 and
2014 as the shocks unwind.
On balance, constraining the funds rate in the forecast has the effect of altering the
composition of shocks away from the discount factor shock and toward the MEI shock. The
result is higher inflation and output growth over the forecast horizon. With inflation running
above target and strong output growth, PRISM forecasts that the funds rate should begin rising
immediately, reaching near 3 percent by mid-2013 -- roughly 300 basis points above the
constrained path federal funds rate at that point. By 2014Q4, the unconstrained funds rate is near
4 percent, roughly 200 basis point above the constrained funds rate path forecast.
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References
Schorfheide, Frank, Keith Sill, and Maxym Kryshko. 2010. “” International Journal of
Forecasting, 26(2): 348-373.
Smets, Frank, and Rafael Wouters. 2007. “Shocks and Frictions in U.S. Business Cycles: A
Bayesian DSGE Approach.” American Economic Review, 97(3): 586-606.
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Figure 1a
Real GDP Growth
10
8
6
4
2
0
−2
−4
−6
−8
−10
2007
2008
2009
2010
2011
2012
2013
2014
2015
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Figure 1b
Core PCE Inflation
6
5
4
3
2
1
0
−1
2007
2008
2009
2010
2011
2012
2013
2014
2015
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Figure 1c
Fed Funds Rate
8
6
4
2
0
−2
−4
2007
2008
2009
2010
2011
2012
2013
2014
2015
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Figure 2a
Conditional Forecast
!
shocks:
TFP:
Gov:
MEI:
MrkUp:
Labor:
Fin:
Mpol:
Total factor productivity growth shock
Government spending shock
Marginal efficiency of investment shock
Price markup shock
Labor supply shock
Discount factor shock
Monetary policy shock
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Figure 2b
Conditional Forecast
!
shocks:
TFP:
Gov:
MEI:
MrkUp:
Labor:
Fin:
Mpol:
Total factor productivity growth shock
Government spending shock
Marginal efficiency of investment shock
Price markup shock
Labor supply shock
Discount factor shock
Monetary policy shock
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Figure 2c
Conditional Forecast
!
shocks:
TFP:
Gov:
MEI:
MrkUp:
Labor:
Fin:
Mpol:
Total factor productivity growth shock
Government spending shock
Marginal efficiency of investment shock
Price markup shock
Labor supply shock
Discount factor shock
Monetary policy shock
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Figure 3
Smoothed Shock Estimates For Conditional Forecast Model
(normalized by standard deviation)
4
labor shock
2
discount factor shock
0
2
−2
0
−2
2006
3
−4
2008
2010
2012
TFP shock
−6
2006
2
2
1
1
0
0
−1
−1
−2
−2
2006
2008
2010
2012
−3
2006
2008
2010
2012
mei shock
2008
2010
2012
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Figure 4a
Unconditional Forecast
!
shocks:
TFP:
Gov:
MEI:
MrkUp:
Labor:
Fin:
Mpol:
Total factor productivity growth shock
Government spending shock
Marginal efficiency of investment shock
Price markup shock
Labor supply shock
Discount factor shock
Monetary policy shock
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Figure 4b
Unconditional Forecast
!
shocks:
TFP:
Gov:
MEI:
MrkUp:
Labor:
Fin:
Mpol:
Total factor productivity growth shock
Government spending shock
Marginal efficiency of investment shock
Price markup shock
Labor supply shock
Discount factor shock
Monetary policy shock
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Figure 4c
Unconditional Forecast
!
shocks:
TFP:
Gov:
MEI:
MrkUp:
Labor:
Fin:
Mpol:
Total factor productivity growth shock
Government spending shock
Marginal efficiency of investment shock
Price markup shock
Labor supply shock
Discount factor shock
Monetary policy shock
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Figure 5
Smoothed Shock Estimates from Unconstrained Forecast Model
(normalized by standard deviation)
3
labor shock
2
discount factor shock
1
2
0
1
−1
0
−2
−1
−2
2006
3
−3
2008
2010
2012
TFP shock
−4
2006
1
2
2008
2010
2012
mei shock
0
1
−1
0
−2
−1
−2
2006
2008
2010
2012
−3
2006
2008
2010
2012
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Figure 6a
Impulse Response to Negative Discount Factor Shock
(one standard deviation shock)
output growth
0.5
inflation
−0.05
−0.1
0
−0.15
−0.5
−0.2
−1
−1.5
−0.25
0
5
10
15
nominal rate
0
−0.3
0
10
15
aggregate hours
0.2
−0.1
5
0
−0.2
−0.2
−0.3
−0.4
−0.4
−0.5
0
5
10
15
−0.6
0
5
10
15
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Figure 6b
Impulse Response to Negative MEI Shock
(one standard deviation shock)
output growth
0.5
0
0
−0.5
−0.05
−1
−0.1
−1.5
0
5
10
15
nominal rate
0
−0.15
−0.2
−0.1
−0.4
−0.15
−0.6
0
5
10
0
15
−0.8
5
10
15
aggregate hours
0
−0.05
−0.2
inflation
0.05
0
5
10
15
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Federal Reserve Bank of Chicago
Subject:
Summary of Chicago Fed DSGE Model for Academic Researchers
From:
Scott Brave
Date:
October 24, 2011
Jeffrey R. Campbell
Jonas D.M. Fisher
Alejandro Justiniano
Overview
In this memo, we describe the Chicago Fed’s estimated dynamic stochastic
general equilibrium model. This framework yields a history of identified
structural shocks, which we apply to illuminate recent macroeconomic
developments. To aid in the understanding of these results, we follow them with
summaries of the model’s structure, the data and methodology employed for
estimation, and the estimated model’s dynamic properties.
In several respects, the Chicago Fed DSGE model resembles many other New
Keynesian frameworks. There is a single representative household that owns all
firms and provides the economy’s labor. Production uses capital, differentiated
labor inputs, and differentiated intermediate goods. The prices of all
differentiated inputs are “sticky”, so standard forward-looking Phillips curves
connect wage and price inflation with the marginal rate of substitution between
consumption and leisure and marginal cost, respectively. Other frictions include
investment adjustment costs and habit-based preferences.
There are, however, several features of the model which distinguish it from these
frameworks. For instance, we include both a shock that dominates changes in
long-run expected inflation and news shocks which provide short-term
guidance regarding the path of the federal funds rate in our Taylor rule. We refer
to the former, captured in a shifting intercept in the Taylor rule, as the inflation
drift shock, and we discipline its fluctuations with data on long-term inflation
expectations. We refer to the latter as forward guidance shocks, and we measure
them with futures market prices.
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Another distinguishing feature of the Chicago model is the use of multiple price
indices. Alternative available indices of inflation are decomposed into a single
model-based measure of consumption inflation and idiosyncratic (series
specific) disturbances that allow for persistent deviations from this common
component. Estimation uses a factor model with the common factor derived
from the DSGE framework.
The model also incorporates a financial accelerator mechanism. We introduce
risk-neutral entrepreneurs into the New Keynesian framework who purchase
capital goods from capital installers using a mix of internal and external
resources. These entrepreneurs optimally choose their rate of capital utilization
and rent the effective capital stock to goods producing firms. The dependence
on internal resources explicity links fluctuations in the external finance
premium, private net worth, and the state of the economy.
To identify parameters governing the financial accelerator, we use multiple
credit spreads and data on borrowing by nonfinancial businesses and
households. Consistent with our definition of investment, which includes
consumer durables and residential investment as well as business fixed
investment, we relate the external finance premium to a weighted average of
High Yield corporate bond and Asset-backed security spreads, where the weight
each receives is derived from the shares of nonfinancial business and household
debt in private credit taken from the Flow of Funds. To capture the impact of
entrepreneurial leverage on financial conditions, we rely on the growth rate of
the ratio of private credit to nominal GDP.
Forecasting Methodology
Constructing forecasts based on this model requires us to assign values to its
many parameters. We do so using Bayesian methods to update an
uninformative prior with data from 1989:Q2 through 2009:Q3. All of our
forecasts condition on the parameters equaling their values at the resulting
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Table 1. Model Forecasts Q4 over Q4
RealGDP
FederalFundsRate
PCECore
Consumption
Investment
Hours
2010
3.09
0.19
0.95
2.79
8.35
2.31
2011
1.54
0.09
1.94
2.64
4.63
1.65
2012
2.02
0.13
1.42
1.66
4.44
Ͳ0.12
2013
1.61
1.52
1.23
1.20
4.35
Ͳ0.62
2014
2.10
2.61
1.21
1.40
6.56
Ͳ0.17
posterior’s mode. These parameter values together with the data yield a
posterior distribution of the economy’s state in the final sample quarter. For the
calculation of this initial state’s distribution, we add a sequence of forward
guidance shocks that signal the future path of the Federal Funds rate. These
shocks begin arriving in 2009:Q4 and continue to the present. By construction,
they match model-based expectations of the policy rate with actual
market-based expectations for the first seven quarters of each quarter’s forecast
horizon. The forecasts begin with 2011:Q4 and extend through 2014:Q4. Our
plug for 2011:Q3 GDP growth was set at 2.1 percent.
Table 1 presents data from 2010 and forecasts for the following four years. The
first three rows correspond to three key macroeconomic observables, Real GDP
growth (Q4-over-Q4), the Federal Funds Rate (Q4 average), and growth of the
Core PCE deflator (Q4-over-Q4). The following rows report forecasts of
Q4-over-Q4 growth for three model-defined aggregates of importance:
Consumption of nondurable goods and non housing services, Investment in
durable goods, residential housing, and business equipment and structures, and
de-trended Hours worked in nonfarm business.1 Figure 1 complements this
with quarter-by-quarter data and forecasts of these series. The plots’ dashed
grey lines indicate the series’ long-run values. The economy’s long-run GDP
1
Hours are detrended using the Hodrick-Prescott filter with smoothing parameter 1e5.
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Figure 1. Quarterly Model Forecasts
Federal Funds Rate
5HDOGDP
3
5
2.5
4
2
3
1.5
2
1
1
0.5
0
0
2011
2012
2013
2014
2011
Consumption
2012
2013
2014
Investment
4
10
3.5
3
8
2.5
6
2
1.5
4
1
2011
2012
2013
2014
2011
2012
PCE Core
2013
2014
Hours
2.5
0
2
-1
1.5
-2
1
-3
-4
0.5
2011
2012
2013
2014
2011
2012
2013
2014
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growth rate – which we identify with potential growth – equals 2.6 percent.
Our forecast for real GDP growth in 2011 falls short of potential growth by
almost 1 percent, and the economy grows near or below potential throughout
the forecast horizon. Consequently, de-trended hours do not return to their
steady-state by the end of 2014. With resource slack remaining elevated, the
forecasted path for core PCE inflation declines at a measured pace from 1.9
percent in 2011 to 1.2 percent in 2014. We show below that this protracted
weakness arises from the ”financial shocks”, a spread and net worth shock, in our
model which have particularly persistent effects on economic activity.
The contractionary forces shaping our forecast have been partially offset by
forward guidance shocks, which in our model capture policy makers’
announcements regarding the path of the federal funds rate over the next seven
quarters. Forward guidance has added about 2 percent to four quarter real GDP
growth over the last year, and roughly 0.6 percent to core PCE inflation over the
same time period. Policy signals have supported consumption and investment
growth, as well as hours.
We hard-wire the current values of monetary policy news shocks to match
current market expectations, and currently these date the tightening of monetary
policy at 2013:Q3. Thereafter, the forecast rate begins to rise as the conventional
Taylor rule dynamics take over.
In the last two quarters, our measure of long-term inflation expectations has
edged down, and is currently 0.75 percent below its steady-state level. The
model interprets this as negative realizations of the inflation drift shock.
Therefore, the Taylor rule sees expected output growth and inflation as weak
enough to merit only the gradual removal of the extraordinary accommodation
in place since 2008.
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Shock Decompositions
Our analysis identifies the structural shocks responsible for past fluctuations. To
summarize this information, we follow a suggestion of Charlie Evans: Fix an
object to be forecast, such as Q4-over-Q4 real GDP growth. Then, pick a date in
the past and forecast the object conditional on the information as of that date.
This is not a real-time forecast, because it uses revised data. The model can be
used to decompose the associated forecast error into structural shocks. (A
detailed explanation of the forecast error decomposition procedure begins below
on page 26.) We repeatedly advance the forecast date, decompose the forecast
error, and finally plot the results. In total, the model features eleven structural
shocks and six idiosyncratic disturbances without structural interpretations. For
parsimony’s sake, we group the shocks according to the following taxonomy.
Demand These are the structural non-policy shocks that move output and
consumption-based inflation in the same direction. The model features
four of them. One changes the households’ rate of time discount. We call
this the Discount shock. Another includes a shock to the sum of
government spending, net exports, and changes in the valuation of
inventories. The remaining two are financial disturbances. The Spread
shock generates fluctuations in the external finance premium beyond the
level warranted by current economic conditions, and the Net Worth shock
generates exogenous fluctuations in private balance sheets.
Supply Five shocks move real GDP and consumption-based inflation in opposite
directions on impact. These supply shocks directly change
– Neutral Technology,
– Investment-Specific/Capital-Embodied Technology,
– Markups of Intermediate Goods Producers,
– Markups of Labor Unions, and
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Table 2. The Model’s Decomposition of Business-Cycle Variance
Real GDP
Real Consumption
Real Investment
Federal Funds Rate
Core PCE Inflation
Demand
0.87
0.88
0.93
0.83
0.28
Supply
0.06
0.08
0.04
0.04
0.55
Monetary Policy
0.07
0.05
0.04
0.13
0.17
Residual
0.00
0.00
0.00
0.00
0.00
Note: For each variable, the table lists the fraction of variance at frequencies between 6
and 32 quarters attributable to shocks in the listed categories. The numbers may not add
to one due to rounding.
– Households’ Disutility from Labor
Policy The model’s monetary policy follows a Taylor rule with interest-rate
smoothing, a time varying intercept, and an i.i.d. policy shock. The time
varying intercept, or Inflation Drift shock, is disciplined by equating
model-based average expected consumer price inflation to a measure of
long-term inflation expectations derived from a reduced form affine term
structure model. Additionally, we have incorporated forward guidance
shocks since 2009:Q4, which are revealed to the model’s agents one to
seven quarters before they affect the federal funds rate. These disturbances
allow our forecasting exercise to match model-based expectations with
information regarding the path of the federal funds rates over the next
seven quarters from futures markets.
Residual We group other shocks that are usually of small importance into a residual
category. These include the idiosyncratic, that is series specific, shocks to
the various price measures as well as the measurement errors in the credit
spread and net worth.
Table 2 reports the fraction of business-cycle variance attributable to shocks in
each category for five key variables, the level of Real GDP, Real Consumption,
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and Real Investment, and the Federal Funds Rate and Core PCE Inflation. Three
facts stand out here. First, demand shocks dominate business cycles. Supply
shocks account for only 6 percent of GDP’s total business-cycle variance, and the
non-systematic part of monetary policy shocks also makes only a minor
contribution. The accounting for the Federal Funds Rate’s variance is similar.
Perhaps this is unsurprising, because we classify the shock that directly moves
households’ rate of time preference as “demand.” Inflation fluctuations are
dominated by supply shocks, with exogenous shocks to intermediate goods’
markups accounting for about three-fourths of supply shocks’ 55 percent
contribution.
The Model’s Specification and Estimation
Our empirical work uses fourteen variables, measured from 1989:Q2 through the
present:
• Growth of nominal per capita GDP,
• Growth of nominal per capita consumption, which sums Personal
Consumption Expenditures on Nondurable Goods and Services;
• Growth of nominal per capita investment; which sums Business Fixed
Investment, Residential Investment, and Personal Consumption
Expenditures on Durable Goods
• Per capita hours worked in Nonfarm Business,
• Growth of nominal compensation per hour worked in Nonfarm Business,
• Growth of the implicit deflator for GDP,
• Growth of the implicit deflator for consumption, as defined above,
• Growth of the implicit deflator for investment, as defined above,
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• Growth of the implicit deflator for core PCE,
• Growth of the implicit deflator for core CPI,
• The interest rate on Federal Funds,
• Ten-year ahead core CPI forecasts from a reduced form affine term
structure model,
• A weighted average of High-Yield corporate and Mortgage-backed bond
spreads with the 10-year Treasury and an Asset-backed bond spread with
the 5-year Treasury; where the weights equal the shares of nonfinancial
business, household mortgage, and household consumer debt in private
credit,
• Growth of private credit-to-GDP; which sums household and nonfinancial
business credit market debt outstanding and divides by nominal GDP.
We do not directly use data on either government spending, net exports, or the
change in the valuation of inventories. Their sum serves as a residual in the
national income accounting identity. To construct series measured per capita, we
used the civilian non-institutional population 16 years and older. To eliminate
level shifts associated with the decennial census, we project that series onto a
fourth-order polynomial in time.
Our model confronts these data within the arena of a standard linear state-space
model. Given a vector of parameter values, θ, log-linearized equilibrium
conditions yield a first-order autoregression for the vector of model state
variables, ζt .
ζt = F (θ)ζt−1 + εt
εt ∼ N (0, Σ(θ))
Here, εt is a vector-valued innovation built from the model innovations
described above. Many of its elements identically equal zero. Table 3 lists the
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elements of ζt . Habit puts lagged nondurable consumption into the list, and
investment adjustment costs place lagged investment there. Rules for indexing
prices and wages that cannot adjust freely require the state to include lags of
inflation and technology growth. Financial frictions place lagged entrepreneurial
borrowing and net worth in the state. The list includes the lagged policy rate
because it appears in the Taylor rule.
Gather the date t values of the fourteen observable variables into the vector yt .
The model analogues to its elements can be calculated as linear functions of ζt
and ζt−1 . We suppose that the data equal these model series plus a vector of
“errors” vt .
yt = G(θ)ζt + H(θ)ζt−1 + vt
vt = Λ(ϕ)vt−1 + et
et ∼ N (0, D(ϕ))
Here, the vector ϕ parameterizes the stochastic process for vt . In our application,
the only non-zero elements of vt correspond to the observation equations for the
three consumption-based measures of inflation, the GDP deflator, and the
spread and private credit-to-GDP measures. The idiosyncratic disturbances in
inflation fit the high-frequency fluctuations in prices and thereby allow the price
markup shocks to fluctuate more persistently. These errors evolve
independently of each other. In this sense, we follow Boivin and Giannoni (2006)
by making the model errors “idiosyncratic”. The other notable feature of the
observation equations concerns the GDP deflator. We model its growth as a
share-weighted average of the model’s consumption and investment deflators.
We denote the sample of all data observed with Y and the parameters governing
data generation with Θ = (θ, ϕ). The prior density for Θ is Π(Θ), which
resembles that employed by Justiniano, Primiceri, and Tambalotti (2011). Given
Θ and a prior distribution for ζ0 , we can use the model solution and the
observation equations to calculate the conditional density of Y , F (Y |Θ). To form
the prior density of ζ0 , we apply the Kalman filter. The actual estimation begins
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Table 3. Model State Variables
Symbol
Ct−1
It−1
p
πt−1
Description
Lagged Consumption
Lagged Investment
Lagged Price Inflation
Kt
At
at
at−1
Stock of Installed Capital
Hicks-Neutral Technology
Growth rate of At
Lagged Growth Rate of At
Zt
zt
zt−1
Investment-Specific Technology
Growth rate of Zt
Lagged Growth Rate of Zt
φt
bt
λw,t
Labor-Supply Shock
Discount Rate Shock
Employment Aggregator’s
Elasticity of Substitution
Intermediate Good Aggregator’s
Elasticity of Substitution
Entrepreneurial Borrowing
Lagged Borrowing
Entrepreneurial Net Worth
Lagged Net Worth
Spread Shock
Net Worth Shock
Government Spending Share Shock
Lagged Nominal Interest Rate
Monetary Policy Shock
Inflation Drift Shock
λp,t
Bt
Bt−1
Nt
Nt−1
νt
ςt
gt
Rt−1
εR,t
πt
Disappears without
Habit-based Preferences
Investment Adjustment Costs
Indexing “stuck” prices
to lagged inflation
Autoregressive growth of At
Indexing “stuck” wages
to lagged labor productivity growth
Autoregressive growth of Zt
Indexing “stuck” wages
to lagged labor productivity growth
Time-varying Wage Markups
Time-varying Price Markups
Need for external finance
Risk-neutral entrepreneurs
Interest-rate Smoothing
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with 1989:Q2. Bayes rule then yields the posterior density up to a factor of
proportionality.
P (Θ|Y ) ∝ F (Y |Θ)Π(Θ)
We calculate our forecasts with the model’s parameter values set to this
posterior distribution’s mode.
Five Key Equations
This section summarizes the inferred parameters by reporting the estimates of
five key equations: the two equations of the financial accelerator capturing the
External Finance Premium and the evolution of private Net Worth, and the
log-linearized forms of the Taylor Rule, the Price Phillips Curve, and the Wage
Phillips Curve.
Financial Accelerator
Financial frictions in the model arise from imperfections in private financial
intermediation due to lenders’ costly state verification of the returns realized by
entrepreneurs’ projects. We introduce risk neutral entrepreneurs into the model
who at the end of period t purchase capital goods, Kt , from the capital installers
at the price Qt , using a mix of internal and external resources, given by end of
period net worth, Nt , and borrowing Bt , such that Qt Kt = Nt + Bt .
In the next period, t + 1, entrepreneurs optimally choose the rate of
utilization, ut+1 , and rent the effective capital stock Kt+1 = ut+1 Kt to the goods
k . At the
producing firms, receiving in return the gross rental rate of capital ωt+1
end of period t + 1 they resell the remaining capital stock, (1 − δ)Kt back to the
capital producers at the price Qt+1 .
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External Finance Premium
We assume that the external finance premium –the ratio of the equilibrium
return to capital and the expected real interest rate– is an increasing function of
the entrepreneurs’ leverage ratio,
Kt Qt
Nt ,
according to
k ]
Et [1 + rt+1
Kt Q t νt
e
=F
1+Rt
Nt
Et [ πt+1 ]
with Rt the nominal interest rate, πt+1 the gross inflation rate and F (1) = 1,
F > 0, F > 0.2 The spread shock, eνt , can be viewed as a disturbance to credit
supply, moving the external finance premium beyond the level dictated by
entrepreneurial net worth. We parameterize the steady state level of F
K Q
N
as
well as its elasticity τ , and estimate them to be 1.93 and 0.05, respectively. The
annualized steady state external finance premium is estimated to be 3.16 percent.
Net Worth
The law of motion for entrepreneurial net worth is given by
k
Nt = 0.89 K t−1 Qt−1 [1 + rtk ] − Et−1 [1 + rt−1
]Bt−1 + 0.11Γt + ςt
where Γt is the transfer from exiting to new entrepreneurs and ςt is a shock to net
worth that can arise for instance from time-varying survival probabilities for
entrepreneurs. The AR(1) laws of motion for the spread and net worth shocks, νt
and ςt , are estimated to have independent autoregressive parameters (0.93, 0.97)
and volatilities i=0.34, 0.36.
Notice that that if entrepreneurs are self-financed, which we rule out in steady state, F (1) = 1
and there is no external finance premium.
2
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Taylor Rule
⎛
⎞
7
1 3
Rt −πt = 0.69(Rt−1 −πt )+0.31×⎝1.36
(πt−j − πt ) + 0.2(yt − yt−4 )⎠+mp
ξt−s
t +
4 j=0
s=1
Besides the lagged interest rate, the variables appearing on the right-hand side
are an inflation drift πt∗ term (which in the context of the model can be
interpreted as the monetary authority’s medium-run desired rate of inflation),
the four-quarter average of consumption inflation, the most recent four-quarter
output growth rate, the current monetary policy shock (mp
t ), and the seven
s
for
previous quarters’ signals of the current monetary policy stance, ξt−s
s = 1, . . . , 7. (These signals play a prominent role in forecasting, but we do not
yet use them during estimation.)
Note that
• Holding the economy’s growth rate fixed, the long-run response of Rt to a
permanent one-percent increase in inflation is 1.36 percent. Thus, the
model satisfies the Taylor principle.
• Since the four-quarter growth rate of output replaces the usual output gap
in the rule, it is difficult to compare the estimated coefficient of 0.2 with the
typical calibrated output response of 0.5.
Furthermore, inflation drift is perfectly credible in the sense that we equate
model-based average expected consumer price inflation over the next forty
quarters to ten-year ahead core CPI forecasts derived from a reduced form affine
term structure model.
Price Phillips Curve
p
p
+ 0.12πt−1
+ 0.004st + pt
πtp = 0.88Et πt+1
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Here, st represents intermediate goods producers’ common marginal cost. The
introduction of inflation drift does not alter the dynamic component of inflation
indexation which is linked to the previous quarter’s inflation rate.
• The slope of the estimated Phillips Curve is fairly flat compared to some
other estimates in the literature. For instance, the associated Calvo
probablity of an individual firm not updating its price in a given quarter
equals 0.93.
• Producers unable to update their price with all current information are
allowed to index their prices to a convex combination of last quarter’s
p
in the
inflation rate with the steady-state inflation rate. This places πt−1
Phillips curve. The estimated weight on steady-state inflation is 0.86.
Wage Phillips Curve
The Wage Phillips curve can be written as
p
p
w
πtw +πtp +jt −ιw πt−1
+ jt−1 = βEt πt+1
+ πt+1
+ jt+1 − ιw (πtp + jt ) +κw xt +w
t ,
where πtw and πtp correspond to inflation in real wages and consumption prices
respectively, jt = zt +
α
1−α μt
is the economy’s technologically determined
stochastic trend growth rate, with α equal to capital’s share in the production
function, zt the growth rate of neutral technology, and μt the growth rate of
p
+ zt−1 + jt arises from
investment-specific technical change. The term πt−1
indexation of wages to a weighted average of last quarter’s
productivity-adjusted price inflation and its steady state value. The estimated
weight on the steady state equals 0.64. The log-linearized expression for the
ratio of the marginal disutility of labor, expressed in consumption units, to the
real wage is
xt = bt + ψt + νlt − λt − wt ,
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where bt and ψt are disturbances to the discount factor and the disutility of
working, respectively, lt hours, λt the marginal utility of consumption and wt the
real wage. Finally, w
t is a white noise wage markup shock.
Note that without indexation of wages to trend productivity, this equation says
that nominal wage inflation (adjusted by trend growth) depends positively on
future nominal wage inflation (also appropriately trend-adjusted), and increases
in the disutility of the labor-real wage gap.
The estimated equation is given by
p
p
w
+ jt−1 = 0.9984×Et [πt+1
+πt+1
+jt+1 −0.36 (πtp + jt )]+0.0034xt +w
πtw +πtp +jt −0.36 πt−1
t ,
The estimated Calvo probability of a wage remaining unadjusted in a given
quarter underlying the estimate of κw = 0.0034 equals 0.76.
The Model’s Shocks
Our discussion of recent macroeconomic developments above featured the
following shocks prominently: The discount rate shock, the “financial” shocks to
the external finance premium and private net worth, as well as both anticipated
and unanticipated monetary policy and inflation drift shocks. In this section, we
provide greater detail on the model’s responses to these six shocks.
Figure 2 plots responses to a discount rate shock that increases impatience and
tilts desired consumption profiles towards the present. The variables examined
are real GDP, the federal funds rate, consumption, investment, inflation, hours
worked, the external finance premium (or spread), and the ratio of private
credit-to-GDP. The responses are scaled so that the change in GDP after 16
quarters equals one percent.
In a neoclassical economy, this shock would be contractionary on impact. Upon
becoming more impatient, the representative household would increase
consumption and decrease hours worked. To the extent that the production
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technology is concave, interest rates and real wages would rise; and regardless
of the production technology both real GDP and investment would drop.
Increasing impatience instead expands activity in this New Keynesian economy.
As in the neoclassical case, consumption rises on impact. However, investment
remains unchanged as adjustment costs penalize the sharp contraction of
investment from the neoclassical model. Instead, investment displays a
hump-shaped response, exhibiting modest co-movement with consumption
with a slight lag. Habit causes the consumption growth to persist for two more
quarters before it begins to decline. Market clearing requires either a rise of the
interest rate (to choke off the desired consumption expansion) or an expansion
of GDP. By construction, the Taylor rule prevents the interest rate from rising
unless the shock is inflationary or expansionary. Therefore, GDP must rise. This
in turn requires hours worked to increase.
Two model features overcome the neoclassical desire for more leisure. First,
some of the labor variants’ wages are sticky. For those, the household is
obligated to supply whatever hours firms demand. Second, the additional labor
demand raises the wages of labor variants with wage-setting opportunities. This
rise in wages pushes marginal cost up and lies behind the short-run increase in
inflation. After inflation has persisted for a few quarters, monetary policy
tightens and real rates rise.
The effect of this shock on financial conditions is somewhat muted, with the
large decline in private credit-to-GDP reflecting for the most part fluctuations in
the denominator. Close to the end of the monetary policy cycle, the external
finance premium and private credit-to-GDP both increase as the demand for
credit rises.
Since the discount rate shock moves output and prices in the same direction, a
Keynesian analysis would label it a shift in “demand.” In the neoclassical sense,
it is also a demand shock, albeit a reduction in the demand for future goods. The
matching neoclassical supply shock in our model is to the spread shock. A
positive shock to it decreases the supply of future goods. Figure 3 plots the
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Figure 2. Responses to a Discount Rate Shock
GDP level
Federal Funds Rate
2
1.5
1
1
0.5
0.5
0
5
10
15
20
0
0
5
Consumption level
10
15
20
Investment level
2
2
1.5
1.5
1
1
0.5
0.5
0
5
10
15
20
0
0
5
Core PCE Inflation
10
15
20
Hours (detrended)
2
0.3
1.5
0.2
1
0.1
0.5
0
5
10
15
20
0
External Finance Premium
5
10
15
20
Private Credit−to−GDP
0.1
0
0.05
−1
0
−0.05
0
−2
5
10
15
20
0
5
10
15
20
Note: The impulse was scaled to yield a one percent increase in GDP after 16 quarters.
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responses to such a shock.3
A positive spread shock reduces the supply of credit available to entrepreneurs,
who are then forced to shrink their demand for capital. The price of installed
capital drops sharply so that the return to capital collapses on impact and is
followed by a prolonged contraction in borrowing by entrepreneurs. The decline
in borrowing is initially smaller than in net worth, which results in a rising
leverage ratio and a further tightening of the external finance premium.
Investment and other measures of real activity all decline. Of particular note is
the fact that the spread shock generates positive co-movement between
consumption and investment on impact. In response to lower activity and
inflation, monetary policy eases and real rates move lower.
Increasing the external finance premium thus lowers investment, consumption,
hours worked, GDP, and the real interest rate. Two aspects of our model stop
consumption from rising on the same shock’s impact. First, habit-based
preferences penalize an immediate increase in consumption. Second, monetary
policy responds to the shock only slowly, so real interest rates are slow to adjust.
The investment adjustment costs give the responses of GDP, hours, and
investment their hump shape. Although this shock changes the economy’s
technology for intertemporal substitution – and therefore deserves the
neoclassical label “supply” – it makes prices and output move in the same
direction. For this reason, it falls into our Keynesian taxonomy’s “demand”
category.
For the same reason, we consider a positive shock to net worth to be in the
“demand” category. It initially reduces entrepreneurs’ needs for external
financing, so borrowing drops in the first few quarters. Combined with a
sustained increase in net worth, this translates into a persistent reduction in the
3
The interpretation of this shock is not unique. The negative spread shock resembles in nature
a positive marginal efficiency of investment (MEI) shock. It could also be interpreted as a shock
to the efficiency of channeling funds to entrepreneurs or, more broadly, variations in the supply
of credit. Barro and King (1984) and Greenwood, Hercowitz, and Huffman (1988) consider the
analogous responses to an MEI shock from a neoclassical model.
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Figure 3. Responses to a Spread Shock
GDP level
Federal Funds Rate
0.2
−0.4
−0.6
0
−0.8
−0.2
−1
−0.4
−1.2
−1.4
0
−0.6
5
10
15
20
0
5
Consumption level
10
15
20
Investment level
0
−0.2
−2
−0.4
−4
−0.6
0
−6
5
10
15
20
0
5
Core PCE Inflation
15
20
Hours (detrended)
0
0
−0.5
−0.05
−0.1
0
10
−1
5
10
15
20
0
External Finance Premium
2
5
10
15
20
Private Credit−to−GDP
−1
1.5
1
−2
0.5
−3
0
0
5
10
15
20
0
5
10
15
20
Note: The impulse was scaled to yield a one percent decrease in GDP after 16 quarters.
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leverage ratio, moving the external finance premium lower. There is a surge in
investment, and consequently GDP and hours, peaking after 8 quarters or so,
together with a delayed modest response from consumption. The effects of this
shock on real activity are very persistent. With inflation also edging up,
monetary policy tightens and real rates rise in response.
As noted in section 2, monetary policy shocks have partially offset negative
demand shocks over the last year. Figures 5 and 6 present the impulse response
functions for two of these, the unanticipated “contemporaneous” shock and the
shock revealed to all agents seven quarters in advance. The responses to the
unanticipated shock are standard, but those following an anticipated shock
require more explanation. At the announcement date, the expected value of the
policy rate seven quarters hence increases by 190 basis points. Because both
Phillips curves are forward looking, this expected contraction causes both prices
and quantities to fall. This anticipated weakness then feeds through the Taylor
rule to create a gradual easing of policy.
Unlike the two monetary policy shocks above, recent negative realizations of the
inflation drift shock have acted to augment the contractionary forces of the
model. Figure 7 displays the impulse response functions for a positive inflation
drift shock. In response, core PCE inflation jumps on impact, as does expected
long-run inflation (not shown). Under the assumption of perfect credibility,
higher inflation is achieved without any contemporaneous movement in the
federal funds rate. Although monetary policy does eventually tighten to return
the real interest rate to its steady-state, lower real rates during the initial
transition fuel an increase in consumption, investment, and hours. Therefore,
GDP moves up on impact as well. Given the high degree of persistence of this
shock, its effects on real activity and inflation dissipate at a glacial pace.
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Figure 4. Responses to a Net Worth Shock
GDP level
Federal Funds Rate
1
0.4
0.8
0.6
0.2
0.4
0.2
0
5
10
15
20
0
0
5
Consumption level
15
20
Investment level
5
0.4
0.3
4
0.2
3
0.1
2
0
0
10
5
10
15
20
0
5
Core PCE Inflation
10
15
20
Hours (detrended)
0.8
0.15
0.6
0.1
0.05
0
0.4
5
10
15
20
0.2
0
External Finance Premium
5
10
15
20
Private Credit−to−GDP
0.5
−0.2
0
−0.3
−0.5
−0.4
−1.5
−1
0
5
10
15
20
0
5
10
15
20
Note: The impulse was scaled to yield a one percent increase in GDP after 16 quarters.
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Figure 5. Responses to an Unanticipated Monetary Policy Shock
Federal Funds Rate
GDP level
3
−0.5
−1
2
−1.5
1
−2
−2.5
0
5
10
15
20
0
5
Consumption level
10
15
20
Investment level
2
−0.5
0
−2
−1
−4
−6
−1.5
0
5
10
15
20
−8
0
5
Core PCE Inflation
10
15
20
Hours (detrended)
0
−0.5
−0.1
−1
−1.5
−0.2
−2
−0.3
0
5
10
15
20
0
External Finance Premium
5
10
15
20
Private Credit−to−GDP
0
0.4
0.2
−1
0
−2
−0.2
0
5
10
15
20
0
5
10
15
20
Note: The impulse was scaled to yield a one percent decrease in GDP 16 quarters after that date.
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Figure 6. Responses to an Anticipated Monetary Policy Shock
GDP level
Federal Funds Rate
−0.5
1
−1
0
−1.5
0
5
10
15
20
−1
0
5
Consumption level
10
15
20
Investment level
−0.4
0
−0.6
−2
−0.8
−1
−4
−1.2
0
5
10
15
20
0
5
Core PCE Inflation
10
15
20
Hours (detrended)
0
−0.1
−0.5
−1
−0.2
−1.5
−0.3
0
5
10
15
20
0
External Finance Premium
0
5
10
15
20
Private Credit−to−GDP
0
−0.1
−1
−0.2
−0.3
0
5
10
15
20
−2
0
5
10
15
20
Note: The monetary policy shock is revealed to all agents five quarters before its realization, and
the impulse was scaled to yield a one percent decrease in GDP 16 quarters after that date.
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Figure 7. Responses to an Inflation Drift Shock
GDP level
Federal Funds Rate
1.4
1.2
1
0.8
0.6
0.4
0.2
1
0.8
0.6
0.4
0
5
10
15
20
0
5
Consumption level
10
15
20
Investment level
2.5
0.8
2
0.6
1.5
0.4
1
0
5
10
15
20
0
5
Core PCE Inflation
10
15
20
Hours (detrended)
1
1.4
0.8
1.35
1.3
0.6
1.25
1.2
0
5
10
15
20
0.4
0
External Finance Premium
0.1
0
−0.1
0
5
10
15
20
5
10
15
20
Private Credit−to−GDP
0.8
0.6
0.4
0.2
0
−0.2
−0.4
0
5
10
15
20
Note: The impulse was scaled to yield a one percent increase in GDP 16 quarters after that date.
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Shock Decomposition Methodology
We credit Charles Evans with the original ideas behind this decomposition. For
the shock decomposition, we set the model’s parameters to their values at the
posterior distribution’s mode, θ̂. Using all available data we use the Kalman
smoother to extract sequences of estimated states {ζ̂t }Tt=1 and a innovations
{ε̂t }Tt=1 . By construction, these satisfy the estimated transition equation for the
state.
ζ̂t = F (θ̂)ζ̂t−1 + ε̂t ,
To keep this discussion simple, we henceforth suppose that the “error” shocks in
vt equal zero. Incorporating them into the analysis changes the actual
calculations only little.
For concreteness, suppose that the forecasted object of interest is Q4-over-Q4
GDP growth for 2010. We position ourselves in 2009:Q4 and calculate
2009:Q4
ζ̂2010:Q1
≡ F (θ̂)ζ̂2009:Q4
2009:Q4
2009:Q4
≡ F (θ̂)ζ̂2010:Q1
ζ̂2010:Q2
= F 2 (θ̂)ζ̂2009:Q4
..
.
2009:Q4
2009:Q4
ζ̂2010:Q4
≡ F (θ̂)ζ̂2010:Q3
These are the “expectations” of the model’s states in each quarter of 2010
conditional on the state at the end of 2009 equalling its estimated value.
With these “state forecasts” in hand, we can construct corresponding forecast
errors by comparing them with their “realized values” from the Kalman
smoother. For the period t state forecasted in 2009:Q4, we denote these with
η̂t2009:Q4 = ζ̂t − ζ̂t2009:Q4 .
These forecast errors are related to the structural shocks by
η̂t2009:Q4 =
t−2009:Q4
F j−1 (θ̂)ε̂2009:Q4+j .
j=1
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The shock decomposition is based on four alternative forecasts, ζ̂(ι)2009:Q4
for
t
t = 2010:Q1, . . . , 2010:Q4 and ι ∈ {D, S, M, R}. Here, ι indexes one of the four
groups of structural shocks. For these, let ε̂(ι)t denote a version of ε̂t with all
shocks except those in group ι set to zero. With these, we construct
ζ̂(ι)2009:Q4
≡ F (θ̂)ζ̂2009:Q4 + ε̂(ι)2010:Q1 ,
2010:Q1
..
.
2009:Q4
2009:Q4
ζ̂2010:Q4
≡ F (θ̂)ζ̂2010:Q3
+ ε̂(ι)2010:Q4 ,
and
η̂(ι)2009:Q4
≡ ζ̂t − ζ̂(ι)2009:Q4
.
t
t
By construction,
η̂t2009:Q4 =
ι∈{D,S,M,R}
η̂(ι)2009:Q4
.
t
That is, each forecast error can be written as the sum of contributions from each
of the shock groups. Using the observation equations, we transform these into
components of the forecast error for observable variables.
With this completed, we can then move the forecast date forward to 2010:Q1.
The decomposition for that date proceeds similarly, except that we treat growth
in 2010:Q1 as data.
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Bibliography
Barro, R. J. and R. G. King (1984). Time-separable preferences and
intertemporal-substitution models of business cycles. The Quarterly Journal of
Economics 99(4), pp. 817–839.
Bernanke, B. S., M. Gertler, and S. Gilchrist (1999). The financial accelerator in a
quantitative business cycle framework. Handbook of Macroeconomics.
Boivin, J. and M. Giannoni (2006). DSGE models in a data-rich environment.
Working Paper 12772, National Bureau of Economic Research.
Greenwood, J., Z. Hercowitz, and G. W. Huffman (1988). Investment, capacity
utilization, and the real business cycle. The American Economic Review 78(3),
pp. 402–417.
Justiniano, A., G. E. Primiceri, and A. Tambalotti (2011). Investment shocks and
the relative price of investment. Review of Economic Dynamics 14(1), 101–121.
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@FedFRASER