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BOARD
OF
GOVERNORS
OF THE
FEDERAL RESERVE SYSTEM
Division of Monetary Affairs
FOMC SECRETARIAT
Date:
June 7, 2013
To:
Research Directors
From:
Deborah J. Danker
Subject: Supporting Documents for DSGE Models Update
The attached documents support the update on the projections of the
DSGE models.
1 of 1
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System DSGE Project: Research Directors Drafts
June 7, 2013
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Federal Reserve Bank of Chicago
Subject:
Summary of Chicago Fed DSGE Model for Academic Researchers
From:
Scott Brave
Date:
June 7, 2013
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, in addition to the usual current monetary policy
shock in the Taylor rule, we account for short-term guidance regarding the
future path of the federal funds rate. A factor structure estimated from federal
funds and Eurodollar futures prices is used to identify both a current policy factor
and a forward guidance factor.
Also included in our Taylor rule is a shock which dominates changes in long-run
expected inflation. We refer to this shock, captured in a shifting intercept in the
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Taylor rule, as the inflation anchor shock, and we discipline its fluctuations with
data on long-term inflation expectations from the Survey of Professional
Forecasters.
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 ratio of private
credit to nominal GDP.
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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 2011:Q4. All of our
forecasts condition on the parameters equaling their values at the resulting
posterior’s mode. These parameter values together with the data yield a
posterior distribution of the economy’s state in the final sample quarter.
In addition, we specify a sample break in our model that begins in 2008:Q1. At
this point, we calibrate three parameters and re-estimate the parameters
governing the decomposition of the current policy and forward guidance factors
on the remaining sample. The three parameters we calibrate effect a structural
break in the persistence of the discount shock which affects households’ rate of
time preference, the variance of the inflation anchor shock, and in the output gap
coefficient in the Taylor rule.
Increasing the persistence of the shock to the discount rate captures the idea that
deleveraging by households following a financial crisis is unusually slow. Its
value in the second half of our sample period raises its half life from a little over
half a year in the pre-crisis sample to more than three years in the second half of
our sample. Similarly, lowering the variance of the inflation anchor shock
reflects the fact that inflation expectations exhibit a downward trend in the early
part of our sample, but have fluctuated considerably less since.
In the second half of our sample period, we also work with a coefficient on the
output gap in our policy rule that is three times larger than its pre-crisis
estimate. Our motivation for doing so is that the FOMC’s policy response to the
recent downturn in activity was more aggressive than in previous recessions in
our sample, each of which was moderate by historical standards. Furthermore,
in combination with the above, this assumption increases the likelihood that the
zero lower bound on the federal funds rate is binding at any given date.
The Chicago model forecast incorporates data through 2013Q1 and uses staff
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Table 1. Model Forecasts
Real GDP
Federal Funds Rate
Core PCE Inflation
Consumption
Investment
Gap in Rule
2012
1.7
0.2
1.5
1.5
7.3
-5.1
2013
3.1
0.1
0.9
2.5
8.0
-2.8
2014
3.5
0.3
0.4
2.3
7.4
-1.0
2015
3.3
0.7
0.7
2.2
6.3
-0.1
projections to plug the necessary inputs for 2013Q2. Of these inputs, the most
important are the annual growth rate of real GDP, growth in the consumption of
nodurables and services, and residential and nonresidential investment growth
excluding inventory investment. The staff projections for Q2 are for real GDP
growth to rise 2.2 percent as real consumption decreases and real investment
increases slightly from their Q1 values.
Table 1 presents data through 2012Q4 and forecasts for the following three 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 two rows report forecasts of
Q4-over-Q4 growth for model-defined aggregates of importance: Consumption
of nondurable goods and non housing services and Investment in durable
goods, residential housing, and business equipment and structures. Finally, the
last row displays the annual average of the measure of the output gap that
enters our Taylor-type policy rule.
Figure 1 complements this with quarter-by-quarter data and forecasts of each of
these series. The plots’ dashed grey lines indicate the series’ long-run values.
The economy’s long-run GDP growth rate – which we identify with potential
growth – equals 2.7 percent. The economy is projected to grow slightly above
potential throughout the forecast horizon. Consequently, the measure of the
output gap that enters our Taylor-type policy rule decreases from -5.4 to -0.1
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Figure 1. Quarterly Model Forecasts
Figure 1: Forecasts starting 2013Q3
Consumption
GDP
4
3
3
2.5
2
2
1
1.5
0
1
2013
2014
2015
2016
2013
Federal Funds Rate
2014
2015
2016
Investment
6
12
5
4
10
3
8
2
6
1
4
0
2013
2014
2015
2016
2013
PCE Core
2014
2015
2016
Gap in Rule
3
0
2.5
-1
2
-2
1.5
-3
1
-4
0.5
-5
0
2013
2014
2015
2016
2013
2014
2015
2016
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percent.
Transitory adverse demand shocks largely explain the recent weakness in
economic activity. In particular, a residual shock to the national income and
product accounting identity, embodying a change in the valuation of
inventories, net exports, and government expenditures in the model, accounts
for much of the weakness in GDP growth in the first half of 2013. Negative serial
correlation in this shock then results in a slight boost to GDP growth in the
second half of 2013 and 2014. Continued declines in government expenditures as
a result of sequestration are likely to diminish such a response. Furthermore, the
recent slow-down in net exports as economies around the world have slowed
could be seen as a risk to the model’s forecast in this regard.
Recent favorable monetary policy shocks, primarily reflecting forward guidance
on the funds rate, and a decrease in spreads beyond what is warranted by firms’
balance sheets according to the model boosts GDP growth in 2013 and 2014.
Their combined effect is partially offset, however, by recent adverse technology
shocks. Both the forward guidance and spread shocks each added roughly 0.1
percentage point to the four quarter average of GDP growth in the second
quarter of 2013, while an adverse neutral technology shock subtracted nearly
0.15 percentage point.
The forecasted path for core PCE inflation is well below the model’s slowly
drifting inflation anchor (currently 2.3 percent)inferred from the SPF forecast for
10-year CPI inflation. Inflation declines from the 1.5 percent observed in 2012 to
0.9 percent in 2013 and 0.4 percent in 2014 before gradually increasing to 1.1
percent in 2016. Small, positive price mark-up shocks inferred from incoming data
account for the slightly higher inflation in 2013 than was projected in March.
However, their effect on the forecast is short-lived.
Our forecast for the federal funds rate is informed by futures prices which hold
the funds rate near or below 0.5 percent through mid-2015. Thereafter, the
forecast rate begins to rise as the conventional Taylor rule dynamics take over,
increasing to about 0.75 percent by the end of 2015. The expected output and
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inflation gaps are weak enough to merit only the gradual removal of policy
accommodation. The increase in the funds rate in 2015 instead largely reflects
mean reversion in our estimated interest rate rule.
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 36.) We repeatedly advance the forecast date, decompose the forecast
error, and finally plot the results. In total, the model features eleven structural
shocks and sixteen 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. The next 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.
Finally, this category also includes a shock to the sum of government
expenditures, net exports, and changes in the valuation of inventories.
Supply Five shocks move real GDP and consumption-based inflation in opposite
directions on impact. These supply shocks directly change
– Neutral Technology,
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– Investment-Specific/Capital-Embodied Technology,
– Markups of Intermediate Goods Producers,
– Markups of Labor Unions, and
– Households’ Disutility from Labor
The shock to households’ disutility from labor is assumed to follow an
ARMA(1,1) process, which is a parsimonious way of addressing low
frequency movements in per capita hours worked and high frequency
variation in wages.
Policy The model’s monetary policy follows a Taylor rule with interest-rate
smoothing, a time varying intercept, and a factor structure which identifies
a Current Policy factor and a Forward Guidance factor. The time varying
intercept, or Inflation Anchor shock, is disciplined by equating
model-based average expected consumer price inflation to a measure of
long-term inflation expectations taken from the Survey of Professional
Forecasters. The Current Policy shock and Forward Guidance factor are
derived from contemporaneous federal funds futures prices zero to four
quarters before they affect the federal funds rate. In the second half of the
sample, we extend the number of futures contracts so as to capture
developments which affect the federal funds rate up to ten quarters ahead.
Residual We group the remaining shocks into a residual category. These include the
idiosyncratic, that is series specific, shocks to the various price measures
and monetary policy signals based on their factor structures, as well as the
measurement errors in the interest rate spread and private credit-to-GDP
ratio we use to capture the external finance premium and entrepreneurial
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,
and Real Investment, and the Federal Funds Rate and Core PCE Inflation. As
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Table 2. The Model’s Decomposition of Business-Cycle Variance
Real GDP
Federal Funds Rate
PCE Core
Consumption
Investment
Real GDP
Federal Funds Rate
PCE Core
Consumption
Investment
1989:Q2-2007:Q4
Demand Supply
0.73
0.12
0.20
0.04
0.15
0.63
0.88
0.08
0.88
0.04
2008:Q1-2011:Q4
Demand Supply
0.62
0.07
0.78
0.01
0.95
0.03
0.96
0.02
0.61
0.04
Policy
0.12
0.77
0.13
0.03
0.08
Residual
0.02
0.00
0.09
0.01
0.00
Policy
0.31
0.21
0.01
0.03
0.34
Residual
0.01
0.00
0.01
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.
already mentioned, we introduce an unanticipated sample break in 2008:Q1 and
hence report decompositions for both sub-samples. Demand shocks dominate
business cycles. This is particulary true in the second half of our sample.
Monetary policy shocks make only a minor contribution in the earlier sample
period, but explain almost one-third of GDP’s total business cycle variance in the
later period, due largely to their effect on Investment.
Inflation fluctuations are dominated by supply shocks in the early part of the
sample, with exogenous shocks to intermediate goods’ markups almost entirely
accounting for supply shocks’ 63 percent contribution. In contrast, supply
shocks account for between 7 and 12 percent of GDP’s total business-cycle
variance depending on the sample period. The accounting for the Federal Funds
Rate’s variance is also very sample-dependent. In the second half of the sample,
demand shocks are the key driver, while policy shocks dominate in the earlier
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period. Perhaps this is unsurprising, considering that we classify the shock that
directly moves households’ rate of time preference as “demand,” and increase
the activity coefficient in our interest rate rule post-2007.
The Model’s Specification and Estimation
Our empirical work uses eighteen 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,
• 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 CPI forecasts from the Survey of Professional Forecasters,
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• 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,
• Ratio of private credit-to-GDP; which sums household and nonfinancial
business credit market debt outstanding and divides by nominal GDP,
• Quarterly averages of federal funds and Eurodollar futures contract rates
one through four quarters ahead.
The ratio of private credit-to-GDP is detrended using the Hodrick-Prescott filter
with smoothing parameter 1e5. We do not directly use data on 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
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
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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.
Table 4 displays the estimated modes for a number of model parameters. 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
with 1989:Q2. Bayes rule then yields the posterior density up to a factor of
proportionality.
P (Θ|Y ) ∝ F (Y |Θ)Π(Θ)
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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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Table 4. Selected Model Parameter Modes
Parameter
ρπ
ρR
φp
φy
α
δ
ιp
ιw
γ?100
γµ100
H
λp
π ss
β
G ss
ν
κp
κw
χ
S
B
N
FKN
τ
ζ
ρb
ρυ
ρς
ρg
ρz
ρµ
ρλ p
ρψ
θψ
Description
Inflation anchor persistence
Inflation rate smoothing
Inflation gap response
Output gap response
Capital Share
Depreciation rate
Indexation Prices
Indexation Wages
Steady state consumption growth
Steady state investment-specific technology growth
Habit
Steady state price markup
Steady state quarterly inflation
Steady state discount factor
Steady state residual expenditure share in GDP
Inverse Frisch elasticity
Price Phillip’s curve slope
Wage Phillip’s curve slope
Utilization elasticity
Investment adjustment elasticity
Steady state borrowing to net worth ratio
Steady state spread
Net worth elasticity
Entrepreneur survival probability
Discount factor persistence
Spread persistence
Net worth persistence
G + NX persistnce
Neutral technology growth persistence
Investment technology growth persistence
Price markup persistence
AR coefficient labor disutility
MA coefficient labor disutility
Mode
0.99
0.85
1.35
0.10
0.17
0.03
0.08
0.28
0.47
0.60
0.89
0.10
0.65
0.997
0.22
2.17
0.001
0.005
4.80
7.84
1.11
0.69
0.002
0.91
0.76
0.99
0.64
0.99
0.10
0.73
0.61
0.95
0.98
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Beginning in 2008:Q1, we set the persistence of the discount shock at 0.95 and
scale the variance of the inflation anchor shock to be one quarter and the
coefficient on the output gap in the Taylor rule to be three times their earlier
values. We re-estimate the volatility and factor loadings of the current policy
and forward guidance factors and the standard deviations of the idiosyncratic
shocks as well as the volatility of the discount shock. All remaining parameters
are held fixed at their values in the first sub-sample. The Kalman filter is
initialized with the necessary pre-sample data, and estimation on this second
sample period proceeds as in the first except that as noted above we include
signals up to ten quarters ahead in the estimation of the policy rule. We then
calculate our forecasts with the model’s parameter values set to this posterior
distribution’s mode.
Table 5 displays the estimate modes for both sample periods for the model
parameters that are re-estimated on the second sub-sample.
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 .
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Table 5. Selected Modes for Re-estimated Parameters
Parameter
σb
σf 1
σf 2
σu1
σu2
σu3
σu4
σu5
σu6
σu7
σu8
σu9
σu10
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
Description
Std. dev. Discount factor shock
Std. dev. Current Policy factor
Std. dev. Forward Guidance factor
Std. dev. 1st idiosyncratic shock
Std. dev. 2nd idiosyncratic shock
Std. dev. 3rd idiosyncratic shock
Std. dev. 4th idiosyncratic shock
Std. dev. 5th idiosyncratic shock
Std. dev. 6th idiosyncratic shock
Std. dev. 7th idiosyncratic shock
Std. dev. 8th idiosyncratic shock
Std. dev. 9th idiosyncratic shock
Std. dev. 10th idiosyncratic shock
Current 1
Current 2
Current 3
Current 4
Current 5
Current 6
Current 7
Current 8
Current 9
Current 10
Lead 1
Lead 2
Lead 3
Lead 4
Lead 5
Lead 6
Lead 7
Lead 8
Lead 9
Lead 10
First Mode
0.14
0.04
0.06
0.04
0.02
0.02
0.05
1.25
0.69
0.42
-0.21
0.80
1.00
0.92
0.43
Second Mode
0.06
0.05
0.07
0.05
0.03
0.03
0.03
0.02
0.02
0.02
0.09
0.09
0.09
1.25
0.43
0.18
0.08
-0.01
0.02
0.01
-0.01
-0.00
-0.02
0.16
0.55
0.78
1.03
1.00
1.09
1.03
1.05
0.91
0.98
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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 .
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 Qt νt
=F
e
1+Rt
Nt
Et [ πt+1 ]
with Rt the nominal interest rate, πt+1 the gross inflation rate and F (1) = 1,
F 0 > 0, F 00 > 0.1 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 FKN as
well as its elasticity τ . We estimate the former to be 2.76 and the latter to be
pretty small. The annualized steady state external finance premium is estimated
to be 2.98 percent.
Net Worth
The law of motion for entrepreneurial net worth is given by
n
o
k
Nt = 0.91 K t−1 Qt−1 [1 + rtk ] − Et−1 [1 + rt−1
]Bt−1 + 0.09Γt + ςt
1
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.
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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 (0.99, 0.64)
and volatilities i=0.23, 0.37.
Taylor Rule
M
2
2
X
1 X
1 X
?
ξt−j,j
Et (πt+j ) − πt + 0.11
Et (x̂t+j )
+
Rt = 0.85Rt−1 +0.32 1.34
4 j=−1
4 j=−1
j=0
[1 + λ(1 − L)2 (1 − F )2 ]x̂t = λ(1 − L)2 (1 − F )2 ŷt
ξt,j = Aj ftc + Bj ftF + ut,j
Besides the lagged interest rate, the variables appearing on the right-hand side
of our interest rate rule are an inflation gap, an output gap, and current and
future deviations from the systematic component of the rule. For any variable v,
v̂ denotes deviations from steady state.
The inflation gap is the deviation of a four quarter average of model inflation
from the time-varying inflation drift, or anchor, πt∗ which varies exogenously
according to an AR(1) process. The four quarter moving average of inflation
includes both lagged, current, and future values of inflation. The monetary
authority uses the structure of the model to forecast the future terms.
The inflation drift term can be interpreted in the context of the model as the
monetary authority’s medium-run desired rate of inflation. It is perfectly
credible in the sense that we equate model-based average expected consumer
price inflation over the next forty quarters to the ten-year ahead CPI forecast
from the Survey of Professional Forecasters.
We define the output gap as the four-quarter moving average of detrended
model output. Following Curdia, Ferrero, Ng, and Tambalotti (2011), the
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detrending is model-based where L and F represent the lag and lead operators
and λ is a smoothing parameter that we estimate to be 9104. The filter above
approximates the Hodrick-Prescott filter. While the methodologies differ, figure
2 demonstrates that our output gap also compares well with the CBO’s output
gap measure from 1989:Q2-2007:Q2.
Holding the economy’s growth rate fixed, the long-run response of Rt to a
permanent one-percent increase in inflation is 1.3 percent. Thus, the model
satisfies the Taylor principle. Our estimated coefficient of the output response to
our rule is 0.1. We scale this coefficient by a factor of 3 in the second half of our
sample.
Monetary policy shocks have a factor structure such that the factors ftc and ftF
represent the i.i.d. current policy shock and the forward guidance factor. The
disturbances ut,j are assumed uncorrelated across both j and t, and the factor
structure identified by restricting the loading matrices, A and B, such that the
forward guidance factor only influences future values of the federal funds rate.
Figure 3 depicts our estimates of both factors from 1989:Q2-2007:Q2.
By including forward looking terms for the inflation and output gaps in the
interest rate rule, we account for news about both up to two quarters ahead from
our forward guidance shocks. We estimate both the current policy and forward
guidance factors using contemporaneous data on the federal funds rate and
federal funds and Eurodollar futures contract prices. In the first sub-sample, this
includes futures contracts one to four quarters ahead; while in the second
sub-sample, we use futures contracts one to ten quarters ahead.
Historical decompositions highlighting the role played by forward guidance
shocks for per capita GDP, core PCE inflation, and the federal funds rate from
1989:Q2-2007:Q2 are shown in figures, 4, 5, and 6. Forward guidance played a
role in explaining each during the 1993-1995 and 2002-2004 periods as detailed
in Campbell, Fisher, and Justiniano (2012). The first episode can be linked to
statements by Chairman Greenspan extending expectations for increases in the
funds rate, while the second is closely related to the extended period of low rates
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Figure 2. The Output Gap
Model−based Gap in Policy Rule
5
0
−5
−10
1990
1992
1994
1996
1998
2000
2002
2004
2006
Model−based Gap and CBO Gap (standardized)
2
1
0
−1
−2
1990
1992
1994
1996
1998
2000
Model−based
2002
2004
2006
CBO
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Figure 3. Current Policy and Forward Guidance Factors
Current Policy Factor
0.05
0
−0.05
−0.1
1990
1992
1994
1996
1998
2000
2002
2004
2006
2004
2006
Forward Guidance Factor
0.1
0.05
0
−0.05
−0.1
1990
1992
1994
1996
1998
2000
2002
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that followed 9/11.
Price Phillips Curve
p
p
πtp = 0.923Et πt+1
+ 0.074πt−1
+ 0.002st + pt
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 considerably flat compared to
some other estimates in the literature. This reflects at least in part our
sample period which starts in 1989.
• 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
inflation rate with the steady-state inflation rate. This places πt−1
in the
Phillips curve. The estimated weight on steady-state inflation is 0.92.
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
investment-specific technical change. The term πt−1
+ zt−1 + jt arises from
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 0.72. The log-linearized expression for the
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Figure 4. Historical Decomposition of per capita GDP
GDP (per capita)
Data
Annualized
6
4
2
0
-2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
Demand
Annualized
5
0
-5
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
Supply
2
1
0
-1
-2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
FG
1
0
-1
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
Other Policy
1.5
1
0.5
0
-0.5
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Counter Factual
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Figure 5. Historical Decomposition of Core PCE Inflation
PCE Core
Data
Annualized
5
4
3
2
1
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
Demand
Annualized
-0.2
-0.4
-0.6
-0.8
-1
-1.2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
Supply
0
-1
-2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
FG
Annualized
0.15
0.1
0.05
0
-0.05
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
Other Policy
2
1.5
1
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Counter Factual
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Figure 6. Historical Decomposition of the Federal Funds Rate
Federal Funds Rate
Annualized
Data
8
6
4
2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
2001Q2
2003Q2
2005Q2
2007Q2
Demand
Annualized
1
0
-1
-2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
Supply
-1
-1.5
-2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Annualized
FG
1
0
-1
-2
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Other Policy
Annualized
3
2
1
0
-1
1989Q2
1991Q2
1993Q2
1995Q2
1997Q2
1999Q2
Counter Factual
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ratio of the marginal disutility of labor, expressed in consumption units, to the
real wage is
xt = bt + ψt + νlt − λt − wt ,
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 −0.28 (πtp + jt )]+0.01xt +w
+ jt−1 = 0.997×Et [πt+1
+πt+1
πtw +πtp +jt −0.28 πt−1
t ,
The Model’s Shocks
The following shocks figure prominently into explaining the structure of the
model: The discount rate shock, the spread shock to the external finance
premium, the neutral technology shock, the price mark-up shock, the monetary
policy (current and forward guidance factor) and inflation anchor shocks. In this
section, we provide greater detail on the model’s responses to these seven
shocks by presenting impulse response functions to a one standard deviation
realization of each of these disturbances.
Figure 7 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, and
hours worked.
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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Figure 7. Responses to a Discount Rate Shock
Discount
Federal Funds Rate
GDP (level)
0.2
0.6
0.15
0.5
0.1
0.4
0.3
0.05
0
5
10
15
0
Consumption (level)
5
10
15
Investment (level)
0.8
0
0.7
0.6
−0.05
0.5
0.4
−0.1
0.3
0
5
10
15
0
Hours
5
10
15
PCE Core
0.7
0.07
0.6
0.06
0.5
0.05
0.4
0.04
0.3
0
5
10
15
0.03
0
5
10
15
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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 negative 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.
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 8 plots the
responses to such a shock.2
2
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
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Figure 8. Responses to a Spread Shock
Spread
Federal Funds Rate
GDP (level)
−0.4
−0.1
−0.6
−0.8
−0.2
−1
−1.2
−0.3
−1.4
0
5
10
15
0
Consumption (level)
5
10
15
Investment (level)
−2
0.4
−4
0.3
−6
0.2
0.1
0
−8
5
10
15
−10
0
Hours
5
10
15
PCE Core
−0.05
−0.4
−0.06
−0.6
−0.07
−0.8
−0.08
−1
0
5
10
15
−0.09
0
5
10
15
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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, with the exception of
consumption, all decline. In response to lower activity and inflation, monetary
policy eases and real rates move lower.
Increasing the external finance premium thus lowers investment, hours worked,
GDP, and the real interest rate. Two aspects of our model limit the response of
consumption 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. 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.
Figure 9 displays the responses to a neutral technology shock. Measures of real
activity, with the exception of hours, all rise after a positive technology shock.
The effects are delayed, however, due to habit persistence in consumption and
investment adjustment costs. As inflation declines on impact, monetary policy
progressively eases over a period of 6 quarters before bringing real rates back to
their steady-state as real activity picks up. This results in a hump-shaped
response in GDP, consumption, and investment. Since the neutral technology
shock moves output and prices in opposite directions, we label it a shift in
“supply.”
Figure 10 depicts the responses to a positive price mark-up shock. Inflation
increases on impact and measures of real activity all decline, thereby resembling
analogous responses to an MEI shock from a neoclassical model.
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Figure 9. Responses to a Neutral Technology Shock
Neutral Technology
Federal Funds Rate
GDP (level)
0.7
−0.02
0.6
0.5
−0.04
0.4
0.3
−0.06
0
0.2
5
10
15
0
5
Consumption (level)
10
15
Investment (level)
1.5
0.6
0.5
1
0.4
0.3
0.2
0.1
0
0.5
5
10
15
0
Hours
5
−3
x 10
10
15
PCE Core
0
0
−0.1
−5
−0.2
−0.3
−10
−0.4
0
5
10
15
0
5
10
15
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a transitory negative technology shock. Monetary policy tightens over a period
of four quarters before real rates gradually return to their steady-state as real
activity picks up.
Figures 11 and 12 present the impulse response functions for our two monetary
policy shocks, the current policy and forward guidance factors. We begin with
the forward guidance factor. A positive realization of this shock signals a
hump-shaped increase in the interest rate given our estimated factor loadings
with limited movement in the rate today. The gradual decline in the interest rate
after four quarters is governed mostly by the autoregressive coefficient in the
rule.
In response to the anticipated tightening, activity contracts immediately,
afterward following a hump-shaped response. Inflation declines primarily on
impact, as forward looking price setters incorporate the weaker outlook for
activity into their decisions today. The current policy factor displays a similar
pattern, except that compared with the forward guidance factor it accelerates the
policy tightening. That is, it displays an immediate jump followed by a steeper
rise and subsequent fall.
The responses to the current policy factor are standard, but those following a
forward guidance shock require more explanation. At the announcement date,
the expected value of the policy rate four quarters hence rises. 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.
Figure 13 displays the impulse response functions for a positive inflation anchor
shock. In response, inflation jumps on impact, as does expected long-run
expected 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,
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Figure 10. Responses to a Price Mark-up Shock
Price Markup
Federal Funds Rate
GDP (level)
−0.02
0.08
−0.03
0.06
−0.04
0.04
−0.05
0.02
−0.06
0
5
10
15
−0.07
0
Consumption (level)
10
15
Investment (level)
−0.01
−0.1
−0.015
−0.15
−0.02
−0.2
−0.025
0
5
−0.25
5
10
15
0
Hours
5
10
15
PCE Core
−0.02
−0.03
0.3
−0.04
0.2
−0.05
0.1
−0.06
−0.07
0
5
10
15
0
0
5
10
15
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Figure 11. Responses to the Current Policy Factor
Contemporaneous Policy Factor
Federal Funds Rate
GDP (level)
−0.1
0.3
0.2
−0.15
0.1
−0.2
0
5
10
15
0
5
Consumption (level)
10
15
Investment (level)
−0.2
−0.04
−0.3
−0.06
−0.4
−0.5
−0.08
−0.6
−0.7
−0.1
0
5
10
15
0
Hours
5
−3
x 10
10
15
PCE Core
−0.05
−5
−0.1
−10
−0.15
−0.2
0
−15
5
10
15
0
5
10
15
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Figure 12. Responses to the Forward Guidance Factor
Forward Guidance Factor
Federal Funds Rate
GDP (level)
0.4
−0.15
0.3
−0.2
0.2
−0.25
0.1
−0.3
0
0
5
10
15
−0.35
0
Consumption (level)
5
10
15
Investment (level)
−0.06
−0.4
−0.08
−0.6
−0.1
−0.8
−0.12
−1
−0.14
−0.16
0
−1.2
5
10
15
0
Hours
5
10
15
PCE Core
−0.1
−0.005
−0.15
−0.01
−0.2
−0.015
−0.25
−0.02
−0.3
−0.35
0
−0.025
5
10
15
0
5
10
15
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GDP moves up as well. Given the high degree of persistence of this shock, its
effects on real activity and inflation dissipate at a glacial pace.
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
ζ̂2010:Q2
≡ F (θ̂)ζ̂2010:Q1
= 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 .
Federal Reserve Bank of Chicago/ June 7, 2013 / Page 36 of 39
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Figure 13. Responses to an Inflation Drift Shock
Inflation Drift
Federal Funds Rate
GDP (level)
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0
5
10
15
0
Consumption (level)
5
10
15
Investment (level)
0.04
0.35
0.3
0.03
0.25
0.2
0.02
0.15
0.01
0
5
10
15
0.1
0
Hours
5
10
15
PCE Core
0.12
0.08
0.115
0.06
0.11
0.04
0
0.105
5
10
15
0
5
10
15
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These forecast errors are related to the structural shocks by
2009:Q4
η̂t
=
t−2009:Q4
X
F j−1 (θ̂)ε̂2009:Q4+j .
j=1
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
2010:Q1 ≡ F (θ̂)ζ̂2009:Q4 + ε̂(ι)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 =
X
η̂(ι)2009:Q4
.
t
ι∈{D,S,M,R}
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.
Campbell, J., J. Fisher, and A. Justiniano (2012). FOMC forward guidance and
the business cycle. Working Paper, Federal Reserve Bank of Chicago.
Curdia, V., A. Ferrero, G. C. Ng, and A. Tambalotti (2011). Evaluating interest
rate rules in an estimated DSGE model. Working Paper 510, Federal Reserve
Bank of New York.
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.
Federal Reserve Bank of Chicago/ June 7, 2013 / Page 39 of 39
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The Current Outlook in EDO: June FOMC Meeting
(Class II – Restricted FR)
Hess Chung
∗
June 6, 2013
1
The EDO Forecast from 2013 to 2016
Given recent data (including expectations for the federal funds rate), EDO projects below-trend
real GDP growth and unemployment around 8 percent until early 2014 (Figure 1).1 This subdued
pace of real activity is accompanied by low inflation, which slowly rises from a low of 43 percent in
the middle of 2013 to 1.7 percent by 2016.
This baseline is heavily shaped by the model’s interpretation of the low level of interest rates. In
particular, low interest rates over the projection reflect, according to the implementation used in the
projection, both the drag on interest rates imparted by past and prospective weakness in activity
and and some degree of monetary accommodation. with the first factor the more important, largely
by assumption (as fluctuations in risk premiums are the dominant factor in accounting for fluctuations in expected interest rates over history, and hence are also assumed to be important over the
projection period). Because market expectations for low interest rates owe (in the model) importantly to weak expected demand, the model projects that the aggregate risk premium will remain
in the neighborhood of its early 2012 levels, lowering GDP growth and boosting unemployment well
above its long-run level. In addition, lower-than-expected labor productivity and surprisingly strong
inflation since last year have led the model to infer a deterioration in aggregate supply conditions,
which modestly reduces GDP growth early in the projection.
Inflation is held below target by a combination of weak aggregate demand and muted pressure
on wages in the labor market. Indeed, the unemployment rate rises slowly through the end of 2014,
∗ Hess Chung (hess.t.chung@frb.gov) is affiliated with the Division of Research and Statistics of the Federal Reserve
Board. Sections 2 and 3 contain background material on the EDO model, as in previous rounds. These sections were
co-written with Michael Kiley and Jean-Philippe Laforte.
1 The baseline forecast for EDO is conditioned on the staff’s preliminary June 2013 Tealbook projection through
2013:Q2 and market expectations that the federal funds rate will remain at its effective lower bound through the second
quarter of 2014 (as indicated by OIS market expectations as of May 31, 2013). We do not impose an unemployment
or inflation threshold on the monetary policy rule.
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Figure 1: Recent History and Forecasts
EDO Projection Summary
Real GDP
Core PCE price index
Percent change, a.r.
5
Percent change, a.r.
5
2.5
4
4
2.0
2.0
3
3
1.5
1.5
2
2
1.0
1.0
1
1
0.5
0.5
0
0
0.0
0.0
-1
-1
-0.5
-0.5
-2
-2
-1.0
-1.0
-3
-3
-1.5
-1.5
-4
-4
-2.0
2011
2012
2013
2014
2015
2016
2011
2012
2013
2014
2015
2016
2.5
-2.0
Federal Funds Rate
Percent
5
5
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
2011
2012
2013
2014
2015
2016
-5
2014
Q4/Q4
Real GDP (a)
Credible set (c)
Federal Funds Rate (b)
Credible set (c)
2016
Q4/Q4
2.1
3.1
3.2
-.4-3.9
.9-5.0
1.3-5.5
Core PCE Price index (a) 1.1
Credible set (c)
2015
Q4/Q4
.5-1.8
1.4
1.6
.7-2.2
.9-2.4
0.3
0.9
1.7
.0-2.1
.0-2.8
.4-3.4
(a) Q4/Q4 percent change, (b) Q4 level, (c) 68 percent
Red, solid line -- Data (through 2013:Q2) and projections; Blue, solid line -- Previous projection (May, 2013, as of 2013:Q1); Black, dashed line -- Steady-state or trend values
Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Green -- Other
driven largely by the aforementioned weak demand conditions. By the end of the forecast, however,
a substantial portion of the elevated unemployment rate is accounted for the stickiness in wages and
prices in EDO, which prevents the real wage from falling sufficiently to bring down unemployment;
indeed, EDO estimates that the real wage must decline notably to clear the labor market.2
2
An Overview of Key Model Features
Figure 2 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
2 As
discussed below, unemployment enters the EDO model through a new-Keynesian wage Phillips curve, without
much specificity regarding structural labor-market features. As such, the primary role of unemployment is as a gauge
of the degree to which real-wage adjustment impedes labor market clearing, and anomalously persistent and elevated
rates of unemployment lead EDO to detect a decline in the real wage needed to clear the labor market. While most
of the runup in unemployment since 2007 is driven by weak demand (in EDO), the model identifies a component of
the increase in unemployment as due to a decline in the market-clearing real wage. Finally, as noted in the model
description below, such a decline is implemented in the model by a shift in labor supply.
3 Chung, Kiley, and Laforte (2011) provide much more detail regarding the model specification, estimated parameters, and model propeties.
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Figure 2: Model Overview
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 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
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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:
• A new-Keynesian structure for price and wage dynamics. Unemployment measures the difference between the amount workers are willing to be employed and firms’ employment demand.
As a result, unemployment is an indicator of wage, and hence price, pressures, as in Gali
(2010).
• Production of goods and services occurs in two sectors, with differential rates of technological
progress across sectors. In particular, productivity growth in the investment and consumer
durable goods sector exceeds that in the production of other goods and services, helping the
model match facts regarding long-run growth and relative price movements.
• 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.
2.1
Two-sector production structure
It is well known (e.g., Edge, Kiley, and Laforte (2008)) 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:
1−α
Xts (j) = (Ztm Zts Lst (j))
α
(Ktu,nr,s (j)) , for s = cbi, kb.
(1)
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In 1, Z m represents (labor-augmenting) aggregate technology, while Z s represents (labor-augmenting)
sector-specific technology; we assume that sector-specific technological 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 a source of business cycle
fluctuations, as in Fisher (2006).
2.2
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:
E0
∞
X
cnn
β t ς cnn ln(Etcnn (i)−hEt−1
(i))+ς cd ln(Ktcd (i))
t=0
+ς r ln(Ktr (i)) −ς l
1+ν
kb
(Lcbi
t (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 not distinguish between developments across these categories of
spending.
2.3
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
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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 residential
investment leads households to shift away from residential investment and towards other types of
productive investment. 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 risk-free savings must be off-set, in part, through a fall in real income, a decline
which 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”.
Movements in financial markets and economic activity in recent years have made clear the role
that frictions in financial markets play in economic fluctuations. This role was apparent much
earlier, motivating a large body of research (e.g.,Bernanke, Gertler, and Gilchrist (1999)). While
the range of frameworks used to incorporate such frictions has varied across researchers studying
different questions, a common theme is that imperfections in financial markets – for example, related
to imperfect information on the outlook for investment projects or earnings of borrowers – drives a
wedge between the cost of riskless funds and the cost of funds facing households and firms. Much of
the literature on financial frictions has worked to develop frameworks in which risk premia fluctuate
for endogenous reasons (e.g., because of movements in the net worth of borrowers). Because the
risk-premium shocks induces a wedge between the short-term nominal risk-free rate and the rate
of return on the affected risky rates, these shocks may thus also be interpreted as a reflection of
financial frictions not explicitly modelled in EDO. The sector-specific risk premia in EDO enter the
model in much the same way as does the exogenous component of risk premia in models with some
endogenous mechanism (such as the financial accelerator framework used Boivin, Kiley, and Mishkin
(2010)), and the exogenous component is quantitatively the most significant one in that research.4
4 Specifically,
the risk premia enter EDO to a first-order (log)linear approximation in the same way as in the cited
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Figure 3: Unemployment Fluctuations in the EDO model
Historical Decomposition for Unemployment
Unemployment Rate
Percent
10
10
8
8
6
6
4
4
2
2
0
0
-2
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
-2
Black, solid line -- Data (through 2013Q2) and projections; Black, dashed line -- Steady-state or trend values
Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Yellow -- Labor supply; Green -- Other
2.4
Unemployment Fluctuations in the EDO model
This version of the EDO model assumes that labor input consists of both employment and hours per
worker. Workers differ in the disutility they associate with employment. Moreover, the labor market
is characterized by monopolistic competition. As a result, unemployment arises in equilibrium – some
workers are willing to be employed at the prevailing wage rate, but cannot find employment because
firms are unwilling to hire additonal workers at the prevailing wage.
As emphasized by Gali (2010), this framework for unemployment is simple and implies that
the unemployment rate reflects wage pressures: When the unemployment rate is unusually high,
the prevailing wage rate exceeds the marginal rate of subsitution between leisure and consumption,
implying that workers would prefer to work more.
In addition, in our environment, nominal wage adjustment is sticky, and this slow adjustment
research if the parameter on net worth in the equation determining the borrowers cost of funds is set to zero; in
practice, this parameter is often fairly small in financial accelerator models.
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of wages implies that the economy can experience sizable swings in unemployment with only slow
wage adjustment. Our specific implementation of the wage adjustment process yields a relatively
standard New-Keynesian wage Phillips curve. 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).
While the specific model on unemployment is suitable for discussions of the links between unemployment and wage/price inflation, it leaves out many features of labor market dynamics. Most
notably, it does not consider separations, hires, and vacancies, and is hence not amenable to analysis
of issues related to the Beveridge curve.
As emphasized above, the rise in unemployment during the Great Recession primarily reflected,
according to the EDO model, the weak demand that arose from elevated risk premiums that depressed spending, as illustrated by the red bars in figure 3.
Indeed, these demand factors explain the overwhelming share of cyclical movements in unemployment over the past two-and-a-half decades, as is also apparent in figure 3. Other factors are
important for some other periods. For example, monetary policymakers lowered the federal funds
rate rapidly over the course of 2008, somewhat in advance of the rise in unemployment and decline in
inflation that followed. As illustrated by the silver bars in figure 3, these policy moves mitigated the
rise in unemployment somewhat over 2009; however, monetary policy efforts provided less stimulus,
according to EDO, over 2010 and 2011 – when the federal funds rate was constrained from falling
further. (As in many other DSGE models, EDO does not include economic mechanisms through
which quantitative easing provides stimulus to aggregate demand).
The contribution of supply shocks – most notably labor supply shocks – is also estimated to
contribute importantly to the low-frequency movements in unemployment, as shown by the yellow
bars in figure 3. Specifically, favorable supply developments in the labor market are estimated
to have placed downward pressure on unemployment during the second half of the 1990s; these
developments have reversed, and some of the currently elevated rate of unemployment is, according
to EDO, attributable to adverse labor market supply developments. As discussed previously, these
developments are simply exogenous within EDO and are not informed by data on a range of labor
market developments (such as gross worker flows and vacancies).
2.5
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:
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p,s
p,s
πtp,s = 0.22πt−1
+ 0.76Et πt+1
+ .017mcst + θts
(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
4wts = 0.014wt−1
+ 0.95Et 4wt+1
+ .012 mrsc,l
t − wt + 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.
The middle panel of figure 1 presents the decomposition of inflation fluctuations into the exogenous disturbances that enter the EDO model. As can be seen, aggregate demand fluctuations,
including aggregate risk premiums and monetary policy surprises, contribute little to the fluctuations
in inflation according to the model. This is not surprising: In modern DSGE models, transitory
demand disturbances do not lead to an unmooring of inflation (so long as monetary policy responds
systematically to inflation and remains committed to price stability). In the short run, inflation
fluctuations primarily reflect transitory price and wage shocks, or markup shocks in the language of
EDO. Technological developments can also exert persistent pressure on costs, most notably during
and following the strong productivity performance of the second half of the 1990s which is estimated
to have lowered marginal costs and inflation through the early 2000s. More recently, disappointing
labor productivity readings over the course of 2011 have led the model to infer sizeable negative
technology shocks in both sectors, contributing noticeably to inflationary pressure over that period
(as illustrated by the blue bars in figure 1),
2.6
Monetary Authority and A Long-term Interest Rate
We now turn to the last agent in our model, the monetary authority. It sets monetary policy in
accordance with an Taylor-type interest-rate feedback rule. Policymakers smoothly adjust the actual
interest rate Rt to its target level R̄t
ρr
Rt = (Rt−1 )
R̄t
1−ρr
exp [rt ] ,
(5)
where the parameter ρr reflects the degree of interest rate smoothing, while rt represents a monetary
policy shock. The central bank’s target nominal interest rate, R̄t depends the deviation of output
from the level consistent with current technologies and “normal” (steady-state) utilization of capital
and labor (X̃ pf , the “production function” output gap) Consumer price inflation also enters the
target. The target equation is:
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R̄t = X̃t
pf
ry Πc rπ
t
Πc∗
R∗ .
(6)
In equation (6), R∗ denotes the economy’s steady-state nominal interest rate, and φy and φπ denote
the weights in the feedback rule. Consumer price inflation, Πct , is the weighted average of inflation
in the nominal prices of the goods produced in each sector, Πp,cbi
and Πp,kb
:
t
t
Πct = (Πp,cbi
)1−wcd (Πp,kb
)wcd .
t
t
(7)
The parameter wcd is the share of the durable goods in nominal consumption expenditures.
The model also includes a long-term interest rate (RLt ), which is governed by the expectations
hypothesis subject to an exogenous term premia shock:
RLt = Et ΠN
τ =0 Rτ · Υt .
(8)
where Υ is the exogenous term premium, governed by
Ln (Υt ) = 1 − ρΥ Ln (Υ∗ ) + ρΥ Ln (Υt−1 ) + Υ
t .
(9)
In this version of EDO, the long-term interest rate plays no allocative role; nonetheless, the term
structure contains information on economic developments useful for forecasting (e.g., Edge, Kiley,
and Laforte (2010)) and hence RL is included in the model and its estimation.
2.7
Summary of Model Specification
Our brief presentation of the model highlights several points. First, although our model considers
production and expenditure decisions in a bit more detail, it shares many similar features with other
DSGE models in the literature, such as imperfect competition, nominal price and wage rigidities, and
real frictions like adjustment costs and habit-persistence. The rich specification of structural shocks
(to aggregate and investment-specific productivity, aggregate and sector-specific risk premiums, and
mark-ups) and adjustment costs allows our model to be brought to the data with some chance of
finding empirical validation.
Within EDO, fluctuations in all economic variables are driven by thirteen structural shocks. It
is most convenient to summarize these shocks into five broad categories:
• Permanent technology shocks: This category consists of shocks to aggregate and investmentspecific (or fast-growing sector) technology.
• A labor supply shock: This shock affects the willingness of to supply labor. As was apparent
in our earlier description of the unemployment rate and in the presentation of the structural
drivers below, this shock captures very persistent movements in unemployment that the model
judges are not indicative of wage pressures. While EDO labels such movements labor supply
shocks, an alternative interpretation would descrbie these as movements in unemployment that
reflect persistent strucutral features not otherwise captured by the model.
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• 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)), as we discuss in our presentation of the model’s properties
below.
• Markup shocks: This category includes the price and wage markup shocks.
• Other demand shocks: This category includes the shock to autonomous demand and a monetary policy shock.
3
3.1
Estimation: Data and Properties
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 13) 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.
The model is estimated using 13 data series over the sample period from 1984:Q4 to 2011:Q4.
The series are:
1. The civilian unemployment rate (U );
2. The growth rate of real gross domestic product (∆GDP );
3. The growth rate of real consumption expenditure on non-durables and services (∆C);
4. The growth rate of real consumption expenditure on durables (∆CD);
5. The growth rate of real residential investment expenditure (∆Res);
6. The growth rate of real business investment expenditure (∆I);
7. Consumer price inflation, as measured by the growth rate of the Personal Consumption Expenditure (PCE) price index (∆PC,total );
8. Consumer price inflation, as measured by the growth rate of the PCE price index excluding
food and energy prices (∆PC,core );
9. Inflation for consumer durable goods, as measured by the growth rate of the PCE price index
for durable goods (∆Pcd );
10. Hours, which equals hours of all persons in the non-farm business sector from the Bureau of
Labor Statistics (H);5
5 We remove a low-frequency trend from hours. We first pad the historical series by appending 40 quarterly
observations which approach the most recent 40-quarter moving average of the data at a rate of 0.05 percent per
quarter. We then extract a trend from this padded series via the Hodrick-Prescott filter with a smoothing parameter
of 6400; our model is not designed to capture low frequency trends in population growth or labor force participation.
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11. The growth rate of real wages, as given by compensation per hour in the non-farm business
sector from the Bureau of Labor Statistics divided by the GDP price index (∆RW );
12. The federal funds rate (R).
13. 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.
3.2
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 aggregate GDP growth is accounted for primarily by the technology shocks
in each sector, although the economy-wide risk premium shock contributes non-negligibly at short
horizons.
Volatility in the unemployment rate is accounted for primarily by the economy-wide risk
premium and business investment risk premium shocks at horizons between one and sixteen quarters.
Technology shocks in each sector contribute very little, while the labor supply shock contributes quite
a bit a low frequencies. 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 the unemployment rate is the series most like a “gap”
variable in the model – that is, the unemployment rate shows persistent cyclical fluctuations about
its long-run value.
Volatility in core inflation is accounted for primarily by the markup shocks.
Volatility in the federal funds rate is accounted for primarily by the economywide risk
premium (except in the very near term, when the monetary policy shock is important).
Volatility in expenditures on consumer non-durables and non-housing services is,
in the near horizon, accounted for predominantly by economy-wide risk-premia shocks. In the far
horizon, volatility is accounted for primarily by capital-specific and economy-wide technology shocks.
Volatilities in expenditures on consumer durables, residential investment, and nonresidential investment are, in the near horizon, accounted for predominantly by their own sector
specific risk-premium shocks. At farther horizons, their volatilities are accounted for by technology
shocks.
With regard to impulse responses, we highlight the responses to the most important shock, the
aggregate risk premium, in figure 4. 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 conventional
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
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Figure 4: Impulse Response to a One Standard Deviation Shock to the Aggregate Risk Premium.
−0.2
−0.2
−0.4
−0.6
−0.8
−0.4
Real Durables
Real Consumption
Real GDP
−0.2
−0.3
−0.4
−0.5
−0.6
−0.8
−1
−1.2
−1.4
−1
−0.6
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
−0.5
−1.5
−2
0
−0.2
−1
−0.4
Hours
Real Investment
Real Housing
−1
−2
−0.6
−0.8
−2.5
−3
−3
−4
−1
5
10
15
20
5
10
15
20
0.005
−0.02
0.4
Core PCE inflation
Fed Funds
−0.06
−0.08
−0.1
Unemployment
0
−0.04
−0.005
−0.01
−0.015
−0.02
0.3
0.2
0.1
−0.025
−0.12
5
10
15
20
5
10
15
20
nondurables and services consumption; each measure of inflation responds gradually, albeit more
quickly than in some analyses based on vector autoregressions (VARs).6
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 long-run 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.
6 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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Figure 5: Innovations to Exogenous Processes
−1
Funds Rate Shock
0
0.2
20
Labor Supply
Wage Markup
Exog. Demand
10
1
5
0
10
0
−10
−5
−20
2000
2010
2
Overall TFP
0
−1
−2
0
−1
2010
1990
Durables Risk−Premium
Housing Risk−Premium
2000
1
2
1
0
−1
−2
1990
2000
2010
1990
2000
2010
2000
50
0
−50
1990
2000
2000
−0.4
2010
1
0
−1
2010
1990
Capital Risk−Premium
1
1990
−0.2
Invest. Price Markup
1990
2000
1990
2000
2010
1990
2000
2010
1990
2000
2010
2
1
0
−1
−2
2010
1
1
Risk−premium
2010
2
1990
Term Premium
2000
Non−Invest. Price Markup
Capital Goods Technology
1990
0
0
−1
2010
0.5
0
−0.5
1990
2000
2010
0.2
0
−0.2
3.3
Estimates of Latent Variable Paths
Figures 5 and 6 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
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Figure 6: Exogenous Drivers
2
1
0
−1
2
TFP Tech.
Exog. Demand
Risk−premium
2
1
0
−1
1
0
−1
−2
1990
1
0
−1
−2
2
0
−2
−4
1990
0
−1
−2
−3
2000
1990
2000
2010
1990
2000
2010
1990
2000
2010
50
0
−50
2010
100
0.5
Labor Supply
1
2010
4
2010
2−y Term premium
2000
2000
Durables Risk−Premium
2010
2
1990
Capital Risk−Premium
2000
Housing Risk−Premium
Capital−specific Tech.
1990
0
50
0
−50
−100
−0.5
1990
2000
2010
1990
2000
2010
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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References
[Bernanke, Gertler, and Gilchrist (1999)] 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.
[Beveridge and Nelson (1981)] Beveridge, S. and C.R. Nelson. 1981. A new approach to the decomposition of economic time series into permanent and transitory components with particular
attention to measurement of the business cycle, Journal of Monetary Economics vol. 7, Pages
151-174.
[Boivin et al. (2010)] 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.
[Carlstom et al (2012)] Carlstrom, Charles T., Timothy S. Fuerst and Matthias Paustian. 2012.
How inflationary is an extended period of low interest rates?, Federal Reserve Bank of Cleveland
Working Paper 1202.
[Chung et al. (2011)] Chung, Hess, J.P. Laforte, David L. Reifschneider, and John
C. Williams. 2010. Have We Underestimated the Likelihood and Severity of Zero
Lower Bound Events. Federal Reserve Bank of San Francisco Working Paper 2011-01
http://www.frbsf.org/publications/economics/papers/2011/wp11-01bk.pdf
[Edge, Kiley, and Laforte (2008)] Edge, R., Kiley, M., Laforte, J.P., 2008. Natural rate measures in
an estimated DSGE model of the U.S. economy. Journal of Economic Dynamics and Control vol.
32(8), Pages 2512-2535.
[Edge, Kiley, and Laforte (2010)] 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 vol. 25(4), Pages 720-754.
[Fisher (2006)] Fisher, Jonas D. M., 2006. The Dynamic Effects of Neutral and Investment-Specific
Technology Shocks. Journal of Political Economy, University of Chicago Press, vol. 114(3), Pages
413-451.
[Gali (2011)] Gali, Jordi, 2011. The Return Of The Wage Phillips Curve. Journal of the European
Economic Association vol. 9(3), pages 436-461.
[Hall (2010)] Hall, Robert E., 2010. Why Does the Economy Fall to Pieces after a Financial Crisis?
Journal of Economic Perspectives vol. 24(4), Pages 3-20.
http://www.aeaweb.org/articles.php?doi=10.1257/jep.24.4.3
[Kiley (2007)] Kiley, M., 2007. A Quantitative Comparison of Sticky-Price and Sticky-Information
Models of Price Setting. Journal of Money, Credit, and Banking 39, Pages 101-125.
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[Kiley (2010a)] Kiley, M., 2010a. Habit Persistence, Non-separability between Consumption and
Leisure, or Rule-of-Thumb Consumers: Which Accounts for the Predictability of Consumption
Growth? The Review of Economics and Statistics vol. 92(3), Pages 679-683.
[Kiley (2010b)] Kiley, M., 2010b. Output Gaps. Federal Reserve Board Finance and Economics
Discussion Series (FEDS), 2010-27.
[Kydland and Prescott (1982)] Kydland, Finn and Prescott, Edward. 1982. Time-to-build and Aggregate Fluctuations. Econometrica vol. 50(6), Pages 1345 - 1370.
[Laforte (2007)] Laforte, J., 2007. Pricing Models: A Bayesian DSGE Approach to the U.S. Economy. Journal of Money, Credit, and Banking vol. 39, Pages 127-54.
[Smets and Wouters (2007)] 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.
[Wieland and Wouters (2010)] 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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Detailed Philadelphia (PRISM) Forecast Overview
June 2013
Keith Sill
Forecast Summary
The FRB Philadelphia DSGE model denoted PRISM, projects that real GDP growth will
run at a fairly strong pace over the forecast horizon with real output growth peaking at about 4.2
percent in the second half of 2014. Inflation is projected to be contained at 1.8 percent or below
through 2016. For this forecast round, we have implemented the assumption that the forecasted
federal funds rate is pinned down by current futures market projections through mid-2015. The
funds rate is unconstrained beginning in 2015Q3, and rises to 1.75 percent in 2015Q4. Many of
the model’s variables continue to be 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 2011 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 2013Q1 supplemented by a 2013Q2 nowcast based on the latest
Macroeconomic Advisers forecast. For example, the model takes 2013Q2 output growth of 1.8
percent as given and the projection begins with 2013Q3. PRISM continues to anticipate a fairly
strong rebound in real GDP growth, which rises to 4.2 percent by the end of 2014. Output growth
begins to taper off a bit in 2015 and 2016 falling to 3.6 percent by 2016Q4. While output growth
is fairly robust, core PCE inflation stays contained at near 1.75 percent through the forecast
horizon. Based on the 68 percent coverage interval, the model sees a minimal chance of deflation
or recession (measured as negative quarters of real GDP growth) over the next 3 years. The
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federal funds rate is constrained near the zero bound through mid-2015. Thereafter, the model
dynamics take over and the funds rate rises gradually to 2.5 percent in 2016Q4.
The key factors driving the projection are shown in the forecast shock decompositions
(shown in Figures 2a-2e) 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), marginal efficiency of investment shocks (labeled MEI), and labor supply
shocks (shocks to leisure, labeled Labor). Over the course of the recession and recovery PRISM
estimated a sequence of large positive shocks to leisure (negative shocks to labor supply) that
have a persistent effect on hours worked and so pushed hours well below steady state. As these
shocks unwind hours worked rebounds strongly over the forecast horizon and so leads to higher
output growth.
The model continues to estimate 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, the de-trended level of consumption
(nondurables + services) remains well below the model’s estimated steady state at this point. As
these shocks wane over the projection period, consumption growth picks up to a bit over a 3
percent annual pace over most of the next three years. The negative discount factor shocks
worked to strengthen investment in 2010 and 2011, but investment was pushed well below
steady state by adverse MEI shocks over 2007 to 2009. A combination of negative investment
shocks and negative TFP shocks held down investment growth in mid-2012, but since then
investment growth has averaged near its steady-state pace. The principal shocks driving strong
investment growth over the forecast horizon are efficiency of investment shocks and labor
shocks. There is a net strong positive contribution to investment growth over the next 3 years as
historical shocks work their way through the system (and MEI shocks are a negative contributor
to consumption growth over the forecast horizon). Note though that the unwinding of the
discount factor shocks that contributed positively to investment growth over 2009-2011 leads to
a downward pull on investment growth over the next three years. Investment growth runs at
about a 9 percent pace in 2014 easing back to about a 4 percent pace by the end of 2016.
The forecast for core PCE inflation is largely a story of upward pressure from the
unwinding of negative labor supply shocks, MEI shocks, and monetary policy 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 lowers real output growth by 1 percent
leads to a 3 times larger drop in inflation that is more persistent. 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
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is a decreasing, but still substantial, downward effect on inflation over the next three years (these
shocks have a very persistent effect on inflation).
Partly offsetting the downward pressure on inflation from discount factor shocks is the
upward pressure coming from the unwinding of negative 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 -- as the labor supply shocks unwind over the
forecast horizon they exert a waning upward push to 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 current market expectations through mid-2015
(using fully anticipated monetary policy shocks) has a modest impact on the PRISM forecast for
output growth and inflation. 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 similar to the conditional forecast for the next 3 years under a lessaccommodative monetary policy (though slightly stronger in 2015 and 2016). The projection for
core PCE inflation is a bit above 2 percent through much the forecast horizon even though the
federal funds rate begins to rise immediately, reaching about 3.3 percent by the end of 2015 and
3.8 percent by the end of 2016 . Thus, the inflation forecast is somewhat stronger if the funds
rate is not constrained at the ZLB through mid-2014.
The fact that the forecast with a substantially more accommodative policy has a weaker
inflation path and only moderately stronger output path is counter intuitive. It is the case in the
PRISM model that an anticipated easing of monetary policy in the future does lead to an
immediate jump in current period output and inflation – the economy strengthens with the easier
policy. Compared to the unconditional forecast, an anticipated easing of monetary policy leads
to a stronger economy and higher inflation today.
Why then the somewhat weaker projection in PRISM under the funds-rate-constrained
policy? The reason is that history is locked down in the model. For example, output growth in
2013Q2 is given at 1.8 percent and inflation is 0.3 percent in both the unconditional and
conditional forecasts since it is treated as historical data (recall that we use a nowcast for 2013Q2
as data to update the March projection). An easing of future monetary policy, by construction,
cannot change 2013Q2 output growth or inflation – or indeed their history. Consequently, the
model re-weights shocks so that negative TFP, discount factor, and MEI shocks offset the
stimulus from anticipated easier monetary policy in order to keep the history of output growth
and inflation unchanged. The persistence of the re-weighted TFP, discount factor, and MEI
shocks then shows through as the model projection unfolds. If we were to instead allow the
PRISM model variables that map into data observations to immediately adjust in response to an
anticipated easing of policy, the economic forecast would look significantly stronger.
As implemented though, leaving the funds rate unconstrained in the forecast shifts the
historical shock decomposition to give an expected path for output growth that is similar and
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inflation that is somewhat higher compared to the conditional forecast. With inflation running at
about target and strong output growth, PRISM forecasts that the funds rate should begin rising
immediately, reaching 3.8 percent by the end of 2016 -- roughly 130 basis points above the
constrained path federal funds rate at that point.
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
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
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Figure 1b
Core PCE Inflation
6
5
4
3
2
1
0
-1
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
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Figure 1c
Fed Funds Rate
8
6
4
2
0
-2
-4
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
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Figure 2a
Conditional Forecast
Real GDP Growth
10
5
0
‐5
‐10
‐15
‐20
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
Labor
2014
Fin
2015
Mpol
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
Core PCE Inflation
4
4
3
3
2
2
1
1
0
0
‐1
‐1
‐2
‐2
‐3
‐3
‐4
‐4
‐5
‐5
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
Labor
2014
Fin
2015
Mpol
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
Federal Funds Rate
4
4
2
2
0
0
‐2
‐2
‐4
‐4
‐6
‐6
‐8
‐8
‐10
‐10
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
2014
Labor
Fin
2015
Mpol
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 2d
Conditional Forecast
Real Consumption Growth
10
5
0
‐5
‐10
‐15
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
Labor
2014
Fin
2015
Mpol
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 2e
Conditional Forecast
Real Investment Growth
30
20
10
0
‐10
‐20
‐30
‐40
‐50
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
Labor
2014
Fin
2015
Mpol
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)
labor shock
discount factor shock
4
5
2
0
0
-2
2008
2010
2012
2014
-5
2008
TFP shock
2010
2012
2014
mei shock
4
2
2
0
0
-2
-2
2008
2010
2012
2014
2008
2010
2012
2014
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Figure 4a
Unconditional Forecast
Real GDP Growth
10
5
0
‐5
‐10
‐15
‐20
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
Labor
2014
Fin
2015
Mpol
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
Core PCE Inflation
4
4
3
3
2
2
1
1
0
0
‐1
‐1
‐2
‐2
‐3
‐3
‐4
‐4
‐5
‐5
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
Labor
2014
Fin
2015
Mpol
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
Federal Funds Rate
6
6
4
4
2
2
0
0
‐2
‐2
‐4
‐4
‐6
‐6
‐8
‐8
‐10
‐10
2008
2009
TFP
2010
Gov
2011
MEI
2012
MrkUp
2013
2014
Labor
Fin
2015
Mpol
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)
labor shock
discount factor shock
4
5
2
0
0
-2
2008
2010
2012
2014
-5
2008
TFP shock
2010
2012
2014
mei shock
4
2
2
0
0
-2
-2
2008
2010
2012
2014
2008
2010
2012
2014
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Impulse Responses to TFP shock
output growth
consumption growth
1
1
0.5
0.5
0
0
5
10
15
0
0
investment growth
0.5
0
0
0
5
10
15
-0.5
0
inflation
0.05
0
0
0
5
15
5
10
15
nominal rate
0.05
-0.05
10
aggregate hours
2
-2
5
10
15
-0.05
0
5
10
15
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Impulse Response to Leisure Shock
output growth
consumption growth
2
2
0
0
-2
0
5
10
15
-2
0
investment growth
0
0
-1
0
5
10
15
-2
0
inflation
0.4
0.2
0.2
0
5
15
5
10
15
nominal rate
0.4
0
10
aggregate hours
5
-5
5
10
15
0
0
5
10
15
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Impulse Responses to MEI Shock
output growth
consumption growth
2
0.2
0
0
-2
0
5
10
15
-0.2
0
investment growth
10
1
0
0.5
-10
0
5
10
15
0
0
inflation
0.4
0
0.2
0
5
10
15
5
10
15
nominal rate
0.1
-0.1
5
aggregate hours
10
15
0
0
5
10
15
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Impulse Responses to Financial Shock
output growth
consumption growth
1
2
0
0
-1
0
5
10
15
-2
0
investment growth
0.5
0
0
0
5
10
15
-0.5
0
inflation
1
0.2
0.5
0
5
15
5
10
15
nominal rate
0.4
0
10
aggregate hours
5
-5
5
10
15
0
0
5
10
15
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Impulse Responses to Price Markup Shock
output growth
consumption growth
0.5
0.5
0
0
-0.5
0
5
10
15
-0.5
0
investment growth
0
0
-0.1
0
5
10
15
-0.2
0
inflation
0.5
0
0
0
5
15
5
10
15
nominal rate
1
-1
10
aggregate hours
1
-1
5
10
15
-0.5
0
5
10
15
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Impulse Responses to Unanticipated Monetary Policy Shock
output growth
consumption growth
0.5
0.5
0
0
-0.5
0
5
10
15
-0.5
0
investment growth
0.2
0
0
0
5
10
15
-0.2
0
inflation
1
0
0
0
5
15
5
10
15
nominal rate
0.1
-0.1
10
aggregate hours
1
-1
5
10
15
-1
0
5
10
15
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Impulse Responses to Govt Spending Shock
output growth
consumption growth
2
0.5
0
0
-2
0
5
10
15
-0.5
0
investment growth
0.4
0
0.2
0
5
10
15
0
0
inflation
0.04
0.01
0.02
0
5
15
5
10
15
nominal rate
0.02
0
10
aggregate hours
0.2
-0.2
5
10
15
0
0
5
10
15
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FRBNY DSGE Model: Research Directors Draft
June 6, 2013
Overview
The FRBNY DSGE model forecast is obtained using data released through 2013Q1, augmented for 2013Q2, with the FRBNY staff forecast for real GDP growth, core PCE inflation
and growth in total hours, and with values of the federal funds rate and the spread between Baa corporate bonds and 10-year Treasury yields based on 2013Q2 observations. The
expected future federal funds rates are constrained to equal market expectations, as measured by OIS rates, through 2015Q2. The 2013Q2 staff projections and OIS rates are those
available on May 30, 2013.
The FRBNY DSGE projections for real activity are similar to those of March. Overall,
the model continues to project a lackluster recovery in economic activity, with output in the
neighborhood of 2 percent throughout the forecast horizon which ends in 2016Q4. Inflation
projections for 2013 and 2014 shifted slightly downward relative to March, and remain below
2 percent through the forecast horizon. The main drivers of the subdued real GDP and
inflation outlook continue to be the same forces behind the Great Recession, namely the two
shocks associated with financial frictions: spread and MEI (marginal efficiency of investment)
shocks, whose impact is long-lasting. Accommodative monetary policy, and particularly the
forward guidance, has partly counteracted the financial headwinds in the past, lifting output
and inflation. However, the impact of policy on the level of output has begun to wane by
now, so that policy is starting to have a negative impact on output growth.
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).
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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
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
the following 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. In addition, data on federal funds rate expectations as measured by OIS rates are now used in the estimation, from 2008Q4 on , i.e.,
from the beginning of the zero bound period. 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
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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
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
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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
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
loans
credit
frictions
spread shocks
deposits
Households
bills
habit
persistence
Government
interest rate
policy
policy
shocks
FRBNY DSGE Group, Research and Statistics
gov’t spending
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 response functions to the main shocks
hitting the economy, which we report in figures 8 to 14.
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
8 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 9. 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 10, a positive TFP shock has a large and persistent
effect on output growth, even if the response 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 11. 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
Real GDP
Growth
2013 (Q4/Q4)
Jun
Mar
1.1
0.9
(0.7,1.4) (0.4,1.4)
2.4
1.3
(1.0,3.3) (-1.0,2.7)
Unconditional Forecast
2014 (Q4/Q4)
2015 (Q4/Q4)
Jun
Mar
Jun
Mar
1.3
1.2
1.5
1.5
(0.4,1.9)
(0.4,1.9)
(0.6,2.3)
(0.5,2.2)
1.9
1.6
1.4
1.3
(-1.4,4.3) (-2.1,4.2) (-1.9,4.3) (-2.2,4.2)
2016 (Q4/Q4)
Jun
Mar
1.7
1.7
(0.8,2.5)
(0.8,2.5)
1.5
1.6
(-1.5,4.8) (-1.5,5.0)
Core PCE
Inflation
Real GDP
Growth
2013 (Q4/Q4)
Jun
Mar
1.0
1.1
(0.7,1.3) (0.6,1.5)
2.3
2.3
(0.9,3.2) (0.1,3.7)
Conditional Forecast*
2014 (Q4/Q4)
2015 (Q4/Q4)
Jun
Mar
Jun
Mar
1.2
1.3
1.5
1.5
(0.4,1.8)
(0.4,1.9)
(0.6,2.2)
(0.5,2.2)
2.1
1.9
1.5
1.4
(-1.2,4.4) (-1.7,4.5) (-1.8,4.4) (-2.1,4.3)
2016 (Q4/Q4)
Jun
Mar
1.7
1.7
(0.8,2.5)
(0.7,2.5)
1.6
1.6
(-1.5,4.8) (-1.6,5.0)
*The
unconditional forecasts use data up to 2013Q1, the quarter for which we have the most recent GDP release, as well as
the federal funds rate and spreads data for 2013Q2. In the conditional forecasts, we further include the 2013Q2 FRBNY staff’s
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 2013-2016: real GDP
growth, core PCE inflation and the federal funds rate. The federal funds rate expectations
in the model are set equal to market expectations for the federal funds rate (as measured by
OIS rates) through mid-2015. We capture policy anticipation by adding anticipated monetary policy shocks to the central bank’s reaction function, following Laseen and Svensson
(2009), after 2008Q4, the beginning of the zero bound period. The standard deviation of
the anticipated shocks is estimated as in Campbell et al. (2012), except that we only use
post-2008Q4 data.
The table above presents Q4/Q4 forecasts for real GDP growth and inflation for 20132016, with 68 percent probability intervals. We include two sets of forecasts. The unconditional forecasts use data up to 2013Q1, the quarter for which we have the most recent
GDP release, as well as the federal funds rate and spreads data for 2013Q2 (we use the
average realizations for the quarter up to the forecast date). In the conditional forecasts,
we further include the 2013Q2 FRBNY staff’s projections for GDP grow, core PCE inflation and hours worked as additional data points (as of May 30, projections for 2013Q2 are
2.1 percent for output growth, 1.0 percent for core PCE inflation, and 0.7 percent growth
for hours worked). Treating the 2013Q2 forecasts as data allows us to incorporate into the
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DSGE forecasts information about the current quarter. In addition to providing the current
forecasts, we report for comparison the forecasts included in the DSGE memo circulated for
the March FOMC meeting. 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
March FOMC meeting. Our discussion will mainly focus on the conditional forecasts, which
are those included in the memo for the FOMC.
The model still projects a lackluster recovery in economic activity, with output growth in
the neighborhood of 2 percent throughout the forecast horizon. Output growth in 2013Q1
and its 2013Q2 projection were in line with the March DSGE model projections. Hence our
current output forecasts are broadly similar to those in March. Conditional output growth
forecasts for 2014, 2015, and 2016 (Q4/Q4) moved to 2.1, 1.5, and 1.6 percent from 1.9, 1.4,
and 1.6 percent, respectively, in March. There is moderate uncertainty around the real GDP
forecasts, with 68 percent bands for the conditional forecasts covering the interval -1.2 to
4.4 percent in 2014 (Q4/Q4). Unconditional output forecasts for 2013 (Q4/Q4) are broadly
similar to the conditional forecasts, but they are sensibly higher than the unconditional
forecasts made in March.
The forecast distribution for inflation changed only slightly relative to March. Core PCE
inflation in 2013Q1 is only slightly different from the previous projection, stronger by about 8
basis points. The 68 percent probability bands for inflation in 2014, 2015, and 2016 (Q4/Q4)
are within the 0.4-2.5 percent interval for the conditional forecasts, implying that the model
places high probability on inflation realizations below the long-run FOMC target. Unconditional inflation forecasts are slightly higher than the conditional ones in 2013 and 2014 but
are otherwise the same.
Finally, as mentioned above, we constrain the federal funds rate expectations to be equal
to the expected federal fund rate as measured by the OIS rates until 2015Q2; after that the
federal funds rate raises gradually but remains below 2 percent until the middle of 2016.
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Figure 2: Forecasts
Unconditional
Conditional
Figure 2:
2008
2009
2010
2011
2012
2013
2014
Output Growth
2015
2016
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2017
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
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
2008
2009
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
2014
2013
2014
2015
2016
2015
2016
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
2017
−2
2007
−1.5
2008
2009
2010
Interest Rate
2011
2012
2013
2014
2015
2016
−2
2017
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
2015
2016
0
2017
Percent Annualized
Percent Annualized
2012
5
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
5
2008
2011
Core PCE Inflation
5
−2
2007
2010
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2017
0
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
0
2017
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
Figure 3:
2008
2009
2010
2011
2012
2013
2014
Output Growth
2015
2016
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2017
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
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
2008
2009
Core PCE Inflation
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
2014
2013
2014
2015
2016
2015
2016
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
2017
−2
2007
−1.5
2008
2009
2010
Interest Rate
2011
2012
2013
2014
2015
2016
−2
2017
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
2015
2016
0
2017
Percent Annualized
Percent Annualized
2012
5
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
5
2008
2011
Core PCE Inflation
5
4.5
−2
2007
2010
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2017
0
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
0
2017
Solid and dashed red lines represent the mean for current and September’s forecast, respectively. Solid and dashed blue lines
represent 90 percent probability intervals.
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Interpreting the Forecasts
We use the shock decomposition shown in Figure 4 to interpret the forecasts. 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 of the
solid line.
The figure shows that all three variables of interest are currently below their steady-state
values, and are forecasted to stay so through the end of the forecast horizon. The outlook
is driven by two main factors. On the one hand, the headwinds from the financial crisis, as
captured initially by the effects of spread shocks, and later by MEI (marginal efficiency of
investment) shocks, result in a subdued recovery, low real marginal costs, and consequently
low inflation. The impact of these shocks on the recovery is long-lasting. On the other hand,
accommodative monetary policy, and particularly the forward guidance about the future
path of the federal funds rate (captured here by anticipated policy shocks) has played an
important role in counteracting the financial headwinds, and in lifting up output and inflation. However, the impact of policy on the level of output has begun to wane by now, so
that policy is starting to have a negative impact on output growth.
The role played by spread and MEI shocks is quite evident in the shock decomposition
for inflation and interest rates, which shows that MEI, and to a lesser extent, 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
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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 spread and MEI shocks on aggregate hours, shown in the impulse responses of Figures 8 and 9, 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.
More insights on 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. Such positive spread shocks raise spreads and have negative impact on economic activity (see Figure 8). The panel labeled “MEI” in Figure 5 shows that
MEI shocks were mostly negative from 2009 onwards, that is, after the end of the recession.
Such negative MEI shocks have a negative impact on economic activity (see Figure 9).
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, and are shown in Figure 6 (not expressed in standard deviation units). The
contemporaneous policy shock was large and accommodative before the beginning of the zero
bound period. After 2008Q4 the estimated contemporaneous policy shock becomes negligible, not surprisingly, and policy accommodation is achieved via forward guidance, which
the model captures via anticipated shocks. Since shocks at different horizon interact with
one another, it is difficult to assess their overall impact from Figure 6. The bars in Figure 4
present their cumulative impact, however. One can see that the cumulative 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. Later in the forecast horizon
the impact of these shocks becomes larger, and reaches almost one percentage point in 2015:
the impact of the forward guidance, combined with the interest rate 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.
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Policy shocks have played an important role in pushing inflation and output upward both
in the immediate aftermath of the recession and in the current period. However, the impact
of policy on the level of output has started to wane by the end of 2012. This implies that the
effect of policy on growth is actually negative after that, which explains why growth is still
at or below trend by the end of 2016. This is partly because the stimulative effect of the forward guidance is front-loaded, and hence has the largest impact when it is first implemented.
The model attributes much of the rise in core inflation in 2011 and in early 2012 to price
mark-up shocks. Increases in mark-ups in our monopolistically competitive setting push
inflation above marginal costs and reduce output. Figure 11 shows that mark-up shocks
capture large but transitory movements in inflation, such as those due to oil price fluctuations. However with the moderation in energy prices since then, mark-up shocks have had
much smaller effects on inflation in recent quarters, and play almost no role in the inflation
forecasts. Since output is returning to trend following mark-up shocks, these actually contribute positively to output growth from 2013 onward.
Forecasts without Incorporating Federal Funds Rate Expectations
As mentioned above, in order to incorporate market expectations into our outlook we add
federal funds rate expectations through 2015Q2 to the usual set of observables, as described
in more detail in the FRBNY DSGE Model Documentation (we actually add federal funds
rate expectations to the observables since the near-zero interest rate policy came into place
in late 2008). We correspondingly allow the central bank’s reaction function to include anticipated monetary policy shocks, following Laseen and Svensson (2009). The model can
therefore match the information about federal funds rate expectations in two different ways:
(i) via the anticipated policy shocks, which capture pre-announced deviations from the estimated policy rule (as in “we expect interest rates to be low because monetary policy is
unusually accommodative”) ; and (ii) by changing its assessment of the state of the economy
(as in “we expect interest rates to be low because the state of the economy is worse than
previously estimated”). The two channels capture the exogenous and endogenous component
of monetary policy, respectively. We discussed the first channel – the effect of anticipated
shocks – in the previous section.
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Figure 7 shows our baseline unconditional (left panels) and conditional (right panels)
forecasts (solid lines) as well as the forecasts without incorporating federal funds rate expectations (dashed lines). The figure shows that the model interprets the data on expected
future federal funds rates as signaling a relatively weak state of the economy and a sluggish
expansion in the next few years. When abstracting from the information provided by expected future federal funds rates, forecasts are indeed a bit more optimistic. Output growth
and inflation forecasts for 2016 are higher by roughly 50 and 20 basis points, respectively,
despite a more rapid tightening of monetary policy. The latter policy tightening occurs
sooner when expected future federal funds rates are not constrained, with the federal funds
rate going to 1 percent in the current quarter and about 3 percent by the end of the forecast
horizon.
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Figure 4: Shock Decomposition
Figure 4:
Percent Q−to−Q Annualized
Output Growth
(deviations from mean)
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
2015
2016
−12
2017
Percent Q−to−Q Annualized
Core PCE Inflation
(deviations from mean)
2
2
1
1
0
0
−1
−2
2007
−1
2008
2009
2010
2011
2012
2013
2014
2015
2016
−2
2017
Percent Q−to−Q 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
MEI
2010
2011
TFP
2012
Policy
2013
2014
Mark−Up
2015
Gov’t
2016
−5
2017
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
Figure 5:
Labor
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
0
0
−1
−1
−2
−3
−4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
Standard Deviations
Standard Deviations
TFP
4
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
2007−1
2013−1
−4
2008−1
2009−1
2012−1
2013−1
Demand
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
0
0
−1
−1
−1
−1
−2
−2
−2
−2
−3
−3
−3
−3
−4
−4
2007−1
−4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
2013−1
−4
2008−1
2009−1
2010−1
2011−1
2012−1
2013−1
Spread
4
4
3
3
2
2
1
1
0
0
−1
−1
−2
−2
−3
−3
Standard Deviations
Mark−Up
Standard Deviations
2011−1
4
Standard Deviations
Standard Deviations
MEI
2010−1
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−4
2007−1
−4
2008−1
2009−1
2010−1
2011−1
2012−1
2013−1
FRBNY DSGE Group, Research and Statistics
−7
2007−1
−6
−7
2008−1
2009−1
2010−1
2011−1
2012−1
2013−1
17
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Figure 6: Anticipated Shock Histories
Figure 6:
Ant 1
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
Percent
Percent
Money
0.2
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.3
−0.3
−0.4
−0.4
2007−1
2013−1
−0.4
2008−1
2009−1
Ant 3
0.2
0.1
0.1
0.1
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.3
−0.3
−0.4
−0.4
2007−1
2013−1
−0.4
2008−1
2009−1
2010−1
2011−1
2012−1
2013−1
Ant 5
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
Percent
Percent
2013−1
0.2
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.3
−0.3
−0.4
−0.4
2007−1
2013−1
−0.4
2008−1
2009−1
Ant 6
2010−1
2011−1
2012−1
2013−1
Ant 7
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
Percent
Percent
2012−1
0.2
Ant 4
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.3
−0.3
−0.4
−0.4
2007−1
2013−1
−0.4
2008−1
2009−1
Ant 8
2010−1
2011−1
2012−1
2013−1
Ant 9
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.4
2007−1
2008−1
2009−1
2010−1
2011−1
2012−1
Percent
Percent
2011−1
0.2
Percent
Percent
Ant 2
2010−1
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.3
−0.3
−0.4
−0.4
2007−1
2013−1
FRBNY DSGE Group, Research and Statistics
−0.4
2008−1
2009−1
2010−1
2011−1
2012−1
2013−1
18
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Figure 7: Effect of Incorporating FFR Expectations
Unconditional
Conditional
Figure 7:
2008
2009
2010
2011
2012
2013
2014
Output Growth
2015
2016
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2017
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
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2007
2008
2009
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
2014
2013
2014
2015
2016
2015
2016
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
2017
−2
2007
−1.5
2008
2009
2010
Interest Rate
2011
2012
2013
2014
2015
2016
−2
2017
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
2015
2016
0
2017
Percent Annualized
Percent Annualized
2012
5
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
5
2008
2011
Core PCE Inflation
5
−2
2007
2010
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2017
0
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
0
2017
Solid and dashed red lines represent the mean for the forecast with and without incorporating FFR expectations, respectively.
Solid and dashed blue lines represent 90 percent probability intervals.
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Figure 8: Responses to a Spread Shock
Figure 8:
Output Growth
Aggregate Hours
0
Percent Annualized
Percent Annualized
0.2
0
−0.2
−0.4
−0.6
−0.8
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
12
0
−0.05
−0.1
−0.15
0
4
Interest Rate
8
12
Spread
0.4
Percent Annualized
0
Percent Annualized
12
0.05
−0.05
−0.05
−0.1
−0.15
−0.2
−0.25
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
20
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Figure 9: Responses to an MEI Shock
Figure 9:
Output Growth
Aggregate Hours
1
Percent Annualized
Percent Annualized
1.5
1
0.5
0
0
4
8
0.8
0.6
0.4
0.2
0
12
0
Labor Share
Percent Annualized
Percent
0.2
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
0.25
0
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
0.15
0.1
0.05
0
0
4
8
12
21
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Figure 10: Responses to a TFP Shock
Figure 10:
Output Growth
Aggregate Hours
1.5
Percent Annualized
Percent Annualized
2
1.5
1
0.5
0
−0.5
0
4
8
1
0.5
0
−0.5
12
0
Labor Share
Percent Annualized
Percent
0
−0.4
−0.6
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
−0.2
0.1
0.05
0
−0.05
8
Core PCE Inflation
0.2
−0.8
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
0.06
0.04
0.02
0
0
4
8
12
22
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Figure 11: Responses to a Mark-up Shock
Figure 11:
Output Growth
Aggregate Hours
0.2
Percent Annualized
Percent Annualized
0.2
0
−0.2
−0.4
−0.6
−0.8
0
4
8
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
FRBNY DSGE Group, Research and Statistics
0
−0.01
−0.02
0
4
8
12
23
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Figure 12: Responses to a Monetary Policy Shock
Figure 12:
Output Growth
Aggregate Hours
0
Percent Annualized
Percent Annualized
0.5
0
−0.5
−1
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
8
Core PCE Inflation
0
−0.2
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
0.01
0
−0.01
−0.02
−0.03
0
4
8
12
24
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Figure 13: Responses to a Labor Supply Shock
Figure 13:
Output Growth
Aggregate Hours
0
Percent Annualized
Percent Annualized
0.2
0
−0.2
−0.4
−0.6
−0.8
0
4
8
−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
25
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Figure 14: Responses to a Government Spending Shock
Figure 14:
Output Growth
Aggregate Hours
0.4
Percent Annualized
Percent Annualized
1
0.5
0
−0.5
0
4
8
0.3
0.2
0.1
0
12
0
Labor Share
Percent Annualized
Percent
0.1
0.05
0
4
8
0.04
0.03
0.02
0.01
0
12
0
4
Interest Rate
8
12
Spread
0
Percent Annualized
0.08
Percent Annualized
12
0.05
0.15
0.06
0.04
0.02
0
8
Core PCE Inflation
0.2
0
4
0
4
8
12
FRBNY DSGE Group, Research and Statistics
−0.005
−0.01
−0.015
−0.02
0
4
8
12
26
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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] Campbell, Jeff R., Jonas D. Fisher, and Alejandro Justiniano, “Monetary Policy Forward Guidance and the Business Cycle,” Federal Reserve Bank of
Chicago Working Paper, 2012.
[4] 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.
[5] Christiano, Lawrence, Roberto Motto, and Massimo Rostagno, “Financial Factors in Economic Fluctuations,” Unpublished, 2009.
[6] Laseen, Stefan and Lars E. O. Svensson, “Anticipated Alternative
Instrument-Rate Paths in Policy Simulations,” NBER Working Paper No. w14902,
2009.
[7] 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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