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Authorized for public release by the FOMC Secretariat on 1/8/2021
BOARD
OF
GOVERNORS
OF THE
FEDERAL RESERVE SYSTEM
DIVISION OF MONETARY AFFAIRS
FOMC SECRETARIAT
Date:
March 9, 2015
To:
Research Directors
From:
Matthew M. Luecke
Subject: Supporting Documents for DSGE Models Update
The attached documents support the update on the projections of the DSGE
models.
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System DSGE Project: Research Directors Drafts
March 9, 2015
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The Current Outlook in EDO: March FOMC Meeting
(Class II – Restricted FR)
Manuel Gonzalez-Astudillo∗
March 4, 2015
1
The EDO Forecast from 2015 to 2017
Given recent data (including expectations for the federal funds rate), the EDO model projects
real GDP growth slightly higher on average than its trend of 2.7 percent in 2015. Subsequently,
real GDP growth declines to an average 21/2 percent through the end of the forecast period. The
unemployment rate rises to 53/4 percent by the end of 2015 and continues rising to reach 61/4 percent
by the end of 2017. (Figures 1 and 3).1 Inflation runs below the Committees 2 percent objective,
averaging around 11/2 percent over the next three years.
The lackluster growth of GDP in 2016 and 2017 is the product of two offsetting forces. First,
the combination of weak growth in consumption along with relatively high real short-term interest
rates has led the model to estimate a relatively elevated aggregate risk premium, the models main
cyclical driver. All else equal, GDP growth would rise above trend as this risk premium converges
to its historical average. However, the model also interprets the market-expected path of the federal
funds rate as unusually accommodative, given the expected state of the economy and the estimated
monetary policy reaction function. Although these lower-than-expected interest rates boost the
current level of real GDP, these effects vanish over the medium term, lowering GDP growth. In
the current forecast, these two forces are balanced, leading to roughly trend GDP growth. In the
near-term, the model has interpreted the decline in oil prices as a short-lived price markup shock,
boosting GDP growth over the second and third quarters of 2015.
∗ Manuel Gonzalez-Astudillo (manuel.p.gonzalez-astudillo@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 Hess Chung and Jean-Philippe Laforte.
1 The baseline forecast for EDO is conditioned on the staff’s preliminary January 2015 Tealbook projection through
2015:Q1 and market expectations that the federal funds rate will remain at its effective lower bound through the second
quarter of 2015 (as indicated by OIS market prices). We do not impose an unemployment or inflation threshold on
the monetary policy rule.
The model’s static structural parameters have been re-estimated using data through 2014:Q3. In particular, the new
estimates incorporate the latest comprehensive revision to NIPA data. For estimation, the observable corresponding
to the model’s concept of investment excludes spending on intellectual property products.
1
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Figure 1: Recent History and Forecasts
EDO Projection Summary
Real GDP
Core PCE price index
Percent change, a.r.
6
6
4
4
2
2
0
0
-2
-2
-4
-4
Percent change, a.r.
2.5
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
-2.0
-6
2012
2013
2014
2015
2016
-6
2017
2.5
2.0
-2.5
-2.0
2012
2013
2014
2015
2016
2017
-2.5
Federal Funds Rate
Percent
5
5
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
2012
2013
2014
2015
2016
2017
-5
2015
Q4/Q4
Real GDP (a)
Credible set (c)
Federal Funds Rate (b)
Credible set (c)
2017
Q4/Q4
2.8
2.3
2.6
.3-5.5
.5-4.0
.5-4.4
Core PCE Price index (a) 1.2
Credible set (c)
2016
Q4/Q4
.8-1.5
1.6
1.9
.9-2.2
1.1-2.4
0.5
1.2
1.9
.0-1.6
.0-3.2
.3-3.7
(a) Q4/Q4 percent change, (b) Q4 level, (c) 68 percent
Red, solid line -- Data (through 2015:Q1) and projections; Blue, solid line -- Previous projection (December, 2014, as of 2014:Q4); Black, dashed line -- Steady-state or trend values
Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Green -- Other
The gradual increase in projected inflation over the forecast horizon is driven by the rebound of
wages following negative markup shocks and a slow return of household labor supply preferences to
long-run levels. Even so, 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 through
early 2015, driven largely by the weak demand conditions. By the end of the forecast, however, a
substantial portion of the elevated unemployment rate is accounted for by 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 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.
2
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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
Figure 2: Model Overview
Specifically, the model possesses two final good sectors in order to capture key long-run growth
facts and to differentiate between the cyclical properties of different categories of durable expenditure (e.g., housing, consumer durables, and nonresidential investment). For example, technological
progress has been faster in the production of business capital and consumer durables (such as computers and electronics).
The disaggregation of production (aggregate supply) leads naturally to some disaggregation of
expenditures (aggregate demand). We move beyond the typical model with just two categories of
(private domestic) demand (consumption and investment) and distinguish between four categories
of private demand: consumer non-durable goods and non-housing services, consumer durable goods,
residential investment, and non-residential investment. The boxes surrounding the producers in the
3 Chung, Kiley, and Laforte (2011) provide much more detail regarding the model specification, estimated parameters, and model propeties.
3
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figure illustrate how we structure the sources of each demand category. Consumer non-durable goods
and services are sold directly to households; consumer durable goods, residential capital goods, and
non-residential capital goods are intermediated through capital-goods intermediaries (owned by the
households), who then rent these capital stocks to households. Consumer non-durable goods and
services and residential capital goods are purchased (by households and residential capital goods
owners, respectively) from the first of economy’s two final goods producing sectors, while consumer
durable goods and non-residential capital goods are purchased (by consumer durable and residential
capital goods owners, respectively) from the second sector. In addition to consuming the non-durable
goods and services that they purchase, households supply labor to the intermediate goods-producing
firms in both sectors of the economy.
The 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, first, an aggregate risk-premium, or natural rate of interest, shock driving a
wedge between the short-term policy rate and the interest rate faced by private decisionmakers
(as in Smets and Wouters (2007)) and, second, fluctuations in the discount factor/risk premia faced by 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
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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)
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:
∞
X
cnn
E0 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 in the early 2000s recession and the most recent
downturn. Many other models do not distinguish between developments across these categories of
spending.
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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
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
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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
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
Black, solid line -- Data (through 2014:Q4) 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
4 Specifically, the risk premia enter EDO to a first-order (log)linear approximation in the same way as in the cited
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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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
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
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real economic activity. In addition, the presence of both price and wage rigidities implies that
stabilization of inflation is not, in general, the best possible policy objective (although a primary
role for price stability in policy objectives remains).
Given the widespread use of the New-Keynesian Phillips curve, it is perhaps easiest to consider
the form of the price and wage Phillips curves in EDO at the estimated parameters. The price
Phillips curve (governing price adjustment in both productive sectors) has the form:
p,s
p,s
+ .017mcst + θts
+ 0.76Et πt+1
πtp,s = 0.22πt−1
(3)
where mc is marginal cost and θ is a markup shock. As the parameters indicate, inflation is
primarily forward-looking in EDO.
The wage (w) Phillips curve for each sector has the form:
s
s
s
w
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
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(5)
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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:
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.
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• A labor supply shock: This shock affects the willingness 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.
• 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
Estimation: Data and Properties
3.1
Data
The empirical implementation of the model takes a log-linear approximation to the first-order conditions and constraints that describe the economy’s equilibrium, casts this resulting system in its
state-space representation for the set of (in our case 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 );
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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
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 at 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,
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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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
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−0.025
−0.12
5
10
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5
10
15
20
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
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
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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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.
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
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
2000
2000
1990
2000
2010
1990
2000
2010
1990
2000
2010
2
1
0
−1
−2
2010
1
1
Risk−premium
1990
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
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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
economy-wide and for housing, as key drivers.
Of course, these stories from a glance at the exogenous drivers yield applications for alternative
versions of the EDO model and future model enhancements. For example, the exogenous risk
premia can easily be made to have an endogenous component following the approach of Bernanke,
Gertler, and Gilchrist (1999) (and indeed we have considered models of that type). At this point
we view incorporation of such mechanisms in our baseline approach as premature, pending ongoing
research on financial frictions, banking, and intermediation in dynamic general equilibrium models.
Nonetheless, the EDO model captured the key financial disturbances during the last several years
in its current specification, and examining the endogenous factors that explain these developments
will be a topic of further study.
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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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FRBNY DSGE Model: Research Directors Draft
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Summary of the Forecasts
The FRBNY model forecasts are obtained using a new version of the FRBNY DSGE model,
which builds on the New Keynesian model with financial frictions used in Del Negro et al.
(2015). This model has been shown to provide a reasonable explanation for the behavior of
inflation in the aftermath of the Great Recession, and relatively accurate forecasts of output
growth and inflation throughout recent history (see Del Negro et al. (2014) and Del Negro
and Schorfheide (2012)). Relative to the previous FRBNY model, the set of observable
indicators is augmented with data on consumption and investment growth, survey-based
long-run inflation expectations, which provide information on the publics perception of the
central banks inflation objective, and the 10-year Treasury yield, in order to incorporate
information about long-term rates. In addition, the model is estimated using two distinct
measures of inflation: the GDP deflator and core PCE inflation. Finally, the model allows
for persistent shocks to both the level and the growth rate of productivity, in an attempt to
allow for the possibility of secular stagnation, and uses John Fernald’s estimate of the growth
rate of productivity as an observable. The model produces estimates and forecasts of the
so-called natural level of output and rate of interest – which we define as output and interest
rate obtained in the absence of nominal rigidities, markup shocks, and financial frictions.
These quantities, which are not directly observable, inform us about the stance of monetary
policy. The attached Model Documentation provides more details on the model.
The FRBNY model forecasts are obtained using data released through 2014Q4, augmented for 2015Q1 with the FRBNY staff forecasts 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 2015Q1 observations. The expected federal funds rate is constrained to equal market expectations, as measured by OIS
rates, through 2015Q2. This constraint is implemented via anticipated policy shocks. The
2015Q1 staff projections, OIS rates and spreads are those that were available on February
27.
The FRBNY DSGE forecast for output growth is slightly stronger than it was in December. The model projects the economy to grow 2.4 percent in 2015 and 2.3 percent in 2016
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and 2017. The headwinds that slowed down the economy in the aftermath of the financial
crisis are finally abating, resulting in an increase of the natural rate of interest toward positive ranges and a gradual closing of the output gap – the difference between output and
natural output. The gap is closing only slowly, however. Moreover, the models estimate of
firms marginal costs suggests that these have not recovered much over the last few years,
due to the weakness in real wage growth. As a consequence, inflation projections are weak:
core PCE inflation is expected to remain below 1.5 percent until the end of 2017. Note that
increases in future real wages and marginal costs, far from being a warning sign of impending
inflationary pressures, are actually a necessary condition for this (albeit slow) convergence
of inflation towards the FOMC long-run objective. In the absence of accelerating wages,
inflation projections would be even weaker.
The change in inflation forecasts relative to December reflects both weak inflation data
since December and the switch to the new version of the model. In terms of inflation
forecasts, the new model differs from the old one in two dimensions. First, it features more
persistence in inflation, which is largely endogenous and due to the fact that the output gap
closes very gradually. Second, it features more persistent mark-up shocks. This is because
mark-up shocks no longer have to capture the substantial high frequency noise in quarterly
core inflation, given that inflation is measured as the common factor between core PCE
inflation and the GDP deflator. In terms of the current forecast, this implies that mark-up
shocks, which capture declines in oil prices and have recently been large, have a relatively
prolonged effect on inflation.
The model projects the federal funds rate to reach 2.4 percent by the end of 2017, well
below its steady state value. This relatively shallow path after lift-off is mostly driven by the
endogenous response of policy to weak inflation, according to the historical reaction function
estimated by the model. However, past forward guidance on interest rates, which is estimated
to have provided consistent support to GDP growth and inflation over the last several years,
also contributes to maintaining a lower expected future federal funds rates than is implied
by the historical reaction function. The estimated natural real rate of interest has been well
below the actual real rate during and after the crisis, indicating that the zero lower bound
imposed a constraint on interest-rate policy. Currently, the natural rate is close to, but still
below, the actual real rate, suggesting that policy is still not particularly accommodative.
Uncertainty around the forecasts is significant, particularly for GDP growth. The width
of the 68 percent probability interval for GDP growth is 3.8 percentage points in 2015,
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ranging from -0.1 to 3.7 percent, and widens to 5.2 percentage points in 2017 – from -0.3 to
4.9 percent. The 68 percent probability intervals for inflation remain relatively tight, ranging
from 0.4 to 1.4 percent in 2015 and from 0.5 to 2.2 percent in 2017.
1
The Model and Its Transmission Mechanism
General Features of the Model
The FRBNY DSGE model is a medium scale, one-sector dynamic stochastic general equilibrium model which is based on the New Keynesian model with financial frictions used in Del
Negro et al. (2015). The core of the model is based on the work of Smets and Wouters (2007)
and Christiano et al. (2005): It builds on the neo-classical growth model by adding nominal wage and price rigidities, variable capital utilization, costs of adjusting investment, and
habit formation in consumption. The model also includes credit frictions as in the financial
accelerator model developed by Bernanke et al. (1999), where the actual implementation
of the credit frictions follows closely Christiano et al. (2014), and a time-varying inflation
target following Del Negro and Schorfheide (2012). In contrast to these papers, the model
features both a deterministic and a stochastic trend in productivity. Finally, it accounts for
forward guidance in monetary policy by including anticipated policy shocks as in Laseen and
Svensson (2011).
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
numerous quarterly data series: real GDP growth, real consumption growth, real investment
growth, real wage growth, hours worked, inflation in the personal consumption expenditures
deflator and inflation in the GDP deflator, the federal funds rate (FFR), the 10-year nominal Treasury bond yield, 10-year survey-based inflation expectations, credit spreads (Baa 10-year Treasury bond yield), and data on total factor productivity. In addition, since 2008,
we use market expectations of future federal funds rates. Model parameters are estimated
from 1960Q1 to the present using Bayesian methods.
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
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the shocks that affect the dynamics of this economy.)
Households derive utility from leisure, supply labor services to firms, and set wages in
a monopolistically competitive fashion. The labor market is subject to frictions because of
nominal wage rigidities. In addition, we allow for exogenous disturbances to wage markups, labeled “wage mark-up” shocks, which capture exogenous changes in the degree of
competitiveness in the labor market, or other exogenous movements in the labor supply.
Households, who discount future utility streams, also have to choose how much to consume and save. Their savings take the form of deposits to banks and purchases of government bills. Household preferences feature habit persistence, a characteristic that affects their
consumption smoothing decisions. In addition, “discount factor” shocks drive an exogenous
wedge between the change in the marginal utility of consumption and the riskless real return.
These shocks possibly capture phenomena like deleveraging, or increased risk aversion.
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, which affect both the temporary and the permanent component of the level of total
factor productivity. Intermediate goods markets are subject to price rigidities. Together with
wage rigidities, this friction is quite important in allowing demand shocks to be a source of
business cycle fluctuations, as countercyclical mark-ups induce firms to produce less when
demand is low. Inflation evolves in the model according to a standard, forward-looking
New Keynesian Phillips curve with indexing, which determines inflation as a function of
marginal costs, expected future inflation, past inflation, and “price mark-up” shocks. Markup 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 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
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loans to all entrepreneurs and charging a spread over the deposit rate. Such spreads vary
endogenously as a function of the entrepreneurs’ leverage, but also exogenously depending
on the entrepreneurs’ riskiness. Specifically, mean-preserving changes in the volatility of
entrepreneurs’ idiosyncratic shocks lead to variations in the spread (to compensate banks for
changes in expected losses from individual defaults). We refer to these exogenous movements
as “spread” shocks. Spread shocks capture financial intermediation disturbances that affect
entrepreneurs’ borrowing costs. Faced with higher borrowing costs, entrepreneurs reduce
their demand for capital, and investment drops. With lower aggregate demand, there is
a contraction in hours worked and real wages. Wage rigidities imply that hours worked
fall even more (because nominal wages do not fall enough). Price rigidities mitigate price
contraction, further depressing aggregate demand.
Capital producers transform general output into capital goods, which they sell to the entrepreneurs. Their production function is subject to investment adjustment costs: producing
capital goods is more costly in periods of rapid investment growth. It is also subject to exogenous changes in the “marginal efficiency of investment” (MEI). These MEI shocks capture
exogenous movements in the productivity of new investments in generating new capital. A
positive MEI shock implies that fewer resources are needed to build new capital, leading to
higher real activity and inflation, with an effect that persists over time. Such MEI shocks
reflect both changes in the relative price of investment versus that of consumption goods
(although the literature has shown the effect of these relative price changes to be small), and
most importantly financial market imperfections that are not reflected in movements of the
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 mark-up shocks which have also a
moving-average component, disturbances to government spending which are allowed to be
correlated with total factor productivity disturbances, and exogenous disturbances to the
monetary policy rule, or “policy” shocks, which are assumed to be i.i.d.
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Figure 1: Model Structure
productivity shocks
Firms
wage
rigidities
utilization
capital
wage mark-up
shocks
intermediate goods
price
rigidities
mark-up
shocks
labor
MEI
shocks
Capital
Producers
investment
adjustment
costs
Final Goods
Producers
investment
Entrepreneurs
consumption
disc. factor
shocks
Banks
loans
credit
frictions
spread shocks
deposits
Households
bills
habit
persistence
Government
interest rate
policy
policy
shocks
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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 10 to 15.
We start with the shocks most closely associated with the Great Recession and the
severe financial crisis that characterized it: the discount factor shock and the spread shock.
The discount factor shock reflects the sudden desire by households to cut down on their
consumption and save more. This may capture the fact that households want to reduce
their debt level, or their increased pessimism about future economic conditions. Figure
10 shows the impulse responses of the variables used in the estimation to a one-standarddeviation innovation in the spread shock. Such a shock results in a decline in consumption
(fourth panel in left column), and hence in aggregate demand, which leads to a decrease
in output growth (top left panel), hours worked (top right panel), and real wage growth.
The implied reduction in marginal costs induces measures of inflation to fall (see inflation
of GDP and PCE deflators, in second and third rows). In addition, the discount factor
shock implies an increase in credit spread (fifth panel in left row) which causes investment
growth to contract. Monetary policy typically attempts to mitigate the decline in activity
and inflation by lowering the FFR, but is unable to fully offset the shock.
The other key shock, the spread 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 ratio
of the Baa corporate bond rate to the 10-year Treasury yield, and the spread’s comovement
with output growth, inflation, and the other observables. Figure 11 shows the impulse
responses to a one-standard-deviation innovation in the spread shock. An innovation of this
size increases the observed spread by roughly 25 basis points (fifth panel in left column).
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
barely higher than at the trough four 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 less than three years
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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 (bottom left panel). The persistent drop in the
level of economic activity due to the spread shock also leads to a prolonged decline in real
marginal costs, and, via the New Keynesian Phillips curve, in inflation. Finally, policymakers
endogenously respond to the change in the inflation and real activity outlook by cutting the
federal funds rate (right panel on the third row).
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. The impulse responses to MEI shocks, shown
in Figure 12, also feature a decrease in investment, output and hours worked, as well as in
real wages, although these are less persistent than in the case of spread shocks. Inflation
responds little however, as marginal costs are expected revert back to steady state relatively
quickly. One key difference between the responses to spread and MEI shocks which 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 is the stationary TFP shock
(the model features shocks to both the level and the growth rate of productivity – we discuss
here the former). As shown in Figure 13, 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 offsetting 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.
The last shock that plays a relevant role in the current economic environment is the price
mark-up shock, whose impulse response is depicted in Figure 14. 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
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less persistence. GDP growth falls on impact after mark-ups increase, but returns above
average after about one year, and the effect on the level of output is absorbed in a little
over four years. 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 passthrough 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
2015 (Q4/Q4)
March
December
0.9
1.1
(0.4,1.4)
(0.4,1.6)
2.4
2.6
(-0.0,3.9) (-0.2,4.8)
Unconditional Forecast
2016 (Q4/Q4)
2017 (Q4/Q4)
March
December
March
December
1.1
1.5
1.4
1.8
(0.3,1.8)
(0.7,2.2)
(0.5,2.2)
(1.0,2.6)
2.3
2.0
2.3
1.9
(-0.6,4.6) (-1.2,5.0) (-0.3,4.8) (-1.4,5.2)
2018 (Q4/Q4)
March
December
1.6
2.0
(0.7,2.4)
(1.2,2.8)
2.3
2.0
(-0.3,5.1) (-1.2,5.4)
Core PCE
Inflation
Real GDP
Growth
2015 (Q4/Q4)
March
December
0.9
1.2
(0.4,1.4)
(0.6,1.8)
2.4
2.0
(-0.1,3.7) (-0.9,4.1)
Conditional Forecast*
2016 (Q4/Q4)
2017 (Q4/Q4)
March
December
March
December
1.1
1.5
1.4
1.8
(0.3,1.9)
(0.8,2.2)
(0.5,2.2)
(1.0,2.6)
2.3
1.9
2.3
1.9
(-0.6,4.6) (-1.4,4.9) (-0.3,4.9) (-1.4,5.2)
2018 (Q4/Q4)
March
December
1.6
2.0
(0.7,2.4)
(1.2,2.8)
2.3
2.1
(-0.3,5.1) (-1.2,5.5)
*The unconditional forecasts use data up to 2014Q4, the quarter for which we have the most recent GDP release, as well as the
federal funds rate and spreads data for 2015Q1. In the conditional forecasts, we further include the 2015Q1 FRBNY projections
for GDP growth, core PCE inflation, and growth in total 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 2014-2017: real GDP
growth, core PCE inflation and the federal funds rate. To obtain the forecast we set federal
funds rate expectations equal to market expectations for the federal funds rate (as measured
by OIS rates) through 2015Q2. We capture policy anticipation by adding anticipated monetary policy shocks to the central bank’s reaction function starting in 2008Q4, the beginning
of the zero bound period, as in Laseen and Svensson (2011). We estimate the standard
deviation of the anticipated shocks as in Campbell et al. (2012), but use only post-2008Q4
data.
The table above presents Q4/Q4 forecasts for real GDP growth and inflation for 20142017, with 68 percent probability intervals. We include two sets of forecasts. The unconditional forecasts use data up to 2014Q4, the quarter for which we have the most recent GDP
release, as well as the federal funds rate and spreads data for 2015Q1 (we use the average
realizations for the quarter up to the forecast date). In the conditional forecasts, we further include the 2015Q1 FRBNY staff projections for GDP growth, core PCE inflation, and
hours worked as additional data points (as of February 27, quaterly annualized projections
for 2015Q1 are 2.5 percent for output growth and 0.9 percent for core PCE inflation). Treating the 2015Q1 staff forecasts as data allows us to incorporate information about the current
quarter into the DSGE forecasts for the subsequent quarters. In addition to providing the
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current forecasts, the table reports the forecasts included in the DSGE memo forwarded to
the FOMC in advance of its December 2014 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 of the daily series. The bands reflect both parameter and shock uncertainty. Figure
3 compares the current forecasts with the December forecasts. Our discussion will mainly
focus on the conditional forecasts, which are those reported in the memo to the FOMC.
The FRBNY DSGE forecast changed substantially since December, especially for inflation, as shown in Figure 3. The trajectory of output is a bit stronger in 2016 and 2017,
while inflation is weaker throughout the forecast horizon. Relative to December, the GDP
growth forecast for 2015 (Q4/Q4) increased from 2.0 to 2.4, and the forecasts for 2016 and
2017 (Q4/Q4) are both at around 2.3 percent. For inflation, the mean core PCE inflation
for 2015 is projected to be 0.9 percent, lower than the 1.2 percent projected in December.
Inflation returns closer to the long term objective of 2 percent over the forecast horizon, but
more gradually than in December. The point forecasts are 1.1 for 2016 and 1.4 for 2017,
below the December point forecasts.
The change in the forecasts is mainly due to the change in the model as opposed to the
new data. Figure 4 shows in fact the change in the forecast that are due to the data only, as
it uses the “old” model for both forecasts. The differences are very small, and largely affect
only core PCE inflation projections in the short run. Figure 5 repeats the same exercise
using the “new” model, and reaches the same conclusions. Note however that changes in
the core inflation forecast in the new model are more persistent than under the old model
– a point we will return to later. Finally, Figure 6 shows the comparison between forecasts
obtained with the old and the new version of the FRBNY model, where both model use
the most recent data. The comparison reinforces the point that projections for inflation
are weaker under the new version. In regard to inflation forecasts, the new model differs
from the old one in two dimensions. First, it features more persistence in inflation, which is
largely endogenous and due to the fact that the output gap closes very gradually. Second, it
features more persistent mark-up shocks. This is because mark-up shocks no longer have to
capture the substantial high frequency noise in quarterly core inflation, given that inflation
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is measured as the common factor between core PCE inflation and the GDP deflator. In
terms of the current forecast, this implies that mark-up shocks, which capture declines in
oil prices and have recently been large, have a relatively prolonged effect on inflation, as
discussed in the next section.
Uncertainty around the real GDP growth, as measured by the 68 percent bands, has
diminished somewhat for output and is roughly unchanged for inflation. For GDP growth,
the 68 percent bands cover the intervals -0.1 to 3.7 percent in 2015, -0.6 to 4.6 in 2016, and
-0.3 to 4.9 in 2017. For inflation, the 68 percent probability bands range from 0.5 to 2.2
percent throughout 2017.
As mentioned above, we constrain the federal funds rate expectations through 2015Q2
to be equal to the expected federal fund rate as measured by the OIS rates on February 27;
after that the federal funds rate rises gradually and is forecasted to be around 1 3/4 percent
at the end of 2016 and around 2.4 percent by the end of 2017.
Finally, note that the March conditional and unconditional forecasts are very close to one
another, indicating that the nowcast for 2015Q1 is in line with the DSGE model predictions.
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Figure 2: Forecasts
5
0
0
−5
−5
2007
2009
2011
2013
2015
2017
Core PCE Inflation
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Output Growth
5
5
0
0
−5
−5
Percent Q−to−Q Annualized
5
Percent Q−to−Q Annualized
Conditional
Output Growth
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Unconditional
2007
2009
2
2
2013
2015
2017
0
Percent Annualized
Percent Annualized
4
2011
2015
2017
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Interest Rate
4
2009
2013
Core PCE Inflation
Interest Rate
0
2007
2011
4
4
2
2
0
2007
2009
2011
2013
2015
2017
0
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
5
0
0
−5
−5
2007
2009
2011
2013
2015
2017
Core PCE Inflation
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Output Growth
5
5
0
0
−5
−5
Percent Q−to−Q Annualized
5
Percent Q−to−Q Annualized
Conditional
Output Growth
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Unconditional
2007
2009
4
4
3
3
2
2
1
1
2013
2015
2017
Percent Annualized
Percent Annualized
5
2011
2015
2017
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Interest Rate
5
2009
2013
Core PCE Inflation
Interest Rate
2007
2011
5
5
4
4
3
3
2
2
1
1
2007
2009
2011
2013
2015
2017
Solid (dashed) red and blue lines represent the mean and the 90 percent probability intervals of the current (previous) forecast.
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Figure 4: Change in Forecasts: Old Model, March
2015 vs. December 2014 Data
5
0
0
−5
−5
2007
2009
2011
2013
2015
2017
Core PCE Inflation
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Output Growth
5
5
0
0
−5
−5
Percent Q−to−Q Annualized
5
Percent Q−to−Q Annualized
Conditional
Output Growth
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Unconditional
2007
2009
4
4
3
3
2
2
1
1
2013
2015
2017
Percent Annualized
Percent Annualized
5
2011
2015
2017
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Interest Rate
5
2009
2013
Core PCE Inflation
Interest Rate
2007
2011
5
5
4
4
3
3
2
2
1
1
2007
2009
2011
2013
2015
2017
Solid (dashed) red and blue lines represent the mean and the 90 percent probability intervals of the current (previous) forecast.
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Figure 5: Change in Forecasts, New Model, March
2015 vs. December 2014 Data
5
0
0
−5
−5
2007
2009
2011
2013
2015
2017
Core PCE Inflation
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Output Growth
5
5
0
0
−5
−5
Percent Q−to−Q Annualized
5
Percent Q−to−Q Annualized
Conditional
Output Growth
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Unconditional
2007
2009
4
2
2
2013
2015
2017
Percent Annualized
Percent Annualized
4
2011
2015
2017
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Interest Rate
6
2009
2013
Core PCE Inflation
Interest Rate
6
2007
2011
6
6
4
4
2
2
2007
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2009
2011
2013
2015
2017
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Figure 6: New vs. Old Model Forecasts, March 2015
Data
5
0
0
−5
−5
2007
2009
2011
2013
2015
2017
Core PCE Inflation
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Output Growth
5
5
0
0
−5
−5
Percent Q−to−Q Annualized
5
Percent Q−to−Q Annualized
Conditional
Output Growth
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Unconditional
2007
2009
4
4
3
3
2
2
1
1
2013
2015
2017
Percent Annualized
Percent Annualized
5
2011
2015
2017
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Interest Rate
5
2009
2013
Core PCE Inflation
Interest Rate
2007
2011
5
5
4
4
3
3
2
2
1
1
2007
2009
2011
2013
2015
2017
Solid (dashed) red and blue lines represent the mean and the 90 percent probability intervals of the current (previous) forecast.
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Interpreting the Forecasts
We use the shock decomposition shown in Figure 7 to interpret the forecasts. This figure
quantifies the importance of the most important shocks 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. We should note that the impact of some shocks
have been aggregated. For example, the “financial” shock (purple) captures both shocks to
the spread as well as shocks to the discount factor.
The dynamics behind the FRBNY DSGE forecast can be described as follows. The
headwinds from the financial crisis, which are captured in the model by the contribution of
the financial (purple) and MEI (azure) shocks, are finally waning, implying that both shocks
have a positive contribution on output growth. Figure 8 shows the output gap – the difference
between output and its “natural” level (the counterfactual level of output in absence of
nominal rigidities, mark-up shocks, and financial frictions) – and the corresponding “natural”
rate of interest through history. The natural interest rate remains below zero, but has risen
recently consistently with the waning of the headwinds from the financial crisis.
The impact of financial shocks on the level of output is still negative throughout the
forecast horizon, however, as can be inferred from their negative contribution to inflation.
In fact, Figure 7 shows that financial shocks are mostly responsible for the slow return of
inflation to the 2 percent target, and for the interest rate being below its steady state value.
The output gap, which is shown in Figure 8, remains negative and closes only gradually.
Financial shocks are mostly responsible for that.
While total factor productivity shocks contributed negatively to economic activity in late
2007 and 2008, these shocks have instead pushed GDP up significantly in 2009 and 2010.
In addition, over the past several years, the negative impact of the headwinds mentioned
above has been partly compensated by expansionary monetary policy. In particular, forwardguidance about the future path of the federal funds rate (captured here by anticipated policy
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shocks) has played an important role in counteracting these headwinds, lifting both output
and inflation. However, the positive effect of this policy accommodation on the level of output
has been negligible over the most recent quarters. Since monetary policy is neutral in the
long run in this model, the impact of policy accommodation on the level of output will wane
eventually, and has already begun to do so by the end of 2014, implying a negative effect
on growth. As a consequence of forward guidance the renormalization path is somewhat
slower than that implied by the estimated rule, as indicated by the yellow bars in the shock
decomposition for interest rates. The comparison between the estimated natural real rate
of interest and the actual real rate of interest, shown in Figure 8, is also revealing in regard
to the stance of policy. The natural rate of interest has been well below the actual real rate
during and after the crisis, indicating that the zero lower bound imposed a constraint on
interest-rate policy. Currently, the natural rate is close to, but still below, the actual real
rate, suggesting that policy is still not particularly accommodative.
The shock decomposition for inflation also shows that mark-up shocks (green bars),
which capture the effect of exogenous changes in marginal costs such as those connected
with fluctuations in commodity prices, play an important role. As explained above, these
shocks tend to have a fairly persistent impact on inflation. Recent negative mark-up shocks,
likely reflecting declines in oil prices, contribute to push inflation down relative to target by
at least half of a percentage point during the current year and the next one. Moreover, the
positive productivity shocks registered in the immediate aftermath of the Great Recession,
have had a negative and persistent impact on inflation.
Finally, Figure 9 shows unconditional (left panels) and conditional (right panels) forecasts
that do not incorporate federal funds rate expectations (dashed lines) as well as our baseline
forecasts (solid lines), which do. The figure shows that the impact of incorporating these
expectations is very small.
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Figure 7: Shock Decomposition
Percent Q−to−Q Annualized
Output Growth
(deviations from mean)
0
0
−5
−5
−10
2007
−10
2018
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
2007
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Core PCE Inflation
(deviations from mean)
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
−1.5
2018
Interest Rate
(deviations from mean)
0
0
−2
−2
−4
2007
2008
2009
2010
Gov’t
2011
Financial
2012
TFP
2013
2014
Mark−Up
2015
Policy
2016
2017
−4
2018
MEI
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 8: Output Gap and the Natural Interest Rate
Output Gap
10
10
8
8
6
6
4
4
2
2
0
0
−2
−2
−4
−4
−6
−6
−8
−8
−10
1960
1970
1980
1990
2000
2010
−10
Natural Rate & Ex-Ante Real Rate
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Figure 9: Effect of Incorporating FFR Expectations
5
0
0
−5
−5
2007
2009
2011
2013
2015
2017
Core PCE Inflation
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Output Growth
5
5
0
0
−5
−5
Percent Q−to−Q Annualized
5
Percent Q−to−Q Annualized
Conditional
Output Growth
Percent Q−to−Q Annualized
Percent Q−to−Q Annualized
Unconditional
2007
2009
2
2
0
0
2013
2015
2017
Percent Annualized
Percent Annualized
4
2011
2015
2017
3
3
2
2
1
1
0
0
2007
2009
2011
2013
2015
2017
Interest Rate
4
2009
2013
Core PCE Inflation
Interest Rate
2007
2011
4
4
2
2
0
0
2007
2009
2011
2013
2015
2017
Solid (dashed) red lines represent the mean for the forecast that does (does not) incorporate FFR expectations. Solid and
dashed blue lines represent the associated 90 percent probability intervals.
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Figure 10: Responses to a Discount Factor Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
1
0
−1
−2
−3
0
4
8
0
−2
−4
−6
12
0
4
0.1
0
−0.1
−0.2
−0.3
0
4
8
0
−0.2
−0.3
−0.4
12
0
4
Percent Annualized
Percent Annualized
−0.1
−0.2
−0.3
4
8
−0.5
−1
0
4
0
−1
−2
4
8
0
−1
−2
−3
12
0
4
Percent Annualized
Percent Annualized
0.5
4
8
0
−0.1
−0.15
−0.2
12
0
Percent Annualized
Percent Annualized
0
−0.2
−0.3
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
−0.1
0
12
−0.05
Long Rate
−0.4
8
Long Inf
1
0
12
1
Spread
0
8
Investment Growth
Percent Annualized
Percent Annualized
Consumption Growth
0
12
0
12
1
−3
8
Interest Rate
0
0
12
−0.1
Core PCE Inflation
−0.4
8
GDP Deflator
Percent Annualized
Percent Annualized
Real Wage Growth
0.2
0.1
0
−0.1
−0.2
12
0
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4
8
12
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Figure 11: Responses to a Spread Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.2
0.1
0
−0.1
−0.2
0
4
8
0.5
0
−0.5
−1
12
0
4
0
−0.01
−0.02
−0.03
−0.04
0
4
8
0.02
0
−0.02
12
0
4
Percent Annualized
Percent Annualized
0.02
0.01
0
4
8
0.05
0
−0.05
−0.1
0
4
Consumption Growth
Percent Annualized
Percent Annualized
0.2
0
4
8
0
−1
−2
−3
12
0
4
Percent Annualized
Percent Annualized
0.3
0.2
0.1
4
8
0.02
0.01
0
12
Percent Annualized
Percent Annualized
0.04
0.02
0
0
4
8
12
0.03
Long Rate
−0.02
8
Long Inf
0.4
0
12
1
Spread
0
8
Investment Growth
0.4
0
12
0.1
12
0.6
−0.2
8
Interest Rate
0.03
0
12
0.04
Core PCE Inflation
−0.01
8
GDP Deflator
Percent Annualized
Percent Annualized
Real Wage Growth
10
4
8
12
−3
Total
Factor Productivity, Util.Unadjusted
x 10
5
0
−5
12
0
0
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4
8
12
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Figure 12: Responses to an MEI Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.05
0
−0.05
−0.1
−0.15
0
4
5
x 10
−5
0
4
x 10
1
4
8
x 10
2
1
0
4
0
−0.02
Percent Annualized
Percent Annualized
−0.02
8
0
4
−0.5
Percent Annualized
Percent Annualized
−0.02
8
3
Percent Annualized
Percent Annualized
0.005
4
8
5
12
0
4
8
12
−3
Total
Factor Productivity, Util.Unadjusted
x 10
0
−5
−10
12
8
Long Inf
1
0
12
0.01
0
4
x 10
2
Long Rate
0
0
−3
−0.01
4
12
0
−1
12
0
0
8
0.5
Spread
−0.03
12
Investment Growth
0
4
8
0.02
Consumption Growth
0
12
3
−0.04
12
0.02
−0.04
8
GDP Deflator
Interest Rate
2
0
4
Core PCE Inflation
3
0
4
0
12
Percent Annualized
Percent Annualized
−3
8
0
−3
Real Wage Growth
−10
4
0
−0.2
−0.4
12
0
−15
0.2
Percent Annualized
Percent Annualized
−3
8
0.4
0
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Figure 13: Responses to a TFP Shock
Output Growth
Aggregate Hours
Percent Annualized
Percent Annualized
0.3
0.2
0.1
0
−0.1
0
4
15
x 10
−0.1
0
4
0
4
8
−0.005
−0.01
−0.015
12
0
4
Percent Annualized
Percent Annualized
−0.005
−0.01
4
8
−0.01
−0.02
−0.03
0
4
0.1
0
4
4
8
0
−0.05
12
0
0
4
8
0
0
−4
0
Percent Annualized
Percent Annualized
−0.005
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
0
0
12
−2
−6
12
8
Long Inf
x 10
Long Rate
−0.01
4
−3
Spread
2
−2
0.1
0.05
Percent Annualized
Percent Annualized
−3
12
Investment Growth
0.05
x 10
8
0.15
Percent Annualized
Percent Annualized
Consumption Growth
0
12
0
−0.04
12
0.15
−0.05
8
Interest Rate
0
0
12
0
Core PCE Inflation
−0.015
8
GDP Deflator
5
0
0
−0.05
Real Wage Growth
10
−5
0.05
12
Percent Annualized
Percent Annualized
−3
8
0.1
0.6
0.4
0.2
0
−0.2
12
0
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Figure 14: Responses to a Price Mark-up Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.6
0.4
0.2
0
−0.2
0
4
8
1
0.5
0
−0.5
12
0
4
0.6
0.4
0.2
0
−0.2
0
4
8
0
−0.2
−0.4
−0.6
12
0
4
Percent Annualized
Percent Annualized
0
−0.2
−0.4
4
8
0.1
0
−0.1
0
4
0.4
0.2
0
4
8
0.5
0
−0.5
12
0
4
Percent Annualized
Percent Annualized
0.02
0.01
4
8
0
−0.01
−0.02
12
0
Percent Annualized
Percent Annualized
0
−0.01
−0.02
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
0.01
0
12
0.01
Long Rate
−0.03
8
Long Inf
0.03
0
12
1
Spread
0
8
Investment Growth
Percent Annualized
Percent Annualized
Consumption Growth
0
12
0.2
−0.2
12
0.6
−0.2
8
Interest Rate
0.2
0
12
0.2
Core PCE Inflation
−0.6
8
GDP Deflator
Percent Annualized
Percent Annualized
Real Wage Growth
0.06
0.04
0.02
0
−0.02
12
0
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Figure 15: Responses to a Monetary Policy Shock
Output Growth
Aggregate Hours
Percent Annualized
Percent Annualized
0.6
0.4
0.2
0
−0.2
0
4
8
0.8
0.6
0.4
0.2
0
12
Percent Annualized
Percent Annualized
0.03
0.02
0.01
0
−0.01
0
4
6
x 10
0
4
8
x 10
4
2
0
0
4
−0.1
−0.15
−0.2
0
4
0
0
−0.5
12
Percent Annualized
Percent Annualized
0
−0.01
4
8
0
1
−1
0
Percent Annualized
Percent Annualized
0
−0.01
−0.015
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
−0.005
0
12
0
−2
12
8
Long Inf
x 10
Long Rate
−0.02
4
−3
0.01
0
12
0.5
Spread
−0.02
8
1
Percent Annualized
Percent Annualized
0.2
8
12
Investment Growth
0.4
4
8
−0.05
Consumption Growth
0
12
0
12
0.6
−0.2
8
GDP Deflator
Interest Rate
2
0
4
Core PCE Inflation
4
−2
6
−2
12
Percent Annualized
Percent Annualized
−3
8
0
−3
Real Wage Growth
0.03
0.02
0.01
0
−0.01
12
0
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Figure 16: Shock Histories
b
2
1
1
0
0
−1
−1
−2
2007
2008
2009
2010
2011
2012
2013
2014
Standard Deviations
Standard Deviations
g
2
−2
2015
2
2
0
0
−2
−2
−4
−4
2007
2008
2009
2010
µ
0
0
−1
−1
2008
2009
2010
2011
2012
2013
2014
Standard Deviations
Standard Deviations
2013
2014
2015
2
2
1
1
0
0
−1
−1
2007
2008
2009
2010
2011
2012
2013
2014
0
0
−1
−1
Standard Deviations
1
2
2
0
0
−2
−2
−4
2008
2009
2010
2011
2012
2013
2014
2015
2007
−4
2008
2009
2010
0.5
0.5
0
0
−0.5
−0.5
−1
−1
2010
2011
2012
2013
2014
2015
Standard Deviations
Standard Deviations
1
2009
2012
2013
2014
2015
w
1
2008
2011
σ
rm
2007
2015
λw
1
2007
2015
1
λf
Standard Deviations
2012
z
1
2007
2011
2
2
0
0
−2
−2
2007
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2009
2010
2011
2012
2013
2014
2015
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Figure 17: Anticipated Shock Histories
Ant 2
0.1
0.1
0
0
−0.1
Percent
Percent
Ant 1
0.1
0.1
0
0
−0.1
−0.1
−0.1
2007 2008 2009 2010 2011 2012 2013 2014 2015
2007 2008 2009 2010 2011 2012 2013 2014 2015
Ant 3
Ant 4
0.05
0
0
−0.05
−0.05
−0.1
−0.1
0
0
−0.05
−0.05
−0.1
−0.1
2007 2008 2009 2010 2011 2012 2013 2014 2015
2007 2008 2009 2010 2011 2012 2013 2014 2015
Ant 5
Ant 6
0.05
0.05
0
−0.05
−0.05
−0.1
−0.1
2007 2008 2009 2010 2011 2012 2013 2014 2015
Percent
0
Percent
0.05
0.05
Percent
Percent
0.05
0
0
−0.05
−0.05
−0.1
−0.1
2007 2008 2009 2010 2011 2012 2013 2014 2015
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References
Bernanke, B. S., M. Gertler, and S. Gilchrist (1999): “The Financial Accelerator
in a Quantitative Business Cycle Framework,” in Handbook of Macroeconomics, ed. by
J. B. Taylor and M. Woodford, Amsterdam: North-Holland, vol. 1C, chap. 21, 1341–93.
Campbell, J. R., J. D. Fisher, and A. Justiniano (2012): “Monetary Policy Forward
Guidance and the Business Cycle,” Federal Reserve Bank of Chicago Working Paper.
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities and
the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, 113,
1–45.
Christiano, L. J., R. Motto, and M. Rostagno (2014): “Risk Shocks,” American
Economic Review, 104, 27–65.
Del Negro, M., M. P. Giannoni, and F. Schorfheide (2015): “Inflation in the Great
Recession and New Keynesian Models,” American Economic Journal: Macroeconomics,
7, 168–196.
Del Negro, M., R. B. Hasegawa, and F. Schorfheide (2014): “Dynamic Prediction Pools: An Investigation of Financial Frictions and Forecasting Performance,” NBER
Working Paper 20575.
Del Negro, M. and F. Schorfheide (2012): “DSGE Model-Based Forecasting,”
FRBNY Working Paper.
Laseen, S. and L. E. Svensson (2011): “Anticipated Alternative Policy-Rate Paths in
Policy Simulations,” International Journal of Central Banking, 7, 1–35.
Smets, F. and R. Wouters (2007): “Shocks and Frictions in US Business Cycles: A
Bayesian DSGE Approach,” American Economic Review, 97, 586 – 606.
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1
General Structure
The FRBNY DSGE model is a medium scale, one-sector dynamic stochastic general equilibrium model which is based on the New Keynesian model with financial frictions used in Del
Negro et al. (2015). The core of the model is based on the work of Smets and Wouters (2007)
(henceforth SW) and Christiano et al. (2005): It builds on the neo-classical growth model by
adding nominal wage and price rigidities, variable capital utilization, costs of adjusting investment, habit formation in consumption. The model also includes credit frictions as in the
financial accelerator model developed by Bernanke et al. (1999b), where the actual implementation of the credit frictions follows closely Christiano et al. (2014), and a time-varying
inflation target following Del Negro and Schorfheide (2012). In contrast to these papers,
the model features both a deterministic and a stochastic trend in productivity. Finally, it
accounts for forward guidance in monetary policy by including anticipated policy shocks as
in Laseen and Svensson (2011).
The model economy is populated by eight classes of agents: 1) a continuum of households, who consume and supply differentiated labor; 2) competitive labor aggregators that
combine labor supplied by individual households; 3) competitive final good-producing firms
that aggregate the intermediate goods into a final product; 4) a continuum of monopolistically competitive intermediate good producing firms; 5) competitive capital producers
that convert final goods into capital; 6) a continuum of entrepreneurs who purchase capital
using both internal and borrowed funds and rent it to intermediate good producing firms;
7) a representative bank collecting deposits from the households and lending funds to the
entrepreneurs; and finally 8) a government, composed of a monetary authority that sets
short-term interest rates and a fiscal authority that sets public spending and collects taxes.
The data set as well as the prior distribution used for the estimation is discussed in
Section ??. Finally, Section ?? discusses how the DSGE model is solved to generate forecasts
as of 2008Q4 and how it is solved to examine the 2009-2012 data in view of zero nominal
interest rate and the forward guidance policy pursued by the Fed.
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2
DSGE Model Specification
Since the derivation of the SW model is discussed in detail in Christiano et al. (2005),
we will only present a summary of the log-linearized equilibrium conditions. We will first
reproduce the equilibrium conditions for the SW model and then discuss the two extensions
that underly the DSGE model used for our analysis.
1.1
The SW Model
All variables in the following equations are expressed in log deviations from their non1
stochastic steady state. In SW this is defined as Zt = eγt+ 1−α z̃t , where γ is the steady
state growth rate of the economy, and z̃t be the linearly detrended log productivity process
which follows the autoregressive law of motion
z̃t = ρz z̃t−1 + σz εz,t .
(1)
The growth rate of Zt in deviations from γ, denoted by zt , follows the process:
zt = ln(Zt /Zt−1 ) − γ =
1
1
(ρz − 1)z̃t−1 +
σz z,t .
1−α
1−α
(2)
Steady state values are denoted by ∗-subscripts and steady state formulas are provided
in the technical appendix of Del Negro and Schorfheide (2012), which is available online.
The consumption Euler equation is given by:
ct = −
(1 − he−γ )
he−γ
(R
−
I
E
[π
]
+
b
)
+
(ct−1 − zt )
t
t t+1
t
σc (1 + he−γ )
(1 + he−γ )
1
(σc − 1) w∗ L∗
+
I
E
[c
+
z
]
+
(Lt − IE t [Lt+1 ]) , (3)
t
t+1
t+1
(1 + he−γ )
σc (1 + he−γ ) c∗
where ct is consumption, Lt is labor supply, Rt is the nominal interest rate, and πt is inflation.
The exogenous process bt drives a wedge between the intertemporal ratio of the marginal
utility of consumption and the riskless real return Rt −IE t [πt+1 ], and follows an AR(1) process
with parameters ρb and σb . The parameters σc and h capture the degree of relative risk
aversion and the degree of habit persistence in the utility function, respectively. The following
condition expresses the relationship between the value of capital in terms of consumption qtk
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and the level of investment it measured in terms of consumption goods:
qtk = S 00 e2γ (1 + β̄) it −
1
β̄
(it−1 − zt ) −
IE t [it+1 + zt+1 ] − µt ,
1 + β̄
1 + β̄
(4)
which is affected by both investment adjustment cost (S 00 is the second derivative of the
adjustment cost function) and by µt , an exogenous process called the “marginal efficiency
of investment” that affects the rate of transformation between consumption and installed
capital (see Greenwood et al. (1998)). The exogenous process µt follows an AR(1) process
with parameters ρµ and σµ . The parameter β̄ = βe(1−σc )γ depends on the intertemporal
discount rate in the utility function of the households β, the degree of relative risk aversion
σc , and the steady-state growth rate γ.
The capital stock, k̄t , evolves as
k̄t =
i∗
1−
k̄∗
i∗
i∗ 00
k̄t−1 − zt + it + S e2γ (1 + β̄)µt ,
k̄∗
k̄∗
(5)
where i∗ /k̄∗ is the steady state ratio of investment to capital. The arbitrage condition
between the return to capital and the riskless rate is:
r∗k
1−δ
k
k
I
E
[r
]
+
IE t [qt+1
] − qtk = Rt + bt − IE t [πt+1 ],
t
t+1
r∗k + (1 − δ)
r∗k + (1 − δ)
(6)
where rtk is the rental rate of capital, r∗k its steady state value, and δ the depreciation rate.
Given that capital is subject to variable capacity utilization ut , the relationship between k̄t
and the amount of capital effectively rented out to firms kt is
kt = ut − zt + k̄t−1 .
(7)
The optimality condition determining the rate of utilization is given by
1−ψ k
r = ut ,
ψ t
(8)
where ψ captures the utilization costs in terms of foregone consumption. Real marginal costs
for firms are given by
mct = wt + αLt − αkt ,
(9)
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where wt is the real wage and α is the income share of capital (after paying mark-ups and
fixed costs) in the production function. From the optimality conditions of goods producers
it follows that all firms have the same capital-labor ratio:
kt = wt − rtk + Lt .
(10)
The production function is:
yt = Φp (αkt + (1 − α)Lt ) + I{ρz < 1}(Φp − 1)
1
z̃t ,
1−α
(11)
1
if the log productivity is trend stationary. The last term (Φp −1) 1−α
z̃t drops out if technology
has a stochastic trend, because in this case one has to assume that the fixed costs are
proportional to the trend. Similarly, the resource constraint is:
yt = gt +
c∗
i∗
r k k∗
1
z̃t ,
ct + it + ∗ ut − I{ρz < 1}
y∗
y∗
y∗
1−α
(12)
1
where again the term − 1−α
z̃t disappears if technology follows a unit root process. Government spending gt is assumed to follow the exogenous process:
gt = ρg gt−1 + σg εg,t + ηgz σz εz,t .
Finally, the price and wage Phillips curves are, respectively:
πt = κ mct +
ιp
β̄
πt−1 +
IE t [πt+1 ] + λf,t ,
1 + ιp β̄
1 + ιp β̄
(13)
and
wt =
1 + ιw β̄
(1 − ζw β̄)(1 − ζw )
1
wth − wt −
πt +
(wt−1 − zt − ιw πt−1 )
(1 + β̄)ζw ((λw − 1)w + 1)
1 + β̄
1 + β̄
β̄
+
IE t [wt+1 + zt+1 + πt+1 ] + λw,t , (14)
1 + β̄
p β̄)(1−ζp )
where κ = (1+ιp(1−ζ
, the parameters ζp , ιp , and p are the Calvo parameter, the
β̄)ζp ((Φp −1)p +1)
degree of indexation, and the curvature parameter in the Kimball aggregator for prices, and
ζw , ιw , and w are the corresponding parameters for wages. wth measures the household’s
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marginal rate of substitution between consumption and labor, and is given by:
wth =
1
−γ
−γ
c
−
he
c
+
he
z
+ νl L t ,
t
t−1
t
1 − he−γ
(15)
where νl characterizes the curvature of the disutility of labor (and would equal the inverse
of the Frisch elasticity in absence of wage rigidities). The mark-ups λf,t and λw,t follow
exogenous ARMA(1,1) processes
λf,t = ρλf λf,t−1 + σλf ελf ,t + ηλf σλf ελf ,t−1 , and
λw,t = ρλw λw,t−1 + σλw ελw ,t + ηλw σλw ελw ,t−1 ,
respectively. Finally, the monetary authority follows a generalized feedback rule:
Rt = ρR Rt−1 + (1 − ρR ) ψ1 πt + ψ2 (yt − ytf )
f
+ ψ3 (yt − ytf ) − (yt−1 − yt−1
) + rtm , (16)
where the flexible price/wage output ytf is obtained from solving the version of the model
without nominal rigidities (that is, Equations (3) through (12) and (15)), and the residual
rtm follows an AR(1) process with parameters ρrm and σrm .
1.2
Time-Varying Target Inflation and Long-Run Inflation Expectations
In order to capture the rise and fall of inflation and interest rates in the estimation sample,
we replace the constant target inflation rate by a time-varying target inflation. While timevarying target rates have been frequently used for the specification of monetary policy rules
in DSGE model (e.g., Erceg and Levin (2003) and Smets and Wouters (2003), among others),
we follow the approach of Aruoba and Schorfheide (2008) and Del Negro and Eusepi (2011)
and include data on long-run inflation expectations as an observable into the estimation of the
DSGE model. At each point in time, the long-run inflation expectations essentially determine
the level of the target inflation rate. To the extent that long-run inflation expectations at
the forecast origin contain information about the central bank’s objective function, e.g. the
desire to stabilize inflation at 2%, this information is automatically included in the forecast.
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More specifically, for the SW model the interest-rate feedback rule of the central bank (16)
is modified as follows:
Rt = ρR Rt−1 + (1 − ρR ) ψ1 (πt − πt∗ ) + ψ2 (yt − ytf )
f
+ψ3 (yt − ytf ) − (yt−1 − yt−1
) + rtm .
(17)
The time-varying inflation target evolves according to:
∗
πt∗ = ρπ∗ πt−1
+ σπ∗ π∗ ,t ,
(18)
where 0 < ρπ∗ < 1 and π∗ ,t is an iid shock. We model πt∗ as a stationary process, although
our prior for ρπ∗ will force this process to be highly persistent. The assumption that the
changes in the target inflation rate are exogenous is, to some extent, a short-cut. For instance,
the learning models of Sargent (1999) or Primiceri (2006) imply that the rise in the target
inflation rate in the 1970’s and the subsequent drop is due to policy makers learning about
the output-inflation trade-off and trying to set inflation optimally. We are abstracting from
such a mechanism in our specification.
1.3
Financial Frictions
Building on the work of Bernanke et al. (1999a), Christiano et al. (2003), De Graeve (2008),
and Christiano et al. (2014) we also add financial frictions to our DSGE model. We assume
that banks collect deposits from households and lend to entrepreneurs who use these funds
as well as their own wealth to acquire physical capital, which is rented to intermediate goods
producers. Entrepreneurs are subject to idiosyncratic disturbances that affect their ability
to manage capital. Their revenue may thus be too low to pay back the bank loans. Banks
protect themselves against default risk by pooling all loans and charging a spread over the
deposit rate. This spread may vary as a function of the entrepreneurs’ leverage and their
riskiness. Adding these frictions to the SW model amounts to replacing equation (6) with
the following conditions:
Et
h
k
R̃t+1
i
− Rt = bt + ζsp,b qtk + k̄t − nt + σ̃ω,t
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and
R̃tk − πt =
r∗k
(1 − δ)
k
rtk + k
qtk − qt−1
,
k
r∗ + (1 − δ)
r∗ + (1 − δ)
(20)
where R̃tk is the gross nominal return on capital for entrepreneurs, nt is entrepreneurial equity,
and σ̃ω,t captures mean-preserving changes in the cross-sectional dispersion of ability across
entrepreneurs (see Christiano et al. (2014)) and follows an AR(1) process with parameters ρσω
and σσω . The second condition defines the return on capital, while the first one determines
the spread between the expected return on capital and the riskless rate. Note that if ζsp,b = 0
and the financial friction shocks σ̃ω,t are zero, (19) and (20) coincide with (6). The following
condition describes the evolution of entrepreneurial net worth:
k
nt = ζn,R̃k R̃tk − πt − ζn,R (Rt−1 − πt ) + ζn,qK qt−1
+ k̄t−1 + ζn,n nt−1
n,σω
σ̃ω,t−1 .
− ζζsp,σ
(21)
ω
1.4
Adding Long Run Changes in Productivity Growth
We add long run changes in productivity and now define Zt as
α
1
Zt = e 1−α z̃t Ztp e(γ+ 1−α log Υ)t ,
(22)
where z̃t – the stationary component of productivity – evolves as in equation 2 while Ztp
p
follows a non stationary process.1 Specifically, ztp = log(Ztp /Zt−1
) follows AR(1) processes:
p
ztp = ρzp zt−1
+ σzp zp ,t , zp ,t ∼ N (0, 1),
(23)
It follows that
zt = log(Zt /Zt−1 ) − γ =
and
Et [zt+1 ] =
1
1
(ρz − 1)z̃t−1 +
σz z,t + ztp ,
1−α
1−α
(24)
1
(ρz − 1)z̃t + ρzp ztp .
1−α
(25)
Since there is a stochastic trend in growth, in equations 11 and 12 the term
be dropped.
1
The production function is Yt (i) = max{ez̃t Kt (i)α (Lt (i)eγt Ztp )
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1−α
1
z̃
1−α t
needs to
− ΦZt , 0}.
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1.5
Anticipated Policy Shocks
This section describes the introduction of anticipated policy shocks in the model, which
follows Laseen and Svensson (2011). We modify the exogenous component of the policy
rule (17) so to incorporate anticipated policy shocks:
rtm
=
m
ρrm rt−1
+
+R
t
+
K
X
R
k,t−k ,
(26)
k=1
where R,t is the usual contemporaneous policy shock, and R
k,t−k is a policy shock that is
known to agents at time t − k, but affects the policy rule k periods later, that is, at time t.
2
We assume that R
k,t−k ∼ N (0, σk,r ), i.i.d..
In order to solve the model we need to express the anticipated shocks in recursive form.
R
For this purpose, we augment the state vector st with K additional states νtR ,. . . ,νt−K
whose
law of motion is as follows:
R
R
+ R
= ν2,t−1
ν1,t
1,t
R
R
ν2,t
= ν3,t−1
+ R
2,t
..
.
R
= R
νK,t
K,t
and rewrite the policy rule (26) as2
m
R
rtm = ρrm rt−1
+ +R
t + ν1,t−1 .
1.6
State Space Representation
We use the method in Sims (2002) to solve the system of log-linear approximate equilibrium
conditions and obtain the transition equation:
st = T (θ)st−1 + R(θ)t .
(27)
We collect all the DSGE model parameters in a vector θ and stack the structural shocks
in a vector t . The state-space representation for our vector of observables yt , which we
describe in the next section, is composed of the transition equation (27), which summarizes
PK
R
R
It is easy to verify that ν1,t−1
= k=1 R
k,t−k , that is, ν1,t−1 is a “bin” that collects all anticipated shocks
that affect the policy rule in period t.
2
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the evolution of the states st , and of a system of measurement equations:
yt = D(θ) + Z(θ)st ,
(28)
mapping the states into the observables, which we describe in detail in the section ??. We
assume that some of the variables are measured with “error”, that is, the observed value
equals the model implied value plus an exogenous process, which evolves as an AR(1). We
add this exogenous process to the vector of states st .
3
Data
The estimation of the DSGE model is based on data on real output growth, consumption
growth, investment growth, real wage growth, hours worked, inflation, interest rates, 10-year
inflation expectations, and spreads. Measurement equations related the model variables that
appeared in Section 2 to the observables:
γ + 100 (yt − yt−1 + zt )
γ + 100 (ct − ct−1 + zt )
γ + 100 (it − it−1 + zt )
γ + 100 (wt − wt−1 + zt )
¯l + 100lt
π∗ + 100πt + epce,t
.
π∗ + λgdp ∗ 100πt + egdp,t
R∗ + 100Rt
1 P40
R
+ eR,t
R∗ + 100IE t 40
t+k
k=1
1 P40
π∗ + 100IE t h40 k=1 πt+k
i
Output growth
Consumption growth
Investment growth
Real Wage growth
Hours
Core PCE Inflation
GDP Deflator Inflation
FFR
10y Nominal Bond Yield
10y Infl. Expectations
=
=
=
=
=
=
=
=
=
=
Spread
k
= SP∗ + 100Et R̃t+1
− Rt
TFP growth
= γ + 100 (zt + ut ) + ez,t
(29)
where all variables are measured in percent. All the e∗,t processes follow an exogenous AR(1)
specification, and can be thought of either measurement error or some other unmodeled
source of discrepancy between the model and the data (e.g., risk premia for the long term
nominal rate). The terms π∗ and R∗ measure the steady state level of net inflation and short
term nominal interest rates, respectively, and ¯l captures the mean of hours (this variable is
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measured as an index). The first seven series are commonly used in the estimation of the SW
model. The 10-year inflation expectations contain information about low-frequency inflation
movements and are obtained from the Blue Chip Economic Indicators survey and the Survey
of Professional Forecasters. As spread variable we use a Baa Corporate Bond Yield spread
over the 10-Year Treasury Note Yield at constant maturity. Details on the construction of
the data set are provided in Appendix A.
In order to estimate the importance of anticipated shocks and their effect on the variables
of interest, we follow Del Negro and Schorfheide (2012) and augment the measurement
equation (28) with the expectations for the policy rate:
e
F F Rt,t+1
= 100(Z(θ)R,. T (θ)1 st + R∗ ),
..
.
(30)
e
= 100(Z(θ)R,. T (θ)K st + R∗ ),
F F Rt,t+K
e
are the market’s expectations for the FFR k quarters ahead, and Z(θ)R,. is
where F F Rt,t+k
the row of Z(θ) corresponding to the interest rate.
4
Inference, Prior and Posterior Parameter Estimates
We use Bayesian techniques in the subsequent empirical analysis, which require the specification of a prior distribution for the model parameters. For most of the parameters we use the
same marginal prior distributions as Smets and Wouters (2007). There are two important
exceptions. First, the original prior for the quarterly steady state inflation rate π∗ used by
Smets and Wouters (2007) is tightly centered around 0.62% (which is about 2.5% annualized)
with a standard deviation of 0.1%. We favor a looser prior, one that has less influence on
the model’s forecasting performance, that is centered at 0.75% and has a standard deviation
of 0.4%. Second, for the financial frictions mechanism we specify priors for the parameters
SP∗ , ζsp,b , ρσω , and σσω . We fix the parameters corresponding to the steady state default
probability and the survival rate of entrepreneurs, respectively. In turn, these parameters
imply values for the parameters of (21).
Information on the the prior and posterior mean is provided in section B. Section C
reports the impulse response functions of the observable variables to the various shocks.
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References
Aruoba, S. B. and F. Schorfheide (2008): “Insights from an Estimated Search-Based
Monetary Model with Nominal Rigidities,” Working Paper.
Bernanke, B., M. Gertler, and S. Gilchrist (1999a): “The Financial Accelerator in
a Quantitative Business Cycle Framework,” in Handbook of Macroeconomics, ed. by J. B.
Taylor and M. Woodford, North Holland, Amsterdam, vol. 1C.
Bernanke, B. S., M. Gertler, and S. Gilchrist (1999b): “The Financial Accelerator
in a Quantitative Business Cycle Framework,” in Handbook of Macroeconomics, ed. by
J. B. Taylor and M. Woodford, Amsterdam: North-Holland, vol. 1C, chap. 21, 1341–93.
Christiano, L., R. Motto, and M. Rostagno (2003): “The Great Depression and the
Friedman-Schwartz Hypothesis,” Journal of Money, Credit and Banking, 35, 1119–1197.
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities and
the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, 113,
1–45.
Christiano, L. J., R. Motto, and M. Rostagno (2014): “Risk Shocks,” American
Economic Review, 104, 27–65.
De Graeve, F. (2008): “The External Finance Premium and the Macroeconomy: US
Post-WWII Evidence,” Journal of Economic Dynamics and Control, 32, 3415 – 3440.
Del Negro, M. and S. Eusepi (2011): “Fitting Observed Ination Expectations,” Journal
of Economic Dynamics and Control, 35, 2105–2131.
Del Negro, M., M. P. Giannoni, and F. Schorfheide (2015): “Inflation in the Great
Recession and New Keynesian Models,” American Economic Journal: Macroeconomics,
7, 168–196.
Del Negro, M. and F. Schorfheide (2012): “DSGE Model-Based Forecasting,”
FRBNY Working Paper.
Erceg, C. J. and A. T. Levin (2003): “Imperfect Credibility and Inflation Persistence,”
Journal of Monetary Economics, 50, 915–944.
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Greenwood, J., Z. Hercovitz, and P. Krusell (1998): “Long-Run Implications of
Investment-Specific Technological Change,” American Economic Review, 87, 342–36.
Laseen, S. and L. E. Svensson (2011): “Anticipated Alternative Policy-Rate Paths in
Policy Simulations,” International Journal of Central Banking, 7, 1–35.
Primiceri, G. (2006): “Why Inflation Rose and Fell: Policymakers Beliefs and US Postwar
Stabilization Policy,” Quarterly Journal of Economics, 121, 867–901.
Sargent, T. J. (1999): The Conquest of American Inflation, Princeton University Press,
Princeton.
Sims, C. A. (2002): “Comment on Cogley and Sargent’s ‘Evolving post World War II U.S.
Inflation Dynamics’ ,” in NBER Macroeconomics Annual 2001, ed. by B. S. Bernanke and
K. Rogoff, MIT Press, Cambridge, vol. 16, 373–379.
Smets, F. and R. Wouters (2003): “An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area,” Journal of the European Economic Association, 1, 1123
– 1175.
——— (2007): “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,”
American Economic Review, 97, 586 – 606.
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A
Data Construction
Data on real GDP (GDPC), the GDP deflator (GDPDEF), core PCE inflation (PCEPILFE),
nominal personal consumption expenditures (PCEC), and nominal fixed private investment
(FPI) are produced at a quarterly frequency by the Bureau of Economic Analysis, and are
included in the National Income and Product Accounts (NIPA). Average weekly hours of
production and nonsupervisory employees for total private industries (AWHNONAG), civilian employment (CE16OV), and the civilian non-institutional population (LNSINDEX) are
produced by the Bureau of Labor Statistics (BLS) at a monthly frequency. The first of these
series is obtained from the Establishment Survey, and the remaining from the Household
Survey. Both surveys are released in the BLS Employment Situation Summary. Since our
models are estimated on quarterly data, we take averages of the monthly data. Compensation per hour for the non-farm business sector (COMPNFB) is obtained from the Labor
Productvity and Costs release, and produced by the BLS at a quarterly frequency. All data
are transformed following Smets and Wouters (2007). The federal funds rate is obtained
from the Federal Reserve Board’s H.15 release at a business day frequency. We take quarterly averages of the annualized daily data and divide by four. Let ∆ denote the temporal
difference operator. Then:
Output growth
Consumption growth
Investment growth
Real wage growth
Hours worked
GDP Deflator Inflation
Core PCE Inflation
FFR
=
=
=
=
=
=
=
=
100 ∗ ∆LN ((GDP C)/LN SIN DEX)
100 ∗ ∆LN ((P CEC/GDP DEF )/LN SIN DEX)
100 ∗ ∆LN ((F P I/GDP DEF )/LN SIN DEX)
100 ∗ ∆LN (COM P N F B/GDP DEF )
100 ∗ LN ((AW HN ON AG ∗ CE16OV /100)/LN SIN DEX)
100 ∗ ∆LN (GDP DEF )
100 ∗ ∆LN (P CEP ILF E)
(1/4) ∗ F EDERAL F U N DS RAT E
Long-run inflation expectations are obtained from the Blue Chip Economic Indicators
survey and the Survey of Professional Forecasters available from the FRB Philadelphia’s
Real-Time Data Research Center. Long-run inflation expectations (average CPI inflation
over the next 10 years) are available from 1991Q4 onward. Prior to 1991Q4, we use the
10-year expectations data from the Blue Chip survey to construct a long time series that
begins in 1979Q4. Since the Blue Chip survey reports long-run inflation expectations only
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twice a year, we treat these expectations in the remaining quarters as missing observations
and adjust the measurement equation of the Kalman filter accordingly. Long-run inflation
expectations πtO,40 are therefore measured as
10y Infl Exp = (10-YEAR AVERAGE CPI INFLATION FORECAST − 0.50)/4.
where 0.50 is the average difference between CPI and GDP annualized inflation from the
beginning of the sample to 1992. We divide by 4 to express the data in quarterly terms.
Finally, we measure Spread as the annualized Moody’s Seasoned Baa Corporate Bond Yield
spread over the 10-Year Treasury Note Yield at Constant Maturity. Both series are available
from the Federal Reserve Board’s H.15 release. Like the federal funds rate, the spread data
are also averaged over each quarter and measured at a quarterly frequency. This leads to:
Spread = (1/4) ∗ (Baa Corporate − 10 year T reasury).
Similarly,
10y Bond yield = (1/4) ∗ (10 year T reasury).
Last TFP growth is measured using John Fernald’s TFP growth, unadjusted for changes in
utilization and expressed in labor augmenting terms:
TFP growth = (1/4) ∗ Fernald’s TFP growth, unadjusted .
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B
Prior and Posterior Distributions
Parameter Estimates: Prior and Posterior Mean
Parameter
α
ιp
Υ
Φ
S 00
h
psi
ιw
β
σc
ρ
F (ω)
spr∗
γ∗
γ
Lmean
σg
σb
σµ
σz
σ λf
σ λw
σrm
σsigw
Prior Mean
0.300
0.500
1.000
1.250
4.000
0.700
0.500
0.500
0.250
1.500
0.750
0.030
2.000
0.990
0.400
-45.000
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.050
Prior Stdd
0.050
0.150
0.000
0.120
1.500
0.100
0.150
0.150
0.100
0.370
0.100
0.000
0.100
0.000
0.100
5.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
4.000
Post Mean
0.167
0.256
1.000
1.120
2.940
0.440
0.725
0.526
0.132
1.120
0.665
0.030
1.752
0.990
0.348
-47.469
2.559
0.029
0.468
0.678
0.085
0.384
0.235
0.043
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90% Lower Band
0.143
0.115
1.000
1.049
1.941
0.353
0.586
0.314
0.055
0.878
0.599
0.030
1.625
0.990
0.277
-49.289
2.352
0.025
0.403
0.612
0.066
0.337
0.213
0.034
90% Upper Band
0.191
0.398
1.000
1.189
3.874
0.530
0.866
0.738
0.202
1.353
0.733
0.030
1.879
0.990
0.423
-45.633
2.760
0.034
0.533
0.743
0.102
0.431
0.258
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Parameter Estimates: Prior and Posterior Mean
Parameter
σmue
σgamm
σlr
σz p
σtf p
σgdpdef
σpce
σant1
σant2
σant3
σant4
σant5
σant6
σant7
σant8
σant9
σant10
σant11
σant12
σant13
σant14
σant15
σant16
σant17
σant18
Prior Mean
0.000
0.000
0.750
0.100
0.100
0.100
0.100
0.200
0.200
0.200
0.200
0.200
0.200
0.200
0.200
0.200
0.200
0.200
0.200
0.000
0.000
0.000
0.000
0.000
0.000
Prior Stdd
0.000
0.000
2.000
2.000
2.000
2.000
2.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
0.000
0.000
0.000
0.000
0.000
0.000
Post Mean
0.000
0.000
0.184
0.194
0.828
0.160
0.100
0.100
0.090
0.090
0.085
0.086
0.109
0.258
0.309
0.251
0.250
0.234
0.236
0.000
0.000
0.000
0.000
0.000
0.000
90% Lower Band
0.000
0.000
0.149
0.104
0.755
0.143
0.081
0.076
0.070
0.069
0.065
0.066
0.083
0.105
0.104
0.106
0.101
0.112
0.108
0.000
0.000
0.000
0.000
0.000
0.000
90% Upper Band
0.000
0.000
0.219
0.288
0.899
0.179
0.120
0.122
0.110
0.110
0.103
0.105
0.134
0.400
0.474
0.399
0.399
0.362
0.366
0.000
0.000
0.000
0.000
0.000
0.000
Parameter Estimates: Prior and Posterior Mean
Parameter
σant19
σant20
ηgz
η λf
η λw
imodel
α
Γgdpdef
δgdpdef
Prior Mean
0.000
0.000
0.500
0.500
0.500
0.000
1.000
0.000
Prior Stdd
0.000
0.000
0.200
0.200
0.200
0.000
2.000
2.000
Post Mean
0.000
0.000
0.768
0.608
0.432
0.000
1.033
0.000
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90% Lower Band
0.000
0.000
0.580
0.401
0.184
0.000
0.951
-0.053
90% Upper Band
0.000
0.000
0.962
0.822
0.683
0.000
1.118
0.054
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C
Impulse Response Functions
Responses to a Discount Rate (b) Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
3
2
1
0
−1
0
4
8
6
4
2
0
12
0
4
Real Wage Growth
Percent Annualized
Percent Annualized
0.3
0.2
0.1
0
−0.1
0
4
8
0.3
0.2
0.1
0
12
0
4
Percent Annualized
Percent Annualized
0.3
0.2
0.1
4
8
0.5
0
4
2
1
0
4
8
2
1
0
−1
12
0
4
Percent Annualized
Percent Annualized
−0.5
4
8
0.2
0.1
0.05
0
12
0
Percent Annualized
Percent Annualized
0.3
0.2
0.1
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
0.4
0
12
0.15
Long Rate
0
8
Long Inf
0
0
12
3
Spread
−1
8
Investment Growth
Percent Annualized
Percent Annualized
Consumption Growth
0
12
1
0
12
3
−1
8
Interest Rate
0.4
0
12
0.4
Core PCE Inflation
0
8
GDP Deflator
0.3
0.2
0.1
0
−0.1
12
0
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Responses to a Spread Shock
Aggregate Hours
0.2
0.1
0
−0.1
1
Percent Annualized
Percent Annualized
Output Growth
0.3
0
4
8
0.5
0
−0.5
12
0
4
0.03
0.02
0.01
0
0
4
8
0.02
0
−0.02
−0.04
12
0
4
0
−0.02
4
8
0.1
0.05
0
−0.05
12
0
4
0.2
0
−0.2
−0.4
0
4
8
2
1
0
−1
12
0
4
Percent Annualized
Percent Annualized
0
−0.2
−0.3
4
8
−0.01
−0.02
Percent Annualized
Percent Annualized
0
−0.02
4
8
0
4
8
12
−3
Long Rate
0
12
0
−0.03
12
0.02
−0.04
8
Long Inf
−0.1
0
12
3
Spread
−0.4
8
Investment Growth
Percent Annualized
Percent Annualized
Consumption Growth
−0.6
12
Interest Rate
−0.01
0
8
0.15
Percent Annualized
Percent Annualized
Core PCE Inflation
0.01
−0.03
12
GDP Deflator
0.04
Percent Annualized
Percent Annualized
Real Wage Growth
8
5
0
−5
−10
12
Total Factor Productivity, Util.Unadjusted
x 10
0
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Responses to an MEI Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.05
0
−0.05
−0.1
−0.15
0
4
5
Real Wage Growth
x 10
−10
0
4
1
4
8
3
2
1
0
4
0
−0.02
Percent Annualized
Percent Annualized
−0.02
8
0
4
−0.5
Percent Annualized
Percent Annualized
−0.02
8
3
Percent Annualized
Percent Annualized
8
12
x 10
0
4
8
12
−3
0.005
4
8
Long Inf
1
Long Rate
0
4
2
0
12
0.01
0
0
−3
−0.01
4
12
0
−1
12
0
0
8
0.5
Spread
−0.03
12
Investment Growth
0
4
8
0.02
−0.04
12
0.02
0
12
GDP Deflator
x 10
Consumption Growth
−0.04
8
Interest Rate
2
0
4
Core PCE Inflation
x 10
3
0
4
0
12
Percent Annualized
Percent Annualized
−3
8
0
−3
0
4
0
−0.2
−0.4
12
−5
−15
0.2
Percent Annualized
Percent Annualized
−3
8
0.4
5
0
−5
−10
12
Total Factor Productivity, Util.Unadjusted
x 10
0
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FRBNY DSGE Model Documentation
Responses to a Price Mark-up Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.6
0.4
0.2
0
−0.2
0
4
8
1
0.5
0
−0.5
12
0
4
0.4
0.2
0
−0.2
0
4
8
0.2
0
−0.2
−0.4
−0.6
12
0
4
0
−0.2
−0.4
0
4
8
0.1
0
−0.1
−0.2
12
0
4
Percent Annualized
Percent Annualized
0.4
0.2
0
4
8
0.5
0
−0.5
12
0
4
Percent Annualized
Percent Annualized
0.02
0.01
4
8
0
−0.01
0
0
−0.01
−0.02
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
Percent Annualized
Percent Annualized
Long Rate
0
12
0.01
−0.02
12
0.01
−0.03
8
Long Inf
0.03
0
12
1
Spread
0
8
Investment Growth
0.6
0
12
0.2
Consumption Growth
−0.2
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
0.2
−0.6
12
GDP Deflator
0.6
Percent Annualized
Percent Annualized
Real Wage Growth
8
0.06
0.04
0.02
0
−0.02
12
0
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FRBNY DSGE Model Documentation
Responses to a Wage Mark-up Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.02
0.01
0
−0.01
−0.02
0
4
8
0.08
0.06
0.04
0.02
0
12
0
4
0
−0.2
−0.4
−0.6
0
4
8
0
−0.01
−0.02
−0.03
12
0
4
−0.02
4
8
0
−0.01
−0.02
12
0
4
0.06
0.04
0.02
0
0
4
4
2
1
0
−0.05
−0.1
−0.15
0
4
8
−0.01
0
Percent Annualized
Percent Annualized
8
4
8
12
Total Factor Productivity, Util.Unadjusted
−0.005
4
12
−0.005
Long Rate
0
8
0
12
0
−0.01
4
Long Inf
3
0
0
Spread
x 10
12
0.05
12
Percent Annualized
Percent Annualized
−3
8
8
Investment Growth
Percent Annualized
Percent Annualized
Consumption Growth
−0.02
12
Interest Rate
−0.01
0
8
0.01
Percent Annualized
Percent Annualized
Core PCE Inflation
0
−0.03
12
GDP Deflator
0.2
Percent Annualized
Percent Annualized
Real Wage Growth
8
0.01
0
−0.01
−0.02
−0.03
12
0
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FRBNY DSGE Model Documentation
Responses to a Monetary Policy Shock
Output Growth
Aggregate Hours
Percent Annualized
Percent Annualized
0.6
0.4
0.2
0
−0.2
0
4
8
0.8
0.6
0.4
0.2
0
12
Real Wage Growth
Percent Annualized
Percent Annualized
0.02
0.01
0
0
4
6
8
12
0
4
8
4
2
0
0
4
−0.1
−0.15
−0.2
0
4
0
0.5
0
−0.5
12
Percent Annualized
Percent Annualized
0.01
0
−0.01
0
4
8
0
1
x 10
0
Percent Annualized
Percent Annualized
−0.01
−0.015
8
4
8
12
Total Factor Productivity, Util.Unadjusted
−0.005
4
12
−1
Long Rate
0
8
Long Inf
0
−2
12
0
−0.02
4
−3
Spread
−0.02
12
1
Percent Annualized
Percent Annualized
0.2
8
8
Investment Growth
0.4
4
12
−0.05
12
0.6
0
8
0
Consumption Growth
−0.2
12
Interest Rate
2
0
8
GDP Deflator
x 10
Core PCE Inflation
x 10
4
−2
6
−2
Percent Annualized
Percent Annualized
−3
4
−3
0.03
−0.01
0
0.03
0.02
0.01
0
−0.01
12
0
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FRBNY DSGE Model Documentation
Responses to a Stationary Productivity Shock
Output Growth
Aggregate Hours
0.2
0.1
0
−0.1
0
4
8
−0.1
0
4
0
4
8
−0.005
−0.01
−0.015
0
4
−0.005
−0.01
4
8
−0.01
−0.02
−0.03
−0.04
12
0
4
0.05
0
4
0.05
0
−0.05
12
x 10
0
0
4
8
0
0
x 10
0
Percent Annualized
Percent Annualized
8
4
8
12
Total Factor Productivity, Util.Unadjusted
−0.005
4
12
−4
Long Rate
0
8
Long Inf
−2
−6
12
0
−0.01
4
−3
Spread
2
−2
0.1
Percent Annualized
Percent Annualized
−3
8
12
0.15
Percent Annualized
Percent Annualized
0.1
4
8
Investment Growth
0.15
0
12
0
Consumption Growth
−0.05
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
0
12
0
12
0
−0.015
8
GDP Deflator
5
0
0
−0.05
Real Wage Growth
x 10
10
−5
0.05
12
Percent Annualized
Percent Annualized
−3
15
0.1
Percent Annualized
Percent Annualized
0.3
0.6
0.4
0.2
0
−0.2
12
0
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FRBNY DSGE Model Documentation
Responses to a Shock to the TFP Growth Rate
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.5
0
−0.5
−1
0
4
8
0
−0.2
−0.4
−0.6
−0.8
12
0
4
−0.05
−0.1
−0.15
−0.2
0
4
8
0.04
0.03
0.02
0.01
0
12
0
4
0.02
0.01
0
4
8
0
−0.05
−0.1
−0.15
12
0
4
Percent Annualized
Percent Annualized
0
−0.5
4
8
0.2
0
−0.2
−0.4
12
Percent Annualized
Percent Annualized
−0.005
−0.01
4
8
0
15
x 10
0
0
Percent Annualized
Percent Annualized
−0.01
8
4
8
12
Total Factor Productivity, Util.Unadjusted
0
4
12
5
Long Rate
0
8
Long Inf
10
−5
12
0.01
−0.02
4
−3
0
0
12
0.4
Spread
−0.015
8
Investment Growth
0.5
0
12
0.05
Consumption Growth
−1
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
0.03
0
12
GDP Deflator
0
Percent Annualized
Percent Annualized
Real Wage Growth
8
0.1
0
−0.1
−0.2
−0.3
12
0
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FRBNY DSGE Model Documentation
Responses to a Government Spending Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.02
0
−0.02
−0.04
0
4
2
Real Wage Growth
x 10
0
4
8
0
−1
12
−0.5
0
4
8
0
Percent Annualized
Percent Annualized
0.01
0
0
4
4
2
1
0
4
0
−1
0
4
8
Interest Rate
x 10
0
4
8
12
Investment Growth
x 10
0
4
0
8
12
Long Inf
x 10
−2
−4
−6
0
4
8
12
−3
−0.5
−1.5
12
−2
Long Rate
x 10
8
0
−8
12
Percent Annualized
Percent Annualized
−3
8
4
−4
3
0
2
Spread
x 10
0
−3
−4
12
Percent Annualized
Percent Annualized
−4
8
GDP Deflator
x 10
−3
0.02
12
−2
−4
12
0.03
8
−1
Consumption Growth
−0.01
4
−3
Core PCE Inflation
x 10
0
−0.5
Percent Annualized
Percent Annualized
−3
−1
−0.03
−3
−2
0
−0.02
−0.04
12
0
−4
−0.01
Percent Annualized
Percent Annualized
−4
8
0
1
0
−1
−2
−3
12
Total Factor Productivity, Util.Unadjusted
x 10
0
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FRBNY DSGE Model Documentation
Responses to a π ∗ Shock
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
0.5
0
−0.5
−1
0
4
8
0
−1
−2
−3
12
0
4
0.1
0
−0.1
−0.2
0
4
8
0
−0.2
−0.4
−0.6
−0.8
12
0
4
−0.2
−0.4
−0.6
0
4
8
−0.2
−0.4
−0.6
−0.8
12
0
4
Percent Annualized
Percent Annualized
0
−0.5
−1
4
8
0
−0.5
−1
−1.5
12
0
4
Percent Annualized
Percent Annualized
0.02
0
−0.02
4
8
0
−0.4
−0.6
0
−0.2
−0.4
−0.6
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
Percent Annualized
Percent Annualized
Long Rate
0
12
−0.2
−0.8
12
0
−0.8
8
Long Inf
0.04
0
12
0.5
Spread
−0.04
8
Investment Growth
0.5
0
12
0
Consumption Growth
−1.5
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
0
−0.8
12
GDP Deflator
0.2
Percent Annualized
Percent Annualized
Real Wage Growth
8
0.1
0.05
0
−0.05
−0.1
12
0
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FRBNY DSGE Model Documentation
Responses to GDP Deflator Measurement Error
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
1
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
0.5
0
−0.5
−1
0
4
8
0
−0.1
−0.2
−0.3
−0.4
12
0
4
0.5
0
−0.5
0
4
8
0.5
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
0
0.5
0
−0.5
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
Percent Annualized
Percent Annualized
Long Rate
0
12
0.5
−1
12
1
−1
8
Long Inf
0.5
0
12
0.5
Spread
−1
8
Investment Growth
0.5
0
12
1
Consumption Growth
−1
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
1
−1
12
GDP Deflator
1
Percent Annualized
Percent Annualized
Real Wage Growth
8
1
0.5
0
−0.5
−1
12
0
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FRBNY DSGE Model Documentation
Responses to Core PCE Measurement Error
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
1
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
−0.1
−0.2
−0.3
0
4
8
0.5
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
0
0.5
0
−0.5
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
Percent Annualized
Percent Annualized
Long Rate
0
12
0.5
−1
12
1
−1
8
Long Inf
0.5
0
12
0.5
Spread
−1
8
Investment Growth
0.5
0
12
1
Consumption Growth
−1
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
0
−0.4
12
GDP Deflator
1
Percent Annualized
Percent Annualized
Real Wage Growth
8
1
0.5
0
−0.5
−1
12
0
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FRBNY DSGE Model Documentation
Responses to Long Rate Measurement Error
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
1
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
0.5
0
−0.5
0
4
8
0.5
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
0
−0.1
−0.2
−0.3
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
Percent Annualized
Percent Annualized
Long Rate
0
12
0.5
−1
12
0
−0.4
8
Long Inf
0.5
0
12
0.5
Spread
−1
8
Investment Growth
0.5
0
12
1
Consumption Growth
−1
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
1
−1
12
GDP Deflator
1
Percent Annualized
Percent Annualized
Real Wage Growth
8
1
0.5
0
−0.5
−1
12
0
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FRBNY DSGE Model Documentation
Responses to TFP Measurement Error
Aggregate Hours
Percent Annualized
Percent Annualized
Output Growth
1
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
0.5
0
−0.5
−1
0
4
8
1
0.5
0
−0.5
−1
12
0
4
0.5
0
−0.5
0
4
8
0.5
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
−1
12
0
4
Percent Annualized
Percent Annualized
1
0
−0.5
4
8
1
0
−0.5
0
0.5
0
−0.5
4
8
4
8
12
Total Factor Productivity, Util.Unadjusted
Percent Annualized
Percent Annualized
Long Rate
0
12
0.5
−1
12
1
−1
8
Long Inf
0.5
0
12
0.5
Spread
−1
8
Investment Growth
0.5
0
12
1
Consumption Growth
−1
8
Interest Rate
Percent Annualized
Percent Annualized
Core PCE Inflation
1
−1
12
GDP Deflator
1
Percent Annualized
Percent Annualized
Real Wage Growth
8
0
−0.1
−0.2
−0.3
−0.4
12
0
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Detailed Philadelphia (PRISM) Forecast Overview
March 2015
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 3.8
percent in the second half of 2016. Core PCE inflation is projected to be contained at below 2
percent through 2017. For this forecast round, we have implemented the assumption that the
forecasted federal funds rate is pinned down by current futures market projections through mid2015. The funds rate is unconstrained beginning in 2015Q3, and rises to about 1.1 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 pace of growth and low
inflation that have characterized U.S. economic performance over the past few years 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 2014Q4 supplemented by a 2015Q1 nowcast based on the latest
Macroeconomic Advisers forecast. For example, the model takes 2015Q1 output growth of 2.4
percent as given and the projection begins with 2015Q2. PRISM anticipates that growth
accelerates to about 3.8 percent by 2016Q3. Output growth then holds eases down to about a 3.6
percent pace at the end of 2017. Overall, the output growth forecast for this round is a bit weaker
compared with December projection. While output growth is fairly robust, core PCE inflation
stays contained at below 2 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 federal funds rate is
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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 and 3.2 percent in 2017Q4. This path
is similar to the December projection.
The key factors driving the projection are shown in the forecast shock decompositions
(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 above-trend real
output growth over the next 3 years are labor supply shocks (labeled Labor), government
spending shocks, and marginal efficiency of investment shocks (labeled MEI). The model
attributes the weak reading on real GDP growth over the past two quarters to negative shocks to
TFP and government spending (which includes net exports). 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.
As seen in Figure 3, the model estimates a sequence of largely negative discount factor
shocks since 2008. All else equal, these shocks push down current consumption and push up
investment, with the effect being very persistent. Consequently, the de-trended level of
consumption (nondurables + services) remains below the model’s estimated steady state at this
point. As these shocks unwind over the projection period, consumption growth gradually
accelerates from about 2.3 percent at the beginning of 2015 to 3 percent at the end of 2017. The
model attributes the recent strength in investment growth (gross private domestic + durable
goods consumption) to the gradual unwinding of a history of negative MEI shocks since the start
of the recession (see Figures 2e and 3). Consequently, the principal shocks driving strong
investment growth over the forecast horizon are efficiency of investment shocks with an
additional boost from labor shocks. Offsetting these factors to some extent are financial shocks:
the unwinding of the discount factor shocks leads to a downward pull on investment growth over
the next three years. Investment growth runs at about a 4 percent pace in 2015, rising to near 5
percent by the start of 2017.
The forecast for core PCE inflation is largely a story of upward pressure from the
unwinding of negative labor supply shocks and MEI 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 is a decreasing, but still
substantial, downward effect on inflation over the next three years (these shocks have a very
persistent effect on inflation).
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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 federal funds rate is projected to rise fairly quickly once the constraint from market
expectations is removed in 2015Q3. The model attributes the low level of the funds rate to a
combination of monetary policy, discount factor and MEI shock dynamics. After 2015Q2, the
positive contribution from labor supply shocks is more than offset by discount factor shock
dynamics, keeping the funds rate below its steady state level through 2017.
References
Schorfheide, Frank, Keith Sill, and Maxym Kryshko. 2010. “DSGE model-based forecasting of
non-modelled variables.” 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.
Page 3 of 19
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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
Page 4 of 19
Page 84 of 99
2015
2016
2017
2018
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 1b
Core PCE Inflation
6
5
4
3
2
1
0
-1
2008
2009
2010
2011
2012
2013
2014
Page 5 of 19
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2015
2016
2017
2018
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 1c
Fed Funds Rate
8
6
4
2
0
-2
-4
2008
2009
2010
2011
2012
2013
2014
Page 6 of 19
Page 86 of 99
2015
2016
2017
2018
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 2a
Conditional Forecast
percent
Real GDP Growth
8
8
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
2010
tech
2011
2012
gov
2013
mei
2014
Date
mrkp
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
Page 7 of 19
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2015
2016
labor
2017
fin
-6
mpol
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 2b
Conditional Forecast
percent
Core PCE Inflation
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
2010
tech
2011
2012
gov
2013
mei
2014
Date
mrkp
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
Page 8 of 19
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2015
2016
labor
2017
fin
-3
mpol
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 2c
Conditional Forecast
percent
Fed Funds Rate
6
6
5
5
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
2010
tech
2011
2012
gov
2013
mei
2014
Date
mrkp
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
Page 9 of 19
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2015
2016
labor
2017
fin
-5
mpol
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Figure 2d
Conditional Forecast
percent
Real Consumption Growth
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
2010
tech
2011
2012
gov
2013
mei
2014
Date
mrkp
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
Page 10 of 19
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2015
2016
labor
2017
fin
-6
mpol
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 2e
Conditional Forecast
percent
Real Investment Growth
30
30
25
25
20
20
15
15
10
10
5
5
0
0
-5
-5
-10
-10
-15
-15
-20
2010
tech
2011
2012
gov
2013
mei
2014
Date
mrkp
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
Page 11 of 19
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2015
2016
labor
2017
fin
-20
mpol
Authorized for public release by the FOMC Secretariat on 1/8/2021
Figure 3
Smoothed Shock Estimates for Conditional Forecast Model
(normalized by standard deviation)
labor shock
discount factor shock
5
4
2
0
0
-2
2005
2010
2015
2020
-5
2005
TFP shock
2010
2015
2020
mei shock
4
2
2
0
0
-2
-4
2005
-2
2010
2015
2020
2005
Page 12 of 19
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2010
2015
2020
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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
Page 13 of 19
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5
10
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Impulse Response to Leisure Shock
consumption growth
output growth
2
2
0
0
-2
0
5
10
15
-2
0
investment growth
5
0
0
-1
-5
0
5
10
15
-2
0
0.4
0.2
0.2
0
5
10
15
5
10
15
nominal rate
inflation
0.4
0
5
aggregate hours
10
15
0
0
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10
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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
1
0
0.5
0
5
10
15
0
0
inflation
0.4
0
0.2
0
5
15
5
10
15
nominal rate
0.1
-0.1
10
aggregate hours
10
-10
5
10
15
0
0
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10
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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
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10
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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
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5
10
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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
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5
10
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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
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5
10
15
@FedFRASER