Research Paper Abstracts
The Federal Reserve Is Not Very Constrained by the Lower Bound on Nominal Interest Rates
I survey the literature on monetary policy at the zero lower bound (ZLB) and effective lower bound (ELB) to make
three main points: First, the Federal Reserve’s forward guidance and largescale asset purchases are
effective monetary policy tools at the Z/ELB. Second, during the 2008–15 U.S. ZLB period, the Fed was not very
constrained in its ability to influence medium and longerterm interest rates and the economy. Third, the risks
of the Fed being significantly constrained by the ELB in the future are typically greatly overstated. I conclude
that the Federal Reserve is not very constrained by the lower bound on nominal interest rates.
Measuring the Effects of Federal Reserve Forward Guidance and Asset Purchases on Financial Markets
I extend the methods of Gürkaynak, Sack, and Swanson (2005) to separately identify the effects of Federal
Reserve forward guidance and largescale asset purchases (LSAPs) during the 2009–15 U.S. zero lower bound
(ZLB) period. I find that both forward guidance and LSAPs had substantial and highly statistically significant
effects, comparable in magnitude to the effects of the federal funds rate before the ZLB. Forward guidance was
more effective than LSAPs at moving shortterm Treasury yields, while LSAPs were more effective than forward
guidance and the federal funds rate at moving longerterm Treasury and corporate bond yields. I estimate that the
effects of LSAPs were very persistent, with the exception of the very large and perhaps special March 2009
“QE1” announcement. The effects of forward guidance are slightly less persistent, but the difference
is not statistically significant and is likely due to the FOMC’s forward guidance announcements having a
relatively shorter horizon.
Measuring the Effects of Unconventional Monetary Policy on Asset Prices
I adapt the methods of Gürkaynak, Sack, and Swanson (2005) to estimate two dimensions of monetary policy
during the 2009–2015 zero lower bound period in the U.S. I show that, after a suitable rotation, these two
dimensions can be interpreted as “forward guidance” and “largescale asset purchases”
(LSAPs). I estimate the sizes of the forward guidance and LSAP components of each FOMC announcement between January
2009 and June 2015, and show that those estimates correspond closely to identifiable features of major FOMC
announcements over that period. Forward guidance has relatively small effects on the longest maturity Treasury
yields and essentially no effect on corporate bond yields, while LSAPs have large effects on those yields but
essentially no effect on shortterm Treasuries. Both types of policies have significant effects on mediumterm
Treasury yields, stock prices, and exchange rates.
A Macroeconomic Model of Equities and Real, Nominal, and Defaultable Debt
Linkages between the real economy and financial markets can be extremely important, as demonstrated by the the
recent global financial crisis and European sovereign debt crisis. In this paper, I develop a simple, structural
macroeconomic model that is consistent with a wide variety of asset pricing facts, such as the size and variability
of risk premia on equities, real and nominal government bonds, and corporate bonds—the equity premium puzzle,
bond premium puzzle, and credit spread puzzle, respectively. I thus show how to unify a variety of asset pricing
puzzles from finance into a simple, structural framework. Conversely, I show how to bring standard macroeconomic
models into agreement with a wide range of asset pricing facts.
Monetary Policy Effectiveness in China: Evidence from a FAVAR Model (with John Fernald and Mark Spiegel)
We use a broad set of Chinese economic indicators and a dynamic factor model framework to estimate Chinese economic
activity and inflation as latent variables. We incorporate these latent variables into a factoraugmented vector
autoregression (FAVAR) to estimate the effects of Chinese monetary policy on the Chinese economy. A FAVAR approach
is particularly wellsuited to this analysis due to concerns about Chinese data quality, a lack of a long history
for many series, and the rapid institutional and structural changes that China has undergone. We find that
increases in bank reserve requirements reduce economic activity and inflation, consistent with previous studies. In
contrast to much of the literature, however, we find that centralbank determined changes in Chinese interest rates
also have substantial impacts on economic activity and inflation, while other measures of changes in credit
conditions, such as shocks to M2 or lending levels, do not once other policy variables are taken into
account. Overall, our results indicate that the monetary policy transmission channels in China have moved closer to
those of Western market economies.
Measuring the Effect of the Zero Lower Bound on Yields and Exchange Rates in the U.K. and Germany (with John Williams)
The zero lower bound on nominal interest rates began to constrain many central banks’ setting of shortterm
interest rates in late 2008 or early 2009. According to standard macroeconomic models, this should have greatly
reduced the effectiveness of monetary policy and increased the efficacy of fiscal policy. However, these models
also imply that asset prices and privatesector decisions depend on the entire path of expected future
shortterm interest rates, not just the current level of the monetary policy rate. Thus, interest rates with a
year or more to maturity are arguably more relevant for asset prices and the economy, and it is unclear to what
extent those yields have been affected by the zero lower bound. In this paper, we apply the methods of Swanson and
Williams (2013) to medium and longerterm yields and exchange rates in the U.K. and Germany. In particular, we
compare the sensitivity of these rates to macroeconomic news during periods when shortterm interest rates were
very low to that during normal times. We find that: 1) USD/GBP and USD/EUR exchange rates have been essentially
unaffected by the zero lower bound, 2) yields on German bunds were essentially unconstrained by the zero bound
until late 2012, and 3) yields on U.K. gilts were substantially constrained by the zero lower bound in 2009 and
2012, but were surprisingly responsive to news in 201011. We compare these findings to the U.S. and discuss
their broader implications.
Implications of Labor Market Frictions for Risk Aversion and Risk Premia
A flexible labor margin allows households to absorb shocks to asset values with changes in hours worked as well as
changes in consumption. This ability to absorb shocks along both margins can greatly alter the household’s
attitudes toward risk, as shown in Swanson (2012). The present paper analyzes how frictional labor markets affect
that analysis. Risk aversion is higher: 1) in recessions, 2) in countries with more frictional labor markets, and
3) for households that have more difficulty finding a job. These predictions are consistent with empirical
evidence from a variety of sources. Traditional, fixedlabor measures of risk aversion show no stable relationship
to the equity premium in a standard real business cycle model with search frictions, while the closedform
expressions derived in the present paper match the equity premium closely.
Risk Aversion, Risk Premia, and the Labor Margin with Generalized Recursive Preferences
A flexible labor margin allows households to absorb shocks to asset values with changes in hours worked as well as
changes in consumption. This ability to absorb shocks along both margins greatly alters the household’s attitudes
toward risk, as shown by Swanson (2012). The present paper extends that analysis to the case of generalized recursive
preferences, as in Epstein and Zin (1989) and Weil (1989), including multiplier preferences, as in Hansen and Sargent
(2001). Understanding risk aversion for these preferences is especially important becasue they are the primary
mechansim being used to bring macroeconomic models into closer agreement with asset pricing facts. Measures of risk
aversion commonly used in the literature—including traditional, fixedlabor measures and CobbDouglas composite
good measures—show no stable relationship to the equity premium in a standard macroeconomic model, while the
closedform expressions derived in this paper match the equity premium closely. Thus, measuring risk aversion
correctly—taking into account the household’s labor margin—is necessary for risk aversion to
correspond to asset prices in the model.
Measuring the Effect of the Zero Lower Bound on Medium and LongerTerm Interest Rates (with John Williams)
The federal funds rate has been at the zero lower bound for over four years, since December 2008. According to standard
macroeconomic models, this should have greatly reduced the effectiveness of monetary policy and increased the efficacy
of fiscal policy. However, these models also imply that asset prices and privatesector decisions depend on the
entire path of expected future shortterm interest rates, not just the current level of the overnight rate.
Thus, interest rates with a year or more to maturity are arguably more relevant for asset prices and the economy, and it
is unclear to what extent those yields have been affected by the zero lower bound. In this paper, we measure the
effects of the zero lower bound on interest rates of any maturity by comparing the sensitivity of those interest rates
to macroeconomic news when shortterm interest rates were very low to that during normal times. We find that yields on
Treasury securities with a year or more to maturity were surprisingly responsive to news throughout 2008&emdash;10,
suggesting that monetary and fiscal policy were likely to have been about as effective as usual during this period.
Only beginning in late 2011 does the sensitivity of these yields to news fall closer to zero. We offer two explanations
for our findings: First, until late 2011, market participants expected the funds rate to lift off from zero within about
four quarters, minimizing the effects of the zero bound on medium and longerterm yields. Second, the Fed’s
unconventional policy actions seem to have helped offset the effects of the zero bound on medium and longerterm rates.
Let’s Twist Again: A HighFrequency EventStudy Analysis of Operation Twist and Its Implications for QE2
This paper undertakes a modern eventstudy analysis of Operation Twist and compares its effects to those that
should be expected for the recent quantitative policy announced by the Federal Reserve, dubbed “QE2”.
We first show that Operation Twist and QE2 are similar in magnitude. We identify five significant, discrete
announcements in the course of Operation Twist that potentially could have had a major effect on financial markets,
and show that three did have statistically significant effects. The cumulative effect of these five announcements
on longerterm Treasury yields is highly statistically significant but moderate, amounting to about 15 basis
points. This estimate is consistent both with Modigliani and Sutch’s (1966) time series analysis and with
the lower end of empirical estimates of Treasury supply effects in the literature.
Risk Aversion and the Labor Margin in Dynamic Equilibrium Models
The household’s labor margin has substantial effects on risk aversion, and hence asset prices, in dynamic
equilibrium models even when utility is additively separable between consumption and labor. This paper derives
simple, closedform expressions for risk aversion that take into account the household’s labor margin.
Ignoring this margin can dramatically overstate the household’s true aversion to risk. Risk premia on assets
priced with the stochastic discount factor increase essentially linearly with risk aversion, so measuring risk
aversion correctly is crucial for asset pricing in the model.
The Bond Premium in a DSGE Model with LongRun Real and Nominal Risks (with Glenn Rudebusch)
The term premium on nominal longterm bonds in the standard dynamic stochastic general equilibrium (DSGE) model
used in macroeconomics is far too small and stable relative to empirical measures obtained from the data—an
example of the “bond premium puzzle.” However, in models of endowment economies, researchers have been
able to generate reasonable term premiums by assuming that investors have recursive EpsteinZin preferences and
face longrun economic risks. We show that introducing EpsteinZin preferences into a canonical DSGE model can
also produce a large and variable term premium without compromising the model’s ability to fit key
macroeconomic variables. Longrun nominal risks further improve the model’s ability to fit the data, but do
not substantially reduce the model’s need for a high level of household risk aversion.
Examining the Bond Premium Puzzle with a DSGE Model (with Glenn Rudebusch)
The basic inability of standard theoretical models to generate a sufficiently large and variable nominal bond risk
premium has been termed the “bond premium puzzle”. We show that the term premium on longterm bonds is
far too small and stable relative to the data in the canonical dynamic stochastic general equilibrium (DSGE) model
used in macroeconomics. We find that introducing longmemory habits in consumption as well as labor market
frictions can help fit the term premium, but only by seriously distorting the DSGE model’s ability to fit
other macroeconomic variables, such as the real wage; therefore, the bond premium puzzle remains.
Convergence and Anchoring of Yield Curves in the Euro Area (with Michael Ehrmann, Marcel Fratzscher, and Refet Gürkaynak)
We study the convergence of European bond markets and the anchoring of inflation expectations in the euro area
using highfrequency bond yield data for France, Germany, Italy, and Spain as well as smaller euro area countries
and a control group comprising the UK, Denmark, and Sweden. We find that Economic and Monetary Union (EMU) has led
to substantial convergence in euro area sovereign bond markets in terms of interest rate levels, unconditional
daily fluctuations, and conditional responses to major macroeconomic announcements. Our findings also suggest a
substantial increase in the anchoring of longterm inflation expectations since EMU, particularly for Italy and
Spain, which have seen their longterm interest rates become much lower, much less volatile, and much better
anchored in response to news. Finally, we present evidence that the elimination of exchange rate risk and the
adoption of a common monetary policy were the primary drivers of bond market convergence in the euro area, as
opposed to fiscal policy restraint and the loose exchange rate peg of the 1990s.
Macroeconomic Implications of Changes in the Term Premium (with Glenn Rudebusch and Brian Sack)
Linearized New Keynesian models and empirical noarbitrage, macrofinance models offer little insight regarding the
implications of changes in bond term premiums for economic activity. We investigate these implications using both a
structural model and a reducedform framework. We show that there is no structural relationship running from the
term premium to economic activity, but a reducedform empirical analysis does suggest that a decline in the term
premium has typically been associated with stimulus to real economic activity, which contradicts earlier results in
the literature.
Bayesian Optimal Policy in the Presence of Regime Change and Local Parameter Uncertainty
This paper proposes an approximation to the optimal policy problem in forwardlooking models with regime change
that allows for tractable solution for the optimal policy even when the parameters of the model and the current
regime are not known with certainty. The linearquadratic framework is adhered to as much as possible, with a
particular emphasis on maintaining the property of separation of estimation and control, which is crucial for
maintaining tractability. Generality is achieved by allowing for full Bayesian updating of all aspects of the
model, including model parameters, the probability that a regime change has occurred, and the values of all
(generally nonnormal) shocks hitting the model each period. The methods of this paper provide results that can be
quite useful in practice—for example, they fit the policy behavior of the Federal Reserve in the late 1990s
very well, which standard methods fail to do.
The Bond Yield “Conundrum” from a MacroFinance Perspective (with Glenn Rudebusch and Tao Wu)
In 2004 and 2005, longterm interest rates remained remarkably low despite improving economic conditions and rising
shortterm interest rates, a situation that former Fed Chairman Alan Greenspan dubbed a “conundrum.” We
document the extent and timing of this conundrum using two empirical noarbitrage macrofinance models of the term
structure of interest rates. These models confirm that the recent behavior of longterm yields has been
unusual—that is, it cannot be explained within the framework of the models. Therefore, we consider other
macroeconomic factors omitted from the models and find that some of these variables, particularly declines in
longterm bond volatility, may explain a portion of the conundrum. Foreign official purchases of U.S Treasuries
appear to have played little or no role.
Inflation Targeting and the Anchoring of Inflation Expectations in the Western Hemisphere
(with Refet Gürkaynak, Andrew Levin, and Andrew Marder)
We investigate the extent to which longrun inflation expectations are well anchored in three western hemisphere
countries—Canada, Chile, and the United States—using a highfrequency eventstudy
analysis. Specifically, we use daily data on farahead forward inflation compensation—the difference between
forward rates on nominal and inflationindexed bonds—as an indicator of financial market perceptions of
inflation risk and the expected level of inflation at long horizons. For the United States, we find that farahead
forward inflation compensation has reacted significantly to macroeconomic data releases, suggesting that longrun
inflation expectations have not been completely anchored. In contrast, the Canadian inflation compensation data
have exhibited significantly less sensitivity to Canadian and U.S. macroeconomic news, suggesting that inflation
targeting in Canada has helped to anchor longrun inflation expectations in that country. Finally, while the
requisite data for Chile are only available for a limited sample period (20022005), our results are consistent
with the hypothesis that inflation targeting in Chile helped anchor longrun inflation expectations in that country
as well.
Does Inflation Targeting Anchor LongRun Inflation Expectations? Evidence from LongTerm Bond Yields in the U.S., U.K., and Sweden
(with Refet Gürkaynak and Andrew Levin)
We investigate the extent to which inflation expectations have been more firmly anchored in the United
Kingdom—a country with an explicit inflation target—than in the United States—which has no such
target—using the difference between farahead forward rates on nominal and inflationindexed bonds as a
measure of compensation for expected inflation and inflation risk at long horizons. We show that farahead forward
inflation compensation in the U.S. exhibits substantial volatility, especially at low frequencies, and displays a
highly significant degree of sensitivity to economic news. Similar patterns are evident in the U.K. prior to 1997,
when the Bank of England was not independent, but have been strikingly absent since the Bank of England gained
independence in 1997. Our findings are further supported by comparisons of dispersion in longerrun inflation
expectations of professional forecasters and by evidence from Sweden, another inflation targeting country with a
relatively long history of inflationindexed bonds. Our results support the view that an explicit and credible
inflation target helps to anchor the private sector’s views regarding the distribution of longrun inflation
outcomes.
Optimal TimeConsistent Monetary Policy in the New Keynesian Model with Repeated Simultaneous Play
(with Gauti Eggertsson)
We solve for the optimal timeconsistent monetary policy in the New Keynesian model with repeated simultaneous play
between the monetary authority, households, and firms. Recent work on optimal timeconsistent monetary policy has
emphasized the existence of multiple Markov perfect equilibria in the New Keynesian model (e.g., King and Wolman,
2004). In this paper, we show that this multiplicity is not intrinsic to the New Keynesian model itself, but is
instead driven by a special timing assumption by previous authors that play is “ repeated
Stackelberg”—in which case the monetary authority must precommit each period to a value for the
monetary instrument—as opposed to repeated simultaneous, in which case the monetary authority and the private
sector determine the economic equilibrium simultaneously and jointly every period. To illlustrate this, we derive a
closedform solution for the set of all possible Markov perfect equilibria in the twoperiod Taylor contracting
version of the New Keynesian model under repeated simultaneous play and show that the equilibrium in that model is
unique.
Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements
(with Refet Gürkaynak and Brian Sack)
We investigate the effects of U.S. monetary policy on asset prices using a highfrequency eventstudy analysis. We
test whether these effects are adequately captured by a single factor—changes in the federal funds rate
target—and find that they are not. Instead, we find that two factors are required. These factors have a
structural interpretation as a “current federal funds rate target” factor and a “future path of
policy” factor, with the latter closely associated with FOMC statements. We measure the effects of these two
factors on bond yields and stock prices using a new intraday dataset going back to 1990. According to our
estimates, both monetary policy actions and statements have important but differing effects on asset prices, with
statements having a much greater impact on longerterm Treasury yields.
Futures Prices as RiskAdjusted Forecasts of Monetary Policy (with Monika Piazzesi)
Many researchers have used federal funds futures rates as measures of financial markets’ expectations of
future monetary policy. However, to the extent that federal funds futures reflect risk premia, these measures
require some adjustment to account for these premia. In this paper, we document that excess returns on federal
funds futures have been positive on average and strongly countercyclical. In particular, excess returns are
surprisingly well predicted by macroeconomic indicators such as employment growth and financial businesscycle
indicators such as Treasury yield spreads and corporate bond spreads. Excess returns on eurodollar futures display
similar patterns. We document that simply ignoring these risk premia has important consequences for the expected
future path of monetary policy. We also show that risk premia matter for some futuresbased measures of monetary
policy surprises used in the literature.
Have Increases in Federal Reserve Transparency Improved PrivateSector Interest Rate Forecasts?
Yes. This paper shows that, since the late 1980s, U.S. financial markets and private sector forecasters have
become: 1) better able to forecast the federal funds rate at horizons out to several months, 2) less surprised by
Federal Reserve announcements, 3) more certain of their interest rate forecasts ex ante, as measured by
interest rate options, and 4) less diverse in the crosssectional variety of their interest rate forecasts. We also
present evidence that strongly suggests increases in Federal Reserve transparency played a role: for example,
private sector forecasts of GDP and inflation have not experienced similar improvements over the same period,
indicating that the improvement in interest rate forecasts has been special.
HigherOrder ‘Perturbation’ Solutions to Dynamic, DiscreteTime Rational Expectations Models
(with Gary Anderson and Andrew Levin)
We present an algorithm and software routines for computing nthorder Taylor series approximate solutions to
dynamic, discretetime rational expectations models around a nonstochastic steady state. The primary advantage of
higherorder (as opposed to first or secondorder) approximations is that they are valid not just locally, but
often globally (i.e., over nonlocal, possibly very large compact sets) in a rigorous sense that we specify. We
apply our routines to compute first through seventhorder approximate solutions to two standard macroeconomic
models, a stochastic growth model and a lifecycle consumption model, and discuss the quality and global properties
of these solutions.
The Sensitivity of LongTerm Interest Rates to Economic News: Evidence and Implications for Macroeconomic Models
(with Refet Gürkaynak and Brian Sack)
This paper demonstrates that longterm forward interest rates in the U.S. often react considerably to surprises in
macroeconomic data releases and monetary policy announcements. This behavior is in contrast to the prediction of
many macroeconomic models, in which the longrun properties of the economy are assumed to be timeinvariant and
perfectly known by all economic agents: Under those assumptions, the shocks we consider would have only transitory
effects on shortterm interest rates, and hence would not generate large responses in forward rates. Our empirical
findings suggest that private agents adjust their expectations of the longrun inflation rate in response to
macroeconomic and monetary policy surprises. We present an alternative model that captures this behavior.
Consistent with our hypothesis, forward rates derived from inflationindexed Treasury debt show little sensitivity
to these shocks, indicating that the response of nominal forward rates is mostly driven by inflation
compensation.
MarketBased Measures of Monetary Policy Expectations (with Refet Gürkaynak and Brian Sack)
A number of recent papers have used different financial market instruments to measure nearterm expectations of the
federal funds rate and have used highfrequency changes in these instruments around FOMC announcements to measure
monetary policy shocks. This paper evaluates the empirical success of a variety of financial market instruments in
predicting the future path of monetary policy. All of the instruments we consider provide forecasts that are
clearly superior to those of standard time series models at all of the horizons considered. Among financial market
instruments, we find that federal funds futures dominate all the other securities in forecasting monetary policy at
horizons out to six months. For longer horizons, the predictive power of many of the instruments we consider is
very similar. In addition, we present evidence that monetary policy shocks computed using the currentmonth federal
funds futures contract are influenced by changes in the timing of policy actions that do not influence the expected
course of policy beyond a horizon of about six weeks. We propose an alternative shock measure that captures changes
in market expectations of policy over slightly longer horizons.
Do Federal Reserve Policy Surprises Reveal Superior Information About the Economy? (with Jon Faust and Jonathan Wright)
A number of recent papers have hypothesized that the Federal Reserve possesses information about the course of
inflation and output that is unknown to the private sector, and that policy actions by the Federal Reserve convey
some of this superior information. We conduct two tests of this hypothesis: 1) could monetary policy
surprises be used to improve the private sector’s ex ante forecasts of subsequent macroeconomic statistical
releases, and 2) does the private sector revise its forecasts of macroeconomic statistical releases in
response to these monetary policy surprises? We find little evidence that Federal Reserve policy surprises convey
superior information about the state of the economy: they could not systematically be used to improve forecasts of
statistical releases and forecasts are not systematically revised in response to policy surprises. One possible
exception to this pattern is Industrial Production, a statistic that the Federal Reserve produces.
Identifying the Effects of Monetary Policy Shocks on Exchange Rates Using HighFrequency Data
(with Jon Faust, John Rogers, and Jonathan Wright)
In this paper, we bring highfrequency financial market data to bear to identify the monetary policy shocks
following the approach of Faust, Swanson, and Wright (2002). The approach begins by calculating changes in exchange
rates, interest rates, and interest rate futures in a narrow window around announced Federal Open Market Committee
(FOMC) policy moves. We assume that these highfrequency changes are driven by the unexpected component of the FOMC
decision and give a measure of the impulse response of these variables to the policy shock. We then impose that the
impulse responses of the exchange rate and U.S. and foreign shortterm interest rates in a standard openeconomy
VAR match the responses we have estimated from the highfrequency financial market data. For Germany, we formally
reject the recursive identification, but we are unable to reject the recursive ordering for the U.K. Our impulse
responses and variance decompositions qualitatively agree with those obtained from the usual recursive
identification, although we find less evidence of a “price puzzle” and more persistent effects of
monetary policy on domestic and foreign output. We are also able to estimate contemporaneous effects of
U.S. monetary policy shocks on exchange rates and foreign interest rates.
Identifying VARs Based on HighFrequency Futures Data (with Jon Faust and Jonathan Wright)
Using prices from federal funds futures contracts, we derive the unexpected component of Federal Reserve policy
decisions and assess their impact on the future trajectory of interest rates. We show how this information can be
used to identify the effects of a monetary policy shock within a standard monetary policy VAR. We find that the
usual recursive identification used in the literature is rejected, but we nevertheless agree with the
literature’s conclusion that only a small fraction of the variance of output is due to monetary policy
shocks.
NAIRU Uncertainty and Nonlinear Policy Rules (with Laurence Meyer and Volker Wieland)
Meyer (1999) has suggested that episodes of heightened uncertainty about the NAIRU may warrant a nonlinear policy
response to changes in the unemployment rate. This paper offers a theoretical justification for such a nonlinear
policy rule, and provides some empirical evidence on the relative performance of linear and nonlinear rules when
there is heightened uncertainty about the NAIRU.
Econometric Estimation when the “True” Model Errors Are Observed
Stochastic disturbance terms in an econometric model encompass two types of error: 1) specification error resulting
from an econometric model that is simpler than the “true” economic model, and 2) stochastic innovations
to the “true” economic model. It is standard practice to minimize these composite errors to estimate
the econometric model. In many interesting cases, however, the “true” model forecasts or errors can be
regarded as observed through futures markets, prediction markets, or surveys of professional forecasters. When the
true model forecasts or errors are observed, econometric estimation can be improved by minimizing the distance from
the econometric model’s residuals to the true model errors, rather than to a vector of zeros. This paper
derives the theory and applies the method to estimate simple time series models. The errormatching estimation
method prescribed by this paper avoids overweighting large model errors that were unforecastable ex ante, and
reduces standard errors substantially, by about 20–40% for the simple time series examples considered.
Optimal Nonlinear Policy: Signal Extraction with a NonNormal Prior
The literature on optimal monetary policy typically makes three major assumptions: 1) policymakers’
preferences are quadratic, 2) the economy is linear, and 3) stochastic shocks and policymakers’ prior beliefs
about unobserved variables are normally distributed. This paper relaxes the third assumption and explores its
implications for optimal policy. The separation principle continues to hold in this framework, allowing for
tractability and application to forwardlooking models, but policymakers’ beliefs are no longer updated in a
linear fashion, allowing for plausible nonlinearities in optimal policy. We consider in particular a class of
models in which policymakers’ priors about the natural rate of unemployment are diffuse in a region around
the mean. When this is the case, it is optimal for policy to respond cautiously to small surprises in the observed
unemployment rate, but become increasingly aggressive at the margin. These features of optimal policy match
statements by Federal Reserve officials and the behavior of the Fed in the 1990s.
Signal Extraction and NonCertaintyEquivalence in Optimal Monetary Policy Rules
A standard result in the literature on monetary policy rules is that of certaintyequivalence: Given the expected
values of the state variables of the economy, policy should be independent of all higher moments of those
variables. Some exceptions to this rule have been pointed out in the literature, including restricting the policy
response to a limited subset of state variables, or to estimates of the state variables that are biased. In
contrast, this paper studies fully optimal policy rules with optimal estimation of state variables. The rules in
this framework exhibit certaintyequivalence with respect to estimates of an unobserved state variable
(“excess demand”) X, but are not certaintyequivalent when (i) X must be estimated by signal extraction
and (ii) the optimal rule is expressed as a reduced form that combines policymakers’ estimation and
policysetting stages. I find that it is optimal for policymakers to attenuate their reaction to a variable about
which uncertainty has increased, while responding more aggressively to variables about which uncertainty has not
changed.
The Relative Price and Relative Productivity Channels for Aggregate Fluctuations
This paper demonstrates that sectoral heterogeneity itself—without any additional bells or whistles—has
firstorder implications for the transmission of aggregate shocks to aggregate variables in an otherwise standard
DSGE model. The effects of sectoral heterogeneity on this transmission are decomposed into two channels: a
“relative price” channel and a “relative productivity” channel. The relative price channel
results from changes in the relative prices of aggregates, such as investment visavis consumption goods, which
occurs in a sectoral model in response to even standard aggregate shocks. The relative productivity channel arises
from changes in the distribution of inputs across sectors. We show that, for standard sectoral models, this latter
channel is secondorder, but becomes firstorder if we consider a nontraded input such as capital utilization or
introduce a wedge that thwarts the steadystate equalization of marginal products of a traded input across
sectors. For reasonable parameterizations, the relative productivity channel causes aggregate productivity to vary
procyclically in response to nontechnological shocks such as changes in government purchases.
Measuring the Cyclicality of Real Wages: How Important is the Firm’s Point of View?
There is a growing consensus among economists that real wages in the postwar U. S. have been moderately to strongly
procyclical, particularly in panel data on workers. This has greatly bolstered technologydriven theories of
business cycles at the expense of more Classical models. This paper makes the point that technological movements
in firm’s labor demand should be tested with a wage that is deflated by the firm’ own price of output,
with appropriate controls for intermediate inputs, and with respect to the cyclical state of the firm’s own
industry, as opposed to the state of the aggregate economy. Failure to control for these factors is found to lead
to substantial overrejection of the Classical model. In detailed industry data, with controls for changes in
worker composition, I find that a vast majority of sectors have paid real product wages that vary inversely (i.e.,
countercyclically) with the state of their industry.
Real Wage Cyclicality in the PSID
Previous studies of real wage cyclicality have made only sparing use of the microdata detail that is available in
the Panel Study of Income Dynamics (PSID). The present paper brings to bear this additional detail to investigate
the robustness of previous results and to examine whether there are important crosssectional and demographic
differences in wage cyclicality. Although real wages were procyclical across the entire distribution of workers
from 1967 to 1991, the wages of lowerincome, younger, and lesseducated workers exhibited greater
procyclicality. However, workers’ straighttime hourly pay rates have been acyclical, suggesting that more
variable pay margins such as bonuses, overtime, late shift premia, and commissions have played a substantial if not
primary role in generating procyclicality.
