Risk Aversion, Risk Premia, and the Labor Margin with Generalized Recursive Preferences
2012-17 :: March 2013
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), all of which are used to bring macroeconomic models into closer agreement with asset pricing facts. Measures of risk aversion commonly used in the literature -- including Cobb-Douglas composite good measures as well as traditional, fixed-labor measures -- show no stable relationship to the equity premium in a standard macroeconomic model, while the closed-form expressions derived in this paper match the equity premium closely. Thus, measuring risk aversion correctly is necessary for it to correspond to asset prices in the model.
Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates
2012-02 :: With Williams :: January 2013
The federal funds rate has been at the zero lower bound for over four years, since December 2008. According to many macroeconomic models, this should have greatly reduced the effectiveness of monetary policy and increased the efficacy of fiscal policy. However, standard macroeconomic theory also implies that private-sector decisions depend on the entire path of expected future short term 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 the economy, and it is unclear to what extent those yields have been constrained. In this paper, we measure the effects of the zero lower bound on interest rates of any maturity by estimating the time-varying high-frequency sensitivity of those interest rates to macroeconomic announcements relative to a benchmark period in which the zero bound was not a concern. We find that yields on Treasury securities with a year or more to maturity were surprisingly responsive to news throughout 2008–10, 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 longer-term yields. Second, the Fed’s unconventional policy actions seem to have helped offset the effects of the zero bound on medium- and longer-term rates.
Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models
2006-01 :: With Anderson and Levin :: January 2006
We present an algorithm and software routines for computing nth order
Taylor series approximate solutions to dynamic, discrete-time rational expectations models around a nonstochastic steady state. The primary advantage of higher-order (as opposed to first- or second-order) 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 seventh-order approximate solutions to two standard macroeconomic models, a stochastic growth model and a life-cycle consumption model, and discuss the quality and global properties of these solutions.
Optimal Time-Consistent Monetary Policy in the New Keynesian Model with Repeated Simultaneous Play
Manuscript :: With Eggertsson :: January 2008
We solve for the optimal time-consistent monetary policy in the New Keynesian model with repeated simultaneous play between the monetary authority, households, and firms. Recent work on optimal time-consistent 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 special timing assumptions by previous authors that play is "repeated Stackelberg"--so that 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 closed-form solution for the set of all possible Markov perfect equilibria in the two-period Taylor contracting version of the New Keynesian model under repeated simultaneous play and show that the equilibrium in that model is unique.
Tractable Bayesian Optimal Policy in the Presence of Regime Change and Local Parameter Uncertainty
Manuscript :: January 2008
This paper proposes an approximation to the optimal policy problem in forward-looking 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 linear-quadratic 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 non-normal) 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.
Econometric Estimation When the 'True' Model Errors Are Observed
Manuscript :: February 2002
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 errors are actually observable through futures markets and other market-based measures of expectations. When the true model errors are observed, econometric estimation can be improved upon 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 a simple time series model. Estimates of parameters and impulse response functions agree with those obtained using the usual method, but standard errors are reduced by 20-50%.
Risk Aversion and the Labor Margin in Dynamic Equilibrium Models
American Economic Review 102(4), June 2012, 1663-1691
The household's labor margin has a substantial effect 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, closed-form 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 understanding asset prices in the model.
The Bond Premium in a DSGE Model with Long-Run Real and Nominal Risks
American Economic Journal: Macroeconomics 4, January 2012, 105-143 :: With Rudebusch
The term premium on nominal long-term 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 Epstein-Zin preferences and face long-run economic risks. We show that introducing Epstein-Zin preferences into a canonical DSGE model can also produce a large and variable term premium without compromising the model's ability to fi
t key macroeconomic variables. Long-run real and nominal risks further improve the model's ability to
fit the data with a lower level of household risk aversion.
Let's Twist Again: A High-Frequency Event-Study Analysis of Operation Twist and Its Implications for QE2
Brookings Papers on Economic Activity Spring, September 2011, 151-188
This paper undertakes a modern event-study analysis of Operation Twist and uses its estimated effects to assess what should be expected for the recent policy of quantitative easing by the Federal Reserve, dubbed "QE2." The paper first shows that Operation Twist and QE2 are similar in magnitude. It then identifies six significant, discrete announcements in the course of Operation Twist that could have had a major effect on financial markets and shows that four did have statistically significant effects. The cumulative effect of these six announcements on longer-term Treasury yields is highly statistically significant but moderate, amounting to about 15 basis points (bp). This estimate is consistent both with time-series analysis undertaken not long after the event and with the lower end of empirical estimates of Treasury supply effects in the literature. The effects of Operation Twist on long-term agency and corporate bond yields are also statistically significant but smaller, about 13 bp for agency securities and 2 to 4 bp for corporates. Thus, the effects of Operation Twist seem to diminish substantially as one moves from Treasury securities toward private sector credit instruments.
Convergence and Anchoring of Yield Curves in the Euro Area
Review of Economics and Statistics 93, February 2011, 350-364 :: With Ehrmann, Fratzscher, and Gurkaynak
We study the convergence of European bond markets and the anchoring of inflation expectations in the euro area using high-frequency bond yield data for France, Germany, Italy, and Spain, some smaller euro area countries, and a control group comprising the U.K., 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 long-term inflation expectations since EMU, particularly for Italy and Spain, which have seen their long-term 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.
Does Inflation Targeting Anchor Long-Run Inflation Expectations? Evidence from Long-Term Bond Yields in the U.S., U.K., and Sweden
Journal of the European Economic Association 8, December 2010, 1208-1242 :: With Gurkaynak and 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--a country with no such target--using the difference between far-ahead forward rates on nominal and inflation-indexed bonds as a measure of compensation for expected inflation and inflation risk at long horizons. We show that far-ahead 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 longer-run inflation expectations of professional forecasters and by evidence from Sweden, another inflation targeting country with a relatively long history of inflation-indexed 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 long-run inflation outcomes.
Examining the Bond Premium Puzzle with a DSGE Model
Journal of Monetary Economics 55, October 2008, S111-S126 :: With 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 long-term bonds in the canonical dynamic stochastic general equilibrium (DSGE) model used in macroeconomics is far too small and stable relative to the data. We find that introducing long-memory 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.
Futures Prices as Risk-Adjusted Forecasts of Monetary Policy
Journal of Monetary Economics 55(4), May 2008, 677-691 :: With 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. 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 business-cycle 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 significantly biases forecasts of the future path of monetary policy. We also show that risk premia matter for some futures-based measures of monetary policy shocks used in the literature.
Real Wage Cyclicality in the Panel Study of Income Dynamics
Scottish Journal of Political Economy 54(5), November 2007, 617-647
Previous studies of real wage cyclicality have made only sparing use of the micro-data 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 the previous results and to examine whether there are important cross-sectional and demographic differences in wage cyclicality. Although real wages were procyclical across the entire distribution of workers from 1967 to 1991, the wages of lower-income, younger, and less-educated workers exhibited greater procyclicality. However, workers' straight-time 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.
Macroeconomic Implications of Changes in the Term Premium
Federal Reserve Bank of St. Louis Review 89(4), July 2007, 241-269 :: With Rudebusch and Sack
Linearized New Keynesian models and empirical no-arbitrage macro-finance models offer little insight regarding the implications of changes in bond term premiums for economic activity. This paper investigates these implications using both a structural model and a reduced-form framework. The authors show that there is no structural relationship running from the term premium to economic activity, but a reduced-form 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.
Market-Based Measures of Monetary Policy Expectations
Journal of Business and Economic Statistics 25(2), April 2007, 201-212 :: With Gurkaynak and Sack
A number of recent papers have used different financial market instruments to measure near-term expectations of the federal funds rate and the high-frequency 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 current-month 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.
Inflation Targeting and the Anchoring of Inflation Expectations in the Western Hemisphere
In Series on Central Banking, Analysis, and Economic Policies: Monetary Policy under Inflation Targeting, 10, ed. by F. Mishkin and K. Schmidt-Hebbel :: Santiago, Chile: Banco Central de Chile, 2007 :: With Gurkaynak, Levin, and Marder
We investigate the extent to which long-run inflation expectations are well anchored in three western hemisphere countries--Canada, Chile, and the United States--using a high-frequency event-study analysis. Specifically, we use daily data on far-ahead forward inflation compensation--the difference between forward rates on nominal and inflation-indexed 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 far-ahead forward inflation compensation reacts significantly to macroeconomic data releases, implying that long-run inflation expectations are not completely anchored. In contrast, the Canadian inflation compensation data do not exhibit significant sensitivity to either Canadian or U.S. macroeconomic news, confirming that inflation targeting in Canada has been successful in anchoring long-run inflation expectations. Finally, while the requisite data for Chile is only available for a limited sample period (2002-2005), our results are consistent with the hypothesis that inflation targeting in Chile has also succeeded in anchoring long-run inflation expectations.
The Bond Yield "Conundrum" from a Macro-Finance Perspective
Monetary and Economic Studies 24(S-1), December 2006, 83-128 :: With Rudebusch and Wu
In 2004 and 2005, long-term interest rates remained remarkably low
despite improving economic conditions and rising short-term interest rates,
a situation that then-Federal Reserve Board Chairman Alan Greenspan
dubbed a "conundrum." We document the extent and timing of this conundrum using two empirical no-arbitrage macro-finance models of the term structure of interest rates. These models confirm that the recent behavior of long-term 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 long-term bond volatility, may explain a portion of the conundrum. Foreign official purchases of U.S. Treasuries appear to have played little or no role.
The Relative Price and Relative Productivity Channels for Aggregate Fluctuations
Contributions to Macroeconomics 6, October 2006, 39
This paper demonstrates that sectoral heterogeneity itself--without any additional bells or whistles--has first-order 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 vis-a-vis 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 second-order, but becomes first-order if we consider a nontraded input such as capital utilization or introduce a wedge that thwarts the steady-state 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 non-technological shocks such as changes in government purchases.
Have Increases in Federal Reserve Transparency Improved Private Sector Interest Rate Forecasts?
Journal of Money, Credit, and Banking 38(3), April 2006, 791-819
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 cross-sectional 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.
Optimal Nonlinear Policy: Signal Extraction with a Non-Normal Prior
Journal of Economic Dynamics and Control 30(2), February 2006, 185-203
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 forward-looking 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, optimal policy responds cautiously to small surprises in the observed unemployment rate, but becomes increasingly aggressive at the margin. These features match statements by Federal Reserve officials and the behavior of the Fed in the 1990s.
Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements
International Journal of Central Banking 1(1), May 2005, 55-93 :: With Gurkaynak and Sack
We investigate the effects of U.S. monetary policy on asset prices using a high-frequency event-study 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 Federal Open Market Committee statements.We measure the effects of these two factors on bond yields and stock prices using a new intraday data set 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 longer-term Treasury yields.
The Sensitivity of Long-Term Interest Rates to Economic News: Evidence and Implications for Macroeconomic Models
American Economic Review 95(1), March 2005, 425-436 :: With Gurkaynak and Sack
This paper demonstrates that long-term 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 long-run properties of the economy are assumed to be time-invariant and perfectly known by all economic agents: Under those assumptions, the shocks we consider would have only transitory effects on short-term interest rates, and hence would not generate large responses in forward rates. Our empirical findings suggest that private agents adjust their expectations of the long-run 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 inflation-indexed Treasury debt show little sensitivity to these shocks, indicating that the response of nominal forward rates is mostly driven by inflation compensation.
Identifying VARs Based on High-Frequency Futures Data
Journal of Monetary Economics 51(6), September 2004, 1107-1131 :: With Faust and 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.
Measuring the Cyclicality of Real Wages: How Important is the Firm's Point of View?
Review of Economics and Statistics 86(1), February 2004, 362-377
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 technology-driven 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's 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 over-rejection 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.
Signal Extraction and Non-Certainty-Equivalence in Optimal Monetary Policy Rules
Macroeconomic Dynamics 8(1), January 2004, 27-50
A standard result in the literature on monetary policy rules is that of certainty-equivalence: 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 certainty-equivalence with respect to estimates of an unobserved state variable ("excess demand") X, but are not certainty-equivalent 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 policy-setting 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.
Do Federal Reserve Policy Surprises Reveal Superior Information about the Economy?
Contributions to Macroeconomics 4(1), 2004, 1-29 :: With Faust and 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 High-Frequency Data
Journal of the European Economic Association 1(5), September 2003, 1031-1057 :: With Faust, Rogers, and Wright
In this paper, we bring high-frequency 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 high-frequency 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 short-term interest rates in a standard open-economy VAR match the responses we have estimated from the high-frequency 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.
NAIRU Uncertainty and Nonlinear Policy Rules
American Economic Review 91(2), May 2001, 226-231 :: With Meyer and 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.