Research
Determinacy and Identification with Taylor Rules
Journal of Political Economy, Vol. 119, No. 3 (June 2011), pp. 565-615. Online Appendix B. JSTOR link, including html, pdf, and online appendix. Manuscript with Technical Appendix The technical appendix documents a few calculations. Don't miss starting on Technical Appendix page 6 a full analytical solution to the standard three equation model. I include the manuscript just so equation references in the Technical Appendix will work, the previous links to the published version are better.
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Journal of Political Economy, Vol. 119, No. 3 (June 2011), pp. 565-615. Online Appendix B. JSTOR link, including html, pdf, and online appendix. Manuscript with Technical Appendix The technical appendix documents a few calculations. Don't miss starting on Technical Appendix page 6 a full analytical solution to the standard three equation model. I include the manuscript just so equation references in the Technical Appendix will work, the previous links to the published version are better.
Most people think Taylor rules stabilize inflation: Inflation rises, the Fed raises interest rates; this lowers “demand’’ and lowers future inflation. New-Keynesian models don’t work this way. In the models, the Fed reacts to inflation by setting interest rates in a way that ends up increasing future inflation. Inflation is “determined” as the unique initial value that doesn't set off accelerating inflation. Alas, there is nothing in economics to rule out accelerating inflation or deflation. I conclude that new-Keynesian models with Taylor rules don’t determine the price level any better than classic fixed interest rate targets. Price level determinacy requires ingredients beyond the Taylor principle, such as a non-Ricaridan fiscal regime. I survey the new-Keynesian literature to verify that no simple answer to this problem exists. All of the fixes slip in a commitment by the government to blow up the world at some point.
Even if the new-Keynesian model did work, The parameters of the Taylor rule relating interest rates to inflation and other variables are not identified. You can't measure "off equilibrium" behavior from data in an equilibrium. Thus, Taylor rule regressions cannot be used to argue that the Fed conquered inflation by moving from a "passive" to an "active" policy in the early 1980s.
The appendix uncovers an interesting mistake in the classic Obstfeld and Rogoff (1983) attempt to prune inflationary equilibria, but also shows that reversion to a price level target can do the trick. The Techical Appendix has algebra for determinacy regions and solutions of the three-equation New-Keynesian model, as well as other issues.
This article supersedes the two papers titled "Inflation Determination with Taylor Rules: A Critical Review"and "Identification with Taylor Rules: A Critical Review" (September 2007).
Quantitative Easing 2
March 3 2011 Comments on Jim Hamilton and Jing Wu, 2011, "The Effectiveness of Alternative Monetary Policy Tools in a Zero Lower Bound Environment", at the spring NBER Monetary Economics meeting. Slides. (The Op-ed section contains several op-eds and blog posts on qe2.)
March 3 2011 Comments on Jim Hamilton and Jing Wu, 2011, "The Effectiveness of Alternative Monetary Policy Tools in a Zero Lower Bound Environment", at the spring NBER Monetary Economics meeting. Slides. (The Op-ed section contains several op-eds and blog posts on qe2.)
Understanding fiscal and monetary policy in the great recession: Some unpleasant fiscal arithmetic.
European Economic Review 55 2-30 ScienceDirect Link.
Why there was a big recession; will we face inflation or deflation, can the Fed do anything about it? Many facets of the current situation and policy make sense if you ask about joint fiscal and monetary policy. A fiscal inflation will look much different than most people think. Slides that go with the paper. Appendix with the algebra for government debt valuation equations. A short simple version, my presentation at the Fall NBER EFG conference. A video of a short presentation given to the University Alumni Club in New York, October 2010. Slides for the New York talk if you were there
European Economic Review 55 2-30 ScienceDirect Link.
Why there was a big recession; will we face inflation or deflation, can the Fed do anything about it? Many facets of the current situation and policy make sense if you ask about joint fiscal and monetary policy. A fiscal inflation will look much different than most people think. Slides that go with the paper. Appendix with the algebra for government debt valuation equations. A short simple version, my presentation at the Fall NBER EFG conference. A video of a short presentation given to the University Alumni Club in New York, October 2010. Slides for the New York talk if you were there
Nova/Atrium Lecture in Macro/Finance (Video)
(Also web page on the event) Lecture given at NOVA school of business and economics in Lisbon, Portugal, 2010. Thinking through fiscal and monetary policy, along the lines later written up in Inflation and Debt and Understanding fiscal and monetary policy in the great recession.
(Also web page on the event) Lecture given at NOVA school of business and economics in Lisbon, Portugal, 2010. Thinking through fiscal and monetary policy, along the lines later written up in Inflation and Debt and Understanding fiscal and monetary policy in the great recession.
The Squam Lake Report: Fixing the Financial System
Princeton: Princeton University Press 2010. With Kenneth R. French, Martin N. Baily, John Y. Campbell, Douglas W. Diamond, Darrell Duffie, Anil K. Kashyap, Frederic S. Mishkin, Raghuram G. Rajan, David S. Scharfstein, Robert J. Shiller, Hyun Song Shin, Matthew J. Slaughter, Jeremy C. Stein, and Rene M. Stultz
Princeton: Princeton University Press 2010. With Kenneth R. French, Martin N. Baily, John Y. Campbell, Douglas W. Diamond, Darrell Duffie, Anil K. Kashyap, Frederic S. Mishkin, Raghuram G. Rajan, David S. Scharfstein, Robert J. Shiller, Hyun Song Shin, Matthew J. Slaughter, Jeremy C. Stein, and Rene M. Stultz
Lessons from the financial crisis
Jan 2010 Regulation 32(4), 34-37. The financial crisis is mainly about too big to fail expectations. The only way out is to limit the government’s authority to bail out.
Jan 2010 Regulation 32(4), 34-37. The financial crisis is mainly about too big to fail expectations. The only way out is to limit the government’s authority to bail out.
Can Learnability Save New-Keynesian Models?
Journal of Monetary Economics 56 (2009) 1109–1113. JME link .This is a response to Bennett McCallum’s “is the New-Keynesian Analysis Critically Flawed” which says yes. I think McCallum got it backwards -- the bounded equilibrium is not learnable, the explosive ones are learnable. Furthermore, I’m not convinced that a hypothetical threat by the Fed to take us to an “unlearnable” equilibrium is a satisfactory foundation for price level determination.
Journal of Monetary Economics 56 (2009) 1109–1113. JME link .This is a response to Bennett McCallum’s “is the New-Keynesian Analysis Critically Flawed” which says yes. I think McCallum got it backwards -- the bounded equilibrium is not learnable, the explosive ones are learnable. Furthermore, I’m not convinced that a hypothetical threat by the Fed to take us to an “unlearnable” equilibrium is a satisfactory foundation for price level determination.
Health-Status Insurance
Feb. 18 2009. In Cato's Policy Analysis No 633. If you get sick and lose health insurance you are stuck -- your premiums skyrocket or you may not be able to get insurance at all. The article shows how private markets can solve this problem. If you get sick, your health premiums go up but a separate "premium increase insurance contract" pays a lump sum so that you can afford the higher health premiums. The big advantage is freedom and competition: now health insurance can freely compete for all customers all the time. This piece is written for a nontechnical popular audience, with a lot of policy discussion. This paper explains the basic framework of Time-Consistent Health Insurance (next) and thinks through lots of real-world issues and answers to "what ifs." "What to do about pre-existing conditions" in the Wall Street Journal August 14 2009 and Health Status insurance Investors Business Daily (local link) April 2 2009 are op-eds explaining the basic idea.
Feb. 18 2009. In Cato's Policy Analysis No 633. If you get sick and lose health insurance you are stuck -- your premiums skyrocket or you may not be able to get insurance at all. The article shows how private markets can solve this problem. If you get sick, your health premiums go up but a separate "premium increase insurance contract" pays a lump sum so that you can afford the higher health premiums. The big advantage is freedom and competition: now health insurance can freely compete for all customers all the time. This piece is written for a nontechnical popular audience, with a lot of policy discussion. This paper explains the basic framework of Time-Consistent Health Insurance (next) and thinks through lots of real-world issues and answers to "what ifs." "What to do about pre-existing conditions" in the Wall Street Journal August 14 2009 and Health Status insurance Investors Business Daily (local link) April 2 2009 are op-eds explaining the basic idea.
State-Space vs. VAR models for Stock Returns
Manuscript July 24 2008. In a “state-space” model, you write a process for expected returns and another one for expected dividend growth, and then you find prices (dividend yields) and returns by present value relations. I connect state-space models with VAR models for expected returns. What are the VAR or return-forecast-regression implications of a state-space model? What state-space model does a VAR imply? I start optimistic. An AR(1) state-space model gives a nice return-forecasting formula, in which you use both the dividend yield and a moving average of past returns to forecast future returns. The general formulas leave me pessimistic however. One can write any VAR in state-space form, and we don’t really have solid economic reasons to restrict either VAR or state-space representations. Still, the connections between the two representations are worth exploring, and if you’re doing that this paper might save you weeks of algebra.
Manuscript July 24 2008. In a “state-space” model, you write a process for expected returns and another one for expected dividend growth, and then you find prices (dividend yields) and returns by present value relations. I connect state-space models with VAR models for expected returns. What are the VAR or return-forecast-regression implications of a state-space model? What state-space model does a VAR imply? I start optimistic. An AR(1) state-space model gives a nice return-forecasting formula, in which you use both the dividend yield and a moving average of past returns to forecast future returns. The general formulas leave me pessimistic however. One can write any VAR in state-space form, and we don’t really have solid economic reasons to restrict either VAR or state-space representations. Still, the connections between the two representations are worth exploring, and if you’re doing that this paper might save you weeks of algebra.
Two Trees
(with Francis Longstaff and Pedro Santa-Clara), Review of Financial Studies 21 (1) 2008 347-385. We solve the model with two Lucas trees, iid dividends and log utility. Surprise: it has interesting dynamics. If one stock goes up it is a larger share of the market. Its expected return must rise so that people are willing to hold it despite its now larger share. Typo: Equation 39 (page 363), the numerator should read (1-s/(1-s))ln(s)/V, not 1-s/(1-s)ln(s)/V. Thanks to Egor Malkov.
(with Francis Longstaff and Pedro Santa-Clara), Review of Financial Studies 21 (1) 2008 347-385. We solve the model with two Lucas trees, iid dividends and log utility. Surprise: it has interesting dynamics. If one stock goes up it is a larger share of the market. Its expected return must rise so that people are willing to hold it despite its now larger share. Typo: Equation 39 (page 363), the numerator should read (1-s/(1-s))ln(s)/V, not 1-s/(1-s)ln(s)/V. Thanks to Egor Malkov.
Bond Supply and Excess Bond Returns
May 2008. Comments on Robin Greenwood and Dimitri Vayanos’ paper for the IGM “Beyond Liquidity ” conference at the GSB Gleacher center, May 9-10 2008. The paper from Dimitri’s website . I learned two important lessons in reading and thinking about this paper. 1) When arbitrageurs are limited by risk-bearing capacity, “downward-sloping” demands depend on correlations. The paper and my comments have a lovely example in which arbitrageurs are asked to hold more long-term bonds and less short-term bonds. The result is that all yields go up! Why don’t long yields go up and short yields go down? Because risks are described by a one-factor model, so all that matters is how much overall duration risk arbitrageurs have to hold. 2) We’re probably doing a bad job of correcting for serial correlation in all predictive regressions. Typically, we think expected returns move slowly over time. The right hand variable also moves slowly over time, but doesn’t capture all of the expected return variation. This situation means that residuals have a slow-moving AR(1) plus an unforecastable component, which is the same thing as an ARMA(1,1). This structure will be very poorly captured by standard “nonparametric” procedures such as Newey-West, since you’re unlikely to put in enough lags to capture the long-run component, and also poorly captured by parametric procedures like fitting an AR(1). “Short” samples make the problem worse. More in the comments.
May 2008. Comments on Robin Greenwood and Dimitri Vayanos’ paper for the IGM “Beyond Liquidity ” conference at the GSB Gleacher center, May 9-10 2008. The paper from Dimitri’s website . I learned two important lessons in reading and thinking about this paper. 1) When arbitrageurs are limited by risk-bearing capacity, “downward-sloping” demands depend on correlations. The paper and my comments have a lovely example in which arbitrageurs are asked to hold more long-term bonds and less short-term bonds. The result is that all yields go up! Why don’t long yields go up and short yields go down? Because risks are described by a one-factor model, so all that matters is how much overall duration risk arbitrageurs have to hold. 2) We’re probably doing a bad job of correcting for serial correlation in all predictive regressions. Typically, we think expected returns move slowly over time. The right hand variable also moves slowly over time, but doesn’t capture all of the expected return variation. This situation means that residuals have a slow-moving AR(1) plus an unforecastable component, which is the same thing as an ARMA(1,1). This structure will be very poorly captured by standard “nonparametric” procedures such as Newey-West, since you’re unlikely to put in enough lags to capture the long-run component, and also poorly captured by parametric procedures like fitting an AR(1). “Short” samples make the problem worse. More in the comments.
Risks and Regimes in the Bond Market
April 2008. Comments on Atkeson and Kehoe’s paper for the 2008 Macroeconomics Annual. Risk premia are important for understanding interest rates, and monetary policy. I see no evidence for “anchored expectations” in interest rate data. Once you take account of risk premiums, expected long run interest rates are still very volatile. The yield curve has not become more downward sloping on average, as it should if inflation risks have decreased. If anything, risk premia in long-term bonds are increasing. Atkeson and Kehoe advocate a fascinating view that risk premia cause monetary policy, not vice versa.
April 2008. Comments on Atkeson and Kehoe’s paper for the 2008 Macroeconomics Annual. Risk premia are important for understanding interest rates, and monetary policy. I see no evidence for “anchored expectations” in interest rate data. Once you take account of risk premiums, expected long run interest rates are still very volatile. The yield curve has not become more downward sloping on average, as it should if inflation risks have decreased. If anything, risk premia in long-term bonds are increasing. Atkeson and Kehoe advocate a fascinating view that risk premia cause monetary policy, not vice versa.
Decomposing the Yield Curve
Manuscript, first big revision, March 14 2008. With Monika Piazzesi. We work out an affine term structure model that incorporates our bond risk premia from “Bond Risk Premia” in the AER. There are lots of interesting dynamics – level, slope and curvature forecast future bond risk premia, and we discover that market prices of risk are really simple. We use the model to decompose the yield curve – given a yield (forward) curve today, how much is expected future interest rates, and how much is risk premium? How does the yield or forward rate premium correspond to the term structure of expected return premia? Was the conundrum a conundrum? Slides from 2010 AFA meetings Data and Programs.
Manuscript, first big revision, March 14 2008. With Monika Piazzesi. We work out an affine term structure model that incorporates our bond risk premia from “Bond Risk Premia” in the AER. There are lots of interesting dynamics – level, slope and curvature forecast future bond risk premia, and we discover that market prices of risk are really simple. We use the model to decompose the yield curve – given a yield (forward) curve today, how much is expected future interest rates, and how much is risk premium? How does the yield or forward rate premium correspond to the term structure of expected return premia? Was the conundrum a conundrum? Slides from 2010 AFA meetings Data and Programs.
Financial markets and the Real Economy
In Rajnish Mehra, Ed. Handbook of the Equity Premium Elsevier 2007, 237-325. Everything you wanted to know, but didn’t have time to read, about equity premium, consumption-based models, investment-based models, general equilibrium in asset pricing, labor income and idiosyncratic risk.
In Rajnish Mehra, Ed. Handbook of the Equity Premium Elsevier 2007, 237-325. Everything you wanted to know, but didn’t have time to read, about equity premium, consumption-based models, investment-based models, general equilibrium in asset pricing, labor income and idiosyncratic risk.
This article appeared four times, getting better each time. (Why waste a good article by only publishing it once?) The link above is the last and the best. The previous versions were NBER Working paper 11193, Financial Markets and the Real Economy Volume 18 of the International Library of Critical Writings in Financial Economics, John H. Cochrane Ed., London: Edward Elgar. March 2006, and in Foundations and Trends in Finance 1, 1-101, 2005.
What ends recessions?
By David and Christina Romer, 1994 NBER Macroeconomics Annual 58-74. JSTOR What are monetary policy shocks? The fed never says “and another 50 bp for the heck of it.” This led to “What do the VARs mean?”
By David and Christina Romer, 1994 NBER Macroeconomics Annual 58-74. JSTOR What are monetary policy shocks? The fed never says “and another 50 bp for the heck of it.” This led to “What do the VARs mean?”
Daily Monetary Policy Shocks and the Delayed Response of New Home Sales
By James D. Hamilton. April 2007 Comments given at NBER Monetary Economics program meeting, NY. Includes some new thoughts on what a monetary policy shock is.
By James D. Hamilton. April 2007 Comments given at NBER Monetary Economics program meeting, NY. Includes some new thoughts on what a monetary policy shock is.
Portfolio theory
Feb. 20 2007 This is a draft of a portfolio theory chapter for the next revision of Asset Pricing. I (of course) take a p = E(mx) approach to portfolio theory before covering the classic Merton-style direct approach. I emphasize the importance of outside income.
Feb. 20 2007 This is a draft of a portfolio theory chapter for the next revision of Asset Pricing. I (of course) take a p = E(mx) approach to portfolio theory before covering the classic Merton-style direct approach. I emphasize the importance of outside income.
“The Returns to Currency Speculation”
by Craig Burnside, Martin Eichenbaum, Isaac Kleshchelski and Sergio Rebelo. Comments given at Jan 2007 AEA/AFA meetings. (Slides only)
by Craig Burnside, Martin Eichenbaum, Isaac Kleshchelski and Sergio Rebelo. Comments given at Jan 2007 AEA/AFA meetings. (Slides only)
‘Macroeconomic Implications of Changes in the Term Premium’
By Glenn Rudebusch, Brian Sack and Eric Swanson. Comments given at the conference “Frontiers in Monetary Policy Research” at the St. Louis Federal Reserve, October 19 2006. Of course, I can’t stick to the topic and offer a survey instead. In particular, lots of salty comments on the “conundrum” in long bond prices (silly, in my view). The paper from the St. Louis Fed website.
By Glenn Rudebusch, Brian Sack and Eric Swanson. Comments given at the conference “Frontiers in Monetary Policy Research” at the St. Louis Federal Reserve, October 19 2006. Of course, I can’t stick to the topic and offer a survey instead. In particular, lots of salty comments on the “conundrum” in long bond prices (silly, in my view). The paper from the St. Louis Fed website.
The Dog that Did Not Bark: A Defense of Return Predictability
Review of Financial Studies 21(4) 2008 1533-1575. Taken alone, returns may not look that predictable. However, price-dividend ratios vary, so either returns or dividend growth must be forecastable (or both). Implications for dividends, and long-run forecasts give strong statistical evidence against the null that returns are not forecatsable. I address the Goyal-Welch finding that forecasts do badly out of sample, and the long literature criticizing long-run forecasts. The most important practical takeaway: even if you assume that all variation in market p/d ratios comes from time-varying expected returns, and none corresponds to dividend growth forecasts, you will typically find that market-timing strategies based on fitting the regression don’t work. Corrected Table 6. Three numbers were wrong in the published version. Thanks to Camilla Pederson for catching it.
Review of Financial Studies 21(4) 2008 1533-1575. Taken alone, returns may not look that predictable. However, price-dividend ratios vary, so either returns or dividend growth must be forecastable (or both). Implications for dividends, and long-run forecasts give strong statistical evidence against the null that returns are not forecatsable. I address the Goyal-Welch finding that forecasts do badly out of sample, and the long literature criticizing long-run forecasts. The most important practical takeaway: even if you assume that all variation in market p/d ratios comes from time-varying expected returns, and none corresponds to dividend growth forecasts, you will typically find that market-timing strategies based on fitting the regression don’t work. Corrected Table 6. Three numbers were wrong in the published version. Thanks to Camilla Pederson for catching it.