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**11 - 18**of**18**### Asset Price Bubbles

, 2007

"... Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street.When you read contemporary accounts of booms or panics the one thing that strikes you most forcibly is how little either stock speculation or stock speculators today differ from yesterday. The game does not change ..."

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Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street.When you read contemporary accounts of booms or panics the one thing that strikes you most forcibly is how little either stock speculation or stock speculators today differ from yesterday. The game does not change and neither does human nature. —From the thinly disguised biography of legendary speculator Jesse Livermore, by E. Lefèvre (1923, p. 180) Speculative bubbles have occurred throughout history in numerous countries and asset markets. The term “bubble ” was coined in England in 1720 following the famous price run-up and crash of shares in the South Sea Company.The run-up led to widespread public enthusiasm for the stock market and a proliferation of highly suspect companies attempting to sell shares to investors. One such venture notoriously advertised itself as “a company for carrying out an undertaking of great advantage, but nobody to know what it is.”The epidemic of fraudulent stock-offering schemes led the British government to pass the so-called “Bubble Act ” in 1720, which was officially named “An Act to Restrain

### Time-Varying U.S. Ination Dynamics and the New Keynesian Phillips Curve

, 2007

"... This paper demonstrates that a plausible departure from fully-rational ination expec-tations allows the New Keynesian Phillips curve to reproduce many quantitative features of U.S. ination data. The representative agent is assumed to behave as an econome-trician, employing a time series model for in ..."

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This paper demonstrates that a plausible departure from fully-rational ination expec-tations allows the New Keynesian Phillips curve to reproduce many quantitative features of U.S. ination data. The representative agent is assumed to behave as an econome-trician, employing a time series model for ination that allows for both permanent and temporary shocks. The near-unity coe ¢ cient on expected ination in the Phillips curve causes the agents perception of a unit root in ination to become close to self-ful
lling. In a consistent expectations equilibrium,the value of the Kalman gain parameter in the agents forecast rule is pinned down using the observed autocorrelation of ination changes. From the agents perspective, the use of a variable Kalman gain parameter is justi
ed by perceived movements in the relative variances of the permanent and temporary shocks to ination. The forecast errors observed by the agent are close to white noise, making it di ¢ cult for the agent to detect a misspeci
cation of the forecast rule. I show that this simple model of ination expectations can generate time-varying ination dynamics similar to those observed in long-run U.S. data. Model-based values for expected ination track

### Rational and Near-Rational Bubbles Without Drift

, 2008

"... This paper derives a general class of intrinsic rational bubble solutions in a standard Lucas-type asset pricing model. I show that the rational bubble component of the price-dividend ratio can evolve as a geometric random walk without drift, such that the mean of the bubble growth rate is zero. Dri ..."

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This paper derives a general class of intrinsic rational bubble solutions in a standard Lucas-type asset pricing model. I show that the rational bubble component of the price-dividend ratio can evolve as a geometric random walk without drift, such that the mean of the bubble growth rate is zero. Driftless rational bubbles are part of a continuum of equilibrium solutions that involve an explicit trade-o ¤ between the mean and volatility of the bubble growth rate. I also propose a near-rational asset pricing solution in which the representative agent does not construct separate forecasts for the fundamental and bubble components of the asset price. Rather, the agent constructs only a single forecast for the total asset price that is similar in form to the corresponding rational forecast, but involves fewer parameters. The parameters of the agents forecast rule are chosen to match the moments of observable data. In the near-rational equilibrium, the actual law of motion for the price-dividend ratio is stationary, highly persistent, and nonlinear. The agents forecast errors exhibit near-zero autocorrelation at all lags, making it di ¢ cult for the agent to detect a misspeci
cation of the forecast rule. Unlike a rational bubble, the near-rational

### PRELIMINARY AND INCOMPLETE

, 2009

"... Shiller (2003) and others have argued for the creation of financial instruments that allow individuals to insure risks associated with their lifetime labor income. In this paper, we analyze two such instruments in the context of a realistic life-cycle model of household portfolio choice. The instrum ..."

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Shiller (2003) and others have argued for the creation of financial instruments that allow individuals to insure risks associated with their lifetime labor income. In this paper, we analyze two such instruments in the context of a realistic life-cycle model of household portfolio choice. The instruments we consider are an income-hedging instrument (a limited liability asset whose returns correlate negatively with income shocks) and income-linked loans (with a rate positively correlated with income shocks). We find that income-linked loans would generally be more useful to households, as they have a lower (opportunity) cost. While for some parameterizations of our model the welfare gains from the presence of income-linked assets can be substantial (above 1% of certainty-equivalent consumption), the assets we consider can only mitigate a relatively small part of the welfare costs of labor income risk over the life cycle. We are grateful to John Campbell, Nicola Fuchs-Schündeln, Rustom Irani, María Luengo-Prado, Julio Rotemberg, and seminar participants at Harvard and the 1st Annual Workshop of the Zurich Center for Computational Financial Economics for helpful comments and discussions. The views expressed in this paper are solely those of the authors and not necessarily those of the Federal Reserve Bank of Boston or the Federal Reserve System.

### United States Revised Draft

, 2012

"... We explore real time, adaptive nonlinear learning dynamics in stochastic macroeconomic systems. Rather than linearizing nonlinear Euler equations where expectations play a role around a steady state, we instead approximate the nonlinear expected values using the method of parameterized expectations. ..."

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We explore real time, adaptive nonlinear learning dynamics in stochastic macroeconomic systems. Rather than linearizing nonlinear Euler equations where expectations play a role around a steady state, we instead approximate the nonlinear expected values using the method of parameterized expectations. Further we suppose that these approximated expectations are updated in real time as new data become available. We argue that this method of real-time parameterized expectations learning provides a plausible alternative to real-time adaptive learning dynamics under linearized versions of the same nonlinear system and we provide a comparison of the two approaches

### credit, including © notice, is given to the source. Natural Expectations, Macroeconomic Dynamics, and Asset Pricing

, 2011

"... and George Evans, and seminar/conference participants for helpful comments and discussions. WeDUH indebted to Brendan Price and Fernando Yu for excellent research assistance. David Laibson acknowledges support from the NIA (P01AG005842). The views expressed herein are those of the authors and doQRW ..."

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and George Evans, and seminar/conference participants for helpful comments and discussions. WeDUH indebted to Brendan Price and Fernando Yu for excellent research assistance. David Laibson acknowledges support from the NIA (P01AG005842). The views expressed herein are those of the authors and doQRW necessarily reflect the views of the National Bureau of Economic Research.