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Asset Return Dynamics and Learning ∗
, 2009
"... This paper advocates a theory of expectation formation that incorporates many of the central motivations of behavioral finance theory while retaining much of the discipline of the rational expectations approach. We provide a framework in which agents, in an asset pricing model, underparameterize the ..."
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This paper advocates a theory of expectation formation that incorporates many of the central motivations of behavioral finance theory while retaining much of the discipline of the rational expectations approach. We provide a framework in which agents, in an asset pricing model, underparameterize their forecasting model in a spirit similar to Hong, Stein, and Yu (2007) and Barberis, Shleifer, and Vishny (1998), except that the parameters of the forecasting model, and the choice of predictor, are determined jointly in equilibrium. We show that multiple equilibria can exist even if agents choose only models that maximize (riskadjusted) expected profits. A realtime learning formulation yields endogenous switching between equilibria. We demonstrate that a realtime learning version of the model, calibrated to U.S. stock data, is capable of reproducing regimeswitching returns and volatilities, as recently identified by Guidolin and Timmermann (2007). 2 There is, by now, an established literature that studies financial market anomalies such as excess volatility, Markov switching returns and volatilities, and predictability of excess returns. (See Lettau and Ludvigson (2005) for a recent discussion.) One important finding in this literature is evidence of multiple regimes each with distinct return and volatility characteristics. See, for example, Guidolin and Timmermann
2012 House price dynamics: Fundamentals and expectations, Bank of Canada Working Paper
"... Bank of Canada working papers are theoretical or empirical worksinprogress on subjects in economics and finance. The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada. ..."
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Bank of Canada working papers are theoretical or empirical worksinprogress on subjects in economics and finance. The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada.
House Prices, Expectations, and TimeVarying Fundamentals ∗
, 2013
"... We investigate the behavior of the equilibrium pricerent ratio for housing in a simple Lucastype asset pricing model. We allow for timevarying risk aversion (via external habit formation) and timevarying persistence and volatility in the stochastic process for rent growth, consistent with U.S. d ..."
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We investigate the behavior of the equilibrium pricerent ratio for housing in a simple Lucastype asset pricing model. We allow for timevarying risk aversion (via external habit formation) and timevarying persistence and volatility in the stochastic process for rent growth, consistent with U.S. data for the period 1960 to 2011. Under fullyrational expectations, the model significantly underpredicts the volatility of the U.S. pricerent ratio for reasonable levels of risk aversion. We demonstrate that the model can approximately match the volatility of the pricerent ratio in the data if nearrational agents continually update their estimates for the mean, persistence and volatility of fundamental rent growth using only recent data (i.e., the past 4 years), or if agents employ a simple movingaverage forecast rule that places a large weight on the most recent observation. These two versions of the model can be distinguished by their predictions for the correlation between expected future returns on housing and the pricerent ratio. Only the movingaverage model predicts a positive correlation such that agents tend to expect higher future returns when house prices are high relative to fundamentals–a feature that is consistent with survey evidence on the expectations of realworld housing investors.
Natural expectations, macroeconomic dynamics, and asset pricing
 NBER MACROECONOMICS ANNUAL
, 2011
"... How does an economy behave if (1) fundamentals are truly humpshaped, exhibiting momentum in the short run and partial mean reversion in the long run, and (2) agents do not know that fundamentals are humpshaped and base their beliefs on parsimonious models that they fit to the available data? A cla ..."
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How does an economy behave if (1) fundamentals are truly humpshaped, exhibiting momentum in the short run and partial mean reversion in the long run, and (2) agents do not know that fundamentals are humpshaped and base their beliefs on parsimonious models that they fit to the available data? A class of parsimonious models leads to qualitatively similar biases and generates empirically observed patterns in asset prices and macroeconomic dynamics. First, parsimonious models will robustly pick up the shortterm momentum in fundamentals but will generally fail to fully capture the longrun mean reversion. Beliefs will therefore be characterized by endogenous extrapolation bias and procyclical excess optimism. Second, asset prices will be highly volatile and exhibit partial mean reversion—i.e., overreaction. Excess returns will be negatively predicted by lagged excess returns, P/E ratios, and consumption growth. Third, real economic activity will have amplified cycles. For example, consumption growth will be negatively autocorrelated in the medium run. Fourth, the equity premium will be large. Agents will perceive that equities are very risky when in fact longrun equity returns will covary only weakly with longrun consumption growth. If agents had rational expectations, the equity premium would be close to zero. Fifth, sophisticated agents—i.e., those who are assumed to know the true model—will hold far more equity than investors who use parsimonious models. Moreover, sophisticated agents will follow a countercyclical asset allocation policy. These predicted effects are qualitatively confirmed in U.S. data.
Asset Pricing in Production Economies with Extrapolative Expectations *
, 2012
"... Introducing extrapolation bias into a standard onesector productionbased real business cycle model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility and high investment volatility relative to output) and financial markets (high equity pr ..."
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Introducing extrapolation bias into a standard onesector productionbased real business cycle model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility and high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, and a low and smooth riskfree rate) with low relative risk aversion and an intertemporal elasticity of substitution in preferences of greater than one. Furthermore, the model matches several conditional stylized facts, such as return predictability based upon dividend yield, Q, and investment rates. These successes derive from the interaction of capital adjustment costs, extrapolative bias, and recursive preferences. Extrapolative bias increases the variation in the wealthconsumption ratio; recursive preferences cause this variation to be strongly priced; and adjustment costs decrease the covariance between marginal utility of consumption and asset returns. We provide empirical support for
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 realtime parameterized expectations learning provides a plausible alternative to realtime adaptive learning dynamics under linearized versions of the same nonlinear system and we provide a comparison of the two approaches
Rational and NearRational Bubbles Without Drift
, 2007
"... This paper derives a general class of intrinsic rational bubble solutions in a standard Lucastype asset pricing model. I show that the rational bubble component of the pricedividend ratio can evolve as a geometric random walk without drift. The volatility of bubble innovations depends exclusively o ..."
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This paper derives a general class of intrinsic rational bubble solutions in a standard Lucastype asset pricing model. I show that the rational bubble component of the pricedividend ratio can evolve as a geometric random walk without drift. The volatility of bubble innovations depends exclusively on fundamentals. Starting from an arbitrarily small positive value, the rational bubble expands and contracts over time in an irregular, wholly endogenous fashion, always returning to the vicinity of the fundamental solution. I also examine a nearrational 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 based on a geometric random walk without drift. The agent’s forecast rule is parameterized to match the moments of observable data. In equilibrium, the actual law of motion for the pricedividend ratio is stationary, highly persistent, and nonlinear. The agent’s forecast errors exhibit nearzero 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 nearrational solution allows the asset price to occasionally dip below its fundamental value. Under mild risk aversion, the nearrational solution generates pronounced lowfrequency swings in the pricedividend ratio, positive skewness, excess kurtosis, and timevarying volatility — all of which are present in longrun U.S. stock market data. An independent contribution of the paper is to demonstrate an approximate analytical solution for the fundamental asset price that employs a nonlinear change of variables.
TimeVarying U.S. In‡ation Dynamics and the New Keynesian Phillips Curve
, 2006
"... This paper introduces a form of boundedlyrational expectations into an otherwise standard New Keynesian Phillips curve. The representative agent’s perceived law of motion allows for both temporary and permanent shocks to in‡ation, the latter intended to capture the possibility of evolving shifts in ..."
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This paper introduces a form of boundedlyrational expectations into an otherwise standard New Keynesian Phillips curve. The representative agent’s perceived law of motion allows for both temporary and permanent shocks to in‡ation, the latter intended to capture the possibility of evolving shifts in the central bank’s in‡ation target. The agent’s perceived optimal forecast rule de…ned by the Kalman …lter is parameterized to be consistent with the observed moments of the in‡ation time series. From the agent’s perspective, the use of a variable Kalman gain parameter is justi…ed by movements in the perceived “signaltonoise ratio, ” which measures the relative variances of the permanent and temporary shocks to in‡ation. I show that this simple model of in‡ation expectations can generate timevarying in‡ation dynamics similar to those observed in longrun U.S. data. The U.S. signaltonoise ratio identi…ed using the model’s methodology exhibits an upward drift during the 1970s, followed by downward drift from the mid1990s onwards. This pattern suggests that the perceived signaltonoise ratio might be viewed as a inverse measure of the central bank’s credibility for maintaining a constant in‡ation target. Modelbased values for expected in‡ation track quite well with movements in surveybased measures of U.S. expected in‡ation.
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 runup and crash of shares in the South Sea Company.The runup 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 stockoffering schemes led the British government to pass the socalled “Bubble Act ” in 1720, which was officially named “An Act to Restrain