Rational expectations and the econometric modeling of markets subject to uncertainty: A Bayesian approach

Rational expectations theory is synthesized with Bayesian econometric theory to yield econometrically relevant models of competitive markets subject to uncertainty. The theory is used to derive both optimal estimators of the parameters of a Cobb-Douglas production function from time series data, and the equilibrium predictor of a future price. It is shown that a rational expectations price predictor is always an unbiased predictor, but that the converse is not true. It is also shown that the rational expectations equilibrium is a natural extension of the usual notion of a competitive equilibrium.     

The return to schooling: Estimates from a sample of young Australian twins

This study uses a sample of young Australian twins to examine whether the findings reported in [Ashenfelter, Orley and Krueger, Alan, (1994). ‘Estimates of the Economic Return to Schooling from a New Sample of Twins’, American Economic Review, Vol. 84, No. 5, pp.1157–73] and [Miller, P.W., Mulvey, C and Martin, N., (1994). ‘What Do Twins Studies Tell Us About the Economic Returns to Education?: A Comparison of Australian and US Findings’, Western Australian Labour Market Research Centre Discussion Paper 94/4] are robust to choice of sample and dependent variable. The economic return to schooling in Australia is between 5 and 7 percent when account is taken of genetic and family effects using either fixed-effects models or the selection effects model of Ashenfelter and Krueger. Given the similarity of the findings in this and in related studies, it would appear that the models applied by [Ashenfelter, Orley and Krueger, Alan, (1994). ‘Estimates of the Economic Return to Schooling from a New Sample of Twins’, American Economic Review, Vol. 84, No. 5, pp.1157–73] are robust. Moreover, viewing the OLS and IV estimators as lower and upper bounds in the manner of [Black, Dan A., Berger, Mark C., and Scott, Frank C., (2000). ‘Bounding Parameter Estimates with Nonclassical Measurement Error’, Journal of the American Statistical Association, Vol. 95, No.451, pp.739–748], it is shown that the bounds on the return to schooling in Australia are much tighter than in [Ashenfelter, Orley and Krueger, Alan, (1994). ‘Estimates of the Economic Return to Schooling from a New Sample of Twins’, American Economic Review, Vol. 84, No. 5, pp. 1157–73], and the return is bounded at a much lower level than in the US.     

House price dynamics: Fundamentals and expectations

We investigate whether expectations that are not fully rational have the potential to explain the evolution of house prices and the price-to-rent ratio in the United States. First, a stylized asset-pricing model solved under rational expectations is used to derive a fundamental value for house prices and the price–rent ratio. Although the model can explain the sample average of the price–rent ratio, it does not generate the large and persistent fluctuations observed in the data. Then, we consider a rational bubble solution, an extrapolative expectations solution and a near rational bubble solution. In this last solution agents extrapolate the future from the latest realizations and the degree of extrapolation is stronger in good times than in bad times, generating waves of over-optimism. We show that under this solution the model not only is able to match key moments of the data but can also replicate the run up in the U.S. house prices observed over the 2000–2006 period and the subsequent sharp downturn.     

On the convergence of genetic learning in a double auction market

We study the learning behavior of a population of buyers and a population of sellers whose members are repeatedly randomly matched to engage in a sealed bid double auction. The agents are assumed to be boundedly rational and choose their strategies by imitating successful behavior and adding innovations triggered by random errors or communication with other agents. This process is modelled by a two-population genetic algorithm. A general characterization of the equilibria in mixed population distributions is given and it is shown analytically that only one price equilibria are attractive for the GA dynamics. Simulation results confirm these findings and imply that in cases with random initialization with high probability the gain of trade is equally split between buyers and sellers.     

On the optimality of pure bundling for a monopolist

This paper considers a monopolist selling two objects to a single buyer with privately observed valuations. We prove that if the virtual valuation for each object is non-negative for all possible types, then the optimal price schedule is such that the objects are sold only in a bundle. Under an additional regularity condition, pure bundling is the optimal sale mechanism among all individually rational and incentive compatible mechanisms.     

Trend inflation,sticky prices,and expectational stability

Micro evidence indicates that each period a fraction of prices is kept unchanged under a positive trend inflation rate. In a sticky price model based on this evidence, recent research shows that high trend inflation is a serious cause for indeterminacy of rational expectations equilibrium under the Taylor rule. This paper examines implications of trend inflation for expectational stability of the equilibrium. An empirically plausible calibration of the model demonstrates that a fundamental rational expectations equilibrium is likely to be expectationally stable even in cases of indeterminacy induced by high trend inflation.     

Stochastic interest rates under rational inattention

This paper introduces state uncertainty due to information-processing constraints into the Vasicek model to examine the impacts of rational inattention. By exploiting the term structure of interest rates, we derive closed-form solutions for the subjective bond price and the corresponding bond yield and find that uncertainty induced by informational frictions plays vital roles in undervaluing the bond price and overestimating the bond yield. Furthermore, we clarify the applications of interest rate dynamics under rational inattention and generate the following results: (i) there is an ambiguous relationship between the investor’s channel capacity and option price; (ii) an increase in state uncertainty via a change in the degree of channel capacity is likely to accelerate investment.     

Equilibrium in incomplete markets: II : Generic existence in stochastic economies

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets.     

Identification and stochastic specification in Rosen's hedonic price model

The use of an explicitly specified utility function to derive the inverse demand functions in S. Rosen's hedonic price model provides considerable insight into the correct stochastic specification of the model. It turns out that except in special cases, the inverse demand equations are nonlinear in parameters and cannot be formulated conveniently as regression models. Moreover, the inverse demand functions and the hedonic price function must be estimated simultaneously to obtain consistent estimates of the parameters of these functions. A tractable estimation technique is described. It is desirable to derive the inverse demand functions from a utility specification that is not a strongly separable function of houses' attributes since strong separability implies the existence of deterministic relations among incomes, prices, and observed housing attributes that may fail to hold in applications. Finally, it is shown that the use of an explicitly specified utility function does not guarantee identification of the parameters of Rosen's model.     

预期对我国住房市场政策调控效果影响的实证分析

预期对房地产行业调控政策的实施效果有着重要的作用。一般来说,从形成机制可以把预期分为静态预期、外推型预期、适应性预期和理性预期,而我国的房地产市场因其特殊性,是介于适应性预期与理性预期之间的准理性预期。通过建立住房价格调控模型并进行实证分析后,可以发现准理性预期是一种效果较好且与实际更相符的预期;预期是影响房价的最主要因素,而预期对于房价的放大效应和预期的不稳定性又使得政策调控增加了一定的难度;房价基本上与预期成正比关系。     

The impact of individual and institutional investor sentiment on the market price of risk

We examine the effect of individual and institutional investor sentiment on the market price of risk derived from DJIA and S&P500 index returns. Consistent with behavioral asset pricing models, we find significant positive response of rational sentiment suggesting greater incentive for rational investors to engage in arbitrage when the compensation for taking risk is greater. Further, an increase in irrational optimism leads to a significant downward movement, but an increase in rational sentiment does not lead to a significant change market price of risk. These results are robust for both market indexes, DJIA and S&P500 and for both individual and institutional investor sentiment.     

Learning to bid in sequential Dutch auctions

We propose an agent-based computational model to investigate sequential Dutch auctions with particular emphasis on markets for perishable goods and we take as an example wholesale fish markets. Buyers in these markets sell the fish they purchase on a retail market. The paper provides an original model of boundedly rational behavior for wholesale buyers׳ behavior incorporating learning to improve profits, conjectures as to the bids that will be made and fictitious learning. We analyze the dynamics of the aggregate price under different market conditions in order to explain the emergence of market price patterns such as the well-known declining price paradox and the empirically observed fact that the very last transactions in the day may be at a higher price. The proposed behavioral model provides alternative explanations for market price dynamics to those which depend on standard hypotheses such as diminishing marginal profits. Furthermore, agents learn the option value of having the possibility of bidding in later rounds. When confronted with random buyers, such as occasional participants or new entrants, they learn to bid in the optimal way without being conscious of the strategies of the other buyers. When faced with other buyers who are also learning their behavior still displays some of the characteristics learned in the simpler case even though the problem is not analytically tractable.     

Price dynamics under imperfect information

The paper considers the pricing decision of a monopolist firm having demand and costs exposed to nominal and real shocks which include both permanent and transitory changes. The firm obtains information through both price and quantity signals and the price equation is found by use of a filtering technique. It is shown that imperfect information implies nominal price smoothing where the price adjusts only partially relative to the past price by incorporating new information observed through price and quantity signals.     

FAMA ON BUBBLES

While Eugene Fama has repeatedly expressed his discontent with the notion of an “irrational bubble,” he has never publicly expressed his opinion on “rational bubbles.” On empirical grounds Fama rejects bubbles by referring to the lack of reliable evidence that price declines are predictable. However, this argument cannot be used to rule out rational bubbles because such bubbles do not necessarily imply return predictability, and return predictability of the kind documented by Fama does not rule out rational bubbles. On data samples that include the 1990s, there is evidence of an explosive component in stock market valuation ratios, consistent with a rational bubble.     

Has a quarter-trillion-dollar settlement helped the tobacco industry?

This paper builds on a growing body of literature analyzing the economic effects of the so-called Master Settlement Agreement (MSA) between the “big four” tobacco companies and the State Attorneys General. Because the marginal cost imposed by the settlement is a function of the market sales of the original four participants, subsequent participating firms will most likely be at a disadvantage. Consistent with increased market power for the original signers, the data since the settlement show increased price overshifting of taxes. Additionally, price undershifting is shown to have occurred prior to the MSA, which would be a rational response of a firm facing a settlement that imposes marginal costs inversely related to sales volume at the time of the agreement. These results suggest that efficiency evaluations may overstate the social benefits of the agreement and the persistent profitability of the industry may be due to the MSA.     

A dynamic analysis of moving average rules

The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules of the type used in practice. In this paper, we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag length used for the MA. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different MA rules. The price dynamics of the MA rule are also examined and one of our main findings is that an increase of the window length of the MA rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.     

Intertemporal recursive utility and an equilibrium asset pricing model in the presence of Lévy jumps

This paper presents an equilibrium formulation of asset pricing in an environment of mixed Poisson–Brownian information with recursive utility. The optimal portfolio choice problem is studied together with a derivation of Euler equation as necessary condition for optimality. It is further shown that the price processes governed by the Euler equation, together with the market clearing conditions, constitute the equilibrium price processes. Closed form formulas are derived for European call options and for other derivative securities in a particular parameterization of the economy. The derived option pricing formula contain many existing models as special cases, and is potentially useful in explaining the moneyness biasedness associated with Black–Scholes model.     

Rational asset pricing bubbles and debt constraints

Rational price bubble arises when the price of an asset exceeds the asset’s fundamental value, that is, the present value of future dividend payments. The important result of Santos and Woodford (1997) says that price bubbles cannot exist in equilibrium in the standard dynamic asset pricing model with rational agents facing borrowing constraints as long as assets are in strictly positive supply and the present value of total future resources is finite. This paper explores the possibility of asset price bubbles under endogenous debt constraints induced by limited enforcement of debt repayment. Equilibria with endogenous debt constraints are prone to have infinite present value of total resources. We show that asset price bubbles are likely to exist in such equilibria. Further, we demonstrate that there always exist equilibria with price bubbles on assets in zero supply.     

浅议工程项目影子价格理论

影子价格是为实现一定的经济发展目标而人为确定的、比市场价格更能反映出资源真实价值、能促进合理利用资源的经济价格,而非真正意义上的市场价格。它不仅能更合理地反映出产品价值,而且还能反映社会劳动消耗、市场的供求关系和资源的稀缺程度,有利于资源的优化配置。影子价格是分析计算项目对国民经济的净贡献,评价项目的经济合理性的重要的参数之一。本文主要阐释了影子价格的概念、类别、选取及计算方法。