Rational Expectations And PIH/LCH Under REHMuth: Rational ExpectationsMore MuthSlide 4Rational ExpectationsSlide 6Rational Expectations Hypothesis (REH)Adaptive vs. Rational ExpectationsConsumption FunctionEarly CritiquesLucas CritiqueHall’s PIH/LCH under REHHall (2)Hall (3)Hall (4)Hall (5)Flavin’s ResponseFlavin (2)Flavin vs. Hall (1)Flavin vs. Hall (2)Flavin vs. Hall (3)Flavin vs. Hall (4)Flavin vs. Hall (5)Flavin vs. Hall (6)Slide 25Rational Expectations Rational Expectations And PIH/LCH Under REHAnd PIH/LCH Under REHMacroeconomics IECON 309 – Cunningham2Muth: Rational ExpectationsMuth: Rational ExpectationsMuth, John F., “Rational Expectations and the Theory of Price Movements,” Econometrica, vol. 29 no. 3 (July 1961).“In order to fairly simply explain how expectations are formed, we advance the hypothesis that they are essentially the same as the predictions of the relevant theory.”“... the economy does not waste information ... ”“What kind of information is used, and how it is put together to frame an estimate of future conditions is important to understand because the character of dynamic processes is typically very sensitive to the way expectations are influenced by the course of actual events.”3More MuthMore MuthTwo major conclusions from studies of expectations data are:–Averages of expectations in an industry are more accurate than naive models and as accurate as elaborate equation systems...–Reported expectations generally underestimate the extent of changes that actually take place.–To order to explain these phenomena, I should like to suggest that expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory.4More MuthMore MuthMore precisely, the expectations (the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction of the theory (or the “objective” probability distributions of outcomes).5Rational ExpectationsRational Expectations0100200300400500600Tally0 1 2 3 4 5 6Predicted Inflation RateInflation SurveySubjectiveObjective6More MuthMore MuthInformation is scarce, and the economic system generally does not waste it.The way expectations are formed depends specifically on the structure of relevant system describing the economy.7Rational Expectations Hypothesis (REH)Rational Expectations Hypothesis (REH)Expectations are formed on the basis of all available relevant information concerning the variable being predicted.Agents understand the underlying economic relationships.As a result, expectational errors are NOT systematic.8Adaptive vs. Rational ExpectationsAdaptive vs. Rational ExpectationsAdaptive ExpectationsRational ExpectationsActualActualxxxxxxxxxxxxxxxxx9Consumption FunctionConsumption FunctionMajor Problem of Empirical Research:–Fitting the part of the model that relates current and past observed income to expected future income.–Usually done with a fixed distributed lag, amounting to adaptive expectations.–Muth (1960) shows that this is only optimal under certain stochastic processes for income.10Early CritiquesEarly CritiquesHaavelmo (1943, Econometrica) and Friedman and Becker (1967, JPE).Problem: failing to account for income as an endogenous variable when it is the major independent variable in the consumption function.–C=C0 + cY, and Y=C+I+G+NX.–This distorts the estimated functions.–Does it even make sense?–Requires simultaneous equation techniques.11Lucas CritiqueLucas CritiqueRobert Lucas (1976), “Critique”.Criticizes 3 structural relations, and one of them is the consumption function. Argues:–It is not merely misspecified. There is no such thing!–There exists a structural relation between permanent income and consumption.–The consumption function asserts a structural relation between observed and permanent income, and there is no reason to expect a stable relation of that type!–Policy changes “apparently” unrelated to consumption behavior can affect the way that the consumer optimizes.–There exist structural relations in the economy, but consumption is not one of them.12Hall’s PIH/LCH under REHHall’s PIH/LCH under REHHall (1978, JPE)Essentially an empirical investigation.Assumes none of the RHS variables is exogenous.When consumers maximize expected future utility, the conditional expectation of future marginal utility is a function of current consumption alone—all other information is irrelevant.Aside from a trend, the marginal utility evolves as a random walkIf the marginal utility is a random walk, then consumption must also be a random walk.–Therefore, only first-lagged consumption should have a nonzero coefficient.–This can be tested without regard to exogeneity.13Hall (2)Hall (2)The consumer seeks to maximize:Subject to:Et = math expectation conditional on all available information = rate of subjective time preferencer = real rate of interest, assumed constant over timeu() = one-period utility function, strictly concave, intertemporally separablect = consumptionwt = earnings from sources (other than savings)At = assets apart from human capital)(11EstsstcutststssAwcr)(1114Hall (3)Hall (3)Browning (1986) relaxes intertemporal separability.The Euler equation expressing the marginal rate of substitutionmarginal utility next year equals the marginal utility this year, except for a trend related to the constant rate of time preference and the constant real interest rate.)(11)(E1 tttcurcu15Hall (4)Hall (4)Implication:  0)(,cov0E)(11)(1tttttttcucurcuNote that Hall does not try to make use of information about the functional form of the utility function. Assuming a quadratic utility function:tttcc 1Test: Put many lags on the RHS, use t-test to test for exclusions.16Hall (5)Hall (5)Result:–Consumption is close to a random walk, but certain variables have enough predictive power that the hypothesis is rejected.•Confirmed for real disposable income. That is, lagged Yd had little predictive power. –The only thing that helps predict next period’s consumption is this period’s consumption.•Rejected when stock prices are included. That is, lagged stock prices inform consumption