The History of Expectations in Macroeconomics

Transcription

1 The History of Expectations in Macroeconomics Jonas Dovern February 12, 2018 Jonas Dovern CES Lecture 1 February 12, / 44

2 Why are you here? What expectations do you have for this course? How did you form these expectations? Jonas Dovern CES Lecture 1 February 12, / 44

3 Expectations Are Everywhere From the most recent account of the ECB monetary policy meeting: The latest staff projections foresaw that the output gap would close in the near future, earlier than previously projected. As economic activity was expected to grow consistently above potential over the projection horizon, it was seen as very likely that capacity constraints would become increasingly binding and lead to higher price pressures. References to expectations show up 34 times in the document Jonas Dovern CES Lecture 1 February 12, / 44

4 Expectations Are Everywhere Source: The Economist. Jonas Dovern CES Lecture 1 February 12, / 44

5 Expectations Are Everywhere Source: DB Research. Jonas Dovern CES Lecture 1 February 12, / 44

6 Importance of Expectations in Economics Central difference between economics and natural sciences: Forward-looking decisions made by humans Expectations of some form are crucial Consumption theory: Expectations about permanent income Investment theory: Net present value calculations Conditional on expected future interest rates, prices and volumes Equity pricing: Expectations about future returns Expectations about future prices Jonas Dovern CES Lecture 1 February 12, / 44

7 Importance of Expectations in Economics Many papers in economics deal with expectations Search for keywords expectation and economic* in titles and abstracts of papers Source: Web of Science. Jonas Dovern CES Lecture 1 February 12, / 44

8 Three CES Lectures The History of Expectations in Macroeconomics Models of Imperfect Information in Macroeconomics Empirical Evidence on Macroeconomic Expectations Jonas Dovern CES Lecture 1 February 12, / 44

9 Agenda 1 The Early Days 2 Adaptive Expectations 3 The Rational Expectations Revolution 4 Beyond FIRE Jonas Dovern CES Lecture 1 February 12, / 44

10 The Early Days Jonas Dovern CES Lecture 1 February 12, / 44

11 Pigou Arthur C. Pigou was the first who articulated that expectations are central to macroeconomic dynamics In Industrial Fluctuations he wrote: [... ] the varying expectations of business men [... ] and not anything else, constitute the immediate and direct cause or antecedents of industrial fluctuations (pp. 34/34) Pigou even anticipated the concept of rational expectations by noting that rational beings would not make systematic errors At the same time, he conjectured that psychological causes might persistently steer the economy away from equilibrium Jonas Dovern CES Lecture 1 February 12, / 44

12 Expectations in Keynes Work Great emphasis on role of expectations: Central: unstable nature and uncertainty of long-term expectations Fokus on two types of expectations: Variables about which it is possible to form subjective probability distributions Variables about which no mathematical expectations can be formulated ( state of ignorance ) Knightian uncertainty Animal spirits Especially investment decisions are subject to the second type of expectations according to Keynes: Capital markets Real productive investment Jonas Dovern CES Lecture 1 February 12, / 44

13 Expectations in Keynes Work Model of expectations? (As always with Keynes,) he provided no formal model of expectation formation Not surprising given the knowledge at this time Expectations taken as exogenous variables Example of Keynes interest rate theory: Expectations about future interest rates important for the demand for cash Theory does not predict how individuals react to expectation errors, i.e. how they adjust their expectations in response to endogenous model dynamics Jonas Dovern CES Lecture 1 February 12, / 44

14 Friedman s Presidential Address Friedman s Presidential Address to the AEA (Friedman, 1968) took expectations to the center stage in economics Context was discussion about Phillips curve: Monetarist counter-revolution Short-run vs. long-run trade-off Long-run as time horizon over which expectations align with reality Talk prepared the RE revolution, although Friedman presumably thought in terms of adaptive expectations Jonas Dovern CES Lecture 1 February 12, / 44

15 Adaptive Expectations Jonas Dovern CES Lecture 1 February 12, / 44

16 The Cobweb Model Consider the famous cobweb model for illustration: d t = m I m p p t + ν dt s t = r I + r p p t t 1 + ν st Equating d t and s t yields the equilibrium price: p t = µ + αp t t 1 + η t, with µ = (m I r I )/m p, α = r p /m p (< 0), and η t = (ν dt + ν st )/m p Dynamics of model depend crucially on how p t t 1 is formed Jonas Dovern CES Lecture 1 February 12, / 44

17 Cobweb Model with AE Let s assume: ) p t t 1 = p t 1 t 2 + λ (p t 1 p t 1 t 2 }{{} forecast error Expectations adapt to changes in price: λ governs speed of adjustment Stationarity is obtained when 1 λ(1 α) < 1 Expectations are conditional on all previously held expectations The two limiting cases: λ = 1: Naive or static expectations λ = 0: Constant expectations Jonas Dovern CES Lecture 1 February 12, / 44

18 Cobweb Model with AE Expectation Price Jonas Dovern CES Lecture 1 February 12, / 44

19 Cobweb Model with NE Expectation Price Jonas Dovern CES Lecture 1 February 12, / 44

20 Problems with AE Purely backward looking: Current conditions are not taken into account What about anticipated shocks? Persistently biased expectations: Especially bad when forecasting trends Agents are not supposed to immediately react to policy changes: Lucas critique Jonas Dovern CES Lecture 1 February 12, / 44

21 Problems with AE Purely backward looking: Current conditions are not taken into account What about anticipated shocks? Persistently biased expectations: Especially bad when forecasting trends Agents are not supposed to immediately react to policy changes: Lucas critique Quote attributed to Abraham Lincoln: You can fool some of the people all of the time, and all of the people some of the time, but you cannot fool all of the people all of the time. Jonas Dovern CES Lecture 1 February 12, / 44

22 The Rational Expectations Revolution Jonas Dovern CES Lecture 1 February 12, / 44

23 Muth s Paper Muth (1961) became prime source for rational expectations in economics, although Simon (1956) uses the same concept Muth describes rational expectations as follows: [Rational] expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory. The hypothesis can be rephrased [... ] as follows: that expectations of firms (or, more generally, 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). Jonas Dovern CES Lecture 1 February 12, / 44

24 Muth s Paper Muth (1961) became prime source for rational expectations in economics, although Simon (1956) uses the same concept Muth describes rational expectations as follows: [Rational] expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory. The hypothesis can be rephrased [... ] as follows: that expectations of firms (or, more generally, 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). Definition of a fixed-point problem rather than a theory on how expectations are formed (Woodford, 2013) This was essentially a paper in microeconomics Jonas Dovern CES Lecture 1 February 12, / 44

25 Features of Rational Expectations RE make use of all available information ( information is not wasted ) RE are model consistent: Model the agents as if they know the model (Muth quoted by Neil Wallace in Hoover and Young, 2011) RE are efficient Jonas Dovern CES Lecture 1 February 12, / 44

26 Cobweb Model with RE We do not change the demand and supply schedules: d t = m I m p p t + ν dt s t = r I + r p p t t 1 + ν st But now, p t t 1 = E t 1 [p t ] Obtained from E t 1 [p t ] = E t 1 [µ + αe t 1 [p t ] + η t ] Jonas Dovern CES Lecture 1 February 12, / 44

27 Cobweb Model with RE Expectation Price Jonas Dovern CES Lecture 1 February 12, / 44

28 Cobweb Model with RE What is gained by using RE in the cobweb model? Production volatility and price volatility are minimized AE NE RE SD(q) SD(p) Jonas Dovern CES Lecture 1 February 12, / 44

29 Reaction to Positive Supply Shock Price Expectations Quantity AE RE AE RE Jonas Dovern CES Lecture 1 February 12, / 44

30 Adoption by Macroeconomists Muth s paper was initially overlooked Rediscovery and application by Lucas and others brought it into mainstream of economics in 1970/80s Lucas claimed that governments cannot manipulate expectation errors in a predictable way if expectations are formed rationally: Policy ineffectiveness proposition You cannot make people hold systematically false expectations The Lucas critique: Expectations of agents will change if policy changes we cannot extrapolate from historic reduced form relationships to gauge the impact of a policy change Use of RE in the context of the efficient markets theory of asset pricing Jonas Dovern CES Lecture 1 February 12, / 44

31 Citation Record of Muth (1961) Source: Web of Science. Jonas Dovern CES Lecture 1 February 12, / 44

32 Did Followers Overplayed It? Barro (1984) writes: One of the cleverest features of the rational expectations revolution was the appropriation of the term rational. Thereby, the opponents of this approach were forced into the defensive position of either being irrational or of modeling others as irrational. (p. 179) For some time, RE became the only concept accepted in most of the macroeconomic community Also, RE became closely connected to conservative policies: Reason to focus on RE models? In fact, many results rely more on assumptions grounded in new classical macroeconomics Is RE assumption a priory less ad-hoc than any other theory about expectation formation? Jonas Dovern CES Lecture 1 February 12, / 44

33 Beyond FIRE Jonas Dovern CES Lecture 1 February 12, / 44

34 Going Back to Muth Muth wrote in the 1980s: It is a little surprising that serious alternatives to rational expectations have never really been proposed. My original paper was largely a reaction against very naïve expectations hypotheses juxtaposed with highly rational decision-making behavior and seems to have been rather widely misinterpreted. Two directions seem to be worth exploring: (1) explaining why smoothing rules work [... ] and (2) incorporating well known cognitive biases [... ]. It was really incredible that so little has been done along these lines. (as cited by Lovell in Hoover and Young, 2011) Jonas Dovern CES Lecture 1 February 12, / 44

35 Combining RE with Limited Information Should we call it LIRE? Common name is models with imperfect information The idea: The world features some information rigidities Agents are aware of this Against this background, agents form expectations rationally Important: assumption of full model knowledge is retained Covered in next lecture: Sticky information model Noisy information model Rational inattention model Jonas Dovern CES Lecture 1 February 12, / 44

36 Alternatives to Rational Expectations Woodford (2013) gives a good overview Formation of beliefs through reflection independent of experience ( eduction ) Inductive approaches: Models of econometric learning Theories of nearly correct beliefs Jonas Dovern CES Lecture 1 February 12, / 44

37 Eductive Expectations Agents understand that the dynamics of variables are determined by a specific model, given the average expectations of other agents Own beliefs need to be able to be rationalized by the conjecture about average beliefs Higher order expectations also need to fulfill this requirement: what I believe you believe I believe you believe... RE are a special case and might emerge as the only possible solution Example for policy implications: Woodford (2013) discusses how assuming this type of expectations leads to the RE equilibrium but with much tighter parameter restrictions needed for stability/to rule out self-fulfilling expectations Jonas Dovern CES Lecture 1 February 12, / 44

38 Learning Much looser requirements on expectations here: Probabilities assigned to possible future outcomes are not too different from actual probabilities with which they occur Idea: agents should be able to recognize predictable features of economic data No need for agents to understand why those regularities exist Initially, research project on learning was mainly seeking a foundation for the RE hypothesis Jonas Dovern CES Lecture 1 February 12, / 44

39 Learning Most common form of learning models assumes that agents recursively derive expectations from econometric models that they estimate based on observed data ˆθ t = Θ t ( ˆθ t 1, ζ t 1, x t ) ˆζ t = Z t ( ˆθ t 1, ζ t 1, x t ) This is used to form expectations about future states, parameters, and observables: [ θ t+1 t ζ t+1 t x t+1 t ] = Ψ( ˆζ t, ˆθ t ) Convergence to RE not automatic Woodford (2013) discusses how learning can make a simple macro model non-ricardian Jonas Dovern CES Lecture 1 February 12, / 44

40 Nearly Correct Beliefs No assumption about the procedure that generates expectations Only requirements on how similar to/different from true probabilities subjective probabilities about the future can be Important: nearly correct refers to conformity of beliefs to actual model dynamics which might be very different from that implied by the RE equilibrium Two influential examples of this type: Rational belief equilibria (Kurz, 1994) Near-rational expectations (Woodford, 2010) Jonas Dovern CES Lecture 1 February 12, / 44

41 Rational Belief Equilibria Probability beliefs only need to imply model-consistent values for some data moments (RE all moments!): Agents should agree on first and second moment of current and past values of growth or CPI inflation which are easily observable There might be disagreement about other variables that Kurz calls belief states : Think of the output gap No learning about these subjective variables Agents can be aware of the fact that their beliefs are different from average beliefs Woodford (2013) discusses that RBE can turn suboptimal policies of commitment that are optimal under RE Jonas Dovern CES Lecture 1 February 12, / 44

42 Near-rational Expectations Why distinguishing a priori between observable data moments and subjective variables? Woodford (2010) instead defines set of probability beliefs that are close enough to the model predictions to be plausibly held by agents: Plausibility is assessed on purely statistical grounds Again near need not be close to RE Key variable: the agent s belief distortion factor m t 0, with E t [m t+1 ] = 1 at all times Woodford (2010, 2013) proposes that policy rules should be chosen as to maximize the lower bound of welfare across set of NREE consistent with the rule Jonas Dovern CES Lecture 1 February 12, / 44

43 Near-rational Expectations Agent s expectations are given by E i,t [X t+1 ] = E t [m t+1 X t+1 ] m t+1 > 1 in a particular state in t + 1 implies that agent exaggerates the probability of reaching that state (conditional on reaching the predecessor state in t) Also E i,t [X t+j ] = E t [m t+1 m t+j X t+j ] Measure of degree of discrepancy suggested by Woodford (2010) is relative entropy between subjective and objective conditional probabilities R t = E t [m t+1 log m t+1 ]: Non-negative convex function Minimum for mt+1 = 1 Jonas Dovern CES Lecture 1 February 12, / 44

44 Summary Long way from Pigou to modern theories of expectation formation History shows struggle between realism and tractability of expectation models Especially in the 1980s also policy considerations seem to have influenced the adoption of the RE paradigm Today many rival theories: Not necessarily a bad thing Jonas Dovern CES Lecture 1 February 12, / 44

45 Summary A last quote from Woodford (2013): [I]t is probably a mistake to suppose that empirical investigations should identify a single model of expectations that can be judged to have been historically valid, and that can then be treated as the way in which expectations must be formed in the future, for purposes of counterfactual policy analyses. It is more reasonable, in my view, to search for policies that should be robust to a variety of possible specifications of expectations. [... ] it is therefore important that macroeconomists continue to seek greater certainty about which models of the economy are more accurate. But one need not settle upon a single model specification [... ]. Jonas Dovern CES Lecture 1 February 12, / 44

46 References I Barro, R. J. (1984). Rational expectations and macroeconomics in American Economic Review, 74(2): Friedman, M. (1968). The role of monetary policy. American Economic Review, 58(1):1 17. Hoover, K. and Young, W. (2011). Rational expectations: Retrospect and prospect. a panel discussion with Michael lovel, Robert Lucas, Dale Mortensen, Robert Shiller, Neil Wallace. CHOPE Working Paper , Center for the History of Political Economy at Duke University. Kurz, M. (1994). On the structure and diversity of rational beliefs. Economic Theory, 4(6): Muth, J. F. (1961). Rational expectations and the theory of price movements. Econometrica, 29: Simon, H. A. (1956). Dynamic programming under uncertainty with a quadratic criterion function. Econometrica, 24: Woodford, M. (2010). Robustly optimal monetary policy with near-rational expectations. American Economic Review, 100(1): Woodford, M. (2013). Macroeconomic analysis without the rational expectations hypothesis. Annual Review of Economics, 5(1): Jonas Dovern CES Lecture 1 February 12, / 44