Bounded Rationality and Heterogeneous Expectations in macroeconomics Cars Hommes

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1 MACFINROBODS: WP Behaviour under uncertainty, heterogeneous agents and herding Bounded Rationality and Heterogeneous Expectations in macroeconomics Cars Hommes Universiteit van Amsterdam MACFINROBODS First Workshop London, January -,

2 MACFINROBODS WP, London, January -, Plan of the Talk WP: Behaviour under uncertainty, heterogeneous agents and herding WP: Expectations formation and belief heterogeneity overview of UvA work on Bounded rationality and heterogeneous expectations in macroeconomics

3 MACFINROBODS WP, London, January -, WP Partners ( PM) Behaviour under uncertainty, heterogeneous agents and herding. UvA, PM postdoc Tomasz Makarewicz. CEP, PM. UCSC, PM. CSIC, PM

4 MACFINROBODS WP, London, January -, WP Objectives Behaviour under uncertainty, heterogeneous agents and herding O.. Use laboratory experiments to characterize micro-level decisions when faces with high uncertainty in transition between normal, boom and crisis times; O.. Test and adapt behavioural assumptions recently used in macro-economic modeling (e.g. conformism and loss aversion); O.. Craft macro-economic models with behaviourally realistic heterogeneous agents and understand how outcomes dier from representative-agent model; O.. Analyze eects of monetary, scal and macro-prudential policies in macro-economic models with behaviourally realistic heterogeneous agents;

5 MACFINROBODS WP, London, January -, WP Tasks Behaviour under uncertainty, heterogeneous agents and herding T.. Carrying out laboratory experiments with human subjects and compiling data sets documenting the experimental results; T.. Testing a range of behavioural assumptions, including bounded rationality, conformism and loss aversion, using experimental data; T.. Constructing and analyzing macro-economic models featuring micro-behavioural realism Developing numerical methods that allow solving history dependent models with heterogeneous agents;

6 MACFINROBODS WP, London, January -, WP Partners (PM) Expectations Formation and Belief Heterogeneity. UvA, 7PM postdoc Tomasz Makarewicz. CERGE, PM. GU, 7PM. UCSC, PM

7 MACFINROBODS WP, London, January -, WP Objectives Expectations Formation and Belief Heterogeneity O.. Advance approaches for explicit modeling formation of heterogeneous expectations, such that they can be implemented in policy-focused macroeconomic models; O.. Investigate the validity of rules attributed to individuals' expectation formation by comparing resulting decision making to experimental evidence in WP; O.. Incorporate heterogeneous expectations in macro-nancial models and explore their empirical t to nancial data relative to homogeneous expectations benchmark;

8 MACFINROBODS WP, London, January -, WP Tasks Expectations Formation and Belief Heterogeneity T.. Extension of behavioural theory of heterogeneous expectations to develop models describing episodes of crises and unusually large uctuations (UvA); T.. Investigation to what extent models with heterogeneous expectations and learning help explain experimental evidence on decision making under uncertainty (UvA)

9 MACFINROBODS WP, London, January -, Bounded Rationality and Heterogeneous Expectations in Macroeconomics Behavioural Heuristics Switching Model agents use simple forecasting rules and gradually switch to better performing rules reinforcement learning / survival of the ttest Empirical estimation of heterogeneous expectations model with endogenous switching Laboratory experimental testing of individual rules and aggregate macro behavior

10 MACFINROBODS WP, London, January -, Some References Cornea, A., Hommes, C.H. and Massaro, D. (), Behavioral heterogeneity in U.S. ination dynamcis, University of Amsterdam,. Assenza, T., Heemeijer, P., Hommes, C.H. and Massaro, D. (). Managing self-organization of expectations through monetary policy: a macro experiment, Universiteit van Amsterdam. Hommes, C.H., (), Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems, Cambridge.

11 MACFINROBODS WP, London, January -, Heuristics Switching Model Heuristics Switching Model Pool of heuristics whose impacts are changing over time according to observable past relative performance U h,t = + x t x e h,t + ηu h,t Discrete choice model with asynchronous updating n h,t = δn h,t + ( δ) exp(βu h,t ) Z t Set of four heuristics ADA π,t+ e =.π t +.π,t WTF π,t+ e = π t +.(π t π t ) STF π,t+ e = π t +.(π t π t ) LAA π,t+ e =.(πt av + π t ) + (π t π t )

12 MACFINROBODS WP, London, January -, Estimation -type NKPC The hybrid New Keynesian Phillips curve Pricing behavior described in the context of models with nominal rigidities (sticky prices) and optimizing agents with rational expectations Forward-looking NKPC π t = δe t π t+ + γmc t Criticism: no intrinsic inertia in ination, i.e., no structural dependence on lagged ination (see, e.g., Rudd and Whelan (a,b)) Hybrid models of the form π t = θe t π t+ + ( θ)π t + γmc t

13 MACFINROBODS WP, London, January -, Estimation -type NKPC Empirical relevance of forward-looking behavior Estimation of the closed-form solution of the model under RE π t = µ δ s E t mc t+s + µ π t + ɛ t s= results in mixed evidence Galì and Gertler (999), Sbordone () and Kurmann (7): predominant role of forward-looking component Fuhrer (997), Lindè () and Rudd and Whelan (): no signicant evidence for forward-looking behavior

14 MACFINROBODS WP, London, January -, Estimation -type NKPC Contributions of Cornea-H-Massaro paper Framework with monopolistic competition, staggered price setting and endogenous switching between dierent forecasting regimes Estimation of a NKPC with heterogeneous expectations using U.S. macroeconomic data Empirical relevance of forward-looking vs backward-looking behavior

15 MACFINROBODS WP, London, January -, Switching Model Simple -type example (fundamentalists vs naive) Fundamental ination (solution under homogeneous RE) π t = γ δ s E t mc t+s s= Fundamentalists expectations E f t π t+ = γ δ s E f t mc t+s s= VAR methodology (Campbell and Shiller (987)) Z t = AZ t + u t Naive expectations E f t π t+ = γe (I δa) AZ t E n t π t+ = π t

16 MACFINROBODS WP, London, January -, Switching Model Evolutionary selection of expectations Discrete choice model (Brock and Hommes, Econometrica 997) n i,t = exp(βu i,t ) I i= exp(βu i,t ) n i,t fraction of agents using predictor i at time t Fitness measure F Ei t U i,t = I i= F Ei t K where F Et i = Et k i π t k π t k, k=

17 MACFINROBODS WP, London, January -, Estimation -type NKPC The full model (fundamentalists vs naive) NKPC with heterogeneous beliefs and endogenous switching where π t = δ(n f,t E f t π t+ + ( n f,t )E n t π t+ ) + γmc t + ξ t, E f t π t+ = γe (I δa) AZ t E n t π t+ = π t n f,t = F E i t = ( ( + exp β F E f t F En t F E f t +F En t )) K Et k i π t k π t k, with i = f, n k=

18 MACFINROBODS WP, London, January -, Estimation -type NKPC Baseline VAR specication Quarterly U.S. data from 9:Q to :Q Fundamentalists forecast E f t π t+ = γe (I δa) AZ t Start with broad VAR in output gap (y t ), unit labor costs (ulc t ), labor share of income (lsi t ), ination rate (π t ) which reduces to a four-lag bivariate VAR Y t = [y t, lsi t ] Z t = [Y t, Y t, Y t, Y t ] A = (Z Z ) Z Z Portmanteau test: p-value Q() =.79, R =.9

19 MACFINROBODS WP, London, January -, Estimation -type NKPC Estimation results Table : NLS estimates of switching model Parameter β γ Estimate.78. Std. error.7. R from Ination Equation.78 R from Output Gap VAR Equation.9 Notes: Standard errors are computed using White's HCCME.,, denote signicance at the %, %, and % level. robust w.r.t. VAR specication (including π t ) robust w.r.t. marginal cost specication

20 MACFINROBODS WP, London, January -, Estimation -type NKPC The t of the model one-period ahead forecasts.. actual predicted.. inflation Figure : Actual vs. predicted ination

21 MACFINROBODS WP, London, January -, Estimation -type NKPC Evolution of weight of fundamentalists n f,t π t f π t E t n f n f on average more backward looking agents Mean. Median. Maximum.9 Minimum. Std. Dev..7 Skewness. Kurtosis. Auto-corr. Q(-).9.. (FE n FE f )/(FE n +FE f ) Top panel: Time series of the fraction of fundamentalists n f,t Middle panel: Distance between actual and fundamental ination Bottom panel: Scatter plot of n f,t vs relative forecast error of naive rule

22 MACFINROBODS WP, London, January -, Laboratory Experiments Learning to Forecasts Laboratory Experiments individuals only have to forecast price, ceteris paribus, e.g. with all other behavior assumed to be rational, demand/supply derived from prot/utility maximization computerized trading yields market equilibrium price, consistent with benchmark model, e.g. cobweb model asset pricing model New Keynesian macro model advantage: clean data on expectations Challenge: universal theory of heterogeneous expectations

23 MACFINROBODS WP, London, January -, Laboratory Experiments A Monetary Economy with Nominal Rigidities Standard model for monetary policy analysis y t = y e t+ ϕ(i t π e t+) + ɛ t output π t = λy t + βπ e t+ + υ t ination i t = Max{π + φ π (π t π), } monetary policy rule Complication: the standard forward looking New Keynesian model requires agents to forecast two variables! Experimental desigh: two dierent groups of forecasters ination and output gap to limit cognitive eorts

24 MACFINROBODS WP, London, January -, Laboratory Experiments Experimental Results Three Treatments: (a) ination target π = and weak Taylor rule (φ π = ); (b) ination target π = and aggressive Taylor rule (φ π =.); (c) ination target π =. and aggressive Taylor rule (φ π =.)

25 MACFINROBODS WP, London, January -, Laboratory Experiments Instructions for Participants General information Participants are assigned the ctitious role of professional forecasters Information about the economy Subjects do not know the data generating process, but receive qualitative information about the economy and the type of expectations feedback ination depends positively on ination forecasts and output gap forecasts; output gap depends positively on ination forecasts and output gap forecasts, but negatively on the interest rate.

26 MACFINROBODS WP, London, January -, Laboratory Experiments Earnings Payo function: score = +f where f is the absolute value of the forecast error expressed in percentage points score 8 absolute value forecast error Absolute forecast error 9 Score

27 MACFINROBODS WP, London, January -, Laboratory Experiments Screenshot Experiment

28 MACFINROBODS WP, London, January -, Experimental Results Experimental Results Three Treatments: (a) ination target π = and weak Taylor rule (φ π = ); (b) ination target π = and aggressive Taylor rule (φ π =.); (c) ination target π =. and aggressive Taylor rule (φ π =.)

29 MACFINROBODS WP, London, January -, Experimental Results Treatment a; ( π =, φ π = ) coordination on some equilibrium level or coordination on exploding inationary/deationary spiral Treatment a, group Treatment a, group Treatment a, group inflation inflation inflation output gap output gap output gap Treatment a, group Treatment a, group Treatment a, group inflation inflation inflation output gap output gap output gap

30 MACFINROBODS WP, London, January -, Experimental Results Treatment b; ( π =, φ π =.) coordination on dampened oscillations Treatment b, group Treatment b, group Treatment b, group inflation inflation inflation output gap output gap output gap Treatment b, group Treatment b, group Treatment b, group inflation inflation inflation output gap output gap output gap

31 MACFINROBODS WP, London, January -, Experimental Results Treatment c; ( π =., φ π =.) coordination on dampened or persistent oscillations Treatment c, group Treatment c, group Treatment c, group inflation inflation inflation output gap output gap output gap Treatment c, group Treatment c, group Treatment c, group inflation inflation inflation output gap output gap output gap

32 MACFINROBODS WP, London, January -, Experimental Results Summary of the Experimental Results Four Dierent Types of Aggregate Behavior emerging through Coordination of Individual Expectations coordination of individual expectations not perfect, some heterogeneity persists weak Taylor rule (φ π = ): unstable dynamics convergence to some non-fundamental steady states exploding ination-output dynamics, either increasing or decreasing aggressive Taylor rule (φ π =.): stable dynamics fast or slow oscillatory convergence permanent oscillations if target ination π =.

33 MACFINROBODS WP, London, January -, HSM Model Heuristics Switching Model Pool of heuristics whose impacts are changing over time according to observable past relative performance U h,t = + x t x e h,t + ηu h,t Discrete choice model with asynchronous updating n h,t = δn h,t + ( δ) exp(βu h,t ) Z t Set of four heuristics ADA π,t+ e =.π t +.π,t WTF π,t+ e = π t +.(π t π t ) STF π,t+ e = π t +.(π t π t ) LAA π,t+ e =.(πt av + π t ) + (π t π t )

34 MACFINROBODS WP, London, January -, HSM Model Coordination on explosive behavior( π =, φ π = ; Tra, gr) through coordination on strong trend-following rule Treatment a, group experiment Predictions of participants, treatment a, group Predictions of rules, treatment a, group simulation ADA WTF STF LAA ACF inflation, treatment a, group Impact of rules (inflation), treatment a, group Impact of rules (output gap), treatment a, group. experiment simulation.9 ADA WTF STF LAA.9 ADA WTF STF LAA ACF output gap, treatment a, group

35 MACFINROBODS WP, London, January -, HSM Model Coordination dampened oscillations ( π =, φ π =.; Trb, gr) through switching from trend-following to adaptive expectations Treatment b, group experiment Predictions of participants, treatment b, group Predictions of rules, treatment b, group simulation ADA WTF STF LAA ACF inflation, treatment b, group Impact of rules (inflation), treatment b, group Impact of rules (output gap), treatment b, group. experiment simulation.9 ADA WTF STF LAA.9 ADA WTF STF LAA ACF output gap, treatment b, group

36 MACFINROBODS WP, London, January -, HSM Model Coordination on RE steady state ( π =., φ π =.; Trc, gr) through coordination on adaptive expectations Treatment c, group experiment Predictions of participants, treatment c, group Predictions of rules, treatment c, group simulation ADA WTF STF LAA ACF inflation, treatment c, group Impact of rules (inflation), treatment c, group Impact of rules (output gap), treatment c, group. experiment simulation.9 ADA WTF STF LAA.9 ADA WTF STF LAA ACF output gap, treatment c, group

37 MACFINROBODS WP, London, January -, HSM Model Coordination persistent oscillations ( π =., φ π =.; Trc, gr) through coordination on learning-anchor-and-adjustment rule (LAA) Treatment c, group experiment Predictions of participants, treatment c, group Predictions of rules, treatment c, group simulation ADA WTF STF LAA ACF inflation, treatment c, group Impact of rules (inflation), treatment c, group Impact of rules (output gap), treatment c, group. experiment simulation.9 ADA WTF STF LAA.9 ADA WTF STF LAA ACF output gap, treatment c, group

38 MACFINROBODS WP, London, January -, Policy Monetary Policy and Macroeconomic Stability Taylor rules targeting ination: i t = π + φ π(π t π)[+φ y(y t y)] New Keynesian DSGE Model: (π t, y t ) = F ( π e t+, ȳe t+ ) absolute value of eigenvalues of linear map ΦΠ ΦΠ managing trend-following behavior: increase φ π to add negative feedback s.t. the macroeconomy becomes suciently stable to prevent survival of trend-following strategies

39 MACFINROBODS WP, London, January -, Conclusions Summary behavioral heuristics switching model ts empirical and experimental data at micro and macro level in NK macro framework Heuristics Switching Model explains coordination on four dierent almost self-fullling equilibria: (non-fundamental) steady state exploding inationary/deationary spirals dampened oscillations persistent oscillations around target π =. a more aggressive Taylor rule can manage the self-organization process, to prevent survival of trend-following behavior and stabilize the economy Policy analysis may benet from behavioral model of expectations

40 MACFINROBODS WP, London, January -, Conclusions Thanks very much! Feedback welcome! References: Assenza, T., Heemeijer, P., Hommes, C.H. and Massaro (), Managing self-organization of expectations through monetary policy: a macro experiment, October. Cornea, A., Hommes, C.H. and Massaro, D. (), Behavioral heterogeneity in U.S. ination dynamcis, University of Amsterdam,. Hommes, C.H., (), Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems, Cambridge.