Business Cycle Dynamics under Rational Inattention
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1 Business Cycle Dynamics under Rational Inattention Bartosz Mackowiak (ECB and CEPR) Mirko Wiederholt (Northwestern) Discussed by: James Costain (Banco de España) ESSIM, Tarragona, 22 May 2008
2 This paper!embed Sims rational inattention mechanism, based on information entropy flow constraint, Motivation: information processing costs The math: from telecommunications engineering inside DSGE framework with standard elements perform standard quantitative exercises (IRFs) and idiosyncratic shocks. study interaction of multiple information processing tasks 2
3 Main findings!sluggish response of prices to monetary shocks!strong real responses to monetary shocks!firms react strongly to their idiosyncratic shocks!idiosyncratic shocks divert attention from money shocks!but greater monetary variance implies more errors in response to money shocks!similar to Calvo, but firms make smaller mistakes 3
4 Progress in rational inattention models!sims (2003)... Rational Inattention Choose best predictor of X s.t. information flow constraint Partial equilibrium: X exogenous!mackowiak/wiederholt (2007) Optimal sticky prices... Monopolistic firm: choose own p s.t. information flow constraint Aggregate P endogenous, also idiosyncratic shocks!mackowiak/wiederholt (2008) Business cycle dynamics... Monopolistic firm: choose own p s.t. information flow constraint DSGE context: firms/workers, idiosyncratic shocks, Taylor rule!adam (2008) Simplified DSGE; analyze monetary policy independence!woodford (2008) Use information flow constraint to study decision to buy full info 4
5 Why not assume perfect rationality?!sims: It is apparent from nearly any VAR study... that most crossvariable relationships among macro time series are smooth and delayed!especially important for monetary nonneutrality!lack of extreme contractual contingency!apparently excessive bubbles / crashes 5
6 Alternatives to rational expectations (1) Structural models of information processing! Learning! Behavioral finance! Finite automata, etc. 6
7 Alternatives to rational expectations (1) Structural models of information processing! Learning Useful for modelling how players become forgetful about historical precedents (bubbles, inflation, defaults)! Behavioral finance! Finite automata, etc. 7
8 Alternatives to rational expectations (1) Structural models of information processing! Learning Useful for modelling how players become forgetful about historical precedents (bubbles, inflation, defaults)! Behavioral finance! Finite automata, etc. General problem: arbitrary restrictions on types of strategies Robustness to change in specification? 8
9 Alternatives to rational expectations (2) Exogenous intermittent adjustment! Calvo (1983)! Mankiw-Reis (2002) 9
10 Alternatives to rational expectations (2) Exogenous intermittent adjustment! Calvo (1983) Far from optimal (no state contingence) Lucas critique! Mankiw-Reis (2002) Far from optimal (no state contingence) Lucas critique unrealistically complex choice space (choose sequences) 10
11 The problem with Calvo and Mankiw-Reis 11
12 Alternatives to rational expectations (2) Exogenous intermittent adjustment! Calvo (1983) Far from optimal (no state contingence) Lucas critique! Mankiw-Reis (2002) Far from optimal (no state contingence) Lucas critique unrealistically complex choice space (choose sequences) Mankiw-Reis motivated by information processing costs, instead of menu costs... nonetheless shares many weaknesses of Calvo. 12
13 Alternatives to rational expectations (3) Frameworks close to full rationality! Smart and stupid populations Akerlof-Yellen ( 85); Galí-Gertler-López ( 05); noise traders, etc.! Sims ( 03): information entropy flow constraint GE versions Mackowiak-Wiederholt ( 07/ 08); Adam ( 08)! Woodford ( 08): information entropy flow constraint Fixed costs of info update and menu update! Generalized (S,s) Caballero-Engel ( 93/ 07); Costain-Nakov ( 08) All these models can be parameterized arbitrarily close to rational expectations 13
14 The main issue Calvo and Mankiw-Reis models can also be parameterized arbitrarily close to full rationality. What s the difference?!should parameterize distance from rationality in a way that is robust to Lucas critique (and meteors). 14
15 The main issue Calvo and Mankiw-Reis models can also be parameterized arbitrarily close to full rationality. What s the difference?!should parameterize distance from rationality in a way that is robust to Lucas critique (and meteors). Calvo, Mankiw-Reis: parameterize w.r.t. frequency of adjustment Obviously that s not a deep parameter, so these models will remain vulnerable to Lucas critique 15
16 The main issue Calvo and Mankiw-Reis models can also be parameterized arbitrarily close to full rationality. What s the difference?!should parameterize distance from rationality in a way that is not vulnerable to Lucas critique (and meteors). Generalized (S,s) : parameterize w.r.t. typical value loss. For example: probability of adjustment = 50% when loss = L* Obviously vulnerable to Lucas critique if we state value in. Idea: as long as we state values in units of time, model should be largely robust to Lucas critique. 16
17 The main issue Calvo and Mankiw-Reis models can also be parameterized arbitrarily close to full rationality. What s the difference?!should parameterize distance from rationality in a way that is robust to Lucas critique (and meteors). Sims, etc: parameterize w.r.t. maximum information entropy flow Amount of effort devoted to collecting information is likely to change if economic situation changes. Idea: include cost of information in budget constraint, stated in units of time. Then model should be largely robust to Lucas critique. 17
18 Near-rationality: common findings All 3 models (Generalized Ss / Woodford / Sims) imply:!degree of rationality parameterized in Lucas-robust way!can calibrate rationality on basis of micro adjustment data!respond quickly to idiosyncratic / slowly to agg. shocks!damped/delayed effects of aggregate shocks!money supply shocks similar to Calvo, but firms make much smaller mistakes 18
19 Near-rationality: differences Generalized (S,s) / Woodford imply:!var(x) increases frequency of adjustment increases Sims-type / Woodford models imply:!var(x) increases less attention to Y, Z... Sims-type models imply:!var(x) increases less accurate response to X 19
20 Near-rationality: DSGE computation Generalized (S,s) / Woodford:!must calculate dynamics of distribution Mackowiak-Wiederholt (2008)!Guess firm s pricing policies!solve optimal attention problem!find implied aggregate price dynamics!solve linear DSGE s.t. aggregate price dynamics!compute implied firm s pricing polices... 20
21 James Costain GRACIAS POR SU ATENCIÓN
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