Optimal Monetary Policy in a Data-Rich Environment

Transcription

1 Optimal Monetary Policy in a Data-Rich Environment Jean Boivin HEC Montréal, CIRANO, CIRPÉE and NBER Marc Giannoni Columbia University, NBER and CEPR Forecasting Short-term Economic Developments... Bank of Canada October 25-26, 27

2 Importance of large data sets: Evidence from factor models Forecasting [Stock and Watson (1999, 22), Forni, Hallin, Lippi, Reichlin (2)] Monetary policy [Bernanke and Boivin (23), Giannone, Reichlin and Sala (24)] VAR [Bernanke, Boivin and Eliasz (25), Forni, Giannone, Lippi, Reichlin (24)]

3 Factor Augmented Vector Autoregression: FAVAR Bernanke, Boivin and Eliasz (25) Observation equation: X t = C t + e t Transition equation (VAR): C t = (L)C t 1 + v t R set of observable series (here Fed funds rate) F set of unobservable factors ( economic activity, in ation,...) X large panel of informational series e series-speci c component (potentially serially and weakly cross correlated)

4 Estimated responses to an identi ed monetary policy shock.1 Federal Funds Rate.1 Industrial Production Price Level (log): CPI Baseline FAVAR (5 factors) VAR [Indus. prod., CPI, FFR] VAR & 1 factor

5 Why are a large set of macro indicators useful? Existing evidence on use of based on largely non-structural models. Limits our ability to: Determine why large data sets are useful Determine sources of uctuations Perform counterfactual experiments Analyze optimal policy

6 Estimated DSGE models Important developments [Altug (1989), McGrattan (1994), Leeper and Sims (1994), Rotemberg and Woodford (1997), Ireland (1997, 21), Kim (2), Schorfheide (2), Christiano, Eichenbaum and Evans (25), Amato and Laubach (23), Smets and Wouters (23, 24), Altig, Christiano, Eichenbaum and Linde (23), Rabanal and Rubio-Ramírez (23), Julliard, Karam, Laxton and Pesenti (24), LOWW (25), Justiniano and Primiceri (26),...] Now increasingly taken seriously as empirical models Promising empirical success [Christiano, Eichenbaum and Evans (25), Smets and Wouters (24)] Estimated based on a handful of data series =) at odds with fact that CB and nancial market participants monitor large number of data series!

7 Goal of the research agenda The more speci c and data-rich the model, the more e ective it will be (Greenspan s memoirs, 27) To explore role of large data sets for estimated DSGE models By product: Provide economic interpretation of latent factors Optimal monetary policy in a data-rich environment

8 Preview of the main results More precise estimation of the state of the economy Improvements in forecasting with additional information Di erent conclusions about structure of economy and sources of business cycles Di erent propagation mechanism (e.g. less habit formation and in ation indexing) Fewer and smaller structural shocks Information from large data set might matter for optimal policy

9 Why more data in a DSGE context?

10 Why more data in a DSGE context? No scope if: Model well speci ed Theoretical concepts directly observed by agents and econometrician

11 Why more data in a DSGE context? No scope if: Model well speci ed Theoretical concepts directly observed by agents and econometrician Empirical evidence: at least one assumption violated

12 Why more data in a DSGE context? No scope if: Model well speci ed Theoretical concepts directly observed by agents and econometrician Empirical evidence: at least one assumption violated We assume theoretical concepts partially observed by econometrician Employment: Discrepancies between household and payroll surveys In ation: GDP de ator, CPI Productivity shock: oil prices, commodity prices If indeed we are missing information in DSGE estimation: all parameter estimates potentially distorted!

13 Outline of presentation Data-rich environment A simple example: RBC model General framework Estimation Application: Smets and Wouters (24) model Results Optimal monetary policy Conclusion

14 Why more information? A simple RBC model Households maximize lifetime utility E 1 X t= t [log (c t ) + v log (1 l t )] ; < < 1; v > subject to y t = e a t k 1 t l t ; < < 1 y t = c t + k t+1 (1 ) k t ; a t = a t 1 + " t ; < 1; " t N (; ) :

15 RBC example continued... Linearized solution has the form: ^y t = d 1^kt + d 2 a t ^c t = d 3^kt + d 4 a t ^lt = d 5^kt + d 6 a t ^k t = g 1^kt 1 + g 2 a t 1 a t = a t 1 + " t 9 >= >; z t = DS t ; z t = h^y t ; ^c t ; ^lt i ) S t = GS t 1 + H" t ; S t = h^kt ; a t i where D, G and H are functions of model parameters Suppose we estimate the model on the basis of only one variable (no stochastic singularity): F t = ^y t = [d 1 d 2 ] S t

16 RBC example: How to link model and data? One indicator, no measurement error X t = ^y t = d 1^kt + d 2 a t e.g. X t = real GDP No scope for judgment or soft data One indicator, measurement error (Sargent, 1989): X t = ^y t + e t = d 1^kt + d 2 a t + e t 1 shock and 1 measurement error: identi cation from dynamics Identi cation problems?

17 RBC example (cont.): Proposed solution Multiple indicators with known relationships to a theoretical concepts X t = = " " real GDP real NI # = " d 1 d 2 NI d 1 NI d 2 1 # NI # " ^kt a t ^y t + e t Helps disentangle meas. error from structural shocks # + e t Multiple indicators with unknown link E.g., soft data X t = " real GDP soft data # = " d1 d # " ^kt a t # + e t

18 Bene ts of exploiting more information: Intuition Measurement error identi able from cross-section of indicators Example: x it = f t + e it, i = 1; :::; n X If n X = 1, and both f t and e it are i.i.d. =) Not identi ed If n X = 1, f t is AR(1) and e it is i.i.d. =) Identi ed (from dynamics) If n X > 1, and both f t and e it are i.i.d. =) Identi ed (from cross-section) Permits the identi cation of more structural shocks Don t have to take a stand a priori on the relative importance of measurement errors vs structural shocks More e cient (consistent) estimate of the latent factors var( ^ft ) is of order 1=n X [Stock Watson (22), Forni et al. (2)]

19 Empirical model: Summary Transition equation: S t = GS t 1 + H" t Observation equation: X t = S t + e t where " XF;t # " ef;t # " F # X t X S;t ; e t e S;t ; S : Comments: Related to non-structural factor models, but we impose DSGE model on transition equation of latent factors Factors have economic interpretation: state variables Interpret info. in data set through lenses of DSGE model Can do counterfactual experiments, study optimal policy

20 Application: Smets and Wouters (24) [i.e., CEE (25) with shocks] State-of-the-art DSGE model: Popular as ts apparently well, good for forecasting Many frictions, many shocks Households Consume aggregate of all goods, habit formation (external) Supply specialized labor on monopolistically competitive labor mkt Rent capital services to rms Decide how much capital to accumulate Firms: Choose labor and capital inputs Supply di erentiated goods on monopolistically competitive goods mkt Prices and wages reoptimized at random intervals (Calvo) If not reoptimized: indexed to past in ation and CB s in ation target

21 Smets and Wouters (24): Model solution 7 variables of interest: F t = [i t ; Y t ; C t ; I t ; t ; w t ; L t ] 9 shocks: s t = h " a t ; "b t ; "G t ; "L t ; "I t ; Q t ; p t ; w t ; i t i State vector S t = h i t 1 ; Y t 1 ; C t 1 ; I t 1 ; t 1 ; w t 1 ; K t 1 ; " I t 1 ; t 1; s t i State-space representation: Transition equation S t = GS t 1 + H" t Observation equation X t = S t + e t

22 Estimation method Di cult problem to estimate (large dimension) Standard methods not successful (e.g. MLE) MCMC methods: Empirical approximation of the posterior distribution. Does not rely on gradient method Draw iteratively from conditional distributions (solves the high-dimensionality problem) Priors can help make the estimation better behaved

23 Speci cations of observation equation: X t = S t + e t Case SW: Standard estimation (as in Smets and Wouters) X F 1;t = F t = S t where X F 1;t = [Fed funds, GDP, cons., invest., %GDP de, real wage, hours worked] Case A = Case SW + Measurement error (as in Sargent, 1989): X F 1;t = F t + e t = S t + e t Restrictions of model used to estimate latent variables in F t (identi cation problems?)

24 Speci cations of observation equation (cont.) Case B = Case A + 7 new indicators of F t (14 series in total) X F;t = F F t + e t = F S t + e t X F;t = h X F 1;t, X 2;t X 2;t = " i cons. excl. food & energy, priv. invest., CPI, core CPI, PCE de, empl. (HH and est. surveys) # E.g. for in ation: use GDP de., PCE de., CPI Case C = Same as case B, but with unrestricted loading matrix larger data set (99 series) X F 1;t = F t + e F 1;t = S t + e F 1;t X 2;t = S S t + e S;t ) () X t = S t + e t

25 Evidence of measurement errors Distribution of correlations between latent concepts and reference indicators 1 Real GDP, Y 6 Consumption, C Investment, I 6 GDP deflator grow th, π Real w age, w 6 Hours w orked, L

26 Empirical results: Estimated latent variables Data A B C 15 Interest rate: i 1 Output: Y Consumption: C 4 Investment: I Real w age: w 1 Employment: L

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28 Empirical results: Estimated in ation 4 3 Inflation: π Data A B C

29 Estimated In ation: Median, 5th and 95th percentiles 4 Case A Case B Case C

30 More information leads to more precise estimates of the latent variables Concept Case A Case B Case C st. dev. Relative to case A Interest rate R t. Output Y t Consumption C t Investment I t In ation (annualized) t Real wage w t Hours worked L t

31 Forecasting performance: One-step ahead RMSE s Primary indicator Case A Case B Case C RMSE Relative to case A Fed funds rate Real GDP Real Consumption Real Investment GDP de. in ation Real wage Hours worked Overall

32 Bene t of adding more information More precise estimates of latent variables, in particular in ation Better forecasts of 7 reference series

33 Correlation between observable indicators and corresponding latent concepts Case A Case B Case C Fed funds rate (12) Real GDP (1) Real Consumption (49) Real xed Investment (74) GDP de. in ation (145) Real wage (18) Hours worked (23) PCE ex. food and Energy (71) Gross Real Investment (73) PCE de ator (146) core-cpi (28) CPI (215) Employment HH Survey (28) Payroll Employment (36)

34 Estimated structural parameters Implied parameters pseudo EIS: Prior Distribution SW Case A Case B Case C Type Mean St.Err. ' Normal (.88) ( 1.11) ( 1.13) ( 1.4) h Beta (.7) (.7) (.27) (.27) Normal (.8) (.7) (.7) (.7) 1= Normal (.6) (.6) (.6) (.6)! Beta (.12) (.14) (.14) (.14) p Beta (.8) (.19) (.15) (.14) r Normal (.8) (.1) (.1) (.9) r 1 Normal (.9) (.12) (.1) (.9) 1 h (1+h) c slope of PC: ( 1 p )(1 p ) (1+ p ) p

35 Estimated time series of capital and shocks SW A B C 4 2 K : Capital stock 2 1 ε a : Productivity shock ε b : Preference shock 2 ε G : Gov. expenditure shock ε L : Labor supply shock 1 ε I : Invest. specific shock

36 Estimated time series of shocks η Q : Equity premium shock η p : Price markup shock η ω : Wage markup shock.4.2 η i : Monetary policy shock SW A B C

37 Variance decompositions 1 Output 1 Consumption 1 Investment SW A B C SW A B C SW A B C 1 Real wage 1 Employment 1 Capital stock SW A B C SW A B C SW A B C 1 Interest rate 1 Inflation SW A B C SW A B C productivity preferences govt. Labor supply Invest. Equ. premium P. markup W. markup Mon. shock

38 Findings Adding more information leads to: More precise estimates of the state of the economy (in ation) Forecasting performance: improvements Di erent conclusions about the nature of propagation and sources of business cycle uctuations To be investigated further... What matters: estimation or ltering? Do info from large data set matter for welfare?

39 Optimal Monetary Policy in a Data-Rich Environment Building on Svensson (1999), Giannoni and Woodford (22), Svensson and Woodford (23, 24) GW (22): General characterization of optimal target criterion a (L) i t + B (L) E t h C L 1 ( t t ) i = Desirable properties: determinacy, robustness to shock processes... Here: Use model and large data set to improve forecasts for implementation of policy

40 Implementation Calibrate standard DGSE model (Giannoni Woodford (23)) and assume structural parameters are known (no estimation, just ltering) Di erent cases: Theoretical variables are unobserved by: By central bank (asymmetric info case) Both central bank and agents (symmetric info case) Investigate: Optimal monetary policy Welfare implication of a central bank that does not account for large information set

41 Preliminary results (based on shortcuts and Giannoni and Woodford, 23) Assume the true variables driving the economy are as estimated under case C Consider two cases: Data-Rich CB: Central bank implements policy on the basis of the true in ation (case C) Data-Poor CB: Central bank ignores data-rich environment and respond instead to actual data (GDP de ator) Comparing loss functions: 23% higher for Data-Poor CB var( t ) var(y t ) Loss Case FI Case AI

42 Avenues for future research Real time application with mixed frequencies