Identification of the New Keynesian Phillips Curve: Problems and Consequences

Transcription

1 MACROECONOMIC POLICY WORKSHOP: CENTRAL BANK OF CHILE The Relevance of the New Keynesian Phillips Curve Identification of the New Keynesian Phillips Curve: Problems and Consequences James. H. Stock Harvard University December 11, 2015 Material in this lecture draws on joint work with Sophocles Mavroeidis (Oxford) and Mikkel Plagborg-Møller (Harvard) 1

2 The Current U.S. Policy Challenge Inflation is ~1.3%, below Fed target Economy has essentially fully recovered from the recession This business cycle is now 8 years old; post-1981 average duration = 8.7 years Fed Funds rate = ~0, debt/gdp ratio is 74%, up from ~35% in

3 Overview The New Keynesian Phillips Curve (NKPC) is the leading conceptual framework for modeling inflation dynamics and is integral to DSGE models The hybrid NKPC combines rational inflation expectations with traditional cost-push and demand components of the original Phillips curve literature The effects of monetary policy (and thus the choice of monetary policy path) depend on the values of these parameters But these parameters are poorly estimated using aggregate time series data o 100+ papers estimating hybrid NKPC parameters, multiple methods. o In NKPC specifications, E t t 1 π t-1 is a key regressor, where E t t 1 is expected π t+1 using t-1 dated data. But it is very difficult to beat a random walk forecast for inflation (makes sense, if inflation is well-controlled) (Atkeson-Ohanian 2000). These problems are intrinsic and cannot be overcome by econometric methods 3

4 Outline I. Review and survey of the NKPC: Specification and estimation methods II. Empirical results: estimator sensitivity III. Weak identification and the NKPC a. Background: weak instrument econometrics b. Evidence of weak identification in the NKPC c. Weak-identification robust inference for the NKPC d. Weak identification is a fundamental problem of the data, not our methods IV. Conclusions & next steps Selected references Mavroeidis (JMCB 2005), Nason and Smith (FRB-Richmond 2003, JAE 2008), Kleibergen and Mavroeidis (JBES 2009), Mavroeidis, Plagborg- Møller, and Stock (JEL 2014) 4

5 I. Review and Survey of the New Keynesian Phillips Curve: Specification Standard hybrid NKPC (Galí and Gertler 1999) (discount factor set to 1) or where E ( ) (1 ) x u t f t t 1 f t 1 t t E ( ) x u t f t t 1 t 1 t t π t = rate of inflation E t = expectation formed at date t u t = cost-push shock x t = is a proxy for marginal cost or a measure of slack (labor share, unemployment gap, output gap) γ f = fraction of forward-looking agents λ = slope of NKPC = effect of real shocks on inflation γ f = 0, purely backwards-looking PC, γ f = 1, purely expectational NKPC 5

6 The values of γ f and λ matter for policy 6

7 Estimation of NKPC (a): Generalized Method of Moments (GMM) Can t just run OLS because E t π t+1 is unobserved and x t is endogenous GMM (generalized instrumental variables; Roberts 1995, Galí-Gertler 1999) Rearrange the NKPC as: E ( ) x u t f t t 1 t 1 t t ( ) x ( E ) u = f t 1 t 1 t f t t 1 t 1 t = f ( t 1 t 1) xt u t. If (i) E t is rational expectation and (ii) Et 1ut = 0, then Et 1u t = 0 so E ( ) x Z 0 t f t 1 t 1 t t 1 (*) where Z t-1 is a vector of t-1 dated data. The GMM (IV) estimator exploits the orthogonality condition (*). GMM (*) reduces to 2 stage least squares without serial correlation/heterosk. 7

8 Estimation of NKPC (b): Vector Autoregression (VAR) methods GMM has advantage of imposing minimal restrictions to obtain identification With more restrictions, in theory high efficiency is possible VAR-based estimators o Conceptually like Limited Information Maximum Likelihood in IV o (π t, x t ) follow VAR(p), with (only) the cross-equation restrictions imposed by the NKPC so estimate VAR imposing restrictions o Technical issues of multiple solutions o Variants of VAR-GMM v. VAR-ML v. VAR-MD discussed in Mavroeidis, Plagborg-Møller, & Stock (2014) o Under textbook conditions (strong identification, homoscedasticity, correct VAR lag length assumption), VAR methods correspond to GMM with optimal instruments o References: Fuhrer and Moore (1995), Lubik and Schorfheide (2004), Sbordone (2005), Kurman (2007) 8

9 Estimation of NKPC (c): Survey expectations as regressors e Replace Et t 1 with t 1 t 1, a survey measure of inflation expectations e Since t 1 t 1, is t-1 dated, estimate NKPC by IV, instrumenting for x t only: ( ) x u. e t f t 1 t 1 t 1 t t x t remains endogenous, so the parameters need to be estimated by GMM e Depending on when survey is taken, t 1 t might also be predetermined Survey expectations also can serve as instruments, or be instrumented if t- e dated expectations are used ( t 1 t) Conceptual issues arise when survey expectations aren t rational which is e typically the case in practice that is, π t+1 - t 1 t is predictable 9

10 II. Empirical results: Estimator sensitivity (1): GG data, updated vintage Galí-Gertler (1999) data with Galí-Gertler-López-Salido (2001) instruments: U.S. data, quarterly, 1970Q1-1998Q1, π t = GDP deflator, x t = labor share gap Z t-1 = {π t-1,, π t-4, x t-1, x t-2, wi t-1, wi t-2, yt 1, y gap t 2 } where wi = wage inflation and y gap = quadratically detrended output. Two vintages: data used by GG (1991), and revised data as of 2012 (Rudd and Whelan 2007) 10

11 Estimator sensitivity (2): Estimates of γ f and λ reported in the literature: All papers with 25+ Google scholar cites as of Sept 2012: 11

12 Researchers face many seemingly minor specification & estimator choices 12

13 Specification choices, ctd. 13

14 Estimator sensitivity (3a): Table 4 specifications, x t = labor share 14

15 Estimator sensitivity (3b): Table 4 specifications, x t = output gap 15

16 III. Weak Identification and the NKPC III(a). Background: Econometrics of weak identification Textbook linear instrumental variables model y = X + u Y = Z + v ( first stage of two stage least squares) X = included endogenous variables (π t+1 π t-1, x t ) Z = instruments (lagged π t, x t, etc.) 2 stage least squares: predicted value from first stage, ˆX, is used as a regressor in the equation of interest The weak instruments problem arises when the true value of is close to zero, so that the instruments contain very little information about Y This occurs for the first stage equation in the NKPC predicting inflation: π t+1 π t-1 = Z t-1 + v t+1 The random walk model of inflation is a good benchmark (more later). 16

17 IV regression with one Y and a single irrelevant instrument ˆ TSLS = Z y ZX = Z ( X +u) ZX = + Zu ZX If Z is irrelevant (as in Bound et. al. (1995)), then X = Z + v = v, so ˆ TSLS = Comments: T 1 Zu Ztu Zv = T t 1 1 T Ztv T divide by zero problem t 1 t t d u z z, where v z z u v ~ 2 u N 0, uv More data doesn t improve inference when the instrument is irrelevant. Distribution of ˆ TSLS is Cauchy-like (ratio of correlated normals) This is one end of the spectrum; the usual normal approximation is the other. If instruments are weak the distribution is somewhere in between uv 2 v 17

18 Weak IV asymptotics for TSLS estimator, 1 included endogenous vble ˆ TSLS = -1 X'Z(Z'Z) Z'y -1 X'Z(Z'Z) Z'X Note: -1 X'Z(Z'Z) Z'X is the explained sum of squares from the first stage Formal modeling device: = C / T (bridges gap between = 0 and large) ˆ TSLS d ( zv) zu ( z )( z ) v v The distribution is governed by 2 = / = population F-statistic on in the first stage (F is large when first-stage ESS is large) If 2 = 0, then unidentified (result above) If 2 large, get the standard normal approximation (the usual limit) 2 v 18

19 Weak-identification robust inference in the linear IV case: The Anderson-Rubin (1949) test and confidence intervals Consider H 0 : = 0 in y = X + u, X = Z + v Under H 0, y X 0 = u, so H 0 can be tested by regressing y X 0 on Z and testing whether the coefficient is zero. This yields the Anderson-Rubin (1949) F-statistic: ( y Y 0) PZ ( y Y 0)/ k AR( 0 ) = ( y Y ) M ( y Y )/( T k) The null distribution is 0 Z 0 2 k /k regardless of 2! GMM version entails HAC variance matrix and inverts GMM objective function (GMM-AR test) Kocherlakota (1990); Burnside (1994), Stock and Wright (2000) Confidence sets are obtained as non-rejection regions of AR( 0 ). The GMM- AR acceptance region is a fully-robust 95% confidence set for 19

20 Summary of weak IV econometrics. 1. If instruments are weak, distributions are nonstandard: o IV and GMM estimators are biased towards OLS & have non-normal distributions o Test statistics (including the J-test of overidentifying restrictions) do not have normal or chi-squared distributions o Conventional confidence intervals do not have correct coverage (coverage can be driven to zero) 2. Inference requires a different toolkit if instruments are weak. o Unbiased estimation not possible in general o Weak-identification robust tests and confidence sets and tests 3. There are several diagnostics for weak instruments (weak identification): o High sensitivity to specification ( divide by zero problem) o In linear IV, first-stage F < 10 (empirical counterpart of 2 ) o Compare robust and standard confidence intervals do they differ? 20

21 III(b). Weak Identification and the NKPC π t = f ( t 1 t 1) xt u t, EuZ ( t t 1) 0 (i) What do distributions of estimators look like for empirically plausible values of first stage? (Simulation evidence) (ii) Diagnostics for weak identification: o In linear IV, first-stage F < 10 (empirical counterpart of 2 ) o High sensitivity to specification ( divide by zero problem) o Compare robust and standard confidence intervals do they differ? 21

22 Weak Identification and the NKPC: Simulation Data generated by VAR(2), estimated from U.S. data subject to hybrid NKPC restrictions; IVs = lagged π t, x t DGP1a: γ f = 0.7, λ = 0.03 DGP 2a: γ f = 0.3 λ = Mavroeidis, Plagborg-Møller, and Stock (2014) show that γ f concentrates around 1 under complete non-identification in VAR-GMM and VAR-MD 22

23 Weak ID and VAR methods Discussion so far has focused on GMM. Under strong instruments, VAR methods have the interpretation of optimal GMM (optimal instruments) so is more efficient under strong instrument asymptotics. But VAR methods don t solve the weak identification problem. Example: o (π t, z t ) follow hybrid NKPC, VAR(1) dynamics, λ = 0. o In the VAR(1), γ f is just identified, so all VAR methods coincide, and 1 ˆVAR f =, 1 ˆ 1 where 1 ˆ is the AR(1) parameter of Δπ t. o But under the random walk model, ρ 1 0 so 1 ˆ concentrates around 0 Weak ID prediction is that mass of ˆVAR f concentrates around 1 23

24 First-stage F First-stage F statistics in regression of π t+1 π t-1 on Z t-1, GMM specifications in Table 4. First-stage F < 10 typically indicates weak instruments 24

25 High sensitivity to specification and estimation method Empirical results: scatterplots of VAR-GMM (red) and GMM (blue): DGP1a: γ f = 0.7, λ =

26 III(c). Weak-ID robust v. standard confidence intervals GMM-AR sets: GMM/std. instruments 26

27 GMM-AR sets, GMM/std. instruments ctd. 27

28 What about replacing E t π t+1 with survey forecasts? Survey forecasts (red) and GMM (blue) 28

29 Replacing E t π t+1 with survey forecasts, ctd. GMM-AR sets with survey forecasts Instruments: 3 lags of ( π t, x t ) 29

30 What about real-time instruments? GMM-AR sets with survey forecasts Inflation: GDP deflator. Instruments: 2 lags of real-time ( π t, output gap, labor share) 30

31 What about full-information system methods? Bayes methods: Schorfheide (2013) survey Frequentist (classical) methods: I. Andrews and Mikusheva (2015), Qu (2015) 31

32 III(d). Weak identification and the NKPC: summary Weak identification is a fundamental problem of the data, not our methods: In the hybrid NKPC, t f( Et t 1 t 1 ) xt ut. E t t 1 t 1 is a regressor in GMM, the predicted change in inflation using t-1 dated predictors o But the random walk model of inflation can be improved upon only modestly. Two reasons for the success of the random walk model: Successful monetary control of π t ; or λ 0 (flat Phillips curve) and unpredictable cost-push shocks o As a result, the regressor E t t 1 t 1 has very little variation and the GMM estimator has the weak-identification divide by zero problem This weak identification problem is intrinsic and isn t solved by LIML (VAR) or FIML (DSGE) methods, unless strong priors are imposed (DSGE estimation) 32

33 IV. Conclusions (a): Hybrid NKPC 1. Estimation of NKPC parameters are subject to severe weak ID problems 2. The evidence is consistent with expectations mattering a lot, or only a little 3. Standard inference methods are misleading 4. VAR evidence that γ f is large is arguably a spurious consequence of weak ID 5. Survey forecast specifications have stronger instruments, but are sensitive to specification; since survey forecasts are not rational (predictable forecast errors), the specifications are hard to interpret 6. Using data revisions (real-time instruments) turned out not to help 7. These findings emerge from several methods, 100+ papers, thousands of empirical estimates. 33

34 Conclusions (b): Moving Beyond γ f? This conference What can be learned from the recent experience of such limited disinflation? What can we learn from micro evidence on formation of inflation expectations? Should we return from marginal-cost based real drivers to demand-pull drivers (e.g. short-run unemployment)? 34