Does In‡ation Adjusts Faster to Aggregate Technology Shocks than to Monetary Policy Shocks LUIGI PACIELLO* Abstract This paper studies in‡ation adjustment speed to aggregate neutral technology shocks and to monetary policy shocks in a Bayesian VAR model. The two structural shocks are identi…ed through model-robust sign restrictions. Determining the speed of in‡ation adjustment to di¤erent types of shocks provides information on the ability of existing models of price setting to match price dynamics. This paper shows that, in the United States, in‡ation adjustment speed to aggregate technology shocks is substantially faster than to monetary policy shocks. This paper also shows that standard Calvo models of sticky prices are able to explain only part of the di¤erence in in‡ation persistence to technology and monetary policy shocks. JEL Classi…cation: E31, E4, C11, C3 Keywords: Bayesian VAR, price responsiveness, monetary policy shocks, technology shocks, sign restrictions

*

Email: [email protected]. Mailing address: Einaudi Institute for Economics and

Finance, Via dei Due Macelli, 73, 00187 Roma. I am grateful to Pierpaolo Benigno, Martin Eichenbaum, Francesco Lippi, Stefano Neri and Giorgio Primiceri for helpful suggestions and comments.

1

Introduction

This paper investigates whether U.S. in‡ation is more persistent to monetary policy shocks than to aggregate neutral technology shocks. Assessing in‡ation persistence to di¤erent types of shocks is an important task in macroeconomics, not only to establish the main sources of business cycle ‡uctuations, but also to understand the way di¤erent shocks transmit through the economy and to distinguish among available models. This paper contributes to the existing literature on two dimensions. First, the paper establishes that U.S. in‡ation is more persistent following monetary policy shocks than following technology shocks. Second, the paper shows that, conditional on the estimated response of marginal costs, plain forward-looking models of price setting explain only part of the di¤erence in in‡ation persistence to the two shocks. I document in‡ation persistence to technology and monetary policy shocks, using a Bayesian VAR (BVAR) model. I identify monetary policy and aggregate technology shocks through robust sign restrictions, similarly to Dedola and Neri (2007), Uhlig (2006) and Canova, Gambetti and Pappa (2007). These restrictions naturally arise in a large class of dynamic stochastic general equilibrium (DSGE) models; they are uncontroversial, since they are common to both RBC style and New-Keynesian style models and robust, in the sense they hold regardless of the parameterization and of the nature of the policy rules. Nevertheless, results are robust to di¤erent identi…cation assumptions. The model is estimated on U.S. data from 1960:I to 2007:II. Finally, in‡ation persistence is measured through a method proposed by Cogley, Primiceri and Sargent (2008), while unit labor costs are used as measures of marginal costs, as suggested by Sbordone (2002, 2005) and Cogley and Sbordone (2008). In‡ation persistence has been, over the past decade, one of the most intensely investigated topics in macroeconomics. Recently, Altig, Christiano, Eichenbaum and Linde (2005) and Dupor, Han and Tsai (2007) have estimated standard DSGE models with sticky prices to match the impulse responses of the U.S. economy to technology 1

and monetary policy shocks. They have shown that these models have a hard time accounting for both responses of in‡ation to technology and monetary policy shocks. Relative to these authors, the contribution of this paper is threefold. First, this paper adopts a Bayesian approach using a di¤erent set of identi…cation assumptions, based on robust sign restrictions, while assessing robustness of …ndings to di¤erent identi…cation assumptions as well. This is important as several authors have recently criticized identi…cation assumptions of technology shocks based on long-run restrictions as in Galì (2009).1 This paper shows that the di¤erent behavior of in‡ation in response to the two types of shocks hold through a wide range of possible models and identi…cation assumptions. Second, the paper provides direct measures of in‡ation persistence conditional on each shock. In particular, the Bayesian approach of the paper provides information on the posterior probability that in‡ation adjusts faster to technology than to monetary policy shocks. Third, in assessing the ability of standard sticky price models to match in‡ation persistence, the path of expected marginal costs is obtained directly from the structural VAR rather than a DSGE model, as suggested by Sbordone (2002, 2005). This has the advantage that it doesn’t involve other maintained hypotheses about the structure of the economy, (for example, about household preferences or about wage- setting) in addition to the assumed model of pricing and supply behavior by …rms and identi…cation assumptions of the VAR. In fact, Schorfheide (2008) shows that when marginal costs, measured as labor share, are included in the set of observables, estimates of the slope of the New Keynesian Phillips curve fall into a much narrower range than if marginal costs were obtained from a DSGE model. Several studies have evaluated the dynamics of U.S. unconditional in‡ation. The inability of New Keynesian Phillips curve models to replicate the high in‡ation persistence found in post-WWII U.S. data, was …rst documented by Fuhrer and Moore (1995). This result spawned a vast e¤ort aimed at “hardwiring” in‡ation persis1

See Erceg, Guerrieri and Gust (2005).

2

tence into macroeconomic models.2 Recently, Benati (2008) has showed that in‡ation persistence has changed over time, in coincidence with changes in monetary policy regimes. Given this evidence, he concludes that intrinsic in‡ation persistence found in post-WWII U.S. data is not structural in the sense of Lucas (1976). Relative to this literature, this paper contributes by studying the persistence of in‡ation response to two fundamental aggregate shocks, technology and monetary policy shocks. This study adds a new dimension along which in‡ation inertia may change, namely the structural shocks. Conditional on the path of marginal costs, the fact that in‡ation response is more persistent to monetary policy than technology shocks supports the view that in‡ation persistence is not structural. This paper also relates to recent work by Sbordone (2002, 2005). Using a VAR to estimate expected marginal costs, Sbordone shows that the New-Keynesian Phillips curve well represent unconditional in‡ation dynamics in the U.S. This paper studies the ability of the New-Keynesian Phillips to match in‡ation persistence conditional on aggregate technology and monetary policy shocks. While the paper …nds that the New-Keynesian Phillips curve correctly predicts in‡ation response to be more persistent to monetary policy than to technology shocks, it also recognizes that such simple models cannot fully explain the di¤erence in in‡ation persistence to the two types of shocks. The paper is organized as follows. Section 2 describes the BVAR model, the data, the prior and the identi…cation assumptions. Section 3 describes results about persistence of in‡ation responses. Section 4 discusses results. Section 5 assesses robustness of …ndings against identi…cation assumptions and sub-sample stability. Section 6 concludes. 2

See Cogley and Sbordone (2008) for a discussion of the literature and interpretation of in‡ation inertia.

3

2

The benchmark BVAR model

This section describes the baseline empirical model consisting of a SVAR for an ndimensional vector of variables, Yt . The SVAR model is given by A0 Y t =

+ A1 Y t

1

+ ::: + Ap Yt

p

where Yt = (y1;t y2;t :::yn;t )0 is the set of time-series at period t, a vector of constants, A0 ; A1 ;..Ap are n

(1)

+ et ; =(

1

2

:::

n)

is

n matrices of structural parameters, p is a

non-negative integer, and et is an n-dimensional Gaussian white noise with unitary covariance matrix, E fet e0t g = I; representing structural shocks. The reduced form VAR model associated to (1) is given by Yt = c + B1 Yt

1

+ B2 Yt

2

+ ::: + Bp Yt

p

(2)

+ ut ;

where c = A0 1 ; Bs = A0 1 As for s = 1; ::p; and ut = A0 1 et : It follows that 0

E fut u0t g = A0 1 A0 1 : Following Banbura, Giannone and Reichlin (2008), model (2) is estimated using a Bayesian VAR approach to overcome the curse of dimensionality. Banbura et al. show that the forecasting power and structural analysis of relatively large VAR models substantially improve when allowing for priors. These priors are set according to the standard practice which builds on Litterman (1986)’s suggestions, which are often referred to as Minnesota priors. In particular, Yt is assumed to evolve according to Yt = c + diag ( 1 ; ::::;

n ) Yt 1

(3)

+ ut ;

where the ith equation in (2) is centered around a random walk with drift if the ith element of Yt is highly persistent;

i

= 1; and around a white noise otherwise,

4

i

= 0.

Therefore, prior beliefs are such that

E (Bs )ij

=

V (Bs )ij

=

8 <

i;

if i = j; s = 1

: 0; 2

2 i ; 2 j

s2

for i = 1; :::; n; j = 1; :::; n; s = 1; :::; p; and the matrix E ( ) = diag ( 21 ; ::::;

2 n) :

;

otherwise

The scale parameters

2 i

has prior expectation

are set equal to the variance of

the residual from a univariate autoregressive model of order p for the ith element of Yt : The hyper-parameter

governs the overall tightness of the prior distribution around

(3) : Notice that, as

! 1; prior beliefs converge to a ‡at prior. Next subsection

describes choices of

and

B = (B1 ; ::::; Bp ; c)0 and

2.1

i:

Under these assumptions, the posterior distribution of

is Normal inverted-Wishart.3

Data and priors

The model we consider is similar to the one studied by Altig, Christiano, Eichenbaum and Linde (2005), and by Banbura, Giannone and Reichlin (2008), corresponding to a medium size model of business cycle. It includes capital utilization, the quarterly average Federal Funds rate, the quarterly average interest rate on 10-years treasury-bond, unit labor costs, GDP-de‡ator in‡ation, and the growth rates of GDP, investment, consumption, total hours worked, labor productivity and M2.4 The time span is from January 1960 through June 2007. The model is estimated on a quarterly frequency, and the number of lags p is set equal to 4. A random walk prior,

i

= 1; is assumed for in‡ation, M2 growth, capital utiliza-

tion, unit-labor costs and interest rates, while a white noise prior,

i

= 0; is assumed

for the remaining variables. These priors are consistent with Stock and Watson (2002). Finally, the hyper-parameter 3 4

is chosen similarly to Banbura, Giannone and

See Appendix B for more details. Appendix A contains detailed information on the data.

5

Reichlin (2008) and set equal to 0:1:5

2.2

Identi…cation of the structural parameters

Given the focus of the paper, I will only identify two structural shocks, a supply shock in the form of a neutral technology shock to total factor productivity, and a demand shock in the form of a monetary policy shock. Identi…cation is achieved through signrestrictions. From a Bayesian point of view, sign restrictions amount to attributing probability zero to reduced-form parameters giving rise to impulse responses which contravene the restrictions. To the extent that these restrictions do not lead to overidenti…cation, they impose no constraint on the reduced form of the VAR. Standard Bayesian methods can thus be used for estimation and inference. Sign restrictions in this paper are similar to the ones assumed by Canova, Gambetti and Pappa (2007), and consistent with identi…cation assumptions by Uhlig (2005) and Dedola and Neri (2006). These sign restrictions are robust in the sense that they are consistent with a wide range of DSGE models.6

Table 1: Sign restrictions Output growth

Invest. growth

Cons. growth

Price level

FedFunds

M2 growth

Technology

0

0

0

0

0

0

Monetary

0

0

0

0

0

0

After a positive technology shocks, quantities (i.e. output, consumption and investment) are expected to have a positive growth rate for the …rst k quarters, while the variation of the Federal Funds rate and M2 growth are expected to be negative 5

I have estimated the model for di¤erent values of ; and results are robust to changes in . In section 5 I report results under a ‡at prior, ! 1: 6 Canova, Gambetti and Pappa (2007), Dedola and Neri (2006) provide detailed examples of standard DSGE models where these restrictions hold. Moreover, these restrictions are consistent with impulse responses estimated in a DSGE model by Smets and Wouters (2007). I refer to these authors for more details.

6

over the same interval. As argued by Canova et al. the behavior of the Federal Funds rate and M2 growth makes unlikely to confuse technology shocks with expectactional shocks (Lubik and Schorfheide, 2004). After a tightening shock to monetary policy, both quantities and M2 are expected to have a negative growth rate for the …rst k quarters, while the variation of the Federal Funds rate is expected to be positive over the same interval. There is an important trade-o¤ to consider when choosing the horizons k over which impulse responses are restricted. When only a few horizons are restricted, shocks with di¤erent medium to long-run implications could be confused. As the number of restricted responses increases, the empirical analysis acquires a more structural character, but if restrictions are invalid, inference is inappropriate and standard errors inaccurate. Since this trade-o¤ is highly nonlinear, it is di¢ cult to optimize. Similarly to Canova, Gambetti and Pappa (2007), I present results obtained imposing restrictions at two horizons (k=0 and k=1), since this choice accounts for both concerns. In addition, given the focus of the paper is on price level impulse responses, I assume relative weak restrictions on these: in particular, I assume that the price level (in deviation from the steady state) has to be weakly negative only in one period during the …rst 8 quarters. This identi…cation assumption allows to potentially encopass also those models that generate a "price puzzle" in the response of prices to monetary policy shocks, or for "over-accomodating" monetary policy responses to technology shocks.7 Finally, while this sign restrictions are robust to a wide range of business cycle models, it is important to emphasize that results of these papers are robust to di¤erent identi…cation assumptions.8 7

See Christiano, Eichenbaum and Evans (2005), and Altig, Christiano, Eichenbaum and Linde (2005). 8 Section 5 reports results relatively to di¤erent identi…cation assumptions.

7

3

Results

In this section the model reduced-form parameters B1 ; :::; Bp and

are drawn from

the estimated Normal inverted-Wishart posterior distribution. For each draw of B1 ; :::; Bp and

; the model structural-form parameters A0 ; :::; Ap are computed

according to the methodology proposed by Ramirez, Waggoner and Zha (2007).

3.1

Impulse responses

For each draw of structural parameters from the posterior distribution, I compute impulse responses of Yt to a one standard deviation technology shock and to a one standard deviation monetary policy shock.9 [Figures 1-4 about here] Figure 1 and 2 plot the median impulse responses to aggregate technology and monetary policy shocks, and the associated 68 and 90 percent con…dence intervals, of the GDP price de‡ator and in‡ation, under k=0 and k=1. Impulse responses are very similar across the two identi…cation assumptions, k=0 and k=1. Therefore, to save on space, I will study the case k=1. In‡ation responses display a high level of persistence to both technology and monetary policy shocks. However, in‡ation is relatively more persistent to monetary policy shocks than to technology shocks. In particular, the median in‡ation response to a monetary policy shock is hump-shaped with a peak around 10 quarters after the shock. Moreover, it takes about 16 quarters before ninety percent of its posterior distribution is below zero. In contrast, in‡ation response to a technology shock displays no hump-shape and is characterized by a monotonic dynamic towards the steady state. 9

Results are based on 5,000 draws and are robust to larger number of draws.

8

Finally, Figures 3 and 4 plot the impulse responses of the remaining macroeconomic indicators of the model. These responses are consistent with results obtained in previous studies.10

3.2

Measuring in‡ation persistence

For convenience, let’s rewrite model (2) in the following form: ~ t Y~t = c~ + BY where Y~t np

[Yt0 ; Yt0 1 ; :::; Yt0 p ]0 and c~

np while A~ is a np

Let’s de…ne in‡ation as

~ t + Ae

(4)

[c0 ; 0; 0; :::; 0] are vectors np

~ is a matrix 1; B

n matrix, 2

~ B

1

6 6 6 6 6 6 6 6 6 4 t

B1

B2

...

Bp

I

0

:::

0

0 .. .

I .. .

::: .. . . . .

0 .. .

0

0

I

0

3

7 7 7 7 7 ~ 7; A 7 7 7 5

2 6 6 6 6 6 6 6 6 6 4

A0 1 0 0 .. . 0

3

7 7 7 7 7 7: 7 7 7 5

(5)

= e0 Y~t ; where e is a column vector of zeros but the entry

corresponding to in‡ation which is one. Then the response of in‡ation j periods ahead to structural shock i is given by ^ j;i

~ j A~i ; B

~ where A~i is the ith column of A: In‡ation persistence is measured according to the methodology proposed by Cogley, Primiceri and Sargent (2008). Relative to other measures of in‡ation persistence, such as half-lives, their measure as the advantage of not relying on the monotonicity 10

See for instance Francis and Ramey (2005), Altig, Christiano, Eichenbaum and Linde (2005), Galì (1999).

9

of responses. Given that in‡ation response to monetary policy shocks is characterized by a hump-shape dynamic, this property is very appealing. In particular, in‡ation persistence to shock i, j periods after the shock, is measured as

rj;i

j X

^ 2j;i

s=0

1

1 X

(6)

: ^ 2j;i

s=0

In‡ation is weakly persistent when the e¤ects of shocks decay quickly, and it is strongly persistent when they decay slowly. When the e¤ects of shock i die quickly, rj;i is pushed close to zero for relatively small j. But when the e¤ects of shock i decay slowly, rj;i is pushed closer to one. Thus, for small or medium j

0, a small rj;i

signi…es weak persistence, and a large rj;i strong persistence. Table 2: BVAR-based in‡ation response, k=1, 50th and (16th , 84th ) quantile of rj;i

Technology

Monetary

Di¤erence

j=0

j=1

j=3

j=7

j=11

0.85

0.74

0.56

0.29

0.14

(0.66,0.98)

(0.48,0.95)

(0.28,0.86)

(0.09,0.64)

(0.03,0.47)

0.95

0.92

0.87

0.69

0.44

(0.74,0.99)

(0.65,0.99)

(0.55,0.97)

(0.35,0.87)

(0.18,0.67)

0.05

0.12

0.23

0.31

0.23

(-0.11,0.26)

(-0.11,0.36)

(-0.08,0.54)

(-0.05,0.61)

(-0.06,0.48)

According to statistics for rj;i in Table 2, in‡ation is persistent to both types of shocks, but relatively more to monetary policy shocks. In‡ation response is more persistent to monetary policy shocks than to technology shocks for all horizons j. For instance, one year after the shock, in‡ation has accomplished, at the median, fortyfour percent of total variability to technology shocks, but less than twenty percent of 10

total variability to monetary policy shocks. Two years after the shock, in‡ation has accomplished, at the median, more than two-thirds of total variability to technology shocks, but less than one-third of total variability to monetary policy shocks.

4

Discussion of results

Why is in‡ation response more persistent to monetary policy shocks than to technology shocks? While in the author’s view giving full answer to this question is an important and challenging task, it is beyond the scope of this paper.11 However, this section provides an initial assessment of what might explain the di¤erent speed of in‡ation adjustment. In principle, such di¤erences in in‡ation adjustment may be due to di¤erences in the systematic response of monetary policy to the two aggregate shocks, or to di¤erences in the responses of production costs, or to di¤erences in price setting behavior of …rms in responses to the two types of shocks. This section evaluates to what extent it is possible to explain the observed behavior of in‡ation through a standard forward-looking Calvo model of price setting.

4.1

The plain forward-looking Calvo model

According to the plain Calvo model, in‡ation in period t,

t

log PPt t 1 ; is a linear

function of the discounted sum of expected future log-real marginal costs, c t

xt

=

xt + u t 1 X i Et log mct+i ;

(7) (8)

i=0

(1

) (1

)

(9)

11 In a companion paper, Paciello (2008), I propose a model that explains di¤erences in in‡ation responses to technology and monetary policy shocks.

11

where

c t

is in‡ation predicted by the Calvo model, mct are marginal costs;

is a discount factor, (1

) is the frequency of price adjustment, and

2 (0; 1)

is the degree

of real rigidities in labor markets.12 The variable ut is a noise included to account for the fact that this equation is an approximation. The assumption is that ut is uncorrelated with xt and structural shocks to technology and monetary policy: Under what circumstances does model (7)

(9) generate di¤erent in‡ation persis-

tence in response to di¤erent structural shocks? The answer to this question is very simple: if and only if the discounted sum of expected future marginal cost has di¤erent persistent conditional on di¤erent shocks. In fact, in this model, the di¤erence in persistence of in‡ation response cannot be explained through a di¤erent price setting behavior of …rms, as the degree of price stickiness (i.e. ), is identical across di¤erent shocks. Unfortunately, there is not direct measure of marginal costs. However, there are indirect measures that have been successfully used as proxy. In particular, Gali and Gertler (1999), Sbordone (2002, 2005) and Cogley and Sbordone (2008) have proposed a measure of marginal costs based on unit labor cost (ulc). I follow their approach.13 Given that unit labor cost is one of the observables in the BVAR model, it follows that the variable xt is given by xt =

e0x

h

~ B

I

i

1

Y~t

where ex is a column vector of zeros but the entry corresponding to unit labor costs which is equal to one, (4) 12 13

~ are de…ned in = 0:99 is the discount factor, and Y~t and B

(5) :14 See Woodford (2003, Ch.3) for the derivation of (7) (9) : In particular, Wt log mct = log = log(1 ) (1 )Yt Pt

1

+ log ulct ;

where Wt is nominal wages, Yt is real GDP,Pt is the GDP de‡ator and (1 ) is the output elasticity to hours of work in the production function. Impulse responses are independent of the value given to : 14 I have also estimated the BVAR including a di¤erent proxy margnal costs, namely a mesure of

12

Let’s de…ne x^j;i as the impulse response of xt to shock i, evaluated j periods after the shock, and let’s construct the associated measure of persistence as

x rj;i

j X s=0 1 X

1

x^2j;i : x^2j;i

s=0

Given that in‡ation in the Calvo model is a linear function of xt ; it follows that persistence of Calvo-model predicted in‡ation response to shock i; ^ cj;i ; is equal to persistence of discounted sum of marginal cost response, x^t ; to that shock. Therefore the value of

is irrelevant to measure in‡ation persistence, once we condition on the

path of expected marginal cost. x Table 3 reports statistics about rj;i to technology and monetary policy shocks for

di¤erent horizons j. Consistently with BVAR based in‡ation responses, the response of ^ cj;i is relatively more persistent to a monetary policy shock than to a technology shock, independently of the horizon j at which we measure persistence. Comparing measures of persistence for in‡ation in Table 2 with the corresponding measures in Table 3, we notice that the plain Calvo model predicts slightly more persistent in‡ation response to technology shocks than the BVAR model. In contrast, the model predicts less persistent in‡ation response to monetary policy shocks than the BVAR model. Quantitatively this is more evident at medium horizons of responses, such as 2 and 3 years, where the Calvo-model predicted median di¤erence in in‡ation persistence is about a half of that estimated by the BVAR model. output-gap: the hp-…ltered output. Results are robust to that.

13

x Table 3: Calvo-based in‡ation response, 50th and (16th , 84th ) quantile of rj;i

Technology

Monetary

Di¤erence

j=0

j=1

j=3

j=7

j=11

0.87

0.77

0.58

0.34

0.20

(0.79,0.97)

(0.62,0.94)

(0.36,0.87)

(0.13,0.72)

(0.05,0.57)

0.94

0.88

0.77

0.54

0.33

(0.87,0.99)

(0.76,0.97)

(0.58,0.93)

(0.33,0.78)

(0.16,0.59)

0.05

0.09

0.15

0.16

0.10

(-0.04,0.15)

(-0.06,0.26)

(-0.12,0.41)

(-0.17,0.44)

(-0.15,0.33)

For illustrative purposes, Figure 5 plots Calvo-based and BVAR-based in‡ation impulse responses to technology and monetary policy shocks, where the frequency of price adjustment (1

) has been set to 0.22 similarly to Golosov and Lucas (2006),

while the degree of real rigidity (2003).

has been set to 0.1, as suggested by Woodford

15

[Figure 5 about here] The plain Calvo model explains only part of the di¤erence in in‡ation persistence to technology and monetary policy shocks. Improving the ability of these types of models to match in‡ation persistence to the two aggregate shocks requires modifying the model in a way that, conditional on the path of marginal costs, increases in‡ation persistence in response to monetary policy shocks, while reducing in‡ation persistence in response to technology shocks relatively. This suggests that hardwiring in‡ation inertia through simple in‡ation indexation as proposed by Christiano, Eichenbaum and Evans (2005) would not work, as it would increase persistence of in‡ation response to technology shocks as well as to monetary policy shocks . 15 Notice changing this parameterization would cause a parallel shift to in‡ation responses, but would not a¤ect persistence.

14

4.1.1

Allowing for trend in‡ation

Recent studies have shown that allowing for trend in‡ation in Calvo models of price setting substantially improves the ability of these models to generate inertia in unconditional in‡ation. In particular, Ascari and Ropele (2007) and Cogley and Sbordone (2008) show that allowing for trend in‡ation in the Calvo model causes the pricing rule to depend not only on the path of expected future marginal costs, but also on the path of the nominal discount factor. This section evaluates in‡ation persistence in response to technology and monetary policy shocks predicted by a Calvo model with constant trend in in‡ation. In this model in‡ation dynamics are given by

t

= '0 (1

'2 '1

'2 ) log mct + '0

y dt = '1 Et Qt;t+1 + gt+1 + '1 (

where '0

1

1

1

1; '1

1 1) Et

and '2 = '1

dt + '2 (1 + '0 ) Et t+1

1

to the plain Calvo model in (7)

(11)

+ '1 Et dt+1 ;

; Qt;t+1 is the log of the nominal

y discount factor, gt+1 is the growth rate in nominal output, and

in‡ation.16 In absence of trend in‡ation,

(10)

t+1 ;

= 1; the model (10)

1+

is trend

(11) boils down

(9) : Variable dt depends on the discounted sum of

future output growth rates. I follow Cogley and Sbordone (2008) and approximate the discount factor Qt;t+1 with the inverse of the FedFunds rate: Marginal costs are approximated by unit labor cost as above. In order to simulate in‡ation impulse responses from model (10) choose values for set

and

(11) ; I need to

; as well as : Similarly to Cogley and Sbordone (2008) I

to 9.8, corresponding to a steady state mark-up of 11 percent. The value of

is

set to have a quarterly frequency of price adjustment of 0.22 as above. Therefore, I simulate the model for di¤erent values of quarter-on-quarter trend in‡ation, namely = 1:0025;

= 1:005 and

= 1:01. Results show that the inclusion of positive

trend in‡ation reduces in‡ation persistence response to both technology and monetary 16

The coe…cient represents the demand elasticity to prices. See Cogley and Sbordone (2008) Appendix A for the derivation of (10) (11) :

15

policy shocks. This is mainly due to the fact that variable dt ; and more speci…cally the nominal discount factor, responds in a way that partially o¤sets the impact of unit-labor costs on in‡ation persistence.17 To save on space, in Table 4 I only report results for the case

= 1:005. However, qualitatively, results for the other cases are

similar. Table 4: Calvo-based in‡ation response with trend in‡ation, 50th and (16th , 84th ) x quantile of rj;i

Technology

Monetary

j=0

j=1

j=3

j=7

j=11

0.85

0.74

0.56

0.28

0.14

(0.66,0.98)

(0.48,0.94)

(0.27,0.85)

(0.09,0.64)

(0.03,0.46)

0.95

0.92

0.87

0.69

0.43

(0.75,0.99)

(0.65,0.99)

(0.55,0.97)

(0.34,0.87)

(0.18,0.67)

Allowing for positive trend in‡ation improves the ability of the Calvo model to match the in‡ation persistence to technology shocks estimated by the BVAR model, but at the expenses of partially worsening results conditional on monetary policy shocks. It is possible, however, that variants of these models, allowing for di¤erent trend in‡ation conditional on di¤erent shocks, may be able to improve results.18 Exploring further this possibility is left for future research. 17

Figure 6 plots impulse responses of dt in the case of = 1:005: I have also considered cases with costant trend de 18 For instance, conditional on the estimated responses of the other variables, I have found that allowing for trend de‡ation increases in‡ation persistence response to both types of shocks. Therefore, one could think of a model that allows for di¤erent trend in‡ation (positive and negative) conditional on di¤erent structural shocks, in order to improve the ability to match di¤erent in‡ation persistence to di¤erent shocks. However, wether this model would be theoretically and empirically well grounded has to be shown.

16

5

Robustness analysis

This section investigates to what extent results from the benchmark BVAR model are robust to several features of the estimation procedure, such as identi…cation assumptions and sub-sample stability. The insights from these exercises reinforce the results obtained in the previous sections.

5.1

Identifying technology and monetary policy shocks as in Altig, et al. (2005)

In this section I show that results of this paper hold under identi…cation assumptions proposed by Galí (1999) and Christiano, Eichenbaum, and Evans (1999).19 This set of assumptions implies relatively stronger restrictions that the ones adopted in the benchmark identi…cation assumption of section 2, in the sense that DSGE models that generally satisfy sign restriction in section 2 encompass the class of models that satisfy identi…cation assumptions of this section. First, it is assumed that only technology shocks may have a permanent e¤ect on the level of labor productivity, as originally proposed by Galí (1999). This restriction is satis…ed by a broad range of business cycle models under standard assumptions.20 In particular, let’s de…ne the matrix C

(I

B1

:::

Bp )

1

A0 1 ; and suppose that

labor-productivity growth is the ith element of vector Yt ; and that the technology shock is the j th element of vector et : It is assumed that all the elements of the ith row of C are zero but the one associated to the j th column. Second, similarly to Christiano, Eichenbaum, and Evans (1999), it is assumed that 19

I have also veri…ed robustness of results against di¤erent speci…cations of sign-restrictions. In particular, I have used restrictions on the response of the level of variables as done by Dedola and Neri (2006) and Uhlig (2005). Results are omitted to save on space. 20 Fisher (2006) distinguishes between total factor productivity shocks and investment-speci…c technology shocks. I have estimated an extended BVAR model with Fisher’s measure of real investment prices and identi…ed the two types of technology shocks. Results for in‡ation responses to neutral technology shocks are robust.

17

monetary policy targets a policy instrument, St ; according to St = f (zt ) + !est ;

(12)

where zt is the information available to the central bank as of time t; ! is a constant and est is the monetary policy shock. Following the Bernanke-Blinder assumption, St is set equal to the 3-months average federal funds rate. Variables in Yt are divided in four subsets, Yt = (Xt ; St ; Zt ; Ft )0 : It is assumed that variables in Xt ; mainly quantities and prices, may respond to monetary policy shocks, est ; with one period lag. It is also assumed that the FED targets the monetary policy instrument so that St is unresponsive to contemporaneous changes in Zt ; where Zt includes M1 and M2 monetary stocks as well as non-borrowed and total reserves.21 Ft is equal to the quarterly average interest rate on 10-years treasury-bond, and there is no short-run restriction on the relationship between Ft and the other variables in Yt .22 Under this set of assumptions the impulse responses of Yt to monetary policy and technology shocks are exactly identi…ed.23 While these identi…cation assumptions have been widely adopted in the literature, there has been a recent debate on the reliability of identi…cation obtained through this approach.24 Figure 7 plots impulse responses of in‡ation and GDP to technology and monetary policy shocks. [Figure 7 about here] In‡ation response to monetary policy shocks is hump-shaped and has a peak around 12 quarters. In‡ation response to technology shocks has its peak in the …rst quarter of the shock, and monotonically converges towards zero. 21

Similarly to Christiano, Eichenbaum, and Evans (1999), results are robust to using non-borrowed reserves, M1 or M2 as the monetary policy instrument, S: 22 This implies that the monetary policy instrument St is allowed to respond contemporaneously to Ft ; as well as Ft is allowed to respond contemporaneously to St : See Appendix D for details. 23 See Appendix C for details. 24 See for a review Erceg et al. (2005), Rudebunsch (1998), Christiano, Einchenbaum and Evans (1999) and Canova (2008).

18

Table 5 reports statistics about rj;i obtained from the estimated impulse responses. Relative to the benchmark identi…cation scheme, in‡ation response appear to be, at the median, relatively more persistent to both types of shocks. Moreover, there is less uncertainty in the measures of in‡ation persistence as a result of the relatively stronger identi…cation restrictions. Finally, and probably most importantly, the difference in measures of in‡ation persistence in response to the two shocks is larger than under the benchmark identi…cation. The latter is the result of the fact that in‡ation response to monetary policy shocks peaks relatively later than under the benchmark identi…cation. Table 5: In‡ation persistence under CEE-Galì identi…cation, 50th and (14th , 84th ) quantile of rj;i

Technology

Monetary

5.2

j=0

j=1

j=3

j=7

j=11

0.79

0.67

0.52

0.24

0.09

(0.69,0.93)

(0.54,0.87)

(0.37,0.75)

(0.14,0.49)

(0.04,0.30)

0.97

0.92

0.88

0.72

(0.93,0.99)

(0.80,0.97)

(0.69,0.94)

(0.50,0.82)

N.A.

Flat prior

As shown by Banbura, Giannone and Reichlin (2008), Minnesota-type priors improve the forecasting power of BVAR models and help overcoming the curse of dimensionality. Nevertheless, in this section I show that results of this paper are robust to assuming a ‡at prior. Figure 8 plots impulse responses of the price level and in‡ation. [Figure 8 about here] Comparing these with the ones obtained under the Minnesota prior, we can see that the path of median responses are very similar, although the estimated responses 19

display relatively more uncertainty under the ‡at prior, due to the relatively weaker restrictions.

5.3

Sub-sample stability

This subsection brie‡y discusses sub-sample stability of results. Boivin and Giannoni (2006) …nd that the impact of monetary policy shocks on the U.S. economy is less e¤ective in the pre-1980 period than in the post-1980 one. The smaller impact of monetary policy shocks is particularly pronounced on in‡ation which displays a statistically zero response in the post-1980 period. Similarly, Galí, López-Salido and Vallés (2003) …nd that the e¤ects of technology shocks on in‡ation di¤er drastically between the two periods before and after Volcker’s tenure at the helm of the Federal Reserve System. Precisely, a positive technology shock causes in‡ation to be much more persistent in the sub-sample up to the early 1980’s than afterwards. Moreover, a similar break in the sample is also suggested by Stock and Watson (2002) who identify the beginning of the Great Moderation in the period between 1982:IV and 1985:III. Given these results, this subsection studies price adjustment speed in two subsamples starting and ending around the mid-80’s. Figure 9 reports price level impulse responses estimated in the pre-80 period, and in the post-83 period.25 [Figure 9 about here] In‡ation response to technology shocks is faster in the post-83 period than in the pre-80 period. This evidence is consistent with Galí, López-Salido and Vallés (2003). Similarly, in‡ation response to monetary policy shocks is faster in the post-83 period than in the pre-80 period. This evidence is consistent with Boivin and Giannoni’s (2006) …ndings. Therefore, in‡ation persistence has decreased in response to both 25

This choice of sub-samples is consistent with Galì et al. who suggest remiving the period from 1980 to 1983, because of uncoventional monetary policy practice by the FED.

20

types of shocks. However, as Tables 6 and 7 show, in‡ation adjusts faster in response to technology shocks than to monetary policy shocks in both sub-samples. Table 6: In‡ation persistence pre-80, 50th and (14th , 84th ) quantile of rj;i

Technology

Monetary

j=0

j=1

j=3

j=7

j=11

0.86

0.75

0.49

0.29

0.19

(0.56,0.93)

(0.42,0.87)

(0.22,0.75)

(0.08,0.49)

(0.04,0.30)

0.92

0.87

0.81

0.67

0.41

(0.60,0.99)

(0.56,0.97)

(0.44,0.95)

(0.30,0.86)

(0.16,0.65)

Table 7: In‡ation persistence post-83, 50th and (14th , 84th ) quantile of rj;i

Technology

Monetary

6

j=0

j=1

j=3

j=7

j=11

0.46

0.36

022

0.08

0.03

(0.22,0.89)

(0.14,0.79)

(0.08,0.64)

(0.01,0.42)

(0.00,0.27)

0.80

0.59

0.40

0.15

0.07

(0.40,0.98)

(0.23,0.91)

(0.14,0.75)

(0.03,0.48)

(0.01,0.33)

Concluding remarks

This paper answers the question of whether, by how much and how likely it is that the U.S. in‡ation adjusts faster to aggregate technology shocks than to monetary policy shocks. The paper …nds that in‡ation is adjusts faster in response to technology shocks than to monetary policy shocks. Two years after the shock, in‡ation has accomplished, at the median, more than two-thirds of total variability to technology shocks, but less than one-third of total variability to monetary policy shocks. These results are robust to di¤erent identi…cation assumptions. These facts challenge existing models of price stickiness. While standard Calvo 21

models of price setting explain part of the di¤erence in in‡ation persistence to technology and monetary policy shocks, they tend to generate too much in‡ation persistence in response to technology shocks or too little in‡ation persistence in response to monetary policy shocks. Exploring further the ability of these models, or other types of models, to explain the estimated di¤erences in price adjustment speed is left for future research.

References [1] Altig, David, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde, (2005): ”Firm-Speci…c Capital, Nominal Rigidities and the Business Cycle,” NBER Working Paper No. 11034. [2] Banbura, M., D. Giannone and L. Reichlin (2008): ”Bayesian VARs with Large Panels,”CEPR DP6326. [3] Bernanke, B., and Alan S. Blinder. (1992): ”The Federal Funds Rate and the Channels of Monetary Transmission”. The American Economic Review, Vol. 82, No. 4, pp. 901-921. [4] Bernanke, B., J. Boivin, and P. Eliasz (2005): ”Measuring Monetary Policy: A Factor Augmented Autoregressive (FAVAR) Approach,”Quarterly Journal of Economics, 120, 387-422. [5] Boivin, J. and Marc Giannoni (2006): ”Has Monetary Policy Become More Effective?”The Review of Economics and Statistics, 88(3). [6] Boivin, J., Marc Giannoni and Ilian Mihov (2008): ”Sticky Prices and Monetary Policy: Evidence from Disaggregated U.S. Data,” Forthcoming American Economic Review.

22

[7] Burstein, Ariel and Christian Hellwig (2007): ”Prices and Market Shares in a Menu Cost Model”. NBER Working Paper No. W13455. [8] Canova, Fabio. 2008. "You can use VARs for structural analyses. A comment to VARs and the Great Moderation." Universitat Pompeu Fabra discussion paper. [9] Canova, F., Luca Gambetti and Evi Pappa. 2007."The Structural Dynamics of Output Growth and In‡ation: "Some International Evidence." The Economic Journal, 117 (March), C167–C191. [10] Chari, V.V. , P. J. Kehoe and E. R. McGrattan (2008): ”Are structural VARs with long-run restrictions useful in developing business cycle theory?” Journal of Monetary Economics, Elsevier, vol. 55(8), pages 1337-1352, November. [11] Christiano, L. J., M. Eichenbaum, and C. L. Evans (1999): ”Monetary policy shocks: What have we learned and to what end?,” in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, vol. 1, chap. 2, pp. 65-148. Elsevier. [12] Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): ”Nominal Rigidities and the Dynamic E¤ects of a Shock to Monetary Policy”. Journal of Political Economy, 2005, vol. 113, no. 1. [13] Christiano, L. J., M. Eichenbaum, and R.Vigfusson (2004): ”What Happens After A Technology Shock?,”NBER Working Paper No. W9819. [14] Del Negro, M. and Frank Schorfheide (2008): ”Forming Priors for DSGE Models (and How it A¤ects the Assessment of Nominal Rigidities)”, Forthcoming Journal of Monetary Economics. [15] Dedola, L. and Stefano Neri. 2006. "What does a technology shock do? A VAR analysis with model-based sign restriction." Journal of Monetary Economics, 54 (2007) 512–549. 23

[16] Doan, T., R. Litterman, and C. A. Sims (1984): ”Forecasting and Conditional Projection Using Realistic Prior Distributions,”Econometric Reviews, 3, 1-100. [17] Dupor, Bill, Jing Han and Yi Chan Tsai (2007): ”What Do Technology Shocks Tells Us about the New Keynesian Paradigm?”. http://web.econ.ohiostate.edu/dupor/tech12_jun07.pdf. [18] Faust, Jon (1998): ”The robustness of identi…ed VAR conclusions about money”. Carnegie-Rochester Conference Series on Public Policy Volume 49, Pages 207244. [19] Erceg, C., Guerrieri, L. and C. Gust, ”Can Long-Run Restrictions Identify Technology Shocks”Journal of the European Economic Association, vol. 3 (December 2005), pp. 1237-1278. [20] Fisher, Jonas. 2006. "The Dynamic E¤ects of Neutral and Investment-Speci…c Technology Shocks.” Journal of Political Economy, June 2006, Vol 114 No. 3., pp. 413-52. [21] Francis, Neville and Valerie A. Ramey (2005): ”Is the technology-driven real business cycle hypothesis dead? Shocks and aggregate ‡uctuations revisited.” Journal of Monetary Economics, Elsevier, vol. 52(8), pages 1379-1399, November. [22] Galí, Jordi, (1999): ”Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?,” American Economic Review, 89(1), 249-271. [23] Galí, Jordi and Mark Gertler (1999): ”In‡ation dynamics: A structural econometric analysis”. Journal of Monetary Economics 44, 195-222. [24] Galí J., J. D. Lopez-Salido and J. Valles, (2003): ”Technology shocks and monetary policy: assessing the Feds performance,” Journal of Monetary Economics 50 (2003) 723743. 24

[25] Gertler, M. and John Leahy (2008): ”A Phillips curve with an Ss foundation.” Vol. 116, No. 3: pp. 533-572. [26] Kadiyala, K. R., and S. Karlsson (1997): ”Numerical Methods for Estimation and Inference in Bayesian VAR-Models,”Journal of Applied Econometrics, 12(2), 99-132. [27] Litterman, R. (1986): ”Forecasting With Bayesian Vector Autoregressions - Five Years of Experience,”Journal of Business and Economic Statistics, 4, 25-38. [28] Lubik, T. and Schorfheide, F. (2004). "Testing for indeterminacy: an application to US monetary policy", American Economic Review, vol. 94, pp. 190–217. [29] Paciello, Luigi (2008): “Price Responsiveness to Aggregate Technology and Monetary Policy Shocks under Rational Inattention.”EIEF WP 08/16. [30] Rudebusch, Glenn D, 1998. "Do Measures of Monetary Policy in a VAR Make Sense?," International Economic Review, vol. 39(4), pages 907-31, November. [31] Ramirez, J. R., Daniel F. Waggoner and Tao Zha (2007): ”Markov-Switching Structural Vector Autoregressions: Theory and Application.” FRB of Atlanta Working Paper No. 2005-27. [32] Schorfheide, Frank. 2008. "DSGE Model-Based Estimation of the New Keynesian Phillips Curve". University of Pennsylvania discussion paper. [33] Sims, Christopher A. (1992): ”Interpreting the Macroeconomic Time Series Facts: the E¤ects of Monetary Policy”. European Economic Review, Elsevier, vol. 36(5), pages 975-1000. [34] Stock, J.H. and M.W. Watson (2002), “Forecasting Using Principal Components from a Large Number of Predictors,” Journal of the American Statistical Association 97, 1167 –1179.

25

[35] Uhlig, Arald. 2006. "What are the e¤ects of monetary policy on output? Results from an agnostic identi…cation procedure." Journal of Monetary Economics, Volume 52, Issue 2, March 2005, Pages 381-419. [36] Waggoner D.F., and T. Zha (2003): ”Likelihood Preserving Normalization in Multiple Equation Models”. Journal of Econometrics, 114, 329-347. [37] Woodford, Michael (2002): ”Imperfect Common Knowledge and the E¤ects of Monetary Policy”. In ”Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps”, Princeton University Press. [38] Woodford, Michael (2003): ”Interest and Prices. Foundations of a Theory of Monetary Policy.”Princeton University Press, Princeton and Oxford.

26

Appendices A Data Mnemon

Series

Lev

Log

d-Log

G D PQ /LBM N U

L a b o r p ro d u c tiv ity

v

LBM NU

In d e x to ta l h o u rs w o rke d

v

FYFF

IN T E R E S T R AT E : F E D E R A L F U N D S

PGDP

G D P p ric e d e ‡a to r

v

JQ C R

R e a l P e rso n a l C o n su m p tio n E x p e n d itu re s

v

IF N R E R

R e a l n o n -re sid e ntia l inve stm e nts

v

U T L11

C a p a c ity u tiliz a tio n

C ES275*LBM N U /G D P

U n it la b o r c o sts

R 10

1 0 -ye a rs tre a su ry IN T E R E S T R AT E

FM 2

M 2 m o n e ta ry sto ck

v

v

v

v

v

v

The source of most of the data is the DRI Basic Economics Database, available on-line at Northwestern University. Output, GDP de‡ator, residential and nonresidential investments were obtained from the BEA website.

B Minnesota prior Let’s rewrite model (2) as a system of multivariate regressions: Y = X B + U ;

T n

T k k n

T n

where Y = (y1 ; :::yT )0 , X = (X1 ; ::::; XT )0 and with Xt = Yt0 1 ; :::; Yt0 p ; 1 ; U = (u1 ; :::; uT )0 ; B = (B1 ; ::::; Bp ; c)0 ; and k = np + 1: The prior beliefs are such that B and

have a Normal inverted Wishart distribution, according to which v iW (S0 ;

0)

and Bj

27

v N (B0 ;

0) :

The prior parameters S0 ;

0 ; B0

and

0

are chosen so that the coe¢ cients in B1 ; B2 ;..,

Bp ; denoted by (Bs )ij ; s = 1; ::p; i = 1; 2::; n; j = 1; 2; ::n; have prior expectations and variances given by

E (Bs )ij

=

V (Bs )ij

=

8 <

if i = j; s = 1

: 0; 2

and the matrix

i;

s2

;

otherwise

2 i ; 2 j

has prior expectation E ( ) = diag ( 21 ; ::::;

Kadiyala and Karlsson (1997). The scale parameters

2 i

2 n) :

For details see

are set equal to the variance

of the residual from a univariate autoregressive model of order p for the variable yi : The prior is implemented by adding T0 dummy observations, Y0 and X0 ; to Y and X respectively. It can be shown that this is equivalent to imposing a normal inverted1

Wishart prior with B0 = (X00 X0 ) and

0

= T0

k

X00 Y0 ;

= (X00 X0 )

0

1

X0 B0 )0 (Y0

; S0 = (Y0

X0 B0 )

1: It follows that the dummy-augmented VAR model is:

n

Y

= X

T

n

T

B + U ;

k k n

T

n

where T = T + T0 ; X = (X 0 ; X00 ) ; Y = (Y 0 ; Y00 )0 and U = (U 0 ; U00 )0 : To insure the existence of the prior expectation of ~j j

(n+3)=2

: The posterior distribution of (B; ) is a Normal inverted-Wishart: jY v iW (S ;

where B = (X 0 X ) =T

it is necessary to add an improper prior

1

X0 Y ;

)

and Bj ; Y v N (B ;

= (X 0 X )

1

; S = (Y

); X B )0 (Y

X B ) and

k + 2: See Banbura, Giannone and Reichlin (2008) for more details.

C Identi…cation through long-run and short-run restrictions Let’s order the variables in the model as Yt = (Xt ; St ; Zt ; Ft )0 ; where the …rst 28

element of Xt and Yt is log-labor productivity: Variables are entered in the VAR according to Appendix A. Following Ramirez, Waggoner and Zha (2007) let’s express the set of linear restrictions onto the structural parameters of A0 as 2

A0

H (A0 ) = 4

(I

1

B (1))

1

A0

1

3 5

D

where B (1) = B1 + ::: + Bp and B1 ; :::; Bp are the estimates of the reduced form autoregressive matrices. D is a 2n

n matrix of restrictions imposed on the impact

and long-run responses to structural shocks. Let’s de…ne nx and nz as the number of variables in X and Z respectively. Let’s order the technology and monetary policy shock as the nth and nth z elements of the vector of structural shocks et respectively. The identifying restrictions are zero restrictions on the matrix D given by 2

6 6 6 6 6 6 6 6 6 D =6 6 6 6 6 6 6 6 6 4 where Tz and Tx are nz

nz and nx

0

0 Tx x

0

x

x

Tz x

x

x

x

x

0

0

0

x

x

x

x

x

x

x

x

x

3

7 7 x 7 7 7 x 7 7 7 x 7 7; 7 x 7 7 7 x 7 7 7 x 7 5 x

(13)

nx matrices respectively, and have the form of

upper triangular matrices with an inverted order of columns: 2

6 6 6 Ti = 6 6 6 4

0

0

0 0

x2;ni .. .

xni ;1

xni ;ni 29

x1;ni 1

1

x2;ni .. . xni ;ni

3

7 7 7 7; 7 7 5

where i = z; x: The zero restrictions on D satisfy both the necessary and su¢ cient (rank) conditions for exact identi…cation derived by Ramirez, Waggoner and Zha (2007). In order to recover A0 from the system of linear equations, H (A0 ) = D and A0 1 A0 10 = (2007). Let

; I recur to an algorithm proposed by Ramirez, Waggoner and Zha 1

= SD 2 be the n n lower diagonal Cholesky matrix of the covariance of

the residuals of the reduced form VAR, that is SDS0 = E[ut u0t ] =

and D = diag( ):

Let’s compute H ( ) and de…ne matrices P1 and P2 as:

P1

P2 where Is

s

2

01

6 6 6 In 4 0n

n

1

n

0n

1

n

0n

1

01

n 1

0n

n 1

In

3

1 n 1

[in ; in 1 ; ::::; i1 ] ;

7 7 ,7 5

(14)

(15)

is the s-dimensional identity matrix and is is an n-dimensional column

vector of zeros with the sth element equal to 1. Proposition 1 For given estimates of B and ated to

; let

be the Cholesky factor associ-

; and let H ( ) ; P1 and P2 be de…ned as in (14) (15) : Let P3 be the Q factor

associated with the QR decomposition of the matrix P1 H ( ) and de…ne P = P3 P20 . Let also A0 satisfy the restriction H (A0 ) = D where D is de…ned as in (13) : It follows that A0 =

1

P.

For a proof see Ramirez, Waggoner and Zha (2007). These restrictions satisfy both the necessary and the rank conditions for exact identi…cation. The structural shocks et are obtained from et = A0 1 ut : Finally, the order of the variables in X and Z can be arbitrarily changed without any e¤ect on the identi…cations of the columns for technology and monetary policy shocks. To see these, consider the matrix A0 :

30

These assumptions impose the following zero restrictions on the matrix A0 ; 2

a11 6 6 6 (nx nx ) 6 6 6 a21 6 6 6 (1 nx ) A0 = 6 6 6 a31 6 6 6 (nz nx ) 6 6 6 a41 4 (1 nx ) Then consider the n

0 nx

0 1

(nx

a22 (1

(1

a32

nz ) a33

1)

(nz

a42 (1

nz ) 0

1)

(nz

a14

nz ) a43

1)

(1

nz )

3

7 7 7 7 7 7 a24 7 7 (1 1) 7 7: 7 7 a34 7 7 (nz 1) 7 7 7 7 a44 5 (1 1) nx

1

n orthonormal matrix 2

6 6 6 W =6 6 6 4 where W11 and W33 are nx

W11 0

0

0

1

0

0 W33

0

0

nx and nz

0

0

0

3

7 7 0 7 7; 7 0 7 5 1

nz orthonormal matrices respectively. If A0

satis…es H (A0 ) = D ; any matrix A~0 = W A0 also satis…es H A~0 = D :

31

Figure 1: Responses of GDP deflator level (p) and inflation ( ) to a one standard deviation shock to technology and monetary policy; k=1. Quarters are on the horizontal axis.

Figure 2: Responses of GDP deflator level (p) and inflation ( ) to a one standard deviation shock to technology and monetary policy; k=0. Quarters are on the horizontal axis.

Figure 3: Responses of GDP, investments (I), consumption (C), FedFunds (R), unit labor cost (ulc) and hours worked (H) to a one standard deviation shock to technology.

Figure4: Responses of GDP, investments (I), consumption (C), FedFunds (R), unit labor cost (ulc) and hours worked (H) to a one standard deviation shock to monetary policy.

Figure 5: Responses of GDP deflator inflation ( ) to a one standard deviation shock to technology and monetary policy predicted by the BVAR-model (solid black line) and by the plain Calvo model (red line with circles). TECH shock

0.025 0.02 0.015 0.01 0.005 0 -0.005

0

5

10

15

20

25

30

35

20

25

30

35

MP shock

0.02 0.015 0.01 0.005 0 -0.005 -0.01

0

5

10

15

Figure 6: Responses of variable d to a one standard deviation shock to technology and monetary policy predicted by the Calvo model with trend in inflation, =1.005.

Figure 7: Responses of GDP and GDP deflator inflation ( ) to a one standard deviation shock to technology and monetary policy; Gali-CEE identification.

Figure 8: Responses of GDP deflator level (p) and inflation ( ) to a one standard deviation shock to technology and monetary policy; flat prior.

Pre-1980 TECH shock

0.3

MP shock

0.1

0.2

0

0.1

-0.1 -0.2 -0.3

-0.2

-0.4

-0.3

-0.5

P

0 -0.1

-0.4

0

5

10

15

20

25

30

35

-0.6

0.03

0.02

0.02

0.01

0.01

0

5

10

15

20

25

30

35

0

5

10

15

20

25

30

35

0

0 -0.01 -0.01 -0.02

-0.02

-0.03

-0.03 -0.04

0

5

10

15

20

25

30

35

-0.04

Post-1983 TECH shock

0.05

MP shock

0.15 0.1 0.05

-0.1

0

-0.15

-0.05

P

0 -0.05

-0.2

-0.1

-0.25

-0.15

-0.3

0

5

10

15

20

25

30

35

-0.2

0.01

0.01

0

0.005

0

5

10

15

20

25

30

35

0

5

10

15

20

25

30

35

0

-0.01

-0.005 -0.02 -0.01 -0.03

-0.015

-0.04

-0.02

-0.05

-0.025

0

5

10

15

20

25

30

35

Figure 9: Responses of GDP deflator level (p) and inflation ( ) to a one standard deviation shock to technology and monetary policy; sub-samples.