Does In‡ation Adjust Faster to Aggregate Technology Shocks than to Monetary Policy Shocks? LUIGI PACIELLO* Einaudi Institute for Economics and Finance, Rome September 2009 Abstract This paper studies U.S. in‡ation adjustment speed to aggregate technology shocks and to monetary policy shocks in a Bayesian VAR model with a large number of macroeconomic variables. According to the model, in‡ation adjusts much faster to aggregate technology shocks than to monetary policy shocks. These results are robust to di¤erent identi…cation assumptions and measures of aggregate prices. Moreover, by separately estimating the model over the pre- and post-1980 periods, this paper shows that in‡ation adjusts much faster to technology shocks than to monetary policy shocks in the post-1980 period, but not in the pre-1980 period.
JEL Classi…cation: E31, E4, C11, C3 Keywords: Bayesian VAR, price responsiveness, monetary policy shocks, technology shocks
*
Email:
[email protected]. Mailing address: EIEF, Via dei Due Macelli, 73, 00187
Roma. This paper is a revised version of Chapter I in my PhD dissertation at Northwestern University. I thank Martin Eichenbaum, Giorgio Primiceri and Mirko Wiederholt for invaluable comments and advice. I am also grateful to Francesco Lippi and Stefano Neri as well as seminar participants at Northwestern University, EIEF and MONCASCA workshop.
1
Introduction
This paper investigates whether U.S. in‡ation adjusts faster to aggregate technology shocks than to monetary policy shocks. Assessing the speed of in‡ation adjustment 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. While a recent strand of the literature studies the degree of price stickiness to sector-speci…c idiosyncratic shocks versus aggregate shocks, relatively less attention has been paid to di¤erences in price stickiness across di¤erent types of aggregate shocks, namely aggregate technology and monetary policy shocks.1 Technology and monetary policy shocks are particularly important as these shocks account together for a large fraction of business cycle ‡uctuations.2 In this paper I document in‡ation adjustment to technology and monetary policy shocks, using a Bayesian VAR (BVAR) model with a large number of macroeconomic indicators and with standard Litterman priors, estimated on the U.S. economy from 1960 to 2007. This paper contributes to the existing literature on several dimensions. First, this paper shows that in‡ation adjusts much faster to aggregate technology shocks than to monetary policy shocks in the post-1980 period, i.e. the period associated to Volcker and Greenspan at the helm of the Federal Reserve, but not in the pre-1980 period. In fact, in the pre-Volcker period in‡ation adjusts faster to monetary policy shocks than to technology shocks. In particular, in‡ation adjustment speed has increased to both types of structural shocks in the Volcker-Greenspan period relatively to the pre-Volcker period, but it has increased much more to technology shocks. Second, on the methodological side, this paper estimates impulse responses to both technology and monetary policy shocks in a relatively larger VAR model than 1 See, for instance, Boivin, Giannoni and Mihov (2008) for an empirical investigation of price adjustment speed to sector-speci…c and aggregate shocks. 2 See, for intance, Smets and Wouters (2007).
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previous studies. Recently Banbura, Giannone and Reichlin (2007) have shown that BVAR models including a large number of variables can be estimated, achieving relatively accurate forecasts and improving the structural analysis to monetary policy shocks.3 I indeed show that increasing the number of macroeconomic indicators improves structural analysis of both technology and monetary policy shocks. Moreover, I show that the fact that in‡ation adjusts faster to technology shocks than to monetary policy shocks is robust to several identi…cation assumptions of the structural shocks. This is important as identi…cation of monetary policy and technology shocks through short- and long-run restrictions as in Altig, Christiano, Eichenbaum and Linde (2005) have recently been questioned by part of the macroeconomic literature.4 Third, I show that in‡ation adjustment speed to both technology and monetary policy shocks is faster when in‡ation is measured through the producer price index than through the GDP de‡ator and the consumer price index. This evidence is consistent with microeconomic studies showing that intermediate goods have a higher frequency of price adjustment than more …nished goods.5 However, wether in‡ation adjusts faster to technology or to monetary policy shocks is independent of how I measure aggregate prices. This is not the …rst paper studying in‡ation responses to technology and monetary policy shocks in the context of VARs. Altig et al. (2005), Edge, Laubach and Williams (2003) and Dupor, Han and Tsai (2009) have recently estimated a structural VAR of the U.S. economy in the post second World War period, and found that in‡ation responds much faster to aggregate technology shocks than to monetary policy shocks. Moreover, these authors argue that standard DSGE models with nominal rigidities have a hard time matching in‡ation adjustment to both technology and monetary 3
The importance of conditioning on a large information set when identifying monetary policy shocks has also been shown in frameworks related to factor analysis by Bernanke, Boivin, and Eliasz (2005) and Giannone, Reichlin, and Sala (2004). 4 See the reference list in Erceg, et al. 2005 for most of the relevant references regarding identi…cation of technology shocks. See Faust (1998) and references therein regarding identi…cation of monetary policy shocks. 5 See Nakamura and Steinsson (2008).
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policy shocks. This paper contributes to this literature by showing that this empirical fact is only true in the Volcker-Greenspan period, where monetary policy has generally been more conservative on price stability. This result may provide useful guidance for future research trying to reconcile existing DSGE models with in‡ation dynamics predicted by the VARs. Moreover, this paper employes a larger VAR than previous studies, has a more systematic approach at measuring in‡ation adjustment speed, and assesses robustness of …ndings obtained from the identi…cation assumptions of Altig et al. (2005) against the ones obtained from other identi…cation assumptions, such as sign restrictions of Uhlig (2006) and Dedola and Neri (2006). In a related literature, Gali, Lopez-Salido and Valles (2003) and Boivin and Giannoni (2006) have shown that, in the Volcker-Greenspan era, in‡ation responsiveness has decreased to technology and monetary policy respectively. These authors argue that the di¤erent behavior of in‡ation in response to the two shocks is to be attributed to the improvement of the FED performance at stabilizing prices in the last decades. This paper contributes to these studies because it estimates in‡ation responses to both technology and monetary policy shocks, and both in the pre-Volcker and in the Volcker-Greenspan periods. This allows to compare in‡ation dynamics both across time and across di¤erent structural shocks. In fact, this paper …nds that in‡ation responsiveness has decreased much more to technology shocks than to monetary policy shocks in the last decades. The paper is organized as follows. Section 2 describes the BVAR model, the data, the prior and the identi…cation assumptions, and derives impulse responses to aggregate technology and monetary policy shocks in the whole sample. Section 3 assesses subsample stability of results. Section 4 assesses robustness of …ndings against the main assumptions behind the procedure adopted in the paper. Section 5 concludes.
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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 (2007), Yt includes a relatively large number of macroeconomic variables. Therefore model (2) is estimated using a Bayesian VAR approach to overcome the curse of dimensionality. This approach consists in imposing prior beliefs on the parameters of (2). These priors are set according to the standard practice which builds on Litterman (1986)’s suggestions, which are often referred to as Minnesota priors. According to these priors, 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.
In particular, prior beliefs are such that
E (Bs )ij
=
V (Bs )ij
=
8 <
i;
if i = j; s = 1
: 0; 2
s2
2 i ; 2 j
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) : Next subsection describes choices of
and
the posterior distribution of B = (B1 ; ::::; Bp ; c)0 and
2.1
i:
Under these assumptions,
is Normal inverted-Wishart.6
Data and priors
Model (2) includes twenty-three U.S. macroeconomic indicators, among which there are four di¤erent indices of aggregate prices: GDP price de‡ator, consumer price index, producer price index and personal consumption expenditure de‡ator.7 This allows the study of the dynamics of di¤erent aggregate price indices within the same model. The time span is from January 1960 through June 2007. Model (2) is estimated on a quarterly frequency, and the number of lags p is set equal to 4. The model is speci…ed so that the vector Yt is stationary, ensuring that all the 6
See Appendix B for more details. The model includes: labor productivity (GDPQ/LBMNU), hours worked (LBMNU), the nominal interest rate (FYFF), the GDP price de‡ator (PGDP), the Standard and Poor’s stock price index (FSPCOM), the number of employees on non-farm payrolls (CES002), personal income (A0M051), real consumption (JQCR), real non-residential investments (IFNRER), real residential investments (JQIFRESR), industrial production (IPS10), capacity utilization (UTL11), unemployment rate (LHUR), housing starts (HSFR), the index of sensitive material prices (PSM99Q), the producer price index (PWFSA), the personal consumption expenditures price de‡ator (GDMC), the consumer price index (PUNEW), average hourly earnings (CES275), M1 monetary stock (FM1), M2 monetary stock (FM2), non-borrowed reserves (FMRRA) and total reserves (FMRNBA). 7
5
roots of the VAR polynomial lie outside the unit circle.8 In particular, all the highly persistent variables enter Yt in log-di¤erences with the exception of the federal funds rate.9 Given that persistent variables enter Yt in log-di¤erences, a white noise prior, i
= 0; is assumed for all variables but the federal funds rate. This choice of
( 1 ; :::;
n)
=
is consistent with Banbura, Giannone and Reichlin (2007) and Stock and
Watson (2005). Results of this paper are robust to di¤erent speci…cations of : Finally, the hyper-parameter
is chosen similarly to Banbura, Giannone and Reichlin (2007)
and set equal to 0:065:10
2.2
Identi…cation of the structural parameters
Identi…cation of (1) amounts to putting enough restrictions on the model to be able to recover A0 ; A1 ::; Ap and
given estimates of the reduced form parameters,
;
B1 ; :::; Bp and c: This is achieved, in the benchmark speci…cation of the model, by appealing to the combination of standard identi…cation assumptions for technology and monetary policy shocks. This choice has the advantage of making results easily comparable to the existing literature.11 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. 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 8
Stationarity of (2) is needed to implement the identi…cation scheme in the next sub-section. The twenty-three indicators are entered in Yt in levels, logarithms or log-di¤erences depending on the persistence of each indicator. See Appendix A for details on how each indicator is entered in Y. 10 The model includes a set of variables similar to Banbura, Giannone and Reichlin. Results are robust to di¤erent choices of : See Appendix C for more details on the choice of : 11 In section 4 I show that results are robust to di¤erent identi…cation assumptions. 9
6
monetary policy targets a policy instrument, St ; according to St = f (zt ) + !est ;
(4)
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 : Similarly to the recursive assumption of Christiano, Eichenbaum, and Evans (1999), 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.12 Ft is equal to the S&P stock price index and there is no short-run restriction on the relationship between Ft and the other variables in Yt .13 Finally, the column of A0 1 corresponding to the impact of monetary policy shocks on Yt is normalized so that monetary policy shocks are associated to a contemporaneous increase in the federal funds rate; the column of A0 1 corresponding to the impact of technology shocks is normalized so that such shocks are associated to a permanent increase in labor productivity.14 Under this set of assumptions the impulse responses of Yt to monetary policy and technology shocks are exactly identi…ed.15 12
Similarly to Christiano, Eichenbaum, and Evans (1999), results are robust to using non-borrowed reserves, M1 or M2 as the monetary policy instrument, S: 13 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. 14 Results are robust to di¤erent normalization assumptions, and in particular to the likelihood preserving normalization proposed by Waggoner and Zha (2003). 15 See Appendix D for details.
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2.3
Impulse responses
Impulse responses are generated according to the methodology proposed by Ramirez, Waggoner and Zha (2007). In particular, the model reduced-form parameters B1 ; :::; Bp and
are drawn from the estimated Normal inverted-Wishart posterior distribu-
tion. For each draw of B1 ; :::; Bp and
; the model structural-form parameters A0 ; :::;
Ap are computed according to the identi…cation assumptions above. Given the structural parameters, the impulse responses of Yt to a one standard deviation technology shock and to a one standard deviation monetary policy shock are computed for each draw.16 [Figures 1-5 about here] Figure 1 plots 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 (PGDP), the consumer price index (PUNEW), the personal consumption expenditure de‡ator (PCEPI) and the producer price index (PWFSA). Figure 2 plots the impulse responses of some key variables such as the federal funds rate, GDP, PGDP-in‡ation and labor productivity. Figures 3 and 4 plot the impulse responses of the remaining macroeconomic indicators of the model. Given the focus on price adjustment, this paper only discusses results about price impulse responses. However, the estimated impulse responses of the other variables in Y are consistent with results obtained in previous studies.17 From the analysis of impulse responses we can draw the following conclusions. First, the aggregate price level is much more responsive to technology shocks than to monetary policy shocks. In particular, the median in‡ation response to a monetary policy shock has its peak about three years after the shock, and it is not statistically di¤erent from zero for the …rst two years. In contrast, in‡ation response to a tech16
Results are based on 5,000 draws and are robust to larger number of draws. See for instance Francis and Ramey (2005), Altig, Christiano, Eichenbaum and Linde (2005), Galì (1999). 17
8
nology shock has its peak in the period of impact of the shock, and monotonically converges towards zero. This evidence suggests that price adjustment is substantially faster to technology shocks than to monetary policy shocks. Second, the shape and the dynamic of in‡ation responses do not change much across di¤erent measures of aggregate price. For a given shock, either to technology or monetary policy, the median responses of the consumer price index, the GDP de‡ator, the personal consumption expenditure de‡ator are very similar both in terms of magnitude and in terms of dynamics. However, the producer price index is relatively more responsive to both types of shocks than the other measures of prices. This evidence is consistent with microeconomic studies showing that intermediate goods have a higher frequency of price adjustment than …nished goods.18 Finally, in Figure 5 I plot impulse responses estimated in the smaller model of Altig et al. (2005), but using the same Bayesian approach of this paper.19 Comparing impulse responses in Figure 5 to the ones in Figure 2, we can see that increasing the number of variables substantially reduces uncertainty surrounding median impulse responses to monetary policy shocks. Reducing uncertainty helps obtaining sharper results about price adjustment speed to the two shocks.
2.4
Measuring in‡ation adjustment speed
In‡ation adjustment speed 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, this measure has the advantage of not relying on the monotonicity of responses. Given that in‡ation response to monetary policy shocks is characterized by a hump-shape dynamic, this property is very appealing. In par18
See Nakamura and Steinsson (2008). This implies estimating the model on a subset of variables: labor productivity, FFR, M2, in‡ation, hours worked, consumption, investments, capital utilization, wages. The speci…cation of hours in levels or di¤erences is irrelevant for the results of this paper. 19
9
ticular, in‡ation persistence to shock i, j periods after the shock, is measured as
rj;i
j X
2 j;i
s=0
1
1 X
:
(5)
2 j;i
s=0
According to this measure, 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 0, a small rj;i signi…es high adjustment speed, and a large rj;i low adjustment
j
speed. Figure 6 displays scatter plots for the values of rj;i obtained from the posterior draws of the structural parameters of the BVAR model; rj;i is evaluated at one year horizon of responses, i.e. j = 4.20 Each plot is associated to one of the four measures of prices. The vertical axis of each plot reports values of rj;i associated to the monetary policy shock, and the horizontal axis values of rj;i associated to the technology shock. By de…nition of rj;i ; draws above (below) the 45 degree line mean that in‡ation adjustment is faster (slower) to technology shocks than to monetary policy shocks. [Figure 6 about here] In Figure 6, the vast majority of draws is above the 45 degree line for all measures of prices. This means that the posterior probability that the price level adjusts faster to technology shocks than to monetary policy shocks is relatively high across all four measures of aggregate price level. Tables 1 and 2 report the median, 16th and 84th percentiles of the posterior distribution of rj;i for the technology and the monetary policy shocks respectively, evaluated 20
Results are qualitatively similar for other horizon j.
10
at j = 2; 4; 8; 12; 16.
[Tables 1-2 about here] From these tables we can draw the following conclusions. First, in‡ation adjustment speed to technology shocks is much faster than to monetary policy shocks, independently of the horizon of the response at which we measure rj;i ; and independently of the measure of aggregate prices. For instance, two years after the shock, GDP de‡ator in‡ation has accomplished at the median about 80 percent of total adjustment to the technology shock, but only 20 percent of total adjustment to the monetary policy shock.21 Second, the fact that in‡ation adjusts faster to technology shocks than to monetary policy shocks is statistically robust. In particular, the fraction of draws in which in‡ation adjustment measured at 1 year horizon is faster to technology shocks than to monetary policy shocks ranges between 93 percent for the GDP de‡ator and 96 percent for the consumer price index. Therefore, the posterior probability of such event is very high. Third, the producer price index is more responsive to both types of shocks than the other measures of aggregate prices. For instance, two years after the shock, the producer price index in‡ation has accomplished at the median about 93 percent of total adjustment to the technology shock, and 42 percent of total adjustment to the monetary policy shock.
3
In‡ation adjustment speed and subsample stability
Monetary policy plays a central role in shaping in‡ation adjustment to di¤erent structural shocks. Boivin and Giannoni (2006) have documented that the impact of monetary policy shocks on the U.S. economy has became less e¤ective in the Volcker21
Notice that the fraction of in‡ation adjustment accomplished j quarters after the shock is measured by 1 rj;i :
11
Greenspan period compared to the pre-Volcker one. The smaller impact of monetary policy shocks is particularly pronounced on in‡ation. These authors argue that, by responding more strongly to in‡ation expectations, monetary policy has stabilized the economy more e¤ectively in the last decades. Similarly, Galí, López-Salido and Vallés (2003) have found 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 technology shock causes in‡ation to be much more persistent in the subsample up to the early 1980’s than afterwards. They also argue that monetary policy stabilization of prices in the Volcker-Greenspan period is the main cause of the reduction in in‡ation persistence to technology shocks. While the papers above document the change in in‡ation responses to each type of shock, there is no evidence on wether the di¤erence in in‡ation adjustment speed between the two shocks has increased or decreased in the Volcker-Greenspan period compared to the pre-Volcker one. Does in‡ation adjust faster to technology shocks than to monetary policy shocks in both subsamples? Is the di¤erence in in‡ation adjustment speed quantitatively similar in the two subsamples? Motivated by these questions, this section evaluates and compares in‡ation adjustment speed to the two shocks in the periods before and after Volcker’s tenure, i.e. 1960:1-1979:3 and 1979:42007:3.
[Figures 7-8 about here] Figures 7 and 8 display in‡ation impulse responses to technology and monetary policy shocks in the pre- and post- 1980 periods respectively. In‡ation response is very persistent to technology shocks in the …rst subsample, but adjusts very fast to such shocks in the second subsample. Similarly, in‡ation is more persistent to monetary policy shocks in the …rst subsample than in the second one. However, the change in the pattern of in‡ation response to monetary policy shocks over the two periods appears less dramatic than to technology shocks. These results hold through the 12
di¤erent measures of aggregate prices. Figures 9 and 10 display scatter plots for the values of rj;i obtained from the posterior draws of the structural parameters of the BVAR model in the 1960:1-1979:3 and 1979:4-2007:3 periods respectively; rj;i is evaluated at one year horizon of responses. [Figures 9-10 about here] These …gures clearly show that the relationship between in‡ation adjustment speed to the two di¤erent shocks has changed over time. In fact, in the 1960:1-1979:3 subsample, the majority of draws is below the 45 degree line, indicating that in‡ation adjusts faster to monetary policy shocks than to technology shocks. In particular, according to rj;i ; the posterior probability that in‡ation adjusts faster to monetary policy shocks than to technology shocks ranges between 67 and 87 percent, depending on the measure of aggregate prices. In contrast, in the 1979:4-2007:3 subsample, the majority of draws is well above the 45 degree line, indicating that in‡ation adjusts faster to technology shocks than to monetary policy shocks. In particular, according to rj;i ; the posterior probability that in‡ation adjusts faster to monetary policy shocks than to technology shocks ranges between 89 and 95 percent, depending on the measure of aggregate prices. To better quantify in‡ation adjustment speed in the two subsamples, Tables 3-4 report the median, 16th and 84th percentiles of the posterior distribution of rj;i in the …rst subsample for the technology and the monetary policy shocks respectively. [Tables 3-4 about here] According to rj;i ; in the …rst subsample, in‡ation adjustment is relatively slow to both types of shocks. For instance, two years after the shock, in‡ation has accomplished only about half of overall adjustment to technology shocks, with median values of rj;i between 45 and 55 percent, depending on the measure of aggregate prices; over 13
the same horizon, this statistic to monetary policy shocks ranges between 37 and 55 percent, being lowest for the producer price index and highest for the GDP de‡ator. It takes four years before in‡ation response has accomplished more than 80 percent of overall adjustment to both shocks. Moreover, with very few exceptions, the median 16th and 84th percentiles of the posterior distribution of rj;i are always higher conditional on technology shocks than conditional on monetary policy shocks, independently of the evaluation horizon and price index. This con…rms results from the impulse responses and scatter plots suggesting that in‡ation adjustment in the …rst subsample has been faster to monetary policy shocks than to technology shocks. Tables 5-6 report the median, 16th and 84th percentiles of the posterior distribution of rj;i in the post-1980 subsample for the technology and the monetary policy shocks respectively. [Tables 5-6 about here] Comparing statistics in Tables 5-6 with the corresponding ones in Tables 3-4, I obtain the following results. First, in‡ation adjusts faster to both types of shocks in the second subsample than in the …rst one. This is true independently of the evaluation horizon, j; and of the price index. Second, the increase in in‡ation adjustment speed has been larger for the consumer price index and for the producer price index than for the other indexes. Third, the increase in in‡ation adjustment speed in the second subsample has been much larger conditional on technology shocks than conditional on monetary policy shocks. For instance, in the post-1980 subsample, one year after the shock, the GDP de‡ator in‡ation has accomplished, at the median, 94 and 38 percent of overall adjustment to technology and monetary policy shocks respectively; in the pre-1980 subsample, these statistics are 15 and 30 percent respectively. According to the producer price index, one year after the shock, median in‡ation response has accomplished 98 and 77 percent of overall adjustment to technology and monetary policy shocks respectively in the second subsample; in the pre-1980 subsample, these statistics are 19 and 44 percent respectively. 14
4
Robustness analysis
This section investigates to what extent results from the benchmark BVAR model estimated on the entire sample are robust to several features of the identi…cation assumptions. The insights from these exercises reinforce the results obtained in the previous sections.22
4.1
Identi…cation through sign restrictions
While extensively adopted, identi…cation of monetary policy shocks through the recursive assumption of Christiano et al. (1999), and identi…cation of technology shocks through long-run restrictions as in Gali (1999) have been recently criticized by part of the macroeconomic literature.23 In order to assess robustness of …ndings against this critique, in this section I identify the two structural shocks of interest through a di¤erent method relying on sign restrictions of impulse responses. This method has been originally proposed by Faust (1998) and then applied by Uhlig (2006) to the identi…cation of monetary policy shocks, and by Dedola and Neri (2007) to the identi…cation of technology shocks. These sign restrictions are robust in the sense that they are consistent with a wide range of DSGE models.24 Another advantage is that this identi…cation scheme allows prices to respond immediately to both types of shocks, while the benchmark identi…cation of Christiano et al. (1999) imposes a zero restriction on the contemporaneous response of in‡ation to monetary policy shocks. Its main disadvantage is that it imposes relatively weak restrictions on the response of the economy to the two types of shocks and, as a consequence, 22
In what folloes I will report impulse responses of output, Federal Funds rate, in‡ation and labor productivity. The other variables are omitted to save on space. 23 See the reference list in Erceg, et al. 2005 for most of the relevant references regarding identi…cation of technology shocks. See Faust (1998) and references therein regarding identi…cation of monetary policy shocks. 24 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.
15
impulse responses may be less tightly estimated than under the benchmark identi…cation scheme. 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. Apart from the di¤erent identi…cation assumptions, the rest of the estimation procedure is as in the benchmark speci…cation of the model. Sign restrictions on the impulse responses to monetary policy shocks are similar to the ones adopted by Uhlig (2006), while sign restrictions on the impulse responses to technology shocks are similar to the ones adopted by Dedola and Neri (2006).25 Intuitively, this method distinguishes the two types of shocks on the basis of the facts that: i) permanent technology shocks have a more persistent impact on quantities than monetary policy shocks; ii) quantities and prices move in opposite directions following a technology shock, but move in the same direction following a monetary policy shock; iii) monetary policy shocks are associated to changes in monetary aggregates and interest rates. Sign restrictions are reported in more details in Table 7.26 [Table 7 about here] Finally, I adopt the algorithm proposed by Ramirez, Waggoner and Zha (2007) to compute the posterior distribution of impulse responses.27 [Figure 11 about here] Figure 11 plots the impulse responses of output, Federal Funds rate, in‡ation and 25
I refer to these authors for a discussion of the ability of these restrictions to distinguish technology from monetary policy shocks as well as from other shocks. 26 Results are robust to di¤erent speci…cations of sign restrictions, and in particular to di¤erent assumptions about the number of periods they are expected to hold for. 27 For more details see Ramirez, Waggoner and Zha (2007) pp. 38-40.
16
labor productivity. Although the identi…cation scheme is very di¤erent from the one adopted under the benchmark speci…cation, impulse responses to the two types of shocks are similar to the ones reported in section 2. In particular, in‡ation response is much faster to technology shocks than to monetary policy shocks.
4.2
A Solow-residual based identi…cation for technology
One of the benchmark identifying assumptions in section 2 is that the technology shock is the only shock a¤ecting labor productivity in the long-run. This restriction holds in a wide range of business cycle models. However, there exist models that do not satisfy it. For example, this assumption is not true in an endogenous growth model where all shocks a¤ect productivity in the long-run, nor is it true in a model where there are permanent shocks to the tax rate on capital income.28 As an additional robustness check on identi…cation, this subsection adopts a di¤erent identi…cation assumption for technology shocks, relying on a Solow-residual measure of quarterly total factor productivity (FTFP) growth estimated by Fernald (2007). Fernald’s quarterly measure explicitly accounts for variable capital utilization and labor hoarding.29 The FTFP series is added to Y and the posterior distribution of (B; ) is estimated as in section 2. Di¤erently from section 2, in this subsection the identifying assumption is that a technology shock is the only shock a¤ecting FTFP in the long-run, while the long-run response of labor productivity is unrestricted. Relative to the identi…cation assumptions of section 2, the advantage of this procedure is that, by explicitly assuming an aggregate production function, it directly estimates total factor productivity growth. This procedure has been originally applied by Christiano, 28
See Chari, Kehoe and McGrattan (2008) for a criticism on long-run restrictions to labor productivity. 29 The growth rate of FTFP is given by: ln(F T F P ) =
ln(GDP )
(
ln(K) +
ln(Z))
(1
) ( ln(QH) +
ln(E)) ;
where Z is capital utilization, K is capital input, E is labor e¤ort per (quality-adjusted) hour worked, Q is labor quality (i.e., a labor composition adjustment), and H is hours worked.
17
Eichenbaum and Vigfusson (2004), suggesting there could be high frequency cyclical measurement error in Solow-residual based measures of total factor productivity, that the long-run restriction might clean out.30 As long as the assumption about the aggregate production function holds at low frequencies, the model provides unbiased estimates of technology shocks. The remaining assumptions required to jointly identify the monetary policy shock are unchanged from section 2. [Figure 12 about here] Figure 12 plots technology shocks between 1961:II and 2007:II, estimated according both to the benchmark identi…cation scheme of section 2 and to the identi…cation scheme of this subsection. The time series of estimated technology shocks are very similar across the two identi…cation assumptions, and have a high correlation equal to 0.96. This suggests that the two identi…cation schemes deliver similar results in terms of price adjustment speed to technology and monetary policy shocks. In fact, impulse responses are almost identical to the benchmark speci…cation and are therefore omitted. Statistics about ri;j computed under the identi…cation assumptions of this subsection are, both quantitatively and qualitatively, very similar to the ones obtained under the benchmark identi…cation scheme, and are therefore omitted.
4.3
Monthly data
The empirical literature investigating the responses of macroeconomic variables to monetary policy shocks often makes use of monthly frequency data. The advantage of using monthly data over quarterly data is that the benchmark identi…cation scheme of section 2 requires economic variables in the sub-vector Xt not to respond to monetary policy shocks only for a month instead of a quarter. Therefore, identi…cation of 30
The technology shock estimated trough long-run restrictions on FTFP, as in this subsection, has a 0.97 correlation with the residual of the equation associated to FTFP in the VAR. Therefore in this case long-run restrictions do not a¤ect the estimates of technology shocks much.
18
monetary policy shocks is less restrictive. The disadvantage is that some economic variables are measured only at the quarterly frequency, as for instance GDP.31 This section estimates model (2) at a monthly frequency. Quarterly interpolated time-series equivalents are used anytime the monthly frequency observations are unavailable.32 The number of lags, p; is set to 13. Data is available from January 1964 to June 2006. Apart from the frequency of the data, the estimation and identi…cation method is identical to the benchmark version of the model. [Figure 13 about here] Figure 13 plots the impulse responses to monetary policy and technology shocks. Impulse responses resemble the ones obtained at the quarterly frequency. In‡ation adjustment is faster to technology shocks than to monetary policy shocks. Therefore, results from the benchmark speci…cation are not a¤ected by the frequency of the data.
5
Concluding remarks
This paper answers the question of whether, by how much and how likely it is that U.S. in‡ation adjusts faster to aggregate technology shocks than to monetary policy shocks. According to a BVAR model for the 1960-2007 sample, this paper …nds that U.S. in‡ation adjusts much faster to technology shocks than to monetary policy shocks. This paper also …nds that this result is robust to di¤erent identi…cation assumptions. However, when investigating more in detail over subsamples, this paper …nds that in‡ation adjusts faster to technology shocks than to monetary policy shocks in the Volcker-Greenspan period, but the opposite is true in the pre-Volcker subsample. This result is due to the fact that in‡ation adjustment speed in the later subsample has 31
GDP is necessary to identify the technology shocks under the benchmark identi…cation scheme. It is needed to compute a measure of labor productivity. 32 Variables unavailable at the monthly frequency are: real GDP, real non-residential and residential investments and GDP price de‡ator. Sims and Zha’s (2007) interpolated series are used instead. These series are constructed through the Chow-Lin interpolation method.
19
increased much more to technology shocks than to monetary policy shocks. Gali, Lopez-Salido and Valles (2003) and Boivin and Giannoni (2006) have argued that the faster adjustment of in‡ation in response to technology and monetary policy shocks respectively is to be attributed to the improvement of the FED performance at stabilizing prices in the last decades. It remains to be shown wether existing models can also account for the fact that a more aggressive monetary policy on prices has a¤ected in‡ation adjustment speed to technology shocks more than to monetary policy shocks. In a companion paper, Paciello (2009), I show that a model of price setting under imperfect information and endogenous attention allocation can provide an explanation.
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 (2007): ”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).
20
[6] Boivin, J., Marc Giannoni and Ilian Mihov (2008): ”Sticky Prices and Monetary Policy: Evidence from Disaggregated U.S. Data,” Forthcoming American Economic Review. [7] 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. [8] Chari, V.V. , P. J. Kehoe and E. R. McGrattan (2008): ”Are structural VARs with long-run restrictions useful in developing business cycle theory?”Forthcoming Journal of Monetary Economics. [9] 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. [10] 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. [11] Christiano, L. J., M. Eichenbaum, and R.Vigfusson (2004): ”What Happens After A Technology Shock?,”NBER Working Paper No. W9819. [12] Cogley, TimothyW., Giorgio Primiceri, and Thomas J. Sargent, “In‡ation-Gap Persistence in the U.S.,”mimeo, University of California at Davis, Northwestern University, and New York University, 2008. [13] 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.
21
[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] Doan, T., R. Litterman, and C. A. Sims (1984): ”Forecasting and Conditional Projection Using Realistic Prior Distributions,”Econometric Reviews, 3, 1-100. [16] Dupor, Bill, Jing Han and Yi Chan Tsai (2007): ”What Do Technology Shocks Tells Us about the New Keynesian Paradigm?”. Forthcoming Journal of Monetary Economics. [17] Edge, Rochelle M., Laubach, Thomas and John C. Williams (2003): "The responses of wages and prices to technology shocks." Finance and Economics Discussion Series 2003-65. [18] 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. [19] Faust, Jon (1998): ”The robustness of identi…ed VAR conclusions about money”. Carnegie-Rochester Conference Series on Public Policy Volume 49, Pages 207244. [20] 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. [21] Galí, Jordi, (1999): ”Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?,” American Economic Review, 89(1), 249-271. [22] Galí, Jordi and Mark Gertler (1999): ”In‡ation dynamics: A structural econometric analysis”. Journal of Monetary Economics 44, 195-222. 22
[23] 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] 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. [25] Litterman, R. (1986): ”Forecasting With Bayesian Vector Autoregressions - Five Years of Experience,”Journal of Business and Economic Statistics, 4, 25-38. [26] Nakamura, Emi, and Jón Steinsson (2008): ”Five Facts about Prices: A Reevaluation of Menu Costs Models”. Quarterly Journal of Economics. [27] Paciello, Luigi (2009): “Monetary Policy Activism and Price Responsiveness to Aggregate shocks under Rational Inattention.”EIEF discussion paper. [28] 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. [29] 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. [30] Smets, F. and Rafael Wouters. 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach." American Economic Review, vol. 97(3), pages 586-606. [31] Stock, J. and Marc Watson (2002): ”Has the Business Cycle Changed and Why?” NBER Working Paper No. 9127.
23
[32] 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. [33] Waggoner D.F., and T. Zha (2003): ”Likelihood Preserving Normalization in Multiple Equation Models”. Journal of Econometrics, 114, 329-347.
24
Appendices A Data Mnemon
Series
Y=(X,S,Z,F)
GDPQ/LBMNU
Labor productivity
X
log
LBMNU
Index total hours worked
X
log
FYFF
INTEREST RATE: FEDERAL FUNDS
S
Level
PGDP
GDP price de‡ator
X
log
FSPCOM
Standard and Poor’s stock price index
F
log
CES002
Number of employees on non-farm payrolls
X
log
A0M051
Personal income (AR, BIL. CHAIN 2000 $)
X
log
JQCR
Real Personal Consumption Expenditures
X
log
IFNRER
Real non-residential investments
X
log
JQIFRESR
Real residential investments
X
log
IPS10
Industrial production
X
log
UTL11
Capacity utilization
X
Level
LHUR
Unemployment rate
X
Level
HSFR
Housing starts (NONFARM)
X
log
PCOM
Index of sensitive material prices
X
log
PWFSA
Producer price index
X
log
PCPEPI
Personal consumption expenditures price de‡ator
X
log
PUNEW
Consumer price index
X
log
CES275
Average hourly earnings
X
log
FM1
M1 monetary stock
Z
log
FM2
M2 monetary stock
Z
log
FMRRA
Non-borrowed reserves
Z
log
FMRNBA
Total reserves
Z
log
FTFP
Fernald’s (2007) TFP estimate
X
log
25
Units
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. Most data is available at a monthly frequency. Output, GDP de‡ator, residential and non-residential investments are not. When I estimate the model at the monthly frequency, I use Sims and Zha (2007) interpolated monthly series for these four time series. LBMNU is also not available at the monthly frequency. In the monthly frequency analysis, the latter is replaced by the BLS index for average weekly hours worked.
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 ;
The prior parameters S0 ;
0 ; B0
and Bj
0)
and
0
v N (B0 ;
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 <
: 0; 2
and the matrix
i;
s2
if i = j; s = 1
;
otherwise
2 i ; 2 j
has prior expectation E ( ) = diag ( 21 ; ::::; 26
2 n) :
For details see
Kadiyala and Karlsson (1997). The scale parameters
2 i
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
and Bj ; Y v N (B ;
)
= (X 0 X )
X0 Y ;
1
; S = (Y
); X B )0 (Y
X B ) and
k + 2: See Banbura, Giannone and Reichlin (2007) for more details.
C Parameterization of Consider an n1
dimensional subset of Y . De…ne the in-sample mean squared
forecast error (MSFE) of the 1-step-ahead mean squared forecast as: ( ;m) M SF Ei
=
T
1 p
T X
1 t=p+1
( ;m)
y^i;t
2
yi;t
;
where i = 1; ::::; n1 indices the variable the MSFE is computed for, T is the length ( ;m)
of the sample, y^i;t
is the one-step-ahead forecast computed in model m with prior
parameterization equal to : This analysis studies three types of models, depending on the number of variables included in the analysis and the value of . The …rst model, m = 1; includes n1 variables and is estimated with a ‡at prior, 27
= 1: The
n1 variables considered are: labor-productivity, hours worked, GDP price de‡ator, Federal Funds rate, M2 money stock, commodity price index, capacity utilization and average hourly earnings of production workers. This set of variables is similar to the one adopted by other authors in the study of the response of the U.S. economy to monetary policy and aggregate technology shocks33 . The second model, m = 2; is the benchmark model. It includes all the n macroeconomic indicators and is estimated with the Minnesota prior described in the main text and depending on : The third model, m = 3; includes all the n variables and is estimated imposing the prior exactly, = 0: Following Banbura, Reichlin and Giannone (2007), I choose
in model m = 2
so to minimize the di¤erence in …t from model m = 1: = arg min z
where z =
1 n1
Pn1
n1 ( ;1) 1 X M SF Ei ; n1 i=1 M SF Ei(0;3)
(1;1)
M SF Ei i=1 M SF E (0;3) i
= 0:35 is the measure of relative …t associated to the
reference model. From this procedure
is equal to 0:065.
D Identi…cation Let’s order the variables in the model as Yt = (Xt ; St ; Zt ; Ft )0 ; where the …rst 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
H (A0 ) = 4
A0 (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 33
See for instance Christiano, Eichenbaum and Evans (1999) and Altig, Christiano, Eichenbaum and Linde (2005).
28
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
x
Tz x
x
x
x
x
x
x
0
0
0
x
x
x
x
x
x
x
x
x
x
x
x
x
3
7 7 7 7 7 7 7 7 7 7; 7 7 7 7 7 7 7 7 5
(6)
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
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 ] =
29
and D = diag( ):
Let’s compute H ( ) and de…ne matrices P1 and P2 as:
P1
P2 where Is
s
2
0 6 1 6 6 In 4 0n
1
01
n 1
n
0n
1
0n
n 1
n
0n
1
n
In
3
1 n 1
[in ; in 1 ; ::::; i1 ] ;
7 7 ,7 5
(7)
(8)
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 (7)
(8) : 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 (6) : It 1
follows that A0 =
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 : 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 )
0 nx
0 1
(nx
a22 (1
1)
(1
nz ) a33
1)
(nz
a42 (1
nz ) 0
a32 (nz
a14
nz ) a43
1) 30
(1
nz )
3
7 7 nx 1 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)
Then consider the n
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
Table 1 : Benchmark BVAR, 1960:1-2007:3. Median inflation adjustment speed to technology shocks. 1 Half-year
1 year
2 years PGDP 0.21
3 years
4 years
0.68
0.50
0.07
0.02
0.61;0.78
0.43;0.63
0.16;0.34
0.04;0.15
0.01;0.06
0.61
0.42
PUNEW 0.16
0.05
0.02
0.51;0.74
0.33;0.56
0.10;0.28
0.02;0.12
0.00;0.05
0.46
0.28
PWSFA 0.07
0.02
0.00
0.35;0.62
0.20;0.44
0.04;0.18
0.00;0.07
0.00;0.02
0.58
0.42
PCEPI 0.18
0.06
0.02
0.51;0.71
0.35;0.56
0.13;0.30
0.04;0.14
0.01;0.06
Table 2 : Benchmark BVAR, 1960:1-2007:3. Median inflation adjustment speed to monetary policy shocks Half-year
1 year
0.99
0.96
2 years PGDP 0.81
0.46
0.14
0.93;1.00
0.83;0.99
0.62;0.91
0.29;0.62
0.06;0.24
0.93
0.89
PUNEW 0.69
0.32
0.07
0.81;0.98
0.71;0.95
0.50;0.80
0.18;0.46
0.02;0.15
0.95
0.88
PWSFA 0.58
0.21
0.04
0.83;0.99
0.71;0.95
0.40;0.72
0.11;0.35
0.01;0.10
0.98
0.92
PCEPI 0.74
0.37
0.09
0.88;1.00
0.75;0.97
0.52;0.85
0.20;0.52
0.03;0.18
1
3 years
4 years
Inflation adjustment speed is measured by rij over different horizons, and for different price indices. Number in smaller characters are the 16th and 84th percentiles. PGDP: GDP deflator; PUNEW: CPI; PWSFA: PPI; PCEPI: personal consumption deflator.
32
Table 3 : Benchmark BVAR, 1960:1-1979:3, Median inflation adjustment speed to technology shocks. Half-year
1 year
0.96
0.85
2 years PGDP 0.55
3 years
4 years
0.28
0.13
0.93;0.98
0.80;0.91
0.46;0.67
0.20;0.40
0.08;0.21
0.89
0.77
PUNEW 0.45
0.24
0.13
0.84;0.94
0.69;0.86
0.35;0.59
0.16;0.37
0.07;0.21
0.92
0.81
PWSFA 0.47
0.27
0.16
0.86;0.96
0.72;0.89
0.36;0.61
0.18;0.40
0.10;0.24
0.91
0.80
PCEPI 0.50
0.28
0.14
0.85;0.96
0.72;0.88
0.40;0.63
0.19;0.40
0.09:0.22
Table 4 : Benchmark BVAR, 1960:1-1979:3, Median inflation adjustment speed to monetary policy shocks. Half-year
1 year
0.88
0.70
2 years PGDP 0.55
0.24
0.12
0.75;0.97
0.52;0.88
0.28;0.75
0.13;0.36
0.04;0.25
0.89
0.74
PUNEW 0.54
0.23
0.18
0.76;0.98
0.50;0.90
0.32;0.67
0.13;0.37
0.06;0.30
0.72
0.56
PWSFA 0.37
0.21
0.16
0.53;0.92
0.38;0.74
0.21;0.53
0.09;0.36
0.06;0.27
0.80
0.68
PCEPI 0.50
0.24
0.19
0.64;0.95
0.48;0.86
0.27;0.67
0.12;0.39
0.06;0.33
33
3 years
4 years
Table 5 : Benchmark BVAR, 1979:4-2007:3, Median inflation adjustment speed to technology shocks. Half-year
1 year
0.20
0.06
2 years PGDP 0.01
3 years
4 years
0.01
0.00
0.13;0.40
0.03;0.20
0.00;0.08
0.00;0.05
0.00;0.02
0.11
0.04
PUNEW 0.02
0.01
0.01
0.06;0.30
0.01;0.14
0.01;0.07
0.00;0.04
0.00;0.02
0.08
0.02
PWSFA 0.01
0.01
0.00
0.04;0.23
0.01;0.09
0.00;0.04
0.00;0.02
0.00;0.01
0.13
0.05
PCEPI 0.02
0.01
0.00
0.07;0.31
0.02;0.17
0.00;0.08
0.00;0.04
0.00;0.02
Table 6 : Benchmark BVAR, 1979:4-2007:3, Median inflation adjustment speed to monetary policy shocks. Half-year
1 year
2 years PGDP 0.34
3 years
4 years
0.96
0.62
0.17
0.07
0.83;1.00
0.43;0.75
0.19;0.48
0.08;0.27
0.03;0.13
0.48
0.29
PUNEW 0.10
0.05
0.03
0.27;0.84
0.14;0.52
0.04;0.22
0.02;0.13
0.01;0.07
0.54
0.23
PWSFA 0.08
0.03
0.01
0.24;0.93
0.09;0.54
0.02;0.25
0.01;0.12
0.00;0.05
0.88
0.68
PCEPI 0.36
0.18
0.08
0.68;0.98
0.47;0.82
0.19;0.50
0.08;0.28
0.03;0.13
34
MP # of Quarters PGDP M2 FYFF IFNRER JQCR GDPQ/ LBMNU LBMNU GDPQ CES275/PGDP
2 2 2 2 2 -
SignRestriction 60 60 90 60 60 -
2 2 -
60 60 -
TECH # of Quarters 20 10 5 20
SignRestriction 60 90 90 90
10 5
90 90
Table 7: Sign- Restrictions. The second and fourth columns contain the least number of quarters it is assumed to hold for. The third and fifth columns contain the sign restrictions. Remaining variables are unrestricted. IFNRER: Real non-residential investments; JQCR: Real Personal Consumption Expenditures; LBMNU: Index total hours worked; CES275: Average hourly earnings.
35
TECH shock
0.01
PGDP
0
0
-0.01 -0.02
-0.02 -0.03
0
2
4
6
8
10
12
14
16
18
-0.04
20
PUNEW
0.02
PWFSA
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0.05
0 0 -0.02 -0.04
0
2
4
6
8
10
12
14
16
18
-0.05
20
0.02
0.1
0
0.05
-0.02
0
-0.04
-0.05
-0.06
0
2
4
6
8
10
12
14
16
18
-0.1
20
0
PCEPI
MP shock
0.02
0.04 0.02
-0.01
0 -0.02 -0.03
-0.02 0
2
4
6
8
10
12
14
16
18
-0.04
20
Figure 1 : Benchmark BVAR. Median, 68th and 90th percentiles inflation impulse responses of different measures of inflation to one standard deviation shock. COLUMNS: Responses to Tech and MP shocks respectively. ROWS: PGDP: GDP deflator; PWFSA: producer price index; PCEPI: consumption expenditure deflator; PUNEW: CPI. Units are in basis points. Horizontal Axis: quarters. TECH shock
GDPQ
0.15
0.2
0.05
0
0
-0.2
-0.05
0
2
4
6
8
10
12
14
16
18
-0.4
20
FFR
0.1 0
1 0.5
-0.2
0
-0.3
-0.5
0
2
4
6
8
10
12
14
16
18
20
dPGDP
0.01
GDPQ/H
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0.02
0
0
-0.01
-0.02
0
2
4
6
8
10
12
14
16
18
-0.04
20
0.2
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
0
1.5
-0.1
-0.02
MP shock
0.4
0.1
0
2
4
6
8
10
12
14
16
18
-0.1
20
Figure 2 : Benchmark BVAR, Median, 68th and 90th percentiles impulse responses to one standard deviation shock. COLUMNS: Responses to Tech and MP shocks respectively. ROWS: GDPQ: real GDP; FFR: annual FedFunds rate; dPGDP: GDP deflator inflation; GDPQ/H: labor productivity.
36
Figure 3 : Benchmark BVAR. Impulse response to one standard deviation technology shock of the remaining variables in the BVAR.
Figure 4 : Benchmark BVAR. Impulse response to one standard deviation monetary policy shock of the remaining variables in the BVAR. .
37
TECH shock
GDPQ
0.3 0.2
0
0.1
-0.1
0
-0.2
-0.1
0
2
4
6
8
10
12
14
16
18
-0.3
20
0.5
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
1
0
FFR
0
1.5
0.5 -0.5 -1
0 0
2
4
6
8
10
12
14
16
18
-0.5
20
0.02
dPGDP
MP shock
0.1
0.02 0.01
0
0 -0.02
GDPQ/H
-0.04
-0.01 0
2
4
6
8
10
12
14
16
18
-0.02
20
0.4
0.1
0.3
0.05
0.2
0
0.1
-0.05
0
0
2
4
6
8
10
12
14
16
18
-0.1
20
Figure 5: Altig et al. (2005) BVAR, Median, 68th and 90th percentiles impulse responses to one standard deviation shock. COLUMNS: Responses to Tech and MP shocks respectively. ROWS: GDPQ: real GDP; FFR: annual FedFunds rate; dPGDP: GDP deflator quarterly inflation; GDPQ/H: labor productivity.
Inflation Adjustment Speed: 1 year horizon PGDP
1
PUNEW
1
0.6
0.6
MP
0.8
MP
0.8
0.4
0.4
0.2
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
0
0.1
0.2
0.3
0.4
TFP
PWSFA
1
0.5
0.6
0.7
0.8
0.9
1
0.6
0.7
0.8
0.9
1
TFP
PCEPI
1
0.6
MP
0.8
0.6
MP
0.8
0.4
0.4
0.2
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
TFP
0
0.1
0.2
0.3
0.4
0.5
TFP
Figure 6 : Benchmark BVAR, draws of inflation adjustment speed to TFP (horizontal axis) and MP (vertical axis) shocks, evaluated at 1 year horizon, and for the four measures of prices (4 plots).
38
TECH shock
0.2
PGDP
0
PUNEW
0.05
-0.2
0
-0.4
-0.05
-0.6
0
2
4
6
8
10
12
14
16
18
-0.1
20
0
0.3
-0.2
0.2
-0.4
0.1
-0.6 -0.8
PWFSA
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0 0
2
4
6
8
10
12
14
16
18
-0.1
20
0.5
0.6 0.4
0
0.2 -0.5 -1
PCEPI
MP shock
0.1
0 0
2
4
6
8
10
12
14
16
18
-0.2
20
0
0.3
-0.2
0.2
-0.4
0.1
-0.6 -0.8
0 0
2
4
6
8
10
12
14
16
18
-0.1
20
Figure 7: Sub-sample 1960:I-1979:III. Median, 68th and 90th percentiles impulse responses of different measures of inflation to one standard deviation shock.
TECH shock
0.1
PGDP
0.05
0.02
0 0
-0.05 -0.1
0
2
4
6
8
10
12
14
16
18
-0.02
20
PUNEW
0.2
0.1
0
0.05
-0.1
PWFSA
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0 0
2
4
6
8
10
12
14
16
18
-0.05
20
0.4
0.15
0.2
0.1
0
0.05
-0.2 -0.4
0
0.15
0.1
-0.2
0 0
2
4
6
8
10
12
14
16
18
-0.05
20
0.05
0.04
0 PCEPI
MP shock
0.04
0.02
-0.05 0
-0.1 -0.15
0
2
4
6
8
10
12
14
16
18
-0.02
20
Figure 8: : Sub-sample 1979:4-2007:3. Median, 68th and 90th percentiles impulse responses of different measures of inflation to one standard deviation shock.
39
Inflation Adjustment Speed: 1 year horizon PGDP
1
PUNEW
1
0.6
MP
0.8
0.6
MP
0.8
0.4
0.4
0.2
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
0
0.1
0.2
0.3
0.4
TFP
PWSFA
1
0.5
0.6
0.7
0.8
0.9
1
0.6
0.7
0.8
0.9
1
TFP
PCEPI
1
0.6
MP
0.8
0.6
MP
0.8
0.4
0.4
0.2
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
0
0.1
0.2
0.3
0.4
TFP
0.5
TFP
Figure 9 : Sub-sample 1960:1-1979:3, draws of inflation adjustment speed to TFP (horizontal axis) and MP (vertical axis) shocks, evaluated at 1 year horizon, and for the four measures of prices.
Inflation Adjustment Speed: 1 year horizon PGDP
1
PUNEW
1
0.6
0.6
MP
0.8
MP
0.8
0.4
0.4
0.2
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
0
0.1
0.2
0.3
0.4
TFP
PWSFA
1
0.5
0.6
0.7
0.8
0.9
1
0.6
0.7
0.8
0.9
1
TFP
PCEPI
1
0.6
MP
0.8
0.6
MP
0.8
0.4
0.4
0.2
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
TFP
0
0.1
0.2
0.3
0.4
0.5
TFP
Figure 10 : Sub-sample 1979:4-2007:3, draws of inflation adjustment speed to TFP (horizontal axis) and MP (vertical axis) shocks, evaluated at 1 year horizon, and for the four measures of prices.
40
TECH shock
GDPQ
0.15 0.1
0
0.05
-5
0
FFR
-0.05
-10 0
2
4
6
8
10
12
14
16
18
-15
20
0.4
40
0.2
20
0
0
-0.2
-20
-0.4
0
2
4
6
8
10
12
14
16
18
-40
20
dPGDP
0.01
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
2
0
0
-0.01 -2
-0.02 -0.03
0
2
4
6
8
10
12
14
16
18
-4
20
0.1
GDPQ/H
MP shock
5
5 0
0.05 -5 0
0
2
4
6
8
10
12
14
16
18
-10
20
Figure 11 : Sign-restrictions identification. Median, 68th and 90th percentiles impulse responses to one standard deviation shock, for the first 10 quarters. Responses to Tech and MP shocks respectively. ROWS: GDPQ: real GDP; FFR: annual FedFunds rate; dPGDP: GDP deflator inflation; GDPQ/H: labor productivity.
Figure 12: Estimates of technology shocks. The solid-blue line is the benchmark identification scheme, the dashed-red line is the estimate obtained by imposing long-run restrictions on the FTFP series in the BVAR model.
41
TECH shock
GDPQ
0.15 0.1
0
0.05
-10
0
-20
-0.05
0
10
20
30
40
50
-30
60
5
FFR
MP shock
10
0
10
20
30
40
50
60
0
10
20
30
40
50
60
0
10
20
30
40
50
60
0
10
20
30
40
50
60
6000 4000
0
2000 -5 -10
0 0
10
20
30
40
50
-2000
60
-3
dPGDP
5
x 10
2
0
1
-5 0
-10 -15
0
10
20
30
40
50
-1
60
GDPQ/H
0.08
20
0.06
10
0.04 0
0.02 0
0
10
20
30
40
50
-10
60
Figure 13 :BVAR estimated on Monthly frequency. Median, 68th and 90th percentiles inflation impulse responses to one standard deviation shock. Responses to Tech and MP shocks respectively. ROWS: GDPQ: real GDP; FFR: annual FedFunds rate; dPGDP: GDP deflator inflation; GDPQ/H: labor productivity.
42
