Productivity Shocks and the Business Cycle

Productivity Shocks and the Business Cycle: Reconciling Recent VAR Evidence James Costain Bank of Spain and UC Davis

Beatriz de-Blas-Perez Univ. de Navarra and UC Davis

May 2006

Preliminary and Incomplete Abstract Galí (1999) used a VAR with productivity and hours worked to argue that technology shocks are negatively correlated with labor and are unimportant for the business cycle. More recently, Beaudry and Portier (2003) studied a VAR in productivity and stock prices. Remarkably, they found that the component which has a permanent impact on productivity is almost identical to that which has no immediate impact on productivity. Moreover, either of these components explains most business cycle variation. Like Galí’s results, these observations are inconsistent with early RBC models, but on the other hand they contradict Gali’s claim that technology shocks are unimportant for cycles. In this paper, we study trivariate VARs in productivity, hours worked, and stock prices to see how these apparently contradictory results can be reconciled. We …nd one VAR speci…cation that qualitatively and quantitatively matches the …ndings of Galí (so that longrun technology shocks drive hours down), and a second speci…cation that matches the main …ndings of Beaudry and Portier (so that long-run technology shocks increase hours, are similar to the short-run shock to stock prices, and play a major role in generating business cycles). Surprisingly, the di¤erence between these two speci…cations has nothing to do with estimating in levels or in di¤erences, or with running VARs or VECMs, or with the ordering of variables. The only di¤erence between the two speci…cations lies in which productivity variable is used: labor productivity (to generate results like Galí’s) or TFP (to generate results like those of Beaudry and Portier). Both the original Beaudry and Portier estimations, as well as our …ndings on the productivity speci…cation, add to the evidence that Galí’s …ndings are not robust. Apparently the cyclical role of technology shocks is only picked up when a su¢ ciently cyclical productivity series is used in the estimation.

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1

Introduction

A recent literature aims to test the basic real business cycle (RBC) theory of Kydland and Prescott (1982) and King, Plosser, and Rebelo (1988) by studying the e¤ects of productivity shocks in the context of vector autoregressions (VARs). Just as Blanchard and Quah (1989) sorted shocks into "demand”and "supply”components, the more recent papers classify impulses into "technology” and "non-technology” components. The in‡uential paper of Galí (1999) constructs a VAR with productivity and hours worked. He separates the series into two components: the part that does not have any permanent e¤ect on productivity, and that which does, which he interprets as a technology shock. He …nds that the non-technology component is responsible for most variation at business cycle frequencies, and that the initial impact of a technology shock on labor is negative. Both these observations appear seriously inconsistent with the RBC theory that business cycles are due in large part to technological innovations. More recently, Beaudry and Portier (2004) study a VAR in productivity and stock prices. Since di¤erent RBC papers have allowed for temporary or permanent productivity shocks as driving forces for business cycles, they consider two identi…cation strategies for separating out the technological component of the data. Their "short-run” identi…cation separates the component that has no immediate impact on productivity from that which does, while their "long-run” identi…cation separates the component that has no permanent impact on productivity from that which does. Remarkably, they …nd that the component which has a permanent impact on productivity is almost identical to that which has no immediate impact on productivity. Moreover, either one of these components explains most business cycle variation. Like Galí’s results, these observations are inconsistent with the early RBC models in which booms are responses to increases in the current level of productivity. Nonetheless, Beaudry and Portier’s results leave open the possibility of an alternative technology-based theory of the business cycle–they argue that technological changes are "news”which could stimulate the economy in the short run even if they do not immediately a¤ect productivity. Thus, while both papers

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could be interpreted as evidence against RBC theory, they appear to provide contradictory evidence on the sources of business cycles: Galí discards permanent shocks to productivity as a cause of business cycles, while Beaudry and Portier …nd them to be the main cause of cycles. In this paper, we ask how these apparently contradictory results can be reconciled. The Galí and Beaudry and Portier papers appear to indicate that the permanent productivity component extracted from a VAR with hours worked is very di¤erent from that extracted from a VAR with stock prices. On the other hand, the con‡icting results might simply indicate nonrobustness to minor di¤erences in methodology or data used. To explore this issue, we study a trivariate VAR with productivity, hours, and stock prices, and we ask what identi…cation strategies give us results like those of Galí or like those of Beaudry and Portier.

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Related literature

Unsurprisingy, since Galí’s …ndings appear inconsistent with RBC theory, they have generated a lot of controversy. First, many papers using di¤erent data sources have supported Galí’s …ndings. In fact, as Galí and Rabanal (2004) discuss, the result on the negative e¤ect of technology shocks on employment had been anticipated in earlier work. Blanchard, Solow and Wilson (1995) argued that exogenous technological change needs to be separated from other factors that may a¤ect measured productivity. Among other results, they …nd that exogenous technological improvements increase unemployment. More recently, Basu, Fernald and Kimball (…rst version 1998, updated 2004) reach similar conclusions to those in Galí (1999). They perform a growth accounting exercise that tries to decontaminate the Solow residual. They …nd that positive shocks to their cleansed measure of technology imply a strong decline in the use of factor inputs while having no signi…cant impact on output. Other work in the same vein includes Kiley (1996), Francis (2001), Franco and Philippon (2004), and Francis and Ramey (2003a). These papers are basically extensions to Galí’s paper using industry data at di¤erent aggregation levels, or capital tax rates in the structural VAR estimation.1 The results point in the same general direction: technology shocks account for a very 1

See Galí and Rabanal (2004) for a more detailed survery of this literature.

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low percentage of business cycle variation, and output growth and employment are negatively correlated after an industry-speci…c technology shock. A second branch of the literature has studied the international evidence on the e¤ects of technology shocks. The analysis has been extended mainly to the G7 countries and the Euro area (Galí, 2004 and 2005). Such studies corroborate the negative correlation between output and employment after a technology shock in the countries considered, with the exception of Japan and the UK.2 But other papers are more critical, and have centered the debate on three main issues. On one hand, the VAR speci…cation and role of long run identi…cation restrictions to capture technology shocks have been questioned. As regards the VAR speci…cation, Cooley and Dwyer (1998) already questioned the robustness of structural VAR inferences. More recently, Chari, Kehoe and McGrattan (2005) …nd that both di¤erence and level speci…cations of hours lead to misleading inferences about technology shocks. In fact, their results indicate that structural VARs may reject RBC theory even in data generated from the RBC model. They argue for an alternative approach they call “business cycle accounting”. On the other hand, the assumptions made on the statistical properties of the series employed (in particular, hours) in the estimation of the VAR are crucial for the results obtained. Christiano, Eichenbaum and Vifugsson (2003) …nd that Galí’s results change if hours are run in levels instead of in di¤erences. In particular, the negative correlation between output and employment after a technology shock turns positive, as in the standard RBC models. This result is found again using the technology series constructed by Basu, Fernald and Kimball (1998). Finally, another set of papers focuses on analyzing the e¤ects of technology shocks on the economy by disentangling investment speci…c shock and neutral technology shocks. In the spirit of Greenwood, Hercowitz and Krusell (2000), Fisher (2003) …nds that investment speci…c technology shocks can account for most of the variance of output, whereas very little role is left for neutral technology in driving the business cycle. We do not intend to address all of the branches of this literature. By now there is evidence that Galí’s result can be picked up in many countries, using di¤erent methodologies to identify 2

Francis and Ramey (2003b), however, are able to recover the negative correlation for the UK.

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productivity. Nonetheless, there is evidence that structural VARs may draw mistaken inferences, and a great deal of attention has been devoted to the e¤ects of di¤erent ways of dealing with possible nonstationarity in hours. In the midst of all this debate, we …nd it remarkable that no attention has been paid to the implications of Beaudry and Portier´s …ndings for those of Galí. After all, B-P’s paper uses a version of Galí’s methodology, and …nds that technology shocks do in fact play an important role in creating business cycles. In this paper, we will limit ourselves to investigating what di¤erences between the two papers lead them to their mutually inconsistent conclusions.

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Econometric method

Our …rst step in this paper is to reproduce Galí (1999) and Beaudry and Portier’s (2004) results, by estimating the same bivariate VARs as they do. We estimate the VARs by OLS, either in di¤erences (which we will call a DVAR): [ xt ; yt ]0 , or in levels (an LVAR): [xt ; yt ]0 . Given the VAR estimate, we can recover its Wold moving average representation, which takes the form xt yt where C(L) = I +

P1

= C(L)

1;t

xt yt

or

2;t

i i=1 Ci L .

Vector

t

= [

1;t ;

0 2;t ]

= C(L)

1;t 2;t

is the vector of reduced form shocks,

contemporaneously correlated perturbations with zero mean and estimated variance-covariance matrix ^ . In the analysis below, Galí’s speci…cation is a DVAR, and the B-P speci…cation is an LVAR. In both cases, the …rst series is productivity (labor productivity and TFP, respectively), while the second variable is hours for Galí, and stock prices for B-P:

xt yt

Galí (1999) labor productivity hours

xt yt

Beaudry-Portier (2004) TFP stock prices (S&P500)

Given the reduced-form Wold representation, the idea is to recover the structural representation, which simply means a representation with orthogonalized disturbances which might be interpreted economically. While some identi…cations are more easily theoretically motivated than others, we mechanically explore a variety of speci…cations in an e¤ort to understand what makes Galí’s results di¤er from those of Beaudry and Portier. In particular, we try imposing both short run and long run restrictions, following B-P (2004). 5

3.1

Long run identi…cation

The basic motivation for Galí’s estimating strategy is that improved technology ought to raise labor productivity in the long run, while most other shocks commonly considered in neoclassical growth models have no long run impact on labor productivity. For example, Galí (1999) considers a constant-returns-to-scale production function Y (K; ZL), where K is capital, L is labor, and Z is an exogenous technology shock. Then the steady-state capital-labor ratio is given by: FK interest rate

=

Kt Zt Lt ; 1

markup

depreciation rate

We see from this equation that the ratio Kt =(Zt Lt ) is constant (or is a stationary random variable) as long as the interest rate, depreciation rate, and markup are constant (or are stationary random variables). Therefore, labor productivity Y =L = ZF

K ZL ; 1

will rise permanently if and

only if Z rises permanently.3 So given any VAR that includes labor productivity, Galí proposes to separate out the component which changes labor productivity in the long run from those unrelated factors that do not. In theory, this should allow him to observe the dynamics of the economy conditional on a change in technology, instead of judging the RBC model only on the basis of its unconditional moments. In general, the reduced-form shocks

t

calculated in the Wold representation will both have

long run e¤ects on labor productivity. Therefore, Galí’s proposal requires …nding a new “structural” (uncorrelated) representation of the shocks, which we will call lr t

lr : t

lr 1;t lr 2;t

=

These shocks yield a new moving average representation for the VAR: xt yt

= ~ (L)

lr 1;t lr 2;t

or

xt yt

= ~ (L)

lr 1;t lr 2;t

In order to be compatible with the reduced-form estimates, we must have ~ i = Ci ~ 0 ; for i

0,

which means we can calculate all the ~ i from our empirical estimates if ~ 0 is known. Using the variance-covariance matrix ^ obtained in the reduced-form estimation, ~ 0 must satisfy 3

Of course, as the equation above suggests, some other shocks could also permanently a¤ect labor productivity, such as permanent shocks to capital tax rates. But Galí and Rabanal (2003) …nd no evidence that capital tax shocks play a role in their results.

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~0 ~0 = ^ 0 However, since ^ is symmetric, this only results in three equations to determine the four elements of

0,

so one equation is still missing.

The missing equation is obtained by imposing Galí’s identifying condition: one of the shocks in

lr t

must have no long run e¤ect on labor productivity. To impose this condition, we will write 1 X ~ i , and similarly we write the long run the long run e¤ect of the structural shocks as ~ (1) = e¤ects of the reduced form shocks as C(1) =

1 X

i=0

Ci . Then since ~ i = Ci ~ 0 and ~ 0 ~ 00 = ^ , we

i=0

have:

~ (1) ~ (1)0 = C(1) ^ C(1)0 : Therefore, ~ (1) can be calculated as the (lower triangular) Cholesky decomposition of C(1) ^ C(1)0 : If the …rst variable x is labor productivity, the restriction that the second shock

lr 2;t

has no long

run e¤ect on labor productivity becomes ~ (1)12 = 0. This restriction then attributes all long run changes in x to the e¤ects of the …rst shock. Note that this argument is not really speci…c to labor productivity: a similar argument can be made for other productivity variables, such as TFP (as we will show below). Moreover, the argument is valid regardless of which non-productivity variables enter into the VAR. Thus, while Galí’s basic estimate is a VAR in labor productivity and hours worked, Beaudry and Portier use the same long-run identi…cation strategy to construct a sequence of technology shocks in a VAR with TFP and stock prices.

3.2

Short run identi…cation

However, Beaudry and Portier also consider a “short run” identi…cation. This identi…cation is not so directly motivated by controversies about the standard neoclassical model as Galí’s methodology is. But since stock prices are commonly believed to re‡ect the impact of all new information in the economy almost instantaneously, they could potentially be a very useful tool for observing the e¤ects of expectations. For instance, to identify the short run e¤ects of a long run change like a technological innovation, one possible way of picking up those e¤ects might be to include stock prices in our VAR. 7

Beaudry and Portier argue that stock prices should re‡ect “news” as soon as it enters into the economy, before other variables are a¤ected. Therefore, they propose to separate out a component that a¤ects only stock prices in the …rst period, which they call “news”, from all remaining components that a¤ect any other variables in the …rst period. Note that this identifying restriction is similar to the one often used in the literature on monetary policy, where money supply shocks are identi…ed as a component that a¤ects only interest rates in the …rst period. Thus, as in the monetary policy literature, Beaudry and Portier impose a triangular structure on the …rst-period e¤ects of shocks. So suppose we write the structural, uncorrelated shocks in the short-run identi…cation as sr t

sr 1;t sr 2;t

=

associated with one of the following moving average representations: xt yt

sr 1;t sr 2;t

= (L)

xt yt

or

We need to compute the distributed lag (L) =

P1

i iL ,

i=0

= (L)

sr 1;t sr 2;t

which is simpler in this case than in

the long run identi…cation. As before, we normalize the structural shocks to have a covariance matrix equal to the identity. We again assume that the reduced form shocks are a linear combination of the structural shocks,

t

=

sr 0 t ,

and since the reduced form shocks have

estimated covariance ^ , the transformation matrix 0 0

0

= ^ or

0

1^

0

(

must satisfy 0

1 0

) =I

Again, since the above system has one more variable than equations, it is necessary to add a restriction to pin down a particular solution. Beaudry and Portier order their variables with stock prices as the second variable y. Therefore, their identifying assumption is to set 0

a b c d

=

; with b = 0:

In other words, the second shock is what Beaudry and Portier call the “news” shock: it only a¤ects stock prices in the …rst period. Therefore, Cholesky decomposition of ^ . Once representation from

i

= Ci

0;

for i

0

0

can be computed as the lower-triangular

is known, we can obtain the rest of the structural

0: 8

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Data description

All the data we work with refer to the postwar US. To reproduce Galí’s results, we run a 2x2 VAR in labor productivity and total hours for 1948:1 to 2002:4. We use the same series as Galí and Rabanal (2003), which were also analyzed by McGrattan (2004). Both series are taken from the St. Louis Fed’s FREDII database, based on BLS data. Labor productivity is computed as the ratio between the real nonfarm business sector output, which is called OUTNFB in FRED II, and total hours worked in the nonfarm business sector, called HOANBS. The second variable in the VAR is the HOANBS total hours variable. Labor productivity and total hours are both converted to logs before running the VAR. To reproduce Beaudry and Portier’s results, we run a VAR in the logs of total factor productivity (TFP) and stock prices, from 1950:1 to 2004:1. Beaudry and Portier construct total factor productivity as follows: T F Pt =

Yt Htsh KSt1

sh

!

;

(1)

where Y denotes the real output measure OUTNFB, and H is the total hours variable HOANBS. Beaudry and Portier use two additional BLS series. The labor share, sh ; is 67:66%, which corresponds to the average value of the annual labor share series reported by the BLS. Capital services KS measures the services derived from the stock of physical assets and software in the nonfarm business sector. This series is also annual, so we need to interpolate to obtain a quarterly series. Like Beaudry and Portier, we interpolate assuming constant growth across quarters in the same year. Beaudry and Portier’s stock price variable is the quarterly Standards & Poors 500 Composite Stock Prices Index (S&P500), de‡ated by the seasonally adjusted implicit prices de‡ator of GDP and transformed into per capita terms by dividing it by the civilian noninstitutional population 16 and over. As the population series is annual, it has been interpolated assuming constant growth within the quarters of the same year. Next, we check for stationarity of the series in order to estimate the model in the most appropriate way. A unit root analysis for all the series that we will run in the VARs is reported

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in Table 1. Table 1: Unit root tests Z[^ ] Series 2:3727 log(Y =H) 3:1899 log(H) 1:5180 log(SP 500) 3:2179 log(T F P )

Series ^ log(Y =H) 2:0974 log(H) 3:4218 1:4182 log(SP 500) log(T F P ) 2:5687 t statistic for the null hypothesis of a unit root in the

^ 7:4593 6:8424 6:5888 8:9017

Z[^ ] 16:8985 7:6315 9:8694 9:4342

level or the …rst di¤erence of each time series, ADF and Phillips-Perron tests with 4 lags, trend and intercept. The 5 percent critical value for the tests is -3.43.

Following the literature, these tests are based on OLS regressions of the augmented DickeyFuller form Xt = X t

1+ + t

p 1 X

aj Xt

j

+ "t :

j=1

The Table shows the statistics for the Augmented Dickey-Fuller (ADF) and Phillips-Perron unit root tests, for the logs of each of the series considered below. These test statistics show that there is no series for which we can reject the null hypothesis of integration of order one at a 5% con…dence level. However, we do reject a unit root in each case for the di¤erenced series. Therefore, the data suggest running VARs in di¤erences. Nonetheless, we will report VARs both in levels and in di¤erences, since there is currently a big debate in the literature regarding the presence of a unit root in the hours series.

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Reproducing Galí’s results

In this section we reproduce the analysis of Galí (1999) and Galí and Rabanal (2004), estimating a bivariate VAR in the logs of labor productivity and hours. However, besides the long run identi…cation proposed by Galí, we also study the implications of a short run identi…cation. We do not claim that the short run identi…cation has a clear theoretical interpretation, but it will be useful for later comparison with Beaudry and Portier’s results and our own 3x3 results. Figure 1 reports the impulse response functions for a 1% shock to labor productivity (top row, abbreviated as PTY), and to hours (bottom row) for the short run identi…cation. The two left panels show the impulse responses to short-run-identi…ed technology shocks. After a short run technology shock, labor productivity jumps up to a permanently higher level, and 10

hours follow it with a one year lag. The right panels report the impulse responses to short run nontechnology shocks, that is, by de…nition, the VAR component that has no immediate e¤ect on labor productivity. This component causes productivity to converge to a permanently lower level, while hours rise permanently. Figure 2 reports the same graphs for the long run identi…cation, which corresponds to Galí’s proposed methodology. The left panels show that after a positive technology shock, productivity jumps up to a permanently higher plateau. At the same time, the shock drives labor hours down in the short run, for about a year and a half, as Galí claims. In fact, these …gures reproduce Galí-Rabanal Fig. 2 almost exactly. This is the result that calls RBC theory into question: technological improvements appear to destroy jobs in the short run instead of creating a boom. To the right, the impulse responses to a long run nontechnology shock show that productivity rises temporarily. Meanwhile, hours rise permanently, with an initial peak two quarters after the peak in productivity. Note that these two shocks appear to have much more potential to reproduce the business cycle, since they would tend to make productivity and hours positively correlated, with hours somewhat lagging. Up to now the analysis has focused on the conditional comovement of labor productivity and hours after di¤erent types of shocks. As we have seen, long run technology shocks do not imply the kind of impulse response functions needed by RBC theory to create business cycles. (“Technology”shocks found by our short run identi…cation do create short run dynamics resembling the business cycle, but by the logic of Galí’s identi…cation, they are unlikely to be true technological innovations.) So the immediate question arises: what is driving business cycles, then? To answer this question, we compute the series for labor productivity and hours implied by each of the identi…ed orthogonal components separately.4 We then pass these series through a Hodrick-Prescott …lter in order to focus only on their cyclical ‡uctuations. The cyclical components of the series are analyzed in Figure 3 for the long run identi…cation, and variance decompositions are shown for both identi…cations in Table 1. In Figure 3 we show the behavior of labor productivity and hours conditional on long run technology shocks (top panel) and long run nontechnology shocks (bottom panel). Note that the 4

Galí graphs the cyclical components of GDP and hours; here we simply graph the cyclical components of the two series that appear in our VAR, as we will do in all the other VAR speci…cations report.

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technology shock creates a strong negative correlation between growth rates of productivity and hours, as Galí claims. When looking at this series in levels, including its trend component (not shown in the …gure), it appears to pick up much of the "productivity slowdown", but the HP cyclical component seen in the top half of Figure 4 shows only small hours ‡uctuations unrelated to NBER business cycle dates. That is, consistently with Galí’s results, long run technology shocks seem irrelevant for business cycles. In contrast, for the long run nontechnology shock (bottom of Figure 3), we …nd a clear positive correlation between productivity and hours, with hours lagging, consistent with cyclical stylized facts. Moreover, the predicted series capture the main recessions in the US, like those of 1974 and 1982. This is re‡ected in the variance decompositions of the HP cyclical components, shown in Table 1. We see that in the long run identi…cation, the nontechnology shock is responsible for almost all the ‡uctuation in hours. Since the HP cyclical component of GDP is simply the sum of the HP cyclical components of labor productivity and hours, we can also explicitly calculate a variance decomposition for GDP. We see that, as Galí claims, the nontechnology shock is the main cause of cyclical ‡uctuation of GDP, accounting for 86% of the variance.

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Reproducing Beaudry and Portier’s results

Next we turn to the results reported by Beaudry and Portier (2003). They say their results can be obtained either from a vector error correction model (VECM) or a VAR in levels (LVAR), so for comparability with our other estimates we stick to LVARs. We estimate a bivariate VAR in levels for the logs of TFP and stock prices for the US from 1950:1 to 2002:1. Following Beaudry and Portier we consider two alternative identi…cations. Figures 4 and 5 report the impulse response functions corresponding to short run and long run shocks, respectively. In each …gure, the left column refers to technology shocks and the right column to nontechnology shocks, and the top panel to TFP and bottom panel to stock prices. The following results stand out. As Beaudry and Portier obtain, a short run shock to stock prices has a permanent e¤ect on productivity, measured as TFP. In particular, the impulse response functions for the short run to stock prices (the nontechnology shock that they call “news”) are very similar to those of BP. Interestingly, as Beaudry and Portier claim, a long run 12

shock to TFP re‡ects almost the same e¤ect on TFP as the short run shock to stock prices. In both cases, productivity and stock prices converge up to a persistently higher level; the e¤ect on the stock price then gradually decays. Long run nontechnology shocks, by contrast, imply a strong negative correlation between productivity and stock prices. However, we also …nd that the short run technology shock (never shown in their paper) also closely resembles the long run technology shock. Also, while our estimation is successful in replicating the shape of the impulse response functions, we fail to reproduce Beaudry and Portier’s result that the size of the e¤ects of the long run technology shocks and the news shocks is almost identical. While they …nd that the impulse response functions due to technology and news are virtually indistinguishable, we …nd that productivity rises more (relative to S&P500) in case of a shock to long run technology than in case of a news shock. When we complete the analysis in parallel to Galí’s results, and compute the business cycles implied by each of our estimated components, we obtain the results shown in Figure 6, and the variance decompositions shown in Table 2. The panels show the predicted series for TFP and stock prices conditional on the news shock (top) and the long run technology shock (bottom). As Beaudry and Portier argue, the long run technology shocks do a good job of picking up the business cycle in the data. Conditional on these shocks, productivity and stock prices are strongly positively correlated, and they clearly pick up the main recessions of the 1970s and 1980s. In the variance decomposition, the long run technology shock explains almost all the variance of productivity and about half of the variation of stock prices. The series used do not permit us to construct a variance decomposition for GDP in this case, but when we try regressing the HP cycle of GDP on the series derived from the long run technology shocks we obtain an R2 of 74%. Thus, Galí’s identifying assumption, applied to these series, provides evidence that technology shocks are indeed important for the cycle. In contrast to Beaudry and Portier’s claims, we …nd that the news shock has much less success in explaining the cycle. There is a moderate positive correlation between TFP and stock prices conditional on these series, but there is little obvious correlation with the business cycle. This component explains most of the variation in stock prices, but almost none in TFP. Short run technology shocks are more important for explaining the cycle on all these measures.

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Thus, our estimates fail to reproduce some of Beaudry and Portier’s results. In particular, while we …nd that the e¤ects of news shocks are somewhat similar to those of long run technology shocks, we come nowhere close to the really striking B-P result that the e¤ects of the two types of shocks is virtually identical. But besides striking, B-P’s claims about the e¤ects of news shocks are rather theoretically surprising. If we could isolate news about technology shocks from all other forms of important economic news, we might expect that the e¤ects of such news would match the e¤ects of long-run-identi…ed technology. But otherwise it is di¢ cult to see theoretical reasons to expect that the two types of shocks should yield nearly identical impulse response functions. Therefore, we …nd the B-P results about the e¤ects of long run technology shocks much more important than their headline result about technology and news. Especially for our purposes in this paper, what matters in the B-P results is their evidence that technological change does, indeed, appear to play an important role in driving the business cycle.

7

Comparing Galí and B-P speci…cations

Beaudry and Portier …nd that the shock they identify in the short run as a¤ecting only stock prices is highly correlated with the long run shock to TFP (around 0:97). In this section we compare that correlation (the BP comparison) with those arising from our estimations to check how close we are from the shocks identi…ed by BP. Additionally, we also compare the correlation between the shocks to technology both in the short and long run (the SR-LR comparison). This analysis is done for both Galí and BP speci…cations. For the Galí speci…cation we …nd a strong negative correlation between the short run nontechnology shock and the long run technology shock ( 0:43). However, technology shocks in the short and long run are highly correlated (0:90): These results also appear if we compare the impulse response functions. The BP comparison impulse responses yield completely di¤erent images: the short run nontechnology shock makes productivity and hours go permanently in opposite directions, whereas the long run technology shock makes productivity go up but hours go temporarily down. Regarding the SR-LR comparison, the shape of the impulse responses is similar.

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When the same analysis is applied to our BP speci…cation we …nd a strong positive correlation in the BP comparison (0:5696). However, the correlation is even higher, for the BP series, if we do the SR-LR comparison (0:8165). Thus in the short run identi…cation, it seems that both technology and nontechnology shocks matter. Regarding the impulse response functions, the BP comparison replicates BP’s result that a shock to stock prices in the short run has a long term impact on productivity. And so does the long run technology shock. Furthermore, the SR-LR comparison shows again very similar shapes to those impulse response functions in BP comparison. That is, there is not such a big di¤erence between short run shocks or long run shocks with respect to the e¤ects on productivity in the long run.

7.1

Reversing the productivity speci…cations

Before turning to the 3x3 VAR results, we check for robustness with respect to another important di¤erence between the Galí and B-P speci…cations.5 First, we investigate the changing the productivity variable. We run the same exercise as Galí but using TFP instead of labor productivity. Remarkably, this apparently small speci…cation change overturns Galí’s main result. We …nd that using TFP implies that hours rise following a positive productivity shock, with a short lag, starting from an impact e¤ect of approximately zero. Also, while we cannot legitimately construct GDP from TFP and hours alone, we can get a rough idea of the importance of technology and nontechnology shocks for the business cycle by looking at how each shock component explains the cyclical ‡uctuations of their product, TFP*hours, which is what is called GDP in the table. Using TFP substantially increases the importance of technology shock for the business cycle, both for the short run and the long run identi…cations (though in the long run identi…cation the nontechnology shock remains more important than the technology shock for output ‡uctuations). A possible explanation is that since TFP follows the cycle more closely than labor productivity, it is easier for the component which is identi…ed as the cause of productivity improvements also to pick up business cycle ‡uctuations. 5 The other speci…cation di¤erence that could be important is the use of DVARs versus LVARs. But we will not try this here, since it is already well known from Christiano et al. that running Galí’s estimates with an LVAR eliminates the fall in hours after a technology shock. On the other hand, running Beaudry and Portier’s estimate with a DVAR has little e¤ect on their results. We will report exercises like these in the 3x3 case below.

15

Next, we do the opposite with Beaudry and Portier’s speci…cation, that is, we run their VAR using labor productivity instead of TFP. The results show that the long run technology shock is more successful than any of the other shocks at picking up the business cycle. The estimation results for all the other three shocks are also qualitatively similar to what we found with TFP. Using labor productivity tends to strengthen our …nding, contrary to B-P, that the short run technology shock is more similar to the long run technology shock than the news shock is. Nonetheless, what we regard as the most important …nding in this framework, that longrun-identi…ed technology shocks are an important driving force for the business cycle, remains true.

8

Estimating the 3x3 VAR

Given the apparently contradictory results of the Galí and BP VARs, the obvious next step is to combine both estimation strategies by running a trivariate VAR in productivity, hours and stock prices. We will estimate 3x3 structural VARs of the following form: 2 3 2 3 2 3 2 3 xt xt 1;t 1;t 4 yt 5 = (L) 4 2;t 5 4 yt 5 = (L) 4 2;t 5 or zt zt 3;t 3;t

where now we add a new variable (stock prices for the case of Galí, or hours for the case of Beaudry and Portier), and therefore must also identify a new shock,

3;t .

As in the sections above,

we mechanically proceed to see what happens under two alternative identi…cation methods: short run and long run Cholesky decompositions. The short run identi…cation will yield three shocks that we denote

sr ; sr ; sr 0 , 1;t 2;t 3;t

and the shocks from the long run identi…cation will be written as

lr ; sr ; lr 0 : 1;t 2;t 3;t

Apart from the set of variables considered, we have seen that there are only three di¤erences between the Galí and B-P speci…cations. First, Galí runs VARs in di¤erences (DVARs), whereas Beaudry and Portier run VARs in levels (LVARs) or VECMs. Since Beaudry and Portier argue that they obtain essentially the same results from LVARs and VECMs, for now we will focus on LVARs. Second, the productivity variable used by Galí is labor productivity (LP), whereas Beaudry and Portier use TFP. Third, while Galí uses a total hours variable, Beaudry and Portier express their (real) stock price series in per capita terms. To avoid inconsistencies between our 16

treatments of hours and stock prices, we will either run both of these series in per capita terms, or neither. (For TFP and LP, population cancels from the numerator and the denominator, so there is no di¤erence between per capita and total speci…cations.) Table 2: 3x3 VAR speci…cations

BENCHMARK 3x3 VARs: Gali 3x3 benchmark (Figs. 9-10) BP 3x3 benchmark (Figs. 11-12) ALTERNATIVE 3x3 VARs: 1: Like Galí, but LVAR (Figs. 13-14) 2: Like BP, but DVAR (Figs. 15-16) 3: Like Galí, but TFP (Figs. 17-18) 4: Like BP, but LP (Figs. 19-20)

DVAR vs. LVAR

Productivity variable

Per capita?

RESULTS:

di¤erences levels

LP TFP

no yes

Like Gali 2x2 Like BP 2x2

levels di¤erences di¤erences levels

LP TFP TFP LP

no yes no yes

Like BP, and Christiano et. al. (2003) Like BP Like BP Long run tech like BP

Table 2 lists the most interesting speci…cations we estimate. The estimation results are shown in Figures 7-18. Additional information is given by Tables 5-10, where we report a variance decomposition (in sample) of the HP-cyclical components of each series in each VAR. The …rst speci…cation is a 3x3 extension of Galí’s 2x2 estimates. That is, it is a DVAR in labor productivity, hours, and stock prices: [

log(labprod);

log(hours);

log(SP 500)]

where neither hours nor stock prices are expressed in per capita terms. We run the DVAR with four lag terms (so that implicitly there are …ve lags in the levels speci…cation.) Figure 7 shows impulse response functions from the long-run identi…cation of this VAR. The left panels show the e¤ects of a shock to productivity, and the right panels show the e¤ects of a shock to hours. From the left panels (a long run shock to productivity), we see that Galí’s main result is reproduced: a long run positive shock to productivity drives hours down in the short run. Interestingly, there is an important similarity to BP’s results as well: the long run technology shock also causes a persistent rise in stock prices. The HP cyclical component of the time series caused by these shocks are shown in the top panel of Figure 8. Although the productivity and stock price series exhibit strong ‡uctuations at most recognized business cycle dates, the movement in hours is strongly negatively correlated with the other two variables. The hours 17

component is also strongly negatively correlated with the HP cyclical component of GDP (which is not shown, but can be constructed by adding the cyclical components of hours and labor productivity). Thus, this component of the series is inconsistent with the most basic cyclical stylized facts. Instead, most of the business cycle component is picked up by the long run shock to hours, which is shown in the right panels of Figure 7. This shock causes productivity to rise temporarily, accompanied by persistent increases in productivity and stock prices. In the bottom panel of Figure 8, we see that this shock tracks the business cycle closely for all three series. The variance decomposition shows that the long run shock to hours explains almost all cyclical variation in hours, and also most of the cyclical variation in GDP. The third long-run shock, by contrast, mostly a¤ects stock prices, picking up a low-frequency stock price residual (falling in the 1970s, rising in the 1990s) with little e¤ect on the other two variables and little role in the cycle. In summary, the results of Galí’s two-variable VAR are closely mimicked by the …rst two shocks identi…ed in this three-variable VAR. Our second speci…cation is a 3x3 generalization of Beaudry and Portier’s estimates. In other words, it is an LVAR in TFP, hours per capita, and stock prices per capita: [log(T F P ); log(hours per capita); log(SP 500 per capita)] The results are shown in Figures 9 and 10. We focus on the same comparison made by Beaudry and Portier: the e¤ects of the "news" shock which, in the short run, a¤ects stock prices only; and the e¤ects of the "technology" shock which is the only shock that a¤ects TFP in the long run. As Beaudry and Portier claim, the short-run "news" shock (left panels of Figure 9) has very similar impulse response functions to the long-run "technology" shock (right panels). In particular, both shocks cause highly persistent increases in TFP, hours, and stock prices. Moreover, in contrast to Galí, the long-run technology shock generates positively-correlated ‡uctuations in all three series at recognized business cycle dates. Likewise, the news shock causes positivelycorrelated ‡uctuations in the three series at business cycle dates, though its contribution to the variance decomposition falls mostly on stock prices. Also, in contrast to Beaudry and Portier’s

18

reported results but consistent with our …ndings for the 2x2 Beaudry-Portier speci…cation, we …nd that the short-run technology shock short-run news shock

sr 3

sr 1

generates a stronger cyclical component than the

does.

Thus, running a 3x3 generalization of the Beaudry-Portier VAR allows us to identify two series,

lr 1

and

sr , 3

with roughly the same properties as the "technology" and "news" shocks

identi…ed in a 2x2 Beaudry-Portier VAR. And, in particular, this way of identifying the longrun technology shock contradicts the claims of Galí, because it shows that a positive technology shock causes hours to rise. Thus, it cannot be the set of variables considered, by itself, that explains the di¤erence between the Galí and B-P results: we can obtain either paper’s results in a 3x3 VAR including productivity, hours, and stock prices. So we next ask which remaining di¤erences between the Galí and B-P speci…cations explain their contrasting results.

8.1

Explaining the di¤erences between the Galí and BP results

The estimates shown in Figures 7 and 8, where technology shocks drive hours down, come from a DVAR in labor productivity, hours, and stock prices. The estimates in Figures 9 and 10, where technology shocks increase hours, come from an LVAR in TFP, hours per capita, and stock prices per capita. We have checked whether the use of total or per capita series has any important e¤ect on the results. The answer is no, so we save space by not showing these uninteresting variations. The interesting variations come from comparing DVARs with LVARs, or from exchanging TFP for labor productivity. Therefore (as Table 2 indicates) we analyze these cases in detail. First, in Figures 11 and 12, we try running a speci…cation (called "Alternative 1") which is identical to our 3x3 Galí baseline, except that we run the estimation in levels instead of di¤erences. As we see from the …gures, the results are completely di¤erent from those of the Galí baseline. After a positive technology shock (an increase in

lr ) 1

labor hours are initially

approximately unchanged, but after a lag we …nd persistent positive e¤ects on all three variables. The HP cyclical components of the series implied by these shocks are strongly positively correlated with movements at NBER business cycle dates. By contrast, the second long-run shock,

lr , 2

leads to ‡uctuations unrelated to business cycle dates in which hours move in the

opposite direction from productivity and stock prices. Unlike in the Galí 3x3 benchmark, the 19

second shock contributes relatively little to the ‡uctuations in hours. These results should not be surprising: Christiano, Eichenbaum, and Vigfusson (2003) already showed that estimated technology shocks have a positive, lagged impact on hours when Galí’s estimates are run as LVARs instead of DVARs. Thus our …ndings simply serve to con…rm that this remains true when when stock prices are also included in the estimation. Second, our "Alternative 2", in Figures 13 and 14 and Table 8, is identical to our 3x3 Beaudry-Portier baseline, except that we run the VAR in di¤erences. Note that the results are very similar to those we found in Figues 9 and 10. In other words, the results of Beaudry and Portier are largely unchanged by running in di¤erences instead of levels. Our main result is seen in "Alternative 3", illustrated by Figures 15 and 16 and Table 9. This case is identical to the Galí baseline, except that the …rst variable in the VAR is TFP instead of labor productivity. Remarkably, the results are almost identical to those of our 3x3 Beaudry-Portier speci…cations (both the LVAR and the DVAR). A positive long-run technology shock causes productivity, hours, and stock prices to rise permanently (with a lag in the case of hours). The long-run technology shock play an important role in generating recognized business cycle events. In the variance decomposition, the long-run technology shock generates much of the cyclical variance in TFP and output and a nontrivial part of that of hours. Finally, the e¤ects of the long-run technology shock are similar to those of the short run news shock

sr , 3

though again the news shock contributes less to GDP ‡uctuations than the short run technology shock does. By contrast, replacing TFP by labor productivity in the Beaudry-Portier speci…cation has a less dramatic e¤ect, at least on the long-run identi…cation. This speci…cation is called "Alternative 4", shown in Figures 17 and 18 and Table 10. We see that long-run technology shocks still have permanent positive e¤ects on all three variables (with a lag, as usual, in the case of hours). The cumulated time series show that these shocks pick up a substantial part of the business cycle (the ‡uctuations in hours are weak, but go in the right direction). On the other hand, the impulse response functions associated with the short run news shocks change substantially when we use labor productivity instead of TFP: the impact on productivity is nonmonotonic. Also, in the cumulated time series implied by this shock, productivity and

20

hours are negatively correlated. Thus, one striking result of Beaudry and Portier— the similarity between the long run technology shock and the short run news shock— is overturned by replacing TFP with labor productivity. But for the purposes of this paper, the more important result of Beaudry and Portier is the claim that long run technological improvements have a positive impact on labor and are important for the business cycle. This result is obtained regardless of whether TFP or LP is used.

9

Summary

Main …ndings of 2x2 VAR analysis: All LVAR estimations: long run tech improvement INCREASES hours (like Christiano et al. 2003) All TFP estimations: long run tech improvement INCREASES hours Only case where long run tech improvement makes hours FALL is DVAR with labor productivity Perhaps because labor productivity is much less cyclical than TFP? Main …ndings of 3x3 VAR analysis: 3x3 DVAR with labor productivity reproduces Galí 3x3 LVAR with TFP reproduces Beaudry-Portier All estimations: long run tech improvement causes permanent rise in stock prices All LVAR estimations: long run tech improvement INCREASES hours (like Christiano et al. 2003) All TFP estimations: long run tech improvement INCREASES hours Only case where long run tech improvement makes hours FALL is DVAR with labor productivity

21

Perhaps because labor productivity is much less cyclical than TFP? Changing order of last two variables in VAR is irrelevant

22

References Altig, D., L. J. Christiano, M. Eichenbaum, and J. Linde. 2002. “Technology shocks and aggregate ‡uctuations.” Mimeo. Basu, S., J. G. Fernald, and M. S. Kimball. 2004. “Are technology improvements contractionary?.” Harvard Institute of Economic Research Discussion Paper, 1986. Beaudry, P. and F. Portier. 2004. “Stock prices, news, and economic ‡uctuations.” NBER Working Paper, 10548. Beaudry, P. and F. Portier. 2004. “When can changes in expectations cause business cycle ‡uctuations in neoclassical settings?.” NBER Working Paper, 10776. Beaudry, P. and F. Portier. 2005. “News view: from Japanese and US data.” NBER Working Paper 11496. Blanchard, O.J. and D. Quah. 1989. “The dynamic e¤ects of aggregate demand and supply disturbances.” American Economic Review, 79 (4), September: 655-673. Blanchard, O.J., R. Solow and B.A. Wilson. 1995. “Productivity and unemployment.”Mimeo. Chari, V. V., P. J. Kehoe, and E. R. McGrattan. 2005. “A critique of structural VARs using real business cycle theory.” Federal Reserve Bank of Minneapolis Working Paper, 631. Chari, V. V., P. J. Kehoe, and E. R. McGrattan. 2005. “Business cycle accounting.” Federal Reserve Bank of Minneapolis Sta¤ Report, 328. Christiano, L. J., M. Eichenbaum, and R. Vigfusson. 2003. “What happens after a technology shock?.” Mimeo. Christiano, L. J., M. Eichenbaum, and R. Vigfusson. 2004. “The response of hours to a technology shock: evidence based on direct measures of technology.”NBER Working Paper 10254. Cooley, T.F. and M. Dwyer. 1998. “Business cycle analysis without much theory: a look at structural VARs.” Journal of Econometrics, 83: 57-88. Fisher, J. 2003. “Technology shocks matter.” Federal Reserve Bank of Chicago. Mimeo. Francis, N. 2001. “Sectoral technology shocks revisited,” mimeo, Lehigh University. Francis, N. and V. A. Ramey. 2003a. “Is the technology-driven real business cycle hypothesis dead? Shocks and aggregate ‡uctuations revisited.” Mimeo. Francis, N. and V. Ramey .2003b. “The source of historical economic ‡uctuations: an analysis using long run restrictions,” forthcoming in NBER International Seminar on Macroeconomics 2004, Clarida, Frankel and Giavazzi editors.

23

Franco, F. and T. Philippon. 2004. “Firms and aggregate dynamics,” mimeo. Galí, J. 1999. “Technology, employment, and the business cycle: do technology shocks explain aggregate ‡uctuations.” American Economic Review, 89 (1), March: 249-271. Galí, J. 2004. “On the role of technology shocks as a source of business cycles: some new evidence.”Journal of the European Economic Association, 2 (2-3) Papers and Proceedings: 372-380. Galí, J. 2005. “Trends in hours, balanced growth, and the role of technology in the business cycle.” Federal Reserve Bank of St. Louis Review, 87(4), July/August: 459-86. Galí, J. and P. Rabanal. 2004. “Technology shocks and aggregate ‡uctuations: how well does the RBC model …t postwar US data?.” NBER Working Paper, 10636. Greenwood, J., Z. Hercowitz, and P. Krusell. 2000. “The role of investment-speci…c technical change in the business cycle.” European Economic Review, 44: 91-115. Greenwood, J. and B. Jovanovic. 1999. “The IT revolution and the stock market.”C.V. Starr Center for Applied Economics Research Report, 99-02. Jovanovic, B. and P. L. Rousseau. 2000. “Technology and the stock market: 1885-1998.” Mimeo. Kiley, M. T. 1997. “Labor productivity in U.S. manufacturing: does sectoral co-movement re‡ect technology shocks?” Federal Reserve Board, unpublished manuscript. King, R. G., C. I. Plosser, and S. Rebelo. 1988. “Production, growth and the business cycles. II. New directions,” Journal of Monetary Economics, 21: 309-341. Kydland, F. E. and E. C. Prescott. 1982. “Time to build and aggregate ‡uctuations,” Econometrica, 50(6): 1345-70. Lettau, M. and S. C. Ludvigson. 2004. “Understanding trend and cycle in asset values: reevaluating the wealth e¤ect on consumption.” American Economic Review, 94 (1), March: 276-299.

24

A A.1

Tables Variance decomposition of HP cyclical components: 2x2 VAR Table 1: Galí’s speci…cation Variance decomposition: SR identi…cation shock 1 shock 2 LABPROD 0:766 0:211 HOURS 0:090 0:755 GDP 0:348 0:450 Variance decomposition: LR identi…cation shock 1 shock 2 LABPROD 0:532 0:355 HOURS 0:045 0:924 GDP 0:060 0:864

Table 2: Beaudry and Portier’s speci…cation Variance decomposition: SR identi…cation shock 1 shock 2 TFP 0:888 0:149 S&P500 0:040 0:996 R2 GDP 0:54 0:251 Variance decomposition: LR identi…cation shock 1 shock 2 TFP 0:916 0:157 S&P500 0:493 0:506 R2 GDP 0:739 0:043

25

Table 3: Galí’s speci…cation with TFP Variance decomposition: SR identi…cation shock 1 shock 2 TFP 0:804 0:120 HOURS 0:231 0:504 GDP 0:497 0:276 Variance decomposition: LR identi…cation shock 1 shock 2 TFP 0:630 0:223 HOURS 0:069 0:735 GDP 0:248 0:529

Table 4: Beaudry and Portier’s speci…cation with LP Variance decomposition: SR identi…cation shock 1 shock 2 LABPROD 0:873 0:058 S&P500 0:040 0:939 2 R GDP 0:279 0:161 Variance decomposition: LR identi…cation shock 1 shock 2 LABPROD 1:01 0:187 S&P500 0:235 0:590 R2 GDP 0:464 0:079

26

A.2

Variance decomposition of HP cyclical components: 3x3 VAR Table 5: Galí’s speci…cation Variance decomposition: SR identi…cation shock 1 shock 2 shock 3 LABPROD 0:737 0:164 0:067 HOURS 0:040 0:604 0:193 S&P500 0:022 0:062 0:971 GDP 0:261 0:345 0:171 Variance decomposition: LR identi…cation shock 1 shock 2 shock 3 LABPROD 0:569 0:252 0:064 HOURS 0:033 0:850 0:184 S&P500 0:016 0:466 0:900 GDP 0:065 0:752 0:163

Table 6: Beaudry and Portier’s speci…cation Variance decomposition: SR identi…cation shock 1 shock 2 shock 3 TFP 0:652 0:229 0:179 HOURS 0:044 0:451 0:309 S&P500 0:029 0:082 0:923 GDP 0:341 0:221 0:298 Variance decomposition: LR identi…cation shock 1 shock 2 shock 3 TFP 0:642 0:156 0:192 HOURS 0:092 0:611 0:333 S&P500 0:323 0:149 0:910 GDP 0:352 0:277 0:320

27

Table 7: Alternative 1 (Galí, but LVAR) Variance decomposition: SR identi…cation shock 1 shock 2 shock 3 LABPROD 0:827 0:057 0:053 HOURS 0:074 0:510 0:289 S&P500 0:046 0:043 0:906 GDP 0:334 0:298 0:237 Variance decomposition: LR identi…cation shock 1 shock 2 shock 3 LABPROD 0:840 0:070 0:051 HOURS 0:120 0:269 0:296 S&P500 0:115 0:297 0:891 GDP 0:434 0:156 0:237

Table 8: Alternative 2 (BP, but DVAR) Variance decomposition: SR identi…cation shock 1 shock 2 shock 3 TFP 0:722 0:088 0:122 HOURS 0:128 0:433 0:217 S&P500 0:036 0:029 0:987 GDP 0:453 0:167 0:202 Variance decomposition: LR identi…cation shock 1 shock 2 shock 3 TFP 0:661 0:088 0:128 HOURS 0:096 0:591 0:230 S&P500 0:204 0:290 1:03 GDP 0:353 0:295 0:213

28

Table 9: Alternative 3 (Galí, but TFP) Variance decomposition: SR identi…cation shock 1 shock 2 shock 3 TFP 0:716 0:101 0:116 HOURS 0:134 0:439 0:197 S&P500 0:035 0:041 0:994 GDP 0:455 0:178 0:186 Variance decomposition: LR identi…cation shock 1 shock 2 shock 3 TFP 0:628 0:118 0:112 HOURS 0:080 0:652 0:186 S&P500 0:178 0:263 0:942 GDP 0:319 0:339 0:176

Table 10: Alternative 4 (BP, but LP) Variance decomposition: SR identi…cation shock 1 shock 2 shock 3 LABPROD 0:783 0:124 0:059 HOURS 0:070 0:562 0:193 S&P500 0:040 0:072 0:909 GDP 0:307 0:347 0:188 Variance decomposition: LR identi…cation shock 1 shock 2 shock 3 LABPROD 0:234 0:393 0:062 HOURS 0:123 0:774 0:192 S&P500 0:650 0:247 0:874 GDP 0:092 0:857 0:187

29

B

Galí’s identi…cation -3

Technology shock 0.01

1

x 10

Nontechnology shock

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

0.008

-1 0.006 -2 0.004 -3 0.002 0

-4

0

5

10 PTY

15

-5

20

-3

7

x 10

0.015

6 5

0.01

4 3 0.005

2 1 0

0

5

10 HOURS

15

0

20

Figure 1: Impulse response functions: technology and nontechnology shocks, short run identi…cation. -3


5

x 10

Nontechnology shock

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

4

0.008

3 0.006 2 0.004 1 0.002 0

0

0

5

10 PTY

15

-1

20

-3

0

x 10

0.02

-0.5 0.015

-1 -1.5

0.01 -2 -2.5

0.005

-3 -3.5

0

5

10 HOURS

15

0

20

Figure 2: Impulse response functions: technology and nontechnology shocks, long run identi…cation.

30

Conditional on LR tech: predicted CYCLE of PTY (solid), HOURS(dash) 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 1940

1950

1960

1970

1980

1990

2000

2010

Conditional on LR NONtech: predicted CYCLE of PTY (solid), HOURS(dash) 0.04 0.02 0 -0.02 -0.04 -0.06 1940

1950

1960

1970

1980

1990

2000

Figure 3: HP cyclical components, long run identi…cation.

31

2010

C

Beaudry and Portier’s identi…cation -3


6

0.01

5

0.008

4

0.006

3

0.004

2

0.002

1

0

0

5

10 PTY

15

0

20

0.02

x 10

Nontechnology shock

0

5

10 PTY

15

20

0

5

10 SP500

15

20

0.1 0.08

0.015

0.06 0.01 0.04 0.005

0

0.02

0

5

10 SP500

15

0

20

Figure 4: Impulse response functions: technology and nontechnology shocks, short run identi…cation. -3


0

0.012

-1

0.01

x 10

Nontechnology shock

0

5

10 PTY

15

20

0

5

10 SP500

15

20

-2

0.008 -3 0.006 -4

0.004

-5

0.002 0

0

5

10 PTY

15

-6

20

0.06

0.07

0.05

0.06 0.05

0.04

0.04 0.03 0.03 0.02

0.02

0.01 0

0.01 0

5

10 SP500

15

0

20

Figure 5: Impulse response functions: technology and nontechnology shocks, long run identi…cation.

32

Conditional on SR NONshock: predicted CYCLE of PTY (solid), SP500(dash) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 1950

1960

1970

1980

1990

2000

2010

Conditional on LR tech: predicted CYCLE of PTY (solid), SP500(dash) 0.2 0.1 0 -0.1 -0.2 -0.3 1950

1960

1970

1980

1990

2000

2010

Figure 6: HP cyclical components. Top panel: short run identi…cation. Bottom panel: long run identi…cation.

33

D

3x3 VAR -3

8

x 10

-3

Shock to productiv ity 4

6

Shock to hours

x 10

2

4 0

2 0

0

5

10 PTY

-3

0

x 10

15

-2

20

0.01

-2

0.005

0

5

10 HOURS

15

0

20

0.015

0.06

0.01

0.04

0.005

0.02

0

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

5

10 S&P500

15

20

0.015

-1

-3

0

5

10 S&P500

15

0

20

Figure 7: Gali”s speci…cation, 3x3 VAR. Both panels: long run identi…cation. Conditional on LR tech: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.04

0.02

0

-0.02

-0.04 1950

1960

1970

1980

1990

2000

2010

Conditional on 2nd LR shock: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 1950

1960

1970

1980

1990

2000

Figure 8: HP cyclical components, long run identi…cation.

34

2010

-3

6

x 10

Shock to stock prices

Shock to productiv ity 0.015

4

0.01

2

0.005

0

0

5

10 PTY

15

0

20

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

5

10 S&P500

15

20

-3

0.01

6

x 10

4 0.005

2 0

0

0

5

10 HOURS

15

-2

20

0.08

0.06

0.06

0.04

0.04 0.02

0.02 0

0

5

10 S&P500

15

0

20

Figure 9: Beaudry and Portier”s speci…cation, 3x3 VAR. Left panel: short run identi…cation. Right panel: long run identi…cation. Conditional on 3rd SR shock: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 1950

1960

1970

1980

1990

2000

2010

Conditional on LR tech: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 1950

1960

1970

1980

1990

2000

2010

Figure 10: HP cyclical components. Top panel: short run identi…cation. Bottom panel: long run identi…cation.

35

E

Alternative speci…cations -3


0

0.02

-1

0.01

-2

0

0

5

10 PTY

15

-3

20

8

0.015

6

0.01

4

0.005

2 0

5

10 HOURS

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

5

10 S&P500

15

20

-3

0.02

0

Shock to hours

x 10

15

0

20

0.06

x 10

0 -0.01

0.04

-0.02 0.02 0

-0.03 0

5

10 S&P500

15

-0.04

20

Figure 11: Alternative speci…cation 1. Both panels: long run identi…cation. Conditional on LR tech: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.1

0.05

0

-0.05

-0.1 1950

1960

1970

1980

1990

2000

2010

Conditional on 2nd LR shock: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 1950

1960

1970

1980

1990

2000

2010

Figure 12: HP cyclical components. Alternative speci…cation 1. Both panels: long run identi…cation.

36

-3

6

x 10



4 0.005 2 0

0

5

10 PTY

15

0

20

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

5

10 S&P500

15

20

-3

0.01

6

x 10

4 0.005

2 0

0

0

5

10 HOURS

15

-2

20

0.1

0.04 0.03

0.05

0.02 0.01

0

0

5

10 S&P500

15

0

20

Figure 13: Alternative speci…cation 2. Left panels: short run identi…cation. Right panels: long run identi…cation. Conditional on 3rd SR shock: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 1950

1960

1970

1980

1990

2000

2010


1960

1970

1980

1990

2000

2010

Figure 14: HP cyclical components. Alternative speci…cation 2. Top panel: short run identi…cation. Bottom panel: long run identi…cation.

37

-3

4

x 10



3 2

0.005

1 0

0

5

10 PTY

15

0

20

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

5

10 S&P500

15

20

-3

0.01

6

x 10

4 0.005

2 0

0

0

5

10 HOURS

15

-2

20

0.1

0.04 0.03

0.05

0.02 0.01

0

0

5

10 S&P500

15

0

20


1960

1970

1980

1990

2000

2010


1960

1970

1980

1990

2000

2010


38

-3

3

x 10



2

0.02

1 0.01

0 -1

0

5

10 PTY

15

0

20

0

5

10 PTY

15

20

0

5

10 HOURS

15

20

0

5

10 S&P500

15

20

-3

0.01

4

x 10

2 0.005 0 0

0

5

10 HOURS

15

-2

20

0.08

0.06

0.06

0.04

0.04 0.02

0.02 0

0

5

10 S&P500

15

0

20


1960

1970

1980

1990

2000

2010

Conditional on LR tech: predicted CYCLE of PTY (solid), HOURS(dash), S&P500(dots) 0.1

0.05

0

-0.05

-0.1 1950

1960

1970

1980

1990

2000

2010


39