Stock Prices, News, and Economic Fluctuations: Comment By André Kurmann and Elmar Mertens Beaudry and Portier (2006) propose an identi…cation scheme to study the e¤ ects of news shocks about future productivity in vector error correction models (VECMs). This comment shows that, when applied to their VECMs with more than two variables, the identi…cation scheme does not have a unique solution. The problem arises from a particular interplay of cointegration assumptions and long-run restrictions. In a highly in‡uential paper, Beaudry and Portier (2006) estimate vector error correction models (VECMs) on U.S. data and …nd that shocks generating a stock market boom but no contemporaneous movement in total factor productivity (T F P ) — henceforth called T F P news — are closely related to shocks driving long-run variations in T F P . Moreover, these T F P news lead to increases in consumption, investment, output, and hours on impact and constitute an important source of business-cycle ‡uctuations. These results run counter to basic dynamic stochastic general equilibrium models and have sparked a new literature attempting to generate news-driven positive comovement among macroeconomic aggregates.1 This comment shows that, in the VECMs with more than two variables estimated by Beaudry and Portier (2006), their identi…cation scheme fails to determine T F P news. Yet these higher-dimension systems are crucial to quantify the business-cycle e¤ects of T F P news.2 The identi…cation problem arises from the interplay of two assumptions. First, the Beaudry-Portier identi…cation scheme, called BP restrictions from here on, requires that one of the non-news shocks has no permanent impact on either T F P or consumption. Second, the VECMs estimated by Beaudry and Portier (2006) impose that T F P and consumption are cointegrated. This cointegration means that T F P and consumption have the Kurmann: Drexel University, LeBow College of Business, School of Economics, 3220 Market Street, Philadelphia, PA 19104 (email:
[email protected]); Mertens: Federal Reserve Board, Division of Monetary A¤airs, 20th Street and Constitution Avenue NW, Washington, DC 20551 (email:
[email protected]). We thank two anonymous referees, Paul Beaudry, Christopher Gust, David López-Salido and Franck Portier for comments on earlier drafts of the paper. We also thank Christopher Karlsten for editing assistance. The views expressed in this paper do not necessarily represent the views of the Federal Reserve System or the Federal Open Market Committee. The authors declare that they have no relevant material or …nancial interests that relate to the research described in this paper. 1 See, for example, Beaudry and Portier (2007), Den Haan and Kaltenbrunner (2009), Jaimovich and Rebelo (2009), or Schmitt-Grohé and Uribe (2012). 2 An equally important reason to work with systems in more than two variables is robustness. If the economy is complicated even in simple ways, then the types of bivariate systems that Beaudry and Portier (2006) use for their baseline analysis are likely to generate inaccurate answers. See Faust and Leeper (1997) for an example in another context. Moreover, adding variables to the information set mitigates the invertibility/fundamentalness problem highlighted in Fernàndez-Villaverde et al. (2007) or Leeper, Walker, and Yang (2013). 1
2
THE AMERICAN ECONOMIC REVIEW
MONTH YEAR
same permanent component, which makes one of the two long-run restrictions redundant and leaves an in…nity of candidate solutions. The results reported in Beaudry and Portier (2006) represent just one arbitrary choice among these solutions.3 Numerical analysis reveals that the range of business-cycle ‡uctuations implied by the candidate solutions is very large, with some solutions re‡ecting the results reported in Beaudry and Portier (2006) and other solutions being unrelated to T F P and generating a prolonged downturn in consumption, investment, and hours. Moreover, simulations in the working paper version of this comment (Kurmann and Mertens, 2013) show that the identi…cation problem cannot be resolved by dropping the cointegration restrictions and instead estimating a vector autoregressive (VAR) system in levels. The problem persists because the bootstrapped distribution for the estimated VAR parameters implies with about a 50 percent chance that T F P and consumption are cointegrated, in which case the BP restrictions fail to identify T F P news. The identi…cation scheme and results presented in Beaudry and Portier (2006) therefore do not shed light on the importance of T F P news shocks for business cycles. The remainder of the comment proceeds as follows: Section 1 explains the identi…cation problem. Section 2 illustrates the signi…cance of the problem by mapping out the range of possible solutions implied by the BP restrictions. Section 3 concludes by describing alternative identi…cation strategies of T F P news in the literature that are not subject to the identi…cation problem. I.
The identi…cation problem
Beaudry and Portier (2006) estimate bivariate, three-variable, and four-variable VECMs in T F P ; a real stock market price (SP ); consumption (C ); hours (H ); and investment (I ). These VECMs can be expressed in vector moving-average form as 2 3 T F Pt 4 SPt 5 = Yt = C(L) t , (1) Xt
where Xt is empty for the bivariate case, Xt = [ Ct ] for the trivariate case, and Xt = [ Ct Ht ]0 or Xt = [ Ct It ]0 for the four-variable variables Pcase. All i is inferred are logged and detrended. The lag polynomial C(L) I + 1 C L i=1 i from the VECM parameter estimates; the vector t contains the one-periodahead prediction errors and has variance covariance matrix E[ t 0t ] = .4 3 The replication …les posted on the American Economic Review website do not include code showing how T F P news were computed by Beaudry and Portier (2006). In private communication, we learned from the authors that their computations relied on a numerical solver that arbitrarily picked one of the in…nite number of candidate solutions. 4 An online appendix available on the American Economic Review website provides details of all derivations and computations.
VOL. VOL NO. ISSUE
COMMENT ON BEAUDRY AND PORTIER (2006)
3
Crucially, the VECM imposes a set of cointegration restrictions 0 Yt I(0), where denotes the matrix of cointegrating vectors. As discussed by King et al. (1991) and Hamilton (1994), cointegration imposes restrictions on C(L). In particular, since 0 Yt is stationary, 0 C(1) = 0, and thus C(1) is singular. This singularity constrains the set of linearly independent restrictions that can be imposed on the VECM to identify structural shocks. The identi…cation problem arising with the BP restrictions stems from these constraints.5 Identi…cation maps t to structural shocks "t by t = 0 "t , with E["t "0t ] = I and thus 0 00 = . Impulse responses to the structural shocks are then given by (L) = C(L) 0 . Beaudry and Portier’s (2006) original idea is that news about future T F P do not have a contemporaneous e¤ect on measured T F P ; i.e., if the T F P news innovation is the second element of "t , then the (1; 2) element of 0 is zero. For the bivariate systems that Beaudry and Portier (2006) use as their baseline case, this restriction, together with 0 00 = , uniquely identi…es T F P news. The identi…cation problem arises in the three- and four-variate systems in which one zero restriction is no longer su¢ cient to identify structural shocks. Beaudry and Portier’s (2006) strategy consists of adding zero restrictions until identi…cation is achieved. In the trivariate case, these additional restrictions are that one of the non-news shocks has no permanent e¤ect on T F P and C , so when this non-news shock is the third element of "t , the (1; 3) and (3; 3) elements of the long-run impact matrix (1) C(1) 0 are zero. In the four-variable case, the additional restrictions consist of the same two long-run restrictions plus the assumption that one of the other non-news shocks can have only a contemporaneous e¤ect on H and I , respectively, so when this other non-news shock is the fourth element of "t , the (1; 4), (2; 4), and (3; 4) elements of 0 are zero. In a typical VAR, the additional zero restrictions, together with the zero-impact restriction on T F P and 0 00 = , would be su¢ cient to uniquely identify all elements of 0 and thus T F P news. Here, this is, unfortunately, not the case because the three- and four-variable VECMs estimated by Beaudry and Portier (2006) are subject to two and three cointegration restrictions, respectively; i.e., 0 is a (2 3) matrix and a (3 4) matrix of linearly independent rows, respectively.6 Since 0 C(1) = 0, the rows of C(1) and (1) are linearly dependent on each other. In fact, given the number of cointegrating relationships, C(1) and (1) are just of rank 1, and only one linearly independent restriction can be imposed on (1). One of the two long-run zero restrictions is therefore redundant, leaving 0 and 5 The implications of cointegrating relationships for structural identi…cation are also discussed by Lütkepohl (2008) and Lucke (2010). However, they do not consider particular examples. 6 See Footnote 8 and the notes to Figures 9 and 10 in Beaudry and Portier (2006) for the number of cointegration restrictions imposed. The notes to the Figures also state that four-variable VECMs with three (or four) cointegration restrictions correspond to VARs in levels. This statement seems to be an obvious typo. As Beaudry and Portier (2006) write themselves on page 1296, a VECM is equivalent to a VAR in levels only if the matrix of cointegrating vectors is of full rank (also see Hamilton, 1994, chapter 19).
4
THE AMERICAN ECONOMIC REVIEW
MONTH YEAR
the shock that is supposed to capture T F P news underidenti…ed.7 Another, perhaps more intuitive way to understand the identi…cation problem is to realize that the imposed cointegration relationships imply that T F P and C share a common trend. But then when a particular shock –the third element of "t , in this case –is restricted to have zero long-run e¤ect on T F P , it automatically also has zero long-run e¤ect on C . The identi…cation problem implies that there exists an in…nity of solutions consistent with the BP restrictions. The results reported in Beaudry and Portier (2006) represent one particular solution, but there is no justi…cation for why this solution should be preferred over any of the other solutions. II.
The range of possible solutions
To illustrate the severity of the identi…cation problem, we take the point estimates of Beaudry and Portier’s (2006) four-variable VECMs and numerically simulate the range of impulse responses spanned by the possible solutions consistent with the BP restrictions.8 The …rst row of Figure 1 reports the results for the VECM in (T F P; SP; C; H ). The second row of Figure 1 reports equivalent results for the VECM in (T F P; SP; C; I ). The blue solid lines replicate impulse responses for the long-run T F P shock reported in Figure 8 of Beaudry and Portier (2006). In each panel, the gray intervals show the range of impulse responses spanned by the possible solutions. Example 1 (dashed black line with squares) and Example 2 (solid magenta line with diamonds) display the impulse responses for two particular solutions. Example 1 corresponds to the solution that …ts the impulse response of T F P to the long-run shock best in a least-squares sense; Example 2 corresponds to the solution that generates a near-zero response of T F P after 40 quarters. Figure 1 about here Consistent with the BP restrictions, none of the candidate solutions a¤ect T F P on impact. Likewise but not shown here, none of the corresponding non-news shocks in the third position of "t have a permanent e¤ect on either T F P or C , and none of the corresponding non-news shocks in the fourth position of "t have a contemporaneous e¤ect on T F P , SP , and C . This simulation con…rms 7 Technically, the (1; 3) and the (3; 3) equations of (1) = C(1) 0 on which the long-run restrictions are imposed are the same, leaving the system short of one equation to identify 0 . Nothing would change about this identi…cation problem if Beaudry and Portier (2006) had imposed cointegrating restrictions only on T F P and C but not on any of the other variables (i.e., if 0 was a row vector with non-zero entries only in the positions related to T F P and C). 8 Beaudry and Portier’s (2006) quarterly sample of U.S. data extends from 1948 to 2000. See their paper for a description. The T F P measure we use is the one adjusted with the Bureau of Labor Statistics’ capacity utilization index (see Section III.B in their paper). Results for Beaudry and Portier’s (2006) trivariate VECM in (T F P; SP; C) as well as results based on estimates with an updated quarterly sample spanning the period from 1947 to 2012 are very similar and available upon request.
VOL. VOL NO. ISSUE
COMMENT ON BEAUDRY AND PORTIER (2006)
5
numerically that there are an in…nity of candidate solutions satisfying the BP restrictions. Let us reemphasize that, throughout this exercise, all results are based on the point estimates of the VECM coe¢ cients. The gray intervals therefore stem solely from the lack of identi…cation and do not re‡ect sampling uncertainty about the VECM coe¢ cients. As is apparent from Figure 1, the gray intervals are very wide, making it impossible to draw any conclusions about the possible e¤ects of T F P news implied by the BP restrictions. Indeed, according to Example 1, one of the possible solutions generates impulse responses that appear very close to the ones reported in Figure 8 of Beaudry and Portier (2006). By contrast, according to Example 2, another solution that is equally consistent with the BP restrictions implies basically no reaction in T F P –together with a persistent drop in consumption, hours, and investment –despite the fact that stock prices temporarily increase.9 Within the con…nes of the VECMs estimated by Beaudry and Portier (2006), it is therefore impossible to draw any conclusions about T F P news based on the BP restrictions. Given these results, a seemingly natural question is whether the identi…cation problem with the BP restrictions can be resolved by dropping the cointegration restriction between T F P and C . Indeed, as Beaudry and Portier (2006) note themselves, the econometric evidence in favor of two cointegration relationships, as opposed to one, between T F P , SP , and C is not clear cut, which leaves open the door that T F P and C do not share a common trend. Furthermore, as Hamilton (1994) emphasizes, if the evidence about cointegration is unclear, it may be preferable to estimate the system without cointegration restrictions – i.e., a VAR in levels –so as to avoid misspeci…cation bias. In the working paper version of this comment (Kurmann and Mertens, 2013), we reestimate the three- and four-variable level VAR counterparts to Beaudry and Portier’s (2006) VECMs using their original data.10 When imposing the BP restrictions on the resulting point estimates, we …nd that T F P news generate impulse responses that are very similar to the ones reported in Beaudry and Portier (2006). However, when trying to assess the uncertainty surrounding the point estimates via bootstraps, we …nd that about 50 percent of all draws imply that T F P and C share a common trend. But then, as described above, the BP restrictions do not identify T F P news, and one is left again with an in…nity of candidate solutions. As detailed in the working paper version, the range of impulse responses implied by the possible solutions for each of these draws is very wide. Hence, even if the cointegration restriction between T F P and C is dropped, 9 Given the large range of possible solutions, it should not come as a surprise that the range of correlation coe¢ cients between the shocks satisfying the BP restrictions and the long-run T F P shock is wide for both VECMs, ranging from about -0.50 to 0.99. 1 0 In the National Bureau of Economic Research working paper version, Beaudry and Portier (2004) estimate one of their baseline bivariate systems as a VAR in levels and report that the implications of T F P news are very similar to the ones implied by their VECMs. However, they do not report any results for level VARs with more than two variables.
6
THE AMERICAN ECONOMIC REVIEW
MONTH YEAR
the common-trend property of the two variables in the data makes it impossible to draw any conclusions about T F P news based on the BP restrictions.11 III.
Conclusion
This comment shows that the identi…cation scheme proposed in Beaudry and Portier (2006) is subject to a fundamental problem that leaves T F P news undetermined. The problem arises from the interplay of long-run restrictions and common-trend properties between T F P and C in U.S. data. It is therefore impossible to draw any conclusions about the business-cycle implications of T F P news from the results reported in Beaudry and Portier (2006). The results raise the important question of alternative identi…cation strategies of T F P news in the literature that are not subject to the identi…cation problem. One example is Beaudry and Lucke (2010), who invoke short- and long-run zero restrictions for non-news shocks that allow identi…cation of T F P news independent of cointegration between T F P and C . As Fisher (2010) shows, however, the implications for T F P news coming out of this full-information identi…cation crucially depend on the number of cointegration relationships imposed. In addition, all results in Beaudry and Lucke (2010) and related full-information identi…cation strategies are contingent on the plausibility of zero restrictions for other non-news shocks necessary to identify T F P news. Another strategy, recently proposed by Barsky and Sims (2011), is to identify T F P news as the shock orthogonal to contemporaneous T F P movements that accounts for the maximum share of unpredictable future movements in T F P . This strategy, which is consistent with Beaudry and Portier’s (2006) original idea that T F P is driven by a contemporaneous component and a slowly di¤using news component, has the advantage that it does not rely on additional zero restrictions for other non-news shocks. As a result, the strategy is robust to di¤erent assumptions about cointegration and can be applied to arbitrary vector movingaverage systems. Interestingly, Barsky and Sims (2011) …nd that the T F P news resulting from their identi…cation accounts for a substantial share of T F P and macroeconomic aggregates at medium- and long-run horizons. However, their T F P news shock does not generate the type of joint increase in real macroeconomic aggregates on impact that Beaudry and Portier (2006) report and that generated a lot of interest in the literature. REFERENCES
Barsky, Robert B., and Eric R. Sims. 2011. “News shocks and business cycles.” Journal of Monetary Economics, 58(3): 273–289. 1 1 Similar
results obtain with an updated quarterly sample spanning the period from 1947 to 2012.
VOL. VOL NO. ISSUE
COMMENT ON BEAUDRY AND PORTIER (2006)
7
Beaudry, Paul, and Bernd Lucke. 2010. “Letting Di¤erent Views about Business Cycles Compete.” In NBER Macroeconomics Annual 2009, Volume 24. NBER Chapters, 413–455. National Bureau of Economic Research, Inc. Beaudry, Paul, and Franck Portier. 2004. “Stock Prices, News and Economic Fluctuations.” National Bureau of Economic Research, Inc NBER Working Papers 10548. Beaudry, Paul, and Franck Portier. 2006. “Stock Prices, News, and Economic Fluctuations.” The American Economic Review, 96(4): 1293–1307. Beaudry, Paul, and Franck Portier. 2007. “When can changes in expectations cause business cycle ‡uctuations in neo-classical settings?” Journal of Economic Theory, 135(1): 458–477. Den Haan, Wouter J., and Georg Kaltenbrunner. 2009. “Anticipated growth and business cycles in matching models.” Journal of Monetary Economics, 56(3): 309–327. Faust, Jon, and Eric M Leeper. 1997. “When Do Long-Run Identifying Restrictions Give Reliable Results?” Journal of Business & Economic Statistics, 15(3): 345–53. Fernàndez-Villaverde, Jesús, Juan F. Rubio-Ramirez, Thomas J. Sargent, and Mark W. Watson. 2007. “ABCs (and Ds) of Understanding VARs.” American Economic Review, 97(3): 1021–1026. Fisher, Jonas D. M. 2010. “Comment on ’Letting Di¤erent Views about Business Cycles Compete’.” In NBER Macroeconomics Annual 2009, Volume 24. NBER Chapters, 457–474. National Bureau of Economic Research, Inc. Hamilton, James D. 1994. Time-Series Analysis. Princeton, NJ:Princeton University Press. Jaimovich, Nir, and Sergio Rebelo. 2009. “Can News about the Future Drive the Business Cycle?” The American Economic Review, 99(4): 1097–1118. King, Robert G., Charles I. Plosser, James H. Stock, and Mark W. Watson. 1991. “Stochastic Trends and Economic Fluctuations.” The American Economic Review, 81(4): 819–40. Kurmann, André, and Elmar Mertens. 2013. “Stock prices, news, and economic ‡uctuations: comment.” Board of Governors of the Federal Reserve System (U.S.) Finance and Economics Discussion Series 2013-08. Leeper, Eric M., Todd B. Walker, and Shu-Chun Susan Yang. 2013. “Fiscal Foresight and Information Flows.” Econometrica, 81(3): 1115–1145.
8
THE AMERICAN ECONOMIC REVIEW
MONTH YEAR
Lucke, Bernd. 2010. “Identi…cation and overidenti…cation in SVECMs.” Economics Letters, 108(3): 318–321. Lütkepohl, Helmut. 2008. “Problems related to over-identifying restrictions for structural vector error correction models.”Economics Letters, 99(3): 512–515. Schmitt-Grohé, Stephanie, and Martin Uribe. 2012. “What’s News in Business Cycles.” Econometrica, 80(6): 2733–2764.
Percent deviation
−0.4 0
−0.2
0
0.2
0.4
0.6
−0.4 0
−0.2
0
0.2
0.4
0.6
10
10
20 Quarters
TFP
20 Quarters
TFP
30
30
40
40
20 Quarters
30
40
−6 0
−4
−2
30
40
−0.8 0
−0.6
−0.4
−0.2
0
0.4
0.6 0.2
20 Quarters
1 0.8
0
10
SP
−0.8 0
−0.6
−0.4
2
4
6
8
−6 0
−4
−2
0 −0.2
0.2
0.4
0.6
0
10
1 0.8
2
4
6
8
SP
10
10
20 Quarters
C
20 Quarters
C
Figure 1: Impulse Responses: VECMs
30
30
40
40
3 2.5 2 1.5 1 0.5 0 −0.5 −1 −1.5 −2 0
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 0
10
10
20 Quarters
I
20 Quarters
H
40
30
40
Candidate set Long−run TFP Example 1 Example 2
30
Notes: The top row depicts estimates generated by a VECM in T F P , SP , C, and H. The bottom row shows estimates from a VECM in T F P , SP , C, and I. Both VECMs are estimated with five lags and three cointegrating vectors, identical to what has been used by Beaudry and Portier (2006, “BP”). In each panel, the solid blue line shows the impulse response to a long-run shock in T F P , the gray shaded area depicts the set of all impulse responses consistent with the BP restrictions, and the dashed line with squares (black) and the solid line with diamonds (magenta) show two particular impulse responses consistent with the BP restrictions. Example 1 is as close as possible to the responses generated by the long-run T F P shocks, while satisfying the BP restrictions. Example 2 has been chosen to generate a near-zero response of T F P after 40 quarters, while also satisfying the BP restrictions.
Percent deviation
