Are predictable improvements in TFP contractionary or expansionary: Implications from sectoral TFP?∗ Deokwoo Nam† Hanyang University
Jian Wang‡ Federal Reserve Bank of Dallas
April 27, 2014
Abstract We investigate the effects of predictable changes in TFP at the sectoral level. Our findings can reconcile the seemingly contradictory findings in the literature. Shocks to predictable changes in investmentsector TFP are also found important for US business cycle fluctuations.
JEL Classification: E1, E3 Keywords: Aggregate and sectoral TFP, News shocks to TFP, Business cycle fluctuations
∗ We would like to thank Pierre-Daniel Sarte (the editor), one anonymous referee, Paul Beaudry, Eric Sims, and seminar participants at several places for very helpful comments. All views are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Dallas or the Federal Reserve System. Deokwoo acknowledges support for this research from the research fund of Hanyang University (HY-2013-N). † Email:
[email protected]. Address: Department of Economics and Finance, Hanyang University, 222 Wangsimniro, Seongdong-gu, Seoul 133-791, Republic of Korea. ‡ Email:
[email protected]. Address: Research Department, Federal Reserve Bank of Dallas, 2200 N. Pearl Street, Dallas, TX 75201.
1
Introduction
Beaudry and Portier (2006) document that predictable improvements in total factor productivity (TFP) are proceeded by a broad economic boom with increases in consumption, investment, and hours worked. One explanation is that agents have information (news) about future technology and use such information to make current economic decisions. Good news about future technology increases agents’ expectations about future fundamentals, and therefore induces an economic boom even before the actual improvement in technology. Following the literature, we call such shocks to TFP news shocks hereafter.1 However, Barsky and Sims (2011) find that a favorable news TFP shock leads to increases in consumption and stock prices, but declines in hours, investment, and output on impact; moreover, the changes in those aggregate variables do not lead the actual increase in TFP, which also stands in contrast to the findings in Beaudry and Portier (2006). We reconcile the above-mentioned findings of two studies by exploring the effects of news shocks to sectoral TFP on US business cycles. Fernald (2010) provides two factor-utilization-adjusted sectoral TFP series: equipment investment and consumer durables sector TFP and consumption sector TFP. We refer to them as investment-sector TFP and consumption-sector TFP, respectively. Two variants of the maximum forecast error variance (FEV) approach (Uhlig, 2003) are employed in this paper to identify news shocks to TFP: the max share method by Francis et al. (2005) and Barsky and Sims’ (2011) method. News shocks to TFP are defined as shocks that have no immediate impact on TFP but explain its future movements as much as possible. As it will become clear later, the key difference between these two methods is that the max share method identifies news shocks that drive future TFP at a particular forecast horizon, while Barsky and Sims’s method identifies news shocks that drive TFP movements at all forecast horizons up to a truncation horizon. We first apply the max share method to a VAR system with sectoral TFP. We find that a favorable news shock to investment-sector TFP is expansionary and the news shocks explain much of the FEV of investmentsector TFP at long horizons, while by contrast, a favorable news shock to consumption-sector TFP is mainly contractionary and the news shocks mostly account for the short-horizon FEV of consumption-sector TFP. Such heterogeneity accounts for the contradictory findings in the literature because Beaudry and Portier’s (2006) method identifies news shocks to long-run movements in TFP that resemble our investment-sector news TFP shocks, while Barsky and Sims’ (2011) method identifies news shocks to TFP whose short-run effects are very similar to those of our consumption-sector news TFP shocks. 1 An alternative explanation is the self-fulling beliefs that cause the economic boom. See Beaudry, Nam, and Wang (2011) for discussions.
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The above argument is supported by comparing the results of the max share and Barsky and Sims’ methods in the system with aggregate TFP. Under the max share method that is similar in spirit to Beaudry and Portier’s method, the estimated impulse responses to a favorable news shock to aggregate TFP are similar to those in the case of investment-sector TFP. However, under Barsky and Sims’ method, the identified news shock to aggregate TFP displays mixed effects of two sectoral news TFP shocks. In particular, the estimated impulse responses of hours, investment, and output to a favorable news shock to aggregate TFP at short horizons resemble the results obtained from consumption-sector TFP. By design, Barsky and Sims’ method captures both short- and long-run predictable TFP movements to identify news TFP shocks. As a result, the identified news shock to aggregate TFP is likely to reflect the effects of news shocks to consumptionsector TFP if consumption-sector news TFP shocks are a dominant component in explaining short-horizon predictable movements of aggregate TFP. In addition, the identified news shocks to investment-sector TFP are found to be important in driving US business cycles. At business cycle frequencies, the identified shocks usually explain about 50% of the FEVs of consumption, hours, investment, and output. However, the identified news shocks to consumption-sector TFP usually account for less than 10% of the FEV of output at business cycle frequencies. This finding is consistent with the results of investment-specific news TFP shocks in Ben Zeev and Khan (2013) and Chen and Wemy (2013). Beaudry and Portier (2005) document that news shocks identified from stock prices proceed TFP increases in the durable goods sector. Vukoti´c (2013) finds that the durable goods sector responds more significantly to aggregate news TFP shocks than the nondurable goods sector. Our results and the studies mentioned above suggest that the durable goods sector is an important source or propagation channel for expectations-driven business cycles. It would be interesting in the future to develop business cycle models to replicate these empirical findings.
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Identification Strategies and Data
Consider the reduced-form moving-average representation of a VAR model:
Yt =
∞ X
B (h) ut−h ,
(1)
h=0
where Yt is an n × 1 vector and ut is reduced-form innovations with the variance-covariance matrix Σu . Let’s first assume that there is a linear mapping A0 between reduced-form innovations ut and structural shocks e0 Q, t (i.e., ut = A0 t ) and the impact matrix A0 satisfies A0 A00 = Σu . Then, we can rewrite A0 as A0 = A
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e0 is any arbitrary orthogonalization of Σu and QQ0 = I. Thus, the identification of a structural where A shock is to uniquely pin down the corresponding column of Q, which is denoted by q, by imposing identifying restrictions. Let TFP be the first element of Yt and q be the unit vector associated with news shocks to TFP. Then, the share of the FEV of TFP attributable to news shocks at a forecast horizon h is expressed as:
Ω (h) = q 0 F (h) q,
(2)
e0 . where F (h) is a positive-definite, symmetric matrix, which is a function of the first rows of B (h) and A For a given h, the max share method identifies news TFP shocks by solving:
q ∗ = arg max Ω(h), s.t. (1) q 0 q = 1; (2) R (0) q = 0, q
(3)
where R (0) q represents the impact impulse response of TFP to the news shock and thus the second constraint imposes the restriction that news shocks have no immediate impact on TFP. Barsky and Sims (2011) identify news TFP shocks by solving:
q ∗ = arg max q
where
PH
h=0
H X
Ω (h) , s.t. (1) q 0 q = 1; (2) R (0) q = 0,
(4)
h=0
Ω1 (h) is the sum of the shares of the FEV of TFP attributable to news TFP shocks over all
forecast horizons up to a finite truncation horizon H. Therefore, it is clear that the max share method identifies news shocks that mainly drive long-run TFP when h is large, while the news shocks identified by Barsky and Sims’ method capture both short- and long-run predictable movements in TFP even when H is large. We use the quarterly US data from 1955Q1 to 2010Q4 for the following variables: aggregate TFP, two sectoral TFP, the price of investment relative to consumption, stock prices, consumption, investment, output, hours worked, and the real interest rate. The factor-utilization-adjusted aggregate and sectoral TFP series and the relative price of investment series are obtained from John Fernald’s website.2 2 See Basu, Fernald, and Kimball (2006) for details on factor-utilization-adjusted TFP. Other series are standard and their details can be found in the working paper version of this paper on the authors’ websites.
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3
Empirical Results
Our benchmark VAR model includes eight variables: a measure of TFP, stock prices, consumption, the real interest rate, hours worked, investment, output, and the relative price of investment.3 Figure 1 presents the impulse responses to a favorable consumption-sector news TFP shock identified by the max share method under different values of h and the forecast error variance (FEV) shares attributable to the identified shocks. Figure 2 displays the impulse response and FEV share results for investment-sector news TFP shocks. For the purpose of presentation, we group our results according to the value of parameter h: h = 4, 8, 20, and 40 quarters represent the short-horizon group and h = 40, 60, 80, and 120 quarters the long-horizon group. Note that the value of h = 40 quarters appears in both groups. For consumption-sector TFP in Figure 1, the impulse responses and FEV shares are nearly identical regardless of the value of the horizon parameter h. Following a favorable news shock to consumption-sector TFP, consumption-sector TFP jumps up immediately with hours, investment, and output all declining significantly on impact. Consumption and stock prices do not respond on impact. It is worthwhile to note that the responses of consumption-sector TFP, hours, investment and output over the first ten quarters are qualitatively the same as those to a favorable news shock to aggregate TFP found in Barsky and Sims (2011). The identified news shocks to consumption-sector TFP account for significant shares of the FEVs of hours, investment, and output over the first ten quarters, but the FEV shares decline as h becomes larger (e.g., 80 and 120 quarters). These results suggest that predictable changes in consumption-sector TFP affect economic fluctuations mainly at short forecast horizons. Figure 2 shows the results for investment-sector TFP. The impulse responses and FEV shares are qualitatively the same for all values of h except for two very small values of h (i.e., 4 and 8 quarters). When h is large, investment-sector TFP does not start to rise above zero until eight quarters following a favorable news shock to investment-sector TFP, and it eventually converges to its new long-run level. This sectoral news shock induces an economic boom: stock prices, consumption, and the real interest rate all jump immediately and consumption continues to increase before settling at a higher long-run level. Hours, investment and output increase gradually above zero and reach their peaks before investment-sector TFP starts to rise. The identified news shocks to investment-sector TFP explain a small share of the FEV of investmentsector TFP in the first eight forecast horizons, but explain most of its FEV at longer horizons (e.g., almost 80% at 40 quarters). The identified news shocks explain more than 50% of the FEVs of consumption, hours, investment, the relative price of investment, and stock prices at business cycle frequencies. There3 All variables enter the VAR system in levels, and a constant and four lags are included. More detailed analysis and results can be found in the working paper version of this paper on the authors’ websites.
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fore, the predictable component of investment-sector TFP is its long-run movements, and a favorable news shock to investment-sector TFP induces a broad boom of the economy that proceeds anticipated increase in investment-sector TFP. These findings echo Beaudry and Portier’s (2006) results based on aggregate TFP. Now, we compare the max share method and Barsky and Sims’ method by using different measures of TFP to see the implications of sectoral news TFP shocks on aggregate news TFP shocks. Figure 3 displays the impulse responses to the new shock identified with the max share method and Barsky and Sims’ method in the benchmark system with either aggregate TFP or each of the sectoral TFP series. The first two panels show the results from the max share method for h = 40 and 80, respectively. The last two panels present the results from Barsky and Sims’ method for H = 40 and 80, respectively. In the below, we describe the results in Figure 3, focusing on identified news shocks to aggregate TFP. First, if h and H are set to 80 quarters, aggregate TFP in both the max share and Barsky and Sims’s methods does not start to rise until 8 to 10 quarters following a favorable news shock to aggregate TFP, which echoes the response of investment-sector TFP to a favorable news shock to investment-sector TFP. The responses of aggregate variables including stock prices and the relative price of investment to a news shock to aggregate TFP are almost identical to those to a news shock to investment-sector TFP. These results suggest that both methods with a relatively long horizon consistently pick up the long-run predictable component of investment-sector TFP that dominates the long-run movements of aggregate TFP. Second, the identified news shocks to aggregate TFP capture the predictable component of consumptionsector TFP if H in Barsky and Sims’ method is set to 40 quarters. Barsky and Sims’ method consider both short- and long-horizon predictable components of aggregate TFP equally importantly, and thus the identified news shocks to aggregate TFP are more likely to reflect the effects of the short-run predictable consumption-sector TFP if H is set to a relatively small number. In the third panel of Figure 3 (i.e., the case for H = 40), a favorable news shock to aggregate TFP leads to decreases in hours, investment, and output on impact and an immediate increase in aggregate TFP, which is qualitatively similar to a favorable news shock to consumption-sector TFP.
4
Conclusion
We show that the seemingly contradictory findings in Beaudry and Portier (2006) and Barsky and Sims (2011) stem from the facts that: (1) Beaudry and Portier focuses on the long-run predictable components of aggregate TFP, while Barsky and Sims consider both short- and long-run predictable components of TFP; (2) long-run predictable changes in aggregate TFP are driven by investment-sector TFP which is expansionary,
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while short-run predictable movements in aggregate TFP are affected by consumption-sector TFP which is mainly contractionary.
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References [1] Barsky, Robert and Eric Sims, 2011. “News Shocks and Business Cycles,” Journal of Monetary Economics 58(3): 273-289. [2] Basu, Susanto, John G. Fernald, and Miles S. Kimball, 2006. “Are Technology Improvements Contractionary?” American Economic Review 96(5): 1418-1448. [3] Beaudry, Paul, Deokwoo Nam, and Jian Wang, 2011. “Do Mood Swings Drive Business Cycles and Is It Rational?” NBER Working Paper No. 17651. [4] Beaudry, Paul and Franck Portier, 2005. “The “News View” of Economic Fluctuations: Evidence from Aggregate Japanese Data and Sectoral U.S. Data,” Journal of the Japanese and International Economies 19(4): 635-652. [5] Beaudry, Paul and Franck Portier, 2006. “Stock Prices, News, and Economic Fluctuations,” American Economic Review 96(4): 1293-1307. [6] Ben Zeev, Nadav and Hashmat Khan, 2013. “Investment-Specific News Shocks and U.S. Business Cycles,” Working Paper, Ben-Gurion University of the Negev and Carleton University. [7] Chen, Kaiji and Edouard Wemy, 2013. “Investment-Specific News Shocks and Aggregate TFP Fluctuations,” Working Paper, University of Emory. [8] Fernald, John, 2010. “A Quarterly, Utilization-Adjusted Series on Total Factor Productivity,” Federal Reserve Bank of San Francisco Working Paper. [9] Francis, Neville, Michael T. Owyang, Jennifer E. Roush, and Riccardo DiCecio, 2005. “A Flexible FiniteHorizon Alternative to Long-run Restrictions with an Application to Technology Shocks,” Working Paper 2005-024F, Federal Reserve Bank of St. Louis. [10] Uhlig, Harald, 2003. “What Drives GNP?” mimeo. [11] Vukoti´c, Marija, 2013. “A Sectoral Approach to News Shocks,” Working Paper, University of Warwick.
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This figure has four panels. The first and second panels display OLS point estimates of impulse responses to a positive unit shock identified by the Max Share Method with the finite horizon h belonging to the short-horizon group of h = 4, 8, 20 and 40 quarters and the long-horizon group of h = 40, 60, 80, and 120 quarters, respectively, in the benchmark eight-variable system with consumption-sector TFP as a measure of TFP. The third and fourth panels display OLS point estimates of FEV shares attributable to that identified shock, corresponding to the first and second panels, respectively. For the first two panels, the unit of the vertical axis is percentage deviation from the situation without shock, and for all panels, the unit of the horizontal axis is the number of quarters following the shock.
1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
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IRF: Short Horizons
Figure 1: Max Share Method with Varying Finite Horizon in the Benchmark System with Consumption-sector TFP as a Measure of TFP
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This figure has four panels. The first and second panels display OLS point estimates of impulse responses to a positive unit shock identified by the Barsky and Sims’ Method with the finite truncation horizon H belonging to the short-horizon group of H = 4, 8, 20 and 40 quarters and the long-horizon group of H = 40, 60, 80, and 120 quarters, respectively, in the benchmark eight-variable system with consumption-sector TFP as a measure of TFP. The third and fourth panels display OLS point estimates of FEV shares attributable to that identified shock, corresponding to the first and second panels, respectively. For the first two panels, the unit of the vertical axis is percentage deviation from the situation without shock, and for all panels, the unit of the horizontal axis is the number of quarters following the shock.
1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
2 1.6 1.2 0.8 0.4 0 −0.4
IRF: Long Horizons
IRF: Short Horizons
Figure 2: Max Share Method with Varying Finite Horizon in the Benchmark System with Investment-sector TFP as a Measure of TFP
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IRFs MaxS = 40
40
40
40
40
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
−0.4
0
0.4
0.8
1.2
1.6
0
0
0
0
TFP
10
10
10
10
20
Output
20
Hours
20
Consumption
20
Zero on impact
40
40
40
40
−0.4
0
0.4
0.8
1.2
1.6
5 4 3 2 1 0 −1 −2 −3
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
0
0
0
0
20
30
20
Investment
20
30
30
10
20
30
Relative Price of Investment
10
10
Real Interest Rate
10
Stock Price
Adjusted Aggregate TFP Adjusted Investment−sector TFP Adjusted Consumption−sector TFP
30
30
30
30
10 8 6 4 2 0 −2
IRFs BS = 40
BS: H = 40
40
40
40
40
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
−0.4
0
0.4
0.8
1.2
1.6
0
0
0
0
TFP
10
10
10
10
20
Output
20
Hours
20
Consumption
20
Zero on impact
30
30
30
30
−0.4
0
0.4
0.8
1.2
1.6
5 4 3 2 1 0 −1 −2 −3
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
0
0
0
0
20
30
20
Investment
20
30
30
10
20
30
Relative Price of Investment
10
10
Real Interest Rate
10
Stock Price
Adjusted Aggregate TFP Adjusted Investment−sector TFP Adjusted Consumption−sector TFP
40
40
40
40
10 8 6 4 2 0 −2
IRFs BS = 80
BS: H = 80
40
40
40
40
This figure has four panels, each of which displays OLS point estimates of impulse responses to a positive unit identified news TFP shock in the benchmark eight-variable system with either aggregate TFP, investment-sector TFP, or consumption-sector TFP as a measure of TFP, and thus each panel has three sets of impulse responses. The first two panels (the last two panels) are impulse responses to the shock identified by applying the Max Share Method denoted by MaxS (Barsky and Sims’ Method denoted by BS) on TFP for the finite horizon h (the finite truncation horizon H) of 40 and 80 quarters, respectively. The unit of the vertical axis is percentage deviation from the situation without shock and the unit of the horizontal axis is the number of quarters following the shock.
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.4 1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8
1.2 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4
−0.4
0
0.4
0.8
1.2
1.6
MaxS: h = 80
MaxS: h = 40
Figure 3: Impulse Responses to a Positive Shock Identified with the Max Share and Barsky and Sims’ Methods in the Benchmark System
