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Is There News in Inventories? ONLINE APPENDIX Christoph Görtz University of Birminghamy Christopher Gunn Carleton Universityz Thomas A. Lubik Federal Reserve Bank of Richmondx May 2020 The views expressed in this paper are those of the authors and not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System. y Department of Economics. University House, Birmingham B15 2TT. United Kingdom. Tel.: +44 (0) 121 41 43279. Email: c.g.gortz@bham.ac.uk z Department of Economics. Loeb Building, 1125 Colonel By Drive. Ottawa, ON, K1S 5B6. Canada. Tel.: +1 613 520 2600x3748. Email: chris.gunn@carleton.ca. x Research Department, P.O. Box 27622, Richmond, VA 23261. Tel.: +1-804-697-8246. Email: thomas.lubik@rich.frb.org. 1 A Additional VAR Evidence A.1 Forecast Error Variance Decomposition Figure 1 reports the forecast error variance decomposition for our baseline speci…cation in the main text. It shows the variance shares explained by the TFP news shock over a 40period (10-year) time horizon. In the long run, the news shock explains about 50% of TFP ‡uctuations, the remainder being due to unanticipated movements in productivity. For all other quantity variables the contribution of TFP news is above 50%, with the contribution of GDP at around three quarters. This is consistent with the …ndings in the literature which attribute similar importance to anticipated TFP movements. A.2 News Shocks and the Response of Inventories over a Longer Sample Period It has been widely documented in the literature (for instance, McCarthy and Zakrajsek, 2007) that changes in the behavior of inventories coincide with the onset of the Great Moderation in the early 1980s. It is this observation, in addition to data availability issues that we highlight in the main text, that we and most of the literature focus on a post-Great Moderation sample. Nevertheless, it is interesting to evaluate whether the rise of inventories in anticipation of higher future TFP is present also over a longer horizon. Figure 2 shows the impulse responses for the 1960Q1- 2018Q2 sample period, computed using the same news shock identi…cation procedure as in the baseline. The individual graphs reveal strong comovement of all macroeconomic aggregates, including inventories, several quarters before TFP increases signi…cantly. This sample is restricted by the availability of the E5Y consumer con…dence measure. Using the S&P500 stock index in its place we can consider a 1948Q1-2018Q2 sample. Figure 3 shows that responses to a news shock based on this sample are qualitatively and also largely quantitatively very similar to the results based on our 1983Q1- 2018Q2 baseline sample and the 1960Q1-2018Q2 sample period. Overall, we …nd that the fact that inventories rise in response to a TFP news shock is robust at longer sample periods. A.3 Robustness to Alternative VAR News Shock Identi…cation In our baseline speci…cation, we identify news shocks using the Max Share method proposed by Francis et al. (2014). This approach is widely used in the literature; it identi…es a news shock as the shock that (i) does not move TFP on impact, and (ii) maximizes the variance 2 of TFP at a 40-quarter horizon. We assess the robustness of our …ndings using three closely related alternative approaches. First, we consider the identi…cation scheme suggested by Barsky and Sims (2011). Their method recovers a news shock by maximizing the variance of TFP over horizons from zero to 40 quarters and the restriction that the news shock does not move TFP on impact. The second alternative identi…cation scheme is Forni et al. (2014), which is similar in spirit to the Max Share method. They identify the news shock by imposing a zero-impact restriction on TFP and maximize the impact of the shock on TFP in the long run. Third, we use identi…cation suggested by Kurmann and Sims (2019), who recover news shocks by maximizing the forecast error variance of TFP at a long horizon without imposing a zero-impact restriction on TFP conditional on the news shock.1 Figure 4 provides a comparison between the median responses based on the Max Share method and the methods proposed by Barsky and Sims (2011) and Forni et al. (2014). The median responses of the Max Share methodology and the Forni et al. (2014) methodology are virtually indistinguishable. In turn, both are very similar to the median responses based on the Barsky and Sims (2011) approach. Figure 5 shows that responses based on the methodology proposed by Kurmann and Sims (2016) are qualitatively and quantitatively close to the ones based on the Max-share method. Perhaps most importantly, all methods suggest inventories increase in anticipation of higher future TFP. A.4 News Shock Identi…cation Based on Patents We also consider as a robustness exercise identi…cation of news shocks that relies on valueweighted patents. In this we follow the idea in Cascaldi-Garcia and Vukotic (2019) who argue that patent …lings include information about future TFP movements since …rms engage in activities to take advantage of expected technological improvements or are the originators of such productivity advancements. The patent system is designed to reveal such news without the full set of improvements necessarily being in place. Kogan et al. (2017) use observations on patents associated with stockmarket listed …rms in the CRSP database. They compute the economic value of a patent based on a …rm’s stock-price reaction to observed news about a patent grant, controlling for factors that could move stock prices but are unrelated to the economic value of the patent. Kogan et al. (2017) provide an annual index, while Cascaldi-Garcia and Vukotic (2019) use the associated micro data to aggregate to a quarterly index. They then use this index to identify responses to 1 Kurmann and Sims (2019) argue that allowing TFP to jump freely on impact, conditional on a news shock, produces robust inference to cyclical measurement error in the construction of TFP. 3 patent-based news shocks in a Bayesian VAR based on a simple Cholesky identi…cation with the patent series ordered …rst. Figure 6 shows impulse response functions to this patent-based news shock. They are broadly consistent with the responses in the baseline setup. TFP rises signi…cantly only with a delay, even though there is no zero-impact restriction applied. Inventories rise on impact together with the other activity variables as well as consumer con…dence. Unfortunately, the availability of the Kogan et al. (2017) value-weighted patents series restricts the sample to end in 2010Q4, while at the same time the composition of the index is limited to stockmarket-listed …rms only. Nevertheless, the qualitative consistency of responses to a patent-based news shock with our baseline results is reassuring since the identi…cation of the former is independent of the observable for TFP. B DSGE Model Equations The DSGE model introduced in section 3 of the main text is described by a set of optimality conditions. They de…ne a symmetric competitive equilibrium as a set of stochastic processes fCt ; It ; Gt ; St ; Yt ; Nt ; ut ; Ft ; Kt ; Ht ; Xt ; At ; wt ; rt ; t; f t; k; t h; t 1 t gt . In the following, we list these equations and detail how to transform the non-stationary system, which is driven by stochastic trends, into a stationary counterpart amenable to solution and estimation. B.1 Optimality Conditions We de…ne Vt = Ct addition, we denote nt Ft as the periodic utility function argument to ease notation. In f t, k, t h, t and t as, respectively, the multipliers on the de…nition of Ft (equation (9) in the main text), physical capital accumulation (equation (10) in the main text), knowledge capital accumulation (equation (11) in the main text) and the household budget constraint (equation (12) in the main text). The …rst-order necessary conditions are then as follows: Ct + t It + Gt = S t ; (1) 1 Ft = Ct f Ft Kt+1 = [1 f 1 ; (ut )] Kt + mt It 1 Ht+1 = Ht h Nt h ; 1 Gt = 1 Yt ; "t 4 (2) S It It ; (3) 1 (4) (5) t Vt + t Vt f t f Nt Ft Ct 1 = Ft = rt = t; (6) t wt H t k t = (7) 0(ut ); t t t Ht+1 h ; t h Nt + k t mt 1 = k t = Et h t = Et t Vt Yt = zt ( It S It S0 1 n + t+1 wt+1 Nt+1 + (ut Kt )1 t Ht Nt ) It It It 1 + (9) 1 2 ; f Ft+1 ; f )Et t+1 Ft Nt + (1 t+1 rt+1 ut+1 It It+1 It It+1 It k t+1 mt+1 S0 + Et f t (8) k t+1 [1 (10) o (ut+1 )] ; Ht+2 h t+1 h Ht+1 (11) ; (12) ; (13) Yt ; t Ht Nt wt = rt = (1 At = (1 (14) Yt ; ut Kt x )Xt 1 + Yt ; ) (15) t Xt = At St ; 1 = (1 x )Et (16) (17) t+1 t+1 ; (18) t t = St + At 1 : In addition, we have laws of motion for the exogenous processes and gt = B.2 t= t 1 (19) t, mt t, gt = t= t 1 as described in the main text. Stationarity and Solution Method The model economy inherits stochastic trends from the two non-stationary stochastic processes for t and t. Our solution method focuses on isolating ‡uctuations around these stochastic trends. We divide non-stationary variables by their stochastic trend component to derive a stationary version of the model. We then take a linear approximation of the dynamics around the steady state of the stationary system. The stochastic trend components of output and capital are given by Xty = Xtk = 1 t, 1 t t and respectively. The stochastic trend components of all another non-stationary variables can be expressed as some function of Xty and Xtk . In particular, de…ne the following 5 Ct , Xty stationary variables as transformations of the above 19 endogenous variables: ct = it = It , Xty gt = xt = Xt , Xty at = and t At , Xty = (Xty ) and gtk = vt = Gt , Xty Vt Xty Xtk Xtk 1 st = wt = t. St , Xty wt , Xty yt = Yt , Xty nt = Nt , ut = ut , ft = Xtk r, Xty t rt = t = t, f t = (Xty ) f t, Ft , Xty qtk = In addition, de…ne the two additional stationary Kt , ht = Ht , Xtk 1 h= Xtk ( kt = t ) , qth = tX y t Xty t Xy variables, gty = X yt kt = t 1 as the growth-rates of the stochastic trends in output and capital, and as the de…nition of the stationary counterpart of the periodic utility function argument Vt de…ned above. The stationary system is then given by: ct + it + gt = st ; (20) ft = ct f kt+1 = [1 1 ft 1 gty (ut )] f ; (21) kt + mt it 1 gtk ht+1 = ht h nt h ; 1 yt ; gt = 1 "t ft f = t; t vt + t f ct ht+1 1 ft = wt ht + qth h ; t vt nt nt t rt = qtk 0(ut ); it gtk 1 = qtk mt 1 S it 1 qtk = = qth = t vt (25) (26) (27) S0 yt = (ht nt ) wt = rt = (1 t yt ; ht nt ) t f )Et t+1 t t+1 ut kt gkk it gtk it gtk it ii 1 t+1 k qt+1 mt+1 S0 t y Et gt+1 gt+1 (22) (24) nt + (1 y Et gt+1 ; (23) y + Et gt+1 gt+1 f t it gtk it 1 S y gt+1 1 ; (28) k it+1 gt+1 it ! f ft+1 ; t+1 ft n k rt+1 ut+1 + qt+1 [1 h wt+1 nt+1 + qt+1 t 1 + 1 h ht+2 ht+1 k it+1 gt+1 it !2 ; (29) o (ut+1 )] ; (30) ; (31) (32) (33) yt ; ut gkkt (34) t 6 at = (1 x) xt 1 + yt ; gty xt = at st ; 1 y = (1 x )Et gt+1 t = st + zt ( gyy = gt gt gtk = gty =gt in addition to the exogenous processes C 1 (35) (36) t+1 t+1 ; ; 1)= (38) ; ; t, (37) t (39) (40) mt t, gt and gt . Shock Processes and Bayesian Estimation To estimate the model, we include the following exogenous disturbances: a shock to the growth rate of TFP (gyy ), a shock to the growth rate of IST (gt ), a marginal e¢ ciency of investment (MEI) shock (mt ), a preference shock ( t ) and a government spending shock ("t ). Each exogenous disturbance is expressed in log-deviations from the steady state as a …rst-order autoregressive process, whose stochastic innovation is uncorrelated with other shocks, has a zero mean, and is normally distributed. In addition to the unanticipated innovations to the above shocks, the model allows for anticipation e¤ects. In particular, all shock processes (with the exception of the preference shock) include four, eight and twelve quarter-ahead innovations. Our treatment of anticipated and unanticipated components is standard and in line with the literature.2 We estimate the model over the period from 1983Q1 to 2018Q2, as in the VAR analysis. We use GDP, consumption, investment, inventories, and hours worked as observables. The variables are expressed in real per-capita terms as outlined in Section 2 in the main text, while GDP, consumption, investment, and inventories enter the vector of observables in …rst di¤erences. We demean the data prior to estimation. We only estimate the persistence parameters of the shocks and their standard deviations, while the remaining parameters shown in Table 1 in the main text are calibrated. The prior distributions follow the assumptions in Schmitt-Grohé and Uribe (2012). The prior means assumed for the news components are in line with these studies and imply that the sum 2 For example Schmitt-Grohé and Uribe (2012) also include news components in the processes for government spending shocks and stationary as well as non-stationary neutral and investment-speci…c technology shocks. News shocks also arrive at the four, eight and twelve quarter-horizons as in Görtz et al. (2017), for example. 7 of the variance of news components is, evaluated at prior means, at most one half of the variance of the corresponding unanticipated component. Table A.1 provides an overview about prior and posterior distributions. Overall, the data are informative and indicate strong persistence in the MEI shock, but also in government spending. At the same time, TFP and IST growth exhibit a reasonably high degree in serial correlation, in line with the behavior of U.S. quantity variables such as GDP. References [1] Barsky, Robert B., and Eric R. Sims (2011): “News shocks and business cycles”. Journal of Monetary Economics, 58(3), pp. 273-289. [2] Cascaldi-Garcia, Danilo, and Marija Vukotić (2019): “Patent-based news shocks”. Forthcoming, Review of Economics and Statistics. [3] Forni, Mario, Luca Gambetti, and Luca Sala (2014): “No news in business cycles”. Economic Journal, 124, pp. 1168-1191. [4] Francis, Neville, Michael Owyang, Jennifer Roush, and Riccardo DiCeccio (2014): “A ‡exible …nite-horizon alternative to long-run restrictions with an application to technology shocks”. Review of Economics and Statistics, 96, pp. 638-647. [5] Görtz, Christoph, John Tsoukalas, and Francesco Zanetti (2017): “News shocks under …nancial frictions”. Technical Report. [6] Kogan, Leonid, Dimitris Papanikolaou, Amit Seru, and Noah Stockman (2017): “Technological innovation, resource allocation, and growth”. Quarterly Journal of Economics, 132(2), pp. 665-712. [7] Kurmann, Andre, and Eric Sims (2019): “Revisions in utilization-adjusted TFP and robust identi…cation of news shocks”. Forthcoming, Review of Economics and Statistics. [8] McCarthy, Jonathan, and Egon Zakrajsek (2007): “Inventory dynamics and business cycles: What has changed?” Journal of Money, Credit and Banking, 39(2-3), pp. 591613. [9] Schmitt-Grohé, Stephanie and Martín Uribe (2012): “What’s news in business cycles?” Econometrica, 80(6), pp. 2733-2764. 8 Figure 1: Forecast error variance decomposition (FEVD) of variables to the TFP news shock. Sample 1983Q1-2018Q2. The solid line is the median and the dashed lines are the 16% and 84% posterior bands generated from the posterior distribution of VAR parameters. Figure 2: IRF to TFP news shock. Sample 1960Q1-2018Q2. The solid line is the median and the dashed lines are the 16% and 84% posterior bands generated from the posterior distribution of VAR parameters. The units of the vertical axes are percentage deviations. 9 Figure 3: IRF to TFP news shock. Sample 1948Q1-2018Q2. The solid line is the median and the dashed lines are the 16% and 84% posterior bands generated from the posterior distribution of VAR parameters. The units of the vertical axes are percentage deviations. Figure 4: IRF to TFP news shock. Sample 1983Q1-2018Q2. The black solid line is the median response identied using the Max-share method. The shaded gray areas are the corresponding 16% and 84% posterior bands generated from the posterior distribution of VAR parameters. The blue line with crosses (red line with circles) is the median response identied using the Barsky and Sims (2011) (Forni et al. (2014)) methodology. The units of the vertical axes are percentage deviations. 10 Figure 5: IRF to TFP news shock. Sample 1983Q1-2018Q2. The black solid (red dash-dotted) line is the median response identied using the Max-share (Kurmann and Sims (2016)) method. The shaded gray areas (dashed red lines) are the corresponding 16% and 84% posterior bands generated from the posterior distribution of VAR parameters. The units of the vertical axes are percentage deviations. Figure 6: IRF to patent based TFP news shock. Sample 1983Q1-2010Q4. The black solid (dash-dotted) line is the median (16% and 84% posterior bands) response identied using the value weighted patent based identication as in Cascaldi-Garcia and Vucotic (2019). Posterior bands are generated from the posterior distribution of VAR parameters. The units of the vertical axes are percentage deviations. 11 Table 1: Prior and Posterior Distributions Parameter Description Shocks: Persistence ρb ρµ ρg ρa ρv Preference Marginal eciency of investment Government spending TFP growth IST growth Shocks: Volatilities σb σµ σµ4 σµ8 σµ12 σg σg4 σg8 σg12 σg σa4 σa8 σa12 σv σv4 σv8 σv12 Preference Marginal eciency of investment MEI. 4Q ahead news MEI. 8Q ahead news MEI. 12Q ahead news Government spending Gov. spending. 4Q ahead news Gov. spending. 8Q ahead news Gov. spending. 12Q ahead news TFP growth TFP growth. 4Q ahead news TFP growth. 8Q ahead news TFP growth. 12Q ahead news IST growth IST growth. 4Q ahead news IST growth. 8Q ahead news IST growth. 12Q ahead news Prior Distribution Posterior Distribution Distribution Mean Std. dev. Mean 10% 90% Beta Beta Beta Beta Beta Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma Inv Gamma 0.5 0.5 0.5 0.5 0.5 0.2 0.2 0.2 0.2 0.2 0.5281 0.9997 0.9552 0.4395 0.6343 0.5216 0.9995 0.9194 0.3798 0.5555 0.5364 0.9999 0.9287 0.5025 0.7173 0.5 0.5 0.289 0.289 0.289 0.5 0.289 0.289 0.289 0.5 0.289 0.289 0.289 0.5 0.289 0.289 0.289 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 2* 0.3177 0.8943 1.3817 0.2860 0.3644 0.2615 0.4545 0.2581 3.0040 0.6382 0.1458 0.1360 0.6294 0.3357 0.6004 0.1664 0.3769 0.1298 0.1856 0.9850 0.0681 0.0966 0.1450 0.1026 0.0681 2.7129 0.5778 0.0861 0.0723 0.5419 0.1652 0.4435 0.0797 0.2352 0.5160 1.3684 1.8498 0.5308 0.6623 0.3772 0.8695 0.5098 3.3181 0.7072 0.2177 0.1959 0.7248 0.4781 0.7898 0.2557 0.5091 Notes. The posterior distribution of parameters is evaluated numerically using the random walk Metropolis-Hastings algorithm. We simulate the posterior using a sample of 500,000 draws and discard the rst 100,000 of the draws. 12