Uncertainty Shocks, Innovation, and Productivity

Dario Bonciani; Joonseok Oh

doi:10.1515/bejm-2021-0074

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Uncertainty Shocks, Innovation, and Productivity

Dario Bonciani und Joonseok Oh

Veröffentlicht/Copyright: 4. März 2022

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Aus der Zeitschrift The B.E. Journal of Macroeconomics Band 23 Heft 1

Abstract

In this paper, we argue that macroeconomic uncertainty shocks cause a persistent decline in economic activity, investment in R&D, and total factor productivity. After providing empirical evidence, we build a DSGE model with sticky prices and endogenous growth through investment in R&D. In this framework, uncertainty shocks lead to a short-term fall in demand because of precautionary savings and rising markups. The reduction in the utilised aggregate stock of R&D determines a fall in productivity, which causes a long-term reduction in the main macroeconomic aggregates. When households feature Epstein–Zin preferences, they become averse to these long-term risks affecting their consumption process (long-run risk channel), which severely exacerbates the precautionary savings motive and the overall adverse effects of uncertainty shocks.

Keywords: uncertainty shocks; R&D; total factor productivity; endogenous growth

JEL Classification: E32; O40

Corresponding author: Dario Bonciani, Bank of England, Threadneedle Street, London, EC2R 8AH, UK, E-mail: dario.bonciani@bankofengland.co.uk

Earlier drafts of this paper were circulated under the titles: “Uncertainty, Innovation, and Slow Recoveries” and “The Long-Run Effects of Uncertainty Shocks.” The views expressed herein are those of the authors and not necessarily those of the Bank of England or its committees. We would like to thank Juan Dolado, Evi Pappa, and Axelle Ferriere for their guidance and support. We particularly benefited from the detailed comments of editor Peng-Fei Wang and an anonymous referee. We are also indebted to Cristiano Cantore, Wouter Den Haan, Federico Di Pace, Roger Farmer, Francesco Furlanetto, David Gauthier, Matteo Iacoviello, Derrick Kanngiesser, Makram Khalil, Mira Kim, Riccardo Masolo, Leonardo Melosi, Francesca Monti, Yeonu Oh, Anna Rogantini Picco, Martino Ricci, Andrea Tafuro, Konstantinos Theodoridis, Alejandro Vicondoa, the participants of the BoE Macro-Finance-Money working group and an anonymous referee for the BoE Working Paper Series for helpful comments and suggestions. All errors are our own.

Appendix A: Empirics

A.1 Correlation Between Uncertainty and TFP

In this section, we test that past movements in TFP do not significantly predict future changes in uncertainty. Table A.1 displays the correlation between the p-quarter-backward-looking moving average of TFP and the q-quarter-forward-looking moving average of uncertainty, i.e., corr TFP ̄ t , t − p , uncertainty ̄ t , t + q . The evidence of TFP predicting future movements in uncertainty is far weaker than that of uncertainty predicting TFP. In most cases, the correlation is small, statistically insignificant, and the sign of the correlation depends on p and q.

Table A.1:

Correlation between future uncertainty and past TFP.

q	p
	1	10	20	30	40
1	−0.02	−0.08	−0.03	0.01	0.04
	(0.06)	(0.06)	(0.06)	(0.06)	(0.06)
10	−0.22	−0.14	0.01	0.09	0.25^**
	(0.16)	(0.18)	(0.15)	(0.12)	(0.12)
20	−0.09	−0.02	0.1	0.24^*	0.33^**
	(0.15)	(0.14)	(0.15)	(0.14)	(0.13)
30	−0.03	0.05	0.21	0.31^*	0.4^**
	(0.13)	(0.15)	(0.16)	(0.16)	(0.16)
40	0.04	0.12	0.23	0.33	0.42^**
	(0.14)	(0.16)	(0.19)	(0.2)	(0.21)

For each correlation (p, q) we show the estimate of β₁ (upper value) and Newey–West standard errors (values in brackets). Asterisks represent 10, 5, and 1 per cent significance levels.

A.1.1 Controlling for Past GDP

In this subsection of the appendix, we display the long-run correlations between p quarters backward-looking moving average of uncertainty and the q quarters forward-looking moving average of TFP growth. The correlations are calculated controlling for past GDP growth. In practice, we run the following regression:

(A.1) tfp t , t + q = β 1 uncertainty t − p , t + β 2 gdp t − p , t + ε t ,

where tfp, uncertainty, and gdp are standardised moving averages, so that β₁ can be interpreted as a correlation. Table A.2 shows the estimates of β₁ for different values of p and q. The table rows represent a different averaging window for the right-hand-side variable (p). The columns are different averaging window for the left-hand-side variable (q). In Table A.3, instead, we show the results from regression:

(A.2) uncertainty t , t + q = β 1 tfp t − p , t + β 2 gdp t − p , t + ε t ,

In other words, this last regression is meant to test whether past TFP growth predicts future movements in uncertainty, after controlling for past GDP growth. In line with the results in Table A.1, the correlation between past TFP growth and future uncertainty is in most cases insignificant.

Table A.2:

Correlation between future TFP and past uncertainty.

q	p
	1	10	20	30	40
1	0.1	−0.22^*	−0.33^**	−0.47^***	−0.59^***
	(0.08)	(0.13)	(0.12)	(0.15)	(0.16)
10	−0.01	−0.19	−0.31	−0.62^**	−0.76^***
	(0.06)	(0.17)	(0.21)	(0.26)	(0.25)
20	−0.03	−0.2	−0.45	−0.65^**	−0.74^***
	(0.06)	(0.2)	(0.28)	(0.3)	(0.24)
30	−0.07	−0.38^*	−0.58^**	−0.69^**	−0.69^***
	(0.06)	(0.21)	(0.27)	(0.27)	(0.22)
40	−0.11^**	−0.42^*	−0.56^**	−0.58^**	−0.55^**
	(0.06)	(0.21)	(0.27)	(0.26)	(0.21)

For each lag-lead combination (p, q) we show the estimate of the correlation (upper value) and Newey–West standard errors (values in brackets). Asterisks represent 10, 5, and 1 per cent significance levels.

Table A.3:

Correlation between future uncertainty and past TFP.

q	p
	1	10	20	30	40
1	0.08	−0.03	−0.01	0.02	0.05
	(0.06)	(0.06)	(0.06)	(0.06)	(0.06)
10	−0.08	−0.14	0.01	0.11	0.3^**
	(0.13)	(0.19)	(0.16)	(0.13)	(0.12)
20	0.01	−0.05	0.11	0.3	0.39^**
	(0.17)	(0.17)	(0.19)	(0.19)	(0.18)
30	0.11	0.04	0.23	0.35	0.41^*
	(0.15)	(0.19)	(0.22)	(0.21)	(0.22)
40	0.12	0.09	0.21	0.29	0.35
	(0.2)	(0.22)	(0.25)	(0.26)	(0.29)

For each lag-lead combination (p, q) we show the estimate of the correlation (upper value) and Newey–West standard errors (values in brackets). Asterisks represent 10, 5, and 1 per cent significance levels.

A.2 VAR

In this subsection we describe the data sources and present the details and results of our robustness tests for the VAR analysis.

Figure A.1:

Conditional volatility of TFP.

The volatility of TFP is estimated using utilisation-adjusted TFP data from Fernald (2014). We assume that TFP follows an AR(1) with stochastic volatility.

A.2.1 Data Sources

Table A.4:

Data used in the VAR analysis.

Name	Source	Ticker
Baseline VAR
S&P 500 index	Yahoo finance	GSPC
Macroeconomic uncertainty	Sydney Ludvigson
Gross domestic product	FRED (BEA)	GDP
Services consumption	FRED (BEA)	PCES
Nondurables consumption	FRED (BEA)	PCEND
Services consumption	FRED (BEA)	PCEDG
Private residential fixed investment	FRED (BEA)	PRFI
Private nonresidential fixed investment	FRED (BEA)	PNFI
Private fixed investment R&D	FRED (BEA)	Y006RC1Q027SBEA
GDP implicit price deflator	FRED (BEA)	GDPDEF
Labour share	FRED	PRS85006173
Shadow interest rate	FRBA
Utilization-adjusted TFP	FRBSF
Robustness exercises
Alternative macro uncertainty	Rossi and Sekhposyan (2015)
Downside macro uncertainty	Rossi and Sekhposyan (2015)
Macroeconomic dataset	FRED	FRED-MD
Industrial production	FRED	INDPRO
Consumer confidence	FRED (OECD)	CSCICP03USM665S
Consumer price index	FRED	CPIAUCSL
Spread yields BAA – 10 yr treasury	FRED	BAA10Y

A.2.2 Robustness Exercises

Uncertainty Ordered Last. First, we change the Cholesky ordering assumed in the baseline setup and allow uncertainty to respond on impact to all the other variables in our model. The other variables instead, will respond only with a quarter lag to an uncertainty shock. The results reported in Figure A.2 confirm those in the baseline VAR. We find a strong persistent decline in all the real macroeconomic variables. The response of prices and interest rate is insignificant throughout the 40 quarters.

Figure A.2:

Uncertainty ordered last.

Variables are in percentage changes except for the interest rate, which is in annualised percentage points. Light grey and dark grey shaded areas represent 95 and 68 per cent bootstrapped confidence bands.

Uncertainty Ordered First. In this robustness check, we allow the S&P500 index to respond on impact to a rise in macroeconomic uncertainty. The results are reported in Figure A.3. The main macroeconomic variables show a significant decline. The falls in consumption and output are especially persistent. The response of TFP is slightly more sluggish on impact than in the baseline case. Overall, the figure shows that this alternative specification delivers results that are both qualitatively and quantitatively in line with the baseline empirical model.

Figure A.3:

Uncertainty ordered first.

Including a Measure of Markup. To test the validity of the proposed short-run mechanism, i.e. uncertainty affecting the economy by raising price markups, we include the inverse of the labour share in our VAR. The markup proxy is placed below the macro uncertainty measure, implying that markup shocks do not affect uncertainty on impact. Similarly as in Fernández-Villaverde et al. (2015), in Figure A.4, we find the markup to initially fall, while it immediately rebounds and significantly rises by 0.1 per cent. The other responses are in line with the baseline results, although the response of capital investment and R&D investment become insignificant after approximately 20 quarters.

Figure A.4:

VAR including markups.

Alternative Measure of Uncertainty I. We also estimate the VAR above using the measure of macroeconomic uncertainty and downside macroeconomic uncertainty from Rossi and Sekhposyan (2015). They define uncertainty based on the percentile in the historical distribution of forecast errors associated with the realized error. Let e_t+h be the h-step ahead forecast error of y_t+h defined as y_t+h − E_t[y_t+h] and let f(e) be its forecast error distribution. Uncertainty is then defined as the cumulative distribution U t + h = ∫ − ∞ e t + h f ( e ) d e . Downside uncertainty is defined as U t + h − = 1 2 + max 1 2 − U t + h , 0 . As can be seen in Figures A.5 and A.6, the median responses of output, consumption, R&D and TFP are extremely persistent and last well beyond the business cycle frequency, qualitatively and quantitative in line with our baseline results. However, for both alternative measures of macroeconomic uncertainty, the responses in the long-run are less significant than in the baseline case.

Figure A.5:

VAR with alternative macro uncertainty.

Figure A.6:

VAR with macro downside uncertainty.

Alternative Measure of Uncertainty II. In line with Bloom (2009), we also consider the VXO, a measure of the implied volatility of the S&P100 index, as a proxy for macroeconomic uncertainty. It bears noting that at a quarterly frequency, it is difficult to disentangle between shocks to the VXO and the S&P500. If ordered second, shocks to the VXO would not have any significant effects. For this reason, we order the VXO first. We display the IRFs in Figure A.7. In this case, we find that a shock increasing the VXO reduces output, consumption and investment. The median responses of consumption and output are very persistent. The pattern of TFP, instead, is slightly ambiguous in the short term. On impact, we find a fall in TFP, followed by an eight-quarters increase. After that, TFP persistently declines (significant with a 68 per cent confidence), in line with the baseline VAR.

Figure A.7:

VAR with VXO.

Alternative Measure of Uncertainty III. We also estimate the VAR above using the volatility of TFP as a proxy for macroeconomic uncertainty. To this end we assume that the level of (utilisation-adjusted) TFP follows an AR(1) process with stochastic volatility defined as:

(A.3) log A t = μ A + ρ A log A t − 1 + σ t A ε t A ,

(A.4) log σ t A = μ σ A + ρ σ A log σ t − 1 A + σ σ A ε t σ A .

Variable A_t represents TFP, whereas the error terms ε t A and ε t σ A follow standard normal distributions. Parameters ρ_A, ρ σ A ∈ 0,1 . Finally, we assume that σ t A , i.e. the conditional volatility of the error term in Eq. (A.3), is time-varying. The model is estimated by maximum-likelihood using an EM algorithm as in Bertsche and Braun (2020). Before estimating the model, we linearly detrend the level of TFP.^[10] Figure A.1 displays the profile of the estimated TFP conditional volatility. Figure A.8 shows the results from the VAR using TFP volatility as a proxy for macroeconomic uncertainty. The median responses are qualitatively in line with those from the baseline VAR, although slightly milder from a quantitative point of view. In particular, a rise in TFP volatility causes a decline in output, consumption, investment, and TFP. The fall in all these variables is significant with a 68 per cent confidence.

Figure A.8:

VAR with TFP volatility.

Increase the Number of Lags. We increase the maximum number of lags included in our VAR to 2 to 5 to show that our baseline results are not due to the number of lags included in our VAR, as in Figure A.9.

Figure A.9:

VAR with 5 lags.

FAVARs. There are two potential issues with our baseline specification. The first one relates to the quarterly frequency of the data and the second to the potential insufficient information contained in the model, which would not allow us to uncover the true effects of uncertainty shocks. One the one hand, the exact identification of uncertainty shocks could be undermined by the quarterly-data specification. Furthermore, by using quarterly data, the time-series dimension may not be sufficiently long considering the size of the VAR. In order to overcome these issues, we estimate a monthly-frequency factor-augmented VAR (FAVAR) model in the spirit of Bernanke, Boivin, and Eliasz (2005). The factors are extracted as principal components from a large monthly dataset for the US economy, FRED-MD (McCracken and Ng 2015), which includes 128 macroeconomic series. We include the first three factors in the VAR, which account for about 55% of the total variance of the data. The FAVAR contains the following variables X_t = [f⁽¹⁾; f⁽²⁾; f⁽³⁾; S&P500; confidence; uncertainty; IP; C; CPI; FFR; spread], where f⁽¹⁾, f⁽²⁾, f⁽³⁾, IP are respectively the three factors and industrial production. We include a measure of consumer confidence from OECD (2015), to avoid that the effects of uncertainty are confounded with the agents’ perception of bad economic times. We also include the spread between the yield on BAA corporate bonds and the 10-year constant-maturity treasury bond. S&P500, confidence, uncertainty, IP, consumption, CPI are in logs to interpret the IRFs in percentage changes terms. Figures A.10 and A.11 display the results of the FAVAR, assuming the ordering described above or placing uncertainty last. The responses confirm those found in the smaller quarterly VAR used in the baseline exercise. In particular, the responses in output and consumption fall significantly both in the short and in the long-run. The response of the nominal variables is less clear-cut, with both price and interest rate falling significantly on impact, but quickly becoming insignificant within the first year.

Figure A.10:

Monthly FAVAR and macro uncertainty.

Figure A.11:

Monthly FAVAR and macro uncertainty ordered last.

Post-Volker sample. Finally, we estimate the baseline quarterly VAR and the monthly FAVAR described above using the sample Jan-1985/Jun-2018 to account for the structural break in monetary policy induced by the Volker disinflation. Also in this case, as displayed in Figures A.12 and A.13, the responses of output and consumption are extremely persistent and last well beyond the business cycle frequency. Prices significantly decline throughout the 40 quarters (120 months).

Figure A.12:

Quarterly VAR: time span 1985Q1 – 2018Q2.

Figure A.13:

Monthly FAVAR: Time span 1985Q1 – 2018Q2.

Appendix B: Model

B.1 Detrended Model

In order to solve the model in Dynare, we detrend the endogenous variables V_t, u_t, C_t, I_t, K_t, S_t, N_t, Y_t, w_t, and Z_t by N_t. We define the detrended variables and the growth rate of R&D as X ̂ t ≡ X t N t and γ N , t ≡ N t N t − 1 . The detrended equilibrium conditions are provided below:

(B.1) V ̂ t = 1 − β u ̂ t 1 − 1 ψ + β E t V ̂ t + 1 γ N , t + 1 1 − γ 1 − 1 / ψ 1 − γ 1 1 − 1 / ψ ,

(B.2) u ̂ t = C ̂ t L ̄ − L t χ

(B.3) γ N , t + 1 K ̂ t + 1 = 1 − δ K x K , t ξ K K ̂ t + Λ K I ̂ t K ̂ t K ̂ t ,

(B.4) Λ K I ̂ t K ̂ t = a K , 1 + a K , 2 1 − 1 τ K I ̂ t K ̂ t 1 − 1 τ K ,

(B.5) Λ K , t ′ = a K , 2 I ̂ t K ̂ t − 1 τ K ,

(B.6) γ N , t + 1 = 1 − δ N x N , t ξ N + Λ N S ̂ t ,

(B.7) Λ N S ̂ t = a N , 1 + a N , 2 1 − 1 τ N S ̂ t 1 − 1 τ N ,

(B.8) Λ N , t ′ = a N , 2 S ̂ t − 1 τ N ,

(B.9) M t , t + 1 = β γ N , t + 1 − 1 ψ u ̂ t + 1 u ̂ t 1 − 1 ψ C ̂ t C ̂ t + 1 V ̂ t + 1 E t V ̂ t + 1 1 − γ 1 1 − γ 1 ψ − γ ,

(B.10) χ C ̂ t L ̄ − L t = w ̂ t ,

(B.11) 1 = q K , t Λ K , t ′ ,

(B.12) q K , t = E t M t , t + 1 r K , t + 1 x K , t + 1 + q K , t + 1 1 − δ K x K , t + 1 ξ K − Λ K , t + 1 ′ I ̂ t + 1 K ̂ t + 1 + Λ K , t + 1 ,

(B.13) r K , t = q K , t δ K ξ K x K , t ξ K − 1 ,

(B.14) 1 = q N , t Λ N , t ′ ,

(B.15) q N , t = E t M t , t + 1 r N , t + 1 x N , t + 1 + q N , t + 1 1 − δ N x N , t + 1 ξ N − Λ N , t + 1 ′ S ̂ t + 1 + Λ N , t + 1 ,

(B.16) r N , t = q N , t δ N ξ N x N , t ξ N − 1 ,

(B.17) 1 = E t M t , t + 1 R t π t + 1 ,

(B.18) w ̂ t = m c t 1 − α Y ̂ t L t ,

(B.19) r K , t = m c t α Y ̂ t x K , t K ̂ t ,

(B.20) r N , t = m c t 1 − α η Y ̂ t x N , t ,

(B.21) ϕ P π t π − 1 π t π = ϕ P E t M t , t + 1 π t + 1 π − 1 π t + 1 π Y ̂ t + 1 Y ̂ t γ N , t + 1 + 1 − ε + ε m c t ,

(B.22) R t R = π t π ρ π Y ̂ t Y ̂ t − 1 γ N , t γ N ρ Y ,

(B.23) Y ̂ t = x K , t K ̂ t α Z ̂ t L t 1 − α ,

(B.24) Z ̂ t = A t x N , t ,

(B.25) Y ̂ t = C ̂ t + I ̂ t + S ̂ t + ϕ P 2 π t π − 1 2 Y ̂ t ,

(B.26) log A t = 1 − ρ A log A + ρ A log A t − 1 + σ t A ε t A ,

(B.27) log σ t A = 1 − ρ σ A log σ A + ρ σ A log σ t − 1 A + σ σ A ε t σ A .

Figure B.1:

Uncertainty shock with different levels of risk aversion.

Inflation and interest rate are expressed in annualised percentage points. All other variables are in per cent change.

Figure B.2:

Uncertainty shock with different levels of price stickiness

Note: Inflation and Interest Rate are expressed in annualised percentage points. All other variables are in per cent change.

Figure B.3:

Uncertainty shock with different levels of technological spillovers.

Inflation and interest rate are expressed in annualised percentage points. All other variables are in per cent change.

Figure B.4:

Uncertainty shock with different levels of capital adjustment costs.

Inflation and interest rate are expressed in annualised percentage points. All other variables are in per cent change.

Figure B.5:

Uncertainty shock with different levels of R&D adjustment costs.

Inflation and interest rate are expressed in annualised percentage points. All other variables are in per cent change.

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Received: 2021-03-30

Revised: 2021-12-07

Accepted: 2022-02-16

Published Online: 2022-03-04

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Artikel in diesem Heft

https://doi.org/10.1515/bejm-2021-0074

Schlagwörter für diesen Artikel

uncertainty shocks; R&D; total factor productivity; endogenous growth