Uncertainty and long-run economy: the role of R &D and business dynamism

We start with a brief description of the IV-SVAR framework to identify the structural VARs using external instruments building on Stock and Watson (2012), Mertens and Ravn (2013), and Piffer and Podstawski (2018). We also discuss the conditions for the instrument to be valid. Consider the following reduced form of the VAR model to be estimated:where \(X_{t}\) is a \(n\times 1\) vector of endogenous variables, M is constant, A(L) denote p-order lag polynomials and \(u_{t}\) is a \(n\times 1\) vector of residuals having zero-mean. Assume that the structural VAR is given bywhere \(\varepsilon _{t}\) is a \(n\times 1\) vector of structural shocks that are assumed to be serially and mutually uncorrelated. Hence, the structural shocks in Eq. 1 are related to the residuals in Eq. 2 through the following equationThe vector \(\varepsilon _{t}\) consists of uncertainty shock and shocks to the other variables in vector \(X_{t}\). Let \(\varepsilon _{t}^{u}\) denote the uncertainty shock and \(\varepsilon _{t}^\textrm{other}\)as the vector of other structural shocks. We can rewrite Eq. 3 as followingwhere \(B_{u}\) is a column vector capturing the impact effect of an uncertainty shock on the variables of the model and \(B_\textrm{other}\) is a matrix collecting the impact effect of other shocks. If we are only interested in the effect of uncertainty shocks, we only need to identify \(\varepsilon _{t}^{u}\), and the identification of \(\varepsilon _{t}^{u}\) boils down to obtaining column vector \(B_{u}\).

Let \(z_{t}\) be a random variable that can serve as an instrument for the uncertainty shock. Assume the following conditions are satisfiedIn the above conditions, Eq. 5 is the relevance condition which says that \(z_{t}\) is correlated with the uncertainty shock and Eq. 6 is the exogeneity condition which says that \(z_{t}\) is uncorrelated with the other shocks. As long as Eqs. 5 and 6 hold, \(z_{t}\) can be used as an instrument to identify \(\varepsilon _{t}^{u}\) since it allows to capture only the effect of \(\varepsilon _{t}^{u}\) on \(u_{t}\). To see this, multiply the terms in Eq. 4 with the instrument and take expectations to obtainNow, use the conditions given in Eqs. 5 and 6 in Eq. 7 to getEquation 8 shows that we can estimate a ratio of the single elements of column \(B_{u}\) by exploiting the correlation between the reduced form residuals and the instrument. To recover the single elements of column \(B_{u}\), one needs to also exploit the information from the variance-covariance matrix of the reduced form residuals. The details of recovering full column vector \(B_{u}\) can be found in Mertens and Ravn (2013) and Gertler and Karadi (2015).

We follow the methodology of Piffer and Podstawski (2018) (P &P, hereon) to construct the instrument for the identification of uncertainty shocks using the IV-SVAR model described in the previous subsection. P &P uses the change in the price of gold around key events as an instrument for the CBOE S &P 100 Volatility Index (VXO).⁴ P &P extends the events already identified by Bloom (2009) through peaks in VXO by adding natural disasters, and other social and political events, and identifies the ones not anticipated by the economic agents as key events. To construct the instrument, P &P calculates the percentage variation in the price of gold between the last and first available auction price before and after the key event, respectively, and then, sums up these variations within a month. P &P shows that their instrument Granger causes various measures of uncertainty and is exogenous, uncorrelated with other identified shocks in the literature such as productivity, monetary and fiscal policies. Furthermore, their results show that the instrument satisfies the relevance and exogeneity conditions.

Considering the advantages of the IV-SVAR model and the suitability of the gold price as an instrument, we follow the P &P methodology and use their extended database.⁵ However, rather than summing up variations within a quarter, we construct the instrument differently. We first identify the monthly variations using Gertler and Karadi (2015) aggregation method and then, sum up the monthly variations within a quarter.⁶ More specifically, we cumulate the variations in the gold price around key events over the last 31 days and then, averaged across each day of the month to create the monthly proxy. In this way, we are able to account for the effect of an event that occurred in the last days of the month over the next month. We then sum up the monthly proxies within a quarter to obtain the quarterly instrument.⁷

The behaviour of the final instrument for the uncertainty shock is shown in Fig. 1.⁸ Similar to P &P, the instrument is well dispersed and not concentrated on certain periods over the sample and positive peaks are larger in magnitude relative to the negative counterparts. The largest peaks are observed around the key events; hence, quarterly aggregation did not trim the value of the instrument during those events.

The data for the main variable of interest, uncertainty, come from the measure of macroeconomic uncertainty estimated by Jurado et al. (2015). We use the US potential GDP from the CBO (Potential Output) to capture the long-run economic activity. We use GDP as a measure of aggregate macroeconomic activity (Output) and Nonfarm Business Sector: Hours Worked for All Workers (Hours) and durable consumption and private fixed investment excluding R &D investment (Capital Investment) to account for the changes in factors of production, namely labour and capital. We use the Federal Funds Effective Rate (Interest Rate) as a measure of US interest rates to control for the stance of monetary policy. We use private fixed investment in R &D (R &D Investment) and firm creation (Firm Entry) as potential variables to capture the changes in productivity. The data for Firm Entry are obtained after merging two series of establishment births: new business incorporations from the Survey of Current Business, which starts in 1948 and ends in 1994, and the establishment births provided by the US Bureau of Labour Statistics Business Employment Dynamics, which starts in 1992. In this way, we can benefit from longer time series in our empirical setup.⁹

The variables Potential Output, Output, Capital Investment, and R &D Investment are divided by the GDP implicit price deflator and civilian non-institutional population, whereas Hours and Firm Entry are divided by the population index.¹⁰ Then, all these six variables are taken in logs to express them in log real per capita terms. We also take logs of Uncertainty to express the IRFs in percentage terms. Further details on our data can be found in “Appendix A.2”.

We set up an IV-SVAR model which contains these eight endogenous variables after the described transformations: Uncertainty, Output, Interest Rate, Hours, Potential Output, Capital Investment, Firm Entry, and R &D Investment.¹¹ The data span the period 1960Q3-2019Q4 at a quarterly frequency. We run the VAR in levels to avoid possible cointegration problems. According to the AIC criterion, we estimate the model on three lags. Since we aim to determine the possible long-run impact of the uncertainty shocks, we look at 40 quarters (10 years) in our impulse analysis. An important note is that the ordering of the variables is not important in our setup since we identify the impulse vector associated with the uncertainty shock using our instrument. We believe this is a robust feature of our method compared to the commonly used recursive identification method because we can bypass the restriction of the timing of the relationship between uncertainty and real activity. Thanks to our empirical model, we can avoid the discussion of whether uncertainty is a source of variations in macro variables or is a response to the developments in those variables. Finally, the reduced form model is estimated equation by equation using Ordinary Least Squares. We compute confidence intervals using the wild bootstrap developed by Gonçalves and Kilian (2004) to account for both estimation and identification uncertainty.¹²

We test the strength of instrument by regressing the residuals from the IV-SVAR model on the instrument following Gertler and Karadi (2015). An instrument is a strong one if it sufficiently correlates with the uncertainty residual and is uncorrelated with the remaining residuals. We conduct the test by running the following regressions for each of the eight variables of the model:where \({\hat{u}}_{it}\) is the estimated residual for variable i and \(z_{t}\) is the instrument. The results of these tests are reported in Table 1.

We use F-test to determine the relevance of the instrument. The standard criterion in the literature is that an F-statistic below 10 indicates a potential problem with relevance of the instrument (Staiger and Stock 1997). However, Olea and Pflueger (2013) show that the threshold can be higher when the residuals are serially correlated. Since serial correlation can be an issue in the estimated residuals from reduced from VAR, we use the Olea and Pflueger effective F-statistics thresholds following Ramey and Zubairy (2018). We select the threshold of 19.7 for the 10-per cent critical value for single instrument. The instrument passes this threshold only for the uncertainty variable and remains below it for the other variables. Moreover, the coefficient is positive when the residual from the uncertainty variable enters Eq. 9 as the dependent variable. These findings indicate that the instrument satisfies the relevance and exogeneity conditions.

Figure 2 depicts the impulse responses obtained from the VAR. The solid lines are the mean responses to a one standard deviationuncertainty shock, while the shaded areas represent 68 (dark grey) and 95 (light grey) per cent wild bootstrapped confidence intervals. The response of output is negative and persistent. The potential output declines slowly over time and reaches a new lower level in response to the uncertainty shock. The responses of these variables are statistically significant at a 95% confidence level, and they do not revert back to their initial level. The response of the R &D investment is negative at all horizons with a larger magnitude in the first two years and does not revert back to its original level similar to output. Firm entry declines swiftly on impact following the shock and starts recovering gradually after the first year. The capital investment and hours decrease in response to the uncertainty shock with a larger effect in the first two years. Although the responses of these variables remain negative, the impact diminishes over time. The interest rates decline following the uncertainty shock possibly to mitigate the negative impact of the shock on real economy by stimulating economic activity.

The empirical evidence in Fig. 2 suggests that uncertainty has a long-run effect on the economy which can be seen from the negative and persistent response of potential output. Assuming that potential output can be proxied by the Cobb–Douglas production function, labour and capital can exert effects on it through changes in hours and capital investment, and technology can affect it through changes in firm entry and R &D investments.^13,14 Although hours worked and capital investment decrease in the short-run, they revert back in the medium-to-long run. This suggests that the persistent decline in the potential output is due to other potential factors including R &D investments and firm entry. The inspection of these mechanisms is the subject of the next section.

The forecast error variances from the IV-SVAR are reported in Table 2.

The uncertainty shock explains a large fraction of the variance of uncertainty on impact, but the explanatory power decreases gradually over time and goes below 30% at 10-year horizon. The uncertainty shock accounts for a sizeable fraction of output, hours, and capital investment in the short and medium run (37, 54, and 44 per cent at 2-year horizons, respectively); however, the effect diminishes in the long run although it still explains more than 25 per cent of the variation of these variables at 10-year horizon. A similar observation can be made for firm entry and R &D investments in the short-run, the effect of uncertainty peaks at 2-year horizon, whereas the effect at similar magnitude continues to be present in the long run as well. At 10-year horizon, uncertainty shock explains 20 and 26% of the variation in firm entry and R &D investments, respectively.

On the other hand, the picture for the potential output is different. The uncertainty shock initially explains a small fraction of variation in potential output, 12% over the 1-year horizon, yet the effect increases over time and roughly accounts for 30% of variation over the 5 and 10-year horizons. This evidence suggests that the effect of uncertainty shock on the potential output builds over time which generates the observed persistent response of the economy in the long run.

We investigate the role played by the estimated uncertainty shocks in driving the variables of the model. Figure 3 shows the historical decomposition of the variables in the IV-SVAR model with respect to the impact of the uncertainty shock.

Several interesting results emerge. The contribution of the uncertainty shock to the real variables such as output, capital and R &D investments, and potential output is limited until the late 80 s. However, the same shock has large effects on the interest rate and firm entry during the same period. Beginning with the 1990s, the uncertainty shock starts contributing substantially to the real variables. The increase in output and potential output during this period until the Great Recession, according to Fig. 3, is largely attributable to the low uncertainty. However, the uncertainty shock occurred during the Great Recession reverses the picture. The shock contributed to the depth of recession and the prolonged decline in the real variables over the last decade after the Great Recession.

We conduct several robustness checks to ensure that the results are not driven by certain assumptions of modelling but remain valid under alternative specifications. This section discusses the solidity of our results with respect to the employment of: (i) an alternative instrument for uncertainty; (ii) alternative measures of macroeconomic uncertainty; (iii) an alternative measure of productivity; and (iv) subsamples.