Short and Long Run Uncertainty

Transcription

1 Short and Long Run Uncertainty Jose Maria Barrero, Nicholas Bloom, and Ian Wright July 8, 2016 Abstract Uncertainty appears to have both a short-run and a long-run component, which we measure using firm and macro implied volatility data from 30 days to 10 years duration. Examining a panel of over 4,000 firms from 1996 to 2013 we find that investment is significantly more sensitive to long-run uncertainty, while employment responds equally to short- and long-run uncertainty. We build a model to investigate this phenomenon, and find that the higher adjustment costs and lower depreciation rates of capital can explain why investment is particularly sensitive to longer-run uncertainty. This suggests that investment in other long-lived and irreversible capital goods - like buildings and intangibles such as R&D and organizational capital - will also be particularly sensitive to long-run uncertainty. We then examine drivers of uncertainty over different time horizons, finding oil price volatility is particularly important for short-run uncertainty, policy uncertainty is particularly important for long-run uncertainty, while currency volatility and CEO turnover appear to equally impact short and long run uncertainty. Acknowledgments: We thank seminar participants at Stanford, the 2015 World Congress of the Econometric Society, and the 2016 SED Annual Meeting for helpful comments. We thank the National Science Foundation and SIEPR for providing generous research support. Disclaimer: This paper was written in Ian Wright s individual capacity and is not related to his role at Goldman Sachs. The analysis, content and conclusions set forth in this paper are those of the authors alone and not of Goldman Sachs & Co. or any of its affiliate companies. The authors alone are responsible for the content. Keywords: Uncertainty, investment, employment. JEL Codes: D92, E22, D8, C23 Stanford University; Stanford University, NBER and SIEPR; and Goldman Sachs. 1

2 1 Introduction Uncertainty has received substantial attention as a potential factor shaping aggregate economic outcomes. For example, the Federal Open Market Committee minutes repeatedly emphasize uncertainty as a key factor driving the 2001 and recessions, while Stock and Watson (2012) state that "the main contributions to the decline in output and employment during the [ ] recession are estimated to come from financial and uncertainty shocks." More recently, in the summer of 2016 the world economy was rocked with one such uncertainty shock when the United Kingdom voted to leave the European Union. But the Brexit vote generated no uncertainty about economic policies or fundamentals in the days and weeks immediately following the vote. Instead, the referendum results created huge questions about the future of the UK s trading relationships, the long-run immigration status of European Union citizens living in the UK and vice versa, and more broadly about the long-run outlook of the British, European, and global economies. Following the Brexit vote IMF Chief Christine Lagarde spoke to the Financial Times urging for "clarity sooner rather than later because we think that a lack of clarity feeds uncertainty, which itself undermines investment appetites and decision making." Underlying her comment are the potential consequences of long-run as opposed to short-run uncertainty in the wake of the UK s decision to leave the European Union. This paper seeks to investigate whether short- and long-run uncertainty impact the economy equally by exploiting the information in the time profile of uncertainty across equity options of different durations. Equity options are issued at a range of durations from 30 days to 2 years for individual equities and 30 days to 10 years for the overall S&P 500 index, yielding firm and macro volatility curves. In Figure 1 we show some examples of the fluctuations in the macro volatility curve, using data that generalizes the well-known VIX (a 30-day implied volatility on the S&P 500) to longer horizons. The changing level and slope of these volatility curves reflects fluctuations in the time profile of uncertainty, which could influence different firm decisions if their payoffs have distinct time profiles. For example, investment as a longer-run decision may respond more strongly to long-run uncertainty than hiring. 2

3 To investigate this hypothesis we build a panel dataset of over 4,000 firms from 1996 to 2013 combining firm and macro equity options data across a range of horizons and a range of real and financial variables. We find that investment and employment are both significantly reduced by uncertainty, but investment is significantly more responsive to longrun uncertainty than employment. We also find that investment is more negatively associated with both short- and long-run uncertainty for smaller, slow-growing, and more highly-levered firms. We then turn to investigating the drivers of short- and long-run uncertainty over the past decade, examining four factors that vary at the firm-quarter level to provide good empirical variation, namely the price of oil, exchange rates, policy uncertainty and CEO turnover. We find that policy uncertainty has a significantly larger impact on long-run than short-run uncertainty, perhaps not-surprisingly given the longer-run focus of many of the major policy debates over this period, including discussions about the debt ceiling, health-care reform and uncertainty over US involvement in foreign wars. On the other hand, oil-price uncertainty appears to play a particularly important role in shaping short-run uncertainty, reflecting perhaps that fact that the oil price as a mean-reverting stochastic process (see for example, Pindyck 1990) has far greater short-run than long-run uncertainty. Finally, currencies and CEO turnover appear to roughly equally impact both short-run and long-run uncertainty. Finally, we simulate a model with short- and long-run uncertainty processes and two factors - capital and labor - which are distinguished by capital having higher adjustment costs and lower depreciation rates. We find that this greater adjustment cost and durability of capital makes it significantly more responsive to long-run uncertainty in the model. This highlights how factor inputs with low depreciation rates (like buildings and long-lived equipment investments) and high adjustment costs (like intangibles such as R&D and organizational capital) are going to be particularly sensitive to long-run uncertainty. As such, the recent increases in policy uncertainty in the US - a key driver of long-run uncertainty - may play a role in explaining the puzzlingly low level of aggregate investment and low TFP growth rates (given the importance of intangible investment for TFP growth). Similarly, we predict that the United Kingdom might face depressed investment and growth in the months and years following the Brexit vote as long as there is outstanding uncertainty about the 3

4 future of British economic policy and trading relationships. Our paper relates most obviously to the empirical literature focused on the impact of uncertainty for investment (and to a lesser extent hiring) - for example, Bernanke (1983), Dixit and Pindyck (1994), Caballero, Engel and Haltiwanger(1995) and Abel and Eberly (1996). It is also related to the empirical literature that studies the impact of real frictions on investment dynamics - for example, Leahy and Whited (1996), Gusio and Parigi (1999) and Bloom, Bond, and Van Reenen (2007) all provide evidence suggesting that firm-level uncertainty shocks reduce firms investment and hiring, while Romer (1990), Ramey and Ramey (1995), Bloom (2009), Fernández-Villaverde et al. (2011) provide evidence suggesting macro uncertainty shocks appear to drive business cycle fluctuations 1. However, none of this literature focuses on the difference between short-run and long-run uncertainty. Perhaps closer to our paper is the asset pricing literature examining the volatility curve, including Bekaert and Hoerova (2014) and Dew-Becker et al (2015). In a closely related paper Berger, Dew-Becker, and Giglio (2016) study whether aggregate realized volatility or expectations of future volatility are associated with contractionary movements in macro variables, finding that volatility expectations have a hard time explaining contractions after accounting for current realized volatility. Our work differs from theirs in that we focus on the idiosyncratic volatility curve and on firm-level outcomes, where we find strong associations between the time profile of volatility and flow variables like investment and hiring. Section 2 describes our data, section 3 contains the main results on the response of investment and hiring to uncertainty, while section 4 investigates the drivers of short- and long-run uncertainty. Section 5 presents a model and simulation results, while section 6 concludes. 1 See also Kehrig (2011) s paper on countercyclical productivity dispersion; Christiano, Motto, and Rostagno (2014) s, Arellano, Bai, and Kehoe (2012) s and Gilchrist, Sim, and Zakrajsek (2014) s papers on uncertainty shocks in models with financial constraints; Basu and Bundick (2012) s paper on uncertainty shocks in a new-keynesian model; Fernandez-Villaverde, Guerron-Quintana, Kuester, and Rubio-Ramirez (2015) s paper on fiscal policy uncertainty; Knotek and Khan (2011) s paper on durable consumption and uncertainty; and Bachmann and Bayer (2013) s paper on microeconomic level uncertainty with capital adjustment costs. Interested readers may also refer to Bloom (2014) for a broad survey of the investment and uncertainty theory and empirical literature. 4

5 2 Data and Measurement 2.1 Measuring Short- and Long-run Uncertainty We use data on option implied volatilities as our empirical measures of short- and long-run uncertainty at the macro and firm levels. Implied volatilities are calculated by taking option trading data and inferring what volatility in the value of the underlying would result in the observed option prices, often using an option pricing model (e.g. the Black-Scholes 1973 formula). Formally, an implied volatility measures the expected risk-neutral volatility of an underlying s price over the horizon covered by the maturity of the option. Roughly speaking, if σ(t) is a stochastic process for the volatility of a firm s share price, then the T -day implied volatility of the firm on date t reflects the market s expectation of the average volatility of the ( ) 1 t+t firm s share price over the life of the option: E t σ T i (s)ds. Often implied volatilities are considered forward-looking measures of uncertainty, because they reflect a market-based measure of expected firm or aggregate volatility of returns on the underlying security. The VIX, published by the Chicago Board of Options Exchange, is a well-known index of the 30- day implied volatility of the S&P 500, and is often used as a proxy for measuring short-run US macro uncertainty. In our main empirical results we focus on firm-specific implied volatility, which can be calculated using options of any horizon, making it possible to measure expected uncertainty over a wide range of durations. We obtain individual firm implied volatility data from 1996 onwards from Option Metrics, a database covering all exchange-listed options in the United States. They provide implied volatility figures for standardized options with horizons of 30, 60, 91, 152, 182, 273, 365, and 730 days, conditional on the firm having options trading at or beyond that maturity 2. t Throughout our empirical work we use the average of the put and call implied volatilities at each given duration, but our findings are robust to using either of the two instead, as the put and call data are nearly identical. Because our data on firm financials is at an annual or quarterly frequency (see Section 2.2), we average daily implied volatility observations into a single uncertainty measure by firm-quarter. In our 2 Option Metrics uses observed option trading data to provide information about theoretical "standardized" options, which are theoretical American put and call options with strike prices equal to at-the-money forward stock prices and fixed maturities. See A for more details. 5

6 empirical specifications, we link a firm s investment behavior in a given quarter with the implied volatility measured in the previous quarter, to mitigate reverse causality concerns and to exploit the fact that implied volatilities are forward-looking. Similarly, we link firmlevel observations in a given fiscal year with the average implied volatility in the last quarter of the previous fiscal year. Because firm equity options with longer maturities (e.g one year and beyond) are traded less frequently, implied volatility data at these longer horizons is often missing. This both decreases sample size when using these longer-run firm-level uncertainty measures, and also potentially raises issues over the selection of larger firms whose equity options trade at these longer horizons. To overcome these problems, we first document the stylized fact that volatility curves (the plot of volatility over different durations) are approximately linear so we can approximate the entire volatility curve with two points, as is analogously done with the term structure of interest rates. Starting with column (1) in Table 1 we show that the quarterly two-year firm-specific implied volatility (the longest duration firm equity option commonly available) is well predicted by the corresponding level (30-day implied vol.) and slope (difference between the 6-month and 30-day volatilities) data, with an R-squared of Hence, if we have data for the 30-day and 6-month implied volatilities for a firm - selecting the 30-day and 6-month durations as these are commonly traded - we can use them to proxy for the intercept and slope of the full (approximately linear) volatility curve. In columns (2) to (5) we repeat this exercise for daily observations of macroeconomic uncertainty using the generalized VIX on the S&P500 index. This data came from Goldman Sachs based on replicating the methodology on the VIX on its entire portfolio of proprietary equity options 3. Again we see consistent R-squared values above 0.9, suggesting that the entire macro volatility curve can also be well described using only two data points. This strong linearity is shown graphically in Figure 2 which plots the 2-year and 5-year VIX against their fitted values from the regressions of the 3 The "true" VIX published by the Chicago Board Options Exchange and what is generally referred to as "the VIX" is a model free measure of the risk neutral implied volatility of the S&P 500 index over the next 30 days. It is computed specifically for that horizon. However, the formula can be generalized to compute a VIX for various horizons, using variance swaps or options. Our generalized VIX data was generously provided by Goldman Sachs, for reasons unrelated to Ian Wright s employment with them. For details, see CBOE (2009). 6

7 30-day and 6-month VIX in columns (2) and (4), where we see both the good overall fit and the fact this fit appears equally good at low, medium and high levels of implied volatility. In our empirical section we will measure short-run and long-run uncertainty using only 30-day and 6-month implied volatility data, which we combine into a level term (30-day implied volatility) and a slope term (6-month-30-day volatility) following the practice for modeling the yield curve. 2.2 Firm-level Data We match our firm-specific implied volatility data with quarterly and annual financial data from Compustat, dropping firm-quarters and firm-years with negative book value of assets, negative sales or stockholders equity, as well as those with missing capital expenditures. Our quarterly sample ranges from 1996Q2 to 2013Q1, while the annual sample covers As is standard in the empirical literature on investment and uncertainty (e.g. Gulen and Ion (2013)), we exclude SIC codes corresponding to utilities and financials. The resulting matched dataset overrepresents large and fast-growing firms as these are the firms with a sufficient volume of equity option transactions for Option Metrics to provide implied volatility estimates. See Appendix Table 2 for summary statistics on the matched quarterly and annual samples, and Appendix Table 3 for some results on what firms have non-missing data on 30-day and 6-month implied volatility. In the quarterly data we measure investment as firms gross capital investment rate (capital expenditures per existing unit of capital). In the annual data we instead focus on growth in the net number of employees and the net stock of plant, property and equipment (PPENT) for comparability to each other and also our theory model in section (5), noting annual results using capital investment rates (shown in column (9) of Table 4) look very similar. Following Davis, Haltiwanger and Schuh (1996), our main specifications measure these growth rates as the change in stock variable x t between years t 1 and t, divided by the average of the two years. In both datasets we construct standard first-moment controls like the ratio of cash flows (i.e. operating income) to assets, Tobin s q (the ratio of the firm s enterprise value to the book value of it s assets) and sales growth (again, measured as the difference over the average). 7

8 3 Investment and Hiring under Short-Run and Long-run Uncertainty In this section we document our main empirical findings that the investment and hiring behavior of large, publicly-traded firms in the US is negatively associated with both shortand long-run uncertainty. Moreover, we find that physical capital investment declines significantly more than hiring during times of high long-run relative to short-run uncertainty, and that smaller, slower-growing and more highly-levered firms invest less intensively during times of high short- and long-run uncertainty. 3.1 Specification and Identification We study the empirical relationship between investment and hiring against short- versus long-run uncertainty by estimating equations of the form Y i,t = α i + γ t + β 1 log(30div OL i,t 1 ) + β 2 (log(6miv OL i,t 1 ) log(30div OL i,t 1 )) +δ 1 Q i,t 1 + δ 2 CF i,t /A i,t 1 + δ 3 G i,t + ε i,t (1) where i indexes firms and t indexes quarters or years depending the specification. α i is a vector of firm fixed effects, γ t is a vector of date fixed effects, 30dIV OL it and 6mIV OL it are the 30-day and 6-month implied volatilities associated with firm i on date t, and Q i,t, CF i,t /A i,t 1, and G it are respectively Tobin s q, the ratio of current cash flows to book value of assets, and sales growth 4. Throughout this section we cluster our standard errors by firm. In order to try and obtain some causal identification we used lagged uncertainty, although our results are conditional correlations between short- and long-run implied volatility and the investment and hiring activity at the firm level. As we shall show in section (5) these conditional correlations do correctly sign the causal impact of uncertainty in our simulation model, so are at least consistent with a causal interpretation under this modeling null. 4 Tobin s q is the ratio of the firm s full enterprise value (common and preferred stock capital plus current and long-term liabilities) over the book value of assets. Cash flow is measured as income from operating activities, and sales growth is measured as the difference over the average of sales in the past year and the previous year following Davis, Haltiwanger, and Schuh (1996). 8

9 To further aid identification we also include firm and date fixed effects as well as several first moment controls, including Tobin s q, the cash flow ratio and sales growth. While we acknowledge that these variables probably cannot control for all unobserved first-moment determinants of investment that may be correlated with short- and long-run uncertainty, controlling for them does restrict the channels by which endogeneity can bias our results. 3.2 Empirical Results In Table 2 column (1) we study the link between quarterly investment measured as the ratio of quarterly capital expenditures (CAPX) per unit of perpetual inventories capital on the level of uncertainty proxied by the log of 30 day implied volatility, and the slope of volatility measured as the log difference between 30 day and 6 month implied volatility. We see that both the level and slope coefficients are significantly negative, suggesting both short-run and long-run uncertainty are negatively associated with capital investment. In column (2) we add cash-flow and sales growth to Tobin s Q as first-moment controls and find a similar negative result. Quantitatively, the results point to significant fluctuations in investment associated with movements in short- or long-run implied volatility at the firm level. A two standard deviation increase in log(30div OL) or log(6miv OL) log(30dv OL) is respectively associated with a decline in the investment rate of 25% and 3%. In column (3) we run a specification using aggregate volatility (the generalized VIX), taking the 5-year volatility as the long-run measure and dropping the date fixed effects. We still find very strong negative associations between investment and the level and slope of the aggregate volatility curve, similar in magnitude to those of firm-specific volatility from columns (1) and (2). In column (4) we examine annual (rather than quarterly) investment using the growth rate of the net stock of plant, property and equipment. Again we see a similar result of negative impact of both the short-run level and long-run slope of uncertainty. The implied magnitudes are also large - a two standard-deviation in the level and slope of uncertainty is associated with a reduction of investment of 4.6 and 0.8 percentage points which are jointly about 60% of the mean value of investment. Having established that gross investment in physical capital is negatively linked to both 9

10 short- and long-run uncertainty, we look at net hiring in column (5). We find that while net hiring is negatively associated with short-run uncertainty there is no relationship between hiring and the slope of uncertainty. As with investment, the magnitude of this uncertainty relationship is also quantitatively large - a two standard-deviation increase in short-run uncertainty is associated with a 2.4 percentage-point drop in net hiring, or a fall of about one half of the overall level. In the last four columns we investigate the relative response of investment versus hiring to the short-run level and slope of uncertainty, regressing the growth rate of net capital less the growth rate of net employment against our uncertainty measures. In column (6) we see a significant level and slope coefficient, highlighting how capital is more responsive to both short-run and long-run uncertainty. As we add more controls in columns (7), (8) and (9) we see this result remains robust, reflecting the key difference between capital and labor is the former s far stronger response to long-run uncertainty. As we discuss in the simulations in section 5 this far stronger response of capital investment to uncertainty - particularly long-run uncertainty - appears to reflect both its greater adjustment cost and also lower depreciation rate. Hence, capital investment decisions are more long-term focused and more sensitive to long-run uncertainty. Thus, when uncertainty shocks occur that particularly increase long-run uncertainty this will tend to disproportionately reduce investment, lowering the capital-labor ratio. As we discussed in the introduction, the currently extremely low levels of investment in the US could be due in part to the high levels of policy uncertainty, which as we shall see in the next section is most closely related to long-run uncertainty. In Table 3 we consider heterogeneity in the way firms invest during times of high shortor long-run uncertainty. In column (1) we reproduce column (2) of Table 2 as a baseline regression. In columns (2) and (3) we split our sample into small and large firms by sales, and note that small firms quantitatively show about double the negative association between investment and short- and long-run uncertainty when compared to large firms. This smaller sensitivity of large firms to uncertainty could be be because they are more diversified (so more able to move assets across sectors in response to idiosyncratic uncertainty) and also less financially constrained. Similarly, in columns (4) and (5) we split the sample into firms with 10

11 above- and below-median sales growth, finding that fast-growing firms show smaller declines in investment during times of heightened short- and long-run uncertainty. In fact, there is no quantitatively or statistically significant relationship with the slope of the volatility curve for these fast-growing firms. This is consistent with basic real-option pricing models (e.g. Dixit and Pindyck (1994)) whereby firms with faster growth rates are less likely to want to disinvest in the future, reducing the option value of current investment decisions. We finally explore the significance of financial constraints by splitting the sample by leverage in columns (6) & (7) and find that highly levered firms see significantly stronger declines in investment in times of high short-run uncertainty, reflecting the importance of the finance-uncertainty multiplier whereby real and financial constraints tend to mutually reinforce each other (see Alfaro et al. (2016)). Their investment also drops when long-run uncertainty is high relative to short-run uncertainty, but the difference in magnitude is smaller in this case. 3.3 Robustness checks Our results regarding investment and hiring are robust to small modifications to the baseline regressions run in Table 2. In Table 4 we again reproduce the base specification from column (2) of Table 2 for comparison and run a series of alternative regressions. In column (2) we drop quarters associated with the 2001 and regressions and find our results are robust, suggesting this is not a relationship driven simply by recessions. By contrast if we include only quarters associated with these downturns, as in column (3), we still find that both short- and long-run uncertainty are negatively associated to investment, and that the slope coefficient actually becomes larger than that on the level of uncertainty. In column (4), we run a specification that uses the levels rather than logs for the investment rate, short-run uncertainty, and the difference between long- and short-run uncertainty finding similar results. In column (5) we show that using the 2-year firm-specific implied volatility to measure long-run uncertainty yields similar results to our baseline choice of 6 months, albeit with a much smaller sample. Furthermore, for the regression in column (6) we predict the log of 2-year implied volatility based on a regression of log 2-year volatility on the contemporaneous 30-day and 6-month log implied volatility, and use this prediction to create the slope variable. 11

12 The results are quantitatively similar to those in column (5), with a slightly larger coefficient on the slope (and also a larger standard error presumably as a result of the prediction). In column (7) we add a lagged dependent variable as a regressor to control for the fact that current investment expenditures may be committed to in advance and subject to timeto-build delays, which does not destroy the strong negative association between current investment and short- and long-run uncertainty. In column (8) we control more flexibly for common determinants of investment by using 3-digit-sector-by-date fixed effects rather than simple time dummies, and finally, in column (7) we run an annual specification using the log investment rate as a dependent variable, instead of the the net growth in net property, plant, and equipment that is used in the annual investment regressions in Table 2. As in the previous cases, our results are qualitatively and quantitatively robust to making these modifications. 4 Drivers of Short- and Long-run Uncertainty In the preceding pages we have documented variation in the level and slope of firm-specific volatility curves and exploited these fluctuations to explore how they correlate with investment and hiring activity among Compustat firms. But what are the economic reasons leading market actors to perceive the volatility of firm equity to be high or low for any given horizon? In this section, we construct firm- and sector-specific measures of exposure to several sources of uncertainty, including economic policy, oil prices, and changes in management. Then we ask whether these exposure measures are differentially associated with short- or long-run uncertainty, shedding some light on what may drive fluctuations in the term structure of uncertainty. 4.1 Data on Uncertainty Drivers We focus on a set of drivers of firm-level uncertainty which can be measured at a quarterly basis. In particular, we focus on oil and currency volatility as suggested by Stein and Stone (2013), economic policy uncertainty (EPU) as measured by Baker, Bloom, and Davis (2015), and CEO turnover as implied by Bertrand and Schoar (2003) s highlighting of the importance 12

13 of CEOs for company performance. We acknowledge that there are potentially many other factors driving idiosyncratic firm-level volatility, with our focus on these four driven by data availability. However, these four factors do capture a number of the key drivers of firm-level uncertainty, and also highlight their differential impacts on short- and long-run uncertainty. We construct sector-level exposure to oil and currency volatility using a two-step procedure. First, we estimate the sensitivity of stock returns to oil and currency fluctuations by two-digit SIC industries, controlling for firm fixed effects and market returns. We estimate the following equation for firm i in sector j and date t : r ijt = α i + β jm r mt + β jo r oilt β jk r kt + ε it. (2) The stock returns data comes from CRSP, and oil price and exchange rate data from Bloomberg. We use data from 19 currencies for which the Federal Reserve s website publishes exchange rates and for which there is also sufficient implied volatility data 5. Each of the β coefficients reflect the sensitivity in the returns of firms in industry j returns to returns on the market, oil, or a particular currency. We run this regression on a pre-sample period ranging from 1985 to 1995 and assume that the estimated sensitivities carry over to our main sample period from 2005 onwards. In the baseline setup we estimate the sensitivities by SIC-2 industry, restricting attention to sectors that have data for at least 20 firms during the estimation period. The second step in constructing volatility exposure variables involves multiplying the absolute value of each industry s sensitivity by a measure of the volatility of the commodity or currency in question. We use the log of 30-day implied volatility for oil and each of our currencies (obtained from Bloomberg and averaged over a calendar quarter), and construct an overall measure of currency volatility exposure by adding up over the individual currencies: 5 The full set of currencies we use is: Canadian Dollar, Mexican Peso, Japanese Yen, Chinese Yuan (Renminbi), Euro (or European Currency Unit prior to 1999), Australian Dollar, Hong Kong Dollar, South Korean Wong, New Zealand Dollar, Norwegian Krone, Swedish Krona, Swiss Franc, Taiwan Dollar, British Pound, Danish Krone, South African Rand, Thai Bahk, Indian Rupee, and Singapore Dollar. The Fed also publishes exchange rates for Venezuelan Bolivar, Sri Lankan Rupee, and Malaysian Ringgit, but we excluded these due to insufficient exchange rate and/or volatility data. k 13

14 OilVolExposure ijt = ˆβ jo log(σ ot ) (3) CurrVolExposure ijt = k ˆβ jk log(σ kt ). (4) In constructing these variables, we attempt to capture the fact that certain industries might be differentially exposed to fluctuations in exchange rates and commodity prices, having controlled for overall market and firm conditions. For example, the air travel and oil and gas sectors might be differentially exposed (respectively, negatively and positively) to oil price increases. We use the absolute value of the sensitivity because firms should care about volatility regardless of whether higher or lower prices have a positive impact on their returns. Data on quarterly firm-specific exposure to economic policy uncertainty (EPU) comes from Baker et al (2015), who construct these variables by scaling the firm s industry share of revenues from Federal Government contracts by the aggregate EPU index. Since each firm is allocated to an industry by its firm-level line of sales data, we get a unique firm-by-year policy uncertainty index (albeit being correlated across firms with similar industry mixes). We refer readers to their paper for details on the construction of this variable and the EPU index more broadly. Data on executive turnover comes from Execucomp a database containing information on top executives in Compustat firms, in particular listing the dates during which CEOs held office. We use these details to flag firm-quarters during which an incumbent CEO stepped down. This is a simple way of capturing an idiosyncratic event with potentially significant repercussions to the firm s future, and potentially affecting the market s uncertainty about the firm. 14

15 4.2 Drivers Results We study how oil and currency volatility, economic policy uncertainty, and CEO turnover are associated with short- and long-run uncertainty at the firm level by regressing quarterly firm implied volatility on each of the exposure measures we consider, as well as firm and date fixed effects. We consider levels specifications, in which we test whether the natural logarithm of 30-day or 6-month implied volatility is positively associated with higher exposure to any of these drivers of uncertainty. However, our main results relate to whether our drivers are differentially linked to short- or long-run implied volatility. Table 5 displays the results, with each observation corresponding to a firm-quarter. The top section refers to regressions that use the logarithm of 30-day implied volatility as the dependent variable, with the middle section using 6-month implied volatility, and the slope (the difference) in the bottom section. Starting with the top panel focusing on short-run 30-day implied volatility we see individually in columns (1) to (4) and jointly in column (5) that these factors are positively correlated with uncertainty to some degree. Moreover, oil and currency volatility exposure and CEO turnover are significantly correlated both individually and in the joint specification. In the middle-panel we look at their association with longer-run (6 month) implied volatility and again see that individually all of economic policy uncertainty, oil, currency and CEO turnovers factors are positively and significantly associated with uncertainty, with quantitatively similar results in the joint specification. Finally, in the bottom panel we examine the drivers predictive power for the slope of uncertainty defined as 6-month less 30-day implied volatility. Here we see that policy uncertainty loads positively and significantly, highlighting its greater role in explaining variations in the relative amount of long-run versus short-run uncertainty, while oil volatility loads negatively and significantly suggesting short-run uncertainty is more related to oil (and more generally energy price) uncertainty. Currency and CEO turnover have very low coefficients suggesting they have a roughly proportional impact on short-run and long-run uncertainty, so shift the entire volatility curve up or down. Overall our results are intuitive, suggesting that slow-moving and potentially more radical 15

16 drivers like economic policy are linked to long-run uncertainty. By contrast, oil price volatility might impact firms bottom lines much more quickly and perhaps transitorily, explaining why it is closely associated with short-run uncertainty. Given the results in the relatively greater sensitivity of investment than hiring to long-run uncertainty, understanding what shapes the time-profile of uncertainty is thus an important tool for assessing the patterns of observed investment and hiring behavior. 5 Model and Simulation In this final section we develop a firm-level model to help interpret our prior results on the differential sensitivity of investment and employment to short- and long-run uncertainty. We consider a partial equilibrium setup in which a firm produces using two factors, capital and labor, and is subject to short- and long-run uncertainty shocks. We solve the model numerically for data-calibrated parameters and then investigate the impact of short- and long-run uncertainty on investment activity on a 5000-firm panel of simulated data. Consistent with the empirical results from Section 3, firms stop investing and hiring in reaction to both short- and long-run uncertainty, but investment drops relatively more than hiring in reaction to long-run uncertainty. Using the model, we show that the longer life and greater irreversibility of capital are responsible for these patterns. 5.1 Model The model is a version of Bloom et al. (2007), modified to allow for short- and long-run uncertainty processes. Firms are assumed to consist of a number of production units, each making the intertemporal decision to invest and hire workers. On date t each production unit has access to a reduced-form supermodular revenue-generation function based on an underlying Cobb-Douglas physical production function, assuming that other inputs (e.g. materials) are optimized out statically: R(A t, K t, L t ) = A t K α k t L α l t (5) 16

17 A t is a stochastic Hicks-neutral shock to revenue-generating capacity, which we assume to be log-normal and follow an AR(1) process with stochastic volatility: log A t = ρ A log A t 1 + σ t ε t, ε t N (0, 1) (6) We introduce short- and long-run uncertainty to the model by assuming that σ 2 t, the variance of innovations to log A, is the sum of a transitory and a persistent component: σ 2 t = σ 2 s,t + σ 2 l,t (7) The two volatility components, σ s and σ l, follow independent, symmetric Markov chains on two points (i.e. a high and a low state), with the persistence of σ l being higher than for σ s. In the simulation we assume production units within a firm have a common volatility process, while innovations to log A, are drawn independently across units within a firm. Firms may choose to invest in new capital and hire workers, both of which become immediately available for production. Capital depreciates at a rate δ k and workers quit at a rate δ l, yielding the following laws-of-motion for K and L: K t = (1 δ k )K t 1 + I t (8) L t = (1 δ l )L t 1 + H t (9) We assume that δ k δ l, making K longer-lived than L. Investment and hiring are both subject to adjustment costs due to partial irreversibility (capital resale and layoffs result in a loss of 1 γ k, 1 γ l, respectively of the value of K and L), and are also subject to fixed adjustment costs denoted F k and F l. By assumption, K has also higher adjustment costs than L, i.e. γ k γ l, and F k F l. These differences in the life of potential investments, as well as the cost of (downward) adjustability are the key elements of the model that drive firms different reactions to short- versus long-run uncertainty. Production units decide every period how much to invest in each of K and L so as to maximize the net present value of cash flows, bearing in mind their current first-moment state A, latest stock of Kand L, and the current state of the persistent and transitory volatility 17

18 processes σ s and σ l. The complete recursive problem can be stated as follows: V (A t, K t 1, L t 1, σ s,t, σ l,t ) = A(K t 1 (1 δ k ) + I t ) α k (Lt 1 (1 δ l ) + H t ) α l max C(I t, H t, K t 1, L t 1 ; γ k, γ l, F k, F l ) I t,h t + 1 E 1+r t[v (A t+1, K t 1 (1 δ k ) + I t, L t 1 (1 δ l ) + H t, σ s,t+1, σ l,t+1 )] s.t. K t = (1 δ k )K t 1 + I t L t = (1 δ l )L t 1 + H t log A t+1 = ρ A log A t + σ t+1 ε t+1 σ 2 t = σ 2 s,t + σ 2 l,t σ s,t+1 Π s (σ s,t ) σ l,t+1 Π l (σ l,t ) (10) 5.2 Calibration, Numerical Solution and Simulation We calibrate the production unit model taking standard parameter values from the literature, when possible, and try to choose reasonable ones when there is no consensus. Following Bloom et al. (2007) we make the revenue elasticities of K and L both equal to 0.4, consistent with constant returns to scale in the physical production function, equal coefficients on K and L, and 25% markups. Because the model is stationary, we add 10% to standard annual depreciation and quit rates to reflect implicit growth in demand for comparability with the Compustat sample we study in the empirical section 6. See Appendix Table 1 for the full parameterization. The model period is set to be one month. The recursive optimization problem is fairly standard, so we solve via conventional policy iteration on a state space of (A, K, L, σ s, σ l ) of (5, 42, 42, 2, 2). Having found the optimal 6 Sales growth in our sample of Compustat firms averages about 13% per year, with the median growth rate at 8%. 18

19 investment policy for each element of the state space, we simulate a panel of 5,000 firms, each consisting of 25 production units that face the investment decision every month. The choice of 25 units per firm should be interpreted as a stand-in for some large number of divisions, offices, etc. within a firm. Each unit experiences idiosyncratic shocks to revenuegenerating ability A, but the volatility σ t of first moment shocks is common across units within a firm. The simulation is run for 360 months (30 years), but we discard the first 300 periods (25 years) to remove the influence of initial conditions. Then we aggregate monthly firm-level figures into quarterly and annual data, measuring stock variables like K and L as the sum across all units of the firm at the end of the period. For flow variables like gross investment and cash flow we take the sum across units and across months within a year or quarter. As a last step in generating our simulated dataset, we add 5% measurement error to all of the simulated data. To measure short- and long-run uncertainty for each firm-month in the simulation, we use the average expected volatility ˆσ over the next S or L months, respectively: ˆσ S,t = E t [ 1 S S σ t+m ] m=1 and ˆσ L,t = E t [ 1 L L σ t+m ], where σ t = m=1 σ 2 s,t + σ 2 l,t. We choose to measure uncertainty in this manner for analogy with option implied volatility, our uncertainty proxy in the empirical sections of the paper. Implied volatility captures the expected future uncertainty about the value of an asset over a given horizon, whose length depends on the maturity of the options used to calculate the implied volatility. See section 2.1 for details. Our baseline choices for S and L are 1 and 24 months, respectively, but our analysis is robust to using 1 and 6 months, which are the implied volatility horizons we consider in the empirical sections of the paper. As with the rest of the simulated data we average monthly uncertainty measures by quarter, but we take a firm s level of short- and long-run uncertainty in year t with the average ˆσ s,t and ˆσ l,t during last quarter in the year. This is analogous to our treatment of the empirical implied volatility data (see Section 2 for details). 19

20 5.3 Simulation Results The model generates a tight negative relationship between capital investment and both shortand long-run uncertainty. In Table 6 we regress the log of the quarterly investment rate in K on lagged and logged expected volatility by firm using 30-day, 6-month, and 2-year horizons, including first moment controls and firm and date fixed effects. Columns (1) through (3) document that our simulated investment series is negatively linked to uncertainty at all three horizons. In columns (4) and (5), we regress logged investment on both the level of short-run (30-day) expected uncertainty, and the slope uncertainty time profile, alternatively using 6 months or 2 years as the long-run horizon. The results indicate strong negative links between investment and both the level and slope, suggesting that firms invest less intensively when the overall level of uncertainty is high, and also when uncertainty over longer horizons is higher than in the short run. Qualitatively, whether we take 6 months or 2 years as the long-run uncertainty horizon makes little difference, so henceforth we focus on 6 months as the long-run horizon, for analogy with the empirical work. See section 2.1 for details. Including additional first-moment determinants of investment, specifically ones that mirror those used in the empirical section, does not qualitatively change the results. In Table 7 we investigate how uncertainty impacts investment in capital versus hiring in the model. As in our empirical specifications we focus on net capital investment (the growth rate of K), net hiring (the growth rate of L) as dependent variables. All specifications in Table 4 include firm and date fixed effects and the first moment controls we use in the empirical section, namely the simulation counterparts to Tobin s q (value/assets), cash flow (operating profits), and sales (output) growth. The results in columns (1) and (2) document negative relationships between net investment and hiring and both short- and long-run uncertainty. The magnitudes of the coefficients, however, suggest that investments in K decline particularly strongly when long-run uncertainty is high relative to short-run uncertainty. Hiring, by contrast, seems mostly sensitive to the level uncertainty, but not significantly linked to the degree of long- versus and short-run uncertainty. In columns (3) to (6) we look more closely at this hypothesis by using relative net capital investment less hiring as an outcome variable, and investigating what features of the model 20

21 are responsible by modifying the calibration. Starting with column (3), we see that in our baseline calibration net growth in K and L seem to decline about equally with the level of short-run uncertainty. However, the negative coefficient on the slope term confirms that investment responds particularly negatively when long-run uncertainty is high relative to short-run uncertainty, but hiring does not. In column (4) we set the depreciation rate of capital at the same level as the quit rate (δ l = δ k ) and obtain negative coefficients for both the level and slope of uncertainty, but with a large drop in the magnitude of the slope coefficient. So when K and L are equally long-lived but K is less reversible net investment is more sensitive to both short-run and long-run uncertainty, although compared to the baseline case its relative sensitivity to long-run uncertainty has fallen by about two thirds. In column (5) we instead equalize the adjustment costs across the two assets, maintaining their differential durability, and find again that the relative response to long-run uncertainty has dropped substantially, this time to about half it s baseline value. Finally in column (6) we equalize both durability and adjustability (so that K and L are perfectly substitutable), confirming that both short- and long-run uncertainty are about equally linked to investment in both assets. Overall, these experiments indicate that both the long-livedness and greater irreversibility in K relative to L contribute to the baseline results that K investments seem particularly affected by higher long-run uncertainty. These insights imply that long-lived assets - like buildings and long-lived equipment - and hard to adjust assets (like intangibles such as organizational changes and R&D) will likely be particular sensitive to long-run uncertainty. So these investments are going to be most acutely reduced, for example, by spikes in policy-uncertainty, which as we saw is a key driver of long-run uncertainty. 6 Conclusion Uncertainty appears to have both a short-run and a long-run component, which we investigate in this paper. To measure the time profile of uncertainty we use firm and macro implied volatility data from 30 days to 10 years duration for a panel of over 4,000 US firms. We find that investment is significantly more sensitive to long-run uncertainty, while employ- 21

22 ment responds equally to short- and long-run uncertainty. We build a model to investigate this phenomenon, and find that the higher adjustment costs and lower depreciation rates of capital can explain why investment is particularly sensitive to longer-run uncertainty. We then examine drivers of uncertainty over different time horizons, finding oil uncertainty is particular related with short-run uncertainty, policy uncertainty is particularly related with long-run uncertainty, and currency volatility and CEO turnover appear to equally impact both short- and long-run uncertainty. References Abel, A. B. and J. C. Eberly (1996): Optimal investment with costly reversibility, The Review of Economic Studies, 63, Alfaro, I., N. Bloom, and X. Lin (2016): The Finance Uncertainty Mulitplier, Stanford Mimeo. Arellano, C., Y. Bai, P. J. Kehoe, et al. (2012): Financial frictions and fluctuations in volatility, Federal Reserve Bank of Minneapolis Research Department Staff Report, 466. Bachmann, R. and C. Bayer (2013): Wait-and-See business cycles? Journal of Monetary Economics, 60, Baker, S. R., N. Bloom, and S. J. Davis (2015): Measuring economic policy uncertainty, Tech. rep., National Bureau of Economic Research. Basu, S. and B. Bundick (2012): Uncertainty shocks in a model of effective demand, Tech. rep., National Bureau of Economic Research. Bekaert, G. and M. Hoerova (2014): The VIX, the variance premium and stock market volatility, Journal of Econometrics, 183, Berger, D., I. Dew-Becker, and S. Giglio (2016): Contractionary volatility or volatile contractions?. 22

23 Bernanke, B. (1983): Irreversibility, Uncertainty and Cyclical Investment, Quarterly Journal of Economics, 98, Bertrand, M., A. Schoar, et al. (2003): Managing with Style: The Effect of Managers on Firm Policies, The Quarterly Journal of Economics, 118, Black, F. and M. Scholes (1973): The pricing of options and corporate liabilities, Journal of Political Economy, Bloom, N. (2009): The impact of uncertainty shocks, Econometrica, 77, (2014): Fluctuations in Uncertainty, The Journal of Economic Perspectives, 28, Bloom, N., S. Bond, and J. Van Reenen (2007): Uncertainty and investment dynamics, Review of Economic Studies, 74, Caballero, R. J., E. M. Engel, J. C. Haltiwanger, M. Woodford, and R. E. Hall (1995): Plant-level adjustment and aggregate investment dynamics, Brookings papers on economic activity, Christiano, L. J., R. Motto, and M. Rostagno (2014): Risk Shocks, American Economic Review, 104, Davis, S. J., J. Haltiwanger, and S. Schuh (1996): Small business and job creation: Dissecting the myth and reassessing the facts, Small Business Economics, 8, Dew-Becker, I., S. Giglio, A. Le, and M. Rodriguez (2015): The price of variance risk, Tech. rep., National Bureau of Economic Research. Dixit, A. K. and R. S. Pindyck (1994): Investment under uncertainty, Princeton university press. Exchange, C. B. O. (2009): The CBOE volatility index VIX, White Paper. 23

24 Fernández-Villaverde, J., P. Guerrón-Quintana, K. Kuester, and J. Rubio- Ramírez (2015): Fiscal Volatility Shocks and Economic Activity, The American Economic Review, 105, Fernández-Villaverde, J., P. Guerrón-Quintana, J. F. Rubio-Ramírez, and M. Uribe (2011): Risk Matters: The Real Effects of Volatility Shocks, The American Economic Review, 101, Gilchrist, S., J. W. Sim, and E. Zakrajšek (2014): Uncertainty, financial frictions, and investment dynamics, Tech. rep., National Bureau of Economic Research. Guiso, L. and G. Parigi (1999): Investment and demand uncertainty, Quarterly Journal of Economics, Gulen, H. and M. Ion (2013): Policy uncertainty and corporate investment, Available at SSRN Kehrig, M. et al. (2011): The cyclicality of productivity dispersion, US Census Bureau Center for Economic Studies Paper No. CES-WP Knotek II, E. S., S. Khan, et al. (2011): How do households respond to uncertainty shocks? Economic Review. Leahy, J. V. and T. M. Whited (1996): The effect of uncertainty on investment: Some stylized facts, Journal of Money, Credit, and Banking, 28, Pindyck, R. S. (1990): Inventories and the short-run dynamics of commodity prices, Tech. rep., National Bureau of Economic Research. Ramey, G. and V. A. Ramey (1995): Cross-Country Evidence on the Link Between Volatility and Growth, The American Economic Review, 85, Romer, C. D. (1990): The great crash and the onset of the Great Depression. Quarterly Journal of Economics,

25 Stein, L. C. and E. Stone (2013): The effect of uncertainty on investment, hiring, and r&d: Causal evidence from equity options, Hiring, and R&D: Causal Evidence from Equity Options (October 4, 2013). 25

26 A Data Appendix A.1 Construction of the Firm-level Implied Volatility Dataset We obtain our implied volatility data from the Option Metrics database. Option Metrics uses observed option trading data to provide information about theoretical "standardized" options, which are theoretical American put and call options with strike prices equal to atthe-money forward stock prices and fixed maturities of 30, 60, 91, 152, 182, 273, 365, and 730 days. They obtain these standardized options by using all available options on the same security and weighting them by vega, maturity, delta, and exercise style. They generate a volatility surface using a normal kernel weighting function and choosing bandwidth empirically, and calculate standardized option prices and implied volatilities from this surface. Details of this procedure are available at Options must have vegas greater than 0.5 and time to maturity greater than 10 days to be input into the standardization process. Note these are integrated volatilities rather than spot volatilities - so for example σ 2 6 month = 6 months 0 σ 2 t dt. An observation in the raw data is a firm-day. To construct the implied volatility dataset we first obtain a single measure of implied volatility for each horizon by firm-day by averaging implied volatility across puts and calls. Put and call data are nearly identical, with correlations close to.99, so using either puts or calls made little difference to the empirical results. Then we compute quarterly measures of implied volatility by horizon by averaging the daily implied variance of the standardized options. That is, the implied volatility of a firm i during quarter tis σ it = where s iτ 1 N t Nt τ=1 s2 iτ is a daily observation of implied volatility for the firm and N t is the number of days in quarter tfor which we have nonmissing volatility observations. Averaging implied variance and then taking the square root of the volatility. A.2 Matching Implied Volatility Data to Compustat We match the quarterly dataset to quarterly and annual firm-level data from Compustat North America. In constructing the annual matched dataset we take the implied volatility for a firm-year to be that of the last quarter of the year. This is useful to obtain less noisy 26

27 implied volatility measures at an annual frequency and allows us to exploit the forwardlooking nature of implied volatility. Since all of our regressions in section 3 use lagged volatility, we effectively regress an annual outcome variable on the implied volatility in final months of the previous fiscal year, which reflects the market s uncertainty about the firm looking forward to the year in question. For the quarterly matched dataset we simply match by quarter. A.3 Additional Details on Testing for Drivers of Short- and Longrun Uncertainty See section 4 for an outline of how we construct the matched firm-quarter dataset containing implied volatility and drivers data. During our estimation of the sector-level sensitivities of equity returns to market, oil, and currency returns we restrict attention to SIC-2 sectors that featured at least 20 distinct firms during the estimation period of When we restricted attention to sectors that included 15 or 25 firms the results did not change very much. All of our uncertainty regressions in Table 5 are weighted by employment, as is standard in this line of literature (e.g. Baker et al., 2015). Following Baker et al. (2015) whenever we have the firm-specific economic policy uncertainty index as a regressor we also include a control consisting of federal spending as a fraction of GDP multiplied by firm-level exposure to government purchases. For the drivers regressions we cluster our standard errors according to the level of variation of the right-hand-side regressors as is standard in applied empirical work. Thus, in columns (1) and (4) of 5 we cluster at the level of the firm, while in columns (2), (3), and (5) we clusted by 2-digit sector. In our baseline regressions in in table 5 we define CEO turnover as an indicator for firmquarters during which Execucomp records a CEO stepping down. In the data, only 78% of these CEO departures have a new CEO taking office in the same calendar quarter, but our regressions are robust to defining CEO turnover as an indicator for firm-quarters with either a CEO stepping down or a new one coming in, or as a dummy for a new CEO taking office. 27

28 B Simulation Appendix We build the simulation model in MATLAB and run it on Stanford s HPC computing clusters. The model is solved using a standard policy iteration algorithm. First we make an initial guess V 0 (A, k, l, σ s, σ l ) for the value function and solve for the optimal policies k (A, k, l, σ s, σ l ) and l (A, k, l, σ s, σ l ) given V 0. Then we iterate on the current guess of the policy functions 300 times, updating the guess of the value function so that V n+1 (A, k, l, σ s, σ l ) = R(A, k, k, l, l, σ s, σ l )+E[V n (A, k, l, σ s, σ l ) A, k, l, σ s, σ l ] where R( ) denotes the period revenue function and E( ) is the conditional expectation based on the current state (A, k, l, σ s, σ l ). We then take the absolude distance d = max A,k,l,σs,σl V 300 V 0 and let V 300 to be the solution to the value function if d is below a pre-determined tolerance level. Otherwise, we replace V 0 with V 300 and repeat the above steps to convergence. To simulate data from the model we use Monte Carlo simulation, in order to accommodate the fact that the firms in our simulation dataset consist of 25 investment units, each making optimal investments according to the value function problem formulated in section 5. The investment units within a firm have independent first-moment shocks but common uncertainty shocks. For each firm-month in the simulation, we first obtain σ s and σ l states for the firm, then draw new first-moment shocks A for all of the units within the firm, then record investment and hiring choices by unit. Finally, we aggregate the unit-level data to firm-level data by adding up K and L across units within a firm-month. We run the simulation for 360 months, dropping data from the first 300 months for ergodicity. We transfer the simulated data to Stata, where we aggregate the monthly simulation data to quarterly and annual frequencies and run the empirical analysis of the simulated data. 28

29 Appendix Table 1: Baseline Calibration Parameters Parameter Description Value Notes 1/(1+r) discount rate.996 r = 0.05, annually α k, α l revenue elasticity of K, L.4 CRS and 25% markups σ sl, σ ll low volatility state for σ s and σ l.24 33% monthly in LL state σ sh, σ lh high volatility state for σ s and σ l.46 66% monthly in HH state ρ s monthly persistence of σ s.85 annual autocorrelation.15 ρ l monthly persistence of σ l.95 annual autocorrelation.49 δ k K effective monthly depreciation % annual depreciation δ l L effective monthly depreciation % annual depreciation γ k K resale loss.25 25% resale loss, conventional value γ l L resale loss γ k F k fixed K adjustment costs.01 N/A F l fixed L adjustment costs.01 N/A ρ A monthly autocorrelation of log(a) quarterly, Khan & Thomas (2008) Notes: Parameters used in the baseline calibration of the simulation model of Section 5.

30 Appendix Table 2: Summary Statistics ANNUAL SAMPLE QUARTERLY SAMPLE Mean SD Mean SD Total Assets ($M) 4,738 9,146 Total Assets ($M) Capital Expenditures ($M) Capital Expenditures ($M) Sales ($M) 4,175 8,096 Sales ($M) ,911 Cash Flow / Assets Cash Flow / Assets PPENT ($M) 1,508 3,361 PPENT ($M) 1,288 2,946 Tobin's Q Tobin's Q Sales Growth Year-on-Year Sales Growth Lagged log(30day IVOL) Lagged log(30day IVOL) Lagged log(6m IVOL) Lagged log(6m IVOL) PPENT Growth Perpetual Inventories Capital ($M) 1,575 4,109 Employment Growth CAPX/PPENT Employees ('000s) N 25,256 N 104,207 Date Range: Date Range: 1996Q2-2013Q1 Notes: Data is from Compustat North America Fundamentals Quarterly and Annual matched with implied volatility data from Option Metrics. Cash flow is defined as operating income. Tobin's Q is measured as the sum of market value, preferred stock capital, current liabilities and long term debt, all divided by the book value of assets. All growth variables measured as the change between the value in the current and the previous year, divided by the average of the two. Perpetual Inventories Capital Stock measured using capital expenditures data and assuming annual depreciation of 10%. Implied volatility by horizon is measured as the average for a firm-quarter, where we identify the implied volatility in a given fiscal year with the average of the last quarter. All variables are winsorized at the 1st and 99th percentiles.

31 Appendix Table 3: What types of firms have non-missing implied volatility? (OLS) Dependent Variable (1) (2) (3) (4) (5) (6) 1(30-day Implied Volatitility Nonmissing) log(quarterly Sales) *** *** *** *** ( ) ( ) ( ) ( ) Sales Growth *** *** *** *** (0.0119) (0.0110) (0.0109) ( ) Lagged log(91-day Realized Vol.) *** *** *** *** ( ) ( ) ( ) ( ) Date Fixed Effects N N N N N Y Firm Fixed Effects N N N N N Y Years in Sample Standard Errors Robust Robust Robust Robust Robust Clustered by Firm R-squared Observations 8,718 8,718 8,718 8,718 6,348 95,619 Dependent Variable 1(6-month Implied Volatility Nonmissing) log(quarterly Sales) *** *** *** *** ( ) ( ) ( ) ( ) Sales Growth *** *** *** *** (0.0128) (0.0119) (0.0116) ( ) Lagged log(91-day Realized Vol.) *** *** *** *** ( ) ( ) ( ) ( ) Date Fixed Effects N N N N N Y Firm Fixed Effects N N N N N Y Years in Sample Standard Errors Robust Robust Robust Robust Robust Clustered by Firm R-squared Observations 8,718 8,718 8,718 8,718 6,348 95,619 Notes: OLS regressions on an indicator for nonmissing 30-day or 6-month implied volatility based on firm characteristics. An observation is a firm-quarter. Financial information is from Compustat, and quarterly average implied and realized volatility of firm equity taken from Optionmetrics. Sales growth is measured as the sum of sales over the past four quarters minus that of the previous four quarters, divided by the average of the two. All variables are winsorized at the 1st and 99th percentiles. *** p<0.01, ** p<0.05, * p<0.1

32 Appendix Figure 1: Fluctuations in Firm Implied Volatility: Gap, Inc. Notes: Average of put and call implied volatilities from standardized options on the equity of Gap, Inc. for the month of June of the indicated year, by days to expiration measured on a logarithmic scale. Source: OptionMetrics.

33 Table 1: Predicting Long-run Implied Volatility Dependent Variable (1) (2) (3) (4) (5) 2-year Firm Implied Vol 1-year VIX 2-year VIX 3-year VIX 5-year VIX 30-day Volatility 0.869*** 0.950*** 0.883*** 0.838*** 0.753*** ( ) (0.0110) (0.0259) (0.0334) (0.0484) 6m - 30-day Volatility 1.162*** 1.240*** 1.360*** 1.385*** 1.349*** (0.0386) (0.0347) (0.0771) (0.0985) (0.135) Constant 4.465*** 1.148*** 2.918*** 4.377*** 7.171*** (0.195) (0.259) (0.604) (0.781) (1.143) Observations 20,907 2,638 2,638 2,638 2,638 R-squared Notes: Column 1 regresses quarterly firm-level 2-year implied volatility (source: Optionmetrics) on 30-day and 6m minus 30-day implied volatility. Columns 2-6 regress the daily VIX for the specified horizon on 30-day and 6m minus 30-day VIX, data courtesy of Goldman Sachs. Columns 2-6 report Newey-West standard errors in parentheses, assuming autocorrelation up to 250 trading days. Column 1 standard errors clustered by firm. All variables are winsorized at the 1 st and 99 th percentiles. *** p<0.01, ** p<0.05, * p<0.1

34 Table 2: Investment and Hiring under Short-Run and Long-run Uncertainty (1) (2) (3) (4) (5) (6) (7) (8) (9) Dependent Variable Investment Investment Investment Investment Hiring Investment - Hiring Frequency Q Q Q A A A A A A Volatility Firm Firm Aggregate Firm Firm Firm Firm Firm Firm Lag log(30d IVOL) *** *** *** *** *** *** *** *** (0.029) (0.028) (0.009) (0.006) (0.008) (0.008) (0.008) (0.008) Lag log(6m IVOL) - log(30d IVOL) *** *** * ** *** *** *** (0.056) (0.055) (0.027) (0.021) (0.025) (0.025) (0.025) (0.025) Lag log(30d VIX) *** (0.032) Lag log(5y VIX) - log(30d VIX) *** (0.045) Lag Tobin's Q 0.113*** 0.091*** 0.120*** 0.047*** 0.023*** 0.025*** 0.024*** 0.024*** (0.005) (0.005) (0.010) (0.002) (0.001) (0.002) (0.002) (0.002) Cash Flow / Assets 0.970*** 1.116*** 0.178*** 0.075*** 0.092*** 0.100*** (0.120) (0.160) (0.030) (0.022) (0.023) (0.024) Sales Growth 0.435*** 0.386*** 0.266*** 0.277*** * (0.025) (0.035) (0.014) (0.013) (0.009) Date Fixed Effects Y Y Y Y Y Y Y Y Observations 104, ,207 67,560 25,256 25,256 25,256 25,256 25,256 25,256 R-squared Firms Notes: Regressions are quarterly (Q) in columns (1) to (3) and annual (A) in columns (3) to (8). All columns include a full set of firm fixed effects, and all but (3) include date fixed effects. Robust standard errors in parentheses, clustered by firm. Data from Compustat for accounting variables matched to data on implied volatility of standardized options taken from OptionMetrics. Quarterly investment in the log of capital expenditure (CAPEX) over lagged net plant property and equipment (PPENT). Annual investment and hiring are the growth rates of PPENT and empoyment, where growth is measured as the current value minus the previous year's value, divided by the average of the two. Tobin's Q is measured as the sum of market value, prefered stock capital, current and long-term liabilities, all divided by the book value of assets. Cash flow is defined as operating income. In annual specifications, the implied volatility for a given fiscal year is taken to be the average implied volatility during the last quarter of the year; in quarterly specifications it is the average implied volatility for the quarter. All variables are winsorized at the 1st and 99th percentiles. *** p<0.01, ** p<0.05, * p<0.1

35 Table 3: Firm Heterogeneity, Short- and Long-run Uncertainty and Investment (1) (2) (3) (4) (5) (6) (7) Dependent Variable Investment Sample All Small Large Slow-growing Fast-growing Low leverage High leverage Lag log(30d IVOL) *** *** *** *** *** *** *** (0.028) (0.043) (0.033) (0.035) (0.036) (0.041) (0.037) Lag log(6m IVOL) - log(30d IVOL) *** *** ** *** * *** (0.055) (0.084) (0.059) (0.071) (0.074) (0.084) (0.070) Lag Tobin's Q 0.091*** 0.080*** 0.109*** 0.092*** 0.076*** 0.072*** 0.149*** (0.005) (0.006) (0.007) (0.014) (0.004) (0.006) (0.010) Cash Flow / Assets 0.970*** 1.000*** 0.875*** 1.217*** 0.785*** 0.832*** 1.088*** (0.120) (0.176) (0.117) (0.147) (0.140) (0.160) (0.141) Sales Growth 0.435*** 0.422*** 0.455*** 0.509*** 0.330*** 0.450*** 0.371*** (0.025) (0.031) (0.032) (0.051) (0.048) (0.033) (0.037) Observations 104,207 52,104 52,103 52,104 52,103 51,559 51,558 R-squared Firms Notes: All regressions are at the firm level at a quarterly frequency and include a full set of firm and date fixed effects. Columns (2) and (3) split the sample into above and below median by quarterly sales; (4) and (5) split by above and below median sales growth; (6) and (7) by leverage. Data is quarterly accounting information from Compustat matched to data on implied volatility of standardized options taken from OptionMetrics. Robust standard errors in parentheses, clustered by firm. Investment is the log of capital expenditures (CAPEX) over lagged net plant, property, and equipment (PPENT). Tobin's Q is measured as the sum of market value, preferred stock capital, current and long-term liabilities, all divided by the book value of assets. Cash flow is defined as operating income. All variables are winsorized at the 1st and 99th percentiles. *** p<0.01, ** p<0.05, * p<0.1

36 Table 4: Robustness Checks Dependent Variable Specification (1) (2) (3) (4) (5) (6) (7) (8) (9) Baseline Exc. Recessions Only Recessions Level of unc. Investment 2-year implied vol 2-year predicted implied vol Lagged investment SICxdate f.e. Annual Frequency Q Q Q Q Q Q Q Q A Lagged log(30d IVOL) *** *** *** *** *** *** *** *** *** (0.028) (0.029) (0.057) (0.004) (0.060) (0.063) (0.019) (0.032) (0.027) Lagged log(6m IVOL) - log(30d IVOL) *** *** *** ** *** *** * (0.055) (0.056) (0.125) (0.010) (0.043) (0.060) (0.071) Lagged log(2y IVOL) - log(30d IVOL) ** (0.079) (0.120) Lagged 30d IVOL *** (0.004) Lagged 6m IVOL - 30d IVOL ** (0.010) Lagged Tobin's Q 0.091*** 0.091*** 0.095*** 1.165*** 0.089*** 0.091*** 0.066*** 0.080*** 0.124*** (0.005) (0.005) (0.011) (0.051) (0.009) (0.005) (0.003) (0.006) (0.005) Cash Flow / Assets 0.970*** 0.997*** 0.566** 8.300*** 0.969*** 0.970*** 0.965*** 1.070*** 0.471*** (0.120) (0.126) (0.243) (1.012) (0.192) (0.120) (0.105) (0.141) (0.072) Sales Growth 0.435*** 0.417*** 0.427*** 3.718*** 0.334*** 0.435*** 0.280*** 0.384*** 0.425*** (0.025) (0.027) (0.057) (0.230) (0.065) (0.025) (0.020) (0.028) (0.027) Lagged Investment 0.368*** (0.015) Date Fixed Effects Y Y Y Y Y Y Y Y Date by Sector Fixed Effects Y Observations 104,207 86,961 17, ,141 20,765 20,765 96, ,207 25,231 R-squared Firms Notes: Regressions are quarterly in columns (1) to (8) and annual in column (9). All columns and include a full set of firm fixed effects. Columns (1) to (7) and (9) have date fixed effects, while column (8) uses date-by-3-digit-sector fixed effects. Data is quarterly accounting information from Compustat matched to data on implied volatility of standardized options taken from OptionMetrics. Robust standard errors in parentheses, clustered by firm. Column (2) excludes quarters comprising the 2001 & recessions, while column (3) only includes these recessions. Investment is measured as the log of capital expenditures (CAPEX) over lagged net plant, property, and equipment (PPENT), except in column (3) where it is measured in levels. Tobin's Q is measured as the sum of market value, preferred stock capital, current and long-term liabilities, all divided by the book value of assets. Cash flow is defined as operating income. In annual specifications, the implied volatility for a given fiscal year is taken to be the average implied volatility during the last quarter of the year; in quarterly specificationsit is the average implied volatility for the quarter. In column (6), log(2y IVOL) used is the fitted value from a regression of true 2-year implied volatility on the concurrent log(30d IVOL) and log(6m IVOL). All variables are winsorized at the 1st and 99th percentiles. *** p<0.01, ** p<0.05, * p<0.1 p<.15

37 Table 5: Drivers of Short-Run and Longer-run Uncertainty Dependent Variable (1) (2) (3) (4) (5) log(30d IVOL) Economic Policy Unc. Exposure (0.072) (0.069) Oil Vol. Exposure 2.082*** 1.805** (0.755) (0.786) Currency Vol. Exposure 0.033** 0.030** (0.013) (0.014) CEO Turnover 0.028* 0.030*** (0.014) (0.011) Dependent Variable log(6m IVOL) Economic Policy Unc. Exposure (0.080) (0.0664) Oil Vol. Exposure (0.731) (0.695) Currency Vol. Exposure 0.033*** *** (0.011) (0.0117) CEO Turnover 0.025* ** (0.013) (0.0108) Dependent Variable log(6m IVOL)-log(30d IVOL) Economic Policy Unc. Exposure 0.059* (0.031) (0.045) Oil Vol. Exposure ** ** (0.329) (0.334) Currency Vol. Exposure (0.005) (0.005) CEO Turnover (0.005) (0.004) Observations ,758 44,759 44,760 44,761 Sectors Firms Notes: All columns include a full set of time and firm fixed effects. Robust standard errors in parentheses, clustered by firm in columns 1) and 4); by SIC-2 sector in columns 2), 3), and 5). One observation is a firm-quarter. Implied volatility data taken from Option Metrics. Firm-specific exposure to Economic Policy Uncertainty by quarter taken from Baker et al (2015). Sectoral exposure to oil and currencies constructed using CRSP data on stock returns, Bloomberg data on oil prices and exchange rates from , and quarterly averages of implied volatility data for oil and currencies covering Exchange rates used are CAD, MXN, JPY, CNY, EUR, AUD, HKD, KRW, NZD, NOK, SEK, CHF, TWD, GBP, DKK, ZAR, THB, INR, SGD. CEO Turnover is from Execucomp, constructed as an indicator for whether the CEO was stepping down during the quarter. Regressions with EPU exposure also control for federal spending as percent of GDP multiplied by firm-level exposure to government purchases. Regressions are weighted by employment. *** p<0.01, ** p<0.05, * p<0.1, p<20

38 Table 6: Simulation Quarterly Capital Investment Under Short- and Long-run Uncertainty Dependent Variable (1) (2) (3) (4) (5) (6) (7) Investment Lagged log(30d Expected Vol.) ** *** *** *** *** (0.025) (0.138) (0.057) (0.137) (0.057) Lagged log(2y Expected Vol.) *** (0.082) Lagged log(6m Expected Vol.) *** (0.039) Lagged log(2y Expected Vol.) *** *** log(30d Expected Vol.) (0.188) (0.186) Lagged log(6m Expected Vol.) *** *** log(30d Expected Vol.) (0.135) (0.133) Lagged Tobin's Q 0.363*** 0.364*** 0.364*** 0.364*** 0.364*** 0.195*** 0.195*** (0.005) (0.005) (0.005) (0.005) (0.005) (0.006) (0.006) Cash Flow/(K+L) *** *** (0.156) (0.156) Proportional Sales Growth (0.057) (0.057) Observations 61,911 61,911 61,911 61,911 61,911 52,094 52,094 R-squared Firms Notes: The dependent variable is the log of investment over the existing capital stock. All columns include a full set of firm and date fixed effects. Robust standard errors in parentheses, clustered by firm. Each observation is a firm-quarter from a 5,000 firm simulation panel. Each firm consists of 25 production units making investment decisions and independent first moment shocks common uncertainty shocks. The model is solved and simulated at a monthly frequency and aggregated to quarterly data. Short- and long-run uncertainty are measured as the average expected volatility of shocks to revenue-generation over the horizon indicated. Tobin's Q is measured as firm value divided by the stock of K and L. Cash flow is defined as revenue. Sales growth is measured as the revenue over the past four quarters, minus that over the previous four quarters, divided by the average of the two. All variables are winsorized at the 1st and 99th percentiles. *** p<0.01, ** p<0.05, * p<0.1

39 Table 7: Simulation Annual Net Investment in K, L (1) (2) (3) (4) (5) (6) Dependent Variable Investment Hiring Investment Hiring Calibration Baseline Baseline Baseline Equal Dep Equal AC Equal Dep & AC Lagged log(30d Expected Vol.) *** *** *** 0.149*** (0.020) (0.026) (0.026) (0.012) (0.017) (0.012) Lagged log(6m Expected Vol.) *** *** * * log(30d Expected Vol.) (0.050) (0.065) (0.065) (0.030) (0.043) (0.030) Lagged Tobin's Q 0.081*** 0.136*** *** ** *** (0.003) (0.004) (0.003) (0.001) (0.002) (0.001) Cash Flow / (K + L) 1.388*** 1.411*** *** 0.135*** (0.018) (0.025) (0.024) (0.006) (0.017) (0.006) Proportional Sales Growth *** *** *** *** 0.009* (0.009) (0.013) (0.012) (0.005) (0.008) (0.005) Observations 20,000 20,000 20,000 20,000 20,000 20,000 R-squared Firms Calibration Parameters: K effective depreciation L effective depreciation K resale loss L resale loss Notes: Columns (4) and (6) have equal depreciation for capital and labor in the simulation, and columns (5) and (6) have equal adjustment costs. All columns have a full set of firm and time fixed-effects. Robust standard errors in parentheses, clustered by firm. Each observation is a firm-year from a 5,000 firm simulation panel. Each firm consists of 25 production units making investment decisions subject to independent first moment shocks and common uncertainty shocks. The model is solved and simulated at a monthly frequency and aggregated to annual data. Short- and long-run uncertainty are measured on the monthly data as the average expected volatility of first moment shocks over the next 30 days and 6 months, respectively. When aggregating to annual data, we take for a given year the average short- and long-run uncertainty over the last quarter of the year. Tobin's Q is measured as firm value divided by the stock of K and L. Cash flow is defined as revenue. All growth variables are constructed as the current value minus the previous year's value, divided by the average of the two. All variables are winsorized at the 1st and 99th percentiles. *** p<0.01, ** p<0.05, * p<0.1

40 Figure 1: Fluctuations in the VIX Notes: Average of the generalized VIX for the indicated month, by days to expiration measured on a logarithmic scale. The generalized VIX uses the formula used for the true VIX (a modelfree measure of the 30-day implied variance on the S&P 500) for horizons other than the standard 30 days. Source: Goldman Sachs.

41 Figure 2: Predicting long-run VIX with 30-day and 6-month VIX A. 2-year VIX Notes: This figure plots the fitted values from a regression of daily observations of 2-year VIX on a constant, and the same day s 30-day and 6-month VIX. Data obtained from Goldman Sachs. R 2 =.98

42 B. 5-year VIX Notes: This figure plots the fitted values from a regression of daily observations of 2-year VIX on a constant, and the same day s 30-day and 6-month VIX. Data obtained from Goldman Sachs. R 2 =.92