Oil Volatility Risk. Lin Gao, Steffen Hitzemann, Ivan Shaliastovich, and Lai Xu. Preliminary Draft. December Abstract

Transcription

1 Oil Volatility Risk Lin Gao, Steffen Hitzemann, Ivan Shaliastovich, and Lai Xu Preliminary Draft December 2015 Abstract In the data, an increase in oil price volatility dampens current and future output, investment, employment, and consumption, controlling for the market volatility and other business cycle variables. High oil uncertainty negatively affects aggregate equity prices, with a very differential impact across industries. We develop a two-sector production model to explain the novel evidence in the data. In the model, oil is an essential input for production and can be stored. At times of high oil supply volatility, firms optimally decide to stock up oil, rather than to invest in physical capital. As a result, investment, production, and consumption go down, while oil inventories go up. These mechanisms are directly supported in the data. Lin Gao (lin.gao@uni.lu) is at the University of Luxembourg. Steffen Hitzemann (hitzemann.6@osu.edu) is at the Ohio State University. Ivan Shaliastovich (ishal@wharton.upenn.edu) is at Wharton School, University of Pennsylvania. Lai Xu (lxu100@syr.edu) is at the Syracuse University. 1

2 1 Introduction There has been a lot of attention in the recent literature to the role of aggregate uncertainty risk for the macroeconomy and asset markets. A rise in aggregate macroeconomic uncertainty is typically associated with lower economic growth in the future. 1 Higher aggregate volatility also depresses real asset valuations, and increases asset risk premia. 2 In this paper, we focus on uncertainty regarding an economically important sector of the economy that involves the production of oil. We show that, in the data, an increase in oil uncertainty dampens output, investment, and consumption, controlling for the aggregate volatility and other business cycle variables. High oil uncertainty also affects asset valuations. It has a negative impact on the market portfolio and on the returns in industries that are sensitive to oil as an input factor (Durables, Autos), while the exposure of industries related to the production of oil and oil products (Energy portfolio) is positive. We develop a two-sector production model, which features optimal decisions regarding physical capital investment and storage of oil, to explain the novel evidence in the data. Our paper is motivated by the novel empirical evidence that oil price variance captures significant information about economic growth and asset prices, above and beyond market volatility and other predictors of future economic conditions. Using regression analysis, we find that an increase in oil variance predicts a decline in current and future growth rates of consumption, output, investment, and employment 1 to 4 quarters ahead, controlling for current growth rate in the corresponding variables, current oil returns, and the market variance. Economically, the oil volatility impact is quite large. Following a one standard deviation in oil variance, consumption growth declines by about 0.30%, annualized, and future output and investment drop by 0.66% and 2.75%, respectively, using a conservative shock orthogonalization in which equity variance 1 Ramey and Ramey (1995), Fernandez-Villaverde et al. (2011), Basu and Bundick (2012), Bansal et al. (2014), Bloom (2014), Gilchrist et al. (2014) emphasize a negative relation between real growth and macroeconomic uncertainty. 2 See Bansal and Yaron (2004), Bansal et al. (2005), Lettau et al. (2008), among many others. 2

3 leads oil variance. Allowing oil variance shocks to lead equity variance increases the responses even further. An increase in oil variance also predicts a decline in oil consumption and increasing oil inventories. Economically, oil inventories increase by 0.5% one quarter after the impact, while oil consumption declines by about 0.6%. At the same time, aggregate TFP and production of oil do not seem to be related to movements in oil volatility. This suggests that the effects of oil volatility on endogenous macroeconomic variables, such as consumption and output, are not mechanically inherited from the exogenous dynamics of productivity. We further show that the market equity price drops at times of high oil uncertainty. Oil prices themselves only have a weak relation to oil uncertainty; in fact, the correlation is positive outside the Financial crisis. This evidence is supported by the cross-section of equity returns, which suggests that industries which are likely to use oil as an essential input, such as Durables and primarily Autos, have a large negative exposure to oil uncertainty. On the other hand, industries which are involved in the production of oil and oil-related products (Energy) have the largest positive exposure to oil volatility. We explain these novel empirical findings by a two-sector macro model in which oil is essential for the production of goods in the macroeconomic sector. The oil supply from existing wells is subject to exogenous fluctuations, and firms manage oil inventories to mitigate the consequences of oil supply shocks. In times of high oil supply volatility, they therefore increase their inventories to alleviate the probability of a stock-out in the event of a large negative supply shock. As a result of this precautionary savings effect, the amount of oil available for production in the general macro sector is reduced, and production, consumption, and investments decrease. This effect especially dominates the usual precautionary savings effect to increase physical capital investments when uncertainty rises, such that consumption and investment jointly 3

4 decrease in our model when (oil) uncertainty goes up. These economic mechanisms are directly supported in the data. Our paper connects the literature on the role of uncertainty for the macroeconomy and for asset prices with the commodity markets literature. For commodity markets, the critical role of inventories has long been recognized and is documented in the classical theory of storage literature (see Kaldor 1939; Working 1948, 1949; Telser 1958). Newer works emphasize the role of supply and demand uncertainty as a main driver of inventory holdings, and point out important implications for forward and futures prices, volatilities, and risk premia (Williams and Wright 1991; Deaton and Laroque 1992; Routledge et al. 2000; Gorton et al. 2012). Very recently, models integrating the oil sector into two-sector production models are developed to analyze the interactions with the broader macroeconomy (Casassus et al. 2009; Ready 2014; Hitzemann 2015). Hitzemann (2015) especially highlights the important role of oil inventories in a general equilibrium model with long-run productivity risk for generating a realistic term structure of oil futures risk premia. We contribute to this literature by considering the effect of changes in oil supply uncertainty and their impact on important macroeconomic variables. As we show in this paper, oil uncertainty shocks lead to a stocking up of oil inventories, which negatively effects production, consumption, and investment in the general macroeconomy due to the reduced effective supply of oil to the market. In the broader macroeconomic literature, Croce et al. (2012) and Pastor and Veronesi (2012) highlight the negative impact of government policy uncertainty on prices and growth. Other papers, such as Gilchrist and Williams (2005), Jones et al. (2005), Malkhozov (2014), and Kung and Schmid (2014) feature alternative economic channels which can generate a positive relationship between uncertainty and investment and thus growth. 4

5 2 Empirical Motivation In this section we present our key empirical findings that an increase in oil price volatility has an adverse effect on aggregate real growth. We further document that a rise in oil volatility lowers consumption of oil and increases oil inventories, while it does not seem to significantly affect aggregate productivity or oil production. These results motivate our economic model specification in which the ability of firms to stock up, rather than consume, oil in high volatility times leads to a negative impact of oil volatility on aggregate growth. 2.1 Data In our empirical analysis we use macroeconomic data related to production and consumption in the aggregate economy as well as the oil sector, and asset price data for spot and derivatives prices of the market portfolio and oil. Due to the availability of the data, our benchmark sample runs quarterly from 1990Q1 to 2014Q1. To show the robustness of the key results, we also consider a larger sample starting in the early 1980s. Our aggregate macroeconomic data are for the United States, and include consumption, comprised of expenditures on nondurable goods and services, GDP, private domestic investment, and employment. The data come from the Bureau of Economic Analysis (BEA). We additionally collect the Total Factor Productivity (TFP) index data which correspond to the the estimates of the Solow residual for the US economy. For robustness, we also consider the utilization-adjusted productivity measure proposed by Basu et al. (2006). The oil quantity data come from the U.S. Energy Information Administration. 3 Our oil supply measure corresponds to the world production of crude oil. To measure 3 The data are available at 5

6 oil usage and inventories, we use observations for total consumption of petroleum products and total petroleum stocks, respectively. The long sample of oil consumption and stock data is only available for the OECD countries. For robustness, we also check the results using the oil consumption and inventories in the United States. All the macroeconomic quantity data are real and seasonally adjusted. In terms of the asset price data, we collect dividends, earnings, and return data for a broad market portfolio from CRSP. Following Gomes et al. (2009), we use the benchmark input-output accounts table in the BEA to identify industries whose final demand has highest value-added to personal consumption expenditures on durable goods, non-durable goods and services. Similar to Eraker et al. (2015), we aggregate non-durables and services into a single value-weighted non-durable portfolio 4. We use crude oil futures data to construct excess returns on oil. These data are obtained from the Commodity Research Bureau (CRB) and are available from 1983Q2 to 2014Q1. An important object for our analysis is the amount of uncertainty in financial and macroeconomic data. Our benchmark uncertainty measures are constructed using the option data on equity and oil prices. Specifically, we use the volatility index VIX, constructed from the cross-section of S&P 500 index option prices, as the modelfree estimate of the aggregate market volatility. In a similar fashion, we construct the option-implied oil volatility measure to capture the ex-ante uncertainty in the oil markets. For robustness, we consider several alternative uncertainty measures. First, we construct realized, rather than ex-ante, uncertainty using the high-frequency return data. That is, we use squared daily equity and oil returns over the quarter to obtain realized variation measures in equity and oil markets, respectively. We further consider other measures of aggregate uncertainty, such as the Baker et al. (2013) economic policy uncertainty index available at the Fred, and the stochastic volatilities of oil supply and real consumption growth. The last two measures are 4 Our results are similar when using only the non-durable-good producing firms in the portfolio. 6

7 constructed from an AR(1)-GARCH(1,1) filter to the oil supply production growth and real consumption growth, respectively. The key summary statistics for the data are reported in Table 1. In our sample, the real aggregate growth rates average about 1-2%. The volatilities of the standard aggregate production and consumption series are about 1%, with the exception of real investment whose volatility is 7%. The oil-related measures are about twice more volatile than the consumption and output growth in the United States. Most of the macroeconomic variables are mildly persistent, except for the oil-related measures for which the autocorrelation coefficients are close to zero or somewhat negative. In terms of the asset-price moments, the equity risk premium is about 6% in our sample, while the average excess oil return is 4%. The volatility of oil return is almost 40%, which is twice as high as the volatility of the equity return. The implied oil volatility is also larger than the implied equity volatility, and is twice as volatile. We show the time series of returns and volatilities in equity and oil markets in Figure 1. Both oil and equity returns are quite volatile and further, the amount of conditional volatility varies persistently in the sample. As shown in Table 2, volatilities in oil and equity markets are quite correlated: the correlation coefficient is about 60% in the benchmark sample, though, it drops to 50% excluding the Financial Crisis. In equity markets, the two largest spikes in volatility correspond to the stock market crash in November of 1987, and the Great Recession at the end of The equity volatility is also elevated in the LTCM crisis of 1998, and the dotcom crash in All of the turbulent equity market periods are associated with a significant decline in equity prices. In oil markets, oil volatility exhibits larger level and variation, relative to equity volatility. Also, a rise in oil volatility can be caused by a sharp increase in the underlying prices, as in the Gulf War of 1990, as well as a decrease in oil prices, as in the Great Recession in Oil volatility is also high in 1986 due to the oil price collapse caused by the decision of Saudi Arabia and several of its neighbors to increase its share in the oil markets. 7

8 2.2 Oil Volatility and Current Growth We start our analysis by considering contemporaneous correlations of volatility with aggregate macroeconomic variables. The first panel of Table 2 shows our evidence for the benchmark sample from 1990 to 2014, and the bottom panel shows the robustness to Financial Crisis period which features abnormally large movements in volatility. The Table shows that all the considered measures of economic growth, such as consumption, GDP, investment, dividend, and employment growth, decline significantly at times of high oil volatility. For example, the correlation between GDP growth and oil implied volatility is -0.55, and it is for investment growth and for change in employment. This evidence is robust to using realized, rather than implied, volatility: many of the correlations actually become more negative using the realized volatility measures. Further, the evidence is quite similar excluding the 2006Q3-2008Q4 period. The economic growth rates also decline at times of high equity volatility. However, the growth rate correlations with equity volatility are all smaller, in absolute value, compared to those with oil volatility. For example, for a benchmark sample, the correlation of GDP growth with oil volatility is -0.55, relative to for equity volatility, and the magnitudes are and -0.37, respectively, for investment growth, and and for employment growth. With a single exception of dividend growth rates, this evidence is robust to using realized variance and for the sample excluding the Financial Crisis. Dividends are quite noisy at quarterly frequency even after removing seasonality, and still likely to be subject to data and measurement errors. Indeed, as shown in Table 1, dividend growth is negatively autocorrelated, and its annualized volatility of 15% substantially exceeds the volatility of annual dividend growth in this period of about 10%. Next we consider the covariation of volatility with oil-related quantity data. Oil consumption declines when oil volatility is high: the contemporaneous correlation is 8

9 -0.36 both in the benchmark sample and excluding the crisis. The correlations are much weaker for equity volatility. Indeed, the correlation between oil consumption growth and equity implied volatility is in fact zero outside the Financial crisis. In our benchmark sample, oil stock goes up at times of high oil volatility, however, these correlations are rather weak. To the extent that there are delays in adjusting oil stock in real world, we expect the oil stock to increase in the future, rather than contemporaneously. We show the evidence for that later in the predictability results. We further examine the link between the volatility and the productivity measures in aggregate and oil sectors. In our model, the TFP and oil production growth are the exogenous processes which drive the economy, so it is important to establish how much of oil volatility effect exists at the level of the economic primitives. Table 2 shows that the TFP growth rates are negatively correlated with oil volatility. However, these correlations are weaker relative to other macroeconomic variables. For example, excluding the Financial Crisis, the correlation of oil volatility with TFP are about twice lower, in absolute value, relative to the correlations of oil volatility with consumption, output, investment, and employment. Similarly, the correlation of oil supply growth with volatility is two to three times weaker than the correlation of oil consumption growth with volatility. This suggests that the effect of oil volatility on endogenous macroeconomic variables is larger than that on the exogenous driving processes. We show further evidence for that in the predictive regressions. Finally, we show the evidence for the co-movements of the aggregate variables with oil return itself. Oil return is weakly procyclical, however, the correlations of oil returns with standard macroeconomic variables are nearly zero outside the Financial Crisis. Oil prices have more substantial correlations with oil-related quantities. In the data, growth rates in oil production and oil stock contemporaneously decline at times of high oil prices, while oil consumption increases. 9

10 Our key results are based on the benchmark sample from 1990 to 2014, given the availability of the option data. To show the robustness of our results, we also consider a longer sample starting from 1983, for which we can use realized volatility measures computed from the daily oil and equity returns. As shown in Table 3, the results for the sample are similar to our benchmark findings. Oil volatility has large and negative correlations with contemporaneous economic growth rates, which are larger, in absolute value, than those with equity volatility. Oil stocks increases, on average, while oil consumption falls at times of high oil volatility. Aggregate TFP and oil production growth tend to co-move less strongly with volatility measures. These findings suggest an important link between oil volatility and economic growth rates, relative to equity volatility. Next we formally examine the information in the two volatility measures for the expected future growth rates 2.3 Oil Volatility and Future Growth To show the distinct information in oil variance for future economic growth, we consider a predictive regression setup: 1 h h y t+j = a h + b hx t + error, j=1 where y is the macroeconomic variable of interest, and x t is the set of predictors. Across all the specifications, the predictors include the lag of the predictive variable itself, oil variance, equity variance, and oil return. For additional controls, we also include asset-price variables such as the market price-dividend ratio, short rate, and the term spread. The regressions are done on quarterly frequency, and the regression horizon varies from h = 0 (contemporaneous relation) to 4 quarters ahead. Our benchmark sample uses the data from 1990 to 2014, and the variance measures correspond to the implied variances from the option data. For robustness, we also consider 10

11 excluding the Financial Crisis and omit 2006Q3-2008Q4 sample, and also using the longer sample in which the uncertainty measures correspond to the realized variances. Tables 4-7 summarize the predictability evidence for future growth in consumption, GDP, investment, and employment. The Table shows that across all the horizons and specifications, the sign of the loadings on oil variance is negative. That is, controlling for equity variance, oil return, and other predictors, a rise in oil variance forecasts a decline in future aggregate growth 1 to 4 quarters ahead. Interestingly, the loadings are larger, in absolute value, in the sample which excludes the Financial Crisis. That shows that our main predictive results are not driven by the abnormally large volatility swings during the crisis. All slope coefficients on oil variance are statistically significant at 1 quarter horizon. The significance drops with the horizon. Excluding crisis tends to improve the significance of the estimates; indeed, the slope coefficient on oil variance is statistically significant for investment and employment series 4 quarters ahead in the baseline specification with no additional controls. The Tables further shows that the sign of the equity variance loading tends to be negative as well. However, across all the horizons the estimates of the impact of equity variance are never significantly different from zero. In terms of the effect of oil prices, the signs of the coefficients are negative for consumption and GDP growth, positive for employment, and the evidence is mixed for future investment growth. Further, the R 2 in these predictability regressions is quite high, and varies from about 20% for future GDP and investment, to about 40% for future consumption, and 70-80% for future employment. To quantify a relative impact of variance on aggregate variables, in Figure 2 we show the impulse responses of future consumption, output, investment, and employment to one-standard deviation shock in oil and equity variance. The impulse responses are based on a VAR(1) specification fitted to the observed equity variance, oil variance, oil 11

12 returns, and the macroeconomic variables of interest, over the benchmark sample from 1990 to To compute the impulse responses, we always put the macroeconomic variable last, and put the oil return before the oil variance. We then consider two orderings for the oil and equity variance. In the first case, we put the equity variance first, so that the shock in equity variance affects future oil variance. We also consider an alternative ordering in which oil volatility comes before equity volatility. The Figure shows that under the first scenario in which oil variance responds to equity variance shocks, the two variances have a very similar negative impact on future economic growth rates. Consumption growth declines by about 0.30%, annualized, following the shock, and declines further one quarter after the shock. Output and investment drop by 0.66% and 2.75%, respectively, and employment growth tends to decline for several quarters after the shock. Interestingly, when we change the ordering and let oil variance lead equity variance, we find that the impact of oil variance significantly increases, while the role of equity variance diminishes by more than a half. At its peak, the impact of oil variance is to drop consumption growth by 0.55%, output by 0.85%, investment by 4.25%, and employment by 0.65%. The impact of equity variance is several times smaller. Table 8 shows the predictability results for future dividends. The dividend series are quite noisy at quarterly frequency and the R 2 s tend to be quite low. While the slope coefficients on oil variance are positive at a 1 quarter horizon, they become negative afterwards, consistent with our evidence for the aggregate macroeconomic series. The slope coefficients are statistically significant for 3 and 4 quarters ahead. Notably, the coefficients on equity variance, while negative, are never significant. Tables 9 and 10 show the predictability results for future aggregate TFP and oil production growth. Oil variance predicts a decline in these measures initially, but within 2-3 quarters the signs on oil variance turn positive. All of the coefficients are insignificantly different from zero. The coefficients on equity variance are positive, and also insignificant. Finally, the R 2 s in these regressions are below 10%. Overall, 12

13 consistent with our contemporaneous correlation evidence in Table 2, the data do not feature a strong link between aggregate TFP and oil production and oil volatility. On the other hand, future oil consumption tends to drop, while future oil inventories increase following an increase in oil variance. Indeed, Table 11 shows that oil variance has negative and significant effect on oil consumption 1 quarter ahead, while Table 12 documents a positive and significant effect for next-quarter oil stock. To gauge quantitative impact of oil variance, we show the impulse responses of future oil consumption and oil inventory to oil volatility shocks in Figure 4. We compute the impulse responses from a VAR(1) fitted to oil supply growth, oil return, oil volatility, oil inventory, and oil consumption growth data, in that order. The Figure shows that oil inventories increase by 0.5% one quarter after the impact, while oil consumption declines by about 0.6%. Overall, our results suggest that oil variance captures a significant information about real growth, above and beyond market volatility and other predictors of future economic conditions. An increase in oil variance predicts a decline in current and future growth rates 1 to 4 quarters ahead. An increase in oil variance also predicts a decline in oil consumption, and increase in oil inventory. At the same time, aggregate TFP and production of oil do not seem to be related to movements in oil volatility. We consider several alternative specifications to check the robustness of our results. First, we consider using a longer sample from 1983 and relying on realized variance measures to capture movements in uncertainty. This does not affect any of our results, as we show in Appendix Tables A.1-A.9. Next we consider alternative measures for aggregate uncertainty, such as the Baker-Bloom-Davis economic policy uncertainty index, and the conditional variance of the output growth. We summarize the key findings for these two measures in Tables Similar to the benchmark results, oil variance predicts a decline in future aggregate growth and an increase in oil inventories controlling for these other measures of uncertainty. Notably, most of the slope coefficients on other uncertainty measures are insignificant from zero. 13

14 2.4 Oil Variance and Asset Prices The correlation evidence in Table 2 suggests that equity returns drop at times of high oil variance. Indeed, the correlation of equity returns with oil implied variance is in the benchmark sample, and about excluding the crisis. Oil returns, on the other hand, have a much weaker correlation with oil variance. Excluding the crisis, the correlation of oil returns with oil implied variance is positive and equal to This is consistent with our earlier discussion that an increase in the underlying oil variance can be caused both by large positive and negative shocks to oil prices. To quantify the dynamic impact of oil volatility on equity prices, we show impulse responses in Figure 3. Similar to before, we consider two alternative orderings in which equity volatility leads or lags oil volatility shocks. The figure shows that independent of the ordering, oil volatility has a pronounced impact on market valuations. The effect of oil volatility on asset valuation varies considerably across industries. Similar to Eraker et al. (2015), we construct durables and non-durables equity portfolios. We regress industry returns on the market return, oil return, and the change in the equity and oil VIX index, which allows us to estimate the sensitivity of the industry portfolios to oil volatility. In Table 15, we see that the durables portfolio exhibits the largest exposure to oil uncertainty, with a negative and statistically significant beta of On the contrary, the impact of oil uncertainty on the non-durables and oil producers portfolio is small in magnitude and statistically insignificant. Using the sample starting from 1983 with realized oil volatility as a robustness check confirms the negative effect of oil uncertainty on the durables portfolio (see Table A.10). As the most striking example, a finer classification shows that the industry with the largest negative exposure to oil uncertainty is Autos. We further consider predictability regressions of future equity returns on the oil variance. In our sample, we do not find a significant link between equity risk premia and oil variance. This fact is partially consistent with the findings in Christoffersen and 14

15 Pan (2014). In a cross-sectional approach, they sort equity portfolios conditional on the past exposure to implied oil volatility. They do not find any predictive power for the cross-sectional returns for the whole sample. Only after 2004 in the so-called financialization period does oil volatility exhibit strong predictive power for equity returns. This predictive power is mainly attributed to the funding liquidity which links the two markets. Given our previous evidence on the impact of oil on real growth and dividends, it suggests that cash flows, rather than discount rates, are the key channel which explains a negative correlation between market prices and oil volatility. 3 Model We explain our empirical findings within a macro model in the style of Ready (2014) and Hitzemann (2015), featuring an oil sector and a general macro sector. As the main novel ingredient, we introduce stochastic uncertainty of the oil supply into the model. Shocks to oil supply uncertainty endogenously translate to changes in oil price volatility, motivating the use of the price-based oil uncertainty measure in our empirical analysis. We show that in line with a precautionary savings motive, oil producers stock up their inventories when oil supply uncertainty increases and sell less oil to the market. The decrease in effective oil supply translates to the macro sector and depresses output, consumption, and investment. 3.1 Setup Final goods producer The representative firm in our model produces a final good Y t = (A t N t ) 1 α Z α t (3.1) 15

16 with the input of labor N t and an intermediate good Z t, where the total factor productivity is denoted by A t. Production of the intermediate good requires general capital K t and oil J t as an input. More specifically, the intermediate good is a CES aggregate of these two input factors, Z t = [(1 ι)k 1 1 o t + ιj 1 1 o t ] o, (3.2) where ι describes the oil share and o is the constant elasticity of substitution. The oil input of the firm is purchased from oil producers as described below. On the other hand, the firm maintains a general capital stock K t in line with the classical real business cycle framework. Accordingly, the capital accumulation equation is given by K t+1 = (1 δ)k t + I t G t K t, (3.3) where I t is physical capital investment and G t is an adjustment cost function G t (I t /K t ) = I t /K t (a 0 + a (I t /K t ) 1 1 ξ ) (3.4) ξ as proposed by Jermann (1998). The firm generates revenues by selling the part of the final output that is not invested again to the households, creating a cash-flow of Y t I t. On the other hand, the oil input J t is purchased from the oil producer at price P t, and workers are paid wages W N t for their hours worked N t. Overall, the final goods producer maximizes the expected sum of discounted cash-flows E t s=0 M t+s (Y t+s I t+s P t+s J t+s W N t+sn t+s ), (3.5) where M t+s is the s-period stochastic discount factor at time t. 16

17 Oil Producer The oil sector is represented by an oil producing firm which is endowed with an amount of oil wells containing U t = A t U (3.6) barrels of oil below ground. To ensure balanced growth, we assume that the oil wells grow with the general macroeconomy at A t. This is in line with a model where firms endogenously invest a certain amount of their output Y t to drill new oil wells (see Hitzemann 2015). Keeping the model as simple as possible, we do not explicitly consider the oil drilling decision in here and take the amount of oil wells as exogenous. Accordingly, the amount of below-ground oil in existing wells is also not reduced by oil extraction in this model. The production of oil takes place at a stochastic extraction rate κ t, such that E t = κ t U t (3.7) barrels of oil are extracted and added to the producer s above-ground inventories. The oil inventories are actively managed and evolve as S t+1 = (1 ω)s t Π t A t + E t+1 D t+1. (3.8) Accordingly, the oil producer decides at each point in time how much oil D t to sell to the firms for production and how much to store above ground at an inventory cost of ω. An important restriction is that inventories cannot become negative, which gives rise to a precautionary savings motive that is at the center of the economic mechanism studied in this paper. Technically, we approximate the non-negativity condition by a smooth stock-out cost function Π t (S t /A t ) = π 2 (S t/a t ) 2, (3.9) 17

18 as proposed by Hitzemann (2015). Given these ingredients, the oil producer maximizes the expected discounted cashflows from oil sales to the final goods producing firm, which are given by E t s=0 M t+s P t+s D t+s. (3.10) Macro and Oil Productivity Risk In our model, both the general macro sector and the oil sector are subject to productivity risk. We specify the productivity of the macro sector in line with Croce (2014), i.e., A t+1 = A t exp{µ + x t + e wt ε A t+1}, (3.11) x t+1 = φx t + e w t+1 ε x t+1, (3.12) w t+1 = ρ w w t + ε w t+1. (3.13) Here ε A t ε x t N(0, σa 2 ) are short-run shocks to macroeconomic productivity growth while N(0, σ 2 x) are persistent (long-run) shocks to productivity growth. In addition, we also consider uncertainty shocks ε w t N(0, σ 2 w) to macro productivity. The productivity risk in the oil sector stems from fluctuations in the extraction rate from existing oil wells given by κ t+1 = η(1 χ) + χκ t + e vt ηε κ t+1, (3.14) v t+1 = ρ v v t + ε v t+1. (3.15) In addition to the level shocks ε κ t N(0, σκ), 2 we introduce oil-specific supply uncertainty shocks ε v t N(0, σv) 2 into the model. As oil supply uncertainty shocks endogenously translate to changes of oil price volatility in our model, we identify the impact of these shocks with the effects of fluctuating oil price volatility documented in our empirical analysis. 18

19 All shocks considered in our model are i.i.d. and mutually independent. Household The representative household consumes a CES bundle of the final consumption good C t and leisure L t, given by C t = [τc 1 1 ξ L t + (1 τ)(a t 1 L t ) 1 1 ξ L ] ξ L, (3.16) and maximizes Epstein and Zin (1991) utility V t = [ (1 β) C 1 1 ψ t ] [ ] ψ 1 ψ 1 + βe t V 1 γ 1 γ t+1 (3.17) with risk aversion γ and an intertemporal elasticity of substitution ψ. The utility maximization is subject to the standard wealth constraint W t+1 = (W t C t + W N t N t )R W t+1 (3.18) and the labor supply constraint N t + L t = 1. (3.19) 3.2 Equilibrium To calculate the model s equilibrium, we derive the firms and the household s first order conditions. 5 oil price As a result, we obtain, first, the intratemporal conditions for the P t = Q S t Y t = Y t = αι J t J 1 o t Z 1 1 o t (3.20) 5 The household s first order conditions are the same as in an endowment economy with the same consumption goods. For the derivation of the firms first order conditions, see Appendix A.1. 19

20 and for labor wages W N t = C L t / C C t = (1 α) Y t N t. (3.21) Second, the intertemporal Euler condition E t [M t+1 R t+1 ] = 1 (3.22) holds for the returns of all assets traded in the economy, with the pricing kernel given by M t+1 = β ( ) 1 Ct+1 C t ξ L ( Ct+1 C t ) 1 1 ξ L ψ V t+1 E t [ V 1 γ t+1 ] 1 1 γ 1 ψ γ. (3.23) The Euler equation especially applies to the return of investment in the general macro sector R I t+1 = α(1 ι) Y t+1 K o 1 t+1 Z 1 o 1 t+1 I + ((1 δ) + G t+1 t+1 K t+1 G t+1 )Q I t+1, (3.24) Q I t with Q I t = 1, and the return on oil inventories 1 G t Rt+1 S = (1 ω Π t)q S t+1. (3.25) Q S t With these expressions, we can define the equity market return as the weighted average of R I and R S, Rt+1 M = K tq I t Rt+1 I + S t Q S t Rt+1 S. (3.26) K t Q I t + S t Q S t Given the risk-free rate R f t = 1 E t [M t+1 ], (3.27) we calculate the equity risk premium as R LEV ex,t = (1 + DE)(R M t R f t 1) (3.28) 20

21 and account for financial leverage by assuming an average debt-to-equity ratio DE of 1 (see, e.g., Croce 2014). Having the first order conditions as well as the market clearing conditions, C t + I t = Y t and D t = J t, we can reformulate the model as a central planner s problem according to the welfare theorems. We solve this problem numerically by a third-order approximation using perturbation methods as provided by the dynare++ package. 3.3 Calibration Table 16 shows the parameters of the calibrated model. Following the literature on long-run risk in consumption- and production-based asset pricing (Bansal and Yaron 2004; Croce 2014), we set the relative risk aversion γ to 10 and the intertemporal elasticity of substitution ψ to 2, such that households in our model have a preference for the early resolution of uncertainty. We set the subjective discount factor β to For the values of the oil share in production ι and its constant elasticity of substituion o, we follow Wei (2003) and Ready (2014), respectively. The parameters α, δ, µ, τ, σ A, φ, σ x, ρ w, and σ w describing the macro sector are chosen in line with Croce (2014). We set the constant elasticity of substitution ξ L between leisure and consumption to 0.9. For the oil sector, we fix the oil inventory cost ω as well as the mean η and the mean-reversion χ of the oil production rate according to the benchmark calibration of Hitzemann (2015). We calibrate the adjustment cost parameter of the macro sector ξ to match the volatility of general consumption relative to output, and the oil inventory stock-out cost parameter π to match the relative volatility of oil inventories relative to oil production, see Table 17. Finally, we match the oil price volatility s level, meanreversion, and volatility by calibrating the corresponding parameters of the oil supply process σ k, ρ v, and σ v. This way, we especially ensure that a one standard deviation 21

22 shock to oil price volatility as considered in the empirical section corresponds to a one standard deviation shock to oil supply volatility in the model. Before we analyze the effect of changes in oil uncertainty on macroeconomic variables in detail, we ensure that our calibration roughly captures the general features of the macroeconomy and the oil sector. For that, consider the price and quantity moments in Table 18 that the model is not explicitly calibrated to. Overall, we see that all moments are in a reasonable order of magnitude, and deviations are in line with the model without an oil sector as proposed by Croce (2014). As a notable improvement compared to that benchmark, we are able to generate a volatility of the equity premium as high as in the data, which is a challenge for most production-based models. Our model is able to produce such high equity volatility thanks to the high supply volatility of oil as an additional input factor. 3.4 Inspecting the Mechanism Our model provides insights into the economic mechanism behind our main empirical finding that an increase of uncertainty in the oil sector depresses macroeconomic growth. The mechanism is illustrated by the impulse response functions for an oil supply uncertainty shock based on our model, as presented by Figure 5. We see that a rise in uncertainty regarding oil supply prompts the oil producer to stock up aboveground oil inventories. The reason is that a positive shock to oil supply uncertainty makes large negative and positive oil supply (level) shocks more likely. To be able to cushion a large negative oil supply shock and to smooth oil consumption over time, oil producers need to increase their inventories to alleviate the probability of a stock-out. As a result of this precautionary savings effect, the oil producer curbs the amount of oil that is sold to the market. As oil is an important input factor for the production of the intermediate good in the general macro sector, the reduced oil supply negatively affects the output of 22

23 the intermediate good and ultimately of the final consumption and investment good. Therefore, the precautionary savings effect in the oil sector spills over to the general macroeconomy. In consequence of the declining output, the investment and consumption of the general good also decreases. The magnitude of the effect of oil supply uncertainty shocks on the macro sector strongly depends on the substitutability of oil in the production of the intermediate good, as specified by the CES parameter o. In our calibration, o is set to a relatively low value of 0.225, which means that oil and general capital are almost complementary inputs, yielding a considerable effect of oil uncertainty shocks on the general macroeconomy. Quantitatively, a one standard deviation increase of oil supply uncertainty in the model leads to a rise in oil inventories by about 1%, reducing the effective oil supply to the market by more than 0.5%. In the macro sector, this yields a decrease in output by about 0.15%, a fall in consumption by 0.2% and investments declining by 0.2%. These effects on the macroeconomy are smaller but roughly in a similar order of magnitude as the ones observed in the data. In a more general context, our model shows that models with inventories are better able to capture the economic intuition related to the effects of an uncertainty shock to the economy. Production-based models that do not consider inventories generally have the flaw that an uncertainty shock does not have an immediate effect on the output of the economy. Therefore, higher uncertainty results either in increased investments if the precautionary savings effect dominates and consumption is reduced, or in increased consumption if the option to wait is valuable (see also Bloom 2014). Both possible outcomes an investment boom or a consumption boom caused by increased uncertainty are, however, at odds with the economic intuition. In contrast, a model with inventories makes it possible to put goods on hold, such that they are neither consumed nor invested. As we have seen for the important example of oil uncertainty shocks, this feature leads to decreasing output, investment, and consumption at the same time due to the precautionary savings effect. 23

24 4 Conclusion We show novel empirical evidence that oil price variance captures significant information about economic growth and asset prices. An increase in oil variance predicts a decline in current and future growth rates of consumption, output, investment, and employment 1 to 4 quarters ahead, controlling for current growth rate in the corresponding variables, current oil returns, and the market variance. We further show that the market equity price drops at times of high oil uncertainty, while oil prices themselves have only a weak relation to oil uncertainty which turns positive outside the Financial Crisis. We provide a two-sector macro model to explain these empirical findings. In the model, firms manage oil inventories to mitigate the consequences of oil supply shocks. In times of high oil supply volatility, they increase their inventories to alleviate the probability of a stock-out. As a result of this precautionary savings effect, the amount of oil available for production in the general macro sector is reduced, and production, consumption, and investments decrease. This effect dominates the usual precautionary savings effect to increase physical capital investments when uncertainty increases, such that consumption and investment jointly decrease in our model when (oil) uncertainty rises. These economic mechanisms are directly supported in the data. 24

25 A Appendix A.1 Firms First Order Conditions Final goods producer Without loss of generality, consider (3.5) at time 0 and add the Lagrange multiplier Q I t for the resource constraint (3.3): max I t,k t+1,n t,j t E 0 t=0 M t (Y t I t P t J t Wt N N t Q I t (K t+1 (1 δ)k t I t + G t K t )). (A.1) Setting the derivative with respect to I t to zero yields Q I t = 1. (A.2) 1 G t Setting the derivative with respect to K t+1 to zero, we obtain E t α(1 ι) M t+1 Y t+1 K o 1 t+1 Z 1 o 1 t+1 I + ((1 δ) + G t+1 t+1 K t+1 G t+1 )Q I t+1 = 1. Q I t (A.3) Setting the derivative with respect to N t to zero, we have W N t = Y t N t = (1 α) Y t N t. (A.4) Finally, we set the derivative with respect to J t to zero and get Y t P t = Y t = αι. (A.5) J t J 1 o t Z 1 1 o t 25

26 Oil Producer Without loss of generality, consider (3.10) at time 0 and add the Lagrange multiplier Q S t for the resource constraint (3.8) max D t,s t E 0 M t (P t D t Q S t (S t (1 ω)s t 1 + Π t 1 A t 1 E t + D t )). t=0 (A.6) Setting the derivative with respect to D t to zero, we get P t = Q S t. (A.7) Setting the derivative with respect to S t to zero yields [ ] (1 ω Π E t M t)q S t+1 t+1 = 1. (A.8) Q S t A.2 Appendix Tables 26

27 Table A.1: Predictability Evidence: Consumption Growth, Sample Lag growth Oil Var Equity Var Oil Return Macro Adj. R sample 1q ahead 0.45 (0.1) (1.63) (3.41) (0.22) No (0.12) (1.72) (3.13) (0.21) Yes q ahead 0.43 (0.11) (1.5) (2.92) (0.18) No (0.12) (1.57) (2.62) (0.18) Yes q ahead 0.47 (0.11) (1.47) (2.84) (0.13) No (0.11) (1.49) (2.59) (0.12) Yes q ahead 0.42 (0.12) (1.36) (2.66) (0.13) No (0.12) (1.35) (2.37) (0.12) Yes sample, excluding 2006Q3-2008Q4 1q ahead 0.36 (0.09) (1.77) (3.38) (0.23) No (0.11) (1.88) (3.2) (0.22) Yes q ahead 0.37 (0.09) (1.6) (2.87) (0.19) No (0.1) (1.7) (2.73) (0.19) Yes q ahead 0.41 (0.09) (1.52) (2.76) (0.12) No (0.1) (1.56) (2.67) (0.11) Yes q ahead 0.38 (0.1) (1.37) (2.6) (0.11) No (0.11) (1.4) (2.44) (0.11) Yes 0.41 The table reports predictability evidence for consumption. Consumption growth is in percentage points. Data are quarterly from 1983Q2 to 2014Q1. In the second last column, we report whether macro variables are controlled for in the regression. The macro variables are price-dividend-ratio, short rate, and term spread. Newey-West standard errors are in parentheses. 27

28 Table A.2: Predictability Evidence: GDP Growth, Sample Lag growth Oil Var Equity Var Oil Return Macro Adj. R sample 1q ahead 0.35 (0.1) (1.85) (2.89) (0.28) No (0.11) (1.98) (3.27) (0.3) Yes q ahead 0.40 (0.08) (1.2) (2.2) (0.25) No (0.07) (1.25) (2.2) (0.25) Yes q ahead 0.34 (0.1) (1.27) (2.3) (0.22) No (0.08) (1.26) (2.32) (0.21) Yes q ahead 0.33 (0.1) (1.39) (2.1) (0.21) No (0.08) (1.36) (2.13) (0.2) Yes sample, excluding 2006Q3-2008Q4 1q ahead 0.29 (0.11) (1.92) (3.04) (0.26) No (0.12) (1.96) (3.48) (0.28) Yes q ahead 0.38 (0.08) (1.36) (2.16) (0.28) No (0.08) (1.35) (2.23) (0.29) Yes q ahead 0.29 (0.09) (1.11) (2.2) (0.2) No (0.08) (1.16) (2.28) (0.19) Yes q ahead 0.31 (0.1) (1.31) (2.08) (0.17) No (0.08) (1.38) (2.14) (0.17) Yes 0.24 The table reports predictability evidence for GDP growth. GDP growth is in percentage points. Data are quarterly from 1983Q2 to 2014Q1. In the second last column, we report whether macro variables are controlled for in the regression. The macro variables are price-dividend-ratio, short rate, and term spread. Newey-West standard errors are in parentheses. 28

29 Table A.3: Predictability Evidence: Investment Growth, Sample Lag growth Oil Var Equity Var Oil Return Macro Adj. R sample 1q ahead 0.22 (0.1) (9.78) (20.75) (1.15) No (0.1) (9.24) (20.27) (1.1) Yes q ahead 0.22 (0.09) (7.05) (13.01) (1.35) No (0.09) (6.39) (11.76) (1.21) Yes q ahead 0.20 (0.09) (6.93) (12.51) (1.31) No (0.09) (6.47) (10.61) (1.17) Yes q ahead 0.16 (0.09) (7.03) (11.15) (1.09) No (0.08) (6.75) (9.08) (0.94) Yes sample, excluding 2006Q3-2008Q4 1q ahead 0.14 (0.1) (9.91) (21.3) (1.07) No (0.11) (9.1) (21) (1) Yes q ahead 0.16 (0.08) (6.91) (11.3) 0.32 (1.49) No (0.09) (6.07) (11.0) 0.13 (1.39) Yes q ahead 0.14 (0.08) (5.75) (10.7) 0.04 (1.23) No (0.08) (5.41) (9.94) (1.11) Yes q ahead 0.12 (0.08) (6.07) (10.1) (0.98) No (0.08) (6.34) (8.67) (0.87) Yes 0.12 The table reports predictability evidence for investment growth. Investment growth is in percentage points. Data are quarterly from 1983Q2 to 2014Q1. In the second last column, we report whether macro variables are controlled for in the regression. The macro variables are price-dividend-ratio, short rate, and term spread. Newey-West standard errors are in parentheses. 29