Price Setting and Volatility: Evidence from Oil Price Volatility Shocks

Layer 1: Overview

This paper asks whether increases in aggregate volatility reduce the effectiveness of monetary policy by making aggregate prices more flexible. The motivation is concrete: policymakers worry that during episodes of high volatility, prices may become more synchronized in their adjustment, reducing monetary non-neutrality and limiting the ability of nominal stimulus to raise real output.

The empirical strategy exploits variation in oil price volatility as a plausibly exogenous source of aggregate cost volatility. Oil price volatility is measured using a stochastic volatility model estimated on monthly WTI spot prices from 1986 to 2014 (Bayesian MCMC with particle filter). The key identification device is a Bartik-style interaction: an industry’s pre-determined oil input share (from the 1997 Input-Output Use Table, expressed as oil spending relative to value added) is interacted with the time-varying aggregate oil price volatility. Industries more dependent on oil should respond more strongly to oil price volatility shocks, while the time fixed effects absorb any aggregate confounders. The micro-price data are confidential item-level Producer Price Index records from the BLS covering 81 four-digit NAICS manufacturing industries from January 1998 to December 2014, with roughly 100,000 prices collected monthly from about 25,000 reporters.

Two price-setting moments are the main outcomes: price change frequency (fraction of items with non-zero price change within an industry-month) and price change dispersion (standard deviation of non-zero price changes within an industry-month).

The main empirical findings, from Table 6 (industry-specific oil demand variable regressions with both industry and time fixed effects):

• A one standard deviation increase in oil price volatility raises price change dispersion by approximately 2 percent relative to the mean for a 90th-percentile oil-share industry relative to a 10th-percentile oil-share industry (coefficient of 4.511, significant at 1 percent). This finding is robust to alternative oil price series (WTI, Brent, RAC), alternative volatility measures (stochastic volatility, GARCH, realized volatility), exclusion of the 2008 crisis period, and alternative dispersion measures (interquartile range).

• The same cross-industry comparison shows that a one standard deviation increase in oil price volatility reduces price change frequency by approximately 1 percent relative to the mean for high-oil versus low-oil industries (coefficient of -2.486, significant at 5 percent in Table 6 column 1). This negative frequency result holds inside and outside the financial crisis period.

• The time-series correlation between price change dispersion and oil price volatility for the top-10-percent oil-share industries is 0.45, versus only 0.08 for the bottom-10-percent industries, previewing the cross-sectional identification.

These findings contrast sharply with what the literature documents for idiosyncratic volatility (Vavra 2014), where both frequency and dispersion rise together. For aggregate (oil) volatility, dispersion rises but frequency does not, implying a different mechanism.

To interpret these facts, the paper constructs and calibrates a general equilibrium state-dependent pricing model. Firms produce using labor and oil (Cobb-Douglas), face menu costs, and receive idiosyncratic productivity shocks with leptokurtic draws. The key modeling choice is random menu costs (drawn each period from a non-degenerate distribution, following Dotsey, King, and Wolman 1999 and Luo and Villar 2020) rather than fixed menu costs. With random menu costs, the selection of which prices adjust is attenuated relative to the common shock: many firms will not adjust because they drew a high menu cost regardless of the oil shock, keeping the mix of adjusting prices more disperse. A fixed-menu-cost model (Appendix A.3) produces a counterfactual negative relationship between oil price volatility and price change dispersion, because the strong selection effect causes prices to bunch in the direction of the cost shock.

The calibrated one-sector random menu cost model matches the positive empirical link between oil price volatility and dispersion, with a muted frequency response. The multisector model (eight sectors calibrated to oil-share octiles of PPI industries) is fed the actual observed oil price and volatility series from 1998 to 2014, and the regression run on model-generated data matches the empirical coefficient on dispersion within one standard error of the data estimate (model: 3.876 versus data: 4.511). The model cannot replicate the empirical negative frequency response.

The key quantitative implication for monetary policy: in the multisector model, a permanent increase in log nominal output of 0.002 (doubling one month’s growth rate) translates 59.1 percent into real output at baseline oil price volatility, and 58.8 percent after a one standard deviation increase in oil price volatility. The ability of nominal stimulus to raise consumption on impact falls by only 0.5 percent. The average decline across the full historical distribution of oil price volatility (1998-2014) is 1 percent lower at peak volatility (e.g. 2009) than at trough volatility (e.g. 2013). Supporting aggregate evidence using state-dependent local projections with Romer-Romer monetary shocks (1974-2007) confirms that the price level response to identified monetary shocks is not significantly different across high and low oil price volatility states.

The policy implication is direct: the output-inflation tradeoff is nearly time-invariant with respect to aggregate volatility. Policymakers who respond to periods of high aggregate volatility by increasing nominal stimulus under the belief that policy effectiveness has declined would be overreacting and would generate unnecessary inflation. The source of volatility — aggregate versus idiosyncratic — matters critically for the price-setting implications and thus for the correct policy response.

Layer 2: Deep Dive

What is the identification strategy and what are the main threats to it?

The strategy is a Bartik-style interaction: each industry’s pre-determined oil input share (oil spending as a share of value added, from the 1997 Input-Output tables, before the sample period) is interacted with aggregate time-varying oil price volatility. Industry fixed effects absorb time-invariant heterogeneity; time fixed effects absorb all aggregate shocks common to all industries in a given month. Identification of the oil price volatility effect is thus from within-industry variation over time, scaling by the pre-existing oil dependence. The main threats are: (1) the interaction term could be correlated with unobserved shocks that are industry-specific and vary with oil price volatility; (2) oil prices could respond to aggregate U.S. economic conditions, threatening exogeneity. The paper defends against (2) by arguing that large oil price movements over the sample can be traced to external events (Middle East conflicts, Venezuelan oil strike, Asian demand expansion, Libyan uprising) rather than U.S. conditions, and that individual industries are price takers in the global oil market. For (1), the paper adds controls for industrial production growth, industry inflation, excess bond premium, and realized stock volatility within industries, and shows results are unchanged.

What two mechanisms operate in a menu cost model when common volatility increases, and how do they differ from idiosyncratic volatility?

Two effects operate. The real options effect: higher volatility increases the option value of waiting, so firms expand the inaction band, decreasing frequency. The volatility effect: larger common shocks push more firms outside the band, but because it is a common shock, the resulting price changes are synchronized in the direction of the cost shock, which compresses dispersion. For idiosyncratic volatility, the volatility effect pushes price changes in both directions symmetrically, so both frequency and dispersion rise. This asymmetry is why aggregate and idiosyncratic volatility have different implications for monetary non-neutrality.

Why is a random menu cost model necessary, and what does a fixed menu cost model predict instead?

A fixed menu cost model (as in Golosov and Lucas 2007) features too strong a selection effect. When oil price volatility rises, more firms are pushed outside the action bands and they all move in the direction of the common cost shock, compressing price change dispersion (model predicts a 2.7 percent decline in dispersion per one standard deviation volatility increase) while frequency rises by 8.1 percent. This is the opposite of the empirical finding. Random menu costs break the tight link between the common shock and which firms adjust, because each firm draws a random menu cost each period. A substantial fraction of firms draw very large menu costs and never adjust regardless of the oil shock, while firms that do adjust include those reacting to idiosyncratic shocks (low menu cost draws), keeping the mix of price changes disperse even when aggregate volatility is high.

What heterogeneity is documented across industries?

The main documented heterogeneity is in oil input intensity. The 10th percentile oil share is approximately 0.001 (oil spending equals 0.1 percent of value added) and the 90th percentile is 0.022 (2.2 percent of value added), with the average at 0.8 percent. The top-10-percent oil-share industries (e.g. Basic Chemical Manufacturing at 16.1 percent, Railroad Rolling Stock Manufacturing at 5.1 percent) show substantially stronger responses to oil price volatility shocks than low-oil industries. In terms of price setting statistics, across the eight octile sectors used in the multisector calibration, price change frequency ranges from 0.10 to 0.27, average size from 0.17 to 0.28, and standard deviation from 0.10 to 0.15 — heterogeneity that the multisector model replicates closely. There is no documented differential effect of oil price volatility between durable and non-durable goods industries.

What are the pass-through estimates from oil prices to producer prices, and why do they matter for the main analysis?

The paper first establishes that oil prices actually pass through to producer prices, validating the cost-channel story. The short-run pass-through (impact month) is 1.0 percent (significant at 1 percent), meaning a 1 percent change in real oil prices raises producer price inflation by 1 percent in the same month. The 12-month cumulative pass-through is 8.6 percent (significant at 1 percent). These estimates are obtained from an industry-level panel regression with industry fixed effects and 12 lags of real oil price changes. The large pass-through relative to the average oil share of 0.8 percent is attributed to indirect transmission through input-output linkages. Pass-through establishes that oil is a relevant cost shifter for manufacturing producers, supporting the premise that oil price volatility would affect price-setting decisions.

What robustness checks are run on the main empirical findings?

The paper conducts extensive robustness checks: (1) Alternative oil price series: WTI, Brent Crude, and Composite Refined Acquisition Cost — all give qualitatively and often quantitatively similar results. (2) Alternative volatility measures: stochastic volatility, GARCH(1,1), and realized volatility (within-month standard deviation of daily log price changes) — all produce consistent findings. (3) Crisis period: splitting the sample into 2008 crisis and non-crisis periods shows the dispersion result holds equally inside and outside the crisis. (4) Alternative dispersion measure: interquartile range of price changes in place of standard deviation — results unchanged. (5) Long-run oil usage: averaging the oil share across 1997, 2002, and 2007 IO tables rather than using only 1997 — dispersion results remain significant. (6) Trimming sensitivity: including all observations regardless of few price changes per industry-month does not change results. (7) Industry-level idiosyncratic volatility control: adding median realized stock volatility within the industry does not alter coefficients on oil price volatility.

How does this paper relate to and differ from Vavra (2014)?

Vavra (2014) studies idiosyncratic volatility and finds that both price change frequency and dispersion are countercyclical using CPI data. He matches these facts with a standard menu cost model with second-moment idiosyncratic productivity shocks. Klepacz differs by studying aggregate (oil price) volatility rather than idiosyncratic volatility, using PPI data, and finding that dispersion rises but frequency does not. These are the opposite implications from the mechanism standpoint: Vavra’s model would predict decreased dispersion when common volatility rises (because more prices synchronize), which is why Klepacz needs to modify the model with random menu costs. Klepacz then confirms that his random menu cost model can also reproduce Vavra’s idiosyncratic volatility facts when augmented with time-varying idiosyncratic volatility, with price change dispersion rising 1.2 percent and frequency rising 0.5 percent per one standard deviation idiosyncratic volatility shock. This shows the models are complementary, not contradictory.

What does the model imply for the magnitude of the change in monetary policy effectiveness across the full empirical distribution of oil price volatility?

Beyond the 0.5 percent decline per one standard deviation oil price volatility increase, the paper simulates the full 1998-2014 oil price and volatility series through the model. At each point, it computes the on-impact output response to a 0.002 permanent log nominal output shock. The average monetary policy efficacy is 1 percent lower on impact during periods of the highest observed oil price volatility (such as 2009) relative to periods of the lowest oil price volatility (such as 2013). The cumulative consumption response is reduced by less than 1 percent throughout the first year following the monetary shock. These magnitudes are small enough that the paper concludes changes in aggregate volatility do not substantially alter the output-inflation tradeoff.

What is the aggregate time-series evidence on monetary policy effectiveness across oil price volatility states?

Section VI uses state-dependent local projections (Auerbach and Gorodnichenko 2013) with Romer-Romer (2004) monetary policy shocks over 1974-2007. The transition function equals one when the three-month moving average of oil price volatility exceeds the sample median. Controls include two lags of the monetary shock, current and two lags of the federal funds rate, log industrial production index, unemployment rate, log PPI, and log real oil price. Results show that the impulse response of the PPI price level to an expansionary monetary shock is not significantly different between high and low oil price volatility states. The high-volatility state estimates are less precise but are consistent with the linear model response, supporting the model’s implication that monetary policy effectiveness is not a function of oil price volatility.

What are the policy implications and their scope conditions?

The paper implies that policymakers should not systematically increase nominal stimulus in response to high aggregate volatility on the grounds that policy is less effective. The output-inflation tradeoff is nearly time-invariant. If policymakers over-stimulate believing effectiveness has declined, the result is unnecessary inflation. However, this conclusion is specific to aggregate (common) volatility shocks, not idiosyncratic volatility — the source of volatility matters for the direction of price-setting response and hence for the policy implications. The paper explicitly states that the analysis applies to oil price volatility but extends conceptually to policy uncertainty, exchange rate volatility, and global demand volatility. One scope condition: the model abstracts from a monetary policy reaction function that responds directly to oil prices (as in Kilian and Lewis 2011 or Bodenstein et al. 2012), so the quantitative results apply to the partial equilibrium price-setting channel rather than to the full general equilibrium policy transmission.

What are the business cycle properties of price change moments in the PPI, and how do they compare to CPI findings?

Table 1 shows that the standard deviation of PPI price changes is countercyclical: the recession dummy adds 0.008 to the mean dispersion of 0.127 (significant at 5 percent). Price change frequency rises during recessions by 0.017 but the coefficient is not statistically significant. These patterns are qualitatively consistent with Vavra (2014) and Bachmann et al. (2019). Comparing PPI and CPI (Table 2): both have frequency around 15 percent and average absolute size around 7-8 percent. The main difference is that the PPI has a higher fraction of small price changes (22 percent vs. 12 percent in the CPI), reflecting a higher frequency of very small adjustments. Price change dispersion is higher in the PPI (standard deviation 0.13) than the CPI (0.08). Monthly inflation correlation between the two series is 0.80 over 1998-2014.

What caveats or limitations does the paper acknowledge?

The main caveats are: (1) The model does not feature a monetary policy reaction function for oil prices, abstracting from the general equilibrium feedback between oil shocks and interest rate policy. (2) The multisector model replicates the positive relationship between oil price volatility and price change dispersion but cannot match the empirically negative frequency response — the model predicts higher relative frequency for high-oil sectors during volatility episodes, while the data show lower relative frequency. (3) The time-varying idiosyncratic volatility extension uses a simplifying assumption that idiosyncratic volatility is perfectly negatively correlated with oil prices, primarily for computational tractability. (4) The model focuses on manufacturer producer prices (the PPI) and on oil as a non-produced input, abstracting from oil in the household consumption function.

Key Concepts

Price change dispersion: The within-industry standard deviation of non-zero price changes in a given month, measuring how spread out the price changes are in the cross-section of items. A more disperse distribution means price changes are scattered across a wide range of sizes and directions, so a monetary shock shifts fewer prices past the adjustment threshold and has larger real effects. The paper measures it as the square root of the mean squared deviation of item-level price changes from the industry mean, computed only over non-zero changes.

Real options effect: One of two mechanisms through which higher volatility affects price-setting in a menu cost model. Higher volatility increases the value of waiting before paying the menu cost to adjust, because the expected loss from being at a suboptimal price for one more period is smaller relative to the cost of adjusting when future shocks are large and uncertain. This pushes the action and inaction bands outward, reducing the frequency of price adjustment.

Volatility effect: The second mechanism through which higher volatility affects price-setting. For idiosyncratic volatility, larger idiosyncratic shocks push prices outside the inaction bands in both directions, increasing both frequency and dispersion. For common (aggregate) volatility, larger common shocks push prices outside the bands mostly in one direction, increasing frequency but decreasing dispersion (in a fixed-menu-cost model). In a random menu cost model, this synchronization is attenuated, allowing dispersion to rise.

Random menu costs: A modeling device where each firm draws an i.i.d. menu cost each period from a non-degenerate distribution (specifically, a transformation of an exponential distribution as in Luo and Villar 2020) rather than paying a single fixed cost. The distribution has fat tails, giving substantial probability of very low or very high cost draws. This randomness breaks the tight selection effect of fixed-menu-cost models: which firms adjust depends not only on how far their price is from optimal but also on their menu cost draw, so many firms do not adjust even when their price gap is large. This attenuates the synchronization of price changes in response to a common shock.

Industry-specific oil demand variable: A Bartik-style instrument constructed by multiplying an industry’s pre-determined oil input share (oil spending as a fraction of value added from the 1997 IO tables) by aggregate oil price volatility or oil price inflation. The pre-determined share measures the industry’s structural sensitivity to oil, while the aggregate oil volatility provides exogenous time variation. The interaction captures the differential exposure of high-oil industries to aggregate oil price volatility shocks, enabling identification via cross-industry variation after controlling for time and industry fixed effects.

Stochastic volatility of oil prices: A latent volatility process estimated from real WTI oil prices using an AR(1) model for the log oil price level and a mean-reverting AR(1) process for the log standard deviation of oil price innovations. Estimated via Bayesian MCMC with a particle filter (Sequential Importance Resampling) to handle the nonlinearity, using data from 1986-2014. Produces a smoothed series of time-varying oil price uncertainty. Key estimated parameters: oil price persistence ρ_o = 0.999, volatility persistence ρ_σ = 0.887, unconditional mean log-volatility σ = -2.607 (implying standard deviation of oil price shock ≈ 7.4 percent), and volatility shock size φ = 0.127.

Selection effect: In state-dependent pricing models, the mechanism by which the prices that actually change are not a random subset but are selected based on how far they are from their optimal level. A strong selection effect (as in Golosov and Lucas 2007) means that only prices far from optimal change, so average price change size is large and price change frequency is low. Under a common volatility shock with a strong selection effect, more prices are pushed far from optimal in the same direction, causing them all to adjust together — compressing dispersion and increasing frequency. Random menu costs weaken the selection effect.

Monetary non-neutrality: The degree to which a change in the money supply (or nominal spending) affects real output rather than just the price level. In menu cost models, non-neutrality arises because not all prices can adjust instantaneously: a monetary shock shifts the desired price change distribution, but only firms near the adjustment threshold respond, leaving real prices for the others unchanged. After conditioning on price change frequency, higher price change dispersion implies fewer prices are near the threshold, so a given monetary shock affects fewer prices in one direction and has larger real effects (greater non-neutrality). This is the key channel linking the paper’s empirical findings to monetary policy effectiveness.