What is an Oil Shock?* James D. Hamilton Department of Economics, 0508 University of California, San Diego La Jolla, CA 92093-0508 [email protected] May 1999 Revised: December 2001

*This paper is based on research supported by the NSF under Grants No. SBR-9707771 and. SES-0076072 and the Department of Energy.

It is adapted from (and replaces) an

earlier paper circulated under the title, “Analysis of the Transmission of Oil Price Shocks through the Macroeconomy.” I thank Julian Betts, Michael Dotsey, and anonymous referees for helpful comments. All data and software used in this paper can be downloaded from http://weber.ucsd.edu/˜jhamilto.

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ABSTRACT

This paper uses a ßexible approach to characterize the nonlinear relation between oil price changes and GDP growth. The paper reports clear evidence of nonlinearity, consistent with earlier claims in the literature— oil price increases are much more important than oil price decreases, and increases have signiÞcantly less predictive content if they simply correct earlier decreases. An alternative interpretation is suggested based on estimation of a linear functional form using exogenous disruptions in petroleum supplies as instruments.

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A large body of research suggests that there is a signiÞcant effect of energy supply disruptions on economic activity. A clear negative correlation between energy prices and aggregate measures of output or employment has been reported by Rasche and Tatom (1977, 1981), Hamilton (1983), Burbidge and Harrison (1984), Santini (1985, 1994), Gisser and Goodwin (1986), Rotemberg and Woodford (1996), Daniel (1997), Raymond and Rich (1997) and Carruth, Hooker, and Oswald (1998), among others. Most recently, Muellbauer and Nunziata (2001) successfully predicted the U.S. recession of 2001 from a multivariate analysis in which oil prices featured prominently. Analyses of microeconomic data sets at the level of individual industries, Þrms, or workers also demonstrate signiÞcant correlations between oil price shocks and output, employment, or real wages (Keane and Prasad, 1996; Davis, Loungani, and Mahidhara, 1996; Davis and Haltiwanger, 2001; Lee and Ni, 2002), and certainly oil shocks are a major factor driving ßuctuations in the international terms of trade (Backus and Crucini, 2000). Nevertheless, the suggestion that oil price shocks contribute directly to economic downturns remains controversial, in part because the correlation between oil prices and economic activity appears to be much weaker in data obtained since 1985; (see Hooker, 1996). A number of authors have attributed this instability of the empirical relation between oil prices and output to misspeciÞcation of the functional form.

Loungani (1986), Davis

(1987a,b), Mork (1989), Lee, Ni and Ratti (1995), Hamilton (1996), Davis, Loungani, and Mahidhara (1996), Davis and Haltiwanger (2001), Balke, Brown, and Y¨ ucel (1999), and Cu˜ nado and de P´erez (2000), among others, have suggested that the relation between oil

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prices and economic activity is nonlinear. Insofar as there has been a shift in the process generating oil prices, a linear approximation to the relation between oil prices and economic activity may appear unstable over time, even if the underlying nonlinear relation is stable. One problem with suggesting that this is indeed what happened is that there is an unbounded universe of alternative nonlinear speciÞcations. How does one decide which nonlinear speciÞcation is the right one to use, and how can we distinguish between a statistically signiÞcant nonlinear relation and the outcome of determined data-mining? This paper applies a methodology recently developed by Hamilton (2001) to address these questions.

This approach provides a valid test of the null hypothesis of linearity against

a broad range of alternative nonlinear models, consistent estimation of what the nonlinear relation looks like, and formal comparison of alternative nonlinear models.

The results

generate strong support for the claim of a nonlinear relation along the lines suggested in the literature: oil price increases affect the economy whereas decreases do not, and increases that come after a long period of stable prices have a bigger effect than those that simply correct previous decreases. These results are exclusively concerned with characterization of the functional form of the conditional expectation of GDP given past GDP and past oil prices. Establishing these facts would seem to be of considerable interest, though it leaves open the question of whether this correlation should be given a causal interpretation.

To address this issue, the paper

attempts to isolate an exogenous component of oil price movements by measuring the oil supply curtailed by Þve separate military conßicts during the postwar period.

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Insofar as

these conßicts were indeed exogenous with respect to developments in the U.S. economy, a correlation between this component of oil price movements and subsequent changes in GDP should be given a causal interpretation. I Þnd that the nonlinear transformation of oil prices suggested by the functional form of the conditional expectation function is in fact quite similar to the Þrst-stage least-squares Þt from a regression of oil price changes on these exogenous supply disturbances, and that the dynamic multipliers from the nonlinear relation are similar to those coming from a linear relation estimated by instrumental variables.

I

conclude that the basic fact being summarized by the nonlinear analysis is the historical tendency of the U.S. economy to perform poorly in the wake of these historical conßicts The plan of the paper is as follows. The Þrst section discusses why an investigation of the linearity of the relationship might be important both for econometric inference and economic interpretation. Section 2 reviews the methodology applied in this paper. Empirical results are presented in Section 3. Section 4 discusses structural stability of the suggested nonlinear formulations.

Section 5 proposes a measure of the exogenous component of oil price

movements and suggests an alternative interpretation of the results in terms of instrumental variable estimation. Conclusions are offered in Section 6.

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1

Why functional form matters.

Many economic analyses of the effects of oil shocks1 begin with a production function relating output to inputs of capital, labor, and energy. An exogenous decrease in the supply of energy reduces output directly by lowering productivity and indirectly to the extent that lower wages induce movement along a labor supply schedule (Rasche and Tatom, 1977, 1981; Kim and Loungani, 1992), changes in business markups (Rotemberg and Woodford, 1996), or capacity utilization rates (Finn, 2000).

These models imply that the log of real GDP

should be linearly related to the log of the real price of oil. One implication of this linearity is that if the price of oil goes down, then output should go up; if an oil price increase brings about a recession, then an oil price decline should induce an economic boom by the same mechanism operating in the reverse direction.2 These models view recessions as supply driven rather than demand driven. According to these models, an oil price increase produces a recession because it makes cars more costly to manufacture. This seems contrary to reports in the trade and business press, in which the problem is invariably perceived as a reduction in the number of cars consumers are willing to buy; see for example the trade press accounts in Lee and Ni (2002). A number of early analyses focused instead on demand-side effects of an oil price increase. In these models, an increase in oil prices would increase the overall price level, which, given 1

Useful reviews of the different mechanisms by which oil shocks could affect economic performance are provided by Bohi (1989) and Mork (1994). 2

Atkeson and Kehoe (1999) offered an interesting extension of this class of models by assuming puttyclay investment technology. In their formulation, an oil price decrease still produces an increase in output, though the output boom from a large oil price decline is smaller in magnitude than the output decline that follows an oil price increase of the same logarithmic magnitude.

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the Keynesian assumption of rigid wages, reduces employment. Examples of such models include Pierce and Enzler (1974), Solow (1980), and Pindyck (1980). Mork and Hall (1980) demonstrated the potential for interactive effects between wage rigidities and supply-side effects. These models again all maintain the existence of a linear relation between the log of the price of oil and the log of GDP, so that again an oil price decline is expected to produce an economic boom. These models also have the characteristic that there is nothing all that special about oil.

The basic economic inefficiency is the familiar Keynesian mismatch between the ag-

gregate wage and the aggregate price level, and oil price disruptions are just one of many developments that might contribute to such a mismatch. Surely the price and availability of gasoline matter for car sales not simply because they affect the overall price level but further because they are key inputs in how cars get used. Is your next car going to be a small foreign car or a large sport-utility vehicle? Your decision depends in part on what you think about gasoline availability. If you are very unsure about where gas prices are headed, you might be inclined to postpone a new purchase until you have a better idea of where the market stands. Energy prices and availability may be quite relevant for a host of other durable goods purchases, including housing. How long a commute to work are you willing to put up with? How energy-efficient should your appliances, windows, and insulation be? What equipment and industrial techniques should a Þrm build a new factory around? When energy prices and availability are as uncertain as they were in early 1974, it is rational to postpone such

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commitments until better information is available. Oil shocks may matter for short-run economic performance precisely because of their ability temporarily to disrupt purchases of large-ticket consumption and investment goods, as in Bernanke (1983).

A major disruption in oil supplies makes people uncertain about

the future, with the result that spending on cars, housing, appliances, and investment goods temporarily falls. A variety of microeconomic evidence suggests that oil shocks have substantial potential to exert such effects. Bresnahan and Ramey (1993) documented that the oil shocks of 1974 and 1980 caused a signiÞcant shift in the mix of demand for different size classes of automobiles with an attendant reduction in capacity utilization at U.S. automobile plants. Sakellaris (1997) found that changes in the stock market valuation of different companies in response to the 1974 oil shock were signiÞcantly related to the vintage of their existing capital.

Davis and Haltiwanger (2001) discovered a dramatic effect of oil price

shocks on the rate of job loss in individual economic sectors, with the job destruction rising with capital intensity, energy intensity, product durability, and plant age and size. See also Loungani (1986), Davis (1987a,b), Hamilton (1988a,b), Santini (1992), and Davis, Loungani, and Mahidhara (1996), and Lee and Ni (2002) for related evidence and discussion. These studies have further noted that, if allocative disturbances are indeed the mechanism whereby oil shocks affect economic activity, then there is no reason to expect a linear relation between oil prices and GDP. An oil price increase will decrease demand for some goods but possibly increase demand for others. If it is costly to reallocate labor or capital between sectors, the oil shock will be contractionary in the short run. Note moreover that

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an oil price decrease could also be contractionary in the short run. A price decrease also depresses demand for some sectors, and unemployed labor is not immediately shifted elsewhere.

Furthermore, if it is primarily the postponement of purchases of energy-sensitive

big-ticket items that produces the downturn, then an oil price decrease could in principle be just as contractionary as an oil price increase. Of course, an oil price decrease is not all bad news, by virtue of the production function and inßation effects noted earlier. But surely it is unreasonable to assume that an oil price decrease would produce an economic boom that mirrors the recession induced by an oil price increase. As a simple statistical illustration of how the speciÞcation of functional form can matter in practice, consider the following example. Let yt denote the growth rate of real GDP and let ot denote the percentage change in the price of oil. Let us assume that the effect of oil prices on output is given by yt = f (ot ) + εt

(1.1)

where εt is a regression error term. Suppose that every one percent increase in oil prices produces a β percent decrease in real GDP, but that a decrease in oil prices has no effect on GDP. Then the function f (ot ) takes the form      α

if ot ≤ 0

f (ot ) = 

   α − βot

.

(1.2)

if ot > 0

I simulated 50 observations from equations (1.1) and (1.2) with a critical precondition—

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all of the o’s in the sample were positive.3 Thus for this particular sample the data satisfy the classic linear regression assumptions. Ordinary least squares (OLS) regression produces excellent inference about the values of α and β (standard errors in parentheses): yt =2.29 − 0.117 ot . (0.47)

(0.044)

(1.3)

Oil prices are inferred to have a strong and statistically signiÞcant effect on the economy, with a t-statistic of -2.66. The simulated data, estimated relation, and true relation are displayed in Figure 1. Now let us double the sample size but allow both positive and negative values for ot , as displayed in Figure 2. The OLS regression estimates now turn out to be yt = 1.65 − 0.029 ot . (0.16)

(0.015)

(1.4)

The result of using the larger sample is that oil prices are only imputed to have 1/4 as big an effect as they seemed to have in the smaller sample, and this effect is no longer statistically signiÞcant. The reason is that if equation (1.2) represents the true model and if the sample includes negative values for o, then regression (1.4) is misspeciÞed and is not providing a consistent estimate of the parameter β. Mork (1989) argued that this is essentially what is going on with the historical U.S. experience.4

In the postwar data up until 1980, there was very little experience with falling

3

The simulation used α = 2, β = 0.1, ut ∼ N (0, 2.25), and ot ∼ N(0, 100), where (ot , yt ) pairs were thrown out if ot ≤ 0 until 50 pairs of observations were generated. These values were chosen to correspond to rough magnitudes that might characterize the actual U.S. relation. 4

Actually, Mork estimated separate coefficients for oil price increases and decreases, and found that the coefficients on decreases were insigniÞcantly different from zero. The argument as presented in the text here jumps to the conclusion in a single step. Mork, Olsen and Mysen (1994) reported more qualiÞed support for this idea in the experience of other countries.

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oil prices, so that the sample was essentially like that in Figure 1.

After 1980, however,

there are a lot of observations of big oil price decreases, so that the sample becomes more like that shown in Figure 2. The result is that when more observations are added to the sample, the estimated effect becomes smaller in magnitude and loses statistical signiÞcance. SpeciÞcally, to get away from simulated data and turn to the actual numbers, consider the results of regressing each quarter’s GDP growth (yt ) on four lags of GDP growth and four lags of the percent change in the nominal price of crude petroleum (ot−j ). When this regression is estimated for data from 1949:II to 1980:IV, the result is yt = 1.19 + 0.20 yt−1 + 0.06 yt−2 − 0.09 yt−3 − 0.20 yt−4 (0.19)

(0.09)

(0.09)

(0.09)

(0.09)

− 0.003 ot−1 − 0.030 ot−2 − 0.036 ot−3 − 0.064 ot−4 . (0.027)

(0.027)

(0.027)

(0.028)

(1.5)

When one calculates the impulse-response function, this regression implies that a 10% increase in oil prices will result four quarters later in a level of GDP that is 1.4% lower than it otherwise would be. Because of the imposed linearity, the regression also requires that a 10% decrease in oil prices will result in a 1.4% higher level of GDP. When the same regression is reestimated using data from 1949:II to 2001:III, the result is yt =

0.72 + 0.28 yt−1 + 0.13 yt−2 − 0.06 yt−3 − 0.12 yt−4

(0.11)

(0.07)

(0.07)

(0.07)

(0.07)

− 0.003 ot−1 − 0.003 ot−2 − 0.004 ot−3 − 0.016 ot−4 . (0.006)

(0.006)

(0.006)

(0.007)

(1.6)

The coefficient on ot−4 is about 1/4 of its value in the smaller sample, though it remains statistically signiÞcant at the 5% level. The reason the coefficient on ot−4 is much smaller 10

in the larger sample is that an oil price decrease of 10% does not add 1.4% to the level of GDP. In order for a linear relation to be consistent with what happened after the oil price declines since 1980, a smaller coefficient is needed. As evidence in support of Mork’s claim that the historical regressions (1.5) and (1.6) are reßecting the same factors as the simulated regression (1.3) and (1.4), consider imposing the functional form (1.2) directly. DeÞne      0

o+ t =   

if ot ≤ 0

 ot

.

(1.7)

if ot > 0

When ot−j in (1.6) is replaced by o+ t−j , the estimated relation over 1949:II to 2001:III is yt = 0.88 + 0.26 yt−1 + 0.12 yt−2 − 0.07 yt−3 − 0.14 yt−4 (0.13)

(0.07)

(0.07)

(0.07)

(0.07)

+ + + − 0.011 o+ t−1 − 0.005 ot−2 − 0.007 ot−3 − 0.023 ot−4 . (0.009)

(0.009)

(0.009)

(0.009)

(1.8)

The estimated effects of oil price increases are considerably larger than those implied by the linear relation (1.6). Although the functional form in equation (1.2) seems consistent with the empirical evidence in regressions (1.5), (1.6), and (1.8), Mork’s interpretation has recently been challenged on two grounds. First, Hooker (1996) argued that even the asymmetric relation (1.8) offers a relatively poor Þt to data since 1986. Second, if the mechanism is indeed that an oil price increase causes postponement of certain major purchases, then equation (1.2) is surely too crude— consumers’ behavior should be based not just on whether oil prices went up, but further on what they believe the increase means for the future. Most of the quarters in which oil prices went up since 1986 followed a quarter in which oil prices had gone down even more, 11

so that the increases were simply partial corrections to a chronic downward trend. Several authors have suggested alternative functional forms that might better represent the true relation. Ferderer (1996) argued that oil price volatility itself depresses spending. Lee, Ni, and Ratti (1995) suggested that what matters is how surprising an oil price increase is based on the observed recent changes.5 Hamilton (1996) claimed that the key question is whether the oil price increase is big enough to reverse any decreases observed in the immediately preceding quarters.

Davis, Loungani, and Mahidhara (1996) and Davis and Haltiwanger

(2001) focused on whether the oil price increase was sufficient to raise the price above its previous 5-year average. All of these speciÞcations have a certain plausibility. One logical way to sort out the various alternatives would be to leave the function f (ot ) in equation (1.1) totally unrestricted, and let the data tell us which of the various nonlinear alternatives is best supported by the data. This paper pursues that idea using a ßexible approach to nonlinear modeling recently suggested by Hamilton (2001). The basic technique is described in the following section. √ Lee, Ni and Ratti constructed a variable e∗t = et / ht where et is the error in forecasting the real price √ of oil based on past observations and ht is the standard error of this forecast as estimated by a GARCH model. The GARCH speciÞcation assumes that et is distributed N (0, ht ), so the probability of observing an increase in oil prices during quarter t as large or larger than what was actually observed is 1 − Φ(e∗t ), where Φ(·) is the cumulative distribution function for a standard Normal variate. Thus the statement that the effect of an oil price increase depends on e∗t is equivalent to the statement that the effect of an oil price increase depends on how surprisng that increase is, given the recent behavior of oil prices. 5

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2

A ßexible approach to nonlinear inference.

Consider a nonlinear regression model of the form

yt = µ(xt ) + δ 0 zt + εt

(2.1)

where yt is a scalar dependent variable, xt and zt are k- and p-dimensional vectors of explanatory variables, and εt is an error term.

The form of the function µ(.) is unknown,

and we seek to represent it using a ßexible class.

On the other hand, there may be

some subset of variables zt for which the researcher is willing to assume linearity, and, if so, signiÞcant efficiency gains can be obtained by imposing this restriction.

In the ap-

plication below, zt = (yt−1 , yt−2 , yt−3 , yt−4 )0 contains lagged values of GDP growth while xt = (ot−1 , ot−2 , ot−3 , ot−4 )0 contains lagged changes in oil prices. The approach suggested by Hamilton (2001) is to view the function µ(.) itself as the outcome of a random Þeld.6 That is, if τ 1 denotes an arbitrary, nonstochastic k-dimensional vector, then the value of the function µ(.) evaluated at τ 1 , denoted µ(τ 1 ), is regarded as a random variable. Hamilton (2001) treats this random variable as being Normally distributed with mean α0 + α0 τ 1 and variance λ2 , where α0 , α, and λ are population parameters to be estimated. Note that if λ = 0, then model (2.1) becomes a simple linear regression model yt = α0 + α0 xt + δ 0 zt + εt . The larger λ, the more the model (2.1) is allowed to deviate from a linear regression model. The other item one needs to know about the random Þeld µ(.) is how the random variable 6

The general approach of viewing µ(.) as stochastic has a very old and extensive tradition in the statistics literature. The particular form for the random Þeld used here is, to my knowledge, original— see Hamilton (2001) for references.

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µ(τ 1 ) is correlated with µ(τ 2 ), for τ 1 and τ 2 again arbitrary k-dimensional vectors. We assume that µ(τ 1 ) is uncorrelated with µ(τ 2 ) if τ 1 is sufficiently far away from τ 2 , speciÞcally, that E{[µ(τ 1 ) − α0 − α0 τ 1 ][µ(τ 2 ) − α0 − α0 τ 2 ]} = 0 h

if (1/2) Σki=1 gi2 (τ i1 − τ i2 )2

i1/2

> 1, where τ i1 denotes the ith element of the vector τ 1 and

g1 , g2 , ..., gk are k additional population parameters to be estimated. The closer that τ 1 gets h

to τ 2 , speciÞcally, the smaller the value of the scalar h12 = (1/2) Σki=1 gi2 (τ i1 − τ i2 )2

i1/2

, the

higher the correlation between µ(τ 1 ) and µ(τ 2 ), with the correlation going to unity as h12 goes to zero. If the nonlinear part of the model includes k = 4 explanatory variables, then the correlation is assumed to be given by      H4 (h12 ) if 0 ≤ h12 ≤ 1

where

Corr(µ(τ 1 ), µ(τ 2 )) = 

   0

h

otherwise

i

H4 (h12 ) = 1 − (2/π) (2/3)h12 (1 − h212 )3/2 + h12 (1 − h212 )1/2 + sin−1 (h12 ) .

(2.2)

See Hamilton (2001) for the motivation behind this speciÞcation. Note that Hk (.) is not a parameterization of the functional relation µ(.) itself, but rather a parameterization of the correlation between the random variables µ(τ 1 ) and µ(τ 2 ); a given realization of µ(.) from this random process can take on any of a variety of different forms, and this is what gives the approach its ßexibility. The parameter gi governs the likely variability of the nonlinear function µ(τ ) as the value of τ i varies; as gi becomes small, the value of µ(τ ) changes little when τ i changes. If gi = 0, then the function µ(τ ) is linear with respect to τ i . 14

The above speciÞcation can be written in the form 0

yt = α0 + α xt + δ0 zt + λm(xt ) + εt

(2.3)

0

= α0 + α xt + δ0 zt + ut where m(.) denotes the realization of a scalar-valued Gaussian random Þeld with mean zero, unit variance, and covariance function given by (2.2) and where ut = λm(xt ) + εt . If the 0

0

regression error εt is assumed to be i.i.d. N (0, σ 2 ) and if the regressors (xt , zt ) are strictly exogenous, then this speciÞcation implies a GLS regression model of the form y|X ∼ N (Xβ, P0 + σ 2 IT ) where y = (y1 , y2 , ..., yT )0 , T is the sample size, X is a (T × (1 + k + p)) matrix whose tth row 0

is given by (1, x0t , zt ), β is the (1 + k + p)-dimensional vector (α0 , α0 , δ 0 )0 , IT is the (T × T ) identity matrix, and P0 is a (T × T ) matrix whose row s, column t element is given by h

λ2 Hk (hst )δ [hst