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Reading the effects of an energy shock in financial markets
J ECO BUSN 1991; 43:115-132
115
Reading the Effects of an Energy Shock in Financial Markets Vincent Reinhart
The impact of an oil price increase on goods output depends, in part, on the response of financial markets. This article adds three distinct effects of energy prices to a Keynesian model peopled with forward-looking investors choosing among a menu of assets. Combining Blanchard's (1981) long-term-asset dynamics with Mussa's (1981) explanation of goods-price stickiness arrives at a perfect foresight adjustment path that can be projected on the traditional IS-LM framework.
I. Introduction The effects of an increase in oil prices ripple through the economy. The number of waves, their timing, and their magnitude vary across historical episodes, but three main influences can be identified. First, there is a direct price level effect, as higher oil prices feed into consumer prices and reduce the real value of fixed stocks of nominal wealth. Second, over a slightly longer horizon, there is an aggregate goods demand effect, as consumers substitute away from their direct use of energy in favor of other final goods. Lastly, over a still longer horizon, there is an aggregate goods supply effect, as manufacturers shift production away from more expensive energy inputs. These differently timed effects produce a complicated pattern of forces on the economy, making policy advice problematic. Every day, participants in financial markets price long-lived assets, requiring them to disentangle these factors to estimate paths for interest rates, incomes, and profits over a long horizon. Can policymakers use this financial market reaction to determine the consequences of an oil shock for income and inflation? We turn to a simple Keynesian model to address this issue. The complete model, detailed in the next section, connects two influential strands of analysis on the monetary transmission mechanism. First, monetary policymakers directly affect short-term rates of return, which in turn affects yields on longer-term assets and, then, aggregate demand. Blanchard's (1981) model, which includes a long-term rate of return in a perfect-foresight IS-LM model, is the starting point. Second, the composition of any policy-induced change in aggregate demand varies over time: Output expands at first, followed by goods-price increases that erode the real effects of
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V. Reinhart
the stimulus. Our explanation of price stickiness takes after Mussa (1981), resulting in a framework with continuous market clearing but enough short-run rigidity to provide policy a role--a role that begins in the short end of the money market. As an analytic tool, we derive a perfect-foresight dynamic adjustment path that can be projected on the traditional IS-LM framework. We first include direct effects of an oil price change on aggregate demand and supply; as long as money demand is not unrealistically interest-sensitive, the long-term asset brings forward some of the steady-state contraction of higher oil prices, raising the current long-term interest rate "and reducing current expenditure. The loss in potential output exceeds the reduction in expenditure, giving way to excess demand for goods and higher inflation in the transition to the steady state. Meanwhile, the short-term nominal interest rate declines, steepening the yield curve at the news of an oil price increase. Thus, this foresight model explains both an apparent "flight to quality" at the short end of the term structure (which is really portfolio reshuffling, not a reaction to perceived risk) and inflation- and real-rate-induced increases in the long-term rate. Policy advice can follow the message of the market, only depending on the calculus of social welfare. If the central bank wants to forestall the inevitable output loss, it should ease policy with the increase in oil prices. If inflation concerns dominate, a policy tightening could eliminate the transition to the new long-run equilibrium. Including a direct effect of oil prices on the general price level renders the response of long-term rates ambiguous. The long-term rate may rise or fall at the impact of a permanent increase in oil prices and virtually any pattern of rates may follow, according to a complicated interaction of parameters. Thus, experiments with the complete model suggest that financial markets do not send a clear signal about the nature of an oil shock and, absent policy action, expenditure may fall or rise on impact. Accordingly, no blanket policy response can be advocated.
II. The Direct and Indirect Effects of an Energy Price Change Energy and the Economy The strong negative correlation between economic activity and relative energy prices in the United States is well documented, most notably by Hamilton (1983). Theory suggests that such an effect may follow from the direct influence of energy prices on aggregate supply and demand. In terms of aggregate supply, the market price of oil represents the cost of a key input to the manufacturing sector. An increase in the price of energy relative to the price of the goods that energy produces should result in a decreased use of that input. Assuming that factors of production are somewhat substitutable, this should make the other inputs, labor and capital, less productive. Berndt and Wood (1975) and Rasche and Tatom (1977) are among the researchers who have quantified this channel, i Suppose, for example, that the output of the final good, Yt, is produced with capital, Kt, labor, Lt, and the intermediate energy input, E t, for simplicity obeying a Cobb-Douglas production function, Yt = AKTLatE] -'~-~.
ISee Rascheand Tatom(1977) and the referencescited therein. For a more recent discussion, see Tatom
(1988).
Reading the Effects of an Energy Shock,
117
If the competitive market uses energy efficiently, the marginal condition on energy defines a derived demand schedule, (o,/s,)
=
(i -
-
in terms of the price of energy, O t, relative to the price of the final good, S t. Substituting this derived demand into the overall production frontier determines a concentrated production function. In the Cobb-Doublas case, this reduces (with lowercase letters representing logarithms) to
y, = B
+
-[(I
[~/(~ -
o~ -
+
~)]k,
~)/(~
+
[~/(~
+/3)](0
+
~)]I,
t - st),
where B is a constant term. A relative price increase causes goods producers to use the more expensive factor less intensely, reducing goods output. If intermediate energy inputs were 5 percent of the production of final output, then the elasticity of output with respect to a change in relative energy prices would be - 5 percent, about the sensitivity found in Tatom (1988), for example. The effect on the other inputs depends on how elastically they are supplied to the market and whether they substitute for or complement the energy input. The impacts of energy prices on aggregate demand are more varied and uncertain. In terms of relative price effects, an increase in real oil prices lowers the current value of the existing capital stock, as it will be less productive with lower energy inputs; thus, the economy's real wealth declines. Meanwhile, for an economy that imports oil, the higher real price acts as an excise tax, lowering consumer spending power. In terms of nominal price effects, an increase in oil prices--because it feeds into the consumer price index--lowers the real value of a fixed nominal stock of money. Additionally, since the pass-through of energy prices to the general price level is not immediate, inflation picks up for time, lowering the real return provided by any asset with a fixed nominal return. Capturing these disparate channels of influence requires a complete model of the economy, many examples of which can be found in a recent comparative survey of large scale models for the Energy Modeling Forum (Hickman, Huntington, and Sweeney 1987). These authors analyzed the impact of a permanent 50 percent increase in oil prices for differing policy stances and found that, with unchanged monetary and fiscal policies, the median response of 14 major models suggests that it would lower real GNP by about 2 1/4 percent after four years (Column 1 of Table 1). The apparent elasticity with respect to energy prices of 4 1/2 percent is about in line with estimates for the supply channel alone. A policy response to the shock, of course, could postpone this adverse effect. Indeed, the simulations for the Energy Modeling Forum that allowed expansionary offsets using monetary and fiscal policies (Columns 2 and 3, respectively) suggest that there is a large scope for such efforts, at least in the short run. The benefit of large-scale models, their ability to incorporate complicated causal patterns, also can be a curse, as it can be difficult to interpret the results and trace the channels of influence. Furthermore, attempts to introduce forward-looklng behavior into these models often becomes computationally burdensome. Instead, this article turns to a small theoretical model, incorporating three distinct effects of energy prices in a Keynesian framework peopled with forward-looking investors who choose among a menu of assets.
V. Reinhart
118
Table 1. Econometric Model Predictions of the Response to a 50 Percent Increase in Energy Prices (Average Annual Change over Four Years) Unchanged policy (1) Percentage difference from baseline Real GNP (level) Aggregate price level Percentage point difference from baseline Unemployment rate Average inflation rate
Accommodativepolicy Monetary Fiscal (2) (3)
- 2.2 1.8
- 0.8 2.6
- 1.7 1.9
1.1 0.5
0.6 0.8
0.9 0.5
Note. Median responseof 14 major econometricmodels to a 50 percent increase in energy prices, as reported in Hickman et al. (1987), p. 56.
Concentrating on short-run policy, we abstract from some of the more interesting questions about the effects of an oil shock by assuming a fixed capital stock and rational expectations. Introducing foresight allows a detailed specification of the anticipatory dynamics set in motion by an energy shock, revealing additional, indirect influences on aggregate demand. However, such simplifications have their costs. Fixing the capital stock removes goods producers' ability to substitute from energy over time through physical investment (as discussed in Phelps, 1978, for example). Thus, we assume a once-and-for-all drop in potential output after an increase in relative energy prices, rather than the more likely drawn-out affair. Eliminating uncertainty by assuming perfect foresight prevents the increased perception of risk associated with a marked change in energy prices from adversely influencing spending in goods markets. Thus, we assume that worries about the future control of the world's stock of oil have no effect on finns' investment plans or households' durable purchases.
A Simple M o d e l To capture an aggregate supply effect, assume that the capacity or potential output level of the economy, q, is negatively related to the price of energy relative to the price of goods. Omitting time subscripts for convenience, we write
q = q(O/S);
(1)
this relative price is assumed to be fixed. 2 Essentially, energy suppliers post a price, and total demand adjusts. Total energy demand has two components: Energy is an input in production and a final good in consumption. The former involves a derived demand consistent with the reduced-form production function, while the latter depends on relative prices and the total scale of spending. 3 For the consumer part of energy
2As in Phelps (1978), Blinder (1981), and Rotemherg (1983). 3This approach follows Phelps (1978) and Findlay (1980) and contrasts with modelling energy as an intermediate good, as in Findlay and Rodriguez (1977) and Obstfeld (1982).
Reading the Effects of an Energy Shock
119
demand, assume that the share of spending on manufactured goods versus energy, or, depends positively on the relative price of energy. Total expenditure on all final goods, e, depends on the real long-term interest rate, R, and aggregate real wealth, W, e, < 0 ,
e=e(R,W),
e2>O.
(2)
The results that follow require an important role for financial wealth in contemporaneous spending plans, which would obtain in the Obstfeld-Uzawa model of endogenous time preference or the Blanchard-Yaari overlapping-generations framework (Obstfeld 1989; Blanchard 1985). However, to keep the example simple, we assume a functional form and accept the inherent dangers spelled out in Fischer (1981), including the risk that the behavioral relationship changes with regime. However, the ad hoc role for wealth and the faith in policy invariance accords with the structure of most large-scale models. Reinhart (1990b) examines the reaction to a supply shock in a framework that captures the household planning problem, given sticky prices. The general price index, P, includes both objects of final demand, manufactured goods and energy,
P=n(o,s), and, like any good price index, the function fl(.) always is increasing in both arguments and homogenous of degree one. This permits rearranging terms, P
=
e(o/s), s
=
o,(o/s), s,
defining the new function, 60, where oJ'/o~ reflects the importance of relative energy prices in the overall price index. Simply, an increase in the general price index follows from either an increase in relative energy prices or an increase in the nominal price of manufactured goods. Because we consider permanent changes in relative energy prices, the overall inflation rate, ~, equals the rate of increase in manufactured goods prices, 7r = D P / P = D S / S ,
where D denotes the time derivative. Perfect foresight having been assumed, 7r is both the expected and actual inflation rate. The scale variable in spending, real wealth, comprises the real values of government bonds and money balances. The government is assumed to have issued consols providing one unit of purchasing power per period, where R is the long-term real rate of return and 1 / R is the price (Blanchard 1981). With k of these consols outstanding and the nominal money stock denoted as M, real wealth equals W = M/P
+ k/R.
It will be convenient to describe real balances in terms of manufactured goods prices, M/P
= (M/S)
. (S/P)
= ( r e ~ S ) " (1/~o),
120
V. Reinhart
or, real balances in terms of the overall price index change with a change in nominal money balances deflated by manufacturing goods prices or through the price level effect of a change in relative energy prices. As a first policy assumption, suppose that the central bank follows an announced commitment to keep the growth of the nominal stock of money constant at ~; at any point in time, the stock of money is predetermined, which provides the baseline case for gauging the impact of an oil price change with unchanged policy. Defining the logarithm of real balances in terms of manufacturing prices as x, x - l o g ( M / S ) , the rate of change in real balances is written: D x = ~ - D S / S = ~ - ~r.
The demand for real balances is assumed to depend on real wealth and the nominal short-period return on holding the consol, i, MIP
= L(M/P
+ k/R,
i),
0 < L , < 1,
L 2 < O.
This relationship can be inverted to find the nominal short-term interest rate consistent with money-market clearing, i=~[R,x/o~(O/S)],
cr1 < 0 ,
o2<0,
(3)
showing that the short-term nominal rate falls when the bond component of wealth falls (that is, the bond yield rises) or the real money stock rises. But strict arbitrage between short- and long-term assets provides a second explanation for the short-term nominal interest rate. The real short-term return on a consol will equal its long-term yield plus expected capital gains (or less expected capital losses). If 1 / R is the price of the consol, its capital gain or loss equals - ( 1 / R ) D R / R . Thus, the instantaneous or short-term real rate approximately equals R - DR/
,
where ,it is a positive constant. Adding expected inflation gives the second definition of i, i = R - DR/el
+ DP/P.
As a last step, note that because inflation can be written in terms of the change in real balances and nominal money growth, the nominal short rate can be written i = R - DR/el
(4)
+ # - Dx.
Asset market clearing requires setting equal our two explanations for the nominal rate, yielding the evolution of the long-term interest rate, D R = e l { R - ~[ R , x / ~ ( O / S ) ]
+ ~ - Dx}.
(5)
This is the first of the two equations of the complete dynamic system. 4 However, this 4As is typicalin rationalexpectationsmodels,the asset marketcontributesexplosivebehaviorto dynamics. If x is heldfixed,equation(5) is an unstabledifferentialequationin R. As shownlater, the initialvalueof R will have to be cat,fully cho6en to avoid dynamicinstability.Shaffrin(1983, pp. 77-87) provides a clear explanationof solvingthese typesof models.
121
Re_J~l_ingthe Effects of an Energy Shock
economy already has enough structure to determine a steady state, even without detailing the short-run inflation process that closes the dynamic system.
The Steady State From a stabilization perspective, the long run is long enough for all prices (both assets and goods) to adjust to any disturbance but short enough to ignore the influences of asset accumulation. In this context, a steady state maintains constant levels of real balances and the real long-term interest rate. As a consequence of the first condition, the rate of inflation equals the rate of growth in the money stock. As for the second condition, no prospect for capital gain or loss sets the short-term equal to the long-term real interest rate. Thus, the nominal short-term rate in the long run equals the long-term real rate plus the rate of money growth, i 0 = R o + ~t, where the zero subscript denotes a steady-state value. This permits asset behavior to be related to the real long-term rate, via the inverted money demand, Equation (3),
O[Ro, Xo/o,(o/s)]
-
Ro =
This determines the long-run pairs of real balances and the real interest rate that clear the money market--it is a long-run LM schedule. As shown in Figure 1, the LM locus slopes downward, as agents hold a higher level of real balances only at a lower nominal interest rate; with the steady-state inflation rate
L$
• S $
,,," / s
R
P,o
/
.........................
-z... M
[ /
IVl
S
"
r
Xo Figure 1. Long-run consequences of an energy price increase.
X
122
V. Reinhart
at # and the short-term equal to the long-term real rate, this translates into a lower real long-term rate as well. The direct price level effect of oil prices, captured in the ~o(.) term, influences the position of the LM. An increase in relative oil prices lowers the final purchasing power represented by a fixed level of real balances measured in terms of manufactured goods prices. That is, an increase in (O/S) shifts the LM upward. In the long run, spending must equal potential output, defining a long-rnn IS curve,
a ( O / S ) " e[ R o, Xo/w(O/S)] = q ( O / S ) .
(6)
Differentiating to evaluate that relationship, we have:
dxo= [O)/(~.2ol)] " {[qt + 32XoO)t/o~2- Eolt]d(O/S) -OlEldRo}.
(6')
The IS locus slopes upward because an increase in the real rate must be offset by an increase in real balances to maintain expenditure at potential. The compound term in the brackets shows that oil prices have three distinct direct effects on the manufactured goods market. An increase in oil prices (1) reduces potential output (q'), (2) increases demand for manufactured goods as consumers substitute away from energy (-ec~'), and (3) reduces demand for manufactured goods, as an unchanged level of real balances measured in terms of manufactured goods represents a lower amount of purchasing power in terms of final goods (E2XoW'/o~2). At an unchanged real rate, the first two effects tend to lower the long run level of real balances, while the third tends to raise it. Given the simple specification, two standard results emerge: • An exogenous increase is spending (a shift in e) raises the steady-state long-term real interest rate and lowers the level of real balances. • An increase in the growth of money, increasing inflation, lowers the steady-state real rate and level of real balances. This Mundell-Tobin effect holds because agents substitute away from the asset with a fixed nominal return, money, toward the one with a return that varies with inflation, consols. An oil price increase, however, is more complicated. The direct aggregate supply and demand effects--as in equation (6)--tend to shift the IS equation upward, while the price level effects pulls it downward. Figure 1 is drawn with the assumption that the latter effect is insignificant, so that cleating in the goods market requires a higher real rate in the long run. At the same time, the direct price level effect reduces the purchasing power of any given level of x: The LM shifts upward. As the figures are drawn, the intersection of the IS and LM dictates a higher steady-state real interest rate, but the level of real balances depends on the relative sizes of these shifts. Again, with a small price level effect, the shift in the IS would be greater, so that real balances unambiguously fall. A significant price level effect clouds this picture, making the shift in the LM more pronounced and perhaps even reversing the shift in the IS. Thus, the long-run response of interest rates depends on the relative size of these direct eff~ts. How the economy moves from one long-run equilibrium to another depends on how nominal magnitudes adjust.
Reading the Effects of an Energy Shock
123
III. The Dynamics Response to an Oil Price Change Prices of goods and services exhibit varying degrees of sluggishness. At one extreme, market quotes for financial assets and tradable commodities adjust freely in response to current and anticipated economic conditions. At the other extreme, many goods and most service prices--particularly wages--are contracted, whether explicitly or implicitly, and negotiated infrequently. Any sudden change in energy prices perturbs the existing pattern of relative prices, perhaps requiring a protracted adjustment. The staggered wage contracting models of Taylor (1980), Phelps (1979), and Calvo (1983) are particularly suited to this and have been applied in a similar model in Reinhart (1990a). However, rather than explicitly introduce a labor market and wage developments, we follow Mussa's framework (Mussa, 1981) and assume that individual prices in the manufacturing sector are costly to adjust and set at staggered and overlapping intervals. There is no pressure on prices to change from their equilibrium path when expenditure equals potential output, e=q.
This can be used to define the "potential output price level" or S*. Given adjustment costs and behavior consistent with maximizing agents with foresight, Mussa has shown that the actual price level grows at the growth rate of S* adjusted for differences in the actual price level relative to the potential output price level:
D S / S = DS*/S* + ~(S* - S).
(7)
Given the difficulties in reconciling menu costs at the individual level and aggregate sluggishness (reviewed in Bertola and Caballero, 1990), equation (7) should be viewed as a convenient reduced-form representation of manufacturing goods price inflation. In this respect, the Mussa framework shares the insight of the "P-star" inflation adjustment equation, because actual inflation moves to close the gap between the actual and an "equilibrium" price level (Hallman, Porter, and Small 1989). Unlike the P-star model, however, that equilibrium is defined as a constantly clearing condition in a single market, rather than a long-run monetary anchor to the overall price level. By adding and subtracting the nominal money stock, the price-setting rule can be written in terms of real balances,
Dx = Dx* + 6( x* - x),
(8)
where x* is the level of real balances that sets expenditure equal to potential output; to arrive at x*, set expenditure on manufactured goods equal to potential output,
ot(O/S) . e[ R , x*/oJ(O/S)] = q ( O / S ) , which is our already discussed long-run IS equation (6). This define.s an implicit function relating x* to R and O / S , say x* = x ( R , O/S). This equation's differential is the same as (6'), which reveals that X~ > 0, while X2 is ambiguous, depending on the relative size of the three direct effects of energy prices. Lastly, differentiating our
124
V. Reinhart explanation of x* and substituting into equation (8), we have
x,DR ÷
- x],
(9)
which relates the growth of real balances to the level and change of the real long-term rate. Our dynamic model describes the paths of real balances and the real long-term rate of interest given in equations (5) and (9). The central bank's pledge to hold nominal balances along a set path combines with sticky goods prices to predetermine the level of real balances. On the other hand, as an asset return, the real rate of interest can adjust to clear markets after an unexpected event. Appendix A shows that stability requires that this dynamic adjustment follow a negatively sloped path (known as the saddiepath) leading to the long run (x, R) pair. In other words, in the long run the economy comes to rest at a unique point in the (x, R) plane, the intersection of the steady-state IS and LM curves. In the short run, any (x, R) point can be an equilibrium, as there are two anticipatory variables, D R and D x , free to clear the goods and money markets. However, only one set of (X, R) points are consistent with stable dynamics leading to the rest point, and those points lie along the negatively sloped saddlepath. At any point along that saddlepath, the values of D R and D x are just sufficient to clear markets and move the system toward the steady state. In what follows, we use the long-run IS and LM schedules to determine the steady-state combinations of x and r and the negatively sloped saddiepath to trace out short-run dynamics. This framework is given in Figure 2 for the two possible configurations. Depending on the magnitude of the relevant parameters, the saddlepath may be more or less steeply sloped than the long-run LM, as in panels a and b. This ambiguity is unimportant for our first exercise. Consider the impact of an unexpected once-and-for-all increase in the nominal stock of money. In the long run, prices are free to adjust so that this change will have no effect on real variables; the steady state ( x 0, Ro) remains unchanged. On impact, the aggregate price level does not respond because individual pricing decisions are spaced over time. The real supply of money increases at first and, in order to clear money markets, induces a decline in the nominal short-term interest rate. If real balances increase from x o to x ~, as in Figure 2, the real long-term rate drops on impact to RI, the corresponding point on the saddiepath. With both x and R lower, expenditure exceeds potential so that ~ increases faster than /~ and real balances decrease. During the transition, the real long-term rate increases in the movement from (x I , R 1) to ( x 0, Ro). Since D R > 0, agents expect capital losses so that the short rate is below the real long-term rate. Thus, the model captures the stylized facts of the response to a policy disturbance that sets the (postshock) money supply above (preshock) money demand: • All interest rates decline on impact. • The yield curve steepens because the short rate decreases by more than the long rate decreases. • Output expands at first but subsequent price increases erode that gain. Monetary control works through an interest rate channel, but any control of real variables is fleeting.
Reading the Effects of an Energy Shock
125
C:l
R
Ro R1
v
b
Xo
X1
X
R
R1 S v
X0
X1
X
Figure 2. Dynamic adjustment path.
Our chief concern is how the system reacts to an exogenous increase in real energy prices, which is complicated by the conclusion of the last section that the comparison of steady states is not straightforward. As a base of comparison, let us temporarily assume away the direct price level effect, oY = 0. 5 Thus, an increase in energy prices lowers potential output and shifts demand toward manufactured goods. Because expenditure equals potential in the steady state, the new long-run IS must lie to the left of the old one, as in Figure 3. Market equilibrium requires an increase in the long rate and a
5As shown in Appendix A, changing the slope of the ~0(.) function does not affect the shape of the adjustment path.
126
V. Reinhart 0
S ' ~
R
.S'
S
m1
Ro R1 .......
S
X1
b
X0
L
R
X
S'
S
S m1
R I
Ro
r
X1
Xo
X
Figure 3. A permanent energy price increase.
reduction in real balances. The exact combination of endogenous contraction (the relative changes in R and x) depends on the interest sensitivity of money demand. Indeed, the old and new steady state lie on the same long-run LM schedule. The nature of the transition depends on how that locus, with slope 02/(1 - ol), compares with the saddlepath. The cost of higher energy prices--lower potential output--is paid permanently. How soon expenditure adjusts downward depends on how much of the contraction is brought forward by financial markets in the current price of long-term assets. Consider the following two cases.
Reading the Effects of an Energy Shock
127
Case 1. A n Exaggerated Response With highly interest-sensitive money demand, the higher interest rates associated with lower long-run potential output requires markedly lower real balances. The old steady state (x o, R0) lies above the new saddlepath or the long-run LM is flatter than the saddlepath (Figure 3a). Given this set of dynamic relationships, at the moment oil prices increase the system is governed by the new saddlepath SS. Perversely, the real long-term rate falls on impact to point (x o, R~), stimulating interest-sensitive expenditure. Expenditure rises above its old level and even further above the new level of potential output. Accordingly, price pressures build, pushing inflation above the constant growth rates of the nominal money stock, eroding the value of real balances over time. As real balances increse, the real long-term rate rises and the system moves left along SS. With interest-sensitive money demand, an adverse supply shock results in an immediate increase in expenditure and an initial fall in the real rate that is subsequently more than reversed.
Case 2. Undershooting With relatively interest-insensitive money demand (as is estimated in Small and Porter 1989, for example), the higher interest rates associated with lower long-run potential output do not significantly lower steady-state real balances. The old steady state lies below the new saddlepath (Figure 3b). At the moment real energy prices increase, the real long-term rate rises, attaining the point (Xo, R ~) on the new saddlepath. Expenditure falls but excess demand remains owing to a proportionately greater reduction in potential. The long-term rate increases on impact and then continues to rise during the transition. Given relatively insensitive money demand, an increase in energy prices raises the real long-term interest rate and lowers real output on impact. Notice that on impact, the long real rate increases along with inflation, so that the long-term nominal rate must have risen. Given the increase in the real long-term rate, the money-demand relationshp, equation (3), tells us that the nominal short-term rate actually falls, as real money balances are unchanged and the bond component of real wealth declines. Thus, the nominal yield curve steepens with the news of an oil price increase--the short-term rate declines, while the longer-term rate rises. Even with our simplifying assumptions, an ambiguity remains. The long rate may rise or fall with the news of a permanent oil price increase. However, rising market rates signal an economy that is settling for a lower level of potential. Or do they? Unfortunately, if we reintroduce the direct price level effect, any pattern of rate response becomes possible. While the adjustment path is unaltered, the relative positions of the new destinations can be markedly different. COnsider Figure 4, which presents a range of cases, under the likely scenario that the interest sensitivity of money demand is not prohibitively large. If the price effect is moderate (Case a) we retain our earlier results. The real rate rises on impact and continues to rise over the transition. On the other hand, if the price effect is large (Case b) the shift in the LM outweighs the shift in the IS and agents seek to rebuild their money balances, when measured in terms of manufactured goods. The long rate increase on, impact and then falls during the transition. Finally, if the price effect so dominates that the IS shifts downward (Case c), the real rate falls on impact, falling even more during the transition.
12g
V. Reinhart co,,, (o) R
"~
I'
/I
M \
....
.~ ira,,.-×
co~,, (b)
S
. L'
,
R
I
case
(c) J
R
X Figure 4. Possible configurations.
IV. The Policy Response to a Supply Shock Suppose that we paint the most favorable case for policy reaction by eliminating the direct price level effect. In this model, the economy adjusts to a supply shock through a neoclassical channel: Prices adjust, engender changes in real balances, and through wealth and liquidity effects move the economy to potential. The conditions for this to be effective include rapid adjustment of prices to excess demand (high 8) and interest-insensitive money demand (high ¢2). Within this model, the former flattens the saddlepath, while the latter steepens the LM. Thus, the more closely the economy attains the neoclassical paradigm, the less likely there are perverse movements in the real rate and output in response to a supply shock. Correspondingly, under the Keynesian prior
Reading the Effects of an Energy Shock
129
that prices respond sluggishly to excess demand and that money holdings are interestsensitive, adjustment will be protracted. If ~ and 02 are sufficiently low, output reverses direction in response to an energy price increse. In either case, there are relative increases in excess demand during the adjustment, as income is higher than the new level of potential. Depending on the calculus of social welfare, policy can step in to speed the expenditure decline (if inflation concerns dominate) or to slow the transit to the permanently lower level of output (if output concerns dominate). From the viewpoint of stabilization policy, the choice of instruments is trivial, as either monetary or fiscal policy can move to achieve potential in this perfect-foresight model. However, since output falls below trend because a nominal magnitude, the price level, does not adjust quickly enough, the natural assignment is to have the central bank, which controls a nominal magnitude, to step in. 6 Consider the configuration of the IS, LM, and saddlepath in our Case b that is consistent with a modest interest-sensitivity of money demand, which were shown in the lower panels of Figures 2 and 3 and the upper panel of Figure 4. If the goal were to limit the price consequences of the oil shock, the central bank could lower nominal balances at the announcement of the oil price hike. Rather than allowing a transition for the economy to slowly adjust real balances from x 0 to x 1 in Figure 3, a once-and-for-all money supply cut could engineer an immediate response. Essentially, the central bank responds to the increase in the long-term rates by raising the short-term rate. On the other hand, the central bank could forestall the inevitable output response by raising real balances on impact, moving the economy further away from the steady state. As the saddlepath slopes downward, the real long-term rate could be lowered sufficiently by an increase in the level of the money stock to keep expenditure unchanged. However, this cushions current expenditure at the cost of higher inflation during the now longer transition, as goods prices will eventually rise by a sufficient amount to reverse any easing steps in real terms. The econometric model responses reported in Table 1 fall into the latter group. Moving from Column 1 to Column 2, the output loss could only be trimmed from 2.1 percent to 1.8 percent over the four-year span by allowing more inflation. Fiscal policy, as it controls a real magnitude in the short and long runs, can have a more lasting effect on this economy's equilibrium. Real rates rise after an oil price hike to damp the private, interest-sensitive component of spending, ultimately bringing total expenditure in line with the lower level of potential output. If fiscal policy were to contract as oil prices rise, the relative position of the IS curve Could remain fixed, instantly bringing income to the new lower level of potential output. By offsetting the decline in aggregate supply with a reduction in government spending, private spending would remain unchanged at an unvarying real interest rate. Of course, the government could lean against the wind of the output loss by expanding fiscal policy when oil prices rise, shifting the IS schedule further leftward. Total expenditure could be temporarily maintained, or even increased, but at the cost of higher current and future real interest rates and an increasing share of the government in total spending. Policy's role diminishes to the extent that a direct price level effect makes the transition more difficult to project. Any pattern of policy response can be justified,
~This is similar to Keynes's advice in Chapter 17 of the General Theory that when the real wage has to decline, it is easier to have a monetary expansion than absolute declines in the money wage (Keynes, 1936).
130
V. Reinhart
depending on relative parameter sizes. Our complete model, with its ad hoc specification of the behavior of firms and households, teaches a negative lesson. A reasonably specified model, capturing several of the main direct influences of energy prices in the manner of its large-scale brethren, produces a variety of possible indirect effects. Thus, advocacy of minding the market to gauge the correct policy falls victim to the complexity of the economic system.
I would like to thank P. Cagan, D. Lindsey, D. Kohn, E. S. Phelps, and C. Reinhart for their helpful comments. The views expressed are my own and do not necessarily reflect the views of the Federal Reserve Board or any other members of its staff.
Appendix
A: An Exact Solution to the Model
This appendix establishes the dynamic properties of the model defined by Equations (5) and (9), by techniques explained in Hirsch and Smale (1974, pp. 47-55) and Sheffrin (1983, pp. 71-87), among others. About a steady state, the movements in real balances and the long-term real rate can be written in matrix form as:
1=
[ 10)~I/~2][Dx(t)
1
[DR(t)]
--~
a29/o~
~ -- (0)~1/~2)][ X(t) -- Xo ] (1 + a2)~'
][R(t)
R0 '
where we place the time index in parentheses to make it distinct from a subscript denoting a steady-state value. More compactly,
[DR(t) = n [ R ( t )
R 0 + C.
Dynamics depend on the two characteristic roots of the matrix A - l B. Since the product of these two roots equals the product of the determinants of A-1 and B (which are positive and negative, respectively), the transition matrix must have a negative determinant and opposite-signed characteristic roots. This evidences saddlepoint stability, so that for any level of real balances, there is one level of the real long-term interest rate, R, that ensures a stable path toward the steady state. Indeed, we can characterize this solution precisely by working through the matrix algebra. The convergent path, known as the saddlepath, depends on the elements on A-IB, A-1B =
1 e2 - e~
[ -(e2~+el02") -(
-elt~[~+'-a,'] ] e2t' - ~2~I" + ~ e l ~ l ,
'
Only the off-diagonal elements of this matrix can be signed unambiguously; its two characteristic roots equal k, = e2[1 - ~rI 4-
~=-8, which, as predicted, are opposite-signed.
- ¢,<~,I,] ;
and
Reading the Effects of an Energy Shock
131
Movements about the steady statedepend on these roots, their associated characteristic vectors, and the choice of initialconditions. For the general solution,
[x(t)-Xo]=[-eloo/e20J(~ R(t) - R o 1
+ '~Ir- 0"1'~)/[(0"2- ~¢.0)'tic] ] 1
Ktexp(hlt)] K2exp(-M) '
where Km and K 2 axe constants determined by initial conditions. Four observations let us anchor this system: (1) Real balances at any time are inherited; (2) the real rate can jump freely in response to any shock; (3) since )~t > 0, a nonzero choice for K I results in an explosive movement away from the steady state; and (4) the parameter K 2 can be nonzero, as it multiplies a term that decays over time. Thus, at any time, say t = 0, we have two equations in K 2 and R(0), once we know x(0) and set K I = 0. Our exact solution becomes
x ( t ) - X o = [x(O) - Xo]" e x p ( - 6 t ) ;
and
R ( t ) - R o = {~I'(a2 - ao~)/[o~(a + ~t, - al~I,)] } • [x(O) - Xo]. e x p ( - a t ) . This dynamic behavior links the movements of these two variables along a transition path. We can link them formally by eliminating initial conditions and the decay term,
R ( t ) - R o = { ~ ( a 2 - 6oJ)/[o;(a + ~ - o,~I')] }" [ x ( t ) - Xo]. This is the saddlepath, a negatively sloped relationship that holds at any time. Depending on the behavioral parameters, the saddlepath may be more or less steeply sloped than the LM curve. Also note that the responsiveness of the price index to oil prices, o/, does not enter. Thus, a change in this responsiveness shifts the steady state but has no effect on the shape of the adjustment path.
References Berndt, E. R., and Wood, D. O. August 1975. Technology, prices, and the derived demand for energy. Review of Economics and Statistics 57(3):259-268. Bertola, G., and Caballero, R. J. 1990. Kinked adjusmmnt costs and aggregate dynamics. NBER Macroeconomics Annual 5:237-288. Blanchard, O. J. March 1981. Output, the stock market, and interest rates. American Economic Review 71(1): 132-143. Blanchard, O. J. April 1985. Debt, deficits, and finite horizons. Journal of Political Economy 93(2):223-247. Blinder, A. S. March 1981. Monetary accommodation of supply shocks under rational expectations. Journal of Money, Credit and Banking 13(4):425:438. Calvo, G. A. November 1983. Staggered contracts in a utility-maximizing framework. Journal of Monetary Economics 12(3):383-398. Findlay, R., and Rodriguez, C. A. May 1977. Intermediate imports and macroeconomic policy under flexible exchange rates. Canadian Journal of Economics 10(2):208-217. Findlay, R. 1980. Oil supplies and employment levels: A simple macro model. In Flexible Exchange Rates and the Balance of Payments (J. Chipman and C. Kindleberger, eds.). Amsterdam: North-Holland, pp. 313-319. Fischer, S. July 1981. Is there a real-balance effect in equilibrium? Journal of Monetary Economics 8(1):25-40.
132
V. Reinhart Gordon, R. G. 1975. Alternative responses of policy to external shocks. Brookings Papers on Economic Activity 6(1): 183-204. Hallman, J. J., Porter, R. D., and Small, D. H. 1989. M2 per unit of potential GNP as an anchor for the price level. StqffStudies. (Board of Governors of the Federal Reserve System) 157. Hamilton, J. D. 1983. Oil and the macroeconomy since World War 1I. Journal of Politcal Economy 91(2): 228-248. Hickman, B. G., Huntington, H. G., and Sweeney, J. L., eds. 1987. Macroeconomic Impacts of Energy Shocks. Amsterdam: North-Holland. Hirsch, M. W., and Smale, S. 1974. D~fferentiaiEquations, Dynamical Systems, and Linear Algebra. New York: Academic Press. Keynes, J. M. 1936. The General Theory of Employment, Interest and Money. London: Macmillan. Mussa, M. December 1981. Sticky prices an disequilibrium adjustment in a rational model of the inflationary process. American Economic Review 71(5): 1020-1027. Obstfeld, M. September 1982. Relative prices, employment, and the exchange rate in an economy with foresight. Econometrica 50(5): 1219-1242. Obsffeld, M. July 1989. Intertemporal dependence, Impatience, and Dynamics. NBER Working Paper No. 3028. Phelps, E., S. May 1978. Commodity supply shocks and full-employment monetary policy. Journal of Money, Credit and Banking 10(2):206-221. Phelps, E. S. 1979. Studies in Macroeconomics, vol. 1. New York: Academic Press. Rasche, R., and Tatom, J. May 1977. The effects of the new energy regime on economic capacity, production, and prices. Federal Reserve Bank of St. Louis Review 59(5):2-12. Reinhart, V. February 1990a. Interest rate smoothing and staggered contracting. Journal of Economics and Business 42(1): 1- 16. Reinhart, V. November 1990b. Targeting nominal income in a dynamic model. Journal of Money, Credit, and Banking 22(4):427-443. Rotemberg, J. J. May 1983. Supply shocks, sticky prices, and monetary policy,. Journal of Money, Credit and Banking 15(4):489-498. Sheffrin, S. M. 1983. Rational Expectations. Cambridge, UK: Cambridge University Press. Small, D. H., and Porter, R. D. April 1989. Understanding the behavior of M2 and V2. Federal Reserve Bulletin 75(4):244-254. Struckmeyer, C. S. May 1987. The putty-clay perspective on the capital-energy complementarity debate. Review of Economics and Statistics 99(2):320-326. Tatom, J. July 1988. Macroeconomic effects of the 1986 oil price decline. Contemporary Policy Issues 6(3):69-82. Taylor, J. B. February 1980. Aggregate dynamics and staggered contracting. Journal of Political Economy 88(1): 1-23.
115
Reading the Effects of an Energy Shock in Financial Markets Vincent Reinhart
The impact of an oil price increase on goods output depends, in part, on the response of financial markets. This article adds three distinct effects of energy prices to a Keynesian model peopled with forward-looking investors choosing among a menu of assets. Combining Blanchard's (1981) long-term-asset dynamics with Mussa's (1981) explanation of goods-price stickiness arrives at a perfect foresight adjustment path that can be projected on the traditional IS-LM framework.
I. Introduction The effects of an increase in oil prices ripple through the economy. The number of waves, their timing, and their magnitude vary across historical episodes, but three main influences can be identified. First, there is a direct price level effect, as higher oil prices feed into consumer prices and reduce the real value of fixed stocks of nominal wealth. Second, over a slightly longer horizon, there is an aggregate goods demand effect, as consumers substitute away from their direct use of energy in favor of other final goods. Lastly, over a still longer horizon, there is an aggregate goods supply effect, as manufacturers shift production away from more expensive energy inputs. These differently timed effects produce a complicated pattern of forces on the economy, making policy advice problematic. Every day, participants in financial markets price long-lived assets, requiring them to disentangle these factors to estimate paths for interest rates, incomes, and profits over a long horizon. Can policymakers use this financial market reaction to determine the consequences of an oil shock for income and inflation? We turn to a simple Keynesian model to address this issue. The complete model, detailed in the next section, connects two influential strands of analysis on the monetary transmission mechanism. First, monetary policymakers directly affect short-term rates of return, which in turn affects yields on longer-term assets and, then, aggregate demand. Blanchard's (1981) model, which includes a long-term rate of return in a perfect-foresight IS-LM model, is the starting point. Second, the composition of any policy-induced change in aggregate demand varies over time: Output expands at first, followed by goods-price increases that erode the real effects of
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116
V. Reinhart
the stimulus. Our explanation of price stickiness takes after Mussa (1981), resulting in a framework with continuous market clearing but enough short-run rigidity to provide policy a role--a role that begins in the short end of the money market. As an analytic tool, we derive a perfect-foresight dynamic adjustment path that can be projected on the traditional IS-LM framework. We first include direct effects of an oil price change on aggregate demand and supply; as long as money demand is not unrealistically interest-sensitive, the long-term asset brings forward some of the steady-state contraction of higher oil prices, raising the current long-term interest rate "and reducing current expenditure. The loss in potential output exceeds the reduction in expenditure, giving way to excess demand for goods and higher inflation in the transition to the steady state. Meanwhile, the short-term nominal interest rate declines, steepening the yield curve at the news of an oil price increase. Thus, this foresight model explains both an apparent "flight to quality" at the short end of the term structure (which is really portfolio reshuffling, not a reaction to perceived risk) and inflation- and real-rate-induced increases in the long-term rate. Policy advice can follow the message of the market, only depending on the calculus of social welfare. If the central bank wants to forestall the inevitable output loss, it should ease policy with the increase in oil prices. If inflation concerns dominate, a policy tightening could eliminate the transition to the new long-run equilibrium. Including a direct effect of oil prices on the general price level renders the response of long-term rates ambiguous. The long-term rate may rise or fall at the impact of a permanent increase in oil prices and virtually any pattern of rates may follow, according to a complicated interaction of parameters. Thus, experiments with the complete model suggest that financial markets do not send a clear signal about the nature of an oil shock and, absent policy action, expenditure may fall or rise on impact. Accordingly, no blanket policy response can be advocated.
II. The Direct and Indirect Effects of an Energy Price Change Energy and the Economy The strong negative correlation between economic activity and relative energy prices in the United States is well documented, most notably by Hamilton (1983). Theory suggests that such an effect may follow from the direct influence of energy prices on aggregate supply and demand. In terms of aggregate supply, the market price of oil represents the cost of a key input to the manufacturing sector. An increase in the price of energy relative to the price of the goods that energy produces should result in a decreased use of that input. Assuming that factors of production are somewhat substitutable, this should make the other inputs, labor and capital, less productive. Berndt and Wood (1975) and Rasche and Tatom (1977) are among the researchers who have quantified this channel, i Suppose, for example, that the output of the final good, Yt, is produced with capital, Kt, labor, Lt, and the intermediate energy input, E t, for simplicity obeying a Cobb-Douglas production function, Yt = AKTLatE] -'~-~.
ISee Rascheand Tatom(1977) and the referencescited therein. For a more recent discussion, see Tatom
(1988).
Reading the Effects of an Energy Shock,
117
If the competitive market uses energy efficiently, the marginal condition on energy defines a derived demand schedule, (o,/s,)
=
(i -
-
in terms of the price of energy, O t, relative to the price of the final good, S t. Substituting this derived demand into the overall production frontier determines a concentrated production function. In the Cobb-Doublas case, this reduces (with lowercase letters representing logarithms) to
y, = B
+
-[(I
[~/(~ -
o~ -
+
~)]k,
~)/(~
+
[~/(~
+/3)](0
+
~)]I,
t - st),
where B is a constant term. A relative price increase causes goods producers to use the more expensive factor less intensely, reducing goods output. If intermediate energy inputs were 5 percent of the production of final output, then the elasticity of output with respect to a change in relative energy prices would be - 5 percent, about the sensitivity found in Tatom (1988), for example. The effect on the other inputs depends on how elastically they are supplied to the market and whether they substitute for or complement the energy input. The impacts of energy prices on aggregate demand are more varied and uncertain. In terms of relative price effects, an increase in real oil prices lowers the current value of the existing capital stock, as it will be less productive with lower energy inputs; thus, the economy's real wealth declines. Meanwhile, for an economy that imports oil, the higher real price acts as an excise tax, lowering consumer spending power. In terms of nominal price effects, an increase in oil prices--because it feeds into the consumer price index--lowers the real value of a fixed nominal stock of money. Additionally, since the pass-through of energy prices to the general price level is not immediate, inflation picks up for time, lowering the real return provided by any asset with a fixed nominal return. Capturing these disparate channels of influence requires a complete model of the economy, many examples of which can be found in a recent comparative survey of large scale models for the Energy Modeling Forum (Hickman, Huntington, and Sweeney 1987). These authors analyzed the impact of a permanent 50 percent increase in oil prices for differing policy stances and found that, with unchanged monetary and fiscal policies, the median response of 14 major models suggests that it would lower real GNP by about 2 1/4 percent after four years (Column 1 of Table 1). The apparent elasticity with respect to energy prices of 4 1/2 percent is about in line with estimates for the supply channel alone. A policy response to the shock, of course, could postpone this adverse effect. Indeed, the simulations for the Energy Modeling Forum that allowed expansionary offsets using monetary and fiscal policies (Columns 2 and 3, respectively) suggest that there is a large scope for such efforts, at least in the short run. The benefit of large-scale models, their ability to incorporate complicated causal patterns, also can be a curse, as it can be difficult to interpret the results and trace the channels of influence. Furthermore, attempts to introduce forward-looklng behavior into these models often becomes computationally burdensome. Instead, this article turns to a small theoretical model, incorporating three distinct effects of energy prices in a Keynesian framework peopled with forward-looking investors who choose among a menu of assets.
V. Reinhart
118
Table 1. Econometric Model Predictions of the Response to a 50 Percent Increase in Energy Prices (Average Annual Change over Four Years) Unchanged policy (1) Percentage difference from baseline Real GNP (level) Aggregate price level Percentage point difference from baseline Unemployment rate Average inflation rate
Accommodativepolicy Monetary Fiscal (2) (3)
- 2.2 1.8
- 0.8 2.6
- 1.7 1.9
1.1 0.5
0.6 0.8
0.9 0.5
Note. Median responseof 14 major econometricmodels to a 50 percent increase in energy prices, as reported in Hickman et al. (1987), p. 56.
Concentrating on short-run policy, we abstract from some of the more interesting questions about the effects of an oil shock by assuming a fixed capital stock and rational expectations. Introducing foresight allows a detailed specification of the anticipatory dynamics set in motion by an energy shock, revealing additional, indirect influences on aggregate demand. However, such simplifications have their costs. Fixing the capital stock removes goods producers' ability to substitute from energy over time through physical investment (as discussed in Phelps, 1978, for example). Thus, we assume a once-and-for-all drop in potential output after an increase in relative energy prices, rather than the more likely drawn-out affair. Eliminating uncertainty by assuming perfect foresight prevents the increased perception of risk associated with a marked change in energy prices from adversely influencing spending in goods markets. Thus, we assume that worries about the future control of the world's stock of oil have no effect on finns' investment plans or households' durable purchases.
A Simple M o d e l To capture an aggregate supply effect, assume that the capacity or potential output level of the economy, q, is negatively related to the price of energy relative to the price of goods. Omitting time subscripts for convenience, we write
q = q(O/S);
(1)
this relative price is assumed to be fixed. 2 Essentially, energy suppliers post a price, and total demand adjusts. Total energy demand has two components: Energy is an input in production and a final good in consumption. The former involves a derived demand consistent with the reduced-form production function, while the latter depends on relative prices and the total scale of spending. 3 For the consumer part of energy
2As in Phelps (1978), Blinder (1981), and Rotemherg (1983). 3This approach follows Phelps (1978) and Findlay (1980) and contrasts with modelling energy as an intermediate good, as in Findlay and Rodriguez (1977) and Obstfeld (1982).
Reading the Effects of an Energy Shock
119
demand, assume that the share of spending on manufactured goods versus energy, or, depends positively on the relative price of energy. Total expenditure on all final goods, e, depends on the real long-term interest rate, R, and aggregate real wealth, W, e, < 0 ,
e=e(R,W),
e2>O.
(2)
The results that follow require an important role for financial wealth in contemporaneous spending plans, which would obtain in the Obstfeld-Uzawa model of endogenous time preference or the Blanchard-Yaari overlapping-generations framework (Obstfeld 1989; Blanchard 1985). However, to keep the example simple, we assume a functional form and accept the inherent dangers spelled out in Fischer (1981), including the risk that the behavioral relationship changes with regime. However, the ad hoc role for wealth and the faith in policy invariance accords with the structure of most large-scale models. Reinhart (1990b) examines the reaction to a supply shock in a framework that captures the household planning problem, given sticky prices. The general price index, P, includes both objects of final demand, manufactured goods and energy,
P=n(o,s), and, like any good price index, the function fl(.) always is increasing in both arguments and homogenous of degree one. This permits rearranging terms, P
=
e(o/s), s
=
o,(o/s), s,
defining the new function, 60, where oJ'/o~ reflects the importance of relative energy prices in the overall price index. Simply, an increase in the general price index follows from either an increase in relative energy prices or an increase in the nominal price of manufactured goods. Because we consider permanent changes in relative energy prices, the overall inflation rate, ~, equals the rate of increase in manufactured goods prices, 7r = D P / P = D S / S ,
where D denotes the time derivative. Perfect foresight having been assumed, 7r is both the expected and actual inflation rate. The scale variable in spending, real wealth, comprises the real values of government bonds and money balances. The government is assumed to have issued consols providing one unit of purchasing power per period, where R is the long-term real rate of return and 1 / R is the price (Blanchard 1981). With k of these consols outstanding and the nominal money stock denoted as M, real wealth equals W = M/P
+ k/R.
It will be convenient to describe real balances in terms of manufactured goods prices, M/P
= (M/S)
. (S/P)
= ( r e ~ S ) " (1/~o),
120
V. Reinhart
or, real balances in terms of the overall price index change with a change in nominal money balances deflated by manufacturing goods prices or through the price level effect of a change in relative energy prices. As a first policy assumption, suppose that the central bank follows an announced commitment to keep the growth of the nominal stock of money constant at ~; at any point in time, the stock of money is predetermined, which provides the baseline case for gauging the impact of an oil price change with unchanged policy. Defining the logarithm of real balances in terms of manufacturing prices as x, x - l o g ( M / S ) , the rate of change in real balances is written: D x = ~ - D S / S = ~ - ~r.
The demand for real balances is assumed to depend on real wealth and the nominal short-period return on holding the consol, i, MIP
= L(M/P
+ k/R,
i),
0 < L , < 1,
L 2 < O.
This relationship can be inverted to find the nominal short-term interest rate consistent with money-market clearing, i=~[R,x/o~(O/S)],
cr1 < 0 ,
o2<0,
(3)
showing that the short-term nominal rate falls when the bond component of wealth falls (that is, the bond yield rises) or the real money stock rises. But strict arbitrage between short- and long-term assets provides a second explanation for the short-term nominal interest rate. The real short-term return on a consol will equal its long-term yield plus expected capital gains (or less expected capital losses). If 1 / R is the price of the consol, its capital gain or loss equals - ( 1 / R ) D R / R . Thus, the instantaneous or short-term real rate approximately equals R - DR/
,
where ,it is a positive constant. Adding expected inflation gives the second definition of i, i = R - DR/el
+ DP/P.
As a last step, note that because inflation can be written in terms of the change in real balances and nominal money growth, the nominal short rate can be written i = R - DR/el
(4)
+ # - Dx.
Asset market clearing requires setting equal our two explanations for the nominal rate, yielding the evolution of the long-term interest rate, D R = e l { R - ~[ R , x / ~ ( O / S ) ]
+ ~ - Dx}.
(5)
This is the first of the two equations of the complete dynamic system. 4 However, this 4As is typicalin rationalexpectationsmodels,the asset marketcontributesexplosivebehaviorto dynamics. If x is heldfixed,equation(5) is an unstabledifferentialequationin R. As shownlater, the initialvalueof R will have to be cat,fully cho6en to avoid dynamicinstability.Shaffrin(1983, pp. 77-87) provides a clear explanationof solvingthese typesof models.
121
Re_J~l_ingthe Effects of an Energy Shock
economy already has enough structure to determine a steady state, even without detailing the short-run inflation process that closes the dynamic system.
The Steady State From a stabilization perspective, the long run is long enough for all prices (both assets and goods) to adjust to any disturbance but short enough to ignore the influences of asset accumulation. In this context, a steady state maintains constant levels of real balances and the real long-term interest rate. As a consequence of the first condition, the rate of inflation equals the rate of growth in the money stock. As for the second condition, no prospect for capital gain or loss sets the short-term equal to the long-term real interest rate. Thus, the nominal short-term rate in the long run equals the long-term real rate plus the rate of money growth, i 0 = R o + ~t, where the zero subscript denotes a steady-state value. This permits asset behavior to be related to the real long-term rate, via the inverted money demand, Equation (3),
O[Ro, Xo/o,(o/s)]
-
Ro =
This determines the long-run pairs of real balances and the real interest rate that clear the money market--it is a long-run LM schedule. As shown in Figure 1, the LM locus slopes downward, as agents hold a higher level of real balances only at a lower nominal interest rate; with the steady-state inflation rate
L$
• S $
,,," / s
R
P,o
/
.........................
-z... M
[ /
IVl
S
"
r
Xo Figure 1. Long-run consequences of an energy price increase.
X
122
V. Reinhart
at # and the short-term equal to the long-term real rate, this translates into a lower real long-term rate as well. The direct price level effect of oil prices, captured in the ~o(.) term, influences the position of the LM. An increase in relative oil prices lowers the final purchasing power represented by a fixed level of real balances measured in terms of manufactured goods prices. That is, an increase in (O/S) shifts the LM upward. In the long run, spending must equal potential output, defining a long-rnn IS curve,
a ( O / S ) " e[ R o, Xo/w(O/S)] = q ( O / S ) .
(6)
Differentiating to evaluate that relationship, we have:
dxo= [O)/(~.2ol)] " {[qt + 32XoO)t/o~2- Eolt]d(O/S) -OlEldRo}.
(6')
The IS locus slopes upward because an increase in the real rate must be offset by an increase in real balances to maintain expenditure at potential. The compound term in the brackets shows that oil prices have three distinct direct effects on the manufactured goods market. An increase in oil prices (1) reduces potential output (q'), (2) increases demand for manufactured goods as consumers substitute away from energy (-ec~'), and (3) reduces demand for manufactured goods, as an unchanged level of real balances measured in terms of manufactured goods represents a lower amount of purchasing power in terms of final goods (E2XoW'/o~2). At an unchanged real rate, the first two effects tend to lower the long run level of real balances, while the third tends to raise it. Given the simple specification, two standard results emerge: • An exogenous increase is spending (a shift in e) raises the steady-state long-term real interest rate and lowers the level of real balances. • An increase in the growth of money, increasing inflation, lowers the steady-state real rate and level of real balances. This Mundell-Tobin effect holds because agents substitute away from the asset with a fixed nominal return, money, toward the one with a return that varies with inflation, consols. An oil price increase, however, is more complicated. The direct aggregate supply and demand effects--as in equation (6)--tend to shift the IS equation upward, while the price level effects pulls it downward. Figure 1 is drawn with the assumption that the latter effect is insignificant, so that cleating in the goods market requires a higher real rate in the long run. At the same time, the direct price level effect reduces the purchasing power of any given level of x: The LM shifts upward. As the figures are drawn, the intersection of the IS and LM dictates a higher steady-state real interest rate, but the level of real balances depends on the relative sizes of these shifts. Again, with a small price level effect, the shift in the IS would be greater, so that real balances unambiguously fall. A significant price level effect clouds this picture, making the shift in the LM more pronounced and perhaps even reversing the shift in the IS. Thus, the long-run response of interest rates depends on the relative size of these direct eff~ts. How the economy moves from one long-run equilibrium to another depends on how nominal magnitudes adjust.
Reading the Effects of an Energy Shock
123
III. The Dynamics Response to an Oil Price Change Prices of goods and services exhibit varying degrees of sluggishness. At one extreme, market quotes for financial assets and tradable commodities adjust freely in response to current and anticipated economic conditions. At the other extreme, many goods and most service prices--particularly wages--are contracted, whether explicitly or implicitly, and negotiated infrequently. Any sudden change in energy prices perturbs the existing pattern of relative prices, perhaps requiring a protracted adjustment. The staggered wage contracting models of Taylor (1980), Phelps (1979), and Calvo (1983) are particularly suited to this and have been applied in a similar model in Reinhart (1990a). However, rather than explicitly introduce a labor market and wage developments, we follow Mussa's framework (Mussa, 1981) and assume that individual prices in the manufacturing sector are costly to adjust and set at staggered and overlapping intervals. There is no pressure on prices to change from their equilibrium path when expenditure equals potential output, e=q.
This can be used to define the "potential output price level" or S*. Given adjustment costs and behavior consistent with maximizing agents with foresight, Mussa has shown that the actual price level grows at the growth rate of S* adjusted for differences in the actual price level relative to the potential output price level:
D S / S = DS*/S* + ~(S* - S).
(7)
Given the difficulties in reconciling menu costs at the individual level and aggregate sluggishness (reviewed in Bertola and Caballero, 1990), equation (7) should be viewed as a convenient reduced-form representation of manufacturing goods price inflation. In this respect, the Mussa framework shares the insight of the "P-star" inflation adjustment equation, because actual inflation moves to close the gap between the actual and an "equilibrium" price level (Hallman, Porter, and Small 1989). Unlike the P-star model, however, that equilibrium is defined as a constantly clearing condition in a single market, rather than a long-run monetary anchor to the overall price level. By adding and subtracting the nominal money stock, the price-setting rule can be written in terms of real balances,
Dx = Dx* + 6( x* - x),
(8)
where x* is the level of real balances that sets expenditure equal to potential output; to arrive at x*, set expenditure on manufactured goods equal to potential output,
ot(O/S) . e[ R , x*/oJ(O/S)] = q ( O / S ) , which is our already discussed long-run IS equation (6). This define.s an implicit function relating x* to R and O / S , say x* = x ( R , O/S). This equation's differential is the same as (6'), which reveals that X~ > 0, while X2 is ambiguous, depending on the relative size of the three direct effects of energy prices. Lastly, differentiating our
124
V. Reinhart explanation of x* and substituting into equation (8), we have
x,DR ÷
- x],
(9)
which relates the growth of real balances to the level and change of the real long-term rate. Our dynamic model describes the paths of real balances and the real long-term rate of interest given in equations (5) and (9). The central bank's pledge to hold nominal balances along a set path combines with sticky goods prices to predetermine the level of real balances. On the other hand, as an asset return, the real rate of interest can adjust to clear markets after an unexpected event. Appendix A shows that stability requires that this dynamic adjustment follow a negatively sloped path (known as the saddiepath) leading to the long run (x, R) pair. In other words, in the long run the economy comes to rest at a unique point in the (x, R) plane, the intersection of the steady-state IS and LM curves. In the short run, any (x, R) point can be an equilibrium, as there are two anticipatory variables, D R and D x , free to clear the goods and money markets. However, only one set of (X, R) points are consistent with stable dynamics leading to the rest point, and those points lie along the negatively sloped saddlepath. At any point along that saddlepath, the values of D R and D x are just sufficient to clear markets and move the system toward the steady state. In what follows, we use the long-run IS and LM schedules to determine the steady-state combinations of x and r and the negatively sloped saddiepath to trace out short-run dynamics. This framework is given in Figure 2 for the two possible configurations. Depending on the magnitude of the relevant parameters, the saddlepath may be more or less steeply sloped than the long-run LM, as in panels a and b. This ambiguity is unimportant for our first exercise. Consider the impact of an unexpected once-and-for-all increase in the nominal stock of money. In the long run, prices are free to adjust so that this change will have no effect on real variables; the steady state ( x 0, Ro) remains unchanged. On impact, the aggregate price level does not respond because individual pricing decisions are spaced over time. The real supply of money increases at first and, in order to clear money markets, induces a decline in the nominal short-term interest rate. If real balances increase from x o to x ~, as in Figure 2, the real long-term rate drops on impact to RI, the corresponding point on the saddiepath. With both x and R lower, expenditure exceeds potential so that ~ increases faster than /~ and real balances decrease. During the transition, the real long-term rate increases in the movement from (x I , R 1) to ( x 0, Ro). Since D R > 0, agents expect capital losses so that the short rate is below the real long-term rate. Thus, the model captures the stylized facts of the response to a policy disturbance that sets the (postshock) money supply above (preshock) money demand: • All interest rates decline on impact. • The yield curve steepens because the short rate decreases by more than the long rate decreases. • Output expands at first but subsequent price increases erode that gain. Monetary control works through an interest rate channel, but any control of real variables is fleeting.
Reading the Effects of an Energy Shock
125
C:l
R
Ro R1
v
b
Xo
X1
X
R
R1 S v
X0
X1
X
Figure 2. Dynamic adjustment path.
Our chief concern is how the system reacts to an exogenous increase in real energy prices, which is complicated by the conclusion of the last section that the comparison of steady states is not straightforward. As a base of comparison, let us temporarily assume away the direct price level effect, oY = 0. 5 Thus, an increase in energy prices lowers potential output and shifts demand toward manufactured goods. Because expenditure equals potential in the steady state, the new long-run IS must lie to the left of the old one, as in Figure 3. Market equilibrium requires an increase in the long rate and a
5As shown in Appendix A, changing the slope of the ~0(.) function does not affect the shape of the adjustment path.
126
V. Reinhart 0
S ' ~
R
.S'
S
m1
Ro R1 .......
S
X1
b
X0
L
R
X
S'
S
S m1
R I
Ro
r
X1
Xo
X
Figure 3. A permanent energy price increase.
reduction in real balances. The exact combination of endogenous contraction (the relative changes in R and x) depends on the interest sensitivity of money demand. Indeed, the old and new steady state lie on the same long-run LM schedule. The nature of the transition depends on how that locus, with slope 02/(1 - ol), compares with the saddlepath. The cost of higher energy prices--lower potential output--is paid permanently. How soon expenditure adjusts downward depends on how much of the contraction is brought forward by financial markets in the current price of long-term assets. Consider the following two cases.
Reading the Effects of an Energy Shock
127
Case 1. A n Exaggerated Response With highly interest-sensitive money demand, the higher interest rates associated with lower long-run potential output requires markedly lower real balances. The old steady state (x o, R0) lies above the new saddlepath or the long-run LM is flatter than the saddlepath (Figure 3a). Given this set of dynamic relationships, at the moment oil prices increase the system is governed by the new saddlepath SS. Perversely, the real long-term rate falls on impact to point (x o, R~), stimulating interest-sensitive expenditure. Expenditure rises above its old level and even further above the new level of potential output. Accordingly, price pressures build, pushing inflation above the constant growth rates of the nominal money stock, eroding the value of real balances over time. As real balances increse, the real long-term rate rises and the system moves left along SS. With interest-sensitive money demand, an adverse supply shock results in an immediate increase in expenditure and an initial fall in the real rate that is subsequently more than reversed.
Case 2. Undershooting With relatively interest-insensitive money demand (as is estimated in Small and Porter 1989, for example), the higher interest rates associated with lower long-run potential output do not significantly lower steady-state real balances. The old steady state lies below the new saddlepath (Figure 3b). At the moment real energy prices increase, the real long-term rate rises, attaining the point (Xo, R ~) on the new saddlepath. Expenditure falls but excess demand remains owing to a proportionately greater reduction in potential. The long-term rate increases on impact and then continues to rise during the transition. Given relatively insensitive money demand, an increase in energy prices raises the real long-term interest rate and lowers real output on impact. Notice that on impact, the long real rate increases along with inflation, so that the long-term nominal rate must have risen. Given the increase in the real long-term rate, the money-demand relationshp, equation (3), tells us that the nominal short-term rate actually falls, as real money balances are unchanged and the bond component of real wealth declines. Thus, the nominal yield curve steepens with the news of an oil price increase--the short-term rate declines, while the longer-term rate rises. Even with our simplifying assumptions, an ambiguity remains. The long rate may rise or fall with the news of a permanent oil price increase. However, rising market rates signal an economy that is settling for a lower level of potential. Or do they? Unfortunately, if we reintroduce the direct price level effect, any pattern of rate response becomes possible. While the adjustment path is unaltered, the relative positions of the new destinations can be markedly different. COnsider Figure 4, which presents a range of cases, under the likely scenario that the interest sensitivity of money demand is not prohibitively large. If the price effect is moderate (Case a) we retain our earlier results. The real rate rises on impact and continues to rise over the transition. On the other hand, if the price effect is large (Case b) the shift in the LM outweighs the shift in the IS and agents seek to rebuild their money balances, when measured in terms of manufactured goods. The long rate increase on, impact and then falls during the transition. Finally, if the price effect so dominates that the IS shifts downward (Case c), the real rate falls on impact, falling even more during the transition.
12g
V. Reinhart co,,, (o) R
"~
I'
/I
M \
....
.~ ira,,.-×
co~,, (b)
S
. L'
,
R
I
case
(c) J
R
X Figure 4. Possible configurations.
IV. The Policy Response to a Supply Shock Suppose that we paint the most favorable case for policy reaction by eliminating the direct price level effect. In this model, the economy adjusts to a supply shock through a neoclassical channel: Prices adjust, engender changes in real balances, and through wealth and liquidity effects move the economy to potential. The conditions for this to be effective include rapid adjustment of prices to excess demand (high 8) and interest-insensitive money demand (high ¢2). Within this model, the former flattens the saddlepath, while the latter steepens the LM. Thus, the more closely the economy attains the neoclassical paradigm, the less likely there are perverse movements in the real rate and output in response to a supply shock. Correspondingly, under the Keynesian prior
Reading the Effects of an Energy Shock
129
that prices respond sluggishly to excess demand and that money holdings are interestsensitive, adjustment will be protracted. If ~ and 02 are sufficiently low, output reverses direction in response to an energy price increse. In either case, there are relative increases in excess demand during the adjustment, as income is higher than the new level of potential. Depending on the calculus of social welfare, policy can step in to speed the expenditure decline (if inflation concerns dominate) or to slow the transit to the permanently lower level of output (if output concerns dominate). From the viewpoint of stabilization policy, the choice of instruments is trivial, as either monetary or fiscal policy can move to achieve potential in this perfect-foresight model. However, since output falls below trend because a nominal magnitude, the price level, does not adjust quickly enough, the natural assignment is to have the central bank, which controls a nominal magnitude, to step in. 6 Consider the configuration of the IS, LM, and saddlepath in our Case b that is consistent with a modest interest-sensitivity of money demand, which were shown in the lower panels of Figures 2 and 3 and the upper panel of Figure 4. If the goal were to limit the price consequences of the oil shock, the central bank could lower nominal balances at the announcement of the oil price hike. Rather than allowing a transition for the economy to slowly adjust real balances from x 0 to x 1 in Figure 3, a once-and-for-all money supply cut could engineer an immediate response. Essentially, the central bank responds to the increase in the long-term rates by raising the short-term rate. On the other hand, the central bank could forestall the inevitable output response by raising real balances on impact, moving the economy further away from the steady state. As the saddlepath slopes downward, the real long-term rate could be lowered sufficiently by an increase in the level of the money stock to keep expenditure unchanged. However, this cushions current expenditure at the cost of higher inflation during the now longer transition, as goods prices will eventually rise by a sufficient amount to reverse any easing steps in real terms. The econometric model responses reported in Table 1 fall into the latter group. Moving from Column 1 to Column 2, the output loss could only be trimmed from 2.1 percent to 1.8 percent over the four-year span by allowing more inflation. Fiscal policy, as it controls a real magnitude in the short and long runs, can have a more lasting effect on this economy's equilibrium. Real rates rise after an oil price hike to damp the private, interest-sensitive component of spending, ultimately bringing total expenditure in line with the lower level of potential output. If fiscal policy were to contract as oil prices rise, the relative position of the IS curve Could remain fixed, instantly bringing income to the new lower level of potential output. By offsetting the decline in aggregate supply with a reduction in government spending, private spending would remain unchanged at an unvarying real interest rate. Of course, the government could lean against the wind of the output loss by expanding fiscal policy when oil prices rise, shifting the IS schedule further leftward. Total expenditure could be temporarily maintained, or even increased, but at the cost of higher current and future real interest rates and an increasing share of the government in total spending. Policy's role diminishes to the extent that a direct price level effect makes the transition more difficult to project. Any pattern of policy response can be justified,
~This is similar to Keynes's advice in Chapter 17 of the General Theory that when the real wage has to decline, it is easier to have a monetary expansion than absolute declines in the money wage (Keynes, 1936).
130
V. Reinhart
depending on relative parameter sizes. Our complete model, with its ad hoc specification of the behavior of firms and households, teaches a negative lesson. A reasonably specified model, capturing several of the main direct influences of energy prices in the manner of its large-scale brethren, produces a variety of possible indirect effects. Thus, advocacy of minding the market to gauge the correct policy falls victim to the complexity of the economic system.
I would like to thank P. Cagan, D. Lindsey, D. Kohn, E. S. Phelps, and C. Reinhart for their helpful comments. The views expressed are my own and do not necessarily reflect the views of the Federal Reserve Board or any other members of its staff.
Appendix
A: An Exact Solution to the Model
This appendix establishes the dynamic properties of the model defined by Equations (5) and (9), by techniques explained in Hirsch and Smale (1974, pp. 47-55) and Sheffrin (1983, pp. 71-87), among others. About a steady state, the movements in real balances and the long-term real rate can be written in matrix form as:
1=
[ 10)~I/~2][Dx(t)
1
[DR(t)]
--~
a29/o~
~ -- (0)~1/~2)][ X(t) -- Xo ] (1 + a2)~'
][R(t)
R0 '
where we place the time index in parentheses to make it distinct from a subscript denoting a steady-state value. More compactly,
[DR(t) = n [ R ( t )
R 0 + C.
Dynamics depend on the two characteristic roots of the matrix A - l B. Since the product of these two roots equals the product of the determinants of A-1 and B (which are positive and negative, respectively), the transition matrix must have a negative determinant and opposite-signed characteristic roots. This evidences saddlepoint stability, so that for any level of real balances, there is one level of the real long-term interest rate, R, that ensures a stable path toward the steady state. Indeed, we can characterize this solution precisely by working through the matrix algebra. The convergent path, known as the saddlepath, depends on the elements on A-IB, A-1B =
1 e2 - e~
[ -(e2~+el02") -(
-elt~[~+'-a,'] ] e2t' - ~2~I" + ~ e l ~ l ,
'
Only the off-diagonal elements of this matrix can be signed unambiguously; its two characteristic roots equal k, = e2[1 - ~rI 4-
~=-8, which, as predicted, are opposite-signed.
- ¢,<~,I,] ;
and
Reading the Effects of an Energy Shock
131
Movements about the steady statedepend on these roots, their associated characteristic vectors, and the choice of initialconditions. For the general solution,
[x(t)-Xo]=[-eloo/e20J(~ R(t) - R o 1
+ '~Ir- 0"1'~)/[(0"2- ~¢.0)'tic] ] 1
Ktexp(hlt)] K2exp(-M) '
where Km and K 2 axe constants determined by initial conditions. Four observations let us anchor this system: (1) Real balances at any time are inherited; (2) the real rate can jump freely in response to any shock; (3) since )~t > 0, a nonzero choice for K I results in an explosive movement away from the steady state; and (4) the parameter K 2 can be nonzero, as it multiplies a term that decays over time. Thus, at any time, say t = 0, we have two equations in K 2 and R(0), once we know x(0) and set K I = 0. Our exact solution becomes
x ( t ) - X o = [x(O) - Xo]" e x p ( - 6 t ) ;
and
R ( t ) - R o = {~I'(a2 - ao~)/[o~(a + ~t, - al~I,)] } • [x(O) - Xo]. e x p ( - a t ) . This dynamic behavior links the movements of these two variables along a transition path. We can link them formally by eliminating initial conditions and the decay term,
R ( t ) - R o = { ~ ( a 2 - 6oJ)/[o;(a + ~ - o,~I')] }" [ x ( t ) - Xo]. This is the saddlepath, a negatively sloped relationship that holds at any time. Depending on the behavioral parameters, the saddlepath may be more or less steeply sloped than the LM curve. Also note that the responsiveness of the price index to oil prices, o/, does not enter. Thus, a change in this responsiveness shifts the steady state but has no effect on the shape of the adjustment path.
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V. Reinhart Gordon, R. G. 1975. Alternative responses of policy to external shocks. Brookings Papers on Economic Activity 6(1): 183-204. Hallman, J. J., Porter, R. D., and Small, D. H. 1989. M2 per unit of potential GNP as an anchor for the price level. StqffStudies. (Board of Governors of the Federal Reserve System) 157. Hamilton, J. D. 1983. Oil and the macroeconomy since World War 1I. Journal of Politcal Economy 91(2): 228-248. Hickman, B. G., Huntington, H. G., and Sweeney, J. L., eds. 1987. Macroeconomic Impacts of Energy Shocks. Amsterdam: North-Holland. Hirsch, M. W., and Smale, S. 1974. D~fferentiaiEquations, Dynamical Systems, and Linear Algebra. New York: Academic Press. Keynes, J. M. 1936. The General Theory of Employment, Interest and Money. London: Macmillan. Mussa, M. December 1981. Sticky prices an disequilibrium adjustment in a rational model of the inflationary process. American Economic Review 71(5): 1020-1027. Obstfeld, M. September 1982. Relative prices, employment, and the exchange rate in an economy with foresight. Econometrica 50(5): 1219-1242. Obsffeld, M. July 1989. Intertemporal dependence, Impatience, and Dynamics. NBER Working Paper No. 3028. Phelps, E., S. May 1978. Commodity supply shocks and full-employment monetary policy. Journal of Money, Credit and Banking 10(2):206-221. Phelps, E. S. 1979. Studies in Macroeconomics, vol. 1. New York: Academic Press. Rasche, R., and Tatom, J. May 1977. The effects of the new energy regime on economic capacity, production, and prices. Federal Reserve Bank of St. Louis Review 59(5):2-12. Reinhart, V. February 1990a. Interest rate smoothing and staggered contracting. Journal of Economics and Business 42(1): 1- 16. Reinhart, V. November 1990b. Targeting nominal income in a dynamic model. Journal of Money, Credit, and Banking 22(4):427-443. Rotemberg, J. J. May 1983. Supply shocks, sticky prices, and monetary policy,. Journal of Money, Credit and Banking 15(4):489-498. Sheffrin, S. M. 1983. Rational Expectations. Cambridge, UK: Cambridge University Press. Small, D. H., and Porter, R. D. April 1989. Understanding the behavior of M2 and V2. Federal Reserve Bulletin 75(4):244-254. Struckmeyer, C. S. May 1987. The putty-clay perspective on the capital-energy complementarity debate. Review of Economics and Statistics 99(2):320-326. Tatom, J. July 1988. Macroeconomic effects of the 1986 oil price decline. Contemporary Policy Issues 6(3):69-82. Taylor, J. B. February 1980. Aggregate dynamics and staggered contracting. Journal of Political Economy 88(1): 1-23.