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An evaluation of blinder's alternative to profit sharing
WILUAM SCARTH McMaster University Hamilton, Ontario, Canada
An Evaluation of Blinder's Alternative to Profit Sharing* Blinder has suggested that wages be partially tied to a firm's own price change, so that the key feature behind Weitzman's profit-sharing proposal might be created without the same need for fundamental institutional change. We examine whether this proposal for labor's remuneration yields the "better disequilibrium properties'" that Weitzman expects from this class of policies. Using a standard quadratic adjustment cost model, we find that a tax-based indexing incentive is equivalent to there being a decreased degree of wage flexibility. We then examine output variability within a conventional macro model, while trying to avoid the Lucas critique by continuing to use the underlying microeconomic analysis at that stage.
1. Introduction
Weitzman's recent work (1985) on the share economy has stimulated much research, and this work has followed two main avenues. One approach (for example, Cooper 1988) has been to consider the microeconomic basis for both share contracts and fixedwage contracts and to explore why decentralized agents might prefer one form of remuneration over the other. Cooper finds that welfare is improved with profit sharing only under rather special conditions. A second approach to profit sharing has been to evaluate Weitzman's claim that it would create a permanent excess demand for labor, and so lead to a lower "natural" unemployment rate. Blinder (1986) and Nordhaus (1988) have questioned the existence of this permanent effect, and Weitzman (1988) has acknowledged that certain theories of unemployment (for example, the efficiency wage hypothesis) would leave his theory with no such prediction. Weitzman's (1988) counter argument is that with hysteresis considerations, the "natural" rate is significantly dependent on the actual unemployment rate, and since profit sharing should lead to "better disequilibrium properties," there is still much to be said for profit sharing in a macroeconomic context. *I thank Gord Myers, Ben McCallum and two referees for helpful comments.
Journal of Macroeconomics, Summer 1992, Vol. 14, No. 3, pp. 417-438 Copyright © 1992 by Louisiana State University Press 0164-0704/92/$1.50
417
William Scarth Weitzman's conjecture opens up a third area of study: how are the built-in stability features of the macroeconomy affected by changes of this sort in labor's remuneration? To our knowledge, no such investigation of macroeconomic dynamics exists. Analysts have simply presumed that profit sharing involves increased wage flexibility and that this structural change has an ambiguous effect on built-in stability (see DeLong and Summers 1986 and others, whose work is discussed below). The purpose of this paper is to investigate the short-run adjustment properties of Alan Blinder's (1986) proposal for labor's remuneration that was intended as a convenient substitute for profit sharing. As just explained, it is the prospect of reduced transitional unemployment costs following alternative macroeconomic shocks that now represents both the main benefit that these remuneration proposals are intended to provide and the aspect of the proposals that has been least adequately researched. Before proceeding, it is useful to ask why the implications of alternative labor payment schemes for short-run macroeconomic dynamics have not been studied more fully at the formal level. The answer, I think, follows from the fact that short-run dynamics usually exist in models of involuntary unemployment because of some temporary wage stickiness, and the Lucas critique has made it quite unappealing to study macro models with no underlying microeconomic rationale for these sticky wages. How would a major institutional change affect the speed of wage adjustment? Since we are not even sure why sluggishly adjusting wages exist in the first place, how can anything beyond a purely mechanical macro analysis of short-run dynamics be accomplished? The way we avoid the full brunt of this concern in this paper is to examine Blinder's indexing proposal, which he views as an excellent substitute for profit sharing. By referring to the simple static theory of the firm, Blinder shows that his indexing scheme makes firms' marginal labor cost less than the wage, and this is the key feature which motivated Weitzman's original recommendation for p~rofit sharing. But since it is the prospect of preferred wage and price dynamics that is now claimed as the major motivation for these alternative remuneration schemes, our strategy is to examine Blinder's proposal from the point of view of a dynamic theory of the firm. Indeed, to ensure focus on the dynamic issue, we assume an exogenous natural rate of employment and output, so that the only role for the alternative wage adjustment scheme is that it might provide more desirable features for the short-run adjustment path 418
An Evaluation of Blinder's Alternative to Profit Sharing that is followed as the natural rate is approached. We specify an adjustment-cost model for wages and then investigate the efficacy of a tax incentive policy which induces firms to tie their wage payments at least partially to the changes in their own product price, just as Blinder suggests. The adjustment cost framework allows us to derive how the short-run wage and price dynamics are affected by the policy, and it is easier to do this explicitly for Blinder's proposal than for Weitzman's. We find that Blinder's indexing proposal makes the short-run Phillips curve flatter, not steeper, as Weitzman and others expect to be the result for profit sharing. Analysts may wish to take either of two interpretations of what our result might mean for profit sharing. If analysts continue to view Blinder's proposal as very similar to profit sharing, then they would be comfortable concluding that the implications of profit sharing for the speed of macroeconomic adjustment may be far from what many (such as Weitzman) have been presuming. However, the fact that we have shown that the tax-based indexing incentive makes the short-run Phillips curve flatter, not steeper, may convince analysts that Blinder's scheme and profit sharing have very different implications for dynamics, and so are quite different policies after all. Without examining a similar microeconomic derivation for profit sharing (which would be more difficult), we simply cannot know whether the common presumption that profit sharing steepens the short-run Phillips curve is correct. In any event, our further dynamic analysis of Blinder's proposal is of interest in its own right. The plan of the rest of the paper is as follows. In Section 2 we explain a microeconomic basis of partial wage adjustment, using a variant of McCallum's (1980) and Mussa's (1981) models. We add the tax incentive scheme to the model, and so derive how Blinder's indexing proposal affects the expectations-augmented Phillips curve relationship. In Section 3, we establish the short-run macroeconomic properties of the model. We examine how the policy insulates the short-run deviations of output from its full information value, from both permanent and temporary shocks to aggregate demand and supply. Concluding remarks are offered in Section 4.
2. Microeconomic Considerations McCallum (1980), and Mussa (1981) have constructed models of gradual price adjustment in which firms minimize a cost function which has two arguments. Firms incur costs whenever price is set 419
William Scarth at a level other than what would be appropriate if adjustment was complete. Firms also incur adjustment costs whenever prices are changed at a rate that differs from what is dictated by equilibrium considerations. Partial adjustment is the optimal response when firms must balance the costs of changing with the costs of not changing. Here we use this same reasoning, but apply the argument to the adjustment of money wages instead of prices (as in Scarth 1988).' For the wage-setting decision, firms are assumed to minimize
where w and w are the logarithms of the wage and that level of wages that would make employment equal its natural level. Further explanation of the natural rate is given below. While all notation is defined as it is introduced, a summary list of all variables also appears as an Appendix. The variable r is the long-run average discount rate which is taken to be a constant, t indicates time, and dots stand for time derivatives. The variable P is taken as a fundamental technology parameter; it specifies the relative size of the adjustment costs compared to the costs of being out of full equilibrium. p depends on the size of wage negotiation costs, and expression (1) involves the assumption that these negotiation costs increase whenever the actual rate of wage change differs from the equilibrium rate of wage change. Workers resist settlement whenever w is less than $, while firms resist settlement whenever w exceeds 6.Below we will add a third term to this cost functionone that specifies the tax payments that a firm incurs if a government policy exists which penalizes firms for not tying the rate of wage change to their own product price change. But first, we explain how an expectations-augmented Phillips curve follows &om this basic cost function. Only by using this as a base for comparison can we derive how the indexing proposal affects the aggregate supply aspects of the economy. Since w is not a decision variable for the individual firm, 'Our derivation follows Scarth (pages 15-20) rather closely, but we extend that discussion by including the tax-based indexing incentive in the basic objective function, and by being much more explicit on issues of market structure and aggregation.
A n Evaluation o f Blinder's Alternative to Profit Sharing
expression (1) is minimized by picking the optimal time path for w. The first-order condition is 2 -
-
(1/[3)x
=
0,
where x = w - tb. T h e characteristic equation for this dynamic rule is
kz - r k -
1/[3=0,
so the characteristic roots are: k,,kz = [r +-- (r ~ + 4/[3)0"5]/2.
(3)
The transversality condition requires that x be zero eventually (that is, that full adjustment must eventually occur). T h e dynamic process is stable only if the characteristic root is negative. Thus, the decision m a k e r must reject the positive square root possibility in (3), and the resulting wage a d j u s t m e n t process is ~ = - a x , or tb = tb + a ( ~ - w ) , where a = [ - r + (r ~ + 4/[3)°5]/2 > 0 .
(4)
W e wish to relate decision rule (4) to an expectations-augm e n t e d Phillips curve, but first we note that the partial adjustment parameter, a, d e p e n d s on the m a g n i t u d e of the adjustment costs. It is easy to verify that #a/a[3 < 0, so that the larger are the adj u s t m e n t costs relative to the costs that are incurred by being away from full equilibrium, the slower is the adjustment of m o n e y wages. This intuitively plausible relationship is exploited in our policy analysis below. A standard expectations-augmented Phillips curve which relates price changes to the o u t p u t gap is 2This first-order condition is derived by applying the standard rules of the calculus of variation: foH(')dt is minimized when Hx - DHo~ = 0, where here H = e-a[x ~ + 13(Dx)2]. Subscripts stand for partial derivatives and D is the time derivative operator. The transversality condition is lm~z(Ho,) ~ 0.
421
William Scarth = g +f(y
-
0).
(5)
This relationship can be derived from (4), if a production function (Equation [6] below), a definition of optimal price setting (Equation [7] below), and an aggregate demand function (Equation [8] below) are specified. We assume y = bn,
(b-1)n =w-p-q, y = ~bg + O(m - p) + OP.
(6) (7) (8)
The variables y, n, p, g and m stand for the logarithms of output, employment, the price level, autonomous spending, and the nominal money supply. As with wages, Ifi is that value of price that makes output equal its natural value, Y- Parameter b is a positive fraction, so the marginal product of labor (which is equated to the real wage in [7]) is positive but a negative function of employment. The variable q is a constant (which is explained below); since it does not vary, it turns out to be unimportant for our analysis. The variables ~b, 0 and t~ are positive aggregate demand parameters. Equation (8) is the reduced form of a standard aggregate demand specification, in which demand depends on expected (equals actual) inflation. Before explaining how Equations (4), (6), (7) and (8) can generate the standard expectations-augmented Phillips curve (that is, Equation [5]), we discuss both the monopolistically competitive environment and the separation of decisions, which are being assumed to keep the analysis manageable. Also, this discussion allows us to be explicit concerning aggregation. Each firm is a monopolistic competitor, and this is why both wage and selling price are choice variables. Firms face very different kinds of costs when adjusting wages, compared to those incurred when adjusting selling prices, and as a result, they separate these two decisions. We can think of there being two departments within each firm: the "labor relations" group which adjusts wages through time, and the "production/marketing" group which picks selling price, output and employment at each point in time. We have already described the wage-setting process above. To be more explicit, we could have included j subscripts throughout Equations (1) to (3), to stand for the individual (jth) firm's relationships. Then, for k firms overall, we define w 422
An Evaluation of Blinder's Alternative to Profit Sharing = (E~=, w~)/k and tb = (Z~=, ~bj)/k, which makes Equation (3) hold with aggregate variables (as it is written above). The segmenting of decisions is natural since we are following the textbook convention that selling prices and output levels can be changed costlessly at any point in time, while wages cannot. It is implicit in this kind of quadratic adjustment cost model for wages, that each firm faces prohibitive costs if wages are not set before each time period. As a monopolistic competitor, each firm assumes that it is small enough to ensure that other firms' decisions are not affected by its own. For price, output and employment decisions, each firm assumes that its share of overall output is an inverse function of its relative price and that this relationship involves a constant elasticity parameter, h:
rj/r Capital rithms), demand over all
=
(I-IJP) -h .
letters stand for the levels of variables (not their logaand 1-I1 is the firm's own price. Note that this individual function can be written in logarithmic terms and summed k firms:
yj=ky-h
lrj-kp
.
j=l
Given that we define aggregate output and employment as per-firm averages, y = Y-~=IyJk, and given the definition for overall price, p = E~=l ~rJk, this equation simply reproduces the definition of aggregate output. We see, then, that this definition of demand for each individual firm's output puts no constraint on how aggregate demand is determined. Thus, there is no inconsistency between this individual specification and the aggregate demand function specified earlier (Equation [8]). This implies, for example, that the demand elasticity at the individual firm level (parameter h) can be large (as it is when the industrial structure approaches perfect competition), while there need be no effect on the elasticity of overall market demand (parameter 0). For this set of decisions, each firm maximizes profits, IIIYj - WflVj, subject to several constraints: its Cobb-Douglas production function, Y1 = N~, the perceived demand function for its product, and the presumptions that the overall market price, P, and the level of industry output, Y, are given from outside. Wj has already been 423
William Scarth
set FIj, ing the
prior to this decision. Using the constraints to eliminate Yj and differentiating with respect to Nj, and re-expressing the resultfirst-order condition in natural logarithms (lower-case letters), decision rule for each firm is (b - 1)nj = wj - ~rj - q j ,
(7a)
w h e r e q) = ln[b + (1 - l / h ) ] . D e f i n i n g n =(Y.~=, n j ) / k , q = (Y~=t q j ) / k and w and p as before, Equation (7a) becomes (7). Since b and h are constant, the q term is constant, and so plays no role in our analysis. In full equilibrium, ~ the production function and labor-demand/price-setting relationships are 0 = bfi and (b - 1)fi = tb # - q; and assuming r~ = ~ = 0, the latter implies ~b =/~. Subtracting the full-equilibrium relationships from Equations (6) and (7), and substituting the results and tb = fi into partial adjustment rule (4), we have tb = fi + a{(~ - p) + [(b - 1 ) / b ] ( O - y)}.
(9)
To eliminate the (# - p) term from (9), we must formally define #. To do this, we use aggregate d e m a n d function (8), along with Equation (5), which is treated for the m o m e n t as a trial solution in which parameter f has yet to be interpreted in terms of the underlying structural parameters of the model. Substituting (5) into (8) to eliminate P, we have (1 - t~f)y = ~bg + O(m - p ) + ~ # - d~fij.
(lO)
In full equilibrium, 0 = d~g + 0(m - #) + t ~ ;
(11)
so by subtraction of (10) from (11) we have (#
-
p)
=
(1
-
~f)(y - 0)/0.
(12)
Also, the time derivative of (i1) implies p = (0/d~)(fi- rh), which 3The "natural" rates of output and employment oPten refer to what emerges in a full competitive equilibrium. Here 0 and h refer to the outcome of a monopolistically competitive equilibrium (as explained above). 424
An Evaluation o f Blinder's Alternative to Profit Sharing
represents an unstable process. To avoid this instability, ~ is assumed to "jump" to the value rh at all times. After taking the time derivative of (10), and using (5) to eliminate the resulting ~ term, we have -f0 0 - - 1-¢f
(v - o),
(13)
since we assume g = ff = rh = 0. The final step in the derivation of the Phillips curve is to eliminate the tb term in (9) by using the time derivative of (7). The time derivative of (6) and Equation (13) are also used to eliminate ri and #. The result is -
a(1 - t~f) 0
( v - 0) + , h .
(14)
Comparing (14) and the trial solution (5), we can identify summary parameter f in terms of the underlying structure: f = 1 / ( , + O/a).
(15)
Clearly, the steepness of the short-run Phillips curve (parameter f ) increases with the degree of wage flexibility (parameter a), but is is also a function of aggregate demand parameters 0 and dg. We have presented this version of the Mussa/McCallum partial adjustment model for two reasons: first, to show that the dependence of the steepness of the short-run Phillips curve on the degree of wage flexibility can be derived (not just assumed); and second, so that we have a clear theoretical basis within which to evaluate policies that are aimed at altering the existing wage settlement system. Before considering how the short-run Phillips curve is affected by Blinder's policy-induced indexing proposal, we note one other feature of this McCallum/Mussa adjustment cost model. Equations (13) and (15) imply = - a ( y - 0).
(16)
Thus, despite the dependence of the short-run Phillips curve's slope on aggregate demand parameters, the speed with which output deviations are eliminated is not dependent on these coefficients. These aggregate demand parameters are important for determining the size 425
William Scarth
of initial output disturbances (as we see below), but only the speed of wage adjustment is important for the speed of adjustment of all endogenous variables. Now we consider how this theory of short-run wage, price and output adjustment is affected by a government policy which makes it costly for firms not to link their wage adjustments at least partially to changes in their o w n product price (that is by Blinder's indexing proposal). A policy in which each firm is penalized for not having its wage adjustment contingent on its own price adjustment would add a third element in the firm's quadratic cost function. With this policy, firms would minimize: fo~ [(wj - co) z + f3(tbj - tb) 2 + a ( t b / - 4rj)2]e-adt ,
where (as before) arj is the logarithm of the individual firm's o w n price. We now re-express this objective function, so that the importance of ct > 0 for short-run wage, price and output dynamics becomes apparent. First, from the individual versions of Equations (6) and (7a), we have 4rj = tbj + (1 - b)Oj/b (since t~ = 0). But before this relationship can be used to eliminate 4rj from the objective function, we must also use the expression for the change in the individual firm's own level of output--an item which cannot be taken as exogenous to this decision-making process. We have already assumed that each individual firm's share of total output is negatively related to the difference between its price and the going market price; that is, = y - h(=j-
(17)
p).
After substituting the time derivative of (17) into the ~j equation, and the result into the objective function to eliminate 4rj, we see that the new term in the cost function is ct[~/(tb/- 16) + S0], where ~/ --- h(1 - b ) / [ b + h(1 - b)], and ~ = (1 - b ) / [ b + h(1 - b)]. We can now proceed by analogy from before, since p, the logarithm of the overall price level, and y are not decision variables of the individual firm. The revised first-order condition for firms who face this tax-based indexing incentive is -
-
[1/(6
+ =
426
-
rz)
-
av
(0 -
+
(18)
A n Evaluation o f Blinder's Alternative to Profit Sharing
where z = ( I b - 1~). By comparing decision rules (2) and (18), we can derive how the wage adjustment process would be affected by this policy. Without the tax-based indexing incentive, the decision rule was a homogeneous second-order differential equation, while with the policy, the behavioral rule is a non-homogeneous equation of the same order. The complete solution of the latter involves a complementary function and a particular integral, and the complementary function is not affected by the presence of the time-dependent z and y terms. 4 Thus, the characteristic roots are now given by: hi, X2 = {r + [r ~ + 4/(13 + ct~/z)]°5}/2 •
(19)
As before, the transversality condition dictates that the negative square root be selected in (19). We see that the presence of the tax-based indexing incentive is equivalent to the adjustment cost parameter, 13, being larger. (Wherever 13 appeared before, (13 + a~/~) now appears.) Thus, this policy makes the short-run Phillips curve flatter, and it makes macroeconomic adjustment speed (as given by parameter a) slower. The basic intuition behind this result is that an increased degree of indexing makes the real wage more rigid. Since a return of real output to its natural value requires an adjustment in the real wage, indexing makes that adjustment more protracted. But before establishing the macroeconomic significance of this effect in the next section, we consider the complete solution of Equation (18). We have already shown that Ib = 19 = rh, so z can be reinterpreted as (16- lfi). Then, using (12), its time derivative, and (16) with !¢ = 0, we have ~ = - a z , and z = (1 - ~sf)!)/O. T h e time derivative of this last relationship and (16) yield: ~ = (1 - t~f)#/O and !7 = -a!). These two relationships and ~ = - a z can be used to simplify the right-hand side of Equation (18) to a~/(a - r)[50/(1 - t~f) - ~1]z/(13 + a~l~). The complete solution for (18) is then x = Ale ~t + A2e ~t + B z ,
and we must solve for the undetermined coefficients A~, Az and B. We have already established that one of the As (say A1) must be set to zero (given the transversality requirement of stability), so the solution is x = Aze ~t + Bz. When t = O, xo = A~ + Bzo, so x 4See Chiang (1984, 541). 427
William Scarth = (Xo -
Bzo)e xt + B z . Taking the time derivative of this solution,
we have .~= h ( x -
B z ) + B ~ = hx + B(~ - h z ) .
(20)
Equations (20) can be i n t e r p r e t e d as follows. In a linear e c o n o m i c model, the speed of a d j u s t m e n t for all e n d o g e n o u s variables must be the same, and we have verified this indirectly above by noting that i = - a x and ~ = - a z . W h e n both of these laws of motion are substituted into (20), it b e c o m e s (k + a)(x - B z ) = 0. Since B is not zero, ~ and since x and z are only zero in full equilibrium, this condition can hold at all times only if a = - k . This result verifies that the discussion following Equation (19) was fully appropriate. W e have now established what the standard m i c r o e c o n o m i c theory of quadratic a d j u s t m e n t costs implies for the tax-based indexing incentive. Blinder's proposal, which was i n t r o d u c e d as a substitute for Weitzman's call for profit sharing that is easier to i m p l e m e n t , makes the short-run Phillips curve flatter, and it makes the s p e e d of macroeconomic a d j u s t m e n t slower. In the next section, we investigate how the short-run deviations of o u t p u t (that follow from both perm a n e n t and t e m p o r a r y shocks) are affected b y t h e s e s t r u c t u r a l changes. In this way, we d e t e r m i n e w h e t h e r this p r o p o s e d change in labor's r e m u n e r a t i o n does or does not lead to " b e t t e r disequilibrium p r o p e r t i e s . " As n o t e d in the introduction, readers who are only i n t e r e s t e d in Weitzman's proposal p e r se may be t e m p t e d to stop reading at this point. If they are convinced (without formal analysis) that profit sharing must involve a s t e e p e r short-run Phillips curve, t h e n t h e y will now see that Blinder's tax-based incentive for indexation is n o t a substitute for profit sharing, and is instead a v e r y different policy as far as its dynamic implications are c o n c e r n e d . If their priors are (like Weitzman's) that profit sharing would involve " b e t t e r disequilibrium p r o p e r t i e s , " and t h e y now see Blinder's proposal as having the opposite effect on the slope of the short-run Phillips curve, t h e n this p a p e r could b e i n t e r p r e t e d as a basis for rejecting Blinder's suggestion. H o w e v e r , we regard this reaction as p r e m a t u r e , for the 5While it is not necessary for our analysis, B is solved by using the trial solution for the partieular integral: x = Bz. We substitute this trial solution and its time derivatives (i = -aBz and ~ = a~Bz) into the left-hand side of (18), equate the result to a~/(r + a)[80/(1 - t~f) - ~l]z/(~ + a~/z), and solve for B. 428
An Evaluation of Blinder's Alternative to Profit Sharing simple reason that increased wage flexibility may be "bad," not "good," for macroeconomic built-in stability. Before a judgement is made on this supplementary issue, we cannot come to a complete evaluation of whether Blinder's indexing proposal involves "better disequilibrium properties" (let alone come to any opinion on the short-run dynamic implications of profit sharing, which is not examined here). The reason that an increased degree of wage and price flexibility can accentuate short-run real output deviations about the natural rate can be appreciated by considering the following example. When there is an exogenous decrease in aggregate demand, the overall reduction in output in the short run is determined in part by the size of a secondary (or induced) decrease in demand. Rational agents know that a fall-off in demand causes a temporary recession, and that this in turn lowers the rate of price change. Agents react to this decrease in expected inflation by cutting that part of aggregate demand that is sensitive to variations in expected inflation by this "secondary" amount. But if the short-run Phillips curve is steeper, rational agents involve this fact in their forecast for lower inflation. For any given size of temporary recession that is caused by the "primary" shock to aggregate demand, the reduction in expected inflation is now larger, so the "'secondary" reduction in aggregate demand is also larger. The net effect is that, with a steeper short-run Phillips curve, aggregate demand shocks cause bigger initial output deviations, even if these temporary disturbances are eliminated more quickly. So it is not at all obvious that a steeper short-run Phillips curve means "better disequilibrium properties"; more analysis is required to establish whether our resuits to this point support or reject Blinder's tax-based incentive for indexation.
3. Macroeconomic Implications Much recent research has explored the macroeconomic implications of increased wage flexibility. D e I ~ n g and Summers (1986) and others 6 have found that increased wage flexibility can cause ambiguous effects on the asymptotic variance of output, in models involving inflationary expectations effects on aggregate demand and rational expectations. The intuition behind this possibility was given 6For example, see Ambler and Phaneuf (1989), Driskill and Sheffrin (1986) and King (1988). 429
William Scarth in the previous paragraph. Since we have established that Blinder's indexing scheme is equivalent to a decreased degree of wage flexibility, it too must have ambiguous effects on output variability. Without any further analysis, then, we know that this proposal involves preferred disequilibrium properties only for a particular range of parameter values. But rather than leaving the matter with this general acknowledgement of ambiguity, we now present a formal analysis of the output effects of decreased wage flexibility. This further analysis is needed for two reasons. First, the existing literature (see footnote 6) focuses on temporary shocks, and we wish to extend the analysis to permanent disturbances. Second, most of the existing literature involves Taylor's (1979b) overlapping multi-period wage contracts instead of the Mussa/McCallum quadratic adjustment cost model, upon which we relied in the last section. Thus, we offer a sensitivity test for the existing empirical analysis, which involves inserting plausible macro parameter values into the formulae for output variance. Since our framework involves agents re-optimizing in the face of the wage-flexibility incentive policy (and the Taylor set up does not permit this re-derivation), this sensitivity test could be of rather general interest. The macro model which we examine is now summarized: 7 y = +g + 0(m - p) + ~ ,
(8)
13 = f ( y - O) + rh,
(6b)
f = 1/(¢ + O/a).
(15)
On the basis of the previous section, the profit-sharing/indexing proposals are viewed as schemes which lower parameter a, and so lower parameter f. First we consider once-for-all changes in the exogenous variables. There are no lasting effects on output, since it is pegged at its natural value, 0, in the long run. But short-run output effects exist, and these can be examined by substituting (6b) into (8) to eliminate ~, and differentiating:
rFor simplicity it is assumed that any tax revenue generated by the indexingincentive policy is redistributed to the private sector in a lump-sum manner, so no other demand or supply-side effects follow from the policy.
430
An Evaluation o f Blinder's Alternative to Profit Sharing dy -
-
d~ =
dg
-
-
dy 0
,
1-,f
dy -
-
1 - t~f
t~ -
drh
0 -
dm
>
dy >0,
-
-
1-,f -t~f - - -
do
>0,
<0.
(21)
1 - t~f
The signs for the multipliers given in (21) involve the assumption that (1 - ~f) > 0. This is the model's stability condition, since from Equation (6b) stability requires dTJ/dp = f ( d y / d p ) < O, and from the output reduced form d y / d p = - 0 / ( 1 - ~f). By using restriction (15) on summary parameter f, the reader can readily verify that the stability condition cannot be violated. The absolute value of all the multipliers in (21) is smaller, the lower is parameter f. This means that Blinder's indexing proposal makes output less sensitive to these permanent shocks. For example, the magnitude of the temporary recession that follows a drop in autonomous expenditure, a drop in the money growth rate, or an increase in productivity, is smaller if this tax-based indexing scheme exists. Other things equal, these results support the policy suggestion. However, while the policy makes the size of these initial recessions smaller, it makes the recessions last longer. This is because the speed with which output deviations are eliminated is given by parameter a (see Equation [16]), and a is reduced by the existence of the policy. Thus, the policy involves a trade-off in terms of its ability to insulate output from once-for-all disturbances--smaller initial output effects, but effects which are eliminated more slowly. Buiter and Miller (1985) have suggested one measure that can be used to have a single indicator of economic loss in circumstances that involve a trade-off such as this: they suggest calculating the undiscounted cumulative net output loss incurred as a result of any permanent shock. They show that this cumulative loss is simply equal to the deviation of output from its natural value during the impact period divided by the speed of output adjustment. 8 After division of the impact multipliers in (21) by the adjustment speed, a, and after simplification based on the microeconomic underpinnings inherent in using (15), the cumulative loss expressions are
8See
-
Buiter and Miller (1985, 23). ~ (y, - fh)dt = (Y,o - O)/a when y(x, t)
0(~, t) = (Y,o-
0,o) e-°"-'~.
431
William Scarth Loss = d~(qJ + O/a)/O
for autonomous expenditure (g) shocks,
Loss = ~(~ + O/a)/O
for monetary growth (rh) shocks,
Loss = (~ + O/a)
for money stock (m) shocks,
Loss = (qJ + O/a)/O
for productivity (9) shocks.9
(22)
The important result to emerge from (22) is that all cumulative output loss calculations are higher if the tax-based indexing incentive policy is involved (if a is smaller), so the analysis does not support the idea that such schemes lead to "'preferred disequilibrium properties." Two important features of this conclusion merit emphasis. The first concerns the Lucas critique. In our a t t e m p t to keep the analysis free of this critique, we have based our work on a specific microeconomic underpinning. This involved the adjustm e n t cost technology being specified as a "primitive" parameter, but the slope of the short-run Phillips curve not being primitive. The relationship between these two parameters was derived and summarized in Equation (15). The results in (22) rely on (15), but it is left for the reader to verify that if restriction (15) is not used, our definite results on cumulative output loss still emerge. Indeed, this is true for all results reported in the remainder of the paper. Thus, the reader does not need to embrace the specific M u s s a / McCallum underpinnings to have interest in our analysis; we have included it simply so that some degree of i m m u n i t y from the Lucas critique can be claimed for the results. The second point worth emphasizing is that this lack of support for Blinder's indexing proposal cannot be derived on a priori considerations alone, if we allow for discounting in the output loss calculations. Without discounting, we are simply adding up the area between the output time path and the time axis: fo(Yo - t))e -Utdt. With discounting at a constant rate, r, we measure fo[(y0 y)e-Ut]e -'~dt = fo(yo - f~)e -(~+ r)tdt, so we must divide the impact multipliers by (a + r), not just by a. Taking autonomous expenditure shocks as the example, the revised (discounted) cumulative loss expression is d~(at~ + O)/O(a + r). The reader can readily verify that w h e n this expression is differentiated with respect to a, losses are smaller if the tax-based indexing incentive is involved (if -
9In the case of productivity shocks, d(y - O)dfl = dy/dO - 1 = -1/(1 - qJf) is the impact effect which is divided by a to get the cumulative output loss. 432
An Evaluation
of Blinder's Alternative
to P r o f i t S h a r i n g
a is smaller) i f f r > 0/$. This same condition holds for all four kinds of shocks, and whether or not restriction (15) is utilized, Clearly, if the discount rate is high enough, the favorable effect of the policy on the impact multiplier can dominate the unfavorable effect of the policy on the speed of adjustment. We can have some idea whether this condition might be satisfied by considering the representative values for 0 and $ that were used by DeLong and Summers (1986). They specify an expectations-augmented IS-LM model of aggregate demand: y = - c l i and i = c2y - c3(m - p ) - ~. When the real interest rate, i, is eliminated by substitution, we see that 0 and t~ have the following structural interpretations: 0 = c a c J c 4 , and = c l / c 4 , where c4 = 1 + CLC2. DeLong and Summers consider values of ca ranging from 1 to 3, and they set" c2 equal to c3, and consider parameter values between 0.2 and 0.6. These representative values (which are plausible if the length of each time period is one year) are referred to in the stochastic analysis below. Here we simply note that 0/~ = c3, so the condition required for the discounted output losses following permanent shocks to be made smaller by the policy is that the social discount rate be greater than a number in the range of 20% to 60%. Most analysts would not be comfortable with such a high discount rate, so overall, our analysis of permanent shocks does not support the tax-based indexing policy. We now consider temporary disturbances by analyzing a stochastic discrete-time version of the model: y, = O(m, - p,) + t ~ [ E t ( p , + l ) - p , ] + u , ,
(23)
P, - p,-, = E t - a ( ~ t ) - 15t-~ + a(13,_, - Pt-a) ;
(24)
0, = 0 + v, = v , .
(25)
The variables u and v are aggregate demand and supply shocks which we assume have zero means, constant variances (¢r2, and cro2), and they involve no serial or cross correlation. McCallum (1980) has analyzed this model, and has focused on the deviations of output from its fidl information value, 0t = Yt - 0t. By following McCallum's use of the undetermined coefficient solution method, the reader can verify that the asymptotic variance of the output deviations is = ct.
. +
433
William Scarth
where
1
[0 + d~a] 2 "
This variance result indicates that the tax-based indexing proposal involves a trade-off in the face of temporary shocks as well. A lower value of parameter a increases the first term in square brackets in the definition of C (the persistence effect), but it lowers the second term in square brackets in the definition of C (the initial disturbance effect). To know the net effect on asymptotic variance of the tax-based indexing proposal, we must determine the overall sign of d C / d a . This dependence is given by dC
da
2(0 + Oa)[Oa - 0(1 - a)] (0 + qJ)s[1 - (1 a)~] z -
The profit-sharing/indexing schemes receive support from this stochastic analysis only if d C / d a > 0. This condition requires ~a > 0(1 - a ) .
(26)
To decide the likelihood that condition (26) is satisfied, we can utilize the plausible parameter values for 0 and dg used by DeLong and Summers (that were discussed above). But to obtain a representative value for the pre-policy value of the adjustment cost parameter a, we must rely on estimated values for the slope of the short-run Phillips curve. McCallum (1980) has shown that the analogue of restriction (15) for this discrete-time specification is f = a/(O + d~), where f is the coefficient on the lagged output gap in t h e i n f l a t i o n e q u a t i o n [Pt - Pt-1 =f(Yt-1 - 0,-1) + E,-I(/~,) - /~t-1]- When this relationship between f and a is substituted into condition (26), it becomes f > 0/(0 + t~)2 . Using the condition Summers condition 434
(27)
IS-LM interpretation of 0 and ~b that was explained above, (27) simplifies to f > cac4/cx(1 + c3)~. Using the D e L o n g / values for these parameters, the alternative versions of (27) are presented in Table 1.
An Evaluation of Blinder's Alternative to Profit Sharing The Condition Required for Policy to Decrease Output Variance for Alternative Aggregate Demand Parameters
T A B L E 1.
Condition f> f > f> f>
0.17 0.07 0.22 0.33
P a r a m e t e r Values cl cl cx c~
= = = =
1 3 3 1
, , , ,
c~ c2 c2 c2
= = = =
c3 c3 c3 c3
= = = =
0.2 . 0.2 . 0.6 . 0.6.
Taylor (1979a) has e s t i m a t e d t h e slope of t h e s h o r t - r u n Phillips curve to b e 0.28 (on an annual basis), and m o s t o t h e r e s t i m a t e s are in this r a n g e or lower. Thus, to h a v e s o m e feel for w h e t h e r condition (27) is m e t , w e can c o m p a r e a value o f f = 0.28 to the critical levels in T a b l e 1. W e see that o u r r a n g e of u n c e r t a i n t y on t h e coefficients is such that we c a n n o t say with any assurance that the taxbased indexing incentive lowers o u t p u t variability, b u t it certainly could do so. ~° O u r analysis of t e m p o r a r y shocks gives only qualified s u p p o r t for Blinder's policy suggestion. W h e n this conclusion is c o m b i n e d with o u r earlier analysis of p e r m a n e n t shocks, w h i c h s h o w e d that u n d i s c o u n t e d c u m u l a t i v e o u t p u t losses are necessarily i n c r e a s e d b y the policy, the s a m e verdict r e m a i n s - - o u r analysis gives t h e policy only limited support.
4. Conclusions W e can s u m m a r i z e the p a p e r v e r y simply. A standard microeconomic m o d e l o f quadratic a d j u s t m e n t costs s h o w e d that Blinder's proposal for labor's r e m u n e r a t i o n receives s u p p o r t f r o m o u r analysis only ff decreased wage flexibility leads to l o w e r o u t p u t variability. But a l o w e r d e g r e e of w a g e flexibility involves a trade-off: it m a k e s impact effects on o u t p u t smaller, while m a k i n g those o u t p u t deviations b e e l i m i n a t e d m o r e slowly. To evaluate this trade-off, w e h a v e considered two s u m m a r y m e a s u r e s of o u t p u t variability. First, considering p e r m a n e n t changes in t h e exogenous variables, w e d e r i v e d ~°It is reassuring that the general nature of our results (which are based on the adjustment cost model) are consistent with studies based on Taylor-type overlapping contracts. For example, DeLong and Summers found that increased price flexibility could only be bad if the short-run Phillips curve is fairly steep. Here, the policy (which is equivalent to decreased price flexibility) is only good if the short-run Phillips curve is steep. 435
William Scarth some results that required only qualitative assumptions: the cumulative undiscounted output loss from permanent changes in any of the exogenous variables is greater if the tax-based indexing incentive policy exists. Second, considering discounted output losses following permanent disturbances and temporary changes in both demand and supply shocks, we derived that quantitative assumptions are required to evaluate the policy's effectiveness. Even when representative parameter values were considered, firm conclusions could not be reached, although in the case of permanent shocks, the results were pretty solidly against the policy. Our overall conclusion is that the analysis provides only limited support for the tax-based indexing incentive policy. Of course our model is highly aggregative, so we do not pretend that it could represent a final word on the subject. Also, we have only examined whether policies of this sort do or do not lead to "better disequilibrium properties." We have assumed that the policy has no effect on the natural rate of employment (so we are not trying to evaluate any potential for a "permanent" excess demand for labor), and we have not considered whether similar results concerning transitional output losses follow from profit sharing. Nevertheless, our results have some novelty. Contrary to Blinder's expectations, our dynamic analysis suggests that his indexing proposal may not be a close substitute for profit sharing. And our analysis is entirely conventional--involving the standard rational expectations aggregate demand/supply model. Also, we have made a significant effort to test the robustness of our conclusions by working through the analysis both with and without reliance on a specific and standard microeconomic rationale for sticky wages, so that our evaluation of the tax-based indexation policy is not wide open to the Lucas critique. As a result, we view the analysis as a useful stepping-stone toward a better understanding of recent thought-provoking proposals for labor's remuneration. Received: July 1989 Final version: September 1991
References Ambler, Steve, and Louis Phaneuf. "The Stabilizing Effects of Price Flexibility in Contract-Based Models." Journal of Macroeconomics 11 (Spring 1939): 233-46. Blinder, Alan. "Comment." NBER Macroeconomics Annual 1 (1986): 335-43. 436
An Evaluation of Blinder's Alternative to Profit Sharing Buiter, William, and Marcus Miller. "Costs and Benefits of an AntiInflationary Policy: Questions and Issues." In Inflation and Unemployment: Theory, Experience and Policy-Making, edited by Victor Argy and John Neville. London: George Allen and Unwin, 1985. Chiang, Alpha. Fundamental Methods of Mathematical Economics. 3d ed. New York: McGraw-Hill, 1984. Cooper, Russell. "Will Share Contracts Increase Economic Welfare?" The American Economic Review 78 (March 1988): 13854. DeLong, Bradford, and Lawrence H. Summers. "Is Increased Price Flexibility Stabilizing?" The American Economic Review 76 (December 1986): 1031-44. Driskill, Robert, and Steven Sheffrin. "Is Price Flexibility Destabilizing?" The American Economic Review 76 (September 1986): 802-7. King, Stephen. "Is Increased Price Flexibility Stabilizing? Comment." The American Economic Review 78 (March 1988): 26772. McCallum, Bennett. "Rational Expectations and Macroeconomic Stabilization Policy: An Overview." Journal of Money, Credit, and Banking 12, part 2 (November 1980): 716-46. Mussa, Michael. "Sticky Prices and Disequilibrium Adjustment in a Rational Model of the Inflationary Process." The American Economic Review 71 (December 1981) 1020-27. Nordhaus, William. "Can The Share Economy Conquer Stagflation?" Quarterly Journal of Economics 96 (February 1988): 20117. Scarth, William• Macroeconomics: An Introduction to Advanced Methods. Toronto: Harcourt, Brace Jovanovich, 1988. Taylor, John. "Estimation and Control of a Macroeconomic Model with Rational Expectations." Econometrica 47 (September 1979a): 1267-86. • "Staggered Wage Setting in a Macro Model." The American Economic Review Papers and Proceedings 69 (May 1979b): 108-13. Weitzman, Martin• "The Simple Macroeconomics of Profit Sharing." The American Economic Review 75 (December 1985): 93753. • "'Comment on "Can The Share Economy Conquer StagflationT' "" Quarterly Journal of Economics 96 (February 1988): 21923. 437
William Scarth
Appendix List of Variables
logarithm of real autonomous expenditure. short-term real interest rate. j = index for denoting an individual firm. k = number of firms. m = logarithm of nominal money supply. n = logarithm of employment level. p = logarithm of the average price of goods. ~rj = logarithm of firm j's price. q = intercept in labor demand function (equals ln[b + (1 - 1/ h)] and so depends on the production function exponent and the elasticity of each individual firm's demand curve). long-run average real discount rate. W--- logarithm of the money wage. U = aggregate demand shock. 19= aggregate supply shock. g ~__
i =
X= y= Z
W
--
U).
logarithm of real output.
=
Bars over variables indicate full-equilibrium values. Dots over variables indicate time derivatives.
438
An Evaluation of Blinder's Alternative to Profit Sharing* Blinder has suggested that wages be partially tied to a firm's own price change, so that the key feature behind Weitzman's profit-sharing proposal might be created without the same need for fundamental institutional change. We examine whether this proposal for labor's remuneration yields the "better disequilibrium properties'" that Weitzman expects from this class of policies. Using a standard quadratic adjustment cost model, we find that a tax-based indexing incentive is equivalent to there being a decreased degree of wage flexibility. We then examine output variability within a conventional macro model, while trying to avoid the Lucas critique by continuing to use the underlying microeconomic analysis at that stage.
1. Introduction
Weitzman's recent work (1985) on the share economy has stimulated much research, and this work has followed two main avenues. One approach (for example, Cooper 1988) has been to consider the microeconomic basis for both share contracts and fixedwage contracts and to explore why decentralized agents might prefer one form of remuneration over the other. Cooper finds that welfare is improved with profit sharing only under rather special conditions. A second approach to profit sharing has been to evaluate Weitzman's claim that it would create a permanent excess demand for labor, and so lead to a lower "natural" unemployment rate. Blinder (1986) and Nordhaus (1988) have questioned the existence of this permanent effect, and Weitzman (1988) has acknowledged that certain theories of unemployment (for example, the efficiency wage hypothesis) would leave his theory with no such prediction. Weitzman's (1988) counter argument is that with hysteresis considerations, the "natural" rate is significantly dependent on the actual unemployment rate, and since profit sharing should lead to "better disequilibrium properties," there is still much to be said for profit sharing in a macroeconomic context. *I thank Gord Myers, Ben McCallum and two referees for helpful comments.
Journal of Macroeconomics, Summer 1992, Vol. 14, No. 3, pp. 417-438 Copyright © 1992 by Louisiana State University Press 0164-0704/92/$1.50
417
William Scarth Weitzman's conjecture opens up a third area of study: how are the built-in stability features of the macroeconomy affected by changes of this sort in labor's remuneration? To our knowledge, no such investigation of macroeconomic dynamics exists. Analysts have simply presumed that profit sharing involves increased wage flexibility and that this structural change has an ambiguous effect on built-in stability (see DeLong and Summers 1986 and others, whose work is discussed below). The purpose of this paper is to investigate the short-run adjustment properties of Alan Blinder's (1986) proposal for labor's remuneration that was intended as a convenient substitute for profit sharing. As just explained, it is the prospect of reduced transitional unemployment costs following alternative macroeconomic shocks that now represents both the main benefit that these remuneration proposals are intended to provide and the aspect of the proposals that has been least adequately researched. Before proceeding, it is useful to ask why the implications of alternative labor payment schemes for short-run macroeconomic dynamics have not been studied more fully at the formal level. The answer, I think, follows from the fact that short-run dynamics usually exist in models of involuntary unemployment because of some temporary wage stickiness, and the Lucas critique has made it quite unappealing to study macro models with no underlying microeconomic rationale for these sticky wages. How would a major institutional change affect the speed of wage adjustment? Since we are not even sure why sluggishly adjusting wages exist in the first place, how can anything beyond a purely mechanical macro analysis of short-run dynamics be accomplished? The way we avoid the full brunt of this concern in this paper is to examine Blinder's indexing proposal, which he views as an excellent substitute for profit sharing. By referring to the simple static theory of the firm, Blinder shows that his indexing scheme makes firms' marginal labor cost less than the wage, and this is the key feature which motivated Weitzman's original recommendation for p~rofit sharing. But since it is the prospect of preferred wage and price dynamics that is now claimed as the major motivation for these alternative remuneration schemes, our strategy is to examine Blinder's proposal from the point of view of a dynamic theory of the firm. Indeed, to ensure focus on the dynamic issue, we assume an exogenous natural rate of employment and output, so that the only role for the alternative wage adjustment scheme is that it might provide more desirable features for the short-run adjustment path 418
An Evaluation of Blinder's Alternative to Profit Sharing that is followed as the natural rate is approached. We specify an adjustment-cost model for wages and then investigate the efficacy of a tax incentive policy which induces firms to tie their wage payments at least partially to the changes in their own product price, just as Blinder suggests. The adjustment cost framework allows us to derive how the short-run wage and price dynamics are affected by the policy, and it is easier to do this explicitly for Blinder's proposal than for Weitzman's. We find that Blinder's indexing proposal makes the short-run Phillips curve flatter, not steeper, as Weitzman and others expect to be the result for profit sharing. Analysts may wish to take either of two interpretations of what our result might mean for profit sharing. If analysts continue to view Blinder's proposal as very similar to profit sharing, then they would be comfortable concluding that the implications of profit sharing for the speed of macroeconomic adjustment may be far from what many (such as Weitzman) have been presuming. However, the fact that we have shown that the tax-based indexing incentive makes the short-run Phillips curve flatter, not steeper, may convince analysts that Blinder's scheme and profit sharing have very different implications for dynamics, and so are quite different policies after all. Without examining a similar microeconomic derivation for profit sharing (which would be more difficult), we simply cannot know whether the common presumption that profit sharing steepens the short-run Phillips curve is correct. In any event, our further dynamic analysis of Blinder's proposal is of interest in its own right. The plan of the rest of the paper is as follows. In Section 2 we explain a microeconomic basis of partial wage adjustment, using a variant of McCallum's (1980) and Mussa's (1981) models. We add the tax incentive scheme to the model, and so derive how Blinder's indexing proposal affects the expectations-augmented Phillips curve relationship. In Section 3, we establish the short-run macroeconomic properties of the model. We examine how the policy insulates the short-run deviations of output from its full information value, from both permanent and temporary shocks to aggregate demand and supply. Concluding remarks are offered in Section 4.
2. Microeconomic Considerations McCallum (1980), and Mussa (1981) have constructed models of gradual price adjustment in which firms minimize a cost function which has two arguments. Firms incur costs whenever price is set 419
William Scarth at a level other than what would be appropriate if adjustment was complete. Firms also incur adjustment costs whenever prices are changed at a rate that differs from what is dictated by equilibrium considerations. Partial adjustment is the optimal response when firms must balance the costs of changing with the costs of not changing. Here we use this same reasoning, but apply the argument to the adjustment of money wages instead of prices (as in Scarth 1988).' For the wage-setting decision, firms are assumed to minimize
where w and w are the logarithms of the wage and that level of wages that would make employment equal its natural level. Further explanation of the natural rate is given below. While all notation is defined as it is introduced, a summary list of all variables also appears as an Appendix. The variable r is the long-run average discount rate which is taken to be a constant, t indicates time, and dots stand for time derivatives. The variable P is taken as a fundamental technology parameter; it specifies the relative size of the adjustment costs compared to the costs of being out of full equilibrium. p depends on the size of wage negotiation costs, and expression (1) involves the assumption that these negotiation costs increase whenever the actual rate of wage change differs from the equilibrium rate of wage change. Workers resist settlement whenever w is less than $, while firms resist settlement whenever w exceeds 6.Below we will add a third term to this cost functionone that specifies the tax payments that a firm incurs if a government policy exists which penalizes firms for not tying the rate of wage change to their own product price change. But first, we explain how an expectations-augmented Phillips curve follows &om this basic cost function. Only by using this as a base for comparison can we derive how the indexing proposal affects the aggregate supply aspects of the economy. Since w is not a decision variable for the individual firm, 'Our derivation follows Scarth (pages 15-20) rather closely, but we extend that discussion by including the tax-based indexing incentive in the basic objective function, and by being much more explicit on issues of market structure and aggregation.
A n Evaluation o f Blinder's Alternative to Profit Sharing
expression (1) is minimized by picking the optimal time path for w. The first-order condition is 2 -
-
(1/[3)x
=
0,
where x = w - tb. T h e characteristic equation for this dynamic rule is
kz - r k -
1/[3=0,
so the characteristic roots are: k,,kz = [r +-- (r ~ + 4/[3)0"5]/2.
(3)
The transversality condition requires that x be zero eventually (that is, that full adjustment must eventually occur). T h e dynamic process is stable only if the characteristic root is negative. Thus, the decision m a k e r must reject the positive square root possibility in (3), and the resulting wage a d j u s t m e n t process is ~ = - a x , or tb = tb + a ( ~ - w ) , where a = [ - r + (r ~ + 4/[3)°5]/2 > 0 .
(4)
W e wish to relate decision rule (4) to an expectations-augm e n t e d Phillips curve, but first we note that the partial adjustment parameter, a, d e p e n d s on the m a g n i t u d e of the adjustment costs. It is easy to verify that #a/a[3 < 0, so that the larger are the adj u s t m e n t costs relative to the costs that are incurred by being away from full equilibrium, the slower is the adjustment of m o n e y wages. This intuitively plausible relationship is exploited in our policy analysis below. A standard expectations-augmented Phillips curve which relates price changes to the o u t p u t gap is 2This first-order condition is derived by applying the standard rules of the calculus of variation: foH(')dt is minimized when Hx - DHo~ = 0, where here H = e-a[x ~ + 13(Dx)2]. Subscripts stand for partial derivatives and D is the time derivative operator. The transversality condition is lm~z(Ho,) ~ 0.
421
William Scarth = g +f(y
-
0).
(5)
This relationship can be derived from (4), if a production function (Equation [6] below), a definition of optimal price setting (Equation [7] below), and an aggregate demand function (Equation [8] below) are specified. We assume y = bn,
(b-1)n =w-p-q, y = ~bg + O(m - p) + OP.
(6) (7) (8)
The variables y, n, p, g and m stand for the logarithms of output, employment, the price level, autonomous spending, and the nominal money supply. As with wages, Ifi is that value of price that makes output equal its natural value, Y- Parameter b is a positive fraction, so the marginal product of labor (which is equated to the real wage in [7]) is positive but a negative function of employment. The variable q is a constant (which is explained below); since it does not vary, it turns out to be unimportant for our analysis. The variables ~b, 0 and t~ are positive aggregate demand parameters. Equation (8) is the reduced form of a standard aggregate demand specification, in which demand depends on expected (equals actual) inflation. Before explaining how Equations (4), (6), (7) and (8) can generate the standard expectations-augmented Phillips curve (that is, Equation [5]), we discuss both the monopolistically competitive environment and the separation of decisions, which are being assumed to keep the analysis manageable. Also, this discussion allows us to be explicit concerning aggregation. Each firm is a monopolistic competitor, and this is why both wage and selling price are choice variables. Firms face very different kinds of costs when adjusting wages, compared to those incurred when adjusting selling prices, and as a result, they separate these two decisions. We can think of there being two departments within each firm: the "labor relations" group which adjusts wages through time, and the "production/marketing" group which picks selling price, output and employment at each point in time. We have already described the wage-setting process above. To be more explicit, we could have included j subscripts throughout Equations (1) to (3), to stand for the individual (jth) firm's relationships. Then, for k firms overall, we define w 422
An Evaluation of Blinder's Alternative to Profit Sharing = (E~=, w~)/k and tb = (Z~=, ~bj)/k, which makes Equation (3) hold with aggregate variables (as it is written above). The segmenting of decisions is natural since we are following the textbook convention that selling prices and output levels can be changed costlessly at any point in time, while wages cannot. It is implicit in this kind of quadratic adjustment cost model for wages, that each firm faces prohibitive costs if wages are not set before each time period. As a monopolistic competitor, each firm assumes that it is small enough to ensure that other firms' decisions are not affected by its own. For price, output and employment decisions, each firm assumes that its share of overall output is an inverse function of its relative price and that this relationship involves a constant elasticity parameter, h:
rj/r Capital rithms), demand over all
=
(I-IJP) -h .
letters stand for the levels of variables (not their logaand 1-I1 is the firm's own price. Note that this individual function can be written in logarithmic terms and summed k firms:
yj=ky-h
lrj-kp
.
j=l
Given that we define aggregate output and employment as per-firm averages, y = Y-~=IyJk, and given the definition for overall price, p = E~=l ~rJk, this equation simply reproduces the definition of aggregate output. We see, then, that this definition of demand for each individual firm's output puts no constraint on how aggregate demand is determined. Thus, there is no inconsistency between this individual specification and the aggregate demand function specified earlier (Equation [8]). This implies, for example, that the demand elasticity at the individual firm level (parameter h) can be large (as it is when the industrial structure approaches perfect competition), while there need be no effect on the elasticity of overall market demand (parameter 0). For this set of decisions, each firm maximizes profits, IIIYj - WflVj, subject to several constraints: its Cobb-Douglas production function, Y1 = N~, the perceived demand function for its product, and the presumptions that the overall market price, P, and the level of industry output, Y, are given from outside. Wj has already been 423
William Scarth
set FIj, ing the
prior to this decision. Using the constraints to eliminate Yj and differentiating with respect to Nj, and re-expressing the resultfirst-order condition in natural logarithms (lower-case letters), decision rule for each firm is (b - 1)nj = wj - ~rj - q j ,
(7a)
w h e r e q) = ln[b + (1 - l / h ) ] . D e f i n i n g n =(Y.~=, n j ) / k , q = (Y~=t q j ) / k and w and p as before, Equation (7a) becomes (7). Since b and h are constant, the q term is constant, and so plays no role in our analysis. In full equilibrium, ~ the production function and labor-demand/price-setting relationships are 0 = bfi and (b - 1)fi = tb # - q; and assuming r~ = ~ = 0, the latter implies ~b =/~. Subtracting the full-equilibrium relationships from Equations (6) and (7), and substituting the results and tb = fi into partial adjustment rule (4), we have tb = fi + a{(~ - p) + [(b - 1 ) / b ] ( O - y)}.
(9)
To eliminate the (# - p) term from (9), we must formally define #. To do this, we use aggregate d e m a n d function (8), along with Equation (5), which is treated for the m o m e n t as a trial solution in which parameter f has yet to be interpreted in terms of the underlying structural parameters of the model. Substituting (5) into (8) to eliminate P, we have (1 - t~f)y = ~bg + O(m - p ) + ~ # - d~fij.
(lO)
In full equilibrium, 0 = d~g + 0(m - #) + t ~ ;
(11)
so by subtraction of (10) from (11) we have (#
-
p)
=
(1
-
~f)(y - 0)/0.
(12)
Also, the time derivative of (i1) implies p = (0/d~)(fi- rh), which 3The "natural" rates of output and employment oPten refer to what emerges in a full competitive equilibrium. Here 0 and h refer to the outcome of a monopolistically competitive equilibrium (as explained above). 424
An Evaluation o f Blinder's Alternative to Profit Sharing
represents an unstable process. To avoid this instability, ~ is assumed to "jump" to the value rh at all times. After taking the time derivative of (10), and using (5) to eliminate the resulting ~ term, we have -f0 0 - - 1-¢f
(v - o),
(13)
since we assume g = ff = rh = 0. The final step in the derivation of the Phillips curve is to eliminate the tb term in (9) by using the time derivative of (7). The time derivative of (6) and Equation (13) are also used to eliminate ri and #. The result is -
a(1 - t~f) 0
( v - 0) + , h .
(14)
Comparing (14) and the trial solution (5), we can identify summary parameter f in terms of the underlying structure: f = 1 / ( , + O/a).
(15)
Clearly, the steepness of the short-run Phillips curve (parameter f ) increases with the degree of wage flexibility (parameter a), but is is also a function of aggregate demand parameters 0 and dg. We have presented this version of the Mussa/McCallum partial adjustment model for two reasons: first, to show that the dependence of the steepness of the short-run Phillips curve on the degree of wage flexibility can be derived (not just assumed); and second, so that we have a clear theoretical basis within which to evaluate policies that are aimed at altering the existing wage settlement system. Before considering how the short-run Phillips curve is affected by Blinder's policy-induced indexing proposal, we note one other feature of this McCallum/Mussa adjustment cost model. Equations (13) and (15) imply = - a ( y - 0).
(16)
Thus, despite the dependence of the short-run Phillips curve's slope on aggregate demand parameters, the speed with which output deviations are eliminated is not dependent on these coefficients. These aggregate demand parameters are important for determining the size 425
William Scarth
of initial output disturbances (as we see below), but only the speed of wage adjustment is important for the speed of adjustment of all endogenous variables. Now we consider how this theory of short-run wage, price and output adjustment is affected by a government policy which makes it costly for firms not to link their wage adjustments at least partially to changes in their o w n product price (that is by Blinder's indexing proposal). A policy in which each firm is penalized for not having its wage adjustment contingent on its own price adjustment would add a third element in the firm's quadratic cost function. With this policy, firms would minimize: fo~ [(wj - co) z + f3(tbj - tb) 2 + a ( t b / - 4rj)2]e-adt ,
where (as before) arj is the logarithm of the individual firm's o w n price. We now re-express this objective function, so that the importance of ct > 0 for short-run wage, price and output dynamics becomes apparent. First, from the individual versions of Equations (6) and (7a), we have 4rj = tbj + (1 - b)Oj/b (since t~ = 0). But before this relationship can be used to eliminate 4rj from the objective function, we must also use the expression for the change in the individual firm's own level of output--an item which cannot be taken as exogenous to this decision-making process. We have already assumed that each individual firm's share of total output is negatively related to the difference between its price and the going market price; that is, = y - h(=j-
(17)
p).
After substituting the time derivative of (17) into the ~j equation, and the result into the objective function to eliminate 4rj, we see that the new term in the cost function is ct[~/(tb/- 16) + S0], where ~/ --- h(1 - b ) / [ b + h(1 - b)], and ~ = (1 - b ) / [ b + h(1 - b)]. We can now proceed by analogy from before, since p, the logarithm of the overall price level, and y are not decision variables of the individual firm. The revised first-order condition for firms who face this tax-based indexing incentive is -
-
[1/(6
+ =
426
-
rz)
-
av
(0 -
+
(18)
A n Evaluation o f Blinder's Alternative to Profit Sharing
where z = ( I b - 1~). By comparing decision rules (2) and (18), we can derive how the wage adjustment process would be affected by this policy. Without the tax-based indexing incentive, the decision rule was a homogeneous second-order differential equation, while with the policy, the behavioral rule is a non-homogeneous equation of the same order. The complete solution of the latter involves a complementary function and a particular integral, and the complementary function is not affected by the presence of the time-dependent z and y terms. 4 Thus, the characteristic roots are now given by: hi, X2 = {r + [r ~ + 4/(13 + ct~/z)]°5}/2 •
(19)
As before, the transversality condition dictates that the negative square root be selected in (19). We see that the presence of the tax-based indexing incentive is equivalent to the adjustment cost parameter, 13, being larger. (Wherever 13 appeared before, (13 + a~/~) now appears.) Thus, this policy makes the short-run Phillips curve flatter, and it makes macroeconomic adjustment speed (as given by parameter a) slower. The basic intuition behind this result is that an increased degree of indexing makes the real wage more rigid. Since a return of real output to its natural value requires an adjustment in the real wage, indexing makes that adjustment more protracted. But before establishing the macroeconomic significance of this effect in the next section, we consider the complete solution of Equation (18). We have already shown that Ib = 19 = rh, so z can be reinterpreted as (16- lfi). Then, using (12), its time derivative, and (16) with !¢ = 0, we have ~ = - a z , and z = (1 - ~sf)!)/O. T h e time derivative of this last relationship and (16) yield: ~ = (1 - t~f)#/O and !7 = -a!). These two relationships and ~ = - a z can be used to simplify the right-hand side of Equation (18) to a~/(a - r)[50/(1 - t~f) - ~1]z/(13 + a~l~). The complete solution for (18) is then x = Ale ~t + A2e ~t + B z ,
and we must solve for the undetermined coefficients A~, Az and B. We have already established that one of the As (say A1) must be set to zero (given the transversality requirement of stability), so the solution is x = Aze ~t + Bz. When t = O, xo = A~ + Bzo, so x 4See Chiang (1984, 541). 427
William Scarth = (Xo -
Bzo)e xt + B z . Taking the time derivative of this solution,
we have .~= h ( x -
B z ) + B ~ = hx + B(~ - h z ) .
(20)
Equations (20) can be i n t e r p r e t e d as follows. In a linear e c o n o m i c model, the speed of a d j u s t m e n t for all e n d o g e n o u s variables must be the same, and we have verified this indirectly above by noting that i = - a x and ~ = - a z . W h e n both of these laws of motion are substituted into (20), it b e c o m e s (k + a)(x - B z ) = 0. Since B is not zero, ~ and since x and z are only zero in full equilibrium, this condition can hold at all times only if a = - k . This result verifies that the discussion following Equation (19) was fully appropriate. W e have now established what the standard m i c r o e c o n o m i c theory of quadratic a d j u s t m e n t costs implies for the tax-based indexing incentive. Blinder's proposal, which was i n t r o d u c e d as a substitute for Weitzman's call for profit sharing that is easier to i m p l e m e n t , makes the short-run Phillips curve flatter, and it makes the s p e e d of macroeconomic a d j u s t m e n t slower. In the next section, we investigate how the short-run deviations of o u t p u t (that follow from both perm a n e n t and t e m p o r a r y shocks) are affected b y t h e s e s t r u c t u r a l changes. In this way, we d e t e r m i n e w h e t h e r this p r o p o s e d change in labor's r e m u n e r a t i o n does or does not lead to " b e t t e r disequilibrium p r o p e r t i e s . " As n o t e d in the introduction, readers who are only i n t e r e s t e d in Weitzman's proposal p e r se may be t e m p t e d to stop reading at this point. If they are convinced (without formal analysis) that profit sharing must involve a s t e e p e r short-run Phillips curve, t h e n t h e y will now see that Blinder's tax-based incentive for indexation is n o t a substitute for profit sharing, and is instead a v e r y different policy as far as its dynamic implications are c o n c e r n e d . If their priors are (like Weitzman's) that profit sharing would involve " b e t t e r disequilibrium p r o p e r t i e s , " and t h e y now see Blinder's proposal as having the opposite effect on the slope of the short-run Phillips curve, t h e n this p a p e r could b e i n t e r p r e t e d as a basis for rejecting Blinder's suggestion. H o w e v e r , we regard this reaction as p r e m a t u r e , for the 5While it is not necessary for our analysis, B is solved by using the trial solution for the partieular integral: x = Bz. We substitute this trial solution and its time derivatives (i = -aBz and ~ = a~Bz) into the left-hand side of (18), equate the result to a~/(r + a)[80/(1 - t~f) - ~l]z/(~ + a~/z), and solve for B. 428
An Evaluation of Blinder's Alternative to Profit Sharing simple reason that increased wage flexibility may be "bad," not "good," for macroeconomic built-in stability. Before a judgement is made on this supplementary issue, we cannot come to a complete evaluation of whether Blinder's indexing proposal involves "better disequilibrium properties" (let alone come to any opinion on the short-run dynamic implications of profit sharing, which is not examined here). The reason that an increased degree of wage and price flexibility can accentuate short-run real output deviations about the natural rate can be appreciated by considering the following example. When there is an exogenous decrease in aggregate demand, the overall reduction in output in the short run is determined in part by the size of a secondary (or induced) decrease in demand. Rational agents know that a fall-off in demand causes a temporary recession, and that this in turn lowers the rate of price change. Agents react to this decrease in expected inflation by cutting that part of aggregate demand that is sensitive to variations in expected inflation by this "secondary" amount. But if the short-run Phillips curve is steeper, rational agents involve this fact in their forecast for lower inflation. For any given size of temporary recession that is caused by the "primary" shock to aggregate demand, the reduction in expected inflation is now larger, so the "'secondary" reduction in aggregate demand is also larger. The net effect is that, with a steeper short-run Phillips curve, aggregate demand shocks cause bigger initial output deviations, even if these temporary disturbances are eliminated more quickly. So it is not at all obvious that a steeper short-run Phillips curve means "better disequilibrium properties"; more analysis is required to establish whether our resuits to this point support or reject Blinder's tax-based incentive for indexation.
3. Macroeconomic Implications Much recent research has explored the macroeconomic implications of increased wage flexibility. D e I ~ n g and Summers (1986) and others 6 have found that increased wage flexibility can cause ambiguous effects on the asymptotic variance of output, in models involving inflationary expectations effects on aggregate demand and rational expectations. The intuition behind this possibility was given 6For example, see Ambler and Phaneuf (1989), Driskill and Sheffrin (1986) and King (1988). 429
William Scarth in the previous paragraph. Since we have established that Blinder's indexing scheme is equivalent to a decreased degree of wage flexibility, it too must have ambiguous effects on output variability. Without any further analysis, then, we know that this proposal involves preferred disequilibrium properties only for a particular range of parameter values. But rather than leaving the matter with this general acknowledgement of ambiguity, we now present a formal analysis of the output effects of decreased wage flexibility. This further analysis is needed for two reasons. First, the existing literature (see footnote 6) focuses on temporary shocks, and we wish to extend the analysis to permanent disturbances. Second, most of the existing literature involves Taylor's (1979b) overlapping multi-period wage contracts instead of the Mussa/McCallum quadratic adjustment cost model, upon which we relied in the last section. Thus, we offer a sensitivity test for the existing empirical analysis, which involves inserting plausible macro parameter values into the formulae for output variance. Since our framework involves agents re-optimizing in the face of the wage-flexibility incentive policy (and the Taylor set up does not permit this re-derivation), this sensitivity test could be of rather general interest. The macro model which we examine is now summarized: 7 y = +g + 0(m - p) + ~ ,
(8)
13 = f ( y - O) + rh,
(6b)
f = 1/(¢ + O/a).
(15)
On the basis of the previous section, the profit-sharing/indexing proposals are viewed as schemes which lower parameter a, and so lower parameter f. First we consider once-for-all changes in the exogenous variables. There are no lasting effects on output, since it is pegged at its natural value, 0, in the long run. But short-run output effects exist, and these can be examined by substituting (6b) into (8) to eliminate ~, and differentiating:
rFor simplicity it is assumed that any tax revenue generated by the indexingincentive policy is redistributed to the private sector in a lump-sum manner, so no other demand or supply-side effects follow from the policy.
430
An Evaluation o f Blinder's Alternative to Profit Sharing dy -
-
d~ =
dg
-
-
dy 0
,
1-,f
dy -
-
1 - t~f
t~ -
drh
0 -
dm
>
dy >0,
-
-
1-,f -t~f - - -
do
>0,
<0.
(21)
1 - t~f
The signs for the multipliers given in (21) involve the assumption that (1 - ~f) > 0. This is the model's stability condition, since from Equation (6b) stability requires dTJ/dp = f ( d y / d p ) < O, and from the output reduced form d y / d p = - 0 / ( 1 - ~f). By using restriction (15) on summary parameter f, the reader can readily verify that the stability condition cannot be violated. The absolute value of all the multipliers in (21) is smaller, the lower is parameter f. This means that Blinder's indexing proposal makes output less sensitive to these permanent shocks. For example, the magnitude of the temporary recession that follows a drop in autonomous expenditure, a drop in the money growth rate, or an increase in productivity, is smaller if this tax-based indexing scheme exists. Other things equal, these results support the policy suggestion. However, while the policy makes the size of these initial recessions smaller, it makes the recessions last longer. This is because the speed with which output deviations are eliminated is given by parameter a (see Equation [16]), and a is reduced by the existence of the policy. Thus, the policy involves a trade-off in terms of its ability to insulate output from once-for-all disturbances--smaller initial output effects, but effects which are eliminated more slowly. Buiter and Miller (1985) have suggested one measure that can be used to have a single indicator of economic loss in circumstances that involve a trade-off such as this: they suggest calculating the undiscounted cumulative net output loss incurred as a result of any permanent shock. They show that this cumulative loss is simply equal to the deviation of output from its natural value during the impact period divided by the speed of output adjustment. 8 After division of the impact multipliers in (21) by the adjustment speed, a, and after simplification based on the microeconomic underpinnings inherent in using (15), the cumulative loss expressions are
8See
-
Buiter and Miller (1985, 23). ~ (y, - fh)dt = (Y,o - O)/a when y(x, t)
0(~, t) = (Y,o-
0,o) e-°"-'~.
431
William Scarth Loss = d~(qJ + O/a)/O
for autonomous expenditure (g) shocks,
Loss = ~(~ + O/a)/O
for monetary growth (rh) shocks,
Loss = (~ + O/a)
for money stock (m) shocks,
Loss = (qJ + O/a)/O
for productivity (9) shocks.9
(22)
The important result to emerge from (22) is that all cumulative output loss calculations are higher if the tax-based indexing incentive policy is involved (if a is smaller), so the analysis does not support the idea that such schemes lead to "'preferred disequilibrium properties." Two important features of this conclusion merit emphasis. The first concerns the Lucas critique. In our a t t e m p t to keep the analysis free of this critique, we have based our work on a specific microeconomic underpinning. This involved the adjustm e n t cost technology being specified as a "primitive" parameter, but the slope of the short-run Phillips curve not being primitive. The relationship between these two parameters was derived and summarized in Equation (15). The results in (22) rely on (15), but it is left for the reader to verify that if restriction (15) is not used, our definite results on cumulative output loss still emerge. Indeed, this is true for all results reported in the remainder of the paper. Thus, the reader does not need to embrace the specific M u s s a / McCallum underpinnings to have interest in our analysis; we have included it simply so that some degree of i m m u n i t y from the Lucas critique can be claimed for the results. The second point worth emphasizing is that this lack of support for Blinder's indexing proposal cannot be derived on a priori considerations alone, if we allow for discounting in the output loss calculations. Without discounting, we are simply adding up the area between the output time path and the time axis: fo(Yo - t))e -Utdt. With discounting at a constant rate, r, we measure fo[(y0 y)e-Ut]e -'~dt = fo(yo - f~)e -(~+ r)tdt, so we must divide the impact multipliers by (a + r), not just by a. Taking autonomous expenditure shocks as the example, the revised (discounted) cumulative loss expression is d~(at~ + O)/O(a + r). The reader can readily verify that w h e n this expression is differentiated with respect to a, losses are smaller if the tax-based indexing incentive is involved (if -
9In the case of productivity shocks, d(y - O)dfl = dy/dO - 1 = -1/(1 - qJf) is the impact effect which is divided by a to get the cumulative output loss. 432
An Evaluation
of Blinder's Alternative
to P r o f i t S h a r i n g
a is smaller) i f f r > 0/$. This same condition holds for all four kinds of shocks, and whether or not restriction (15) is utilized, Clearly, if the discount rate is high enough, the favorable effect of the policy on the impact multiplier can dominate the unfavorable effect of the policy on the speed of adjustment. We can have some idea whether this condition might be satisfied by considering the representative values for 0 and $ that were used by DeLong and Summers (1986). They specify an expectations-augmented IS-LM model of aggregate demand: y = - c l i and i = c2y - c3(m - p ) - ~. When the real interest rate, i, is eliminated by substitution, we see that 0 and t~ have the following structural interpretations: 0 = c a c J c 4 , and = c l / c 4 , where c4 = 1 + CLC2. DeLong and Summers consider values of ca ranging from 1 to 3, and they set" c2 equal to c3, and consider parameter values between 0.2 and 0.6. These representative values (which are plausible if the length of each time period is one year) are referred to in the stochastic analysis below. Here we simply note that 0/~ = c3, so the condition required for the discounted output losses following permanent shocks to be made smaller by the policy is that the social discount rate be greater than a number in the range of 20% to 60%. Most analysts would not be comfortable with such a high discount rate, so overall, our analysis of permanent shocks does not support the tax-based indexing policy. We now consider temporary disturbances by analyzing a stochastic discrete-time version of the model: y, = O(m, - p,) + t ~ [ E t ( p , + l ) - p , ] + u , ,
(23)
P, - p,-, = E t - a ( ~ t ) - 15t-~ + a(13,_, - Pt-a) ;
(24)
0, = 0 + v, = v , .
(25)
The variables u and v are aggregate demand and supply shocks which we assume have zero means, constant variances (¢r2, and cro2), and they involve no serial or cross correlation. McCallum (1980) has analyzed this model, and has focused on the deviations of output from its fidl information value, 0t = Yt - 0t. By following McCallum's use of the undetermined coefficient solution method, the reader can verify that the asymptotic variance of the output deviations is = ct.
. +
433
William Scarth
where
1
[0 + d~a] 2 "
This variance result indicates that the tax-based indexing proposal involves a trade-off in the face of temporary shocks as well. A lower value of parameter a increases the first term in square brackets in the definition of C (the persistence effect), but it lowers the second term in square brackets in the definition of C (the initial disturbance effect). To know the net effect on asymptotic variance of the tax-based indexing proposal, we must determine the overall sign of d C / d a . This dependence is given by dC
da
2(0 + Oa)[Oa - 0(1 - a)] (0 + qJ)s[1 - (1 a)~] z -
The profit-sharing/indexing schemes receive support from this stochastic analysis only if d C / d a > 0. This condition requires ~a > 0(1 - a ) .
(26)
To decide the likelihood that condition (26) is satisfied, we can utilize the plausible parameter values for 0 and dg used by DeLong and Summers (that were discussed above). But to obtain a representative value for the pre-policy value of the adjustment cost parameter a, we must rely on estimated values for the slope of the short-run Phillips curve. McCallum (1980) has shown that the analogue of restriction (15) for this discrete-time specification is f = a/(O + d~), where f is the coefficient on the lagged output gap in t h e i n f l a t i o n e q u a t i o n [Pt - Pt-1 =f(Yt-1 - 0,-1) + E,-I(/~,) - /~t-1]- When this relationship between f and a is substituted into condition (26), it becomes f > 0/(0 + t~)2 . Using the condition Summers condition 434
(27)
IS-LM interpretation of 0 and ~b that was explained above, (27) simplifies to f > cac4/cx(1 + c3)~. Using the D e L o n g / values for these parameters, the alternative versions of (27) are presented in Table 1.
An Evaluation of Blinder's Alternative to Profit Sharing The Condition Required for Policy to Decrease Output Variance for Alternative Aggregate Demand Parameters
T A B L E 1.
Condition f> f > f> f>
0.17 0.07 0.22 0.33
P a r a m e t e r Values cl cl cx c~
= = = =
1 3 3 1
, , , ,
c~ c2 c2 c2
= = = =
c3 c3 c3 c3
= = = =
0.2 . 0.2 . 0.6 . 0.6.
Taylor (1979a) has e s t i m a t e d t h e slope of t h e s h o r t - r u n Phillips curve to b e 0.28 (on an annual basis), and m o s t o t h e r e s t i m a t e s are in this r a n g e or lower. Thus, to h a v e s o m e feel for w h e t h e r condition (27) is m e t , w e can c o m p a r e a value o f f = 0.28 to the critical levels in T a b l e 1. W e see that o u r r a n g e of u n c e r t a i n t y on t h e coefficients is such that we c a n n o t say with any assurance that the taxbased indexing incentive lowers o u t p u t variability, b u t it certainly could do so. ~° O u r analysis of t e m p o r a r y shocks gives only qualified s u p p o r t for Blinder's policy suggestion. W h e n this conclusion is c o m b i n e d with o u r earlier analysis of p e r m a n e n t shocks, w h i c h s h o w e d that u n d i s c o u n t e d c u m u l a t i v e o u t p u t losses are necessarily i n c r e a s e d b y the policy, the s a m e verdict r e m a i n s - - o u r analysis gives t h e policy only limited support.
4. Conclusions W e can s u m m a r i z e the p a p e r v e r y simply. A standard microeconomic m o d e l o f quadratic a d j u s t m e n t costs s h o w e d that Blinder's proposal for labor's r e m u n e r a t i o n receives s u p p o r t f r o m o u r analysis only ff decreased wage flexibility leads to l o w e r o u t p u t variability. But a l o w e r d e g r e e of w a g e flexibility involves a trade-off: it m a k e s impact effects on o u t p u t smaller, while m a k i n g those o u t p u t deviations b e e l i m i n a t e d m o r e slowly. To evaluate this trade-off, w e h a v e considered two s u m m a r y m e a s u r e s of o u t p u t variability. First, considering p e r m a n e n t changes in t h e exogenous variables, w e d e r i v e d ~°It is reassuring that the general nature of our results (which are based on the adjustment cost model) are consistent with studies based on Taylor-type overlapping contracts. For example, DeLong and Summers found that increased price flexibility could only be bad if the short-run Phillips curve is fairly steep. Here, the policy (which is equivalent to decreased price flexibility) is only good if the short-run Phillips curve is steep. 435
William Scarth some results that required only qualitative assumptions: the cumulative undiscounted output loss from permanent changes in any of the exogenous variables is greater if the tax-based indexing incentive policy exists. Second, considering discounted output losses following permanent disturbances and temporary changes in both demand and supply shocks, we derived that quantitative assumptions are required to evaluate the policy's effectiveness. Even when representative parameter values were considered, firm conclusions could not be reached, although in the case of permanent shocks, the results were pretty solidly against the policy. Our overall conclusion is that the analysis provides only limited support for the tax-based indexing incentive policy. Of course our model is highly aggregative, so we do not pretend that it could represent a final word on the subject. Also, we have only examined whether policies of this sort do or do not lead to "better disequilibrium properties." We have assumed that the policy has no effect on the natural rate of employment (so we are not trying to evaluate any potential for a "permanent" excess demand for labor), and we have not considered whether similar results concerning transitional output losses follow from profit sharing. Nevertheless, our results have some novelty. Contrary to Blinder's expectations, our dynamic analysis suggests that his indexing proposal may not be a close substitute for profit sharing. And our analysis is entirely conventional--involving the standard rational expectations aggregate demand/supply model. Also, we have made a significant effort to test the robustness of our conclusions by working through the analysis both with and without reliance on a specific and standard microeconomic rationale for sticky wages, so that our evaluation of the tax-based indexation policy is not wide open to the Lucas critique. As a result, we view the analysis as a useful stepping-stone toward a better understanding of recent thought-provoking proposals for labor's remuneration. Received: July 1989 Final version: September 1991
References Ambler, Steve, and Louis Phaneuf. "The Stabilizing Effects of Price Flexibility in Contract-Based Models." Journal of Macroeconomics 11 (Spring 1939): 233-46. Blinder, Alan. "Comment." NBER Macroeconomics Annual 1 (1986): 335-43. 436
An Evaluation of Blinder's Alternative to Profit Sharing Buiter, William, and Marcus Miller. "Costs and Benefits of an AntiInflationary Policy: Questions and Issues." In Inflation and Unemployment: Theory, Experience and Policy-Making, edited by Victor Argy and John Neville. London: George Allen and Unwin, 1985. Chiang, Alpha. Fundamental Methods of Mathematical Economics. 3d ed. New York: McGraw-Hill, 1984. Cooper, Russell. "Will Share Contracts Increase Economic Welfare?" The American Economic Review 78 (March 1988): 13854. DeLong, Bradford, and Lawrence H. Summers. "Is Increased Price Flexibility Stabilizing?" The American Economic Review 76 (December 1986): 1031-44. Driskill, Robert, and Steven Sheffrin. "Is Price Flexibility Destabilizing?" The American Economic Review 76 (September 1986): 802-7. King, Stephen. "Is Increased Price Flexibility Stabilizing? Comment." The American Economic Review 78 (March 1988): 26772. McCallum, Bennett. "Rational Expectations and Macroeconomic Stabilization Policy: An Overview." Journal of Money, Credit, and Banking 12, part 2 (November 1980): 716-46. Mussa, Michael. "Sticky Prices and Disequilibrium Adjustment in a Rational Model of the Inflationary Process." The American Economic Review 71 (December 1981) 1020-27. Nordhaus, William. "Can The Share Economy Conquer Stagflation?" Quarterly Journal of Economics 96 (February 1988): 20117. Scarth, William• Macroeconomics: An Introduction to Advanced Methods. Toronto: Harcourt, Brace Jovanovich, 1988. Taylor, John. "Estimation and Control of a Macroeconomic Model with Rational Expectations." Econometrica 47 (September 1979a): 1267-86. • "Staggered Wage Setting in a Macro Model." The American Economic Review Papers and Proceedings 69 (May 1979b): 108-13. Weitzman, Martin• "The Simple Macroeconomics of Profit Sharing." The American Economic Review 75 (December 1985): 93753. • "'Comment on "Can The Share Economy Conquer StagflationT' "" Quarterly Journal of Economics 96 (February 1988): 21923. 437
William Scarth
Appendix List of Variables
logarithm of real autonomous expenditure. short-term real interest rate. j = index for denoting an individual firm. k = number of firms. m = logarithm of nominal money supply. n = logarithm of employment level. p = logarithm of the average price of goods. ~rj = logarithm of firm j's price. q = intercept in labor demand function (equals ln[b + (1 - 1/ h)] and so depends on the production function exponent and the elasticity of each individual firm's demand curve). long-run average real discount rate. W--- logarithm of the money wage. U = aggregate demand shock. 19= aggregate supply shock. g ~__
i =
X= y= Z
W
--
U).
logarithm of real output.
=
Bars over variables indicate full-equilibrium values. Dots over variables indicate time derivatives.
438