Wage stickiness and the non-neutrality of money

Journal of Monetary Economics 20 (1987) 25-50. North-Holland

WAGE STICKINESS

AND THE NON-NEUTRUITY A Cross-Industry Analysis *

OF MONEY

Shaghil AHMED Pennsylvania

State University,

University

Park,

PA 16802,

USA

The paper provides an empirical test of sticky wage models of business fluctuations by focusing on industry level cross-sectional implications that emerge. This breaks the observational equivalence, existing at the aggregate level, between rational expectations, long-term contracting and imperfect information models. The specific implication tested is whether output responses to nominal disturbances (industry Phillips Curve slopes) are inversely related to wage indexation elasticities. The Phillips Curve slopes are found to vary across industries for the Canadian economy, but bear no relationship to indexation elasticities, casting doubt on the role of nominal wage rigidity in generating the observed non-neutrality of money.

1. Introduction An important and popular class of rational expectations macroeconomic models of the variety of Fischer (1977a), Gray (1976) and Taylor (1980) emphasizes the stickiness of nominal wages in generating the observed positive correlation between money and output. Many economists invoke some version of these theories to justify Keynesian style policy implications. This paper provides a direct empirical test of such ty-pe of models by focusing on key industry level cross-sectional implications that emerge. The strategy followed is to test whether industry output responses to exogenous changes bear a systematic relationship with variations in contract characteristics across industries. The source of the exogenous change in this study is a nominal demand disturbance and the contract characteristic highlighted is the degree of indexation of wages to the general price level. * This research is partly supported by a grant from the Sub-Committee on Monetary Research of the social Science Research Council. Special thanks are due to Robert Ring and Peter Garber for their continuous guidance and encouragement during the course of this study. I am also grateful to Robert Barro, Charles Plosser, Alan Stockman, John Taylor, Jeff Wrase, an anonymous referee of this journal as well as seminar participants at Brown, Federal Reserve Bank of Richmond and Western Ontario, including Marvin Goodfriend, Jeremy Greenwood, Herschel Grossman, and Robert Hetzel for helpful comments on earlier versions. Finally, I am indebted to David Card for generous permission to use his data All remaining errors (except for white noise) are solely my own responsibility. 0304-3932/87/$3.5001987,

Elsevier Science Publishers B.V. (North-Holland)

26

S. Ahmeci,

Wage stickiness

and the non-neutraliv

of money

Focusing on these cross-sectional implications is one method of breaking the observational equivalence that exists - at the aggregate level - between long-term contracting models and an alternative class of rational expectations theories of business fluctuations. Both the sticky wage explanation mentioned above and the equilibrium imperfect information models with some source of persistence, exemplified by Lucas (1975) and Barro (1976), predict that current and lagged unanticipated nominal demand changes will have a larger impact on output than anticipated ones. Thus Barro’s (1981a) results on the effects of unanticipated money on economic activity are consistent with either model. This observational equivalence problem is discussed by Fischer (1980), who argues that the explanation based on wage rigidity of Barro’s results is more plausible than any other interpretation. In a recent study, Grossman and Haraf (1985) argue that the observational equivalence problem does not arise if all contracts are synchronized - and hence of equal length - and if their duration is greater than one period. With such contracts, certain testable lag patterns emerge in the response of aggregate output to nominal shocks. The authors implement this model empirically for the Japanese economy, and End some support for the contracts explanation, but their model is developed under certain restrictive assumptions about the behavior of target output over time. The present study can be regarded as breaking the observational equivalence even in an environment of overlapping contracts, and providing new evidence on the importance of wage stickiness in generating the non-neutrality of money. The importance of distinguishing between the two kinds of models described above for both positive and normative purposes is well known. First the economic mechanism which is operative is quite different in each model. In Fischer-Gray type theories, it is central that the nominal wage is locked in for a time due to the existence of implicit or explicit labor contracts. Then, following an unanticipated rise in nominal demand which causes an unanticipated price level increase, the real wage will be bid down. Consequently, since labor quantities in such models are typically determined by demand, there is short-run non-neutrality of money with a positive association between unanticipated nominal aggregate demand, prices, employment and output. By contrast, in the Lucas-Barr0 models, information confusion is central to the real effects of nominal disturbances. Imperfect information about aggregate variables leads agents to mistakenly, but rationally, perceive nominal disturbances as partly relative in character. This also leads to a positive association between unanticipated nominal demand, prices, employment and output. Second, the models have substantially different implications for policy. In the Fischer-Gray type models, activist monetary policy can be stabilizing, provided the monetary authority can react at intervals which are shorter than those at which contracts are renegotiated. But, in the Lucas-Barr0 type models, policy irrelevance results of the Sargent and Wallace (1975) variety

S. Ahmed,

Wage stickiness

and the non-neu:rality

of money

21

typically hold, if private agents have the same information set as the govemment which consists only of lagged values of variables1 The theoretical framework used in this paper begins with a simple extension of Fischer’s (1977a) two-period overlapping contracts model that allows for different industries, as well as partial ex post indexation of nominal wages to inflation that was not anticipated at the signing of the contracts. The aggregate output and price level solutions for such a model are then shown to be observationally equivalent, in general, to the solutions that are obtained from a simple imperfect information model with some unspecified source of persistence. However, the models can be distinguished at the industry level with the main result emerging from the contracts model being that labor quantities - and hence outputs - are less responsive to changes in unanticipated nominal aggregate demand, the higher is the degree of indexation of wages to the general price level. With substantial cross-industry variations in indexation provisions, this implication is testable and forms the main focus of this study. The empirical evidence focuses on nineteen Canadian manufacturing industries, using data over 1961-1974, which are chosen because Card (1980) reports widely varying average indexation elasticities for these industries. In first-stage time-series regressions, substantial variations across industries in the effects of unanticipated nominal disturbances on total hours worked (industry Phillips Curve slopes) are found. However, a second-stage cross-section regression shows no systematic relationship between these Phillips Curve slopes and indexation intensities. These results are sharply at variance with the predictions of sticky wage explanations of business fluctuations. The balance of this paper is divided into four sections. Section 2 presents variants of each model which help to demonstrate observational equivalence at the aggregate level and show how the two models can be distinguished at the industry level. Section 3 discusses the implications of endogenizing the degree of wage indexation, and section 4 presents the empirical strategy followed and the results obtained. Finally, section 5 offers a summary and some concluding remarks. 2. Examples of theoretical models This section develops two simple models of money-induced business fluctuations, one being a version of Fischer (1977a) and the other being a variant of Lucas (1975). These examples help to illustrate observational equivalence at the aggregate level and to show how the models can be distinguished at the ‘If there is differential partial current information across industries the policy irrelevance proposition breaks down as demonstrated by King (1980) and Weiss (1980). However, in such models it is not clear that active feedback policy would be desirable. It seems to depend on the source of the differential information. For example, King and Weiss reach opposite conclusions on this issue.

28

S. Ahmeri,

Wage stickiness

and the non-neutrality

of money

industry level. The contracts model is then used to derive the explicit irnplicai tion to be tested in this paper, although, as discussed later, the applicability of the empirical results is not restricted to the particular variant of the model presented here. 2.1. The demand side

Consider a simple islands framework, where the islands should ed as different industries. The demand side is identical for the two the demand functions being stochastic versions of ones in which nominal money balances spent on a particular good is constant. yt.= m,-

ptj + Aj + Etj9

be interpretmodels with the share of Specifically,

0)

where y$ and P,j are respectively the log of output demanded and price of the jth industry’s good at time t, m, is the log of nominal money balances at time I, and Xj is a fixed parameter. exp(Xj) can be interpreted as the normal share of money balances going to good j. The actual share is exp(qj) . exp(Xj), where ey is a N(0, uf) relative demand shock with cjeri = 0. 2.2. Money supply process

For illustrative purposes the source of unanticipated changes in aggregate nominal demand used in the theory are monetary disturbances, which are modelled by the following specification for money supply: m,= m,-1 + bZ,-, + u,,

(2)

where m, is the log of nominal money balances at time t, Z,-, is the vector of exogenous variables whose values are known at t - 1, b is the vector of fixed coefficients chosen by the monetary authority, and u, is a N(0, u,‘) aggregate shock, hereafter referred to as the monetary shock. The process governing the behavior of Z, for simplicity is assumed to be Z,=dZ,.sl+u,,

(3)

where u, is a white noise disturbance term. Next consider two formulations of industry and aggregate outputs and prices derived by using alternative supply specifications. 2.3. A simple contracts model

Consider the Fischer supply function given by

(4

S. Ahmed,

Wage

stickiness

and the non-neutrality

of money

29

where J$ P,j and W,j are respectively the log of output supplied, log of price and log of nominal wage for the jth industry at time t, and (Y,/3 are fixed parameters with p > 0. This supply behavior embodies the notion that employment is demand determined and, therefore, chosen so that the value of the marginal product of labor is equal to the nominal wage. The essential feature of contracts models is that W,j is locked-in in the short run due to the existence of explicit or implicit labor contracts. Assume, following Fischer, that contracts are of two-period duration and overlap such that, at any particular time, half the fhms in an industry are operating under contracts signed one period ago and the other half under those signed two periods ago. Specifically, in our model, the contractually fixed nominal wage at time t of those industry j firms which signed contracts at time t - i is assumed to be given by i=1,2,

,-iw,j=E,-iP,+Yj(P,-E,_iP,),

(5)

where E,-iP, refers to the rationally expected value of the log of the aggregate price level, P,, and yj is the degree of indexation. With an appropriate normalization, the above specification implies that wages are prespecsed to equal the level that clears markets in the expected value sense, plus a contingent cost of living adjustment - represented by the elasticity vi- which may differ across industries. The objections to using arbitrary contracts of the type represented by (5) are well known. Barro (1977) argues that such contracts are inefficient, since efficient contracts would specify an employment rule as well, where employment would not respond to perceived nominal demand changes. The stance taken here on this issue is that of Fischer (1977b), who notes that the kind of contracts focused on should be those that exist in the real world, which is reasonable for empirical work employing contract data. To show that (5) is not grossly at variance with actually observed wage setting behavior, consider the following equation obtained from (5) with i = 1: r-1Wtj-t-3F-1,

j=

(l-

Yj)(Et-lPt-

Et~3Pt-l)

This divides the percentage change in the nominal wage at the signing of new contracts into two components, the tist being prespecitied non-contingent increases and the second representing contingent escalator clauses, which typically are two important elements of observed contracts, at least for the Canadian economy. Wtj = $( l-lWtj + ,-,W,j), the industry average nominal

B

30

S. Ahmed,

wage, is given by

Wage stickiness

and the non-neutrality

o/money

.

W;j= :E;-,P;+

:E;-,P;+

$Yj(P;-

E;-,P;)

+ iyj(p;-

E;-,P;)* (7)

2.4. Rational expectations solutions of contracts model

The contracts model has the following rational expectations solutions for market clearing industry and aggregate prices and outputs, where aggregate values are geometric averages of industry vaIues.2 It is assumed, following Fischer, that, although labor markets clear only ex ante, the goods market clears after the resolution of uncertainty, when ah shocks are contemporaneously observed: P

P(l

+

Yj)

--

%=3+

[

1+p

(1+/3)(2+fl-By) PYj (l+P)(l+P-PY)

--

I

(Kim,

- E,-2m,>

+&$Erj, 1h-E,-d 1(E,-lm, (8)

PO + Y)

--

(l+p)(2+P-PY)

F-9,)

PY

--

(1+P)O+P-PY)

I

(m, - E,-lm,)9

(9)

P;j = roj + E,-2m, 1 l+P+

P(l + Yj) (1+P)(2+B-Pu)

I

(Lm,

- Lm,)

1

PYj + [ 1+P + (l+P)(l+P-PY) 1 + l+BE,is Pl = r. + E,-2m, +

I

Cm, - E,-14

2+;+y@,-w-,-2m,)

1 + 1+B--PY

00)

(m, - k-d9

*The model is solved using the method of undetermined coefficients.

(11)

S. Ahme

Wage stickiness

and the non-neutrality

of money

where y = (l/J)~~,,v, is the average degree of indexation, number of industries, h = (l/J)L;-,hj, ad E,-gn,

31

J being the

= m,-* + b(1 + d)Z,-2,

E,-lm,-E,-,m,=u,-l+bZ,-I-bdZ,-~, m, - E,-lm,

= II,.

The first feature of these solutions to highlight is that the component of money anticipated before the signing of all contracts that are binding today, E,-,m,, has a one to one effect on prices and no real effects. This reflects the property of Fischer’s model that long-run neutrality of money holds. However, money growth unanticipated at the time when at least some of the contracts binding today were signed, has both output and price effects. It can be verified that changes in money unanticipated at the signing of all contracts, (m, E,-im,), have larger output and lower price effects than changes which were unanticipated by fifty percent of the contracts, (E,-im, - E,-,m,). Also, the choice of the money supply rule (i.e., the choice of b) matters for the behavior of outputs, which holds because the monetary authority is able to generate changes in money which are correctly perceived, but were unanticipated at the signing of half the contracts. Finally, the non-neutrality of money and the possibility of active stabilization policy do not stem from any misperceptions, but through effects on real wages. Thus, with full indexation on average, y = 1, money would be neutral with respect to aggregate output and, if in addition yj = 1, monetary neutrality holds with respect to the jth industry’s output also. In general, the higher is the degree of indexation, the lower is the output response and the higher is the price response to a nominal disturbance. 2.5. A simple imperfect information model

Now consider a simple Lucas type supply curve and assume that, while the current price in industry j, Ptj, is observed by industry j agents, the current money supply and hence the aggregate price level are not observed. Assuming some unspecified source of technological persistence the supply function can be written as 02)

where E,,.P, refers to the rationally expected value of the aggregate price level conditional on all information available in industry j at time t. Thus, here the relevant relative price is the ratio of the currently observed price in industry j to the expectation formed in that industry of the general price level.

32

S. Ahmeci,

Wage stickiness

and the non-neutrality

of money

2.6. Rational expectations solutions for imperfect information model

The market clearing rational expectations solutions for this model can be obtained by noting that

where

ej= - 4

a,” -I- aj2 *

The solutions are given by 1

1 x[h-Et-d +Etj] -&Yt-l.jf$~t-l,(13)

P,j=~oj+

E,-lm,+

P,=q,+E,-,m,+

1+ j-

OL+ P(“oj-rO’o) Ytj=

1_

x [hff

Yt=G++

-fJ

E,-lm,) 1

Pej

I+P

+ (1+m+ww

pe (mt-

’ +m

Et-lmt)

- ~~1-1,

P

wj

[ l+p-

(l+p)(l-p-pe)

PP

1

+ El/] + 1 + /3 1 - ?&y+i3 P 1+8-

pe (l+fi)(l+p-pe)

I

05)

-Lm,), 1(m, (16)

where 7)= p/(1 + fl) < 1, 19= (l/J)c$iej, and L is the lag operator. In this model anticipated money is neutral while current and lagged changes in unanticipated money afIect both outputs and prices. The solutions also iIlustrate the property of imperfect information models that the higher is the variance of monetary shocks relative to the total variance of the shocks, ej, the lower is the response of outputs to both nominal and real disturbances. This follows because the higher is 8,. the more an observed increase in P,j is attributed to nominal factors and less to relative real shifts.

S. Ahme

Wage

stickiness

and the non-neutrality

of money

33

2.7. Observational equivalence and industry level implications

To discuss the observational equivalence problem and the different industry level implications that emerge for each model, rewrite the output solutions in the contracts model as follows: ytj=kj+

B P(l +Yj) --Et-n-d [ 1h-1 -- BYj1h-Lm,) +Yj) -- S(l 1+p

(l+p)(2+/3-&4

(1+P)O+P-PY)

(l+P)(l+B-BY)

--

yt=k+

B

[ 1+/9 (l+--

P

lw+v)

(l+p)(2+B-Py) SY

(1+/3)(1+/3-By)

so +v> (1+P)(2+/3--SY)

b(Z,-1

- Et-Ad

I

-Lmt-l) 1(m,-l 1 -%A-1) 1b(Z,-, (mr-EE,-lmJ

(18) Comparing (18) with (16) aids us in understanding the observational equivalence problem at the aggregate level. In general, given that only one y and one 0 is observed, the data cannot distinguish between the Fischer model and the Lucas model. Both models have current and lagged money shocks affecting output positively, with the weights declining with the length of the lag. Strictly, in the versions presented here, the imperfect information model generates a much greater degree of persistence than the contracts model where the weights for lags greater than two are zero. But, increasing either the length of contracts or the degree of overlap of contracts within and across industries would generate much greater persistence.3 “Taylor (1980), in a rather difkrent contracts model, shows that a degree of persistence even greater than the duration of the longest contract can be generated.

34

S. Ahmeci,

Wage stickiness

and the non-neutrality

of money

It also appears that we can distinguish the models at the aggregate level by including 2,-i and Z,-, as additional variables in our regression. But, this is only because of the assumption in the imperfect information model that the Z variables cannot affect output, except through their influence on money. There does not appear to be any compelling a priori reason to suppose that this would necessarily hold. Finally, it might be argued that the price equations can be used to distinguish the models at the aggregate level, for in the contracts model lagged money shocks raise the price level, whereas in the misperceptions model they lower it. There are at least two reasons why this result is not general. First, introducing the same type of persistence in the Fischer model as in the Lucas supply function would tend to lower prices in response to past money shocks. Second, the money demand function implied by our demand side is a quantity theoretic one, with the nominal interest rate not appearing. The price level effects of lagged money shocks would be different with a more generalized money demand function. Eqs. (17) and (15) show how the models can be distinguished at the industry level. Specifically, in the contracts model, the higher is the degree of wage indexation the lower are the industry output responses of current and lagged monetary disturbances. Similarly, in the imperfect information model, given the total variance of all shocks, the industry output responses to current and lagged monetary disturbances are directly related to the variances of the relative shocks. Here, the focus being on testing the contracts model, attention is confined to the first of the implications mentioned above. 3. Endogenous indexation, varying supply elasticities and other extensions In arguing that the observational equivalence problem has been overcome, the restrictive assumption that indexation is exogenous has been made so far. It is possible to endogenize the degree of indexation, along the lines of Gray (1976), by choosing it to minimize the variance of output around its full information value. Given the assumptions of the formal model presented earlier though,. which include complete current information, full indexation turns out to be optimal, making it a little difficult to interpret empirical results which depend on cross-industry variations in this variable. In order to deal with this problem, some features that may justify partial indexation that differs across sectors are introduced. First, the supply elasticities are allowed to vary across industries. Second, as in Gray (1976), tirms are only allowed to have partial current information when making employment and output decisions. Third, it is assumed, as in Fethke and Policano (1984) and Card (1980), that the aggregate price level may reveal some information about relative real shocks. Since sticky wage models incorporating these features are well developed theoretically, the formal model is not reworked mathematically. Rather, in what follows, an intuitive discussion is provided of

S. Ahmed,

Wage stickiness

and the non-neutrality

of money

35

the implications of these extensions for the proposed empirical test of the contracts model. The following two equations (assumed linear for simplicity) will prove helpful for this purpose: cj = d, + dlyj + dzbj + d3uj2 + d,a,,j + wj,

Yj

=

40

+

41Pj

+

42aj'

+ 43*uj

+ 9js

(19) (20)

where cj is the cumulative effect of a nominal demand disturbance on industry man-hours, bj is the supply elasticity, uj is the indexation elasticity, 52 is the variance of relative shocks, crUjis the covariance between nominal and relative disturbances, and wj, nj are error terms. The hypothesis of interest that provides a test of Fischer-Gray type contracts models is that d, < 0. The formal contracts model presented earlier has constant supply elasticities (pi = /3), full information, implying d, = 0, and independence of relative and aggregate shocks ( uUj = 0). As mentioned above, in that model full indexation is optimal with (20) reducing to yj = 1. Now consider generalizations of the original model along the lines indicated earlier. First, with information confusion between relutiue disturbances and nominal shocks, output responses to the latter will depend positively on the variance of relative shocks, that is d, > 0, as demonstrated in the Lucas model. However, as long as the aggregate price level provides no information about relative shocks, indexation turns out to be independent of aj2, as discussed in Gray (1983).4 In this case d, < 0 as a test of the importance of wage contracts in generating monetary non-neutrality still goes through. Second, consider contracts models of the variety of Fethke and Policano (1984), which is a two-sector model in which at the time when one sector is negotiating, the whole of the other sector is locked-in. Then, if there are offsetting relative shocks, employment in the negotiating sector does not change, while it does in the locked-in sector, leading to an overall effect on employment, and hence on the price level, through a shift in aggregate s~pply.~ Then, indexation may turn out to depend negatively on the variance of relative shocks (uj2), so that q2 -C0, and with uj2 omitted from (19), the 4This point should not be confused with the point made in Gray (1976) where the economy is subject to aggregate real disturbances and nominal disturbances. Then, with information confusion, optimal indexation turns out to depend negatively on the variance of the aggregate real shocks and positively on the variance of monetary shocks. These features would imply that d, and 9c will depend on these variances, but since these variances are not industry specific, nothing substantive from the viewpoint of this study would change. ‘This is in contrast to the contracts model presented in this paper, where the aggregate price level does not reveal any information about relative shocks, because a fraction of the firms in each industry are locked in, while a fraction are negotiating. Therefore, offsetting relative shocks lead to offsetting movements in employment with no aggregate effects.

36

S. Ahme

Wage stickiness

and the non-neutrality

of money

indexation elasticities may end up capturing the Lucas effect, leading to observational equivalence even at the industry level. Another version of the contracting models is that of Card (1980), who allows the covariance between nominal and relative disturbances, uUj, to be non-zero. In this model, with imperfect information, cumulative output responses, cj:, and indexation elasticities, yj, may both be positively correlated with uUj, biasing a test that looks for a negative relationship between cj and yj towards underemphasizing the role of wage stickiness. Finally, with varying supply elasticities, a positive relationship of these with both Cj and Yj (dz, 41 > 0), which appears plausible, will create the same bias. Since the claim of this paper is that the empirical results apply to a broader class of contracts models than the specific formal set-up laid out in the theoretical section, it is necessary to resolve the problems discussed above. The obvious solution seems to be to directly keep the effects of supply elasticities, variance of relative shocks and covariance between relative and purely nominal disturbances fixed separately in the proposed cross-section test, which will be the strategy followed here. However, if an equation like (20) describing indexation behavior fits well, then multicollinearity problems in (19) may make it difficult to separate out the effects of indexation on output responses from the effects of these other variables. Therefore, it is also important to estimate (20) and attempt to isolate the empirical determinants of indexation. Results from doing so are provided in Ahmed (1985) and will be summarized in the next section.

4. Estimation

and testing

As mentioned in the previous section, the main issue to be focused on is the following: Do the responses of industry outputs to a nominal demand disturbance (i.e., the industry Phillips Curve slopes) bear a systematic relationship with the degree of indexation of nominal wages to aggregate price level changes? Since contract length variations can act as a substitute for higher indexation, an investigation of the link between the output responses and contract length is also undertaken. The empirical strategy is as follows. First, time-series regressions of different industries outputs on current and lagged nominal shocks are performed. Second, a cross-section regression is undertaken to see how much of the cumulative response of industry outputs to these nominal disturbances can be explained by variations in industry indexation elasticities, which are treated as exogenously given. The cross-section regressions are then extended to allow for other effects discussed in section 3 above, which arise from endogenizing the degree of indexation.

S. Ahmed,

Wage stickiness

and the non-neutrality

31

of money

Table 1 Wage indexation elasticities and contract length.*

No.

Industry description

1 2 3 4 5 6 I

Slaughtering/Meat Soft Drinks Textile Products Saw and Planing Mills Veneer and Plywood Pulp and Paper Iron and Steel Iron Foundries Smeltina and Refinine Non-FeGous Metal R’olling Wire and Wire Products Agricultural Implements Motor Vehicles Assembling Motor Vehicles Parts Major Appliances Household Radios/T.V.‘s Industrial Equipment Electric Cable Non-Metallic Mineral

8 9 10 11 12 13 14 15 16 17 18 19

Indexation elasticity

Contract length (in months)

(7j)

tLji,

0.11 0.61 1.10 0.15 0.15 1.13 0.40 1.33 0.47 1.11 0.49 0.96 0.11 0.68 0.83 1.23 0.29

28.2 36.0 34.3 24.0 27.0 16.0 35.1 17.5 36.0 36.0 36.0 35.8 35.8 34.6 27.0 30.8 26.5 24.0 34.0

1.23

Y9ource: Card (1980, table 1).

4.1. The data The analysis focuses on nineteen 3-digit SIC Code Canadian manufacturing industries due to availability of required data. A brief description of the data follows, with details of the sources listed in the appendix.

Indexation elasticities: The particular industries considered in this study are chosen because for these Card (1980) has already calculated industry level indexation elasticities, using data on individual contracts in force between 1968 and 1975. The contracts on which these elasticities are based contain both prespectied non-contingent increases in wages, as well as increases that are contingent on the general price level. The elasticities are defined as the ratio of the percentage change in the base wage rate arising as a result of all explicit contingent cost of living allowances to the percentage change in the consumer price index over the life of the contract. They are thus ex post escalation elasticities and their values are shown in table 1, along with the average duration of contracts signed in a particular industry. The indexation

38

S. Ahme

Wage stickiness

and the non-neutrality

of money

elasticities vary widely across industries which is encouraging from the viewpoint of the power of the proposed cross-section test. Unanticipated nominal demand disturbances: Various methods for calculating nominal disturbances are used to show robustness of the results. The first is the money shock series calculated by Saidi and Barro (1976) for the period 1951-1974. It was calculated by regressing growth rates of money on certain exogenous and predetermined variables, different equations being used for fixed and flexible exchange rate periods. The difference between actual and fitted values was then taken to be unanticipated growth in money. The second method involves following the techniques employed in Gordon (1982) who used U.S. data. Nominal GNP and money growth rates are regressed on their own past values and the past values of the GNP deflator. Once again the differences between actual and fitted values are taken as measures of nominal demand disturbances, for the period 1950-74 for nominal GNP and the period 1961-74 for money.6 For completeness, just the actual growth rates of nominal GNP and money supply have also been used in the regressions run. This amounts to assuming that x, - E,-ix, = x, - x,-i, where x, is altematively the log of nominal GNP and money supply. Total industry hours: Due to availability for a larger number of industries, total hours worked in a given industry are used as a proxy for industry output here. Series of average weekly hours per employee and an employment index for each industry are available, which are enough to be able to calculate the effect of nominal demand disturbances on total hours.

4.2. The empirical strategy

Consider running the following regression equation for each industry: EMP,j + N,j = aj + r#j( L)(x,

- E,-ix,)

+ ajt + e,j,

(21)

where EMP,, represents the log of an employment index, N,j is the log of average weekly hours per employee in industry j at time t, x, is a measure of nominal aggregate demand, (p,.(L) = $I~~+ +ijt + +2jL2, L being the lag operator, and e,j is an error term. For simplicity of notation assume Cj = +oj + cplj + $2j. We may interpret cj as the cumulative effect on total industry hours of an unanticipated unit change in the growth rate of nominal demand.7 6Resuh with restricting GNP equation to 1961-74 were similar to those obtained using actual nominal GNP growth. ‘Further lags of x, - E,-Ix, were not included because of sample size limitations.

S. Ahmed,

Wage stickiness

and the non-neutrality

of money

39

The hypothesis that the lower is the escalation elasticity (yj) the higher is the cumulati.ve response of output to a monetary disturbance ( cj) can be tested formally by running the following regression:

(22) where wj is an error term. If the hypothesis is true then d, should be negative and significantly different from zero. Extensions of (22) to allow for other effects are reported later. 4.3. The results

Tables 2 and 3 present the results of estimating (21) for each industry over the period 1961-74 using annual data.* For brevity, in all of the reported results below, attention is confined to two of the five methods of constructing unanticipated nominal demand disturbances reported earlier. These are the Saidi-Barro money shock series and nominal GNP disturbances using Gordon’s method. Unless otherwise noted, the results with other methods are almost exactly similar. The tables show that there are substantial variations across industries in the cumulative effects of a nominal shock on total industry hours (cj), for each of the two methods reported. The F-statistic reported in the table is for the null hypothesis Ha: cj= 0. A large number of the cumulative effects are significant at conventional levels, specially for nominal GNP disturbances. Also, although this information is not directly discernible from the tables, the peak effect occurs at one lag which, though not explained welI theoretically, is consistent with studies done using aggregate data. All of the reported Durbin-Watson statistics fall into the inconclusive range. Quite similar results are obtained for the cumulative and current responses when first-order autocorrelation is allowed for and a GLS procedure followed. To answer the question of whether these differences in Phillips Curve slopes can be explained by differences in the degree of indexation, consider figs. 1 and 2. These figures show the cross-section plots of the cumulative output responses to a nominal disturbance ( cj), against the indexation elasticities ( yj). There appears to be no systematic relationship between the two variables, no matter which method for calculating unanticipated nominal demand is used, although only two are reported. This is confirmed by the results of estimating the cross-section regression (22), which are reported as eqs. 1 and 2 in table 4. The coefficient on yj is positive and opposite in sign to the prediction of the theory, but statistically sThe sample begins at 1961 due to availability of employment and hours data at the industry level for the 1960 SIC codes, and is truncated at 1974 because of wage and price controls which came into effect in Canada in 1975.

40

S. Ahmed, Wage sfickiness and the non-neutrality of money

Effects of unanticipated No. 1 2 3 4 5 6 7 t 10 11 12 13 14 15 16 17 18 19

Table 2 money on total industry hours using Saidi-Barro (1961-74).‘*b

Industry description

+Oj

‘Oj

‘i

money shock series

F

S

12

D.W.

Slaughtering/Meat Soft Drinks Textile Products Saw and Planing Mills Veneer and Plvwood Pulp and Pap& Iron and Steel

-0.11 -0.64 0.68 1.30 1.00 -0.52 0.05

- 0.64 -0.96 1.74 3.91 1.19 - 1.78 0.11

0.21 0.05 1.87 2.56 3.52 0.78 2.09

0.40 0.00 5.92 15.58 4.62 1.90 5.82

0.54 0.97 0.04 0.00 0.06 0.20 0.04

0.26 - 0.22 0.50 0.86 0.10 0.81 0.85

1.57 0.63 0.86 1.66 0.72 1.71 1.34

Iron Smehing Foundries and Refinina Non-Fekous Metal Rkling Wire and Wire Products Agricultural Implements Motor Vehicles Assembling Motor Vehicles Parts Major Appliances Household Radios/T.V.‘s Industrial Equipment Electric Cable Non-Metallic Mineral

--1.23 0.18 - 0.38 0.10 2.34 1.06 0.75 0.65 1.38 - 0.36 - 0.42 0.44

--0.19 2.97 - 0.81 0.16 2.12 1.02 0.68 0.82 2.01 - 0.48 - 0.72 0.91

- 1.82 1.06 - 1.11 2.18 10.23 4.45 3.07 2.58 2.81 1.33 1.55 2.61

1.00 1.71 1.44 3.04 22.54 4.90 2.05 2.76 4.37 0.83 1.84 7.57

0.34 0.22 0.26 0.11 0.00 0.05 0.19 0.13 0.06 0.39 0.20 0.02

0.54 0.72 0.71 0.67 0.61 0.73 0.77 0.01 0.68 0.14 0.71 0.51

0.78 2.07 1.19 0.61 1.04 0.78 0.77 1.01 2.32 0.87 1.35 0.92

‘Model: EMP,, + N,j = a0 + +j(L)(x, - E,-rx,) + Sit, where $j(L) = +oj + I$,~L.+ $2jL2 and cj = +oj + +i. + hzi, is the cumulative response of man-hours to unanticipated money growth (sample size = 1Q. broj is the t-statistic corresponding to Ho: $~~~oi=O.F is the F-statistic and S is the critical significance level corresponding to Ho: cj = 0. AB Durbin-Watson statistics (D. W.) are in the inconclusive range (at 5% level). x2 is the adjusted R2.

insignificant. The sign of the coefficient becomes negative when the money shock series constructed using Gordon’s method is used, but remains insignificant. The R2’s from most of these regressions are almost zero and in fact the adjusted R2’s are negative.

Contract length: An issue stems from ignoring the effects of contract length in the regressions run. Variations in contract length across industries create two types of difhculties. First, if the optimal degree of indexation is constrained by some exogenous factors, shorter contract length can act as a substitute for higher indexation, and contract length must be held hxed separately in regressions like (22). This is easy to correct for, and the results are reported as eqs. 3 and 4 in table 4. Once again, no systematic relationship emerges between cj and uj or for that matter between cj and contract length Lj. Second, if contracts are for longer duration than one period, then the appropriate variable to appear as a measure of unanticipated growth in

S. Ahmeci,

Effects of unanticipated No. 1 2 3 4 5 6 8 9

10 11 12 13 14 15 16 17 18 19

Wage stickiness

and the non-neutrality

41

of money

Table 3 nominal GNP growth (calculated using Gordon’s method) on total industry hours (1961-74).kb

Industry description

+Oj

lOj

‘1

F

Slaughtering/Meat Soft DrinksTextile Products Saw and Planing MiIls Veneer and Plywood Pulp and Paper Iron and Steel Iron Foundries Smelting and Refining Non-Ferrous Metal Rolling Wire and Wire Products AgricuIturaI Implement Motor Vehicles Assembling Motor Vehicles Parts Major Appliances Household Radios/T.V.‘s Industrial Equipment Electric Cable Non-Metallic Mineral

0.01 -0.07 0.81 1.33 1.38 -0.28 0.63 0.31 -0.72 -0.25 0.60 2.15 1.23 1.07 1.09 1.79 -0.18 -0.14 0.81

0.06 -0.12 2.66 3.06 2.36 -1.03 1.78

0.31 1.67 2.10 1.34 4.35 1.12 2.58 3.54 -0.13 0.20 3.10

0.97 2.81 18.73 3.74 21.95 6.94 21.02 10.28 0.02 0.05 18.02

0.44

-1.39 -0.45 1.30 2.20 1.69 1.07 1.77 2.03 -0.32 -0.25 2.61

8.95

32.97

5.21 4.01 3.52 2.17 2.48 1.93 2.95

20.22 6.43 12.93 2.38 7.83

S’x2

D.W.

0.35 0.13 0.00 0.08

0.14 0.10 0.75

0.00

0.64 0.87

0.03 0.00

0.01 0.88 0.82 0.00 0.00 0.00

0.03 0.00

4.69

0.16 0.02 0.06

36.23

0.00

0.79

0.92 0.79

0.63 0.68 0.86 0.74 0.89

0.84 0.51 0.57 0.60 0.78 0.83

1.88 1.03 1.44 1.27 1.10 2.02 1.56 1.11 1.94 1.47 1.11 1.57 1.09 1.15 1.43 2.11 1.22 1.45 1.16

‘Model: EMP,j + N,, = a0 + $j(L)(X, - El-1x1) + 8,f, where +j(L) = $0, + +ijL + &IL2 and cj = +oj + $I~j + #2j, is the cumulative response of man-hours to unanticipated nominal GNP growth (sample size = 14). bloj is the t-statistic corresponding to Ho: eoj = 0. F is the F-statistic and S is the critical significance level corresponding to Ho: cj = 0. AlI Durbin-Watson statistics (D. W.) are in the inconclusive range (at 5% level). x2 is the adjusted R2.

nominal

demand is x,- E,-L x ,, where L represents contract length. Using x r, for instance when contracts are of two-period duration, amounts to making the whole term in curly brackets in (17) part of the error term. Since elj is white noise and IT,-, and Z,-, are part of the information set at time t - 1, by the properties of rational expectations forecasts, the error term will be orthogonal to x, - E,-rx, but not necessarily to x,-r - E,-zxl-l. This implies that the estimated cumulative .response (c,) may be an inconsistent estimate of the true cumulative response, but that the estimated current response (+sj) would still be consistent. For this reason, the relationship of just +Oj with y, is also investigated, with the results given as eqs. 5 and 6 in table 4. None of the conclusions reached earlier are overturned, with all results generalizing to other measures of nominal demand disturbances also. X,-%1

4.4. Interpretation

of results

These simple results provide several insights about the importance of, wage stickiness in generating monetary non-neutrality. If indexation can be re-

S. Ahme

Wage stickiness

INDEXATION

and the non-neutrality

of money

ELASTICITY

Fig. 1. Plot of cumulative hours response to Saidi-Barro elasticities.

money shock series against indexation

garded as determined by forces external to the model, then the results clearly indicate that the observed correlation between unanticipated nominal demand and output cannot be explained adequately by the existence of contractually fixed nominal wages. Of course, this does not by itself imply that the Lucas-Barr0 information confusion equilibrium explanations are any better. Statistically, in the test of the contracts model provided here, there is no explicit alternative model to be accepted if the test fails. The Lucas type model was merely used in the theoretical section to illustrate the observational equivalence problems that arise in attempting to test either model at the aggregate level. An issue touched upon earlier, which is important for the interpretation of the results, is the following: Clearly it is not realistic to regard the degree of indexation as exogenous. A number of factors besides indexation may affect the response of industry outputs to money shocks and these factors have all been thrown into the error term in eq. (22). Is it not likely that some of these ‘factors will be correlated with the degree of indexation and bias the results? Models of Gray (1983), Fethke and Policano (1984) and Card (1980) suggest that the likely candidates for these factors are industry specitic supply elastici-

S. Ahme

H 0

Wage stickiness

4-

and the non-neutrality

of money

43

0 0 0 0

0

0 0

0

-11,. , . , . , - , _y - , . , . , . ) . , . , - , - , . , 0.0

0.1

0.2

0.3

0.4

0.5 0.5 INDkXATION

0.7

0.8 0.0 ELASTICITY

1.0

1.1

1.2

1.3

1.4

Fig. 2. Plot of cumulative hours response to nominal GNP shocks (calculated using Gordon’s method) against indexation elasticities.

ties (g), variance of relative shocks ( 52) and the covariance between nominal and relative shocks (uUj). The solution to this problem proposed in section 3 was to keep these factors fixed separately in cross-section regressions like eq. (22). In order to implement this strategy empirically, measures of two of these variables were constructed as follows: First, industry supply elasticities, pi, were constructed for twelve of the nineteen industries for which output data are also available, by regressing the logs of industry outputs on the log of aggregate total man-hours in all manufacturing industries, using Zellner’s seemingly unrelated regression technique. The aggregate labor input is used as an instrument for the relevant industry labor inputs to minimize simultaneity problems.’ Second, a rough measure of the variance of relative shocks, zj2, was obtained by calculating the sample variance of the log of the ratio of industry selling prices to the implicit Gross National Expenditure deflator, ( plj - p,), for the twelve industries considered above. 9No intercept term was allowed in the equations, as this led to values for parameters which implied increasing returns. In addition, when industry man-hours instead of the aggregate level instrument are used, all of the inference results reported liter remain unchanged.

44

S. Ahmed,

Wage stickiness

and the non-neutrality

of money

Table 4 Cross-section regressionsa

Dependent variable 1

clj

2

=2j

3

clj

4

=*I

5 6

Intercept 1.61

Explanatory variables Indexation elasticity (Vi)

Contract length (L;)

0.15

-

0.02

- 0.04

-

0.03

- 0.02

0.05 (0.55) 0.05 (0.67) -

0.04

- 0.08

0.06

- 0.06

0.03

-0.03

-

0.03

- 0.02

(1.54)

(1.35)

2.11 (2.28) 0.14 (0.04) 0.55 (0.22)

0.86 (0.75) 0.73 (0.53) 0.84 (0.72)

QlOj

0.08 (0.21)

0.33 (0.69)

+*Oj

0.38 (1.08)

0.34 (0.77)

R*

x2

%statistics are given in parentheses. cS, and +o,j represent, respectively, the cumulative and current hours response to nominal demand shocks using method ‘s’ (with s = 1 for Saidi-Barro money shock series and s = 2 For nominal GNP disturbances using Gordon’s method). x2 is the adjusted R*, and the sample size is 19.

With respect to the covariance between relative and nominal shocks (uUj), Card (1980) constructs a measure of these rigorously. However, Card finds no significant evidence of a relationship between indexation, yj and uUi, so that omitting the latter variable from a cross-section regression hke (22) is unlikely to bias the coefficient on yj.10 The results from including the supply elasticities, pi, and the variance of relative shocks, Sjz, in the cross-section regressions are reported in table 5. These indicate that q2 does not add anything at all to the fit of the regressions. However, the supply elasticities, pi, do have a significantly positive effect on the Phillip’s Curve slopes, cj, as would be expected, but including them does not change the inference results on the effects of indexation.” However, at least the signs of the coefficients on yj for the current output responses (table

i’luloreover, in Ahmed (1985), I constructed my own rough measure of uU, as the sample covariance between the flrst difference of the log of the Gross National Expenditure implicit deflator and the relative industry selling prices, that is cov(p, -p,-i, p,, -p,). This implicitly assumed random walk behavior for the money supply. The correlation between this variable and indexation, y , is found signiftcantly negative, so that, with this measure, omitting u,,, from (22) would actu ad y lead to a bias towards overemphasizing the role of contracts. “When ff s is dropped, the coet&ients on 8, in the current response (t$o,) equations also become signfficant.

S. Ahmed, Wage stickiness and the non-neutrality of money

45

Table 5 Cross-section regressions with supply elasticities and variance of relative shockan Explanatory variables Dependent, variable

Intercept

1

clj

-

29.26 (- 1.93)b

2

c2j

- 32.30 (- 2.21)b

3

+lOj

4

+*Oj

- 6.94 (-0.83) - 6.67 (- 0.87)

Indexation elasticity (Y,)

SUPPlY elasticity CBj)

Variance of relative stocks vj*:,

0.07 (0.06) 0.45 (0.W -0.38 ( - 0.64) - 0.32 (-0.60)

83.05 (2.OO)b 92.13 (2.31)’ 19.13 (0.84) 19.39 (0.93)

-4.90 (- 0.08) - 12.57 ( - 0.21) 25.00 (0.71) 17.81 (0.55)

R*

x*

0.50

0.31

0.56

0.39

0.35

0.10

0.33

0.08

%tatistics in parentheses. c~, and &,j represent, respectively, the cumulative and current hours response to nominal demand shocks using method ‘s’ (with s = 1 for Saidi-Barre money shock series and s = 2 for nominal GNP disturbances using Gordon’s method). x2 is the adjusted R*, and the sample size is 12. bSignificance at 10% level. CSignificance at 5RI level.

5, eqs. 3,4) and the cumulative output responses to unanticipated money using Gordon’s method (not reported) are now consistent with the contracting models. Another issue discussed in section 3 concerned the extent to which results, such as those in table 5, are meaningful if the degree of indexation is highly linearly correlated with the supply elasticities, aj, and the variance of relative shocks, q?. This can be resolved by directly considering the contribution that S, and 4? make to explaining movements in indexation. The relevant equatron, using the twelve industries for which flj and 4’ were constructed earlier, is reported below (r-ratios in parentheses): yj = 2.18 + 16.566: - 4.64fij, (0.47)

R2 = 0.09,

x2= -0.11.

(0.87) (-0.36)

. There is no relationship between indexation and supply elasticities or between indexation and the variance of relative shocks.12 For a detailed “This result is reinforced when my constructed measure of the covariance between nominal and relative shocks (see footnote 10) is included in the indexation equation above. It has a negative sign in the equation and is significant, implying that omitting it in table 5 leads to a bias towards overemphasizing the role of contracts. In any case, cross-section regressions including this variable (not reported) did not change the inference results on the coe8kient of y,.

46

S. Ahme

Wage stickiness

and the non-neutrality

of money

discussion of the theoretical and empirical determinants of indexation, see Ahmed (1985). In summary, endogenizing the degree of indexation does not overturn the conclusions reached earlier for two reasons. First, directly holding fixed the effects of the potential determinants of indexation in the cross-section regressions leads to no change in the results. Second, this turns out not to be surprising, since the determinants of indexation predicted by the theory to be important are found not to be so empirically. This may also itself be construed as indirect evidence against wage contracting models.

4.5. Some further issues

The following additional points must be borne in mind when interpreting the results presented above: Sample size: The time-series regressions represented by (21) were run on

annual data over 1961-1974. With five variables on the right-hand side this leaves nine degrees of freedom only. Also, the indexation elasticities are based on contracts signed between 1968 and 1975, so that, although there is overlap, these do ‘not exactly come from the same sample as the output effects of nominal shocks. There is thus an implicit assumption that the yj’s have been stable over time between 1961 and 1975. Contract data limitations, price and wage controls from 1975 and a new industrial classification code in 1960 prevent an easy extension to larger samples for the Canadian economy.

Errors in variables: There are several potential sources of measurement error that should be noted. First, to what extent is the ex post indexation elasticity

measure an appropriate measure of the degree to which real wages will change following a change in the general price level? If (5) is strictly adhered to as a description of wage setting behavior, then the ex post elasticity is the correct measure. To see this consider eq. (6). The lirst term on the right-hand side may be regarded as the non-contingent wage increase subtracting which from the left-hand side gives us the percentage change in the base wage rate due to explicit cost of living allowances. Dividing this percentage contingent wage change by the percentage change in the CPI, which is exactly how the ex post elasticity is measured, gives us yj, the variable of interest. However, there could be a measurement error problem when the adjustment of wages even to anticipated inflation is less than one to one. Then, what becomes relevant is the response of real wages to all nominal changes, not just anticipated ones. At first, this suggests taking the actual wage change (not

S. Ahmed,

Wage stickiness

and the non-neutrality

of money

47

subtracting non-contingent increases) to construct elasticities, but to the extent that not all of the non-contingent wage adjustment is due to anticipated inflation, and some of it may be due to anticipated real changes like productivity increases, this creates a measurement error in the other direction. One solution could be to attempt to divide the non-contingent increases into its various components, but this seems beyond the scope of this paper. The second source of measurement error arises from the cumulative hours responses, cj, being a constructed variable. However, because this variable is the dependent variable, consistency of the estimates is not at issue, but efficiency may be. In this regard note that, in most of the cross+ection regressions, the signs on the coefficients themselves are opposite to the predictions of the theory, and, in any case, even when the sign is correct, it would require a four- to fivefold fall in the standard error for the estimates to become significant. Finally, some of the explanatory variables in table 5, namely the variance of relative shocks and the supply elasticities, are also constructed variables, which is potentially a more serious problem for the results in which the degree of indexation is allowed to be endogenous. The difficulties raised above are certainly not trivial and imply that the evidence presented earlier cannot be regarded as entirely conclusive. Despite this, it deserves serious consideration since there is very little empirical work - that does not suffer from the observational equivalence problem - in the literature on evaluating the macroeconomic importance of wage-stickiness, and this paper does provide a beginning. 5. Summary and concluding remarks

This study was motivated by two observations. First, existing empirical evidence on the differential response of economic activity to anticipated and unanticipated changes in nominal demand is subject to widely differing interpretations. Much of it involves the problem of observational equivalence, at the aggregate level, of Fischer-Gray type rational expectations long-term contracting models and the Lucas-Barr0 type imperfect information rational expectations models. For example, Barro’s (1981a) results on the effects of unanticipated changes in money are consistent with either model. Second, there has not been too much work in the way of direct empirical testing of contracts models of business fluctuations in the macroeconomics literature. This study argued that observational equivalence can be broken by concentrating on the industry level variants of the models, and tested the contracts model using the industry level cross-sectional implications that emerged. The main implication that was derived was that the response of industry output to unanticipated changes in nominal demand is inversely related to the degree of indexation of the industry’s wages to the general price level.

48

S. Ahme

Wage stickiness

and the non-neutraliiry

of money

Empirically, for the Canadian economy, substantial variations were found in the cumulative response of total industry man-hours to unanticipated changes in nominal demand, for several different measures of nominal demand disturbances. However, no systematic relationship could be found between these Phillips Curve slopes and industry indexation elasticities, which also vary widely across industries. These empirical results are sharply at variance with the predictions of sticky wage models of business cycles under the assumption that indexation is exogenously given. The results were extended in the direction of endogenizing the degree of indexation by keeping the potential determinants of indexation fixed separately. This led to almost no change in the results, which was not surprising, given that the factors proposed by contracting models as determining optimal indexation - such as variance of relative shocks and supply elasticities - turned out to be unimportant empirically in doing so. In conclusion, the results in this paper cast considerable doubt on the empirical importance of the rigidity of nominal wages in generating the observed short-to-medium-run non-neutrality of money. While some problems of small sample bias and possible measurement error remain, the evidence presented can be interpreted, at the very least, to reinforce the theoretical arguments that question the use of wage contracting models to explain the comovements of money and real economic activity. Appendixz Data sources and definitions (i) Indexation elasticities (vi): Average (over all contracts signed in industry j during 1968-75) of the ratio of the percentage change in the base wage rate (arising as a result of all contingent cost of living allowances) to the percentage change in the CPI over the life of the contract - Card (1980, table 1) [see Wilton (1977), which is Card’s source, for details]. (ii) Employment (EMP,,): Employment indexes by industry, 1961-74 (1961= loo), 3-digit SIC codes for industries used are 101,109,180,251,252, 271, 291, 294, 297, 305, 311, 323, 325, 332, 334, 336, 338, 359 - CANSIM Tapes. (iii) Average weekly hours (N*,): Average weekly hours of hourly rated wage earners by industry, 1961-74, 3-digit SIC codes as above in (ii) CANSIM Tapes. (iv) Nominal GNP: Gross national product in current dollars - Canadian Statistical Review, Historical Summary 1970 for 1950-60 and Canadian Statistical Review (CSR), September 1983 for 1961-74.

S. Ahme

Wage stickiness

and the non-neutrality

of money

49

(v) Money supply: Percentage change in Ml, 1961-74 - Bank of Canada Reuiew (various issues) [note: -latest revised figures used]. (vi) Price level: Gross national expenditure deflator (1971= 100) - CSR Historical Summary 1970 for 1950-60 and CSR, September 1983 for 1961-74. (vii) Contract length (Lj): Average contract length for all contracts signed in industry i over the period 1968-75 - Card (1980, table 1). (viii) Industry output: Industry domestic product indexes, 1961-74 - Real Domestic Product by Industry, Statistics Canada (various issues). (ix) Industry prices: Industry selling price indexes by major groups (1971 = 100) - Industry Selling Prices, Statistics Canada (various issues). (x) Aggregate employment: Aggregate employment index (1961= 100) CSR Historical Summay 1970 and CSR (various issues). (xi) Aggregate hours: Average weekly hours worked in all manufacturing industries, 1961-74 - CSR Historical Summary 1970 and CSR (various issues). References Ahmed, S., 1985, An exploratory investigation into the determinants of wage indexation, Typescript, Aug. (Brown University, Providence, RI). Barre, R.J., 1981a, Unanticipated money growth and economic activity in the U.S., in: Money, expectations and business cycles (Academic Press, New York). Barre, R.J., 1981b, An equilibrium approach to business cycles, in: Money, expectations and business cycles (Academic Press, New York). Barre, R.J., 1977, Long term contracting, sticky prices and monetary policy, Journal of Monetary Economics, July. Barre, R.J., 1976, Rational expectations and the role of monetary policy, Journal of Monetary Economics, Jan. Barre, R.J. and Z. Hercowitz, 1980, Money stock revisions and unanticipated money growth, Journal of Monetary Economics, March. Boschen, J. and H.I. Grossman 1982, Tests of equilibrium macroeconomics using contemporaneous monetary data, Journal of Monetary Economics, Nov. Card, D., 1982, Cost of living escalators in major union contacts, Typescript, Nov. (University of Chicago, Chicago, IL). Card, D., 1980, Determinants of the form of long term contracts, Working paper no. 135, June (Princeton University, Princeton, NJ). Christofides, C.N. and D.A. Wilton, 1983, The determinants of contract length: An empirical analysis based on Canadian micro-data, Journal of Monetary Economics, Aug. Fethke, G.C. and A.J. Policano, 1984, Wage contingencies, the pattern of negotiations and aggregate implications of alternative contract structures, Journal of Monetary Economics, Sept. Fethke, G.C. and A.J. PoIicano, 1982, Determinants and implications of staggered wage contracts, Typescript, Oct. (University of Iowa, Iowa City, IA).

50

S. Ahmed,

Wage stickiness

and the non-neutrality

of money

Fischer, S., 1980, On activist monetary policy with rational expectations, in: S. Fischer, ed., Rational expectations and economic policy (University of Chicago Press for NBER, Chicago, IL). Fischer, S., 1977a, Long term contracts, rational expectations and the optimal money supply rule, Journal of Political Economy, Feb. Fischer, S., 1977b, Long term contracting, sticky prices and monetary policy: A comment, Journal of Monetary Economics, July. Fischer, S., 1977c, Wage indexation and macroeconomic stability, in: Stabilization of the domestic and international economy, Carnegie-Rochester conference series on public policy (NorthHolland, Amsterdam). Gordon, R.J., 1982, Price inertia and policy ineffectiveness in the U.S.: 1890-1980, Journal of Political Economy, Dec. Gray, J.A., 1983, Wage indexation, imperfect information and the aggregate supply curve, in: Rudiger Dombusch and Mario Hemique Siionsen, eds., Inflation, debt and indexation (MIT Press, Cambridge, MA). Gray, J.A., 1978, On indexation and contract length, Journal of Political Economy, Feb. Gray, J.A., 1976, Wage indexation: A macroeconomic approach, Journal of Monetary Economics, April Grossman, H.I. and W.S. Haraf, 1985, Shunto: Rational expectations and output growth in Japan, Typescript, July (Brown University, Providence, RI). King, R.G., 1982, Monetary policy and the information content of prices, Journal of Political Economy, April. Kormendi, R.C. and P.G. Meguire, 1984, Cross-regime evidence of macroeconomic rationality, Journal of Political Economy, Oct. Lucas, R.E., 1977, Understanding business cycles, in: Stabilization of the domestic and intemational economy, Carnegie-Rochester conference series on public policy (North-Holland, Amsterdam). Lucas, R.E., 1976, Economic policy evaluation: A critique, in: The Phillips curve and labor markets, Carnegie-Rochester conference series on public policy (North-Holland, Amsterdam). Lucas. R.E.. 1975. An eauihbrium model of the business cvcle. Journal of Political Economv. Dec. Lucas; R.E.; 1973; Some’intemational evidence on output~inflation tradeoffs, American Economic Review, June. Lucas, R.E., 1972, Expectations and the neutrality of money, Journal of Economic Theory, April. McCalIum, B.T., 1979, The current state of the policy ineffectiveness debate, American Economic Review, May. Muth, J.F., 1961, Rational expectations and the theory of price movements, Econometrica, July. Riddel, W.C., 1979, The empirical foundations of the PhiBips curve: Evidence from Canadian wage contract data, Econometrica, Jan. Saidi, N. and R.J. Barro, 1976, Unanticipated money, output and unemployment in Canada, Typescript, July (University of Rochester, Rochester, NY). Sargent, T.J., 1976, The observational equivalence of natural and unnatural rate theories of macroeconomics, Journal of Political Economy, June. Sargent, T.J., and N. Wallace, 1975, Rational expectations, the optimal monetary instrument and the optimal money supply rule, Journal of Political Economy, April. Taylor, J.B., 1983, Union wage settlements during a disinflation, American Economic Review, Dec. Taylor, J.B., 1980, Aggregate dynamics and staggered contracts, Journal of Political Economy, Feb. Weiss, L., 1980, The role for active monetary policy in a rational expectations model, Journal of Political Economy, April. Wilton, D.A., 1977, An analysis of Canadian wage contracts with cost of living allowance clauses (Centre for the Study of Inflation and Productivity, Ottawa).