Centre de recherche sur l'emploi et les uctuations economiques (CREFE ) Center for Research on Economic Fluctuations and Employment (CREFE) Universite du Quebec a Montreal Cahier de recherche/Working Paper No. 69
Wage Contracts and Labor Adjustment Costs as Endogenous Propagation Mechanisms Steve Ambler
CREFE /UQAM
Alain Guay
CREFE /UQAM and CIRANO
Louis Phaneuf CREFE /UQAM Fevrier 1999
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Ambler: CREFE , UQAM, C.P. 8888, Succ. Centre-ville, Montreal, Qc, H3C 3P8, telephone (514) 987-3000 poste 8372, courrier electronique
[email protected] Guay: CREFE , UQAM, C.P. 8888, Succ. Centre-ville, Montreal, Qc, H3C 3P8, telephone (514) 987-3000 poste 8377, courrier electronique
[email protected] Phaneuf: CREFE , UQAM, C.P. 8888, Succ. Centre-ville, Montreal, Qc, H3C 3P8, telephone (514) 987-3000 poste 8364, courrier electronique
[email protected] We thank the Fonds FCAR and the SSHRC for their nancial support and Leif Danziger, Pierre-Yves Henin, and participants in seminars at the Bank of Canada, York University, the University of Alberta and the University of Toronto for their comments. The usual caveat applies.
Resume:
Dans ce travail, nous etudions le r^ole des co^uts d'ajustement du travail et des contrats salariaux imbriques en tant que mecanismes endogenes de propagation pour un modele du cycle economique. Nous montrons qu'un modele dynamique d'equilibre general qui inclut ces deux elements est capable d'expliquer a la fois les fonctions d'autocorrelation du taux de croissance de la production et du taux de croissance du salaire nominal, et la presence d'une composante transitoire importante pour la production. Les chocs transitoires dans ce modele proviennent de chocs au taux de croissance de la monnaie. Les parametres structurels du modele sont estimes a l'aide de la methode des moments generalises pour un echantillon couvrant les E tats-Unis d'apres-guerre. Un test de speci cation base sur les restrictions de suridenti cation ne peut rejeter le modele.
Abstract:
We examine the dual role of labor adjustment costs and staggered wage contracts as endogenous propagation mechanisms. We show that a dynamic general equilibrium model which combines these two features explains the autocorrelation functions of output growth and nominal wage growth, as well as the signi cant trend-reverting component in aggregate output. Transitory shocks are measured as shocks to the growth of money supply. The structural parameters of the model are estimated for the US postwar economy using a GMM procedure. The overidentifying restrictions implied by our model are very far from being rejected.
Keywords: Wage contracts, Labor adjustment costs, Business cycles, Endogenous propagation mechanisms JEL classi cation: E32, E62
1 Introduction This paper considers the dual role of labor adjustment costs and staggered wage contracts in generating persistent cyclical movements in output and nominal wages. These endogenous propagation mechanisms were central in accounting for the persistent character of output uctuations in the seminal rational expectations models of Sargent (1978) and Taylor (1979, 1980a). We incorporate them into an otherwise standard dynamic general equilibrium (DGE ) model that we estimate and test for the U.S. postwar economy using a generalized method of moments (GMM ) procedure. We show that these transmission channels help explaining three main stylized facts which most business cycle models have been unsuccessful to account for simultaneously: (i) output growth is positively and signi cantly autocorrelated over short horizons and has negative but insigni cant autocorrelations over longer horizons, (ii) aggregate output has an important trend-reverting component which is characterized by a hump-shaped impulse response function, and (iii) nominal wage growth is positively and signi cantly autocorrelated over short and longer horizons. Recent work by Watson (1993), Cogley and Nason (1995), and Rotemberg and Woodford (1996) has uncovered an important failure of standard real business cycle (RBC ) models: their inability to generate enough persistence through their internal propagation channels to account for the key aspects of output dynamics. For instance, Cogley and Nason (1995) show that the autocovariance generating functions of output growth predicted by most RBC models are essentially white noise processes. Therefore, these models fail to explain facts (i) 1
and (ii) unless they rely on external sources of dynamics (or impulse dynamics) which are empirically implausible. In response to these ndings, several authors including Andolfatto (1996), Burnside and Eichenbaum (1996), and Hall (1996) have emphasized various types of labor market frictions in an attempt to solve the persistence problem in RBC models. Andolfatto models labor-market search as a costly activity which creates an incentive for rms to hoard labor. Burnside and Eichenbaum combine labor hoarding with variable capital utilization rates. Hall stresses the distinction between straight time shift and overtime to generate endogenous propagation. These labor market frictions give rise to positive autocorrelations of output growth at short horizons but are unable to generate a response of output following a transitory shock which is suciently large and persistent to match the observed response. In Burnside and Eichenbaum, and Hall the transitory shock is measured as a shock to government consumption. Recently, several authors have assumed that nominal wages are set in advance of the period in which they are paid in DGE models (for example, Cho, 1993; Cho and Cooley, 1995; Benassy, 1995; Cho, Cooley and Phaneuf, 1997; Bils and Chang, 1998). These wage rigidities signi cantly alter the short-run response of the economy to shocks, especially monetary shocks. Until now, researchers have assumed that nominal wage rates are set at their expected market-clearing levels following Gray (1976) and Fischer (1977). Moreover, the length of contracts has been exogenously xed in the experiments: one-period contracts, two-period contracts, etc. These models face two problems. First, as Taylor (1998) points out, expected market-clearing contracts do not provide an 2
explanation of the high persistence of monetary shocks.1 Second, the cyclical implications of wage contracts turn out to be very sensitive to the length of contracts assumed in the experiments. For instance, in the model of Cho and Cooley (1995), increasing the duration of contracts from one to two quarters generates excessive output volatility in the economy. Unfortunately, without an estimate of contract duration, it is hard to tell what is the appropriate average length of time between wage adjustments. In this paper, we adopt the type of wage contracts proposed by Taylor (1979, 1980a).2 Contracts are staggered and workers nd that other wages in the economy are relevant for their decisions in setting their own wages. Taylor (1980b,1983) provided evidence that wage setting is a highly unsynchronized process, and that relative wage considerations have exerted a signi cant impact on postwar U.S. wage settlements. However, we depart from Taylor by using a random duration version of staggered wage setting in the vein of Calvo (1983) and Backus (1984). This setup has several attractive features for our purpose. It allows for easy aggregation over contracts signed at di erent times. Moreover, when the average duration of contracts is taken as a free parameter, the parameter space is compact and the contract length parameter can be estimated with aggregate data along with the other structural parameters of the model. Therefore, instead of arbitrarily xing the length of contracts, we can rely on In fact, these models cannot account for any of the three stylized facts mentioned above. Like the other researchers who have incorporated nominal wage contracts into general equilibrium models, we beg the dicult question of why agents agree to these arrangements. Here, we take their existence for granted and concentrate on studying their impact on aggregate uctuations. Some microeconomic justi cation for their prevalence can be found in Okun (1981) and Danziger (1988,1992), among others. 1 2
3
an estimate of their average duration. Our model has two shocks: a technology shock and a monetary shock. The GMM procedure used for the estimation of the model exploits a criterion func-
tion that penalizes deviations of a set of unconditional moments predicted by the model from those in the data. Because we emphasize the role of nominal wage rigidities in the dynamic propagation of shocks, we base the estimation on a set of moments that includes not only the relative volatilities of real variables and comovements between these variables as in most RBC studies, but also the volatilities of nominal relative to real variables, comovements between nominal and real variables, and autocorrelations in output growth and nominal wage growth. The structural parameters of our model are estimated with precision and are economically meaningful. More importantly, the over-identifying restrictions implied by our theoretical model are very far from being rejected. We nd that the combination of staggered wage contracts and labor adjustment costs accounts for the serial correlation in output growth, generates a substantial persistence in wage in ation, and yields a highly persistent e ect of a monetary shock on real output. In contrast, a model where the labor adjustment costs are the only transmission channel explains none of the stylized facts mentioned above, whereas one with only the wage contracts performs better in this respect but only with an implausibly high average duration of contracts. The paper is organized as follows. The next section presents a description of our theoretical model. The third section discusses the econometric methodology used for the estimation and testing of the model and presents the estimation 4
results. The fourth section looks at the separate role of wage contracts and labor adjustment costs in the propagation of shocks. Section ve contains concluding remarks.
2 The Model The economy consists of a representative household, a collection of perfectly competitive rms, and a government. Nominal wages are set in advance of the period in which they are paid by contracts. Under this arrangement, households cede the right to determine total hours worked to rms. Firms rent capital and labor services from households. They maximize the present value of pro ts, weighting future pro ts by the expected marginal utility of consumption. Firms are subject to convex adjustment costs when they adjust labor inputs.
2.1 Households Households have in nite planning horizons and consist of a large number of individuals. The economy has di erent groups of rms-workers renegotiating wage contracts at di erent times. Each household sends workers to work at di erent rms in proportion to the size of the rms' workforce in the total population. Consequently, all households receive the same average wage, which is the relevant wage for each household's optimization problem. Hence, the household sector can be treated as if there is one representative household. Households hold capital which they rent to rms. Households' assets consist of physical capital and cash balances. They have preferences de ned over consumption and
5
leisure. The representative household maximizes
Et
1 X i=0
i ! ln (c1t+i ) + (1 ? !) ln (c2t+i ) + ln (1 ? nt+i ) ;
(1)
with 0 < < 1 and 0 < ! < 1. Hours worked are given by nt , and the endowment of time per period is normalized to equal one.3 There are two types of consumption goods; c1 is a cash good and c2 is a credit good. Purchasing the cash good requires the use of cash balances. Expectations in the model are rational and the information set on which they are based includes the current and lagged values of all variables and shocks. Households enter the period with nominal money balances mt carried over from the previous period. They receive a nominal lump sum transfer Tt at the beginning of the period. Purchases of the cash good must satisfy the cash-in-advance constraint
Pt c1t mt + Tt ;
(2)
where Pt is the price level. Household allocations must also satisfy the sequence of budget constraints given by
c1t+i + c2t+i + it+i + mPt+i+1 t+i
t+i n + R k + Tt+i + mt+i ; =W Pt+i t+i t+i t+i Pt+i Pt+i
(3)
where kt denotes the household's holdings of capital, Wt is the average nominal wage in the economy, Rt is the capital rental rate, and it is gross investment. Household expenditures on the left hand side of (3) include purchases of the two 3 We use the convention throughout that lower case letters denote individual choice variables and capital letters denote their aggregate per capita counterparts, which are exogenous from the point of view of the household.
6
consumption goods, gross investment, and money carried into the next period. Available funds include labor and capital incomes, currency carried over from the previous period, and cash transfers from the government. Agents maximize (1) subject to (2), (3), and non-negativity constraints. The household's holdings of capital evolve according to
kt+1 = (1 ? ) kt + it ;
(4)
where is the (constant) depreciation rate of capital.
2.2 Firms Firms discount pro ts using the representative household's subjective discount rate. They weight future pro ts by the expected marginal utility of consumption, which corresponds to the expected marginal utility of a dollar to the rms' owner, the household. Firms maximize
Et
1 X i=0
i uc;t+i t+i ;
(5)
where t denotes real pro ts at time t and uc;t denotes the marginal utility of consumption of the representative household at time t. Pro ts at time t are given by
q t 2 t = Yt ? W P Nt ? Rt Kt ? 2 At (Nt ? Nt?1 ) ; t
(6)
where Yt At Nt Kt(1? ) , is the representative production function, At is a measure of labor-augmenting technological progress, Kt is the aggregate per capita capital stock, and Nt is the per capita number of hours worked by the representative household. Following Sargent (1978) and Cogley and Nason (1995), the 7
last term in (6) captures the costs incurred by the rm to vary employment.4 The rm's adjustment costs are made to depend on the level of technology in order to ensure the existence of a balanced growth path in the economy. We assume that the representative rm deals with di erent groups of workers in the same proportion as the total population. At the margin, the rm adjusts its employment by hiring and ring workers in the same proportion as their distribution in the population, with the average real wage being the relevant marginal cost to the rm of hiring workers. The natural log of labor-augmenting technological progress At follows a random walk with drift, ln (At+1 ) = ln (A) + ln (At ) + "t+1 ;
(7)
where "t is an i.i.d. shock.
2.3 Wage Contracts The contract wage is given by
Et
1 X i=0
ln (Xt ) = ?
?
?
(1 ? d) di ln (Wt+i ) + ln (Nt+i ) ? ln Nto+i
:
(8)
where Xt is the contract wage negotiated in period t, which sets the nominal wage rate received by workers during the contract, Wt is the economy-wide average nominal wage rate, Nto is notional labor supply, and (1 ? d) is a constant probability that a given contract expires at the beginning of each period after its starting date. 4 Bils and Cho (1994) incorporate costs of changing capital per worker in a model which allows cyclical variation in labor and capital utilization.
8
The contract wage set in period t depends on the average nominal wage over the life of the contract. As in Taylor, this term captures the concern of workers about relative wages. The contract also includes a term re ecting the impact of anticipated tightness in the labor market on wage settlements. This term is measured as the anticipated di erence between the total hours worked chosen by the rms and notional labor supply. The expected variables on the right-hand side of (8) are weighted by (1 ? d)di . This fraction represents the probability that a contract does not expire before the ith period. Conveniently, the mean of the contract length is given by (1 ? d)?1 . If d = 0, the contracts last one period, and since new contracts are renegotiated every period after the current values of stochastic shocks are revealed, the nominal wage is set at the ex-post market clearing level. Therefore, d = 0 implies that the model simply reduces to a DGE market-clearing wage model. This type of contract has important advantages for our purposes. First, it guarantees that the steady states of economies with and without wage contracts are identical. Second, when the average contract length is a free parameter of the model, the parameter space is compact, and the contract length parameter can be estimated using aggregate data. The current average nominal wage is the weighted sum of all contracts still in force at time t:
Wt =
1 X i=0
(1 ? d) di Xt?i :
(9)
Given (9), it is easy to see that ln(Xt ) in (8) embodies a backward-looking component through the term ln(Wt+i ). Shocks are passed on from one contract 9
to another through this channel. Taylor identi es this channel as the contract multiplier. De ning the lag operator L as LEt zt+j Et zt+j?1 for any variable
z , and applying the operator to (8) and (9), respectively yields ln (Xt ) = dEt ln (Xt+1 ) + (1 ? d) (ln (Wt ) + (ln (Nt ) ? ln (Nto ))) ;
Wt = dWt?1 + (1 ? d) Xt :
(10) (11)
Hence, the dynamics of the contract wage and the average wage are captured by two rst-order di erence equations independently of the average contract length.
2.4 The Government The government transfers cash balances to households. The government's ow budget constraint is given by
Mt+1 ? Mt = Tt ;
(12)
where Mt is the per capita money stock. In most DGE models, monetary policy is modeled as the outcome of an exogenous process (for example, Cho, 1993; Cho and Cooley, 1995; Benassy, 1995; Bils and Chang, 1998). We adopt a slightly di erent approach. We assume that the monetary authority follows a money supply rule which is partly exogenous and partly endogenous. It is given by ln (Mt+1 =Mt ) ln (gt ) = (1 ? m )m + m ln (gt?1 ) + "t + t ;
(13)
with 0 < m < 1. According to this rule, the monetary authority may respond contemporaneously to the technology shock. In the special case where 10
= 0, (13) reduces to a purely exogenous, autoregressive speci cation for money growth. Given the change in the money stock, transfers are determined endogenously in order to satisfy the government's budget constraint.
2.5 Stationary Transformations Because the economy's production technology follows a random walk with drift, the economy will exhibit balanced growth in the long run, with real variables (except for hours) growing at a rate ln (A) on average. In order to generate a stable dynamical system which can be simulated by linearizing around a well-de ned steady state, we rede ne the endogenous variables of the model by de ating them by the level of labor productivity. For most trending variables
Qt , we de ne Q~ t Qt =At : For cash balances and capital, we normalize by the lagged value of labor productivity, so that
k~t kt =At?1 ;
m~ t mt =At?1 :
For the price level, we de ne
P~t Pt At =Mt+1: For the nominal contract wage and the nominal average wage, we de ne
X~t Xt =Mt+1;
W~ t Wt =Mt+1 :
11
2.6 Maximization Problems and First Order Conditions After some algebraic manipulation, the representative household's maximization problem can be expressed as the following Lagrangian: max L = Et
1 X i=0
i
(
! ln (~c1t+i ) + (1 ? !) ln (~c2t+i ) + ln (1 ? nt+i )
~ +1t+i W~ t+i nt+i + Rt+i k~t+i exp (? (A + "t )) ? m~ ~t+i+1 Pt+i Pt+i
?c~2t+i ? k~t+i+1 + (1 ? )k~t+i exp (? (A + "t ))
)
~ t+i + gt+i ? 1 ? c~ +2t+i m 1t+i ; P~t+i gt+i
(14)
The rm's pro t maximization problem can be expressed as: 1 X
max = Et i ~1 i=0 Ct+i
(
Nt +i K~ t(1+?i ) = (A exp ("t+i ))(1? ) : )
~ t+i q 2 ?Rt+i K~ t+i = (A exp ("t+i )) ? W Pt+i Nt+i ? 2 (Nt+i ? Nt+i?1 ) ;
(15)
where we de ne per capita aggregate consumption as
C~t C~1!t C~2(1t ?!) ; so that the marginal utility of total consumption is just 1=C~t. The rst order conditions for the maximization problem of the representative household with respect to choice variables at time t can be written as follows:
c~1t : c~! ? 2t = 0; 1t c~2t : 1 c~? ! ? 1t = 0; 2t ~ nt : 1 ?? n + 1t W~ t = 0; Pt t 12
(16) (17) (18)
k~t+1 : Et ? 1t + 1t+1 (Rt+1 + (1 ? )) exp (? (A + "t )) = 0; m~ t+1 : Et ~ 2t+1 ? ~1t = 0: Pt+1 gt+1 Pt
(19) (20)
We have omitted the rst order conditions with respect to Lagrange multipliers. The condition with respect to c~2t stipulates that the marginal utility of consumption of the credit good is equated to the marginal utility of wealth as given by 1t . The condition with respect to c~1t equates the marginal utility of consumption of the cash good to the multiplier 2t . According to the condition with respect to m ~ t+1 , the representative household chooses its holdings of cash balances in order to equate the current marginal utility of credit goods with the expected future marginal utility of cash goods, where the value of cash balances is adjusted for expected in ation and expected transfers of balances from the government. The condition with respect to nt says that the representative household equates the marginal sacri ce in terms of foregone leisure to the marginal bene t from increased consumption. This condition holds in the versions of the model without the wage contracts. The condition with respect to k~t+1 gives a fairly standard Euler equation for the evolution of the marginal utility of consumption. The marginal cost of foregone consumption at time t, measured in units of the marginal utility of wealth, must equal the expected future bene ts of increasing the capital stock by one unit. There are two components to this marginal revenue. First, there is the rental income from capital at time t + 1. Second, there is the value of the capital left over at the end of t + 1 after depreciation. 13
The rst order conditions of the representative rm with respect to its choice variables at time t can be written as follows:
Kt : (1 ? ) Nt K~ t? = (A exp ("t ))(1? ) ? Rt = (A exp ("t )) = 0;
(21)
~ 1 Nt : ~ Nt( ?1) K~ t(1? ) = (A exp ("t ))(1? ) ? W~ t Ct Pt
+q (Nt ? Nt?1 ) ? Et ~ q (Nt+1 ? Nt ) = 0: (22) Ct+1 The rm equates the marginal product of capital to its cost, which is the rental rate of capital. It equates the expected marginal bene t of labor, weighted by the discounted marginal utility of consumption, to labor's expected marginal cost. The marginal costs include adjustment costs paid at time t to increase the work force, direct wage costs at time t, and the expected change in adjustment costs at time t + 1 from adjusting the work force at time t.
2.7 General Equilibrium We de ne a recursive competitive equilibrium in our model in the standard way. Firms and households maximize subject to their constraints. The decision rules of individual rms and households are compatible with the corresponding aggregate decision rules, and quantity variables chosen by households are equal to their per capita counterparts. In particular,
mt = Mt ; kt = Kt ; c1t = C1t ; c2t = C2t ; nt = Nt : In the version of the model without the wage contracts, the labor market clears and employment satis es simultaneously the labor demand and the notional labor supply equations. In the version of the model with the wage contracts, 14
employment is determined by rms' demand for labor. Notional labor supply (the value of nt that satis es the representative household's rst order condition for nt given the values of its other choice variables) a ects only the evolution of the contract wage via equation (8). However, in the deterministic steady state the labor market clears. The model is then solved by linearizing the equations of the model around the steady-state values of its endogenous variables. This leads to a state-space representation of the dynamics of the economy from which forward-looking variables can be eliminated using techniques described by King, Plosser and Rebelo (1987) and Blanchard and Kahn (1980). This log-linearized version of the model can be written in a space-state representation:
Xt+1 = A()Xt + D()t+1 ;
(23)
Zt = C ()Xt ;
(24)
where we rede ne Xt to be a vector of state variables which includes the monetary shock and the unobservable technology shock with the other state variables. The vector Zt contains the endogenous variables. The vector t+1 contains innovations to the technology and money growth processes. The matrices A(), D() and C () are functions of the structural parameters of the model. Using this space-state representation and given assumptions about the variance-covariance properties of the t+1 innovations, equations (23) and (24) can be used to derive analytical expressions for the asymptotic covariance matrices of the state and endogenous variables. In this way, we can calculate the unconditional second 15
moments of the model without actually simulating the exogenous processes.
3 Estimation Methods and Results
3.1 Econometric Methodology
The structural parameters of the model are estimated using the generalized method of moments (GMM ). The estimator of the parameter vector () is the solution of the following problem: !0
!
T T 1X 1X f ( z ; ) W f (zt ; ) ; ^T = arg min T T 2 T t=1 t t=1
(25)
where WT is a random non-negative symmetric matrix, zt is the entire set or a subset of the model's variables, f (zt ; ) is a q-vector of unconditional moments restrictions. An optimal weighting matrix WT is obtained as the inverse of the variance-covariance matrix of the moment conditions evaluated at the rst-step estimates. This matrix is consistently estimated using the estimator proposed by Newey and West (1994). This method of estimation has several attractive features. First, it enables us to concentrate on variables which are measured accurately. For example, the capital stock is not used because this variable is known to be poorly measured. Second, we can obtain an estimator of the structural parameters relative to the monetary shock and the unobservable technology shock.5 Third, when the dimension of the vector of moments (q) is greater than the dimension of the vector of structural parameters, a test of the overidentifying restrictions implied 5 We estimate the parameters of the forcing variables of the model at the same time as its other structural parameters. This is similar to the approach of Bansal, Gallant, Hussey and Tauchen (1995) and di ers from many other simulated method of moments techniques, in which the laws of motion of the forcing variables are xed by preliminary estimates.
16
by the model can be performed to judge the goodness of t of the model. The model is estimated using a total of 25 moment restrictions. Most of these moments are deviations of unconditional second moments predicted by the model from those in the data. To compute the unconditional second moments for the model, the log-linearized version is used. As we note in the previous section, the unconditional second moments predicted by the model can be calculated for given values of the structural parameters without having to simulate the model numerically. We now describe the vector of unconditional moment restrictions used. First, we use the di erence between the level of per-capita hours in the data and the steady-state level of labor supply in the model in order to estimate the value of
, the weight on leisure in the utility function. This gives E [ln Nt ? ln N ] = 0;
(26)
where N is the steady-state level of labor supply. Second, we use the di erence between the rate of growth of per-capita output in the data and the steady-state rate of growth of per-capita output in order to identify ln(A). The moment restriction is
E [ ln Yt ? ln(A)] = 0:
(27)
Third, we use the di erence between the rate of growth of M 2 in the data and the steady-state rate of money growth in the model in order to estimate more precisely the value of m . This gives the condition
E [ ln Mt ? m ] = 0: 17
(28)
In order to identify the AR(1) parameter in the money growth equation, we use the following moment:
E [(ln(gt?1 ) ? m ) ((ln(gt ) ? m ) ? m (ln(gt?1 ) ? m ))] = 0:
(29)
We impose a zero covariance between the innovations to the aggregate technology and money supply processes. In order to obtain the variance of t , we use the following moment: h i ? E ((ln(gt ) ? m ) ? m (ln(gt?1 ) ? m ))2 ? 2 "2 + 2 = 0:
(30)
This moment restriction is a direct consequence of the law of motion for the money supply described in equation (13). The other moment restrictions correspond to the deviations of unconditional second moments predicted by the model from those in the data. These second moments consist of variances, relative standard deviations, contemporaneous correlations and autocorrelations. More speci cally, they include: the variance of output growth; the standard deviations of the consumption growth, investment growth, employment growth, in ation, and nominal wage growth relative to the standard deviation of output growth; the contemporaneous correlations of consumption growth, investment growth, employment growth, in ation, and nominal wage growth with output growth; the autocorrelations of output growth, nominal wage growth, and employment growth of orders one, two and three. Our choice of second moments re ects the following considerations. First, some of these moments purport to the relative volatilities of real variables and comovements between real variables which have been the main 18
focus of RBC studies. Second, the relative volatilities of nominal and real variables and comovements between these variables re ect our emphasis on nominal rigidities. Third, the autocorrelations in real and nominal growth variables are included because we want to assess the strength of the propagation mechanisms incorporated in our model.
3.2 Data The data cover the period 1960:I to 1993:IV. Private consumption, Ct , is measured as the sum of private-sector expenditures on nondurable goods plus services. Private investment, It , is de ned as the sum of purchases on consumer durables, gross private nonresidential (structures and equipment) and residential investment. Private output, Yt , is the sum of private consumption and private investment. The price level, Pt , is the de ator corresponding to our measure of private output. Our measure of hours worked, Nt , is the seasonally adjusted hours series from the Household Survey. The nominal wage, Wt , is the hourly compensation in the nonfarm business sector. Finally, the money stock,
Mt , is measured by M2. Consumption, investment, output, hours worked, and the money supply are converted to per capita terms using the civilian noninstitutional population aged 16 and over. All series are from Citibase (a complete list of mnemonics can be found in an appendix).
3.3 Estimation Results Table 1 presents the parameter estimates of the model when labor adjustment costs and staggered wage contracts are combined. Since it was not possible 19
to identify both d and simultaneously, we adopted the following estimation strategy. Initially, we xed the value of and estimated d. Then, we xed d and estimated . The results reported in Table 1 are those obtained by xing
, setting it equal to :1. This value is consistent with the empirical evidence presented in several studies including Taylor (1980b), West (1988), Phaneuf (1990), Levin (1991), and Fuhrer and Moore (1995). As we show later, assuming
= :1 implies an amount of persistence in wage in ation which is approximately that observed in the data (which is not the case for signi cantly higher values of ), and a better overall t of the model. The results are quite striking. We succeed in estimating a large number of structural parameters, and these estimates are in general quite accurate. The overidentifying restrictions implied by our model easily pass a standard Hansen
J -test, with the p-value for the test equal to .34. Therefore, we cannot reject the null hypothesis that the 25 unconditional moments predicted by our estimated model are the same as those in the data. Some of these estimated parameters are worthy of comment. The average length of wage contracts is estimated very precisely. The estimate d = :746 implies an average duration of contracts of about four quarters. This is in close conformity with the evidence from a wide range of studies surveyed by Taylor (1998). The labor adjustment cost parameter, q, is estimated at 7.755. Based on a one-side test, the null hypothesis that q = 0 is safely rejected at the 5% level. Our estimate of !, the relative weight on the cash good in total consumption, is close to the value assigned by Cooley and Hansen (1995) based on Lucas' 20
(1988) approach which relates the parameters of conventional money demand functions to the parameters of preferences in a cash-in-advance model, and on surveys of consumer transactions. They set ! equal to .84 while our estimate is .814. We also obtain an estimate of the discount rate, , of .9908. It is typical when estimating representative consumer models to obtain a value above unity. Our estimates for and are close to those used in calibrated business cycle models, even though we do not rely on data on labor's share in national income to estimate , or on gross investment and capital stock data to estimate . The estimate = :3388 indicates that the Federal Reserve has responded to positive technology shocks by increasing the rate of monetary growth, suggesting that monetary policy has been procyclical in response to supply-side shocks. The variation in money growth not explained by the Fed's endogenous response to shocks is = :0083, and the estimate m = :6471 indicates that shocks to the rate of money growth tend to persist. These estimates for the money supply rule are broadly consistent with those obtained by Ireland (1996) in a model where monopolistically competitive rms have to pay a cost for changing their prices. Finally, the size of the estimated standard deviation of the aggregate technology shocks, " , is about the same as in standard RBC models. Using the same set of moments, we have reestimated the model xing d to .75. We were then able to estimate . Our estimate for was close to .1 (.15) and there were only minor di erences in the estimates of the structural parameters of the model. Consequently, we do not report them.
21
4 Model Dynamics In this section, we assess the relative contributions of labor adjustment costs and staggered contracts as propagation mechanisms. We begin by generating the autocorrelation functions of output growth and nominal wage growth corresponding to the estimated version of our model. Then, we present the dynamic response functions of output following technology and monetary shocks. Finally, we explore the sensitivity of our results to changes in key structural parameters of the model in more detail.
4.1 Persistence of Output Growth and Nominal Wage Growth One central feature of output dynamics stressed by Cogley and Nason (1995) is that real GNP growth is positively autocorrelated over short horizons and has weakly negative autocorrelations over longer horizons. The actual autocorrelations for our measure of private output from the rst to the sixth lag are depicted by the solid line in upper left-hand panel in Figure 1. The dotted lines are 95% con dence interval bands.6 The rst three autocorrelation coecients are positive and signi cant, being respectively equal to .41, .21 and .18. The fourth-order coecient is statistically insigni cant, the fth-order coecient is signi cantly negative, and the sixth-order coecient is once again insigni cant. We also present the actual autocorrelations for nominal wage growth in the lower left-hand panel of Figure 1. In contrast to output growth, nominal wage growth is positively autocorrelated over short and longer horizons. In fact, judging by 6 The autocorrelations are estimated by GMM, and the con ence intervals are computed
with an estimate of the variance-covariance matrix following Newey and West (1994).
22
the autocovariance-generating function of the growth rate of the nominal wage, wage in ation is characterized by a substantial amount of persistence. This is the rst time that a study has focused on the autocorrelations of nominal wage growth in the context of a DGE model with wage contracts. The autocorrelations from lag 1 to lag 6 for output growth and nominal wage growth implied by the estimated version of our model are presented in the upper and lower right-hand panels of Figure 1, respectively. First, note that the autocorrelations of output growth produced by the model display a pattern which is quite similar to the one describing actual autocorrelations, and that all autocorrelation coecients but one are statistically signi cant at the 5% level. Interestingly, the model generates positive autocorrelations for the rst and second lag (.3 and .1, respectively), and negative autocorrelations from the fourth to the sixth lag (-.05, -.07 and -.07, respectively). The joint hypothesis that the six autocorrelation coecients implied by the model are the same as those in the data cannot be rejected at conventional signi cance levels. Our model also predicts that wage in ation is highly persistent, and it correctly captures the fact that nominal wage in ation is positively autocorrelated at short and longer horizons. We conclude from this examination that the combination of labor adjustment costs and staggered wage contracts provides a satisfactory explanation of the autocovariance-generating functions of both output and nominal wage growth. In particular, it correctly implies that output growth is positively autocorrelated only at short horizons while at the same time explaining that the 23
autocorrelations in nominal wage growth are positive at short and longer horizons.
4.2 Impulse-Response Functions As Cogley and Nason point out, although the autocorrelation function for output growth conveys useful information about business-cycle periodicity, it is only partially informative about the dynamics of output. The problem arises from the fact that within the context of a multi-shock DGE model, the autocorrelation function depends on various impulse-response functions. Since output may respond quite di erently to various kinds of shocks, the impulse-response functions may provide additional and insightful information about output dynamics. Following Blanchard and Quah (1989), Cochrane (1994) and Cogley and Nason (1995), we estimate a bivariate representation in the rate of growth of output and the di erence between the log of output and the log of consumption. The empirical impulse-responses of output to permanent and temporary shocks are displayed in the upper and lower left-hand panels of Figure 2, respectively, along with 95% con dence interval bands around the estimated responses.7 Following a permanent shock, output rises for several quarters before reaching a plateau after about 24 quarters. After a transitory shock, output exhibits a pronounced positive hump-shaped response. The response is hightly persistent as output returns to its steady-state level only after about thirty quarters. The impulse-reponses implied by our estimated model appear in the righthand panels of Figure 2. These gures illustrate the response of output to one7 Con dence intervals were obtained by bootstrapping and include a rst-order bias correction following Killian (1995).
24
standard deviation shocks to technology and to money supply growth. As most RBC models, our model has some diculty reproducing the gradual increase
of output after a permanent shock. However, for the most part, the response of output generated by our model is well within the 95% con dence interval bands. The model does remarkably well in explaining the reponse of output to a transitory shock. The predicted response remains within the 95% con dence interval around the empirical response along its entire path. Other dynamic general equilibrium models have generated a hump-shaped responses of output to temporary shocks (for example Burnside and Eichenbaum, 1996), but to our knowledge ours is the rst DGE model that predicts both the qualitative hump-shaped response of output and its magnitude after a temporary shock.
4.3 Sensitivity Analysis This section explores in greater detail the separate role of labor adjustment costs and staggered contracts in the propagation of shocks. We examine the sensitivity of results to changes in three key parameters (q, d, and ) as the other parameters of the model take their estimated values reported in Table 1. Figure 3 illustrates the dynamics of output growth, nominal wage growth, and the impulse-responses of output to one-standard deviation shocks to technology and to the growth of money supply if there are labor adjustment costs and market-clearing wages (i.e. d = 0). This model can be seen as an in ation tax-model, along the lines of Cooley and Hansen (1989), augmented by the labor adjustment costs. The rst column of Figure 3 shows how increasing the adjustment cost parameter, q, a ects the autocorrelations of output growth. 25
Without labor adjustment costs (i.e. q = 0), the model reduces to a standard cash-in-advance model and does not endogenously generate serial correlation in output growth. Therefore, the autocovariance generating function of output growth is close to a white noise process. This is the problem that plagues most RBC models as shown by Cogley and Nason. Assigning positive values to q produces weakly positive autocorrelations from the rst to the sixth lag. However, there is little increase in the amount of serial correlation as q increases. For example, with q set as high as 20, the rst two autocorrelation coecients are only .09 and .06 compared to .40 and .21 in the data. The second column reveals that if there are only labor adjustment costs, the model dramatically fails to explain the autocorrelation function of nominal wage growth. The rst three autocorrelation coecients are about .29, .19, and .12 for the three q values compared to .65, .64 and .62 in the data. Therefore, the market-clearing model with labor adjustement costs is unable to generate substantial persistence in wage in ation. The third column shows that labor adjustment costs have only a negligible impact on the reponse of output following a technology shock. Finally, the fourth column indicates that labor adjustment costs do not propagate the e ect of a monetary shock in a market-clearing economy. Taken together, these results show that a model that relies exclusively on labor adjustment costs fails to account for the main aspects of output and wage dynamics. Figure 4 illustrates the sensitivity of the model's predictions to changes in contract length when wage contracts are the sole propagation mechanism (i.e. 26
q = 0). We assume that d is successively equal to .5, .75 and .875, implying an average contract duration of respectively two, four and eigth quarters. The rst column shows that if the wage contracts have a relatively short duration (d = :5), the six autocorrelation coecients of output growth are all weakly negative. With d = :75, the rst two autocorrelation coecients become positive (.10 and .03) but are too low to match the actual autocorrelations. Assuming that all wages in the economy are set by contracts that last two years on average, we nd that the serial correlation in output growth produced by the model is closer to the actual autocorrelation function of output growth, although the rst autocorrelation coecient is still two standard deviations lower than the value observed in the data. Therefore, wage contracts alone can generate a persistence in output growth closer to the stylized facts, but only if an implausibly high average length of contracts is assumed. The second column presents the impact of contract duration on the autocorrelation generating function of nominal wage growth. As expected, nominal wage growth becomes more persistent as d increases. However, the predictions of the model are more in con rmity with the stylized facts if wage contracts are assumed to last one year on average (d = :75), otherwise the autocorrelation coecients are either too high or too low. The third column summarizes the e ect of changes in d on the response of output to a technology shock. Increasing d magni es the e ect of a technology shock on output. In fact, if d = :875, the response of output generated by the model is outside the 95% con dence interval bands for the rst twenty quarters. A model with a lower average dura27
tion of contracts performs much better in this respect. The last column studies the impact of wage contracts on the response of output to a monetary shock. Wage contracts can magnify the e ect of a monetary shock on output. Note, however, that if d = :5, the response is weak and does not persist. In contrast, if d = :875, the response is too strong, especially in the rst four or ve quarters where it is found to be outside the con dence interval. With one-year contracts, the model provides a satisfactory account of the response of output after a monetary shock, except that it is too pronounced initially, exceeding the upper 95% con dence interval for the empirical response. We also analyzed the e ects on the model's predictions of changes in (which measures the sensitivity of wage contracts to anticipated labor market tightness). Figure 5 reports simulation results for successively equal to .1, .5 and 1.0, for a model that includes both wage contracts and labor adjustment costs. Increasing lowers the serial correlation in output growth and nominal wage growth. With = :5 or = 1:0, the autocorrelations of output growth at lags of one, two and three quarters are all signi cantly di erent from those in the data. Wage in ation is also much less persistent with a higher . In fact, with
= :5 or = 1:0, nominal wage growth is weakly autocorrelated over longer horizons, a feature which is inconsistent with the data. A technology shock has a somewhat larger impact on output in the short run if is smaller. The response of output to a monetary shock is more a ected by changes in . Increasing reduces both the magnitude of the response and its persistence. Setting to .1, as con rmed by the non-rejection of the over-identifying restrictions implied by 28
our model in Table 1, produces much better results. To summarize the results presented in this section, we have shown that the most important weaknesses of a model with only labor adjustment costs are its inability to generate enough serial correlation in the growth rates of output and nominal wage, and to produce a signi cant trend-reverting component in aggregate output. A model with solely the wage contracts provides a better account of the serial correlation in output growth but only if contracts are implausibly long (i.e. two years on average). However, with two-year contracts, the short-run responses of output after a technology and a monetary shock are too strong. Therefore, it only by combining labor adjustment costs and wage contracts that the model delivers satisfactory results on all accounts.
5 Conclusions Recent evidence shows that standard RBC models fail to explain the most salient aspects of output dynamics. This nding is paradoxical given that the purpose of the research program initiated by Kydland and Prescott (1982) was precisely to explain the business cycle, which many believe to be essentially a dynamic phenomenon. We view the basic message of the present paper as a refreshing one: central elements of the rational expectations revolution of the 1970's can be uni ed with the main ingredients of the RBC approach to obtain an encompassing model that can explain business cycle dynamics. Labor adjustment costs and staggered wage contracts have long been celebrated as key propagation channels. We have shown that their incorporation into a dynamic 29
general equilibrium framework succesfully accounts for the most critical aspects of business cycles.
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Backus, David (1984), \Exchange Rate Dynamics in a Model with Staggered Wage Contracts", discussion paper 561, Queen's University Bansal, Ravi, A. Ronald Gallant, Robert Hussey and George Tauchen (1995), \Nonparametric Estimation of Structural Models for High-Frequency Currency Market Data", Journal of Econometrics 66, 251-287 Benassy, Jean-Pascal (1995), \Money and Wage Contracts in an Optimizing Model of the Business Cycle", Journal of Monetary Economics 35, 303-315 Bils, Mark and Yongsung Chang (1998), \Wages and the Allocation of Hours and E ort", mimeo, University of Rochester Bils, Mark and Jang-Ok Cho (1994), \Cyclical Factor Utilization", Journal of Monetary Economics, 33, 319-354
Blanchard, Olivier J. and Charles M. Kahn (1980), \The Solution of Linear Di erence Models under Rational Expectations", Econometrica 48, 13051313 Blanchard, Olivier J. and Danny Quah (1989), \The Dynamic E ects of Aggregate Supply and Demand Disturbances", American Economic Review 79, 655-673 30
Burnside, Craig and Martin Eichenbaum (1996), \Factor Hoarding", American Economic Review 86, 1154-1174
Calvo, Guillermo (1983), \Staggered Contracts and Exchange Rate Policy" in J.A. Frenkel, ed., Exchange Rates and International Economics. (Chicago, University of Chicago Press) Cho, Jang-Ok (1993), \Money and the Business Cycle with One-period Nominal Contracts", Canadian Journal of Economics 26, 638-659 Cho, Jang-Ok and Thomas F. Cooley (1995), \The Business Cycle with Nominal Contracts", Economic Theory 6, 13-33 Cho, Jang-Ok, Thomas F. Cooley and Louis Phaneuf (1997), \The Welfare Costs of Nominal Wage Contracting", Review of Economic Studies 64, 465484 Cochrane, John H. (1994), \Permanent and Transitory Components of GNP and Stock Prices", Quarterly Journal of Economics 107, 241-265 Cogley, Timothy and James M. Nason (1995), \Output Dynamics in RealBusiness-Cycle Models", American Economic Review 85, 492-511 Cooley, Thomas F. and Gary D. Hansen (1989), \The In ation Tax in a Real Business Cycle Model", American Economic Review 79, 733-748 Cooley, Thomas F. and Gary D. Hansen (1995), \Money and the Business Cycle", in T. Cooley, ed., Frontiers of Business Cycle Research. (Princeton, Princeton University Press) Danziger, Leif (1988), \Real Shocks, Ecient Risk Sharing, and the Duration of Labor Contracts", Quarterly Journal of Economics 103, 435-440 31
Danziger, Leif (1992), \On the Prevalence of Labor Contracts with Fixed Duration." American Economic Review 82, 195-206 Fischer, Stanley (1977) \Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule", Journal of Political Economy 85, 191-205 Fuhrer, Je rey C. and George R. Moore (1995), \Monetary Policy Trade-o s and the Correlation between Nominal Interest Rates and Real Output", American Economic Review 85, 219-239
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Hall, George J. (1996), \Overtime, E ort, and the Propagation of Business Cycle Shocks", Journal of Monetary Economics 38, 139-160 Ireland, Peter N. (1996), \A Small Structural Quarterly Model for Monetary Policy Evaluation", Carnegie-Rochester Conference on Public Policy 47, 83-108 Killian, L. (1995), \Small-Sample Con dence Intervals for Impulse Response Functions", mimeo, University of Pennsylvania King, Robert G., Charles I. Plosser and Sergio T. Rebelo (1987), \Production, Growth, and Business Cycles: Technical Appendix", mimeo, University of Rochester Kydland, Finn and Edward C. Prescott (1982), \Time to Build and Aggregate Fluctuations", Econometrica 50, 1345-1370 Levin, Andrew (1991), \The Macroeconomic Signi cance of Nominal Wage Contract Duration", Working Paper no.91-08, University of California at San 32
Diego Lucas, Robert E. Jr. (1988), \Money Demand, A Quantitative Review", in Karl Brunner and Bennett McCallum, eds., Money, Cycles and Exchange Rates; Essays in Honor of Alan Meltzer. Carnegie-Rochester Conference Series on
Public Policy 29 Newey, Whitney and Kenneth West (1994), \Automatic Lag Selection in Covariance Matrix Estimation", Review of Economic Studies 61, 631-653 Okun, Arthur M. (1981), Prices and Quantities: A Macroeconomic Analysis. (Washington, DC: Brookings Institution) Phaneuf, Louis (1990), \Wage Contracts and the Unit Root Hypothesis", Canadian Journal of Economics 23, 580-592
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Taylor, John B. (1983), \Union Wage Settlements during a Disin ation", American Economic Review 73, 981-993
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Appendix: Data Sources The series are from Citibase and the (quarterly) sample is 1960:1 to 1993:4, with de nitions as follows.
Ct : private consumption, composed of consumption of non-durables
(gcnq) and services (gcsq). It : private investment, de ned as gross private domestic investment (gpiq) and consumption of durable goods (gcdq). Yt : output, measured as private consumption plus private investment. Pt : the price level, which is just the de ator for our measure of output, measured as ((gcn + gcs + gcd + gpi)/(gcnq + gcsq + gcdq + gpiq)), where the series in the numerator are nominal values and the series in the denominator are measured in constant dollars. Nt : total hours worked (lhours). Wt : compensation per hour, nonfarm business sector (lbpur). Mt : M2 (fm2).
Consumption, investment, output, hours worked, and the money supply are de ated by total civilian population aged 16 and over (p16).
34
Table 1
Model Parameter Estimates (US Economy 1960:I to 1993:IV) Parameter
Value
s.e.
ln(A)
.0052 .0145 .9903 .6060 .0202 3.184 .8144 7.755 .7463 .6471 .3388 .0098 .0083
.0009 .0007 .0042 .0674 .0075 .3597 .0384 4.381 .0190 .0326 .1623 .0020 .0006
J-test
13.46 p-value=.34
m ! q d m "
Figure 1
Autocorrelation Functions for Output Growth and Nominal Wage Growth AFC for Output Growth (US Data)
AFC for Output Growth (Model)
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
−0.2
−0.2
−0.4
1
2
3
4
5
6
−0.4
1
AFC for Nominal Wage Growth (US Data) 1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
1
2
3
4
5
6
3
4
5
6
AFC for Nominal Wage Growth (Model)
1
0
2
0
1
2
3
4
The long-dashed lines indicate the estimated autocorrelations. The short-dashed lines indicate 95% con dence bands. The solid lines are the autocorrelations predicted by the model.
5
6
Figure 2
Impulse Response Functions Permanent Impulse−Response Function (US Data) 0.02
Permanent Impulse−Response Function (Model) 0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
0
−0.005
−0.005
−0.01
0
10
20
30
40
Transitory Impulse−Response Function (US Data) 0.025
−0.01
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
0 0
10
20
30
40
10
20
30
40
Transitory Impulse−Response Function (Model) 0.025
0.02
−0.005
0
−0.005
0
10
20
The central dashed lines indicate the estimated impulse response function of output. The two outer dashed lines of each gure indicate 95% con dence bands. The solid lines are the impulse responses predicted by the model.
30
40
Figure 3
Model with Labor Adjustment Costs AFC for Output Growth
AFC for Nominal Wage Growth
q=0
q=0
0.5
2
4 q = 10
6
q=0
0.02
0.02
0
0
0
2
4 q = 10
6
0
20 q = 10
40
0
20 q = 10
40
0
20 q = 20
40
0
20
40
1
0
0.02
0.02
0
0
0.5
2
4 q = 20
6
0.5
0
2
4 q = 20
6
0
20 q = 20
40
1
0
−0.5
q=0
0.5
0.5
−0.5
Transitory Impulse Response Function
1
0
−0.5
Permanent Impulse Response Function
0.02
0.02
0
0
0.5
2
4
6
0
2
4
6
0
20
40
See notes to Figure 1 for the autocorrelation functions. See notes to Figure 2 for the impulse response functions.
Figure 4
Model with Wage Contracts AFC for Output Growth
AFC for Nominal Wage Growth
d = .5
d = .5
0.5
2
4 d = .75
6
d = .5
0.02
0.02
0
0
0
2
4 d = .75
6
0
20 d = .75
40
0
20 d = .75
40
0
20 d = .875
40
0
20
40
1
0
0.02
0.02
0
0
0.5
2
4 d = .875
6
0.5
0
2
4 d = .875
6
0
20 d = .875
40
1
0
−0.5
d = .5
0.5
0.5
−0.5
Transitory Impulse Response Function
1
0
−0.5
Permanent Impulse Response Function
0.02
0.02
0
0
0.5
2
4
6
0
2
4
6
0
20
40
See notes to Figure 1 for the autocorrelation functions. See notes to Figure 2 for the impulse response functions.
Figure 5
Sensitivity to Gamma Parameter AFC for Output Growth
AFC for Nominal Wage Growth
gamma = .1
gamma = .1
0.5
2 4 gamma = .5
6
gamma = .1
0.02
0.02
0
0
0
2 4 gamma = .5
6
0
20 gamma = .5
40
0
20 gamma = .5
40
0
20 gamma = 1
40
0
20
40
1
0
0.02
0.02
0
0
0.5
2 4 gamma = 1
6
0.5
0
2 4 gamma = 1
6
0
20 gamma = 1
40
1
0
−0.5
gamma = .1
0.5
0.5
−0.5
Transitory Impulse Response Function
1
0
−0.5
Permanent Impulse Response Function
0.02
0.02
0
0
0.5
2
4
6
0
2
4
6
0
20
40
See notes to Figure 1 for the autocorrelation functions. See notes to Figure 2 for the impulse response functions.
