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Labor adjustment costs, macroeconomic shocks and real business cycles in a small open economy
PENE KALULUMIA University of Sherbrooke Sherbrooke, Quebec, Canada
FRANCINE NYAN KIYE International Monetary Fund Wc~hington, D.C.
Labor Adjustment Costs, Macroeconomic Shocks and Real Business Cycles in a Small Open Economy* This paper analyses a real business cycle model of a small open economy subjected to productivity, terms-of-lxade and fiscal shocks, and characterized by imperfect mobility of labor due to costly adjustment in labor input and job market segmentation. A dynamic and stochastic equilibrium model is used to perform empirical simulations. The model is calibrated to evaluate its ability to rationalize observed business cycle patterns in Cameroon. The results indicate that the model reproduces stylized facts of this country remarkablywell. Particularly, terms-of-trade shocks could explain most of the empirical regularities. The inclusion of labor adjustment costs explains the persistence of shocks or longer duration of business cycles.
1. Introduction
The real business cycle (RBC) models, which originated from the pioneering work of Kydland and Prescott (1982) and Long and Plosser (1983), have received substantial attention by many researchers in dynamic macroeconomics during the last decade. The aim of these models is to explain business cycles, identify their sources, and outline the propagation mechanisms through which cyclical fluctuations are generated. Particularly, a significant portion of this literature has been devoted to the extension of the basic closed-economy model to open economies, with a view to explaining additional stylized facts observed in the world economy. These include, among others, the positive correlation observed between national savings and investment (see Feldstein 1983; Mendoza 1991, 1992; and Cardia 1991), *This paper comes out of a research project that was funded by CIDA as part of the PARADI, managed by the CRDE, University of Montreal and the CREFA, Laval University. The authors axe indebted to Bernard Decaluwe, Benoit Carmichael, Emanuela Cardia, Mario Fortin, and the two anonymous referees for their constructive criticism.
Journal of Macroeconomics, Fall 2000, Vol. 22, No. 4, pp. 671-694 Copyright © 2000 by Louisiana State University Press 0164-070412000/$1.50
671
Pene Kalulumia and Francine Nyankiye the countercyclical movement of the current account (see Backus, Kehoe, and Kydland 1989; and Mendoza !991), and the Harberger-Larsen-Mertzler's effect (HLM) (Mendoza 1992; Macklem 1993). In addition, earlier research has shown that the cycles are generated not only by traditional productivity shocks but also by other sources of business fluctuations (see for instance, Christiano and Eichenbaum 1990; Cardia 1991; and Mendoza 1992). Until recently, RBC models were developed under the assumption of perfect mobility and costless adjustment of labor. These models, in which labor is freely acquired, overstate the degree of labor substitution across sectors, resulting in unrealistically high elasticities of employment between sectors in the face of exogenous shocks that affect the job market conditions. Normally there exist huge differences across sectors in terms of job skill requirements and labor productivity standards, particularly in developing economies, and this generally induces costly adjustment of labor across sectors and labor market segmentation, which limit labor force mobility (see Agdnor and Montiel 1996). In this paper we extend the previous work by introducing labor adjustment costs and job market dualism in a three-good RBC model of a small open economy subjected to productivity, terms-of-trade and government spending shocks. The objective of the paper is to examine in the presence of these labor market rigidities, the ability of the model to reproduce observed business cycle patterns of an actual small open economy, Cameroon, which relies on exports of a few number of commodities (oil, coffee and cocoa). More specifically, the paper analyzes the stylized facts of the economy, the relative importance of individual shocks in explaining business cycles, and the impact of labor adjustment costs and market segmentation on the dynamics of the economy, mainly on the persistence of shocks. The model studied in this paper assumes that labor adjustment costs are entirely borne by businesses and are mainly directed to the training of new recruits to allow them to reach the desired level of productivity. It is also assumed that the job market is dichotomized into a primary and a secondary segment as in Demekas (1990), but instead of wage rigidities, the segmentation is induced by sectoral differences in labor skill requirements as businesses will not hire workers with high initial training costs (Spence 1973). These assumptions lead to a short-rnn equilibrium characterized by the differences between wages across sectors since the labor input is not free of movement instantaneously. In the long-run, labor becomes perfectly mobile across sectors as a result of human capital improvement, since workers gradually acquire the skills necessary to be functional in all sectors of economic activity. The current model also includes a multi-sector structure that highlights the role of relative prices (such as the real exchange rate and 672
Labor Adjustment Costs in a Small Open Economy terms-of-trade). This is crucial in explaining economic fluctuations in developing economies. In particular, the relative importance of terms-of-trade versus fiscal and productivity shocks cannot be explored in a one-sector RBC framework. Finally, we use a dynamic stochastic model to perform numerical simulations from the method proposed by Blanchard and Khan (1980) and Blanchard (1983). The shocks affecting the economy are modeled as stationary stochastic processes and their variance-covariance matrix is estimated as in Cardia (1991). This contrasts with Macklem's (1993) work which uses a dynamic non-stochastic model. The results indicate that the model reproduces markedly well the empirical regularities we found for Cameroon, including the procyclicality of the trade balance, the HLM effect and the positive correlation between investment and saving. Particularly, we find that termsof-trade shocks are the most important source of business cycles since they can explain most of these empirical regularities. The dynamic responses of the economy to temporary shocks are quite different from what were predicted by previous models that assumed perfect mobility of labor. Shocks are more persistent in this model, explaining the longer duration of business cycles. Moreover, contrary to previous findings, a temporary terms-of-trade deterioration induces a contraction of the non-tradeables sector and an appreciation of the real exchange rate one period after the shock, due to shortrun rigidities in the labor market. The remainder of the paper is organized as follows. Section 2 describes the model; Section 3 summarizes the numerical resolution method., and the results of the stochastic simulations are reported and discussed in Section 4.
2. The Model The model describes the behavior of a small open economy which is specialized in the production of non-tradeables (goods n) and exportables (goods x), while importables (goods m) are produced abroad. Domestic consumption is only composed of importables and non-tradeables which also contribute to national capital formation. The great part of capital, however, is imported. 1 As in Demekas (1990) and Ag6nor and Montiel (1996, 56), it is assumed by simplicity that the labor market is segmented in relation to the production structure. The first segment, which is close to Demekas' 1The exportables sector comprises primary industries (oil, mining and exports crops), while nontradeables includes services, transport and communication, construction, local food crops, and wholesale and retail trade. Importables sector is defined residually and is mainly constituted by manufactured goods. This classification reflects the fact that Cameroon is a net exporter of commodities and net importer of manufactured goods.
673
Pene Kalulumia and Francine Nyankiye
secondary market definition, provides labor to the export sector, while the second part is connected to the non-tradeables sector. Contrary to Demekas (1990), however, the wage is flexible in both sectors. This segmentation corresponds to the case of Cameroon where the export sector, dominated by oil industries, involves high technology and heavy equipment that generally requires specific skills and higher levels competence among workers, in addition to being submitted to labor legislation. Conversely, construction, retail trade, food crops and many non-traded services are more labor intensive and mainly belong to the so-called informal labor market sector. 2 The model also includes a government which plays a role by financing its expenditures with taxes and debt. The fiscal policyis effective via the wealth effects of government debt since the Ricardian neutrality does not hold. Importables are assumed to be the numeraire good, so that the relative price ofnontradeables (p~) in terms of importables is interpreted as the real exchange rate and is endogenous for the domestic economy. In turn, the relative price (p~) of exportables in terms of importables provides the terms-of-trade and for a small open economy, it is exogenously determined abroad on world markets. In what follows, we will analyze the behavior of the three defined economic agents (producers, consumers, and government). Production
It is assumed that each production sector has a large number of identical firms working in perfect competition. In producing both tradeables and exportables, firms combine capital and labor (supplied by consumers). The factor intensities are, however, different across sectors. The problem of the representative firm is to maximize the expected present discounted value of profits: max
e -r(s-t) [/~,(s)Y/(s) -
VA(t) = Et
Fi(s)
Ni(t),Ki(t) -
w~N,(s)
-
"V~(s)
-
I,(s)]ds
,
i
=
~,x,
(1)
whel'e
Zln Cameroon, the great majority of the labor force in the non-tradeables sector is employed in food crops and retail trade. A farmer in the food crops sector, who generally does not use heavy agricultural equipment, cannot move in the short run to the oil sector (a high technology sector), while tile converse is true, with a worker in the oil sector_
674
Labor Adjustment Costs in a Small Open Economy Ii(t) = ~.(t) + ~ ( t ) ,
F~(t) = ~
v,(t)
-
w ~(t) ~ e ~.(t) "
Here K and N represent the capital and labor inputs respectively, r is the real interest rate, Y is the output, I is gross investment, and 5 is a constant rate of depreciation. In both sectors, firms have to deal with quadratic and convex costs of adjusting labor (F) and capital stock (W), formulated as in Georges (1995) and Summers (1981), respectively. The coefficients "fi and ~i are the costs-of-adjustment parameters. The above formulation of capital adjustment cost guarantees that investment will be a growing function of Tobin's q. Government imposes ad-valorem tax (~) to exports only, so that after tax, firms receive p~(t) = (1 - ~)p~(t) for exportables and p,(t) = pn(t) for non-tradeables. Aggregate outputs of both goods are given by the following constantreturns-to scale Cobb-Douglas production functions that also satisfy Inada conditions:
Yn(t) = exp[a(t)]K~(t)ON~(t) (1-~) ,
and
Yx(t) = exp[a(t)]Kx(t)nN~(t) (l-n) ,
(2)
where a(t) represents technological shocks affecting productivity. Output of exportables is also confronted with exogenous changes in terms-of-trade p~(t). Those two shocks are modeled later as stationary stochastic processes. To make things simpler, we drop the operator E. Meanwhile, each change = dx/dt of a variable is interpreted as an expected change. Under the wellknown transversality conditions, the system of Euler equations derived from profit maximization problem (1) in both sectors are:
675
Pene Kalulumia
and Francine
Nyankiye
1
N~(t) = -
(3)
q~(t) ,
71~(t) -
ii(t)
=
/~(t)
[q,(t) - 1],
(4)
[ 1 [q~(t)- 1] + 5~}K~(t),
(5)
where q_i(t) =
ft ~ e - r ( s - t ) [ p i ( s ) y N ( s )
-- wi(s)]ds
(6)
,
and qi(t)
=
e-+-t){pi(s)Y~(s) + (wl2)[~(s)/I~.(s)] z
-
Bids,
i = n,x.
(7)
The dynamic equations for q and q are obtained by differentiating Equations (6) and (7) over time: (I,(t) = rqi(t) q~(t) = rq,(t)
-
[p,(t)Y~(t) (pi(t)Y~(t)
-
(8)
wi(t)],
+ (~td2)[~(t)lK~(t)] z -
3J,
i = n,x.
(9)
Above yN and YtK are, respectively, marginal products of labor and capital. The q variable, which translates the shadow value of the labor stock perceived by the firm, is equal to the expected present value of future profit flows obtained from an additional unit of labor. Equation (3) provides the law of motion for labor stock accumulation. The steady-state labor demand is obtained when q = 0. Hence, ifq is above (below) zero, labor demand will be above (below) its steady state or long-run level. Equations from (3) to (9) indicate that both labor and capital are historical variables, while q and q are nonhistorical or jump variables. Georges (1995) proved that there will be a unique nonexplosive solution to (3) and (8) if the cost-of-adjustment parameter 7 is positive (7 > 0). Since capital adjustment cost is a linear homogenous function in I and K (Tobin average and marginal q's coincide), the firm's value is given by the product: q~(t)Ki(t), i = n,x. 676
L a b o r A d j u s t m e n t Costs' in a Small Open E c o n o m y Consumption
The consumer problem is derived from Blanchard's (1985) uncertain lifetimes approach. Due to the uncertainty of life expectancy, the absence of inheritance, and the stochastic state of the economy, we can infer that there is a contingent market of life insurance agencies that guarantees, through the use of premium, consumers' outstanding debts when they die. The insurance agent is also in charge of redistributing any credit balance of the deceased to members of his generation yet alive. The objective function of an individual of generation v working in the labor market i, at time t, is as follows:
max
c~ (v,s),q~ (v,s)
Et
e-(O+~)(~ t)[alnci,~(v,s) + (1 - ct)lncim (v,s) + O~lnL~(v,s)Jds,
i = 1,2;
(10)
where p stands for the subjective discount rate, 7t for the individual's probability of death, cn for the consumption of non-tradeables, Cm for that of importables, and L for leisure. If we normalize the endowment of time to one, Ni(v,t) = 1 - L~(v,t) will be the time allocated to work at time t for each individual born at time v. As we choose imported goods as a numeraire, total consumption is given by: ci(v,t)=p~(t)ci,(v,t)+ Cim(V,t ). Financial wealth W~(v,t) of a consumer working in market i comprises claims on firms of both sectors, on government bonds (b) and on foreign assets (f). This wealth, in real terms, is given by Wi(v,t) = bi(v,t) + fi(v,t) + qi~(v,t)Ki,(v,t)
+ qi~(u,t)K~(v,t).
(11)
At the end of period t, each individual receives rWi(v,t) in interest and nWi(v,t) from the insurance company in addition to the net current revenue of labor. The dynamic budgetary constraint that each category of workers has to face is thus given by Wi(v,t) = (n + r)W~(v,t) + wi(t)N~(v,t) - ci(v,t) -
Ti(t),
(12)
where m~(t) is the basic wage rate of individuals in market i, and Ti(t) denotes lump-sum taxes paid by consumers working in sector i. Both basic wage rate and taxes are independent of the consumers" age or generation. Here, the basic wage reflects the opportunity cost of working in each sector. To make things simpler, it is always set equal to the wage effectively paid by firms in each sector (wl(t) = w~(t) and w~(t) = w~(t)). 677
Pene Kalulumia and Francine Nyankiye
The objective of each consumer is to maximize the expected utility (10) subject to (11) and (12). We use the first-order conditions of this problem, the intertemporal budgetary constraint and the definition of human wealth to derive the individual plans of optimal consumption and labor
supply, a Aggregate Consumption
Aggregate consumption and labor supply at time t are obtained by integrating over generations of consumers and labor markets. The relationship between aggregate variables x(t) and individual variables x(v,t) is given by 2 • (t)
=
(13)
_
Optimal aggregate consumption and labor supply plans are thus given by c~(t) = aC(t)/p~(t),
where (14)
c ( t ) = cl(t) + ~ d t ) , cat)
= (1 -
(~5)
~)c(t),
C(t) = (p + lt)[W(t) + h(t)] ,
(16)
]~(t) = (r + 7t)h(t) - w~(t)Nl(t) - wxN2(t) + T ( t ) ,
(17)
aThe optimal paths of individual consumplaon and labor supply are given by
c,,(v,t) = aq(v,t)/pn(t), and
c,~(v,t) = (1 - ~)c,(v,t); Ni(v,t)
= 1 -
O~c~(v,t)/w~(t) ;
and c~(v,t)
where: h~(v,t) = at time t.
678
= (p + rc)[Wi(v,t)
ft~ e-(~+=)('-t~[wi(s)Ni(v,s)
-
+ hi(v,t)],
Ti(s)]ds defines the individual human wealth
L a b o r A d j u s t m e n t Costs in a Small O p e n E c o n o m y W ( t ) = r W ( t ) + w~(t)Nl(t) + w~(t)N2(t) -
C(t) -
C(t) = (r - p)C(t) - n(rt + p)W(t) , Nl(t) = 1 -
01c1(t)/wn(t),
N2(t) = 1 -
02c2(t)/w~(t).
T(t),
(18) (19)
and
(20)
Equations (14) and (15) give respectively the aggregate consumption of non-tradeables and aggregate consumption of importables. Both are proportional to total consumption expenditures. The aggregate total consumption and aggregate human and financial wealth are given by Equations (16), (17), and (18). While individual financial wealth is discounted at the rate ( r + n ) , Equation (18) shows that aggregate financial wealth accumulates at a rate r. This is because individual wealth is transferred to an insurance company at death. The equation of motion (19) for aggregate total consumption is obtained after differentiating Equation (16) and substituting W and/~ by their respective values. If n = 0 (infinite horizon), Equation (19) translates into Friedman's consumption standard plan. Equation (20) provides the optimal aggregate labor supply adapted to each sector, and which depends on aggregate consumption of each category of workers (c,(t)). Government
Government purchases nou-tradeables (g.) and importables (gin) and finances these expenditures (g) by imposing lump-sum taxes (T~)on individual consumption and income, ad-valorem taxes on exports (T~), and by issuing public debt (b). The government's budget constraint is defined by b(t) = rb(t) + g(t) -
T(t) -
Tx(t),
(21)
where T,(t) = xp,(t)Y~(t). Government faces a solvency constraint that allows it to sustain a debt level that is equal to the present value of future budget surpluses. To satisfy this solvency condition, taxes are set as a positive function of outstanding public debt and above interest payments: T(t) + T~(t) = (4 -
r)b(t) + T ( t ) ,
(22)
where ~ > r and T is the exogenous component of tax revenue. In allocating its expenditure between non-tradeables and importables, government does 679
Pene Kalulumia and Francine Nyankiye
not have an impact on household's utility functions or firms' production functions. Its optimal consumption plan is4 g,~(t) = pg(t)/p~(t),
and gin(t) = (1 - g)g(t).
(23)
General Equilibrium The following equations describe the general equilibrium of goods, labor, and assets markets: Z(t) = L(t)
+ L(t)
+
w~(t) 2 wrY(t) 2 + 2 /Z(t) 2 K~(t) '
Ynt(t) = c~,(t) + g~(t) + (1 -
c0)z(t),
M(t) = Cm(t ) q- gin(t) + 03I(t),
N~(t) + N~(t) <_ Nl(t) + N2(t) [w~th w~(t) ~ wx(t)], f(t) = r f(t) + p~(t)Y~(t) - M ( t ) , GDP(t) = p~(t)Y~(t) + px(t)Y~(t), s(t) = f(t) + I(t) .
(24)
(25)
(26)
(27) (28) (29) (30/
To complete this general equilibrium definition, Equations (3) to (22), and the stochastic processes {at,gt,P~t} must be integrated. The gross domestic investment I(t) is given by Equation (24). It includes costs of adjusting capital in both sectors. A fraction (1 - co) of investment is produced locally. Equation (25) translates a closed economy equilibrium for non-tradeables. Equation (26) reflects the idea that for our small open economy, the demand of manufactured products as well as that of equipment goods are in most part 4The governmentstatic optimization'sprogramis as follows: max u(g~(t), gin(t)) = Ix lng,,(t) + (1 - Ix)lng~(t)subject to g(t) = p~(t)g,~(t) + gin(t) .
gn(t),gm(t)
680
Labor Adjustment Costs in a Small Open Economy satisfied by imports (M). On the other hand, Equation (27) translates the equilibrium of the labor market with possible unemployment, as in shortrun total employment may be less than total labor force and wages do not equalize across sectors. The current account is defined by Equation (28) as the change in net foreign assets, which is the sum of trade balance and net interest payments. The gross domestic product (GDP) is given by Equation (28), while gross domestic saving is given by Equation (30) as the sum of total investment cost and current account balance.
3. Numerical Solution Method In general, it is difficult to solve a non linear stochastic system of equations analytically. For this reason, all the equations that define general equilibrium are linearized by using a first-order Taylor expansion around the steady state as in King, Plosser and Rebelo (1988). The discrete version of linearized equations are provided in the appendix, where ~ denotes the deviation of a variable xt from its steady-state value x0. The state-space representation of the system is defined as follows (see the appendix): E~Xt + I = AXt + BZ, ,
(31)
where X~ = [[(~n,t_l, ~.x,t_l, Nn.t_l, Nxt_l qnt, qxt, ~n,t, ~x,t, Ct, fgt, fct, v~Vt,] and Z; = Ida, ~t, ~ ] . X is the vector of the state variables and Z, that of exogenous shocks. It is assumed to be a first-order vector autoregressive process:
Zt + l = f~Zt -If- ~ - t + l
,
where et ~ i.i.d.N(O, Z) ,
(32)
with air ~ i.i.d N(0, cry), E(e~tejt ) = a~j, i = j = 1. . . . . 3. The elements of the matrices A and B are derived in the ap~pendix. The state vector includes seven predetermined variables {/~,,t-~ K~,t- 1, Nn.t- 1, N,,t- z, bt, ~, ~Vt}, which are associated with the initial conditions and five forward-looking variables {Cl~,t,(1~, (t,t, (1~, ~t}. The system will admit a unique and stable solution that corresponds to a saddle point equilibrium, if we find seven stable characteristic roots and five unstable roots in the matrix A (see Blanchard and Khan 1980). To solve and simulate numerically the system of stochastic difference Equations in (31) and (32), we use the method proposed by Blanchard (1983). 681
Pene Kalulumia and Francine Nyankiye TABLE 1.
Values of Some Parameters
= 0.30 = 0.20 13 = 0.51
p = 0.04 5 = 0.10 ot = 0.75
7~ = 7x = 2.0 v = 0.80 01 = 02 = 2.11
n = 0.018 ~ = 0,05 ~ = ~ = 2.0
4. Empirical Results Stationary State and Calibration Steady-state equilibrium is characterized by the constancy in variables, the absence of exogenous shocks that disturb the economy (a0 = Px0 = 1), and by the absence of labor and capital adjustment costs. This means that in the long-run, both capital and labor factors become perfectly mobile and the wages equalize in both sectors. Thus, the steady-state expressions of the real exchange rate (P~0) and wage (w0) are given by p e~0 = ( ( 1 -
z)px0)~]-~ (1
1 wo =
(1 -
(r
TI)\
13 ]
\
q
/
'
+ ~l~[J-1 p
]
(34) -
Investment in the steady state is given by the relationship: I o = 8(K~0 + K~0). Accordingly, knowing Pno, Wo and the ratio of total investment allocated to each sector, we can recursively determine the values of all other endogenous variables in the steady state. However, these variables are the function of parameters whose values need to be established before. Previous studies and calibration techniques were used to fix parameter values. The idea is to reproduce the reality of the Cameroon economy, as reflected by the steady-state data. These steady-state data are computed as the means of variable observations over the period 1968-1993. Each variable is expressed in proportion of real GDP and deflated by the imports price index, since importables are the nnmeraire good in the theoretical model. Data used in this study were obtained from the World Bank's World Tables and IMF's International Financial Statistics. Table 1 presents all parameter values used in our simulations. The rate of capital depreciation and the world real interest rate are respectively established at 10% and 4%, as in Kydland and Prescott (1982). Following the study of Timothy, Dahl and Devarajan (1986) and the Cameroon social accounting's matrix of 1991, about 55% of Cameroon capital is used by the non-tradeables sector, which also employs 80% of labor. The share of importables in private and government con682
Labor Adjustment Costs in a Small Open Economy sumption is 25%, respectively. The share of capital (13) in the production of non-tradeables is 51%, whereas it represents 20% 01) in the production of exportables. Exports sector is more capital intensive as k~o = 4.85 versus k.0 = 0.71 in the non-tradeables (here, ki = ~/Ni). On the other hand, our data reveals that in 1992, life expectancy at birth (l/n) was 54.6 in Cameroon. Accordingly, the probability of death (n) is set to 0.018, following that 1/n = 54.6_ Other model's parameters were determined by calibration to reproduce the Cameroon data base. Thus, cost-of-adjustment parameters have been fixed at 2, whereas the values of leisure share parameters were set to 2.11. Some steady-state values of state variables, derived endogenously~ are as follows: 68% of GDP for private consumption (C), 23% for exports (X), 24% for imports (M), 23% for investment (I), 10% for public spending (g), and - 1% for the current account.
Simulation of Stylized Facts of the Cameroon Economy This section deals with the study of real business cycles in Cameroon. Empirical regularities observed in the country are first derived. They are then compared with the properties of data simulated from our theoretical model. Sample statistics measuring variable correlation, volatility and autocorrelation are used for this endeavor. Stylized facts. Stylized facts of the Cameroonian economy are reproduced from actual data for the period under study (1968-1993). The series have been transformed logarithmically and filtered by using the HodrickPrescott filter5 with a smoothing coefficient of 100, as in some previous studies (Ambler and Cardia 1995; Cardia 1991; and Backus, Kehoe, and Kydland 1989). Filtered data indicate, in whole, a decade of persistent recession that started in the 80s and the worsening of the terms of trade during the same period. The first four columns of Table 2 represent the stylized facts of the Cameroon economy. The following facts are observed: consumption, investment, saving, and trade balance are all procyclical. There is a positive correlation between trade balance and terms of trade (the HLM effect), as well as between saving and investment. These stylized facts are qualitatively similar to those reported by Mendoza (1992) and Cardia (1991) using industrial country data, except for the procyclicality of the trade balance. In many developed economies, in fact, trade balance is countercyclical.
5Cogleyand Nason (1995) suggestthat the HP filter may create artificialcyclesif the prefiltered series is first-orderedintegrated. Park (1997) showsthat this problem deepens as the degree of integrationbecomeshigher. He finds,however,that the filter-orientedsensitivityof the stylizedfacts are symmetricbetween the actualdata and the simulateddata, implyingthat the sensitdvityitselfdoes not invalidatethe performanceof RBC modelsin replicatingthe actual economy. 683
Pene Kalulumia and Francine Nyankiye The procyclicality of the trade balance in developing countries stems from that GDP growth is mainly driven by exports of commodities. The better is the performance of exports over imports (which means a trade balance surplus), the stronger will be the rate of GDP growth. Simulation of Empirical Facts. The shocks disturbing the economy {at, g~, p~} were modeled as stationary AR(1) processes (see Equation 32), which autocorrelation coefficients were, respectively, 0.908, 0.95 and 0.95, and which error term variances were, respectively, 0.038, 0.053, and 0.210. Their covariances were 0-12 = 6.1e - 4, o'13 1.2e - 4 and 0"23 = - 5.7e - 4. Particularly, productivity shocks were estimated as residuals of the Mankiw, Romer and Well (1992) neoclassical regression, which includes saving, labor force growth and other exogenous parameters of technology (the rates of depreciation and technological progress were fixed at 0.1 and 0.4, respectively). The Gauss software random number generator was used to simulate stochastically the model by generating repeatedly the error term vector ~+ 1, using 300 replications and 36 periods. The first 10 observations were removed to offset the effect of the initial conditions on computed statistics, especially standard deviations and correlation coefficients. This data truncation enabled us to have a sample of 26 observations corresponding to the size of the genuine database, spanned over 26 years. The solution to the state-space model was stable and unique since the conditions established by Blanchard and Khan (1980) were satisfied. Indeed, five eigenvalues of the A matrix were outside the unit circle, and this amounted exactly to the number (five) of jump variables in the model. Simulated Cameroon data were also filtered by using the Hodrick-Prescott filter with a smoothing coefficient 100 after taking their logarithmic transformation. Statistical properties of simulated series are reported in the last four columns of Table 2. They were computed as empirical means over the 300 drawings. From these results, we can conclude that the model mimics remarkably well the stylized facts of the Cameroon economy. Empirical covariations and autocorrelations are close to those calculated with genuine data in the first four columns of the Table. In particular, the model reproduces the observed procyclical behavior in various aggregates, as well as the higher volatility of investment relative to GDP. The model also reproduces the positive correlation observed in Cameroon, between investment and saving and the Harberger-Larsen-Metzler (HLM) effect, or in other words, the positive correlation between terms of trade and trade balance. =
- -
Relative Importance of Shocks The relative importance of shocks in explaining economic fluctuations in Cameroon is analyzed by comparing the results of Table 2, which include all three shocks, with those in Table 3 obtained by subjecting the economy 684
TABLE 2.
Stylized Facts and Simulation Results A. Stylized facts: Cameroon data
Variables (x ) GNP GDP(y) Consumption Investment Exports Imports Trade balance Savings RER External debt
B. Simulated facts: Theoretical model
cr,
crx/~y
px,y
p(1)
o,
cy,/cry
Px,y
p(1)
0.043 0.043 0.042 0.110 0.065 0.057 0.049 0.041 0.051 0.034
1.00 1.00 0.98 2.53 1.52 1.12 1.13 0.95 1.09 0.79
1.00 1.00 0.67 0.63 0.72 0.79 0.23 0.53 0.23 0.35
0.92 0.92 0.45 0.30 0.53 0.70 0.35 0.92 0.53 0.98
0.032 0.032 0.028 0.083 0.034 0.031 0.034 0.037 0.040 0.026
1.00 1.00 0.86 2.56 1.06 0.97 0.77 1.15 1.23 0.81
1.00 1.00 0.75 0.75 0.98 0.75 0.35 0.54 0.30 0.34
0.92 0.92 0.41 0.36 0.59 0.58 0.40 0.95 0.57 0.93
Correlations:
Correlations:
Savings-Investment: 0.77 Terms-of-trade-TB: 0.12
Savings-Investment: 0.98 Terms-of-trade-TB: 0.37
NOTE: *RER is the real exchange rate. For each x variable, p(1) represents the autocorrelation coefficient, p~,ythe cross-correlationwith GDP and ~/~y, the ratio of its standard deviation to that of the GDP. Data have been filtered using Hodrick-Prescott filter with a smoothing coefficientof 100, after taking their logarithmictransformation.
TABLE 3.
Relative Importance of Shocks C. Productivity shocks (o~)
Variables(x) GNP GDP (y) Consumption Investment Exports Imports Trade balance Savings RER External debt
ox 0.0137 0.0137 0.0142 0.0426 0.0135 0.0141 0.0134 0.0131 0.0142 0.0141
Px,y p(1) 1.00 1.00 0.37 0.32 0.30 0.41 0.15 0.37 0.71 0.57
0.42 0.42 0.15 0.60 0.93 0.98 0.65 0.42 0.85 0.58
D. Fiscal policy shocks (g,) o~
0.0271 0.0271 0.0265 0.0796 0.0274 0.0265 0.0274 0.0240 0.0270 0.0250
px,y p(1) 1.00 1.00 0.97 0.98 0.97 0.69 0.33 0.83 0.51 0.45
0.91 0.91 0.45 0.24 0.49 0.57 0.35 0.98 0.63 0_90
D. Terms-of-trade shocks (p~) O2 0.0341 0.0341 0.0286 0.0857 0.0359 0.0385 0.0359 0.0370 0.0390 0.0270
p~,y p(1) 1.00 1.00 0.89 0.75 0.96 0.75 0.32 0.54 0.37 0.38
0.92 0.92 0.42 0.31 0.59 0.58 0.38 0.96 0.57 0.95
685
Pene Kalulumia and Francine Nyankiye to each shock individually. The values of %, p,,y, and p(1) are used for the comparison. It is dear that the numbers in the three last columns of Table 3 are very dose to those in Table 2 (in both Panel A and B). This suggests that most empirical regularities observed in Cameroon can be explained by using only the terms-of-trade shocks. The addition of other shocks does not appear to affect significantly the volatility of output, investment, saving and consumption. The results also show that terms-of-trade shocks are followed by fiscal policy disturbances and technological shocks, which play a minor role. Given these findings, we conclude that terms-of-trade changes are a very important source of economic fluctuations in Cameroon. Thus, in our analysis of temporary shocks presented below, the focus is only on the effects of terms-of-trade disturbances in short and medium-term.
Analysis of Impulse Responses to Shocks This section deals with the dynamic effects of shocks to assess the impact of the inclusion of labor adjustment costs on economic fluctuations, especially on the persistence or duration of cycles. We consider the impact of a 10% temporary terms-of-trade deterioration that occurs in the third period (t = 3), and its magnitude decreases gradually over time. The quantitative effects of this shock, which are interpreted as percentage deviations from the initial steady state, are depicted graphically in Figure 1. It is indicated that this terms-of-trade deterioration induces first (after one period) a contraction of the export sector (4%). Even though the non-tradeables sector, now becoming more profitable, offers a wage relatively higher than that of the export sector ( - 2 . 8 % versus -5.8%), it would not be able to attract more labor inputs because of the high cost of adjusting labor. This imperfect mobility of labor explains why there is a decline in the output of non-tradeables (-2.3%) and an appreciation of the real exchange rate (11%), a period after the shock (at t = 4). However, output goes up to 0.13% at period t = 5 before converging to its steady-state equilibrium. Wage and employment in the non-tradeables sector follow the same path as production (down and then up). The contraction of exports causes a reduction of current and expected profits of the export sector, leading to a fall in both the Tobin's q and the consumers' wealth. Consumers have therefore to lower their levels of consumption and investment. Since the contracted export sector is more capital intensive, investment decreases more than consumption ( - 8.6% versus - 5.7%). The fall of aggregate demand (C and I) explains why imports decline. The real exchange rate also depreciates ( - 12.6%) later at period t = 5, following the reduction in demand and as labor gradually moves to the non-tradeables sector. The trade balance credit goes down by 1.4%, for a while, after the terms-of-trade deterioration and then goes up by 0.32% before returning to its long-term level. The jerky 686
Labor Adjustment Costs in a Small Open Economy TRADE BALANCE AND FOREIGN DEBT
SDP. CONSUMP-OON AND INVESTMENT ,
o! o
' 4~
,
.,
~
,
1"~
,.
,
16
,'
i I~ORT~ .
IMPOR~ AND OUTPUT OF NON-TRAD~BLES .
,
1
~ //~] "~~
: l
REAL EXCHANGE RATE
,,
'
l~.
12
a
,
,
/i :i
/[---. ..... LABOR IN BOTH SECTORS
'
T"
'
"-~'
~
J
'
i'~
WASE IN BOTH SECTORS
'
~'o
'
///
1 Figure 1. Impact of a 10% Temporary Terms-of-Trade Deterioration
expansion path of the trade balance is due to the real exchange rate path and the exports and imports path. The economy also records a growth of its external debt (5.7%) to finance the temporary deficit of its trade balance (see Equation (28)). However, this debt is dampened later as the economy experiences a trade balance surplus. Some of these findings contrast with the results obtained by Macklem (1993) or Carmichael, Keita and Samson (1995) because of the concept of limited mobility of labor in this model. These studies envisaged, in general, an expansion of the non-tradeables sector (with a rise in wage and employ687
Pene Kalulumia and Francine Nyankiye ment) and a depreciation of the real exchange rate one period after the terms-of-trade shock. Moreover, shocks are persistent in this model. Its effects last almost 7 periods while they never outlasted more than 3 periods in Macldem's model (without labor adjustment costs). We have also analyzed the impact of temporary government spending and productivity shocks. The quantitative effects of these shocks were smaller than those of the export price disturbance for the same magnitude of shock, confirming the finding that terms-of-trade shocks are the major source of economic fluctuations in Cameroon. The results also indicated that restricted fiscal policies, such as cutting government spending, can be used to mitigate and offset the negative effects of terms-of-trade deterioration. They result in the depreciation of the real exchange rate, stimulate over time the export sector and liberate a trade balance surplus that helps the country deal with its external liabilities.
5. Conclusions In this paper, we developed a dynamic and stochastic equilibrium model of a small open economy, which is subjected to productivity, fiscal spending and terms-of-trade shocks. The important feature of this study was to analyze the role of both labor adjustment costs and exogenous macroeconomic shocks in explaining real business cycles of an open economy with a segmented labor market. The model was calibrated and simulated to evaluate its ability to replicate the stylized facts observed in Cameroon. The results of numerical simulations indicated that the model reproduces remarkably well most of the empirical regularities of the Cameroon economy, particularly, the procyclical behavior of consumption, investment, saving and trade balance, as well as the higher volatility of investment relative to GDP. The model also generated the positive correlation between investment and saving and the Harberger-Larsen-Metzler (HLM) effect, which many previous studies failed to reproduce. The analysis of the relative importance of shocks revealed that terms-of-trade disturbances have been the most important source of business fluctuations in Cameroon for the period under study. They are followed by fiscal policy shocks and technological changes, the latter shocks playing a small role. The analysis of dynamic responses to shocks indicated that shocks are more persistent in this model, which contrasts with the predictions of previous models that have assumed perfect mobility of labor (such Macklem 1993). If the economy is faced with a terms-of-trade deterioration, previous models suggested an expansion of the non-tradeables sector and a depreciation of the real exchange rate one period after the shock. The current model predicts a decline in the output of non-tradeables and an appreciation of the real exchange rate, as a result of short-run rigidities in the labor market. 688
Labor Adjustment Costs in a Small Open Economy Overall, this paper belongs to a group of few studies that have succeeded in analyzing business cycles in developing countries. Our results are generally consistent with the studies by Carmichael, Keita and Samson (1995), Tanner (1989) and Khan and Knight (1983) that provided evidence of the HLM effect and identified the terms-of-trade disturbances as an important source of business fluctuations in developing countries. The results also support the findings by Amano and Macldem (1996) suggesting that unemployment persistence is mainly a result of costly adjustment of labor, and confirm the findings by Demekas (1990) that the job market structure affects the real exchange rate and unemployment. Finally, extensions of the current paper can consider the inclusion of labor adjustment costs in the offer side, and this would be properly addressed in a one-sector model (to reduce the number of parameters) and in a context where reliable data on skilled and unskilled workers are available. Received: April 1998 Final version: November 1999
References Amano, Robert A., and R. Tiff Macklem. "Unemployment Persistence and Costly Adjustment of Labor: A Canada-U.S. Comparison." Manuscript, Bank of Canada, Ottawa, Canada, 1996. Ambler, Steve, and Emanuela Cardia. "Les Modeles Reels de la Transmission Internationale du Cycle Economique." L'Actualite Economique 71 (1995): 164-93. Ag6nor, Pierre-Richard, and Peter J. Montiel. "Development Macroeconomics." Princeton: Princeton University Press, 1996. Backus, David K., Patrick J. Kehoe, and Finn E. Kydland. "International Borrowing and World Business Cycles." Working paper, 426R, Federal Reserve Bank of Minneapolis, 1989. Blanchard, Olivier J. "Methods of Solution and Simulation for Dynamic Rational Expectations Models." NBER Technical Working Paper No. 28, 1983. --. "Debt, Deficits and Finite Horizons." Journal of Political Economy 93 2 (1985): 223-47. Blanchard, Olivier J, and Charles M. Kahn. "The Solution of Difference Models under Rational Expectations." Econometrica 48 (1980): 1305-11. Cardia Emanuela. "'The Dynamics of a Small Open Economy in Response to Monetary, Fiscal, and Productivity Shocks." Journal of Monetary Economics 28 (1991): 411-34. Carmichael, Benoit, Sikoro Keita, and Lucie Samson. "Cycles Economiques 689
Pene Kalulumia and Francine Nyankiye au Senegal: Une Approche RBC." Cahier de recherche, No. 9506, CREFA, Universite Laval, Canada, 1995. Christiano, Lawrence J., and Martin Eichenbann. "Current Real Business Cycle Theories and Aggregate Labor Market Fluctuations." Northwestern University, Evanston, IL, 1990. Mimeo. Cogley, Timothy, and James M. Nason. "Effects of the Hodrick-Prescott Filter on Trend and Difference Stationary Time Series: Implications for Business Cycle Research." Journal of Economic Dynamics and Control 19 (1995): 253-78. Condon, Timothy, H. Dahl, and Shantayanan Deverajan. "Implementing a Computable General Equilibrium Model on Gams: The Cameroon Model." World Bank Staff Working Papers, The World Bank, Washington, 1986. Demekas, Dimitri G. "Labor Market Segmentation in a Two-Sector Model of an Open Economy." IMF Staff papers 37, no. 4 (1990): 849-64. Feldstein, Martin. "'Domestic Saving and International Capital Movements in the Long Run and the Short Run." European Economic Review 79 (1983): 733-48. Georges, Christophe. "Adjustment Costs and Indeterminacy in Perfect Foresight Models." Journal of Economic Dynamics and Control 19 (1995): 39-50. Khan, Moshini S., and Malcom D. Knight. "Determinants of Current Account Balances of Non-Oil Developing Countries in the 1970s: An Empirical Analysis." IMF Staff Papers 30, no. 4 (1983): 819-42. Fdng Robert G., Charles I. Plosser and Sergio T. Rebelo. "Production, Growth and Business Cycles: The Basic Neoclassical Model." Journal of Monetary Economics 21 (1988): 195-232. Kydland Finn E., and Edward C. Prescott. "Time to Build and Aggregate Fluctuations." Econometrica 50 (1982): 1345-70. Long, John B., and Charles I. Plosser. "Real Business Cycle." Journal of Political Economy 91 (1983): 39-69. Macldem, R. Tiffs. "Terms-of-Trade Disturbances and Fiscal Policy in a Small Open Economy." The Economic Journal 103, no. 419 (1993): 91636. Mankiw, Gregory N., David Romer, and David Weil. "A Contribution to the Empirics of Economic Growth." Quarterly Journal of Economics 2 (1992): 407~37. Mendoza, Enrique G, "Real Business Cycles in a Small Open Economy." American Economic Review 81 no. 4 (1991): 787-819. . "The Effects of Macroeconomic Shocks in a Basic Equilibrium Framework." IMF Staff Papers 39, no. 4 (1992): 855-99.
690
Labor Adjustment Costs in a Small Open Economy Park, Gonyung. "The Role o f D e t r e n d i n g M e t h o d s in a M o d e l of Real Business Cycles." Journal of Macroeconomics 18, no. 3 (1996): 479-501. Spence, Michael. "Job M a r k e t Signaling." Quarterly Journal of Economics 87, no. 2 (1973): 355-74. S u m m e r s , L a w r e n c e H. "Taxation and C o r p o r a t e I n v e s t m e n t : A q - T h e o r y A p p r o a c h . " Brookings Papers on Economic Activity 1 (1981): 67-127.
Appendix The System of Linearized Equations and the State-Space Form L e t us d e n o t e the deviation o f xt f r o m its steady-state value x0 b y xt = xt - x0, and recall t h a t xt = E t X t + l -- Xt in discrete form. Thus, the discrete version of l i n e a r i z e d e q u a t i o n s are w r i t t e n as follows: K,
= K,,-,
+ (~o/V.)0., ,
(48)
&
=
q- (K-xo/lqlx)~lxt,
(49)
~,t-1
R.t = & , - 1 + (1/~)0.t,
(50)
iV~ = N~,t-1 + ( 1 / y , ) ~ ,
(51)
vVt+l = D,+~ + ~+~ + &~ + O°.~+#qo + K~ + cT~,,+~Iqo,
(52)
EtO.,t + 1 = (1 + r)[gl,t - P,t¥~o K - p ~ o ¥~'~ , o / ^q t KN ~ - p.oY~o N.t - p.oY~gtt],
(53)
E~.,+I
EtO..t+l_
= ( i + r)[O~, -
=
z)YS#~t-
z)p~oY~oR_.t - (1 - x)Y~omViv~ + (1 - ~)p~oY~gtt], (i -
(1 + r)[gt.,t_ -- P^n t ~ ON
(i -
-- PnoY~oNN*N.t NK ^
Na - p,oY~o K~t - p,oY~oat - do,t] ,
(54)
(55)
E~,t+~_ = (1 + r)[0~,_ - (1 - x)/3~oYN - (1 - x)P~oY~oNN'N,~ ~+1
(i .
z)p~oYNK~, t . .
N~- - d o ~ ] , x)p~oY~oat
(56)
+ Y~o~,~ + p~oY~o[<~ + p~oyNoN,=t + p,oY~oat - (1 - a ) O t - (i - ~t)gt - 5.K,~t - 8~R.~] ,
(57)
.
(i
= (1 + r ) g
/~t+l = (i + r EtCt+l
~)/~t + (1 + r ) ~ ,
= [(1 + r)/(1 + p)](7 t -
(58)
rcOEtlTVt+ 1
where
691
Pene Kalulumia and Francine Nyankiye 0 = [(1 + 7t)(1 + p) -
1]/[(1 + g)(1 + p ) ] ,
(59)
OtvCt 01vCo N.t w,~,t - (1 - N~o) + (1 - - - ~ o ) 2 ' -
~
(1
Y~o
"C)p~oyNagtt
-
~'~ -]-
(1 -
r)p~oY~o N,~ +
+
Pnt = ~
(60)
-
NK^ '~)p~o¥;~o K~
7(N~
-
N~,t-t),
p~o¥~NoN (Nn,
Y~o
-
-
Nnt-1)
N
"
Y~o
(61)
(69,)
Nnt "
Here, Y[0 denotes the derivative of Yi with respect to x, evaluated at the steady-state value. The system comprises 15 endogenous variables and 15 equations. In compact matrix notation, it is written as EtXt+l
= MIE~t+I
+
M2Xt + MaYt +
M4Zt,
Y = T1E~t+I + TeXt + TaYt + T4Zt,
(63) (64)
where
X; = ER.~,t_x, [i..,t_l, <,t_l, £ , t _ l , gl~,, gl~t, gl~,t, gl~,t, Ct, Dt, ~, l?Vt], Y2
and
z;
=
[a,, ~, ~ ] .
The state-space representation of the system is given by E t X t + I = A X t q- B Z t ,
(65)
where
A = [M2 + MaT~(I - T3)-J][I - M1 - MaTI(I - Ta)-I] -1, B = [M 4 + MaT4(I - %)1[I - M1 - MaTI(I - Ta)-I] -1 . The matrices M1, M2, Ma, M4, T1, T2, Ta, and T4 are provided below.
692
I
~
I
~
0
~
~
I
I
÷ v
I ÷
~
+
+
+
I
I
~
o
~
~
+
I
~
°~°°°°÷°°°~1
~
+
.4
~ /
I
I II
I
I il
693
M3
M4
T2 =
0 0 0 0 0
0 0 0 0 0
o
o
0 -(l+r) 0 0 0 0
0 0 -(l+r) 0 0 0
-(l+~)r~o
0 - (1 +r)¥No 0 0 0 0
0 0 0 0 0 - (1 + r)p~oY~ -(l+r)(1-x)p,oY ~ - ( I +r)P~oyN~ -(l+r)(l-x)p.oY~o 0 0 (l+r)P~oY~o
0 0 0 0 0 0 0 0 0 0 (l+r) (1-7~)
0 0 0 0 0 0 - (1+ r ) ( 1 - z)Y~o 0 - (1 + r ) ( 1 - z ) Y N 0 0 Y.o
0
01vCo/(1 - N,~o)2
(1 - r )p~oY~oK
o
[!o 0 0
o
oooooooi]
0 (1
~ ) p ~ o Y ~ o NN -
-
(~,~ - p~or~o~)/y~o
0 0 0 0 0 0 0 0 0 0 0 0 0 0
7~
o
0
0
0
0
0
0
Olv/(1-N.o)
0
0
0 -~,~n%
¥ o
0 o
0 o
0 o
0 o
0 o
0 o
00oJ , o
o
=
0
694
0 0 0 0 0
.T,
Eo
-(l+r)p~oY~ °
o
0
0
(1-)Y5
.
01
FRANCINE NYAN KIYE International Monetary Fund Wc~hington, D.C.
Labor Adjustment Costs, Macroeconomic Shocks and Real Business Cycles in a Small Open Economy* This paper analyses a real business cycle model of a small open economy subjected to productivity, terms-of-lxade and fiscal shocks, and characterized by imperfect mobility of labor due to costly adjustment in labor input and job market segmentation. A dynamic and stochastic equilibrium model is used to perform empirical simulations. The model is calibrated to evaluate its ability to rationalize observed business cycle patterns in Cameroon. The results indicate that the model reproduces stylized facts of this country remarkablywell. Particularly, terms-of-trade shocks could explain most of the empirical regularities. The inclusion of labor adjustment costs explains the persistence of shocks or longer duration of business cycles.
1. Introduction
The real business cycle (RBC) models, which originated from the pioneering work of Kydland and Prescott (1982) and Long and Plosser (1983), have received substantial attention by many researchers in dynamic macroeconomics during the last decade. The aim of these models is to explain business cycles, identify their sources, and outline the propagation mechanisms through which cyclical fluctuations are generated. Particularly, a significant portion of this literature has been devoted to the extension of the basic closed-economy model to open economies, with a view to explaining additional stylized facts observed in the world economy. These include, among others, the positive correlation observed between national savings and investment (see Feldstein 1983; Mendoza 1991, 1992; and Cardia 1991), *This paper comes out of a research project that was funded by CIDA as part of the PARADI, managed by the CRDE, University of Montreal and the CREFA, Laval University. The authors axe indebted to Bernard Decaluwe, Benoit Carmichael, Emanuela Cardia, Mario Fortin, and the two anonymous referees for their constructive criticism.
Journal of Macroeconomics, Fall 2000, Vol. 22, No. 4, pp. 671-694 Copyright © 2000 by Louisiana State University Press 0164-070412000/$1.50
671
Pene Kalulumia and Francine Nyankiye the countercyclical movement of the current account (see Backus, Kehoe, and Kydland 1989; and Mendoza !991), and the Harberger-Larsen-Mertzler's effect (HLM) (Mendoza 1992; Macklem 1993). In addition, earlier research has shown that the cycles are generated not only by traditional productivity shocks but also by other sources of business fluctuations (see for instance, Christiano and Eichenbaum 1990; Cardia 1991; and Mendoza 1992). Until recently, RBC models were developed under the assumption of perfect mobility and costless adjustment of labor. These models, in which labor is freely acquired, overstate the degree of labor substitution across sectors, resulting in unrealistically high elasticities of employment between sectors in the face of exogenous shocks that affect the job market conditions. Normally there exist huge differences across sectors in terms of job skill requirements and labor productivity standards, particularly in developing economies, and this generally induces costly adjustment of labor across sectors and labor market segmentation, which limit labor force mobility (see Agdnor and Montiel 1996). In this paper we extend the previous work by introducing labor adjustment costs and job market dualism in a three-good RBC model of a small open economy subjected to productivity, terms-of-trade and government spending shocks. The objective of the paper is to examine in the presence of these labor market rigidities, the ability of the model to reproduce observed business cycle patterns of an actual small open economy, Cameroon, which relies on exports of a few number of commodities (oil, coffee and cocoa). More specifically, the paper analyzes the stylized facts of the economy, the relative importance of individual shocks in explaining business cycles, and the impact of labor adjustment costs and market segmentation on the dynamics of the economy, mainly on the persistence of shocks. The model studied in this paper assumes that labor adjustment costs are entirely borne by businesses and are mainly directed to the training of new recruits to allow them to reach the desired level of productivity. It is also assumed that the job market is dichotomized into a primary and a secondary segment as in Demekas (1990), but instead of wage rigidities, the segmentation is induced by sectoral differences in labor skill requirements as businesses will not hire workers with high initial training costs (Spence 1973). These assumptions lead to a short-rnn equilibrium characterized by the differences between wages across sectors since the labor input is not free of movement instantaneously. In the long-run, labor becomes perfectly mobile across sectors as a result of human capital improvement, since workers gradually acquire the skills necessary to be functional in all sectors of economic activity. The current model also includes a multi-sector structure that highlights the role of relative prices (such as the real exchange rate and 672
Labor Adjustment Costs in a Small Open Economy terms-of-trade). This is crucial in explaining economic fluctuations in developing economies. In particular, the relative importance of terms-of-trade versus fiscal and productivity shocks cannot be explored in a one-sector RBC framework. Finally, we use a dynamic stochastic model to perform numerical simulations from the method proposed by Blanchard and Khan (1980) and Blanchard (1983). The shocks affecting the economy are modeled as stationary stochastic processes and their variance-covariance matrix is estimated as in Cardia (1991). This contrasts with Macklem's (1993) work which uses a dynamic non-stochastic model. The results indicate that the model reproduces markedly well the empirical regularities we found for Cameroon, including the procyclicality of the trade balance, the HLM effect and the positive correlation between investment and saving. Particularly, we find that termsof-trade shocks are the most important source of business cycles since they can explain most of these empirical regularities. The dynamic responses of the economy to temporary shocks are quite different from what were predicted by previous models that assumed perfect mobility of labor. Shocks are more persistent in this model, explaining the longer duration of business cycles. Moreover, contrary to previous findings, a temporary terms-of-trade deterioration induces a contraction of the non-tradeables sector and an appreciation of the real exchange rate one period after the shock, due to shortrun rigidities in the labor market. The remainder of the paper is organized as follows. Section 2 describes the model; Section 3 summarizes the numerical resolution method., and the results of the stochastic simulations are reported and discussed in Section 4.
2. The Model The model describes the behavior of a small open economy which is specialized in the production of non-tradeables (goods n) and exportables (goods x), while importables (goods m) are produced abroad. Domestic consumption is only composed of importables and non-tradeables which also contribute to national capital formation. The great part of capital, however, is imported. 1 As in Demekas (1990) and Ag6nor and Montiel (1996, 56), it is assumed by simplicity that the labor market is segmented in relation to the production structure. The first segment, which is close to Demekas' 1The exportables sector comprises primary industries (oil, mining and exports crops), while nontradeables includes services, transport and communication, construction, local food crops, and wholesale and retail trade. Importables sector is defined residually and is mainly constituted by manufactured goods. This classification reflects the fact that Cameroon is a net exporter of commodities and net importer of manufactured goods.
673
Pene Kalulumia and Francine Nyankiye
secondary market definition, provides labor to the export sector, while the second part is connected to the non-tradeables sector. Contrary to Demekas (1990), however, the wage is flexible in both sectors. This segmentation corresponds to the case of Cameroon where the export sector, dominated by oil industries, involves high technology and heavy equipment that generally requires specific skills and higher levels competence among workers, in addition to being submitted to labor legislation. Conversely, construction, retail trade, food crops and many non-traded services are more labor intensive and mainly belong to the so-called informal labor market sector. 2 The model also includes a government which plays a role by financing its expenditures with taxes and debt. The fiscal policyis effective via the wealth effects of government debt since the Ricardian neutrality does not hold. Importables are assumed to be the numeraire good, so that the relative price ofnontradeables (p~) in terms of importables is interpreted as the real exchange rate and is endogenous for the domestic economy. In turn, the relative price (p~) of exportables in terms of importables provides the terms-of-trade and for a small open economy, it is exogenously determined abroad on world markets. In what follows, we will analyze the behavior of the three defined economic agents (producers, consumers, and government). Production
It is assumed that each production sector has a large number of identical firms working in perfect competition. In producing both tradeables and exportables, firms combine capital and labor (supplied by consumers). The factor intensities are, however, different across sectors. The problem of the representative firm is to maximize the expected present discounted value of profits: max
e -r(s-t) [/~,(s)Y/(s) -
VA(t) = Et
Fi(s)
Ni(t),Ki(t) -
w~N,(s)
-
"V~(s)
-
I,(s)]ds
,
i
=
~,x,
(1)
whel'e
Zln Cameroon, the great majority of the labor force in the non-tradeables sector is employed in food crops and retail trade. A farmer in the food crops sector, who generally does not use heavy agricultural equipment, cannot move in the short run to the oil sector (a high technology sector), while tile converse is true, with a worker in the oil sector_
674
Labor Adjustment Costs in a Small Open Economy Ii(t) = ~.(t) + ~ ( t ) ,
F~(t) = ~
v,(t)
-
w ~(t) ~ e ~.(t) "
Here K and N represent the capital and labor inputs respectively, r is the real interest rate, Y is the output, I is gross investment, and 5 is a constant rate of depreciation. In both sectors, firms have to deal with quadratic and convex costs of adjusting labor (F) and capital stock (W), formulated as in Georges (1995) and Summers (1981), respectively. The coefficients "fi and ~i are the costs-of-adjustment parameters. The above formulation of capital adjustment cost guarantees that investment will be a growing function of Tobin's q. Government imposes ad-valorem tax (~) to exports only, so that after tax, firms receive p~(t) = (1 - ~)p~(t) for exportables and p,(t) = pn(t) for non-tradeables. Aggregate outputs of both goods are given by the following constantreturns-to scale Cobb-Douglas production functions that also satisfy Inada conditions:
Yn(t) = exp[a(t)]K~(t)ON~(t) (1-~) ,
and
Yx(t) = exp[a(t)]Kx(t)nN~(t) (l-n) ,
(2)
where a(t) represents technological shocks affecting productivity. Output of exportables is also confronted with exogenous changes in terms-of-trade p~(t). Those two shocks are modeled later as stationary stochastic processes. To make things simpler, we drop the operator E. Meanwhile, each change = dx/dt of a variable is interpreted as an expected change. Under the wellknown transversality conditions, the system of Euler equations derived from profit maximization problem (1) in both sectors are:
675
Pene Kalulumia
and Francine
Nyankiye
1
N~(t) = -
(3)
q~(t) ,
71~(t) -
ii(t)
=
/~(t)
[q,(t) - 1],
(4)
[ 1 [q~(t)- 1] + 5~}K~(t),
(5)
where q_i(t) =
ft ~ e - r ( s - t ) [ p i ( s ) y N ( s )
-- wi(s)]ds
(6)
,
and qi(t)
=
e-+-t){pi(s)Y~(s) + (wl2)[~(s)/I~.(s)] z
-
Bids,
i = n,x.
(7)
The dynamic equations for q and q are obtained by differentiating Equations (6) and (7) over time: (I,(t) = rqi(t) q~(t) = rq,(t)
-
[p,(t)Y~(t) (pi(t)Y~(t)
-
(8)
wi(t)],
+ (~td2)[~(t)lK~(t)] z -
3J,
i = n,x.
(9)
Above yN and YtK are, respectively, marginal products of labor and capital. The q variable, which translates the shadow value of the labor stock perceived by the firm, is equal to the expected present value of future profit flows obtained from an additional unit of labor. Equation (3) provides the law of motion for labor stock accumulation. The steady-state labor demand is obtained when q = 0. Hence, ifq is above (below) zero, labor demand will be above (below) its steady state or long-run level. Equations from (3) to (9) indicate that both labor and capital are historical variables, while q and q are nonhistorical or jump variables. Georges (1995) proved that there will be a unique nonexplosive solution to (3) and (8) if the cost-of-adjustment parameter 7 is positive (7 > 0). Since capital adjustment cost is a linear homogenous function in I and K (Tobin average and marginal q's coincide), the firm's value is given by the product: q~(t)Ki(t), i = n,x. 676
L a b o r A d j u s t m e n t Costs' in a Small Open E c o n o m y Consumption
The consumer problem is derived from Blanchard's (1985) uncertain lifetimes approach. Due to the uncertainty of life expectancy, the absence of inheritance, and the stochastic state of the economy, we can infer that there is a contingent market of life insurance agencies that guarantees, through the use of premium, consumers' outstanding debts when they die. The insurance agent is also in charge of redistributing any credit balance of the deceased to members of his generation yet alive. The objective function of an individual of generation v working in the labor market i, at time t, is as follows:
max
c~ (v,s),q~ (v,s)
Et
e-(O+~)(~ t)[alnci,~(v,s) + (1 - ct)lncim (v,s) + O~lnL~(v,s)Jds,
i = 1,2;
(10)
where p stands for the subjective discount rate, 7t for the individual's probability of death, cn for the consumption of non-tradeables, Cm for that of importables, and L for leisure. If we normalize the endowment of time to one, Ni(v,t) = 1 - L~(v,t) will be the time allocated to work at time t for each individual born at time v. As we choose imported goods as a numeraire, total consumption is given by: ci(v,t)=p~(t)ci,(v,t)+ Cim(V,t ). Financial wealth W~(v,t) of a consumer working in market i comprises claims on firms of both sectors, on government bonds (b) and on foreign assets (f). This wealth, in real terms, is given by Wi(v,t) = bi(v,t) + fi(v,t) + qi~(v,t)Ki,(v,t)
+ qi~(u,t)K~(v,t).
(11)
At the end of period t, each individual receives rWi(v,t) in interest and nWi(v,t) from the insurance company in addition to the net current revenue of labor. The dynamic budgetary constraint that each category of workers has to face is thus given by Wi(v,t) = (n + r)W~(v,t) + wi(t)N~(v,t) - ci(v,t) -
Ti(t),
(12)
where m~(t) is the basic wage rate of individuals in market i, and Ti(t) denotes lump-sum taxes paid by consumers working in sector i. Both basic wage rate and taxes are independent of the consumers" age or generation. Here, the basic wage reflects the opportunity cost of working in each sector. To make things simpler, it is always set equal to the wage effectively paid by firms in each sector (wl(t) = w~(t) and w~(t) = w~(t)). 677
Pene Kalulumia and Francine Nyankiye
The objective of each consumer is to maximize the expected utility (10) subject to (11) and (12). We use the first-order conditions of this problem, the intertemporal budgetary constraint and the definition of human wealth to derive the individual plans of optimal consumption and labor
supply, a Aggregate Consumption
Aggregate consumption and labor supply at time t are obtained by integrating over generations of consumers and labor markets. The relationship between aggregate variables x(t) and individual variables x(v,t) is given by 2 • (t)
=
(13)
_
Optimal aggregate consumption and labor supply plans are thus given by c~(t) = aC(t)/p~(t),
where (14)
c ( t ) = cl(t) + ~ d t ) , cat)
= (1 -
(~5)
~)c(t),
C(t) = (p + lt)[W(t) + h(t)] ,
(16)
]~(t) = (r + 7t)h(t) - w~(t)Nl(t) - wxN2(t) + T ( t ) ,
(17)
aThe optimal paths of individual consumplaon and labor supply are given by
c,,(v,t) = aq(v,t)/pn(t), and
c,~(v,t) = (1 - ~)c,(v,t); Ni(v,t)
= 1 -
O~c~(v,t)/w~(t) ;
and c~(v,t)
where: h~(v,t) = at time t.
678
= (p + rc)[Wi(v,t)
ft~ e-(~+=)('-t~[wi(s)Ni(v,s)
-
+ hi(v,t)],
Ti(s)]ds defines the individual human wealth
L a b o r A d j u s t m e n t Costs in a Small O p e n E c o n o m y W ( t ) = r W ( t ) + w~(t)Nl(t) + w~(t)N2(t) -
C(t) -
C(t) = (r - p)C(t) - n(rt + p)W(t) , Nl(t) = 1 -
01c1(t)/wn(t),
N2(t) = 1 -
02c2(t)/w~(t).
T(t),
(18) (19)
and
(20)
Equations (14) and (15) give respectively the aggregate consumption of non-tradeables and aggregate consumption of importables. Both are proportional to total consumption expenditures. The aggregate total consumption and aggregate human and financial wealth are given by Equations (16), (17), and (18). While individual financial wealth is discounted at the rate ( r + n ) , Equation (18) shows that aggregate financial wealth accumulates at a rate r. This is because individual wealth is transferred to an insurance company at death. The equation of motion (19) for aggregate total consumption is obtained after differentiating Equation (16) and substituting W and/~ by their respective values. If n = 0 (infinite horizon), Equation (19) translates into Friedman's consumption standard plan. Equation (20) provides the optimal aggregate labor supply adapted to each sector, and which depends on aggregate consumption of each category of workers (c,(t)). Government
Government purchases nou-tradeables (g.) and importables (gin) and finances these expenditures (g) by imposing lump-sum taxes (T~)on individual consumption and income, ad-valorem taxes on exports (T~), and by issuing public debt (b). The government's budget constraint is defined by b(t) = rb(t) + g(t) -
T(t) -
Tx(t),
(21)
where T,(t) = xp,(t)Y~(t). Government faces a solvency constraint that allows it to sustain a debt level that is equal to the present value of future budget surpluses. To satisfy this solvency condition, taxes are set as a positive function of outstanding public debt and above interest payments: T(t) + T~(t) = (4 -
r)b(t) + T ( t ) ,
(22)
where ~ > r and T is the exogenous component of tax revenue. In allocating its expenditure between non-tradeables and importables, government does 679
Pene Kalulumia and Francine Nyankiye
not have an impact on household's utility functions or firms' production functions. Its optimal consumption plan is4 g,~(t) = pg(t)/p~(t),
and gin(t) = (1 - g)g(t).
(23)
General Equilibrium The following equations describe the general equilibrium of goods, labor, and assets markets: Z(t) = L(t)
+ L(t)
+
w~(t) 2 wrY(t) 2 + 2 /Z(t) 2 K~(t) '
Ynt(t) = c~,(t) + g~(t) + (1 -
c0)z(t),
M(t) = Cm(t ) q- gin(t) + 03I(t),
N~(t) + N~(t) <_ Nl(t) + N2(t) [w~th w~(t) ~ wx(t)], f(t) = r f(t) + p~(t)Y~(t) - M ( t ) , GDP(t) = p~(t)Y~(t) + px(t)Y~(t), s(t) = f(t) + I(t) .
(24)
(25)
(26)
(27) (28) (29) (30/
To complete this general equilibrium definition, Equations (3) to (22), and the stochastic processes {at,gt,P~t} must be integrated. The gross domestic investment I(t) is given by Equation (24). It includes costs of adjusting capital in both sectors. A fraction (1 - co) of investment is produced locally. Equation (25) translates a closed economy equilibrium for non-tradeables. Equation (26) reflects the idea that for our small open economy, the demand of manufactured products as well as that of equipment goods are in most part 4The governmentstatic optimization'sprogramis as follows: max u(g~(t), gin(t)) = Ix lng,,(t) + (1 - Ix)lng~(t)subject to g(t) = p~(t)g,~(t) + gin(t) .
gn(t),gm(t)
680
Labor Adjustment Costs in a Small Open Economy satisfied by imports (M). On the other hand, Equation (27) translates the equilibrium of the labor market with possible unemployment, as in shortrun total employment may be less than total labor force and wages do not equalize across sectors. The current account is defined by Equation (28) as the change in net foreign assets, which is the sum of trade balance and net interest payments. The gross domestic product (GDP) is given by Equation (28), while gross domestic saving is given by Equation (30) as the sum of total investment cost and current account balance.
3. Numerical Solution Method In general, it is difficult to solve a non linear stochastic system of equations analytically. For this reason, all the equations that define general equilibrium are linearized by using a first-order Taylor expansion around the steady state as in King, Plosser and Rebelo (1988). The discrete version of linearized equations are provided in the appendix, where ~ denotes the deviation of a variable xt from its steady-state value x0. The state-space representation of the system is defined as follows (see the appendix): E~Xt + I = AXt + BZ, ,
(31)
where X~ = [[(~n,t_l, ~.x,t_l, Nn.t_l, Nxt_l qnt, qxt, ~n,t, ~x,t, Ct, fgt, fct, v~Vt,] and Z; = Ida, ~t, ~ ] . X is the vector of the state variables and Z, that of exogenous shocks. It is assumed to be a first-order vector autoregressive process:
Zt + l = f~Zt -If- ~ - t + l
,
where et ~ i.i.d.N(O, Z) ,
(32)
with air ~ i.i.d N(0, cry), E(e~tejt ) = a~j, i = j = 1. . . . . 3. The elements of the matrices A and B are derived in the ap~pendix. The state vector includes seven predetermined variables {/~,,t-~ K~,t- 1, Nn.t- 1, N,,t- z, bt, ~, ~Vt}, which are associated with the initial conditions and five forward-looking variables {Cl~,t,(1~, (t,t, (1~, ~t}. The system will admit a unique and stable solution that corresponds to a saddle point equilibrium, if we find seven stable characteristic roots and five unstable roots in the matrix A (see Blanchard and Khan 1980). To solve and simulate numerically the system of stochastic difference Equations in (31) and (32), we use the method proposed by Blanchard (1983). 681
Pene Kalulumia and Francine Nyankiye TABLE 1.
Values of Some Parameters
= 0.30 = 0.20 13 = 0.51
p = 0.04 5 = 0.10 ot = 0.75
7~ = 7x = 2.0 v = 0.80 01 = 02 = 2.11
n = 0.018 ~ = 0,05 ~ = ~ = 2.0
4. Empirical Results Stationary State and Calibration Steady-state equilibrium is characterized by the constancy in variables, the absence of exogenous shocks that disturb the economy (a0 = Px0 = 1), and by the absence of labor and capital adjustment costs. This means that in the long-run, both capital and labor factors become perfectly mobile and the wages equalize in both sectors. Thus, the steady-state expressions of the real exchange rate (P~0) and wage (w0) are given by p e~0 = ( ( 1 -
z)px0)~]-~ (1
1 wo =
(1 -
(r
TI)\
13 ]
\
q
/
'
+ ~l~[J-1 p
]
(34) -
Investment in the steady state is given by the relationship: I o = 8(K~0 + K~0). Accordingly, knowing Pno, Wo and the ratio of total investment allocated to each sector, we can recursively determine the values of all other endogenous variables in the steady state. However, these variables are the function of parameters whose values need to be established before. Previous studies and calibration techniques were used to fix parameter values. The idea is to reproduce the reality of the Cameroon economy, as reflected by the steady-state data. These steady-state data are computed as the means of variable observations over the period 1968-1993. Each variable is expressed in proportion of real GDP and deflated by the imports price index, since importables are the nnmeraire good in the theoretical model. Data used in this study were obtained from the World Bank's World Tables and IMF's International Financial Statistics. Table 1 presents all parameter values used in our simulations. The rate of capital depreciation and the world real interest rate are respectively established at 10% and 4%, as in Kydland and Prescott (1982). Following the study of Timothy, Dahl and Devarajan (1986) and the Cameroon social accounting's matrix of 1991, about 55% of Cameroon capital is used by the non-tradeables sector, which also employs 80% of labor. The share of importables in private and government con682
Labor Adjustment Costs in a Small Open Economy sumption is 25%, respectively. The share of capital (13) in the production of non-tradeables is 51%, whereas it represents 20% 01) in the production of exportables. Exports sector is more capital intensive as k~o = 4.85 versus k.0 = 0.71 in the non-tradeables (here, ki = ~/Ni). On the other hand, our data reveals that in 1992, life expectancy at birth (l/n) was 54.6 in Cameroon. Accordingly, the probability of death (n) is set to 0.018, following that 1/n = 54.6_ Other model's parameters were determined by calibration to reproduce the Cameroon data base. Thus, cost-of-adjustment parameters have been fixed at 2, whereas the values of leisure share parameters were set to 2.11. Some steady-state values of state variables, derived endogenously~ are as follows: 68% of GDP for private consumption (C), 23% for exports (X), 24% for imports (M), 23% for investment (I), 10% for public spending (g), and - 1% for the current account.
Simulation of Stylized Facts of the Cameroon Economy This section deals with the study of real business cycles in Cameroon. Empirical regularities observed in the country are first derived. They are then compared with the properties of data simulated from our theoretical model. Sample statistics measuring variable correlation, volatility and autocorrelation are used for this endeavor. Stylized facts. Stylized facts of the Cameroonian economy are reproduced from actual data for the period under study (1968-1993). The series have been transformed logarithmically and filtered by using the HodrickPrescott filter5 with a smoothing coefficient of 100, as in some previous studies (Ambler and Cardia 1995; Cardia 1991; and Backus, Kehoe, and Kydland 1989). Filtered data indicate, in whole, a decade of persistent recession that started in the 80s and the worsening of the terms of trade during the same period. The first four columns of Table 2 represent the stylized facts of the Cameroon economy. The following facts are observed: consumption, investment, saving, and trade balance are all procyclical. There is a positive correlation between trade balance and terms of trade (the HLM effect), as well as between saving and investment. These stylized facts are qualitatively similar to those reported by Mendoza (1992) and Cardia (1991) using industrial country data, except for the procyclicality of the trade balance. In many developed economies, in fact, trade balance is countercyclical.
5Cogleyand Nason (1995) suggestthat the HP filter may create artificialcyclesif the prefiltered series is first-orderedintegrated. Park (1997) showsthat this problem deepens as the degree of integrationbecomeshigher. He finds,however,that the filter-orientedsensitivityof the stylizedfacts are symmetricbetween the actualdata and the simulateddata, implyingthat the sensitdvityitselfdoes not invalidatethe performanceof RBC modelsin replicatingthe actual economy. 683
Pene Kalulumia and Francine Nyankiye The procyclicality of the trade balance in developing countries stems from that GDP growth is mainly driven by exports of commodities. The better is the performance of exports over imports (which means a trade balance surplus), the stronger will be the rate of GDP growth. Simulation of Empirical Facts. The shocks disturbing the economy {at, g~, p~} were modeled as stationary AR(1) processes (see Equation 32), which autocorrelation coefficients were, respectively, 0.908, 0.95 and 0.95, and which error term variances were, respectively, 0.038, 0.053, and 0.210. Their covariances were 0-12 = 6.1e - 4, o'13 1.2e - 4 and 0"23 = - 5.7e - 4. Particularly, productivity shocks were estimated as residuals of the Mankiw, Romer and Well (1992) neoclassical regression, which includes saving, labor force growth and other exogenous parameters of technology (the rates of depreciation and technological progress were fixed at 0.1 and 0.4, respectively). The Gauss software random number generator was used to simulate stochastically the model by generating repeatedly the error term vector ~+ 1, using 300 replications and 36 periods. The first 10 observations were removed to offset the effect of the initial conditions on computed statistics, especially standard deviations and correlation coefficients. This data truncation enabled us to have a sample of 26 observations corresponding to the size of the genuine database, spanned over 26 years. The solution to the state-space model was stable and unique since the conditions established by Blanchard and Khan (1980) were satisfied. Indeed, five eigenvalues of the A matrix were outside the unit circle, and this amounted exactly to the number (five) of jump variables in the model. Simulated Cameroon data were also filtered by using the Hodrick-Prescott filter with a smoothing coefficient 100 after taking their logarithmic transformation. Statistical properties of simulated series are reported in the last four columns of Table 2. They were computed as empirical means over the 300 drawings. From these results, we can conclude that the model mimics remarkably well the stylized facts of the Cameroon economy. Empirical covariations and autocorrelations are close to those calculated with genuine data in the first four columns of the Table. In particular, the model reproduces the observed procyclical behavior in various aggregates, as well as the higher volatility of investment relative to GDP. The model also reproduces the positive correlation observed in Cameroon, between investment and saving and the Harberger-Larsen-Metzler (HLM) effect, or in other words, the positive correlation between terms of trade and trade balance. =
- -
Relative Importance of Shocks The relative importance of shocks in explaining economic fluctuations in Cameroon is analyzed by comparing the results of Table 2, which include all three shocks, with those in Table 3 obtained by subjecting the economy 684
TABLE 2.
Stylized Facts and Simulation Results A. Stylized facts: Cameroon data
Variables (x ) GNP GDP(y) Consumption Investment Exports Imports Trade balance Savings RER External debt
B. Simulated facts: Theoretical model
cr,
crx/~y
px,y
p(1)
o,
cy,/cry
Px,y
p(1)
0.043 0.043 0.042 0.110 0.065 0.057 0.049 0.041 0.051 0.034
1.00 1.00 0.98 2.53 1.52 1.12 1.13 0.95 1.09 0.79
1.00 1.00 0.67 0.63 0.72 0.79 0.23 0.53 0.23 0.35
0.92 0.92 0.45 0.30 0.53 0.70 0.35 0.92 0.53 0.98
0.032 0.032 0.028 0.083 0.034 0.031 0.034 0.037 0.040 0.026
1.00 1.00 0.86 2.56 1.06 0.97 0.77 1.15 1.23 0.81
1.00 1.00 0.75 0.75 0.98 0.75 0.35 0.54 0.30 0.34
0.92 0.92 0.41 0.36 0.59 0.58 0.40 0.95 0.57 0.93
Correlations:
Correlations:
Savings-Investment: 0.77 Terms-of-trade-TB: 0.12
Savings-Investment: 0.98 Terms-of-trade-TB: 0.37
NOTE: *RER is the real exchange rate. For each x variable, p(1) represents the autocorrelation coefficient, p~,ythe cross-correlationwith GDP and ~/~y, the ratio of its standard deviation to that of the GDP. Data have been filtered using Hodrick-Prescott filter with a smoothing coefficientof 100, after taking their logarithmictransformation.
TABLE 3.
Relative Importance of Shocks C. Productivity shocks (o~)
Variables(x) GNP GDP (y) Consumption Investment Exports Imports Trade balance Savings RER External debt
ox 0.0137 0.0137 0.0142 0.0426 0.0135 0.0141 0.0134 0.0131 0.0142 0.0141
Px,y p(1) 1.00 1.00 0.37 0.32 0.30 0.41 0.15 0.37 0.71 0.57
0.42 0.42 0.15 0.60 0.93 0.98 0.65 0.42 0.85 0.58
D. Fiscal policy shocks (g,) o~
0.0271 0.0271 0.0265 0.0796 0.0274 0.0265 0.0274 0.0240 0.0270 0.0250
px,y p(1) 1.00 1.00 0.97 0.98 0.97 0.69 0.33 0.83 0.51 0.45
0.91 0.91 0.45 0.24 0.49 0.57 0.35 0.98 0.63 0_90
D. Terms-of-trade shocks (p~) O2 0.0341 0.0341 0.0286 0.0857 0.0359 0.0385 0.0359 0.0370 0.0390 0.0270
p~,y p(1) 1.00 1.00 0.89 0.75 0.96 0.75 0.32 0.54 0.37 0.38
0.92 0.92 0.42 0.31 0.59 0.58 0.38 0.96 0.57 0.95
685
Pene Kalulumia and Francine Nyankiye to each shock individually. The values of %, p,,y, and p(1) are used for the comparison. It is dear that the numbers in the three last columns of Table 3 are very dose to those in Table 2 (in both Panel A and B). This suggests that most empirical regularities observed in Cameroon can be explained by using only the terms-of-trade shocks. The addition of other shocks does not appear to affect significantly the volatility of output, investment, saving and consumption. The results also show that terms-of-trade shocks are followed by fiscal policy disturbances and technological shocks, which play a minor role. Given these findings, we conclude that terms-of-trade changes are a very important source of economic fluctuations in Cameroon. Thus, in our analysis of temporary shocks presented below, the focus is only on the effects of terms-of-trade disturbances in short and medium-term.
Analysis of Impulse Responses to Shocks This section deals with the dynamic effects of shocks to assess the impact of the inclusion of labor adjustment costs on economic fluctuations, especially on the persistence or duration of cycles. We consider the impact of a 10% temporary terms-of-trade deterioration that occurs in the third period (t = 3), and its magnitude decreases gradually over time. The quantitative effects of this shock, which are interpreted as percentage deviations from the initial steady state, are depicted graphically in Figure 1. It is indicated that this terms-of-trade deterioration induces first (after one period) a contraction of the export sector (4%). Even though the non-tradeables sector, now becoming more profitable, offers a wage relatively higher than that of the export sector ( - 2 . 8 % versus -5.8%), it would not be able to attract more labor inputs because of the high cost of adjusting labor. This imperfect mobility of labor explains why there is a decline in the output of non-tradeables (-2.3%) and an appreciation of the real exchange rate (11%), a period after the shock (at t = 4). However, output goes up to 0.13% at period t = 5 before converging to its steady-state equilibrium. Wage and employment in the non-tradeables sector follow the same path as production (down and then up). The contraction of exports causes a reduction of current and expected profits of the export sector, leading to a fall in both the Tobin's q and the consumers' wealth. Consumers have therefore to lower their levels of consumption and investment. Since the contracted export sector is more capital intensive, investment decreases more than consumption ( - 8.6% versus - 5.7%). The fall of aggregate demand (C and I) explains why imports decline. The real exchange rate also depreciates ( - 12.6%) later at period t = 5, following the reduction in demand and as labor gradually moves to the non-tradeables sector. The trade balance credit goes down by 1.4%, for a while, after the terms-of-trade deterioration and then goes up by 0.32% before returning to its long-term level. The jerky 686
Labor Adjustment Costs in a Small Open Economy TRADE BALANCE AND FOREIGN DEBT
SDP. CONSUMP-OON AND INVESTMENT ,
o! o
' 4~
,
.,
~
,
1"~
,.
,
16
,'
i I~ORT~ .
IMPOR~ AND OUTPUT OF NON-TRAD~BLES .
,
1
~ //~] "~~
: l
REAL EXCHANGE RATE
,,
'
l~.
12
a
,
,
/i :i
/[---. ..... LABOR IN BOTH SECTORS
'
T"
'
"-~'
~
J
'
i'~
WASE IN BOTH SECTORS
'
~'o
'
///
1 Figure 1. Impact of a 10% Temporary Terms-of-Trade Deterioration
expansion path of the trade balance is due to the real exchange rate path and the exports and imports path. The economy also records a growth of its external debt (5.7%) to finance the temporary deficit of its trade balance (see Equation (28)). However, this debt is dampened later as the economy experiences a trade balance surplus. Some of these findings contrast with the results obtained by Macklem (1993) or Carmichael, Keita and Samson (1995) because of the concept of limited mobility of labor in this model. These studies envisaged, in general, an expansion of the non-tradeables sector (with a rise in wage and employ687
Pene Kalulumia and Francine Nyankiye ment) and a depreciation of the real exchange rate one period after the terms-of-trade shock. Moreover, shocks are persistent in this model. Its effects last almost 7 periods while they never outlasted more than 3 periods in Macldem's model (without labor adjustment costs). We have also analyzed the impact of temporary government spending and productivity shocks. The quantitative effects of these shocks were smaller than those of the export price disturbance for the same magnitude of shock, confirming the finding that terms-of-trade shocks are the major source of economic fluctuations in Cameroon. The results also indicated that restricted fiscal policies, such as cutting government spending, can be used to mitigate and offset the negative effects of terms-of-trade deterioration. They result in the depreciation of the real exchange rate, stimulate over time the export sector and liberate a trade balance surplus that helps the country deal with its external liabilities.
5. Conclusions In this paper, we developed a dynamic and stochastic equilibrium model of a small open economy, which is subjected to productivity, fiscal spending and terms-of-trade shocks. The important feature of this study was to analyze the role of both labor adjustment costs and exogenous macroeconomic shocks in explaining real business cycles of an open economy with a segmented labor market. The model was calibrated and simulated to evaluate its ability to replicate the stylized facts observed in Cameroon. The results of numerical simulations indicated that the model reproduces remarkably well most of the empirical regularities of the Cameroon economy, particularly, the procyclical behavior of consumption, investment, saving and trade balance, as well as the higher volatility of investment relative to GDP. The model also generated the positive correlation between investment and saving and the Harberger-Larsen-Metzler (HLM) effect, which many previous studies failed to reproduce. The analysis of the relative importance of shocks revealed that terms-of-trade disturbances have been the most important source of business fluctuations in Cameroon for the period under study. They are followed by fiscal policy shocks and technological changes, the latter shocks playing a small role. The analysis of dynamic responses to shocks indicated that shocks are more persistent in this model, which contrasts with the predictions of previous models that have assumed perfect mobility of labor (such Macklem 1993). If the economy is faced with a terms-of-trade deterioration, previous models suggested an expansion of the non-tradeables sector and a depreciation of the real exchange rate one period after the shock. The current model predicts a decline in the output of non-tradeables and an appreciation of the real exchange rate, as a result of short-run rigidities in the labor market. 688
Labor Adjustment Costs in a Small Open Economy Overall, this paper belongs to a group of few studies that have succeeded in analyzing business cycles in developing countries. Our results are generally consistent with the studies by Carmichael, Keita and Samson (1995), Tanner (1989) and Khan and Knight (1983) that provided evidence of the HLM effect and identified the terms-of-trade disturbances as an important source of business fluctuations in developing countries. The results also support the findings by Amano and Macldem (1996) suggesting that unemployment persistence is mainly a result of costly adjustment of labor, and confirm the findings by Demekas (1990) that the job market structure affects the real exchange rate and unemployment. Finally, extensions of the current paper can consider the inclusion of labor adjustment costs in the offer side, and this would be properly addressed in a one-sector model (to reduce the number of parameters) and in a context where reliable data on skilled and unskilled workers are available. Received: April 1998 Final version: November 1999
References Amano, Robert A., and R. Tiff Macklem. "Unemployment Persistence and Costly Adjustment of Labor: A Canada-U.S. Comparison." Manuscript, Bank of Canada, Ottawa, Canada, 1996. Ambler, Steve, and Emanuela Cardia. "Les Modeles Reels de la Transmission Internationale du Cycle Economique." L'Actualite Economique 71 (1995): 164-93. Ag6nor, Pierre-Richard, and Peter J. Montiel. "Development Macroeconomics." Princeton: Princeton University Press, 1996. Backus, David K., Patrick J. Kehoe, and Finn E. Kydland. "International Borrowing and World Business Cycles." Working paper, 426R, Federal Reserve Bank of Minneapolis, 1989. Blanchard, Olivier J. "Methods of Solution and Simulation for Dynamic Rational Expectations Models." NBER Technical Working Paper No. 28, 1983. --. "Debt, Deficits and Finite Horizons." Journal of Political Economy 93 2 (1985): 223-47. Blanchard, Olivier J, and Charles M. Kahn. "The Solution of Difference Models under Rational Expectations." Econometrica 48 (1980): 1305-11. Cardia Emanuela. "'The Dynamics of a Small Open Economy in Response to Monetary, Fiscal, and Productivity Shocks." Journal of Monetary Economics 28 (1991): 411-34. Carmichael, Benoit, Sikoro Keita, and Lucie Samson. "Cycles Economiques 689
Pene Kalulumia and Francine Nyankiye au Senegal: Une Approche RBC." Cahier de recherche, No. 9506, CREFA, Universite Laval, Canada, 1995. Christiano, Lawrence J., and Martin Eichenbann. "Current Real Business Cycle Theories and Aggregate Labor Market Fluctuations." Northwestern University, Evanston, IL, 1990. Mimeo. Cogley, Timothy, and James M. Nason. "Effects of the Hodrick-Prescott Filter on Trend and Difference Stationary Time Series: Implications for Business Cycle Research." Journal of Economic Dynamics and Control 19 (1995): 253-78. Condon, Timothy, H. Dahl, and Shantayanan Deverajan. "Implementing a Computable General Equilibrium Model on Gams: The Cameroon Model." World Bank Staff Working Papers, The World Bank, Washington, 1986. Demekas, Dimitri G. "Labor Market Segmentation in a Two-Sector Model of an Open Economy." IMF Staff papers 37, no. 4 (1990): 849-64. Feldstein, Martin. "'Domestic Saving and International Capital Movements in the Long Run and the Short Run." European Economic Review 79 (1983): 733-48. Georges, Christophe. "Adjustment Costs and Indeterminacy in Perfect Foresight Models." Journal of Economic Dynamics and Control 19 (1995): 39-50. Khan, Moshini S., and Malcom D. Knight. "Determinants of Current Account Balances of Non-Oil Developing Countries in the 1970s: An Empirical Analysis." IMF Staff Papers 30, no. 4 (1983): 819-42. Fdng Robert G., Charles I. Plosser and Sergio T. Rebelo. "Production, Growth and Business Cycles: The Basic Neoclassical Model." Journal of Monetary Economics 21 (1988): 195-232. Kydland Finn E., and Edward C. Prescott. "Time to Build and Aggregate Fluctuations." Econometrica 50 (1982): 1345-70. Long, John B., and Charles I. Plosser. "Real Business Cycle." Journal of Political Economy 91 (1983): 39-69. Macldem, R. Tiffs. "Terms-of-Trade Disturbances and Fiscal Policy in a Small Open Economy." The Economic Journal 103, no. 419 (1993): 91636. Mankiw, Gregory N., David Romer, and David Weil. "A Contribution to the Empirics of Economic Growth." Quarterly Journal of Economics 2 (1992): 407~37. Mendoza, Enrique G, "Real Business Cycles in a Small Open Economy." American Economic Review 81 no. 4 (1991): 787-819. . "The Effects of Macroeconomic Shocks in a Basic Equilibrium Framework." IMF Staff Papers 39, no. 4 (1992): 855-99.
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Appendix The System of Linearized Equations and the State-Space Form L e t us d e n o t e the deviation o f xt f r o m its steady-state value x0 b y xt = xt - x0, and recall t h a t xt = E t X t + l -- Xt in discrete form. Thus, the discrete version of l i n e a r i z e d e q u a t i o n s are w r i t t e n as follows: K,
= K,,-,
+ (~o/V.)0., ,
(48)
&
=
q- (K-xo/lqlx)~lxt,
(49)
~,t-1
R.t = & , - 1 + (1/~)0.t,
(50)
iV~ = N~,t-1 + ( 1 / y , ) ~ ,
(51)
vVt+l = D,+~ + ~+~ + &~ + O°.~+#qo + K~ + cT~,,+~Iqo,
(52)
EtO.,t + 1 = (1 + r)[gl,t - P,t¥~o K - p ~ o ¥~'~ , o / ^q t KN ~ - p.oY~o N.t - p.oY~gtt],
(53)
E~.,+I
EtO..t+l_
= ( i + r)[O~, -
=
z)YS#~t-
z)p~oY~oR_.t - (1 - x)Y~omViv~ + (1 - ~)p~oY~gtt], (i -
(1 + r)[gt.,t_ -- P^n t ~ ON
(i -
-- PnoY~oNN*N.t NK ^
Na - p,oY~o K~t - p,oY~oat - do,t] ,
(54)
(55)
E~,t+~_ = (1 + r)[0~,_ - (1 - x)/3~oYN - (1 - x)P~oY~oNN'N,~ ~+1
(i .
z)p~oYNK~, t . .
N~- - d o ~ ] , x)p~oY~oat
(56)
+ Y~o~,~ + p~oY~o[<~ + p~oyNoN,=t + p,oY~oat - (1 - a ) O t - (i - ~t)gt - 5.K,~t - 8~R.~] ,
(57)
.
(i
= (1 + r ) g
/~t+l = (i + r EtCt+l
~)/~t + (1 + r ) ~ ,
= [(1 + r)/(1 + p)](7 t -
(58)
rcOEtlTVt+ 1
where
691
Pene Kalulumia and Francine Nyankiye 0 = [(1 + 7t)(1 + p) -
1]/[(1 + g)(1 + p ) ] ,
(59)
OtvCt 01vCo N.t w,~,t - (1 - N~o) + (1 - - - ~ o ) 2 ' -
~
(1
Y~o
"C)p~oyNagtt
-
~'~ -]-
(1 -
r)p~oY~o N,~ +
+
Pnt = ~
(60)
-
NK^ '~)p~o¥;~o K~
7(N~
-
N~,t-t),
p~o¥~NoN (Nn,
Y~o
-
-
Nnt-1)
N
"
Y~o
(61)
(69,)
Nnt "
Here, Y[0 denotes the derivative of Yi with respect to x, evaluated at the steady-state value. The system comprises 15 endogenous variables and 15 equations. In compact matrix notation, it is written as EtXt+l
= MIE~t+I
+
M2Xt + MaYt +
M4Zt,
Y = T1E~t+I + TeXt + TaYt + T4Zt,
(63) (64)
where
X; = ER.~,t_x, [i..,t_l, <,t_l, £ , t _ l , gl~,, gl~t, gl~,t, gl~,t, Ct, Dt, ~, l?Vt], Y2
and
z;
=
[a,, ~, ~ ] .
The state-space representation of the system is given by E t X t + I = A X t q- B Z t ,
(65)
where
A = [M2 + MaT~(I - T3)-J][I - M1 - MaTI(I - Ta)-I] -1, B = [M 4 + MaT4(I - %)1[I - M1 - MaTI(I - Ta)-I] -1 . The matrices M1, M2, Ma, M4, T1, T2, Ta, and T4 are provided below.
692
I
~
I
~
0
~
~
I
I
÷ v
I ÷
~
+
+
+
I
I
~
o
~
~
+
I
~
°~°°°°÷°°°~1
~
+
.4
~ /
I
I II
I
I il
693
M3
M4
T2 =
0 0 0 0 0
0 0 0 0 0
o
o
0 -(l+r) 0 0 0 0
0 0 -(l+r) 0 0 0
-(l+~)r~o
0 - (1 +r)¥No 0 0 0 0
0 0 0 0 0 - (1 + r)p~oY~ -(l+r)(1-x)p,oY ~ - ( I +r)P~oyN~ -(l+r)(l-x)p.oY~o 0 0 (l+r)P~oY~o
0 0 0 0 0 0 0 0 0 0 (l+r) (1-7~)
0 0 0 0 0 0 - (1+ r ) ( 1 - z)Y~o 0 - (1 + r ) ( 1 - z ) Y N 0 0 Y.o
0
01vCo/(1 - N,~o)2
(1 - r )p~oY~oK
o
[!o 0 0
o
oooooooi]
0 (1
~ ) p ~ o Y ~ o NN -
-
(~,~ - p~or~o~)/y~o
0 0 0 0 0 0 0 0 0 0 0 0 0 0
7~
o
0
0
0
0
0
0
Olv/(1-N.o)
0
0
0 -~,~n%
¥ o
0 o
0 o
0 o
0 o
0 o
0 o
00oJ , o
o
=
0
694
0 0 0 0 0
.T,
Eo
-(l+r)p~oY~ °
o
0
0
(1-)Y5
.
01