1-s2.0-S0161893804000055-main

Journal of Policy Modeling26 (2004) 95112

Public capital and long-term labour marketperformance in BelgiumGerdie Everaert, Freddy Heylen

SHERPPA, Ghent University, Hoveniersberg 24, B-9000 Gent, Belgium

Received 1 June 2002; received in revised form 1 July 2003; accepted 1 November 2003

Abstract

This paper investigates the long-term output and labour market effects of public cap-ital in Belgium within a broad model explaining private sector output and costs, privateemployment and capital formation, wage bargaining, price setting and aggregate demand.Model simulations show strong positive effects of public capital on private output and capitalformation. Public capital and private employment, however, are found to be substitutes. Aclear negative effect of public capital on employment remains, also after taking into accountthe effects of public investment on aggregate demand, productivity and wage formation.As to policy, this paper supports the case for an increase in public investment spending,complemented by structural labour market reform. 2004 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.

JEL classification: E62; J23; O40

Keywords: Public capital; Public investment; Employment; Economic growth

1. Introduction

Following Aschauer (1989a), a huge literature has studied the macroeconomiceffects of the decline in public investment in most OECD countries since the1970s. Most of this literature has concentrated on the consequences for output andproductivity. More than 10 years later, the results are still controversial. Aschauer

Corresponding author. Tel.: +32-9-264-7878; fax: +32-9-264-8996.E-mail address: [email protected] (G. Everaert).

0161-8938/$ see front matter 2004 Society for Policy Modeling.doi:10.1016/j.jpolmod.2003.11.002

96 G. Everaert, F. Heylen / Journal of Policy Modeling 26 (2004) 95112

(1989a, 1989b) found highly positive and significant effects of infrastructure onproductivity growth in the US and the G7. In more recent work, however, manyauthors have re-examined these results, often within another theoretical frameworkor using another methodology. Some confirm Aschauers conclusions, others rejectthem (see Sturm, Kuper, & Haan, 1998, for a survey).

This paper studies the effects of public capital formation on the labour market.We focus on Belgium, which like many other European countries is characterisedby relatively rigid labour markets and high unemployment. For two reasons thisresearch may be important. First, extensive studies of the labour market effects ofpublic investment are still very scarce. Second, despite the previous, it has oftenbeen recommended that in the fight against European unemployment, investmentin public infrastructure should be raised (see e.g., the European CommissionsWhite Paper of 1993 or Drze & Malinvaud, 1994). Our main goal in this pa-per is to evaluate the relevance of this recommendation. Focusing on Belgium, weinvestigate whether or not public capital formation improves labour market perfor-mance in general, and employment in particular. To answer this question, we havedeveloped and estimated a dynamic structural model for the Belgian economy ex-plaining private sector output and costs, private employment and unemployment,private capital formation, wage bargaining, price setting and aggregate demand.The model allows for three channels of influence of public capital on employment:(i) direct complementary or substitution effects for given output, (ii) indirect effectson real wages, due to changes in labour productivity and/or the unemployment rate,(iii) indirect effects caused by changes in aggregate demand and the output level.Due to space limitations, we will concentrate in this paper on the main charac-teristics of the model and on the most important estimated long-run equilibriumrelations and parameters. A complete and detailed description can be found inan underlying working paper (see Everaert & Heylen, 2000). Once estimated, weuse the model to simulate private sector performance under an alternative publicinvestment policy. More specifically, we analyse the economys evolution if a verystrong decline in public investment during the period 19821989 had not occurred.

It should be emphasised that the perspective of this paper is broader than whathas usually been done in the literature. First, as we have mentioned before, existingresearch has paid relatively little attention to the influence of public capital onemployment. Second, relevant findings on the employment effects of public capitalgenerally concern only the direct complementary or substitution effects. Estimatingprivate sector cost functions and/or factor share or input demand equations, moststudies find that (i) public capital reduces private sector costs, (ii) public capitalacts as a substitute for intermediate inputs and often also labour, (iii) public andprivate capital are complements (see again Sturm et al., 1998). In this paper wedefine and simulate all relevant channels of influence.

The remainder of the paper is as follows. Section 2 discusses our model.Section 3 presents the estimates of the model for Belgium using annual data for19651996. To detect the effects of public capital on economic growth and thelabour market, Section 4 reports the results of our simulation experiment. We find

G. Everaert, F. Heylen / Journal of Policy Modeling 26 (2004) 95112 97

that public investment stimulates economic growth, confirming Aschauers publiccapital hypothesis. Surprisingly, however, public investment also generates moreunemployment. Section 5 discusses the policy implications of our findings.

2. The model

Our model relies heavily on Layard and Nickell (1986). It describes a represen-tative, imperfectly competitive firm, operating in a small open economy. The firmdecides on its required inputs (labour, capital and materials) to produce a certainlevel of output, taking factor prices, technology and the public capital stock asgiven. The output level is determined by demand, which is itself a function of theprices set by the firm on the domestic market and abroad. To maximise its profits,the firm determines these prices as mark-ups on marginal cost. As for costs, thecost of capital and the price of materials are exogenous to the small open economythat we consider. Wages, however, are endogenous. They are bargained betweenunions and employers. The following subsections briefly describe production, in-put prices, output price setting and aggregate supply and demand.

2.1. Production technology and factor demand

Imagine a small open economy where output is produced by N identical privatefirms and an (exogenous) government sector. We consider one of these firms. Itsreal gross output (X) is produced by services from private capital (K), employedlabour (E), imported intermediate inputs (materials, M) and public capital (KG).The production function is of the form

X = F(+A, +K, +E,+

KG,+M) (1)

where A reflects technology. The firm minimises total cost TC = PEE+ PKK +PMM subject to the production function under (1). This results in a cost functionof the type

C = C(+X, +P,

KG,A) (2)

with P the vector of variable factor prices, P = [PE, PK, PM]. Public capital andtechnology are treated as unpaid fixed inputs. As an adequate approximation ofthe cost function under (2), we consider the translog flexible functional form. Fordetails we refer to Everaert and Heylen (2000). As is well-known from the litera-ture, estimation of this cost function reveals relevant information on a number ofimportant variables and parameters. To start with, using Shephards lemma, factordemand equations for variable inputs (E, K, M) can be derived. Furthermore, undera number of standard conditions the cost function is dual to the production functionand all relevant characteristics of the latter can be derived from the cost function.A first important characteristic of the production function that can be derived from


the estimated translog cost function is the elasticity of substitution between inputs.Second, one can extract from the estimated cost function the willingness-to-pay forpublic capital by calculating the shadow price PSKG, i.e., the reduction in the firmsminimised total cost due to one additional unit of public capital. Very importantfor our purpose also are the elasticities of variable input factors with respect topublic capital (i,KG, with i = E, K, M). These elasticities are the result of twoeffects. First, an increased supply of productive public infrastructures may implythat a given output X can be produced at lower cost. This is the case where theshadow price of public capital is positive. For given factor cost shares, more publiccapital then implies a reduced need for any private factor of production. Next,however, an increase in public capital may change optimal factor cost shares. Thecost share of some private inputs may rise, the share of others may fall. In the end,for a complementary relationship to show up between public capital and a privatefactor of production, the bias of public capital on that factors cost share must bepositive and (more than) compensate the negative total costs effect. Otherwise,the relationship will be substitutive. Finally, one can compute from the estimatedcost function the elasticity of output with respect to each variable input factor i(X,i) and with respect to public capital (X,KG). Observing these, one can calculatereturns to scale in the production function.

2.2. Input price formation

When the firm decides on the volume of inputs to be used, input prices PM , PKand PE are given. PM is the price of imported intermediate inputs, expressed indomestic currency. It is assumed exogenous to the small open economy considered.The nominal user cost of capital is a function of the real long-term interest rate (R),the depreciation rate of private capital (k) and the price of capital goods (Pinv).Each of these determinants is assumed to be exogenous:

PK = (R+ k)Pinv (3)The nominal user cost of labour is a function of the nominal gross wage (W) andexogenous taxes on labour to be paid by the firm (tbs).

PE = (1 + tbs)W (4)The nominal gross wage has been bargained ex ante with the union. In Everaertand Heylen (2000) we maximise a standard Nash bargaining function to obtain aconventional theoretical long-run wage equation, similar to equations presentedby Manning (1993) and Nixon and Urga (1999). The long-run nominal wageequation that we estimate in the next section allows for a little more flexibility inthe parameters. It is described by Eq. (5):

ln(W)= 0 + (1 p)ln(PX)+ p ln(Pc)+ q ln(Q) u ln(u)+b ln(Brr) tbs ln(1 + tbs)+ ln()+ z ln(z) (5)


withQ = YE, Y = XM and i > 0 (5)

The bargained nominal gross wage is proportional to the firms output price (PX, tobe discussed below) and to consumer prices (Pc). Given automatic wage indexationto consumer prices in Belgium, we expect that in the long-run p = 1. Further-more, the nominal wage responds positively to the productivity of labour (Q), the(exogenous) unemployment benefit replacement ratio (Brr), the firms profit perunit of value added () and the (exogenous) relative bargaining power of the union(z). Note that the productivity of labour is defined in (5) as real value added Y perworker. A higher aggregate unemployment rate (u) and higher taxes on labour tobe paid by the firm (tbs) lead to lower wages. Taxes are exogenous.

2.3. Price setting

The representative firm sells its real output (X) on both the domestic market(Xd) and abroad (Xf ) at prices Pd and Pf , respectively. Prices are set to maximisethe (nominal) profit function:

n = PdXd + PfXf C(X,P,KG, A) (6)subject to X being equal to Xd +Xf and to the demand equations for Xd and Xf .Demand rises in real aggregate domestic spending and real world imports, respec-tively, and falls in the firms relative price at home and abroad. Our assumption thatthe firm has market power, implies the well-known mark-up conditions for pricesetting, described by (7) and (8). In these equations C/X indicates marginal cost,whereas d and f denote the absolute value of the price elasticity of demand foroutput at home and abroad.

Pd = dd 1

C

X= d

C

X, with d > 1 (7)

Pf = ff 1

C

X= f

C

X, with f > 1 (8)

Theoretically, there are good reasons for the price elasticity of demand and thusthe mark-up on marginal cost to depend on the business cycle. The sign of thisrelation is unclear, however (Layard, Nickell, & Jackman, 1991). We come backto this in the empirical section. Once Pd and Pf are known, the firms (weightedaverage) output price PX can be defined as an identity:

PX = Pd + (1 )Pf , with : =XdX

= XdXd +Xf (9)

2.4. Aggregate supply and demand

To move to the aggregate economy, we basically follow Layard and Nickell(1986). Given the assumption of identical firms, aggregate wages and prices will


be equal to the level determined by the representative firm (W, Pd , Pf , PX). Othervariables like private sector output, value added, employment, profits and inputvolumes are at the aggregate level equal to N times their individual firm size. Itshould be emphasised that from now on all our variables (X, E, K, etc.) refer to theaggregate level.

Eq. (10) describes the equilibrium of supply and demand for real aggregate pri-vate output. Aggregate supply X follows from the optimal behavior of firms iden-tified earlier. Firms produce output in response to demand, given relative prices.The RHS of Eq. (10) is real aggregate demand for output. EXPd stands for realaggregate domestic demand, Xf IM is net exports of final products:

X = EXPd + (Xf IM) (10)Eq. (11) identifies real aggregate domestic demand as the sum of (endogenous) realprivate consumption (Cp), (exogenous) real non-wage government consumption(Cg) and (endogenous) real aggregate gross investment (I). Real private consump-tion in Eq. (12) is assumed mainly (i.e., in the long-run) to be a function of realhousehold disposable income (Ydis/Pc). Nominal disposable income (Ydis) containsboth after-tax labour income and capital income. It is described in Eq. (13). Taxrates are respectively tw and tc and exogenous. The main endogenous determinantsof labour income are the private sector gross wage bill (EW) and unemploymentbenefits (uLsBrrW), with Ls being aggregate labour supply, u the aggregate unem-ployment rate and Brr the unemployment benefit replacement rate. Both Ls and Brrare exogenous, u is explained in Eq. (14). A third component of labour incomeare government wages (EWg), which are exogenous. Nominal capital income (Yc)is composed of dividends and interest income on private and public long-termbonds. Dividends are a fixed fraction (%1) of aggregate after-tax business profits,(1 tbd)n. As to interest income, we assume that the long-term nominal interestrate (Rn) is equal for private and public bonds and exogenous. Furthermore, thestock of bonds (BH ) is driven by the assumption that households invest a fixedfraction (%2) of their savings in bonds (Eq. (16)). Finally for private consumption,Eq. (17) specifies the consumer price level as a weighted average of the domesticoutput price (Pd) and the (exogenous) price of imported goods and services (PIM).The rate of indirect taxes is tind. It is also exogenous:

EXPd = Cp + Cg + I (11)

Cp = Cp(YdisPc

)(12)

Ydis = Yd0 + (1 tw)[(EW + EWg)+ uLsBrrW] + (1 tc)Yc (13)

with : u = Ls E EgLs

(14)

Yc = %1(1 tbd)n + RnBH1 (15)


BH = BH1 + %2(Ydis CpPc) (16)

Pc = (1 + tind)(

Xd

Xd + IMPd +IM

Xd + IMPim)

(17)

I = Ik + Ig + Ih (18)K = (1 k)K1 + Ik (19)

IM = IM(Pd

Pim,EXPd

)(20)

Xf = X(Pf

P,EXPw

)(21)

Eq. (18) defines real aggregate gross investment as the sum of real capital forma-tion by the private business sector (Ik), the government (Ig) and households (Ih).Household and government investments are taken to be exogenous. Private firmschoose investment in Eq. (19) to obtain their optimal capital stock (K). The latterfollows from the firms cost minimisation process described in Section 2.1.1 Asmentioned before, k is exogenous. Eq. (20) explains real aggregate imports offinal goods and services (IM) as a function of real domestic demand EXPd and therelative price Pd /PIM. Imports are expected to rise in both arguments. The modelfor the demand side is closed by assuming in Eq. (21) that real exports are deter-mined by (exogenous) real world imports (EXPw) and by the price of exports (Pf )relative to the (exogenous) price of foreign competitors on the world market (P).

The demand effects of changes in public investment can now briefly be de-scribed. An immediate effect on aggregate output runs via (18), (11) and (10). Sec-ondary effects are caused by the influence of changed output on (un)employment,which further affects wage formation, productivity and prices. Via real householddisposable income and consumption on the one hand, and competitiveness (relativeprices) and net exports on the other, aggregate demand is again affected. Further-more, there may be a role for the way in which changes in public investment arefinanced. This is evident in the case of changes in taxes, which are prominent inEqs. (13), (15) and (17). In the case of bond financing, however, the financingdecision has no immediate influence in our model. This may seem strange giventhe role of bonds (BH ) in Eqs. (15) and (16). The reason is double. First of all,households may substitute government bonds for private sector bonds. Second,foreigners may buy the newly issued government bonds. Obviously, one mightargue that in the case of bond financing, taxes may have to be raised in the future.Rational consumers may anticipate this and change their current behavior. Ad-mittedly, our model does not capture these effects. On the other hand, one shouldrecognise that a lot depends on the effects of changes in government investment on

1 See our brief discussion of the cost function in Section 2.1 from which factor demand equationscan be derived.


future output and government income for given tax rates. If future output is strong,future taxes may be avoided! As we shall see in Section 4.2, this expectation maynot be unrealistic. It also brings us to the final equations in our model.

2.5. Government budget balance

Three identities in (22) describe the government budget balance as the differ-ence between nominal revenues (T) and nominal expenditures (G). The formerare mainly determined by the sum of taxes on gross wages in the business sector,taxes on the unemployed, indirect taxes on nominal domestic demand, direct taxeson business profits and taxes on households capital income. Expenditures mainlyare government wages, public non-wage consumption, public investment, unem-ployment benefits and interest payments. T0 captures other revenue categories,e.g., taxes on wages earned in the government sector. G0 captures other spendingcategories, e.g., transfers other than unemployment benefits:

Budget = T GT = T0 + (tbs + tw)WE + twBrrW(Ls E Eg)

+ tind1 + tind (Pc(Cp + Cg)+ PinvI)+ tbd+ tcYc

G = G0 +WgEg + PcCg + PinvIg + BrrW(Ls E Eg)+ RnGD1

(22)

with GD (=GD1 Budget) denoting nominal gross government debt.

3. Empirical analysis

Our empirical analysis relies on annual data from 1965 to 1996 for Belgium.Our data are taken from the OECD, the National Bank of Belgium and the BelgianFederal Planning Bureau. Data sources are described in detail in Everaert andHeylen (2000). Note that as a proxy for technology (A) we use cumulated data forpatents granted by the US Patent and Trademark Office (for details and justification,see Everaert & Heylen, 2001).

The empirical implementation of the stochastic long-run equilibrium relationsdescribed in Section 2 requires a model of disequilibrium adjustment. Usingthree-stage least squares,2 we have simultaneously estimated separate error-correc-tion models for each of the four sectors of the economy, i.e., factor demand andprice setting by firms,3 wage bargaining, total domestic demand and the external

2 Endogenous variables are instrumented using all exogenous variables and once lagged endogenousvariables.

3 The dynamic specification of the cost function, which allows for a consistent derivation of a setof interrelated factor demand equations in general error-correction form, is taken from Urga (1996)and Allen and Urga (1999).


sector, conditioning on the exogenous variables and the endogenous variables de-termined in the other sectors of the economy. Everaert and Heylen (2000) providea detailed explanation of our dynamic empirical model and all results. Due tospace limitations we concentrate in this paper on the relevant estimated long-runequilibrium relations and on a number of important parameters. For all these re-lations the null hypothesis of no cointegration can be rejected at the 5% level ofsignificance.

3.1. Dynamic cost function and dynamic factor demands

For parameter estimates of the dynamic cost function and related dynamicfactor share equations, we refer to Everaert and Heylen (2000). The cost functionis theoretically and empirically well-behaved. Furthermore, the duality conditionshold, which implies that we can use the parameter estimates of the cost functionand related factor share equations to uncover the characteristics of the underlyingproduction function. A first important characteristic is that all variable input factorsare found to be substitutes (see again Everaert & Heylen, 2000, for details).

Table 1 reports the long-run elasticities of output with respect to labour, privatecapital and materials, a measure of returns to scale (), the shadow price of publiccapital and the long-run elasticities of variable inputs with respect to public capital,all evaluated at the sample mean. The statistically significant positive shadow priceof public capital (PSKG) shows that public capital is cost saving. Our estimates implythat an increase in the public capital stock by 1 euro reduces long-run private sectorcost by 0.24 euro. This positive shadow price is an important element underlyingthe negative impact of public capital on private employment. Another element (notshown) is the negative bias of public capital on the optimal labour cost share. Asa result, an increase in the public capital stock by 1%, for a given output, reducesprivate sector employment by about 0.32%, indicating a substitutive relationship(see E,KG). On the other hand, the private capital cost share is increasing in publiccapital. In net terms, public and private capital are complements. A 1% increasein the public capital stock raises private sector capital by 0.33% (see E,KG). Thiseffect is not accurately measured though.

Evaluated at the sample mean, the production function is characterised by in-creasing returns over all inputs, including public capital ( = 1.40). The individual

Table 1Characteristics of the production functiona

Output elasticities, cost flexibilityand returns to scale

Shadow price and elasticitieswith respect to public capital

X,E 0.51 (0.03) X,KG 0.31 (0.05) PSKG 0.24 (0.05) E,KG 0.32 (0.17)X,M 0.45 (0.02) c,X 0.92 (0.03) c,KG 0.28 (0.05) M,KG 0.46 (0.18)X,K 0.13 (0.01) 1.40 (0.07) K,KG 0.33 (0.29)

a Evaluated at the sample mean. Standard deviations in parentheses.


elasticities of output with respect to private inputs (X,E, X,K, X,M) are very muchin line with expectations. Furthermore, the obtained positive and significant elas-ticity of output with respect to public capital (X,KG = 0.31) supports Aschauerspublic capital hypothesis. It also confirms the result obtained by Everaert andHeylen (2001), using a different methodology.

3.2. Wage bargaining and price setting

To estimate the wage Eq. (5), we use union membership in percent of thelabour force as a measure of union bargaining power (z). Data are mainly fromEbbinghaus and Visser (1990). The results are reported in Table 2. Since estimatingan unrestricted wage function yields no significant effects for taxes to be paid bythe firm (tbs) and for the profit rate (), we only report results imposing tbs = = 0. Note though that tbs has a strong short-run impact on the bargained wage(not shown). Next, the observation that p is not statistically different from 1, isconsistent with wages being automatically indexed to consumer prices. However,we do not impose p = 1 because this slightly deteriorates the fit of the model.Furthermore, the coefficient on labour productivity is significantly smaller than1, indicating that over the sample period productivity growth is not fully

Table 2Parameter estimates (3SLS) and residual diagnostics for price setting, wage bargaining, aggregateconsumption and the external sector (19651996)a

Wage bargaining (estimated long-run relation)ln(Wt )ln(zt ) = 2.564(1.260) + 0.708 ln(Pc,t )(0.196) + 0.292 ln(Px,t)() + 0.743(0.092) ln(Qt)0.112(0.035) ln(ut)+ 0.262(0.068) ln(Brr,t )+ 1.030(0.112)

Price setting (estimated long-run relation)Pd,t = (1.464(0.063) + 3.403bct (0.797) 0.008oilt (0.002))(Ct/Xt)+ 0.321(0.048)d9693

Aggregate consumption function (estimated long-run relation)Cp,t = 251, 491(155,864) + 0.822(0.024)(Ydis,t/Pc,t )

The coverage rate of exports over final imports (estimated long-run relation)ln(Xf /IM)t = 7.518(1.099) 0.197(0.081) ln(Pd/Pim)t 0.425(0.169) ln(Pf /P)t 0.413(0.071)

ln(EXPd)t

-ln(Wt) -Pd ,t -Cp,t -ln(Xf /IM)tR2 and residual diagnostics (dynamic specification)b

R2 0.97 0.88 0.90 0.61Normality 2(2) = 0.52 [0.77] 0.77 [0.68] 1.77 [0.41] 0.57 [0.75]Serial correlation 2(4) = 3.71 [0.45] 4.60 [0.33] 2.84 [0.58] 4.93 [0.30]

a Due to space limitations we only report the estimated long-run equations. For all these relationsthe null hypothesis of no cointegration can be rejected at the 5% level of significance. For detailedresults on the dynamic specification and cointegration tests, we refer to Everaert and Heylen (2000).Standard errors in parentheses, P-values between square brackets.

b JarqueBera (JB) test for residual normality and BoxPierce (BP) test for fourth-order serialcorrelation.


reflected in wages. The remaining coefficients all have signs confirming theoreticalpredictions. Unemployment appears to exert only a moderate downward pressureon real wages, though. Union membership in contrast has a strong impact on thebargained wage. The estimated equilibrium domestic price equation is

Pd = (d0 + d1bc + d2oil)C

X

The mark-up (d) on marginal cost (C/X, which is estimated jointly with thecost function) in the long-run specification is a function of the business cycle (bc)and the evolution of oil prices (oil).4 The motivation for including oil prices in themark-up stems from the observation that firms appear to be reluctant to transmitoil price shocks fully into domestic prices. The results in Table 2 show that in thelong-run, when the business cycle is neutral and oil prices are at their average value(bc = oil = 0), firms set domestic prices 46% higher than the marginal productioncost. The positive coefficient on bc implies that the mark-up is pro-cyclical. Thesignificant negative coefficient on oil confirms that oil shocks are not fully reflectedin domestic prices, but partly absorbed by firms profits.5

Although graphical inspection reveals a close relationship between export prices(Pf ) and marginal cost, we are unable to detect a stable causal relation runningfrom marginal cost to export prices. Rather, export prices exert some feedback onmarginal cost. This observation suggests that, in contrast to the theory in Section 2,Belgian exporting firms are price takers on the world market. In order to safeguardprofitability (marginal) cost has to adjust to changes in prices on the export market(e.g., through changes in labour productivity). Although deviations appear to belong lasting, a tentative exploration of the relation between Pf and P indeed showsa close connection in the long-run. In what follows, export prices are thereforeassumed to be exogenously determined on the world market.

3.3. Aggregate consumption and net exports

Estimation of the private consumption function reveals a long-run marginalpropensity to consume equal to 0.82. As for international trade, to eliminate theimpact of the steady increase in openness of the Belgian economy, we estimate theratio of exports over imports of final products (i.e., Xf /IM) instead of Eqs. (20)and (21) separately. Both higher domestic demand, higher domestic prices andhigher export prices reduce exports relative to final imports. Higher import prices

4 The business cycle variable bc is the percentage deviation of business sector GDP from itsHodrickPrescott trend; oil is the percentage deviation from the average oil price over the sampleperiod.

5 Note that we have also included a level-shift dummy (d9396 ), being 1 in the period 19931996, inthe cointegrating relationship for domestic prices. The reason is that the price indices used, were nolonger available from 1993 onwards. The extension of the series over 19931996 has been done at theNational Bank of Belgium with a slightly less sophisticated methodology, resulting in a possible breakin the series in 1993.


and higher prices on the world market have the opposite effect. Real foreign ex-penditures have no significant long-run effect on Xf /IM and have therefore beendropped from the cointegrating vector.

4. System simulations

This section explores the impact of changes in the public capital stock on pri-vate sector performance, especially (un)employment, by simulating the model ofSection 3 under an alternative public investment policy. We analyse how the Bel-gian economy would have evolved if a strong decline in public investment in19821989 had not taken place. Section 4.1 briefly goes into the ability of the es-timated model to capture the endogenous variables actual evolution. Section 4.2discusses the effects of the alternative public investment policy.

4.1. Benchmark simulation

Everaert and Heylen (2000) compare the actual evolution in total cost (C),the cost shares of labour, capital and materials, real output (X), the productivityof labour (Q), the nominal gross wage (W), the consumer price level (Pc), theunemployment rate (u) and the government budget with these variables evolutionobtained from the dynamic simulation of the model over the period 19701996,taking the evolution of the exogenous variables as given.6 In general, our modelis well able to capture the movements in the endogenous variables.

4.2. Alternative public investment policy

To fight its huge debt and deficits the Belgian government adopted two long-lasting fiscal consolidation programs, in particular in 19821987 and in 19921996.A strong cut in public investment was an important part of the 19821987 con-solidation program (see Fig. 1). Real public investment in Belgium fell back from4.63% of (business sector) GDP in 1981 to less than 1.75% in 1989. Consolidationin the 1990s left public investment largely unaffected. In this section we analysehow the economy would have evolved if the strong decline in public investmentin 19821989 had not occurred and if to finance this more bonds had beenissued. The alternative public investment series (Ig sim) is obtained by fixing theshare of public investment in (business sector) GDP on its 1981 level during theperiod 19821989. From 1990 onward, the simulated investment rate is again al-lowed to vary starting from its higher 1989 level with the actual rate (see

6 The model is simulated over the period 19701996 since no data are available for the 1960s forsome variables in some identities. Due to lack of data, %2 is in the simulation assumed to be equal to1. Data for %1 are provided by the Belgian Federal Planning Bureau and taken as given. Further, tc isfixed at 15%.


Fig. 1. Real public investment (in % of business sector GDP) and real public capital stock (in billions)under the alternative investment policy, 19701996.

Fig. 1). From the alternative investment series, we then calculate the correspondingpublic capital stock (Kg sim). In 1996 this hypothetical capital stock would havebeen 28.5% higher than observed in reality.

Obviously, an interesting question would be to assess the effects of alternativeways to finance the simulated rise in public investment. We keep this for futureresearch. As for now, it will be important to keep an eye on the long-run conse-quences of bond financing for the government debt and deficit. If these went offthe rails, it would clearly not be possible to call our simulation results realistic(because of their unsustainability).

Inserting Ig sim and Kg sim, the model is dynamically simulated over the period19701996. Table 3 compares the simulation results for key endogenous variableswith these variables evolution according to the benchmark simulation. We con-centrate on the long-run effects, i.e., the deviation from the benchmark in 1996.A number of interesting observations stand out. (i) Although public capital is costsaving, a shock to public investment does not lower the volume of private sectorcost. In contrast, 1996 costs are 2.7% higher than the benchmark. (ii) The costshares of labour and materials decrease slightly, in favour of a higher cost shareof private capital. Given the small increase in total costs, the 1996 private capitalstock is 13.2% larger. (iii) Compared to the benchmark, 1996 real private sectoroutput is 5.8% higher. (iv) Private sector labour productivity is 13.3% higher. (v)

Table 3Long-run effects of the alternative public investment policy (difference between alternative and bench-mark simulation in 1996)Total cost (C) 2.7 Nominal wage (W) 6.8 Cost share of capital 1.6aOutput (X) 5.8 Private consumption (Cp) 4.7 Unemployment rate 3.8aPrivate capital (K) 13.2 Investment/output (I/X) 4.0a Profit rate 3.4aPrivate employment (E) 6.9 Consumer price (Pc) 0.2 Government budget 0.9aMaterials (M) 1.9 Cost share of labour 1.3aLabour productivity (Q) 13.3 Cost share of materials 0.3a

a These data are differences in percentage points. All other data are differences between levels inpercentage.


Table 4Long-run effects of the alternative public investment policy on unemployment (difference betweensimulated alternative outcome and benchmark, 1996)

Production channel Demand channel Wage channel Total effect

Unemployment rate(in percentage points)

+3.3 0.13 +0.7 +3.8

The average annual growth rate of nominal wages is 0.4% points higher, result-ing in a 6.8% higher nominal wage in 1996. Since consumer prices are largelyunaffected, the increase in the nominal wage implies a similar increase in the realwage. (vi) Given the moderate increase in cost, the decrease in the cost share oflabour combined with the increase in wages implies a 6.9% decrease in privateemployment. As a result, the 1996 unemployment rate is 3.8% points higher. (vii)Higher output being produced with fairly stable costs, the profit rate rises strongly(+3.4% points).

Our results for the labour market are surprising. Public investment programmesas such seem to undermine employment, at least in Belgium. Table 4 shows thethree sub-effects that are behind the simulated unemployment rise: (i) substitutioneffects for given output and factor prices (production channel), (ii) effects fromchanges in aggregate demand and the level of output (demand channel) and (iii)effects from changes in real wages (wage channel).

The production channel undermines employment. First, given the positiveshadow price of public capital, total cost (for given output, wages and prices)in 1996 decreases with 5%. Second, for given total cost, higher public capitalexerts a negative bias on the cost share of labour. In total, substitution of publiccapital for labour accounts for a 3.3% points increase in the unemployment rate(for further details, see Everaert & Heylen, 2000). Demand effects are due to thefact that higher public capital raises aggregate spending and output. In the firstplace, there is the increase in public investment itself. Furthermore, the effects ofhigher public capital propagate through the system. Private investment, calculatedfrom changes in the private capital stock, as well as private consumption, affectedby household disposable income and consumer prices, contribute to further outputincreases. The total increase in 1996 output amounts to 5.8%. (Exports are notaffected since they are sold on the world market at an exogenous price.) The directeffect of this aggregate demand increase on employment is unfavourable since thecost share of labour falls in output. Indirectly, however, given a cost flexibility ofoutput of 0.92 (see c,X in Table 1), the increase in private output implies a risein 1996 total cost of about 5.2%. For given cost shares, this generates an increasein private employment. Combining both effects, a small positive net demand ef-fect on private employment remains (+0.3%). The unemployment rate decreasesby 0.13% points. Finally, there is the wage channel. Real wages are influencedby an increase in the public capital stock through changes in labour productivity,changes in the unemployment rate and changes in domestic prices. Prices being


Fig. 2. Government budget balance (in % of business sector GDP), simulation under the alternativeinvestment policy (19701996).

largely unaffected (see Table 3), we further disregard them. Due to higher outputbeing produced with less labour, 1996 labour productivity is 13.3% higher thanin the benchmark. This partially feeds through into higher wages (+9.9%). De-spite a fall in unit labour costs, employment is negatively affected because thegrowth in real wages induces an increase in the relative cost of labour and substi-tution of cheaper capital and materials.7 Since the production channel and the risein labour productivity raise the unemployment rate, the full impact of wages on(un)employment depends on how unions react. Given the estimated low respon-siveness of real wages to unemployment, rising unemployment offsets only partof the rise in real wages, leaving a net increase of 7.0%. This 7.0% wage increaseaccounts for a 0.7% points rise in the unemployment rate.

A final and very important result in Table 3 concerns the governments financialbalance. As can be seen, the simulated bond financed rise in public investment doesnot undermine the governments budget in the long-run. Fig. 2 provides a detailedpicture. Mainly thanks to higher economic growth and tax receipts, in 1996 theincrease in the deficit compared to the benchmark is only 0.9% points of GDP(coming from a maximum of 2.61% points in 1989). Extrapolation of the evolutionof the budget suggests a decrease in the deficit, relative to the benchmark, fromabout 1998 onwards. Clearly, for the reliability of the above mentioned simulationresults and for the assumptions on private consumption that we have made inSection 2, this result is reassuring.

5. Conclusion and policy implications

In this paper we develop and estimate a structural model to analyse thelong-run impact of public capital on private sector performance, in particular

7 Note that the substitution of capital and materials for labour for a given output in the secondround further raises labour productivity. As a result, the unemployment rate will increase further.


(un)employment, in Belgium. The estimates show that services from public capitalsignificantly reduce private sector cost, for given output and wages. An increase inthe public capital stock with 1 euro reduces long-run private cost with 0.24 euro.The output elasticity of public capital implied by these estimates equals 0.31,which confirms Aschauers public capital hypothesis as well as our earlier results(Everaert & Heylen, 2001), although a totally different methodology has beenused. With respect to private sector inputs, public capital and labour are found tobe substitutes, public capital and private capital complements. Model simulationsshow that the basic negative relationship between public capital and employmentis not altered once the effects of a change in public capital on aggregate demandand wages are taken into account, on the contrary.

As to policy, our research strongly supports the case for an increase in publiccapital spending, although not unconditionally. The main benefits are obvious.We find at least for Belgium that public capital contributes significantlyto higher output and productivity growth. In the light of current concerns, e.g.,about the growth gap between the EU and the US or about the future retirementburden, it is clearly important to strengthen the economys productive capacity.Public capital spending should not, however, be raised unconditionally. This pa-per has also demonstrated the need for complementary measures. First of all, incontrast to suggestions by, e.g., the European Commission (1993), higher publiccapital spending may cause (more) unemployment. Part of the rise in unemploy-ment is due to upward pressure on real wages prompted by an increase in labourproductivity. Part is also due to the often observed weak responsiveness of Belgianwages to rising unemployment itself (see also Abraham, De Bruyne, & Auwera,2000; Heylen & Van Poeck, 1995). If policy makers want higher public invest-ment spending to contribute to employment, complementary measures to enhancewage moderation and wage flexibility are (again) called for. In this respect, ourresults support recommendations by, e.g., Calmfors (1998) or Wyplosz (2001).Furthermore, labour market performance may benefit from a careful selection ofpublic investment projects. Our empirical analysis relies on a broad concept ofpublic capital. It does not imply that all investment projects bring about substi-tution of labour. For example, investment in training facilities or mobility for theunemployed may be beneficial for employment. So may infrastructure investmentaimed at structural conversion of weak regions. Further research on the labourmarket effects of sub-categories of public capital is required here. Complemen-tary public investment and labour market policy is important also from a differentperspective. It has often been argued that labour market reform is unlikely to suc-ceed in an unfavorable macroeconomic environment (e.g., Allsopp & Vines, 1998;Wyplosz, 2001). The growth stimulating effect of public investment can be usedto raise the short-run benefits of structural reform and consequently its probabilityof success.

The second reason for not unconditionally increasing public investment resultsfrom existing budgetary constraints. Given the enduring need in Belgium to reducethe government debt ratio, as well as the restrictions imposed by the EMU Stability


and Growth Pact, there is no room for deficits anymore, not even temporary ones.On the one hand, one may regret this. Our analysis confirms that an increase ingovernment investment strengthens the productive capacity of the economy, withno permanent worsening of the government budget. Furthermore, it has been shownin various studies that fiscal consolidation has a higher probability of success whengovernment investment is increased rather than cut (e.g., Alesina & Perotti, 1996;Heylen & Everaert, 2000). On the other hand, as long as this narrow frameworkexists, it will force policy makers to carefully balance the costs and benefits of theirspending decisions and to improve the composition of their expenditures. Higherpublic investments are still possible, but they should be financed from budgetarymargins created by reductions elsewhere (e.g., declining interest payments or othertransfers). Even then, the long-run benefits of public investment should still bebalanced against the benefits of faster debt reduction.

Acknowledgments

The authors thank Jakob de Haan, Gerd Hansen, Glenn Rayp and Rudi Van-der Vennet for helpful suggestions. They have also benefited from comments byparticipants at the 13th Annual EALE Conference (September 2001, Jyvskyl)and participants at the conference on Macroeconomic Transmission Mechanisms:Empirical Applications and Econometric Methods (May 2000, Copenhagen). Anyremaining errors are ours.

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Public capital and long-term labour market performance in BelgiumIntroductionThe modelProduction technology and factor demandInput price formationPrice settingAggregate supply and demandGovernment budget balance

Empirical analysisDynamic cost function and dynamic factor demandsWage bargaining and price settingAggregate consumption and net exports

System simulationsBenchmark simulationAlternative public investment policy

Conclusion and policy implicationsAcknowledgementsReferences

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