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An analysis of past and future GDP growth in Slovenia Growth in GDP and inputs in the past Working paper 3/2004 IMAD 29 In preliminary work Miækoviæ and Vasle (2004) calculate a capital-output ratio of 1.43 in 1996, compared to 1.73 in our series. For the period 1992-2002 they further calculate an average annual growth of capital of 6.0%, compared to 6.4% in our series. Below we are mostly interested in the growth rate of capital, which is quite similar. Doyle et al. (2001) obtain a value for the capital-output ratio of 2.11 in 1996, compared to 1.73 in our series. They further calculate an average annual growth in capital over the period 1992-2002 of 4.1%, compared to 6.4% in our series. Their growth rate is quite a bit lower. This is likely to be due to their relatively high starting value. Their capital series starts in 1985, where they assume that the capital-output ratio in Slovenia was the same as in Hungary. This may be too favourable. A growth of 4.1% implies, for example, that there was virtually no capital-deepening over this period. This does not seem to accord with the decline in the user cost of capital over the period 1992-2002. 41 Finally, Piatkowski (2003) obtains a value of 2.28 for the capital-output ratio in 1996, compared to 1.73 in our series. For the period 1995-2000 he finds an average annual growth of capital of 5.3%, compared to 7.5% in our series. Perhaps the difference is due to the different data sources used. We use national accounts of Slovenia directly, Piatkowski (2003) uses them indirectly (investment series are taken from the World Development Indicators, 2003). Another difference is the assumed drop in the capital stock during the late 1980s/early 1990s. Piatkowski (2003) assumes a one-off drop of 25%, we raise the depreciation rate by 7.5% over a five year period, a cumulated additional drop in capital of 32%. 41 Furthermore, the share of gross fixed capital formation in GDP in real terms was on average 24% in Slovenia over the period 1993- 2002, compared to just 20% in the EU-15 (source: Eurostat, 30-04-2004). This also suggests capital deepening in Slovenia, given that we do not expect Slovenia to have started with a higher capital-output ratio than the EU-15 average in 1993.
30 IMAD Working paper 3/2004 An analysis of past and future GDP growth in Slovenia Growth in GDP and inputs in the past Intermezzo: Substitutability between capital and labour We do not reject that the production function is Cobb-Douglas In the next section we consider the individual contributions to GDP growth of the inputs considered above. However, we first take a detour to consider the functional form of the aggregate production function. This will have some relevance for the growth accounting exercise below, but is mostly relevant for the subsequent projections for the future. Suppose that aggregate output Y(t) at time t is given by the CES-function Y ( t) = A ( t) Y 1 γ γ ( β ( A ( t) N( t)) + (1 − β )( A ( t) K( t)) ) γ , N K where A Y (t), A N (t) and A K (t) denotes neutral, (effective) labour and capital augmenting progress respectively, N(t) and K(t) denote (effective) labour and capital, â and ã a parameter where ã determines the elasticity of substitution between labour and capital ç ≡ ã/(ã-1). In the analysis below we are mostly interested in whether ã differs significantly different from 0, in which case the CES-production function above reduces to the more convenient Cobb-Douglas function (see e.g. Barro and Sala-i-Martin, 1998) β Y ( t) = A ( t)( A ( t) N( t)) ( A ( t) K( t)) Y N K Cost minimisation given labour costs and the user cost of capital gives expressions for labour and capital demand. Unfortunately, the capital demand equation gave poor results. This is likely to be the result of the user cost series, in which we do not have great faith, in particular at the beginning of the series (see above). Therefore, we focus on the substitution elasticity implied by the estimated labour demand equation. Denote average labour costs by wc(t). 42 Furthermore, suppose that A Y (t) and A N (t) are of the form A x (0)(1+g x ) t with g x sufficiently small so that log(1+g x ) ≈ g x . Starting with the CES-production function above, cost minimisation gives the following relation between the demand for (effective) labour and labour costs. 43 1−β log( wc( t)) = c' + γ ( g + g ) t + ( γ −1)log( N( t) / Y ( t)) + ε ', Y N where c’ ≡ log(â(A Y N ã Y (0)A N (0))),, ã ) g Y and g N denote the growth rate in neutral and labour augmenting technological change, and å t ’ denotes an (identically and independently distributed) error term. The estimation results are given in Table 2. For comparison, Hamermesh (1993) suggests a reasonable guess for the substitution elasticity between labour and capital is about –1, or ã=0 (the Cobb-Douglas case). When we use employment (in FTE) for the period 1993-2002, we find a value for ã of -0.06, very close to the Cobb-Douglas case (indeed the estimate does not differ significantly from –1(ã=0). ã When we use the labour composite with employment (in FTE) multiplied by the . t 42 For 1995-2002 we take labour costs per employee of rapid report no. 112 of the SORS. For 1993-1994 and 2001-2002 we calculate labour costs using compensation of employees in the National Accounts plus ‘employers’ payroll taxes’ (introduced in 1994) and taking the corresponding number of employees of the national accounts. The two series are very close in 1995 and 2000 (in both years the difference is less than 1 percent). 43 We rewrite the first-order condition to labour costs, believing that it is in fact labour that is exogenous and wages that are endogenous.
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