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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 27 Figure 8: User cost of capital 32 28 User cost of capital Real interest rate + depreciation rate 24 20 In % 16 12 8 4 0 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Source: Own calculations using SORS and Bank of Slovenia data. ( 1+ r( t)) p ( t) = p ( t) + (1 − δ ) p ( t), or i k p ( t) = ( r( t) − ( p ( t) − p ( t −1)) / p ( t −1)) p ( t −1) + δp ( t), k i i i i where p i (t) denotes the investment price at time t. We take the lending rate for long-term loans of capital assets as the relevant interest rate for capital. 38 As the price of capital goods we take the implicit deflator for gross fixed capital formation from the National Accounts. Using a depreciation rate of ä of 0.075 as before, we can calculate the nominal user cost of capital. 39 However, capital is accumulated until the marginal product of capital equals the nominal user cost of capital over i i Figure 9: Capital stock using the marginal productivity condition 2.00 1.80 1.60 1.40 1.20 K/Y 1.00 0.80 0.60 0.40 0.20 Capital-output ratio (v ary ing output elasticity of capital) Capital-output ratio (constant output elasticity of capital) 0.00 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Source: Own calculations. 38 See Table 2.4.1 in the Monthly Bulletin of the Bank of Slovenia. 39 We assume that individuals have perfect foresight regarding investment prices. We could try to model investment price expectations with an ARIMA specification. However, substantial swings in inflation rates (with annual inflation rising up to 1000+%!) probably imply that there is little to gain from this approach.
28 IMAD Working paper 3/2004 An analysis of past and future GDP growth in Slovenia Growth in GDP and inputs in the past the price of output. Figure 8 plots the ‘real’ user cost of capital, the nominal user cost of capital deflated by the GDP deflator. Figure 8 suggests a substantial fall in the user cost of capital over the period 1993- 2002, reflecting the net effect of a fall in interest rates and inflation in investment prices. 40 Indeed, there was a substantial drop in real interest rates, due to e.g. a declining risk premium or opening up of financial markets. The user cost drops from 0.32 in 1993 to 0.16 in 2002. Finally, assuming that our constructed series for the capital income share and the user cost of capital are correct, and assuming that capital is paid its marginal product, Figure 9 shows the capital-output ratio implied by the optimality condition for a Cobb-Douglas production function (i.e. the capital income share over the user cost of capital). Using either the actual capital income shares over the period 1993-2002 for the elasticity of output with respect to capital, or assuming a constant elasticity of output with respect to capital of 0.3, we find a dramatic rise in the capital-output ratio – from 0.67 in 1993 to 1.85 in 2002 using the former, and from 0.95 in 1993 to 1.85 in 2002 using the latter, see Figure 9. The end values are perhaps not too far from the series in the previous subsection, 2.14, the starting values are much lower though. Even the capital series from the optimality condition using a constant elasticity of output with respect to capital of 0.3 suggests an annual growth in the capital-output ratio of 8% over the period 1993-2002. This seems unrealistic. The results are probably more informative about the difficulties of determining the elasticity of output with respect to capital and calculating the user cost of capital in the rather volatile early 1990s, than about the growth in capital. 2.4.3. Comparison with other studies The growth in the capital series after 1993 is somewhat higher in this paper than in related studies The perpetual inventory method suggests an annual growth of the capital stock of 6.8% over the period 1993-2002. The optimality condition suggests a much higher growth rate, but the marginal product and the marginal cost of capital are rather hard to determine in the early years following the transition. Below we therefore use the capital stock series from the perpetual inventory method. Supporting ‘evidence’ comes from capital series constructed for Slovenia by other authors. Bovha Padilla and Padilla Mayer (2002) obtain a value for the capital-output ratio of 1.5 in 1992, their base year. Our capital series has 1.7 in 1992, somewhat higher. They use the optimality condition to determine this initial capital-output ratio. As we saw above, this produces a relatively low capital-output ratio in the early 1990s. Over the period 1992-2000 Bovha and Padilla (2002) calculate a much lower growth in capital of 1.1% per year, compared to 6.2% in our series. The low growth in Bovha Padilla and Paddila and Mayer (2002) is a bit puzzling given that their initial capital stock is lower whereas they use the same national accounts for subsequent investments. 40 The user cost of capital is close to but not exactly the same as the sum of the real interest rate and the depreciation rate used in Mrkaic (2002) and Bovha Padilla and Padilla Mayer (2002), see also Figure 8. The difference is due to a difference in the inflation rate implicit in the user cost of capital, derived from investment prices, and the inflation used by the Bank of Slovenia to calculate the real interest rate, derived from consumer prices.
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