The supply side block

The supply block determines potential GDP, investment, labour demand, and the rate of operation by estimated behaviours equations. The other variables such as gross fixed capital accumulation and the unemployment rate are calculated by a bridge and an identity equation respectively. A Cobb-Douglas production function with labour and capital inputs is

employed to derive investment and labour demand and estimate the potential GDP in this block.

3.3.2.1.(a) Investment and labour

Firstly, the long-run relationship between capital, output and the user cost of capital is derived from the first order condition (F.O.C.), which is that the value of the marginal product of capital is equal to the price of capital, with respect to capital from a profit-maximising firm.

where denotes the capital stock, GDP, the output elasticity of capital, the real capital cost. According to Hall and Jorgenson (1967), the real capital cost can be defined as:

where corresponds to the price of capital goods, the real interest rate, and the depreciation rate.

The investment variable is not observed yet, so that an additional specification for the relationship between capital and investment is imposed using the capital accumulation identity, which is as follows:

where denotes the capital stock and investment expenditure. Taking natural logarithms in the capital accumulation identity implies in the steady state,

where corresponds to the rate of depreciation, the growth rate of capital. Substituting equation (3.42) into (3.41) yields the desired level of investment in the long-run, which is as follows:

As we assumed earlier, firms might not adjust the actual investment completely to obtain the desired level in any given period. Thus, the adjustment process can be expressed as:

where is the adjustment coefficient. Rearranging the two equations for investment yields the following equation³⁴:

Note that the capital cost includes the real interest rate in equation (3.44), thus the investment is a function of the real interest rate.

In the same manner as with the investment decision, modelling labour employment adopts a partial adjustment mechanism based on two assumptions: the actual increase in labour employment is related to the discrepancy between the desired level and the previous labour employment. Second, the firm chooses the desired level of labour inputs so as to maximize its profits. Thus, the desired level of labour employment is derived from the first order condition (F.O.C.) for profit maximization, which is given by:

34 and can be reduced, as they are assumed to be constant, which does not affect the estimation of equation xx.

where represents the desired level of the labour employment, and indicate the GDP and real wage respectively. As we assumed earlier, employers might not adjust the actual employment completely to obtain the desired level in any given period. Thus, the adjustment process can be expressed as:

where is the adjustment coefficient. Rearranging the two equations for yields the labour employment equation as follows³⁵:

( )

Table 3.4 provides the comparison of estimation results for the investment equation (3.45) and labour equation (3.48) correspondingly. The calculated F statistics for the ARDL bounds testing, which are higher than the upper bound critical value at 10% level, indicate that a long term equilibrium relationship exists between dependent and explanatory variables in both equations (3.45) and (3.48).

The coefficients on the lagged and desired level of investment are statistically significant and have the expected sign. The coefficient of the independent variables can be interpreted as the value of elasticity in the short-run. The coefficient of the lagged dependent variable is regarded as the speed of adjustment from the short-rum equilibrium to the long-run equilibrium. The lagged variable of the investment and labour equation shows that around 48%

and 15% of the adjustment to the long-run desired level take place in each year respectively.

35 The output elasticity, can be reduced, as it is a constant which does not affect the estimation of equation (3.45).

The results show that investment is more responsive to the output and cost than labour in the short-run; the F.O.C. short-run elasticity of investment and labour are 1.251 and 0.086 respectively. While the F.O.C long-run elasticity³⁶ of investment, 2.156, is higher than unity in the specification of Cobb-Douglas function, the labour elasticity, 1.037, is found to be consistent with the Cobb-Douglas function. These results are verified by a set of diagnostic tests indicated in Table 3.4; no serial correlation and heteroskedasticity in the error term, and no problem with normality of the error term and functional formation.

Table 3.4. Estimation of investment and labour equations

Parameter Investment (sample: 1987~2011) Labour (sample: 1970~2011)

(Constant) -18.026^**

AR(1) Cochrane-Orcutt procedure is conducted to adjust the investment model for serial correlation in the error term

3.3.2.1.(b) Potential GDP

This model employs a production function approach for the potential GDP estimation.

The production function approach requires estimating a production function. We adopt the

36 The long elasticity can be computed by dividing the short-run elasticity by one minus the coefficient of one lagged dependent variable.

Cobb-Douglas function with two input factors; natural labour and capital and under the assumption of Hicks neutral technological progress. Note that we do not include an energy variable, since the preliminary estimation result of the Cobb-Douglas with energy input yields an insignificant and negative elasticity coefficient, which is caused by the simplicity of substitution elasticity assumed in the Cobb-Douglas function. Therefore, the model adopts an alternative approach based on the Bank Of Korea‟s macro-econometric model (Hwang et al.

2004) in which the potential GDP is indirectly determined by the energy variable by means of the rate of operation which is set up as a function of energy prices. This is more reasonable given the purpose of this study which gives priority to analyse impacts of increases in energy prices rather than energy supply disturbances. The Cobb-Douglas function is given by:

where denotes GDP, capital stock, labour, and total factor productivity the rate of technology progress. The parameters and are the output elasticity of labour and capital respectively. The parameter is the rate of operation. Given the assumption of constant returns to scale (CRTS), the production function is normalised by the labour factor to satisfy CRTS, and then taking natural logarithm on both sides of equation (3.49) yields:

The process for calculating the potential GDP is as follows; firstly estimate equation (3.50). And then substitute natural labour inputs; and into the corresponding input factor in the estimated parameters ̂ ̂ ̂ in the production function. The natural labour and capital inputs are as follows:

where is the non-accelerating inflation rate of unemployment (NAIRU) and is economically active population. is the natural rate of operation³⁷.

Table 3.5 describes the estimation result for equation (3.50). All of the coefficients on variables have the expected sign. The rate of technological progress is found to equal 0.014, and the output elasticity of capital 0.306. As seen in the cointegration, a long-run relationship between the variables exists. The equation passes a set of diagnostic tests.

Table 3.5. Estimation of the Cobb-Douglas function (a) Regression model

Dependent Variable : log Sample : 1980 ~ 2011

Regressor Coefficient Standard Error T-value P-value

Constant 11.416 0.944 12.092 0.139

0.014^*** 0.005 3.125 0.005

0.306^*** 0.005 5.879 0.000

Note: ^***,^**, and ^* indicate significance at 1 %, 5 %, and 10 % respectively. The p-values are given in parenthesis.

The estimation includes a dummy variable equal to unity for the period 1997~1999

AR(1) Cochrane-Orcutt procedure is conducted to adjust the model for serial correlation in the error term

(b) Cointegration test : = 15.364^***

(c) Diagnostic tests

̅ = 0.999 = 1.823

̂ = 0.012 = 812.291 (0.000)

= 0.021 (0.886) = 0.218 (0.897)

= 1.174 (0.290) = 0.932 (0.477)

Note: the right-hand side value in parentheses indicates p-value

37 Based on “Putty-Clay” hypothesis is derived as: [ ]

3.3.2.1.(c) The rate of operation

The rate of operation is assumed to be a function of the lagged dependent variable, the gap between the actual and the natural rate of unemployment , GDP, and the industrial energy price index . The rate of operation function is given by:

The estimation result is described in Table 3.6. The F statistics for the ARDL bounds testing shows that it is higher than the upper bound critical value at 1% level, which implies that a long term equilibrium relationship exists between dependent and explanatory variables in equations (3.45). All the coefficients on variables have the expected sign; the unemployment and energy price have a negative impact and GDP has a positive impact on the rate of operation, which are all statistically significant.

Table 3.6. Estimation of the rate of operation (a) Regression model (sample: 1989~2011)

Dependent Variable : Sample : 1989 ~ 2011

Regressor Coefficient Standard Error T-value P-value

Constant 2.072 1.237 1.675 0.116

-0.503^*** 0.091 -5.533 0.000

-0.118^*** 0.016 -7.535 0.000

0.165^*** 0.045 3.675 0.003

-0.090^** 0.033 -2.702 0.017

Note: ^***,^**, and ^* indicate significance at 1 %, 5 %, and 10 % respectively. The p-values are given in parenthesis.

The estimation includes a dummy variable equal to unity for the period 2004~2011 (b) Cointegration test : = 10.059^***

(c) Diagnostic tests

̅ = 0.897 = 2.421

̂ = 0.002 = 27.216 (0.000)

= 1.359 (0.264) = 3.389 (0.184)

= 2.467 (0.140) = 0.400 (0.887)

Note: the right-hand side value in parentheses indicates p-value