Production Function Approach

The production function approach concerns the type of production technology used with core inputs, and how effectively inputs and technology are applied. Thus, the production function approach encompasses the entire production structure and process. Theoretically, a production function shows the maximum possible output that can be produced with the given level of inputs and technology. The maximum possible output is generally called the potential output. Therefore, estimation of the potential output requires the knowledge of the share of capital (K), share of labor (L), value added (Y) and total factor productivity (TFP) of the economy, which can be estimated using the observed values of Y, K, and L.

In the case of India, it is not expected to be able to decipher cyclical changes in unemployment and productivity where unemployment is not documented in the same way as in developed economies. Further, Indian government laws do not permit an easy way of firing labour. Therefore, filtering employment or TFP for the cyclical effects is not expected to make much sense.

With such limitations, a direct approach to estimate the production function itself is considered as an alternative way to fit potential output for India with total productive labor force (LABT) available in the economy as the proxy for labour. A simple Cobb-Douglas (CD) production function with the following specification in value added (Y), capital K and labour L is considered to obtain potential output Y p .

y;

=1

In the above equation A is a constant, a is technical progress, and ß and y represent the shares of capital and labour, respectively, in the total output. Actual output need not be equal to potential output due to weather conditions, supply bottlenecks of other inputs, organizational factors and demand conditions. For example, a given labour and capital will produce more output with favourable rain than drought. Thus, the actually observed output can be represented as follows:

Yt =Ytp +e t (5.17)

Where, et is the deviation of output from potential output and can be named as the output gap. Also, £, is assumed to capture other leftover effects of any factor on output, measurement errors in output and deviation from the assumed production structure. Any possible first order auto correlation in et has been corrected applying the method discussed in Pesaran and Pesaran (1997). The first order auto correlation correction can also be interpreted as the correction for the fluctuation in utilization of capital and labour in the production process.

With the estimated series of Ytp , the time series for the output gap (GAPY) can be calculated, as et itself represents the difference between actual output and potential output as per the definition stated earlier. However, et represents not only the difference between output and potential output, but also, the impact of other left out variables, deviation from the assumed Cobb-Douglas technology and measurement errors.

Now, concerning the estimation of the potential output, output Y is the real gross domestic product at market price. The measure of capital is the real net fixed capital

stock (NFCS), which is obtained by the method of perpetual inventories with five percent depreciation and 1993-94 as the base year as discussed in Appendix AA of this thesis. The instruments include lagged values of NFCS, LABT, deviation of rain from normal (DRAIN), net direct foreign investment as a percentage of gross domestic investment (FDINZI), and real imports (RIM). A summary of data is provided in Annexure 5.1 of this chapter while full details are provided in Appendix AA of the thesis. All variables appearing in non-linear two-stage least squares estimation of output are transformed into indices with 1993-94 as 100. Similarly, time is considered relative to 1993-94, with r=0 for 1993-94. Estimation results of the non-linear two-stage least squares are given in Table 5.2. The period of estimation is 1972 to 1998 (27 observations). The instruments used are: NFCS(-2), DRAIN, LABT(-2), FDINZI(-l), and RIM(-l). The value of ‘e ’ in estimation equation (5.19) is taken as 2.71828.

Table 5.2 Non-Linear Two-Stage Least Squares estimation of potential output (1972-98)

Parameter Estimate Standard Error T-Ratio [Prob]

A 1.018 0.0047 216.6 [0.00]

a 0.0098 0.0038 2.58 [0.02]

P 0.721 0.1206 5.98 [0.00]

Y = (1-ß) 0.279

GR-Squared = 0.996, GR-Bar-Squared59 = 0.996, R-Squared = 0 995, R-Bar-Squared = 0.994, S.E. of Regression = 2.28, Sargan’s C H SQ (l) = 2.29[.130]

Diagnostic Tests

LM(1) test for Serial Correlation CHSQ(l) = 1.257 [0.26]; Sargan’s test statistic for serial correlation CHSQ(3) = 4.53 [0.21]; Ramsey’s RESET test of Functional Form CHSQ(1)= 0.070 [0.79]; Normality test based on a test of skewness and kurtosis of residuals CHSQ(2) = 0.77 [0.68]; Heteroscedasticity test based on the regression of squared residuals on squared fitted values CHSQ(

1)= 0.04 [0.84]

The above coefficients are estimated quite precisely. The shares of labour in the national income during the period of 1993-94 to 1996-97 are presented in Table 5.3 to show that the above estimates compare very well with the actual data. At the same time, the estimation is statistically sound with all the diagnostic results well within limits. Since the actual factor shares and the estimated factor shares of capital and labour are very similar and this indicates that the impact of other left out variables

59 Generalized R-Squared and Generalized R-Squared Bar are appropriate measures of overall fit when estimation is done by using instrumental variables as discussed in Pesaran and Smith (1994)

and the deviations of the production structure from the assumed Cobb-Douglas framework are not important. Thus et can be expected to represent output gap reasonably well.

Table 5.3 Actual factor incomes during 1993-94 - 1996-97

Y e a r G D P at c u r r e n t M a r k e t P r ic e ( R s m il lio n ) C E a t c u r re n t M a r k e t P r ic e ( R s m il lio n ) O S /M I at cu r re n t M a r k e t P r ic e ( R s m il lio n ) N D P at c u r re n t M a r k e t P r ic e ( R s m il lio n ) C E a s p e r c e n t a g e o f G D P C E a s p e r c e n t a g e o f N D P 1 9 9 3 - 9 4 8 7 6 9 5 2 0 2 5 2 9 4 4 0 4 6 3 1 7 4 0 7 1 6 1 1 8 0 2 8 . 8 4 3 5 . 3 2 1 9 9 4 - 9 5 1 0 3 7 8 4 2 0 3 0 0 8 2 0 0 5 4 5 5 8 8 0 8 4 6 4 0 8 0 2 8 . 9 9 3 5 . 5 4 1 9 9 5 - 9 6 1 2 1 7 9 6 3 0 3 5 2 5 3 8 0 6 3 6 5 9 1 0 9 8 9 1 2 9 0 2 8 . 9 4 3 5 . 6 4 1 9 9 6 - 9 7 1 4 0 9 8 4 9 0 4 0 5 3 5 5 0 7 4 8 6 2 2 0 1 1 5 3 9 7 7 0 2 8 . 7 5 3 5 .1 3

Note: CE = Compensation to employees; OS = Operating surplus; MI = mixed income; NDP = net domestic product; GDP = Gross domestic product.

Source: National Accounts Statistics 1999, Government of India.