Comparing the results obtained from all the estimated variants of production functions, we can make the following conclusions:
1. All three approaches used give very good fits as measured by the R2 statistic, namely the linear regression from aggregate time series (LATS), the linear regression from pooled cross-section and time series data (CS-TS), both, however, only after correcting the data for the first order autocorrelation in the error, and the nonlinear regression from aggregated time series (NLATS). Yet the estimated coefficients are frequently not statistically significant on any reasonable level. The estimated values of the parameters also vary widely according to the chosen approach and model.
2. In the models with no technical progress, the estimated capital elasticities are generally very high (around .7) . This is not surprising, because in those cases the growing capital output ratio becomes a proxy for the time trend and, therefore, capital takes the effect of technical change on itself. In the models with technical change, the estimated capital elasticities differ according to the approach used. In the LATS and NLATS approaches the capital elasticity is unusually high, in the CS-TS approaches it is normal or very low.
3. No clear-cut conclusions about returns to scale can be made. Some variants indicate economies, others diseconomies of scale. Frequently the deviation of n from unity is small and statistically insignificant. This is not true for NLATS estimates the nonlinear estimates of n are not very reliable. All that leads us to the conclusion that the best thing may be to assume constant returns to scale.
4. The estimates of the average rate of technical change vary between -.01 and 6.5 percent. Low estimates of r are combined with unusually high estimates at b and vice versa, and very high estimates of r are combined with unrealistically low returns to scale (variant 10). If we have preconceptions about realistic values of b, we are able to make conclusions about the rate of technical change in Soviet industry, For instance, if we accept the estimates of b between .32 and .34 on a priori grounds, the rate of technical change is 3 - 3.3 percent annually. If we think that estimates of b between .45 and .6 are “better”, the rate of technical change in Soviet industry is reduced to 1.2 — 2 per cent. If we have no idea about “good” values of b, the whole exercise results only in estimated pairs of b and r. And no conclusions about the actual rate of technical progress can be made.
5. The CS-TS estimates of the CD production function with a variable rate of technical change (variants 5c,d,e and 6c,d,e) lead to a trend declining .1 to .2 percent annually. Although the estimates of r1 are not significantly different from 0 the existence of such a trend seems plausible. It is not very likely that such a linear decline in the rate of technical change would continue forever. More, likely the declining trend would lose its power so that the rate of technical change may level on a new, lower level, The opposite result as of the LATS approach (variants 5 a, b) cannot be called completely implausible either: the declining rate of growth in Soviet industry will be explained in this case by reduced increases of factor inputs together with an average negative time trend which, however, is improving over the whole period.
6.The same fact can be explained by an elasticity of substitution smaller than one. Unfortunately the quality of NLATS estimates is not good enough to justify any definite conclusion about the exact value of the elasticity of substitution.
Finally, the different results for the parameter values of b, r and s will have a certain effect upon the estimated growth potential, as was laid down in section 3.2. For the period of observation l951-1970 the instantaneous rates of growth have been for industrial output g = .0854, for capital stock k = 964, and for labor (number of workers and employees) l = .0332. That is to say, we observed a situation of Case II.
Solving with this set of data equations (5b) and (11b), we get the range of the equilibrium rates of growth of labor productivity (g - l) for different values of b (see Diagram 4)
If our uncertainty about the “true value” of b is restricted to the area between .3 and .65, as may be suggested from the above estimates, the equilibrium growth of labor productivity will vary between 4.7 and 3.2 per cent. A span of uncertainty of about 1.5 percentage points should not be too serious. It would be premature to judge from the equilibrium rate of growth upon the actual future rate of growth of labor productivity.
It would be premature to judge from the equilibrium rate of growth upon the actual future rate of growth of labor productivity.
For Soviet economic policy is (certainly not completely) free to choose a rate of growth for capital that it thinks appropriate or necessary. This all the more since we are dealing with only one sector of the economy. Projections should rather be made directly with probable rates of growth of the productive factors and the estimated production functions. However, if ,for instance, the Soviet planners envisage a rise in industrial labor productivity of more than 6 percent as they do in the Five Year Plan 1971-1975, we may conclude from the above that they will need a further increase in the rate of accumulation in industry to implement the plan.