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Empirical Studies

HOCKE, KYN, WAGENER  PRODUCTION FUNCTIONS ESTIMATES FOR SOVIET INDUSTRY

 2. Data

2.1 In our estimations, we used either the aggregate time series (1951-1970) for the total industry or the sectoral time series for ten major industrial branches (energy, fuels, ferrous metals, non-ferrous metals, machine-building, construction materials, wood and paper, chemicals, light in­dustry, food) of the following data²⁾:  

(i) The gross value of output (excluding turnover tax) (Y),  
(ii) The stock of fixed assets at the beginning of the year (K),  
(iii) The number of employees (L) or alternatively the number of manhours (L*)  

The choice of gross value of output as the left hand variable may not be fully satisfactory from the theoretical point of view, however, it was inevitable because the data on net output were not available for industrial branches³⁾    

The fact that the intermediate inputs - including the intrabranch turnover - are part of the gross value of output, but do not appear on the right-hand side of the regression equa­tion would not really matter if the share of intermediate product in the gross value of output would remain constant over the whole observed period. It is, however, very unlikely that this would be the case.⁴⁾  

  2.2. We have decided to use the official Soviet Statistics whenever possible and therefore we have accepted also the official Soviet prices as weights and the price indices as conversion factors to constant prices. This adds an additi­onal grave problem, namely that part of inflation which is disguised as improvements in the quality of goods and therefore hidden in the official Soviet price indices.⁵⁾    

Another difficult problem was created by variations in the degree of utilization of input factors. It has been recog­nized that the Soviet type economies undergo periodical fluctuations in their economic activities. The proper approach would be to subtract the unutilized portion of a factor before regression. Unfortunately we have not had enough information to do that. In the capitalist countries with the flexible labor market it can be assumed that the prevailing part of unutilized labor appears in the category of “unemployed” so that the data on employment do not contain any large unutilized labor. Under Soviet socialism the situ­ation is different: the rigid central planning and the strict labor laws make firing of workers almost impossible so that the downswings in economic activity results in a lower degree of utilization of employed labor rather than in increased unemployment.     

2.3. Probably the main obstacle is a very high degree of multicolinearity in data. The following correlation matrices very clearly indicate this difficulty.

 Table 1 Correlation matrix of the variables

  Table 2 Correlation matrix of logarithms of variables

Multicolinearity is particularly severe in Soviet-type economies because centralized planning makes the economic growth relatively smooth so that the variables ln K and ln L are highly correlated with time. When the number of employees (L) is replaced by the number of manhours worked (L* ) the correlation coefficients are slightly diminished:

It may be interesting to note here that our set of data is almost identical with that of Weitzman (70, p.677), although it was derived in a somewhat different way. The correlation coefficient between the two output series is  .9998, between the two capital stock series it is  .9999. Naturally, the correlation matrix of Weitzman’s data shows a pattern similar to ours. ⁶⁾