FOOTNOTES

1

   Most of the research for this paper was done during the stay at the University of California at Berkeley and was supported from its Center for Slavic Studies. The stimulating environment and facilities of the Russian Research Center of Harvard University and a grant from the Graduate School of Boston University were very helpful in finishing the manuscript. We are particularly grateful to professors Gregory Grossman, Thomas Marschak, Benjamin Ward, Thomas Rothenberg, Paul Zarembka, Jan Kmenta, Arnold Zellner, Zvi Griliches, Ray Jackson, John Hughes and Phillip Swan and Mr. E. Gendel who helped us by their comments at various stages of the research.

2

See Kmenta (5) pp.462-463. Kmenta obtained hi%: formula by taking the Taylor's expansion of

lgF(K/L,1) = -(1/w)lg[d(K/L)-w + 1 - d]

around  =  0 and dropping all the terms containing  ws  with s > 1.

3

Suppose, that each variable is expressed in two alternative units of measurement, so that we have two sets of observed variables Y, K, L and Y*, K*, L*, related by the relations:

 

(2.23)          Y = kYY*, K = kKK*, L = kLL*,

 

Substituting (2.23) in (2.18) we get 

 

(2.24)   lg(Y*/L*) + lg( kY /kL )  =   a + d[lg( kK /kL ) + lg(K*/L*)] 

                  + f{[lg( kK /kL )]2 + 2lg( kK /kL )lg(K*/L*) + [lg(K*/L*)]2}

                   + rt + (1/2)l2 + mSst + e

and after simple rearrarrangements we find

 

(2.25a)          a*    =   a - lgkY + dlgkK + (1 - d)lgkK   + f[lg( kK /kL ) ]2

 

(2.25b)           d* =  d[1 +2flg( kK /kL )]

 

(2.25c)            f* = f,  r* = r,  l* = l,  m* = m. 

 

It is apparent from (2.25 a, b) that any change in units of measurement of output Y does influence the constant a only. Changes in units of measurement of capital K and labor L do influence both the constant a and the distribution parameter d. The estimates of parameters f, r, l, and m are apparently independent of units of measurement. The estimates of parameter w and therefore also of the elasticity of substitution s, are obtained from the estimates of d and f. They are, therefore, also dependent on units of measurement.

4This procedure was used for example by Tlusty and Strnad (13), (14).
5

This type of models were investigated for example by Balestra and Nerlove (1), Mundlak (8), Wallace and Hussain (15), and Kmenta (4). To the large extent we follow here the Kmenta's suggestion of estimating the cross-sectionally heteroscedastic and time-wise autoregressive models.

6We are greatful to Dr. Thad Alton and his colleagues who provided us with some yet unpublished estimates of GNP or industrial output for Czechoslovakia and some East European countries.
7See, for example, Novotny (9).
8

Coefficients in Table 3 are calculated as simple arithmetic means of sectoral coefficients. The more correct procedure would be to use the weighted arithmetic mean with logarithms of factors as weights, as can be seen from (3.2). However, the results would not be very different. The simple arithmetic mean remains to be correct for calculating the mean values of the technical progress parameters r, l and m.

9See tables 6-13.
10The Durbin-Watson statistics were evaluated in the timewise direction with "gaps" between sectors. This gives the same results as taking the weighted arithmetic mean of sectoral Durbin­Watson statistics with sectoral sums of squared residuals as weights.
NoteThe coefficients b, g and n are directly comparable for RG and LG models, however, the coefficients r, l and mobtained from LG models must be multiplied by 100 to make them comparable with the RG estimates. In fact, they should be exponentiated first, which would slightly increase their nominal values.

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