Empirical Studies




All the production functions were estimated in “per capita” form and in logarithmic transformation, that is by using the regression equation (i) or the regression equations obtained by deleting either t2 or vt or both from (i)


yit = a + bkit +  rot  +  r11/2 t2 +  mvt + eit 









The literature on pooling cross-sectional and time series data5 suggests that the random disturbance eit may be composed of two or more additive components, be cross-sectionally heteroscedastic and be time-wise auto­regressive.


This clearly happened in our case. We shall therefore make the following assumptions


eit    =   ai + e*it  



where ai  and e*it are normally and independently distributed random variables of which we assume


E(ai) = 0,    E(ai 2) =   sa2    ,  E(ai aj) = 0   for j ¹ i


e*it  =   li(1) e*it-1  +   li(2) e*it-2  +  e**it   


We further assume, that the random disturbances e**it    are normally distributed and cross-sectionally as well as time-wise independent. We do, however, assume that they are cross-sectionally heteroscedastic, so that for each i


(e**it)  =  0,   E(e**it 2)   =   s2i,   E(e**it    e**js    ) = 0    for s ¹ t   



It It is to be noted that the autoregression coefficients  li(1) and li(2) are assumed to be specific to each sector. As a result, the random disturbance would be heteroscedastic, even if  e**it    was not.


Assuming |li(1) + li(2)|  < 1, the variance of  e*it    will be


var(e*it )  =   s2i  /[1 - (li(1) + li(2)) ]


It is to be expected, therefore, that the removal of serial correlation in sectors will considerably diminish the cross-sectional heteroscedasticity. In estimating our production functions we have chosen the standard procedure of removing the sectoral error components by introducing sectoral dummy variables — i. e. allowing for differentiated intercepts of regression lines — and removing the autocorrelation and heteroscedasticity by transforming variables.




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