Consider a translog production function where output is measured as fim sales and there are three inputs : capital , labor , and materials . This function can be written as LSALES = Bc + BxK + B_L + BM + BkxK + Bula + BM + Bxl ( KxL ) + Bxx ( KxM ) + BM ( LXM ) + e , where LSALES is the log of sales , and K , L , and M are the logs of capital , labor and materials , respec tively . The translog function is often known as a flexible functional form , intended to approximate a variety of possible functional forms . There are two hypotheses that are likely to be of interest : H " : Bax = 0 , Buz = 0 , Baum = 0 . BxL = 0.Bxm = 0.B.m = 0 ( A Cobb - Douglas function is adequate ) 1 H ) : Bx + B. + BM = 1 2Bxx + BxL + BxM = 0 Bxz + 2B + B = 0 BKM + BM + 2BMM = 0 ( constant returns to scale ) The data file chemical_small contains observations on 1200 firms in a chemical industry in the year 2006. It is a subset of the data used by Baltagi , Egger , and Kesina . ( a ) Use these data to estimate the translog production function . Are all the coefficient estimates significant at a 5 % level of significance ? ( b ) Test H , " at a 5 % level of significance . ( c ) Test H2 ) at a 5 % level of significance .
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