Question

REAL GDP, EMPLOYMENT, AND REAL FIXED CAPITAL, MEXICO, 1955–1974

Year GDP Employment Fixed capital

1955 1956 1557 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 114043 120410 129187 134705 139960 150511 157897 165286 178491 199457 212323 226977 241194 260881 277498 296530 306712 329030 354057 374977 8310 8529 8738 8952 9171 9569 9527 9662 10334 10981 11746 11521 11540 12066 12297 12955 13338 13738 15924 14154 182113 193745 205192 215130 225021 237026 248897 260661 275466 295378 315715 337642 363599 391847 422382

455049 484677 520553 561531 609825

Notes: aMillions of 1960 pesos. h GDP = A LogGDP = log A + a * log K + beta*l * c L+logu Y= phi+a X1+ beta X2+e

Answer 1

For the regression model be , which is the usual CD-production function, the linear transformation would be as or or , for Y be the natural log of GDP, k be the natural log of Fixed capital and l be the natural log of Employment.

The R-script for the regression estimation would be as below.

Year <- c(1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974) GDP <- c(114043, 120410, 129187, 134705, 139960, 150511, 157897, 165286 ,178491, 199457, 212323, 226977, 241194, 260881, 277498, 296530, 306712, 329030, 354057 ,374977) Employment <- c(8310, 8529, 8738 ,8952 ,9171, 9569, 9527, 9662, 10334, 10981, 11746, 11521, 11540, 12066, 12297, 12955, 13338, 13738, 15924, 14154) FixedCapital <- c(182113, 193745, 205192, 215130, 225021, 237026, 248897, 260661, 275466, 295378, 315715, 337642, 363599, 391847, 422382, 455049, 484677, 520553, 561531, 609825) summary(lm(log(GDP) ~ log(FixedCapital) + log(Employment)))

The output would be as below.

Call: lm(formula = log(GDP) ~ log(FixedCapital) + log(Employment)) Residuals:       Min        1Q    Median        3Q       Max -0.057142 -0.016250 -0.005793 0.023512 0.038739 Coefficients:                  Estimate Std. Error t value Pr(>|t|)   (Intercept)      -1.65233    0.60619 -2.726   0.0144 * log(FixedCapital) 0.84600    0.09335   9.063    6.42e-08 *** log(Employment) 0.33972    0.18569   1.830   0.0849 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.02829 on 17 degrees of freedom Multiple R-squared: 0.9951,   Adjusted R-squared: 0.9945 F-statistic: 1719 on 2 and 17 DF, p-value: < 2.2e-16

Hence, the estimated regression model would be as , ie .

Further solving, we have

or

ie , which is the required CD-production function.