Introduction to Modern Economic Growth First, data on capital and labor shares across countries are not widely available This makes the use of equation (3.27) far from straightforward Consequently, almost all calibration or levels-accounting exercises that estimate technology (productivity) differences use the Cobb-Douglas approach of the previous subsection (i.e., a constant value of αK equal to 1/3) Second, even if data on capital and labor shares were available, the differences in factor proportions, e.g., differences in Kj /Hj , across countries are large An equation like (3.27) is a good approximation when we consider small (infinitesimal) changes As illustrated in Exercise 3.1, when differences in factor proportions are significant between the two observations, the use of this type of equation can lead to significant biases To sum up, the approach of calibrating productivity differences across countries is a useful alternative to the regression analysis, but has to rely on a range of stringent assumptions on the form of the production function and can also lead to biased estimates of technology differences when factors are mismeasured 3.6 Estimating Productivity Differences In the previous section, productivity/technology differences are obtained as “residuals” from a calibration exercise, so we have to trust the functional form assumptions used in this strategy But if we are willing to trust the functional forms, we can also estimate these differences econometrically rather than rely on calibration The great advantage of econometrics relative to calibration is that not only we obtain estimates of the objects of interest, but we also have standard errors, which show us how much we can trust these estimates In this section, we will briefly discuss two different approaches to estimating productivity differences 3.6.1 A Naăve Approach The first possibility is to take a production function of the form (3.26) as given and try to estimate this using cross country data In particular, taking logs in this equation, we obtain: (3.28) log Yj = (1 − α) log Kj + α log Hj + α log Aj Given series for Yj , Kj and Hj , this equation can be estimated with ordinary least squares with the restriction that the coefficients on log Kj and log Hj sum to one, 141