Introduction to Modern Economic Growth The augmented Solow model with human capital is a generalization of the model presented in Mankiw, Romer and Weil (1992) As noted in the text, treating human capital as a separate factor of production may not be appropriate Different ways of introducing human capital in the basic growth model are discussed in Chapter 10 below Mankiw, Romer and Weil (1992) also provide the first regression estimates of the Solow and the augmented Solow models A detailed critique of the Mankiw, Romer and Weil is provided in Klenow and Rodriguez (1997) Hall and Jones (1999) and Klenow and Rodriguez (1997) provide the first calibrated estimates of productivity (technology) differences across countries Caselli (2005) gives an excellent overview of this literature, with a detailed discussion of how one might correct for differences in the quality of physical and human capital across countries He reaches the conclusion that such corrections will not change the basic conclusions of Klenow and Rodriguez and Hall and Jones, that cross-country technology differences are important The last subsection draws on Trefler (1993) Trefler does not emphasize the productivity estimates implied by this approach, focusing more on this method as a way of testing the Heckscher-Ohlin model Nevertheless, these productivity estimates are an important input for growth economists Trefler’s approach has been criticized for various reasons, which are secondary for our focus here The interested reader might also want to look at Gabaix (2000) and Davis and Weinstein (2001) 3.9 Exercises Exercise 3.1 Suppose that output is given by the neoclassical production function Y (t) = F [K (t) , L (t) , A (t)] satisfying Assumptions and 2, and that we observe output, capital and labor at two dates t and t + T Suppose that we estimate TFP growth between these two dates using the equation xˆ (t, t + T ) = g (t, t + T ) − αK (t) gK (t, t + T ) − αL (t) gL (t, t + T ) , where g (t, t + T ) denotes output growth between dates t and t+T , etc., while αK (t) and αL (t) denote the factor shares at the beginning date Let x (t, t + T ) be the true TFP growth between these two dates Show that there exists functions F such that xˆ (t, t + T ) /x (t, t + T ) can be arbitrarily large or small Next show the same 151