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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 1 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

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