1. Human Capital The exogenous growth model of Solow presents a number of unresolved questions: –The growth rate of the economy in the steady state is not explained by the model –The preferences of the population (the propensity to save) do not affect the growth rate of growth, and therefore, this rate is insensitive to the economic policy –The hypothesis of convergence between countries predicted by the model finds little empirical support

2. Human Capital The introduction of human capital in the neoclassical growth model, initially proposed by Uzawa (1965) and later taken over by Lucas (1988), is a possible way out of these difficulties. We will see later the endogenous growth model

3. Human Capital change in Cobb-Douglas qL: improving human capital, where q changes in production efficiency and quality production function of the final good, in Cobb- Douglas form, is amended as:: Y= T* K α (qL) β Where T *: remaining technical progress, qL: human capital By investing in 'education' workers increase their productivity.

4. Human Capital change in Cobb-Douglas But not enough to express the production function as a function of human capital improvements, but we need to take account of changes in the age composition of the labor : Δ(qL)/(qL) = ΔL/L + δ L - δ L ΔE namely, the improvement of the work is given by: Growth of physical units Average rate of growth of quality The effect of changes on the average

5. The growth of production is explained in more detail: r Y = r T *+ αr K + αδ k - αδ k ΔA + βr L + βδ L + βΔE Two influencing factors: -Work Experience -Specialty Schools that influence the average quality L and its distribution by age Human Capital change in Cobb-Douglas

6. Human Capital Agents can accumulate human capital by transferring part of their working time from production to investment in 'education'. Lucas assumes that the increase in human capital is proportional to both the initial stock of human capital, both at the time of labor employed: ΔH=δH(1-u) Where u is the fraction of time spent working in the production of the final good Y, and δ is a constant

7. Human Capital With these assumptions the steady state growth rate of per capita income is: gy = δ (1-u) exactly equal to the growth rate of the stock of human capital. In this way, you get growth 'endogenous' in a double sense: -the growth rate is explained by investments in human capital -The growth rate depends on the choice of allocating labor time to produce work or invest in human capital and is therefore dependent on the preferences of the agents

8. Human Capital Policy implications: encouraging or less human capital investment, the decision maker of economic policy can affect the growth rate of per capita of the economy.

9. Human Capital The issue of convergence: 'checking' for human capital, that is, by inserting the rate of investment in human capital between the dependent variables of the equation for estimating the growth rate of per capita, the convergence hypothesis is partially confirmed (Mankiew, Romer and Weil, 1992). This result is known as 'conditional convergence': once you take into account the different level of human capital in the various countries it is true that having a low stock of physical capital has a positive effect on growth.

10. However: There remains the question of causality between human capital and growth. And 'the growth rate of the economy to be influenced by human capital or vice versa? The estimates cross-section used in the literature on convergence are able to identify correlations rather than causal relations Human Capital