# The the Solow model: INSERT DAs shown,

The standard Solow model is a neoclassical exogenous growth model arguing that the steady-state level of income per capita (pc) is determined by the savings rate and population growth rate, both taken to be exogenous variables. Mankiw, Romer, and Weil (1992) augment the model by including human capital. The overarching result of this addition is that the steady-state level of income pc is lower and convergence is slowed, better reflecting the real trends seen in empirical data.

I will then be looking at the data to evaluate the true effectiveness of the augmented model in explaining observed rates of economic growth.   Paragraph one: The Solow growth model uses the rates of saving, population growth and technological progress as exogenous drivers of the steady-state level of income pc. According to the model, this is positively dependent on the rate of saving and negatively dependent on the rate of population growth.

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The two inputs are capital and labour; for all K>0 and L>0, F(.) exhibits positive and diminishing marginal products with respect to each input:Insert e Assuming a Cobb-Douglas production function, there are three properties that we require for the Solow model: INSERT DAs shown, (a) and (b) show a positive first derivative and negative second derivative. The third condition is the Inada condition::  Insert fIn the assumed production function, production at time t is given by (1). (2) and (3) show the exogenous growth of L and A occurring at rates n and g respectively, thus the effective units of labour, A(t)L(t) grows at rate n+g. There is also a constant proportion of output that is invested, s, used in (4) to show the equation of motion of k. A steady-state capital-labour ratio occurs when this equation equals 0, and thus k converges to the steady-state value k* as defined by (5). Here we can see the positive dependence of the steady-state capital-labour ratio on the rate of saving and the negative dependence on the rate of population growth.

The model’s predictions are based upon the impact of these on real income, hence we substitute (5) into the production function and take take logs to find the steady-state income pc as defined by (6). The model assumes g and ? to be constant across countries as g represents the advancement of knowledge, which is not country specific, and ? has little reason to vary across countries. It also assumesInsert triangleHence, at time 0, log income pc is given by (7):/Assuming that s and n are independent of ?. This allows (7) to be estimated using ordinary least squares (OLS). The results of this are shown in table 1. Solow estimates equation (7) for three different sample groups, totalling 195 countries with and without the constraint that the coefficients of ln(s) and ln(n+g+ ?) are equal in magnitude and opposite in sign.

The results, as shown in table 1, are supportive of the Solow model as, firstly, the restrictions on the coefficients are not rejected. The coefficients on s and n have the predicted sign and are highly significant for two-thirds of the samples. However, most importantly, we see that a large fraction of cross-country variation in come pc can be accounted for by difference in the saving rate and population growth rate; R² = 0.59 for the non-oil and intermediate samples, a significant result. However, the capital share in income, ?, which is predicted to be roughly ? is thus much lower than the value implied by the coefficients; the estimated impacts of s and n are in fact much larger than the model predicts.

This subjects that the model is not fully successful in predicting the steady-state of economic growth.

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