Original Solow growth modelIn 1956 Robert Solowproposed an economic model that attemptsto explain long-run economic growth by looking at physical capital accumulation, exogenous populationgrowth and exogenous technological progress. It predicts that countriesreach different steady states. The higher the saving rate and the lower thepopulation growth rate, the richer a country is.
The underlying assumptionsof this model are: decreasing returns to K, positive diminishing marginalproducts, constant returns to scale and the Inada condition. The model is based on a ?obb-Douglas production function (Y) withtwo inputs, physical capital (K) and labour (L), while also considering thelevel of technology (A): Yt=Kta(AtLt)1-a Where a is capital’sshare of income, 0 If there was no g, growth in this model wouldeventually stop. However, the formulationof the model allows for increases in efficiency to offset the diminishingreturns to K. Therefore, economic growth is unaffected by changes in s or n inthe long-run. Changes in these parameters vary the level of the long-run pathonly and not its slope. Thus, in the long-run the economy converges to a steadywith a growth rate of g. We can test whether themodel is accurate or not by showing that the model predicts correct signs and magnitudeseffects of the s and n on Y/L. This can be done by imposinga based on our actual dataand then asking how much of thecross-country variation in income the model can account for (R2). Weestimate the model by OLS, we also estimate our a that is compared to the actual a. If the values of a differ significantly, we can reject the hypothesisthat Solow growth model is correct.To perform the test, countries that had accurate primarydata available and whose population was above one million since 1960 wereselected. These countries were separated into three groups based on furthercriteria: non-oil, intermediate and OECD countries. We measure n as the averagerate of growth of the working-age population, s as the average share of realinvestment (including government investment) in real GDP and Y/L as real GDP in1985 divided by the working-age population in that year. We chose the values ofa » 1/3 and g + d » 0.05 to match the actual data.According tothe test we can see that the coefficients on s and n do have the predictedsigns and, for two of the three samples, are highly significant. The assumptionthat the coefficients on ln(s) and ln(n + g + d) are equal in magnitude and oppositein sign cannot be rejected. However, themodel is not fully successful. R2 for non-oil and intermediatecountries is 59%, which represents an accurate fit of the model but for OECDcountries it takes a value of 6%. Also, the estimated impacts of s and n aremuch larger than the model predicts. We established that a must » 1/3. The OLS estimates imply that intwo out of three cases a is statistically significant. For non-oil countries a = 0.6 ± 0. 02 > 0.33; forintermediate countries a = 0.59 ± 0. 02 > 0.33; for OECD countries a = 0.36 ± 0.15 » 0.33. Therefore, original Solowgrowth model is mostly incorrect. ais… Human capital augmented Solow growth modelThe Solow model wasaugmented by introducing the effect of human capital accumulation, H. Theaugmented model lowers the estimated effects of s and n rates to Y/L. Moreover,it accounts for approximately 80% of the cross-country variation in income. Theaugmented model provides an almost complete explanation on why some countriesare rich and others are poor.The augmented Solow growthmodel follows the same assumptions as the original model. The new productionfunction is: Yt=KtaHtb(AtLt)1-a-b To explain why this modelworks, we must firstly consider three further assumptions. People devote afraction of their income to human capital (sH) the same as they doto physical capital (sK), so a » b » 1/3. sH depreciates at thesame rate as sK, d, sotheaccumulation of H mirrors that of K. Y produced in the economycan be used for either consumption or both types of investment. Following this we are going to prove that the level of growthshould be positively correlated with the initial level of H the same as it isfor K.Now we rewrite ourproduction function in the effective labour units (AL) and obtain: yt=ktahtb, where y=Y/AL, k=K/AL, h=H/ALFrom this we can determinethe behavior of k and h:kt· = sKyt- (n+g+d)kt =sKktahtb-(n+g+d)kt ht· = sHyt- (n+g+d)ht =sHktahtb-(n+g+d)ht Then by setting the valuesof kt·=ht·=o, we get the steady statevalues for k and h:According to thebehavioral equations above, the level of steady-state Y/L is positively relatedto sK and sH.. Therefore, an increase in sHshifts the steady-state level of income upwards, leading to a higher long-rungrowth path. The transitional dynamics of this model aresimilar to those of the original Solow model. An upward shift of the steadystate due to an increase in either rate of investment leads to a temporarilyhigher economic growth rate while the economy converges to its new steadystate. The graphs below describes the evolution of the growth rate when eithersH or sK are changed. In the augmented model, the elasticity ofincome with respect to the rate of investment is higher than in the originalSolow model. This is because a higher s raises the steady-state level ofincome. Therefore, H increases as well even if sH remains unchanged.Consequently, the level effect due to a change in the investment rate is morepronounced in the augmented Solow model than in the original version without H.According to thebehavioral equations, sH has no effect on the long run economicgrowth rate, but the rate of technological progress does (g). The augmented model treats H in exactly same way as K.It is accumulated by investing a fraction of income in its production, it depreciatesat the same rate as K and it is produced with the same technology as both K andconsumption. Therefore, like in the original Solow model, long-run growth isexogenous and its rate is the same as g.Testinghypotheses is done similarly as before. We must show that estimated a »estimated b »1/3. All the same parameters are chosen as previously and sH (orSCHOOL) is chosen as the percentage of the working-age population that is insecondary school. We can see that R2 has increased significantlyto » 80% for non-oil and intermediate countries,and to 28% for OECD countries. This represents a better fit of the model. Furthermore,the estimated values of a are lower for all the samplescompared to the original model and a » b » 1/3 in general. Fornon-oil countries a = 0.31 ± 0.04 » 0. 33 and b = 0.28 ± 0.03is not statistically different from 0.33; for intermediate countries a = 0.29 ± 0.05 » 0.33 and b = 0.30 ± 0. 04 » 0.33; for OECDcountries a = 0.14 ±0.15 is proven to be notstatistically different from 0.33 and b = 0. 37 ± 0.12 » 0.33.The conclusion is that the augmented Solow growthmodel is an extension of the original model. We assume that our extra input inthe production function – H – is accumulated in the same way as K. When weincrease the stock of H, it does not have any effect on the long-run growthrate (g). Instead, it has a level effect, which means that the transitionalgrowth occurs. Y/L grows faster than g in the short run, but in the long run itconverges back to g. The model also predicts that, other things being equal, acountry should have a higher level of Y/L if it has a high amount of H. Theseresults are the same as in the original Solow growth model. The only differenceis that the results estimated by the augmented model are closer to reality: themagnitude effects of the s and n coefficients on the Y/L are lower than inthe original model. References:· Lecture Notes· Mankiw N.G., Romer D. and Weil D.N., May1992, “A contribution to the Empirics of Economic Growth”· Schütt F., August 2003, IWIM – Institute forWorld Economics and International Management; “The importance of human capitalto economic growth “· DalgaardC.J. “Growth and Human Capital Accumulation – The Augmented Solow model”· Ding S. and Knight J., Janyary 2008,”Can the Augmented Solow model explain China’s economic growth? A Cross-CountryPanel Data Analysis”
