## Exercise: Replicating the Estimate of the Capital Share in Mankiw, Romer, and Weil (1992)

An assignment for my intermediate macro class this semester that I was never able to put together/find time to actually assign during the semester.

If you want to use this, please link back to this webpage, and drop me a note at brad.delong@gmail.com:

Exercise: Replicating the Estimate of the Capital Share in Mankiw, Romer, and Weil (1992) by J. Bradford DeLong is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.

Based on a work at www.jstor.org.

Here is Table VI from a paper on the reading list: the cross-country growth regression paper of N. Gregory Mankiw, David Romer, and David N. Weil (1992), "A Contribution to the Empirics of Economic Growth," *Quarterly Journal of Economics* 107:2 (May), pp. 407-437 http://www.jstor.org/stable/info/2118477?seq=1:

We are going to take a look at the estimate of α, the capital share in the production function, for the "intermediate sample" over 1960-85.

Mankiw, Romer, and Weil assume that the economies' production function is:

And derive an approximate equation for the convergence of economies to their respective balanced growth paths from initial values given as of time 0:

with Y being the level and y being the log of output, L being the level and l being the log of the labor force, E being the level of the efficiency of labor, K being the physical capital stock, H being the human capital stock, α and β being fixed parameters of the production function, n being the labor force growth rate, g being the efficiency-of-labor growth rate, δ being the joint depreciation rate of physical and human capital, s_{k} being the physical capital savings-investment share of output, s_{h}

Suppose one assumes that δ+g = 0.05, and then runs a cross-country regression on the global productivity distribution as of time t in order to estimate the c parameters:

(1) What is the relationship between the various c parameters estimated by the regression and the parameters of the model? Specifically, solve for α, β, and λ as functions of the c's.

(2) Suppose that you don't have knowledge of the true human capital savings-investment share of output, but you are willing to assume that this share is proportional to the percentage of the working-age population currently attending secondary school. How does this change your interpretation of the coefficients?

(3) Download the data given in http://www.j-bradford-delong.net/2008_xls/MRW_REPLICATE.xls and attempt to replicate the intermediate-sample regression reported by Mankiw, Romer, and Weil in their Table VI. Compare the results of your replication to the regression results in their table. Compare the data you have downloaded to the data in the appendix to their paper at <>. Account for the differences between your estimates and theirs.

(4) Derive estimates of the parameters of the model--especially α, β, and λ. Derive approximate 95% confidence intervals for those parameters.

(5) According to the model, there should be a relationship between the average λ in the sample and the other parameters of the model:

Is it sensible to attempt to use this relationship as a testable restriction to evaluate the model? Why or why not?

(6) The production function assumed by MRW has the somewhat odd implication that vastly more of the factor of production human capital is produced when a working-age person from a rich country attends secondary school than when a working-age person from a poor country does. Suppose we take an alternative, Mincerian specification of the role of education and assume the production function:

that is, education amplifies the efficiency of labor beyond its current baseline value E_{t} by a factor equal to the share of the working-age population h attending secondary school raised to the power of the parameter b. What regression does this model suggest that you run? How do the results of running this regression differ from your replication of MRW? How does your interpretation differ from your interpretation of the results of MRW?

(7) MRW "assume that the rates of saving and population growth are independent of country-specific factors shifting the production function." How might this assumption go wrong? How the possibility that this assumption has gone wrong alter your interpretation of your (and their) results?

*N.B.:* http://www.j-bradford-delong.net/2008_xls/MRW_REPLICATE_ANS.xls