Question

One of the most frequently estimated equations in the macroeconomics growth literature are so-called convergence regressions. To investigate this matter, you collect data from 104 countries for the sample period 1960-1990 and estimate the following relationship:

g₆₀₉₀ = 0.020 – 0.360 × g_pop + 0.004 × Educ – 0.053×RelProd₆₀

where g₆₀₉₀ is the growth rate (in percentage) of GDP per worker for the 1960-1990 sample period, RelProd₆₀ is the initial starting level of GDP per worker relative to the United States in 1960, g_pop is the average population growth rate of the country, and Educ is educational attainment in years for 1985.

(a) What is the effect of an increase of 5 years in educational attainment? What would happen if a country could implement policies to cut population growth by one percent?

(b) It has been suggested to you to interact education with the initial condition to test for additional effects of education on growth. To test for this possibility, you estimate the following regression:

g₆₀₉₀ = 0.015 -0.323 × g_pop + 0.005 × Educ –0.051×RelProd₆₀ –0.0028 × (Educ.RelProd₆₀)

Write down the effect of an additional year of education on growth. West Germany has a value for RelProd60 of 0.57, while Brazil's value is 0.23. What is the predicted growth rate effect of adding one year of education in both countries?

Answer 1

A. The coefficients of the model (beta/slope coefficients) say that if the independent variable increases by one unit, then average dependent variable will increase by the value of coefficient, keeping other things given.

For example, if RelProd60 increases by one unit, then average g6090 will decrease by 0.053 units.

We can now answer the question asked.

i. If educational attainment increase by 5 years, then the average growth rate, g6090 will increase by 0.004*5 = 0.020 units (here, percentage). Thus, average growth rate will increase by 2 percent.

ii. According to the model, if population variable, gpop increase by one unit/one percent, then average growth rate, g6090 increase by (-0.360) or we can say that g6090 falls by 0.360 percent.

So, if gpop is cut by one percent/ falls by one percent, the the growth rate, g6090 increase by (-0.360*-1)= 0.360 percent.

B. In the second model, an interaction term, educ*RelProd60 has been added. This means that effect of the terms will now be interdependent. When there were no interaction term, coefficient o f educ was interpreted as the unique effect of educ on g6090. But the interaction means that the effect of educ on g6090 is different for different values of RelProd60.  

The unique effect of Educ (education) is represented by everything that is multiplied by Educ in the model, that is, coefficient of Educ + (coefficient of interaction term)*RelProd60

Thus, for West Germany, the effect of one additional year of education, Educ means that g6090 will increase by 0.005- 0.0028*0.57 = 0.005-0.001596 = 0.003404

For Brazil, the effect of one additional year of experience, Educ means that g6090 will increase by 0.005-0.0028*0.23= 0.005-0.000644 = 0.004356