One of the central predictions of neo-classical macroeconomic growth theory is that an increase in the growth rate of the population causes at first a decline the growth rate of real output per capita,

but that subsequently the growth rate returns to its natural level, itself determined by the rate of technological innovation. The intuition is that, if the growth rate of the workforce increases, then more has to be saved to provide the new workers with physical capital. However, accumulating capital takes time, so that output per capita falls in the short run.

Under the assumption that population growth is exogenous, a number of regressions of the growth rate of output per capita on current and lagged population growth were performed, as reported below. (A constant was included in the regressions but is not reported. HAC standard errors are in brackets. BIC is listed at the bottom of the table).

Regression of Growth Rate of Real Per-Capita GDP on Lags of Population Growth,
United States, 1825-2000

(1) (2) (3) (4) (5)
Lag
number Dynamic multipliers Dynamic multipliers Dynamic multipliers Dynamic multipliers Dynamic multipliers
0 -0.9
(1.3) -1.1
(1.3) -1.3
(1.7) -0.2
(1.7) -2.0
(1.5)
1 3.5
(1.6) 3.2
(1.6) 1.8
(1.6) 0.8
(1.5) -
2 -1.3
(1.7) -3.0
(1.6) -2.2
(1.4) - -
3 0.2
(1.7) 1.5
(1.2) - - -
4 -2.0
(1.5) - - - -
BIC -234.4 -236.1 -238.5 -240.0 -241.8

(a) Which of these models is favored by the information criterion?
(b) How consistent are these estimates with the theory? Is this a fair test of the theory? Why or why not?
(c) Can you think of any improved data to test the theory?
What will be an ideal response?

Answer:
(a) BIC has a minimum for no lag and this criterium therefore favors a static specification.
(b) The estimates tell us that there is no dynamic multipliers other than the contemporaneous or impact effect. Even the impact effect is not statistically significant. It is unlikely that population growth is exogenous and therefore this does not represent a fair test of the theory. In addition, there is omitted variable bias with other relevant variables, such as the savings rate, education, etc. missing as regressors.
(c) Per capita output or income is likely to be a determinant of fertility. As a result, population growth is not likely to be exogenous. Perhaps the working age population would be a better choice here, but data for early periods are almost impossible to obtain.