One of the central predictions of neo-classical macroeconomic ...

[nummyann]

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?

Question 2

In your intermediate macroeconomics course, government expenditures and the money supply were treated as exogenous, in the sense that the variables could be changed to conduct economic policy to influence target variables,
 
  but that these variables would not react to changes in the economy as a result of some fixed rule. The St. Louis Model, proposed by two researchers at the Federal Reserve in St. Louis, used this idea to test whether monetary policy or fiscal policy was more effective in influencing output behavior. Although there were various versions of this model, the basic specification was of the following type:
 
  ln(Yt) = 0 + 1ln mt + ... + pln mt-p-1 + p+1ln Gt + ... + p+qln Gt-q-1 + ut
 
  Assuming that money supply and government expenditures are exogenous, how would you estimate dynamic causal effects? Why do you think this type of model is no longer used by most to calculate fiscal and monetary multipliers?
 
  What will be an ideal response?

[ecox1012]

Answer to Question 1

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.

Answer to Question 2

Answer: If the money supply and government expenditures were exogenous, then a distributed lag model could be used to estimate the dynamic multipliers and cumulative dynamic multipliers using OLS. The coefficients in the above equation are then the dynamic multipliers. To obtain the h-period cumulative dynamic multipliers, all coefficients over the h-periods have to be added up. There is an alternative form for the above equation which allows for statistical testing of the cumulative dynamic multipliers. This involves differencing the regressors with the exception of the last lag, p and q, in the above equation. The coefficient on the p and q lagged regressor then represents the long-run cumulative multiplier. The OLS estimator of the coefficients in the above equation is consistent. However, the errors are likely to be autocorrelated since omitted variables from the above equation are probably serially correlated themselves. In that case the OLS standard errors are inconsistent and statistical inference based on these standard errors will be misleading. To avoid this problem, heteroskedasticity- and autocorrelation-consistent standard errors can be calculated. The reason why this type of model is no longer used by most to calculate fiscal and monetary multipliers is that researchers are not willing to assume that the money supply and government expenditures are exogenous. Both monetary and fiscal policy takes into account current and future expected output growth in setting their policy instruments, which are therefore endogenous.