Example 195


To study the behavior of U.S. state and local government expenditure, the authors developed the following simultaneous equation model:

where EXP = state and local government public expenditures AID = level of federal grants-in-aid INC = income of states POP = state population PS = population of primary and secondary school children u and v = error terms

In this model, INC, POP, and PS are regarded exogenous.

Because of the possibility of simultaneity between EXP and AID, the authors first regress AID on INC, POP, and PS (i.e., the reduced-form regression). Let the error term in this regression be Wj. From this regression the calculated residual is w. The authors then regress


11If more than one endogenous regressor is involved, we will have to use the F test.

12Pindyck and Rubinfeld, op. cit., p. 304. Note: The regressor is Pt and not Pt.

13Pindyck and Rubinfeld, op. cit., pp. 176-177. Notations slightly altered.


EXP on AID, INC, POP, and w, to obtain the following results:

EXP =-89.41 + 4.50AID + 0.00013INC - 0.518POP - 1.39W

t = (-1.04) (5.89) (3.06) (-4.63) (-1.73) (19.4.10)14

At the 5 percent level of significance, the coefficient of wt is not statistically significant, and therefore, at this level, there is no simultaneity problem. However, at the 10 percent level of significance, it is statistically significant, raising the possibility that the simultaneity problem is present.

Incidentally, the OLS estimation of (19.4.8) is as follows:

Notice an interesting feature of the results given in (19.4.10) and (19.4.11): When simultaneity is explicitly taken into account, the AID variable is less significant although numerically it is greater in magnitude.

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