# The Reduced Form Equations

The reduced form equations express each endogenous variable as a linear function of every exogenous variable in the entire system. So, for our example

Qi =пц + П21 psi + П31 dii + П41 pfi + Vii (11.3)

Pi =П12 + П22 pSi + П32 dii + П42Р/ + Vi2 (11.4)

Since each of the independent variables is exogenous with respect to q and p, the reduced form equations (11.3) and (11.4) can be estimated using least squares. In gretl the script is

1 open "@gretldirdatapoetruffles. gdt"

2 list z = const ps di pf

3 ols q z

4 ols p z

The gretl results appear in Table 11.1 Each of the variables are individually different from zero q = 7.89510 + 0.656402 ps + 2.16716 di – 0.506982 pf

(2.434) (4.605) (3.094) (-4.181)

T = 30 R2 = 0.6625 F(3, 26) = 19.973 <r = 2.6801

(t-statistics in parentheses)

p = -32.5124 + 1.70815 ps + 7.60249di + 1.35391 pf

(-4.072) (4.868) (4.409) (4.536)

T = 30 R2 = 0.8758 F(3, 26) = 69.189 <r = 6.5975

(t-statistics in parentheses)

Table 11.1: The least squares estimates of the reduced form equations. at 5%. The overall F-statistics are 19.97 and 69.19, both significant at 5% as well.

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