10.6 Expectational Variables and Adjustment Lags

In previous sections we discussed models in which the expectational variables were functions of lagged values of the relevant variables for which expectations were formed. There is another source of lagged relationships. This is lags in adjustment to desired levels. In practice both these lags will be present and there is an econometric problem of isolating (or identifying) the separate effects of these two sources.

A simple model incorporating adjustment lags is the partial adjustment model, which says that firms adjust their variables (say, capital stock) only partially toward their desired levels. Suppose that a firm anticipates some change in the demand for its product. In anticipation of that, it has to adjust its productive capacity or capital stock denoted by y,. But it cannot do this immediately. Let yf be the "desired" capital stock. Thenyf - y, , is the desired

(10.15) or the simple OLS estimation of the autoregressive form ( .14). Both equations (10.14) and (10.15) ignore the fact that the same endogenous variable p, occurs on both the left-hand side and the right-hand side of the equation. Equation (10.14) can also be rearranged similarly. We rewrite it as

m,-p, = fl(l - X) + X(m, , - p,„,) + b{\ - K){p, - p, ,) + v,

We have to gather the coefficients of p„ normalize the equation with respect to p„ and estimate it using p, as the dependent variable and m„ m, „ and p, , as the explanatory variables. The problem of lagged dependent variables and serially correlated errors still remains and we have to estimate the equation by instrumental variables using, say, m,„2 as an instrument.

In summary, the estimation of the hyperinflation model under adaptive expectations is not as straightforward as it appears at first sight looking at equation (10.14) or (10.15). An important aspect of the model under adaptive expectations (and also some naive expectations) that has not been noticed often is the occurrence of the endogenous variable p, on the right-hand side of the equation, which makes OLS estimation inapplicable unless some rearranging of the variables is made. The appropriate dependent variable should be p„ and the explanatory variables are m, and lagged values of m, and p,.

Since the estimation of the hyperinflation model under adaptive expectations is only of historic interest, we will not present the results here. The estimation of equations (10.14), (10.14"), (10.15), and (10.15") is left as an exercise for students. Tables 10.1 and 10.2 on the following pages present the data for Hungary and Germany, respectively. The last periods (particularly since June 1924) can be omitted in the analysis. The data have been provided here because the same data can be used for the estimation of the rational expectations model discussed in Section 10.10.

415 • 10 MODELS OF EXPECTATIONS

Table 10.1 Price Index and Money Supply for Hungary, 1921-1925"

Notes in Current Accounts

Circulation and Deposits Price Index

1921

Jan. 15.21 3.85 -

Feb. 15.57 5.53 -

Mar. 15.65 5.25 -

Apr. 13.12 6.80 -

May 13.69 5.76 -

June 18.10 1.16 -

July 15.80 3.53 4.20

Aug. 17.33 2.98 5.40

Sept. 20.84 2.41 6.25

Oct. 23.64 2.15 6.75

Nov. 24.74 2.35 8.30

Dec. 25.18 2.24 8.25 1922

Jan. 25.68 2.49 8.10

Feb. 26.76 2.35 8.50

Mar. 29.33 2.22 9.90

Apr. 30.58 2.90 10.75

May 31.93 3.29 11.00

June 33.60 3.74 12.90

July 38.36 3.93 17.40

Aug. 46.24 5.42 21.40

Sept. 58.46 5.93 26.60

Oct. 70.00 5.19 32.90

Nov. 72.02 6.41 32.60

Dec. 75.89 4.76 33.40

1923

Jan. 73.72 5.89 38.50

Feb. 75.14 6.60 41.80

Mar. 82.21 11.15 66.00

Apr. 100.10 9.79 83.50

May 119.29 10.61 94.00

June 155.00 12.74 144.50

July 226.29 21.98 286.00

Aug. 399.49 23.63 462.50

Sept. 588.81 60.25 554.00

Oct. 744.93 60.18 587.00

Nov. 853.99 74.97 635.00

Dec. 931.34 84.79 714.00 1924

Jan. 1084.70 105.48 1026.00

Feb. 1278.40 164.84 1839.10

(contd)

Table 10.1 (Cont.)