Adaptive expectations and partial adjustment

1. Adaptive expectations and partial adjustment Presented by: Monika Tarsalewska Piotrek Jeżak Justyna Koper Magdalena Prędota

2. Adaptive expectations

3. Expectations Either the dependent variable or one of the independent variables is based on expectations. Expectations about economic events are usually formed by aggregating new information and past experience. Thus, we might write the expectation of a future value of variable x, formed this period, as Example: Forecast of prices and income enter demand equation and consumption equations.

4. Adaptive expectations Regression: The error of past observation: and a mechanism for the formation of the expectation:

5. Adaptive expectations The expectation variable can be written as Inserting equation (3) into (1) produces the geometric distributed lag model.

6. Adaptive expectationsKoyck transformation

7. Adaptive expectations There is a problem of simultaneity as yt-1 is correlated in time with There is nonlinear restriction in our model which should de included in the regression

8. Adaptive expectations Measurement of permanent income might be approached through the use of the adaptive expectations hypothesis, where permanent income (inct) alters between periods in proportion to the difference between actual income (inct) in a period, and permanent income in previous period. And after Koyck transformation

9. Adaptive expectations ivreg conspr (l.conspr = l2.conspr l3.conspr l4.conspr) housedisp Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 10 -------------+------------------------------ F( 2, 7) = 4419.15 Model | 14.1834892 2 7.09174462 Prob > F = 0.0000 Residual | .011197658 7 .001599665 R-squared = 0.9992 -------------+------------------------------ Adj R-squared = 0.9990 Total | 14.1946869 9 1.57718743 Root MSE = .04 ------------------------------------------------------------------------------ conspr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- conspr | L1 | .5213197 .0819684 6.36 0.000 .3274953 .7151441 housedisp | .4497056 .0927137 4.85 0.002 .2304726 .6689387 _cons | .2452798 .1028115 2.39 0.048 .0021692 .4883904 ------------------------------------------------------------------------------

10. Partial adjustment

11. Partial adjustment The partial adjustment model describes the desired/optimal level of yt which is unobservable adjustment equation looks as following where denotes the fraction by which adjustment occurs

12. Partial adjustment If we solve the second equation for ytand insert the first expression for y*, then we obtain: This formulation offers a number of significant practical advantages. It is intrinsically linear in the parameters (unrestricted), error term nonautocorrelated therefore the parameters of this model can be estimated consistently and efficiently by ordinary least squares.

13. Partial adjustment Consumer is viewed as a having desired level of consumption, which is related to the current income. When current income changes, inertial factors prevent An immediate movement to the new desired level of consumption. Instead, a partial movement is made, so that: with:

14. Partial adjustment This leads to an estimating form:

15. Partial adjustment reg conspr l.conspr housedisp Source | SS df MS Number of obs = 13-------------+------------------------------ F( 2, 10) = 1.19 Model | 12.1068721 2 6.05343604 Prob > F = 0.3447 Residual | 51.0017001 10 5.10017001 R-squared = 0.1918-------------+------------------------------ Adj R-squared = 0.0302 Total | 63.1085722 12 5.25904768 Root MSE = 2.2584------------------------------------------------------------------------------conspr | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------conspr | L1 | .3468319 .2890923 1.20 0.258 -.2973059 .9909698housedisp | .3928808 .3495421 1.12 0.287 -.3859475 1.171709_cons | 1.385804 2.130896 0.65 0.530 -3.362129 6.133738