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

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adaptive expectations and partial adjustment

Adaptive expectations and partial adjustment

Presented by:

Monika Tarsalewska

Piotrek Jeżak

Justyna Koper

Magdalena Prędota

expectations
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.

adaptive expectations1
Adaptive expectations

Regression:

The error of past observation:

and a mechanism for the formation of the expectation:

adaptive expectations2
Adaptive expectations

The expectation variable can be written as

Inserting equation (3) into (1) produces the geometric distributed lag model.

adaptive expectations3
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

adaptive expectations4
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

adaptive expectations5
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

------------------------------------------------------------------------------

slide11

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

slide12

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.

slide13

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:

slide14

Partial adjustment

This leads to an estimating form:

slide15

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

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