Adaptive expectations and partial adjustment

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Adaptive expectations and partial adjustment

• Presented by
• Monika Tarsalewska
• Piotrek Jezak
• Justyna Koper
• Magdalena Predota

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Adaptive expectations
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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.

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Adaptive expectations

• Regression
• The error of past observation
• and a mechanism for the formation of the
  expectation

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Adaptive expectations

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

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Adaptive expectations Koyck transformation
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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

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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
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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 gt 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
  Pgtt 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
• --------------------------------------------------
  ----------------------------

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Partial adjustment
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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

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Partial adjustment

• If we solve the second equation for yt and 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.

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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

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Partial adjustment

• This leads to an estimating form

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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 gt 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
Pgtt 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
Partial adjustment