INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 126
the actual value is greater, The expected value is adjusted upwards for the next period.If it is lower, the expected value is adjusted downwards. The size of the adjustment is hypothesized to be proportional to the discrepancy between the actual and expected value. If
X is the variable in question, and is the
value expected in time period t given the information available at time period
t–1,
(
)( )
…[4.20] This canbe rewritten
( )
( )
…[4.21] Which states
that the expected value of X in the next period is a weighted average of the actual value of
X in the current period and the value that had been expected. The larger the value of
, the quicker the expected value adjusts to previous actual outcomes. For example, suppose that you hypothesize
that a dependent variable,
, is related to the expected value of the descriptive variable,
X, in year
t+1,
:
…[4.22]
expresses in terms of , which is unobservable and must somehow be replaced by observable variables, that is, by actual current and lagged values of
X,
and perhaps lagged values of Y. We start by substituting for
,
(
( )
)
( )
)
…[4.23] Of course, we still have unobservable variable
as an descriptive variable, but if it is true for time period
t, it is also true for time period
t–1:
( )
…[4.24]
Substituting for , in [4.23] we now have
