2
I
Each application involves (1) the FORMULATION OF A MODEL
(functional form,
variable classification as well as the theoretical foundation), (2) ESTIMATION
of unknown
parameters, (3) TESTING
hypotheses, and (4) PREDICTION
.
A. Models and Basic Concepts
1.
The formulation of the model
is generally based upon economic considerations.
Example 1
. Consumer Demand Theory
Maximize U(X
1
, X
2
)
Subject to P
1
X
1
+ P
2
X
2
= Y
where Y denotes income and the P
i
and X
i
, respectively, denote the price and quantity of the
i
th
good.
The solution of this problem yields demand equations for X
1
and X
2
X
i
= D
i
(P
1
, P
2
, Y)
i = 1, 2
where the functional form is unknown unless the utility function U( ) is specified. If
advertising (A) effects preferences (U(X
1
, X
2
, A)), then demand will also depend upon
advertising expenditure, X
i
= D
i
(P
1
, P
2
, Y, A). Statistical data for X
i
, P
i
, A and Y and
econometric procedures are then used to estimate the demand equations and any unknown
parameters.
Example 2
. A Simple Macro Model
C
t
= β
1
+ β
2
(Y
t
- T
t
)
Y
t
= C
t
+ I
t
+ G
t
+ X
t
where C
t
, Y
t
, I
t
, G
t
, T
t
, and X
t
respectively denote consumption, total production, investment,
government expenditure, taxes, and net exports in period
t
.
β
1
and β
2
are unknown
parameters or unknown constants which we may want to estimate.