Transcript The large scale econometric models

The large scale
econometric models
The first large-scale econometric model was built by
Professor Lawrence Klein in the 1950s.
The equations which formed the model represented a
“synthetic” or artificial economy.The model
went through various iterations and evolved into
the MIT-FR-Wharton model
Uses of the model
•Using this model, it was possible to simulate the effects of
proposed fiscal policy measures such as increased military
spending and tax cuts on a wide array of aggregate (Y, I, C, S, ...)
and disaggregate level variables (truck sales, employment in
construction trades, cement prices).
• For example, The people who ran the model were asked to
simulate the impact of the proposed Kennedy-Johnson tax cuts in
the early 60s (took effect in 1964) on a broad array of economic
variables.
A simple macro model
Consider the following economy:
Yt = Ct + It + Gt + Xt – Mt
[5.5]
Equation [5.5] can be read as follows: Total output in
period t is equal to total spending for new goods and
services in period t , or consumption plus investment
plus government expenditure plus imports minus
exports.
Equation [5.5] is an
identity—that is, it is
true by definition
The behavioral equations
Ct = a + b(Yt – Tt) + dPt – 1
[5.6]
Tt = e + fYt
[5.7]
It = h + jYt – 1 + kRt
[5.8]
Mt = n + qYt
[5.9]
Pt = s + uYt + vPt – 1
We call these behavioral equations
because they describe the way the
way the spending category has
behaved in the past as a function of
the explanatory variables.
[5.10]
Finding the reduced
form
First, we substitute the behavioral equations [5.6] through
[5.10] into [5.5] to obtain the following (we have dropped
the t subscripts to economize on notation):
Y = [a + b(Y – e – fY) + dPt – 1] + (h + jYt-1 + kR) + G + X – (n + qY)
By rearranging this equation, we obtain the following
reduced form equation
a  be  dP  1  hJ  1  kR  n  G  X
Y
1  b(1  f )  q
[5.11]
Exogenous and
endogenous variables
•Exogenous variables are determined outside the model.
They may be know by forecasters—or forecasters may have
to forecast them
In our model: X, G, and R
•Endogenous variables are determined within the model—
specifically, by equation [5.11]
In our model: Y, C, I, T, M, and P
Forecasting using the
reduced form
1. The forecaster can estimate the values of a, b, d, e,
f, h, j, k, n, q, s, u, and v with time series regression
analysis.
2. Pt – 1 and Yt – 1 are known
3. That leaves the exogenous variables Gt, Xt, and Rt.
Perhaps Gt is known. The forecaster will have to
estimate (forecast) the values of the other
exogenous variables
The Suits modela
Y=C+I+G
(1)
C = 20 + 0.7(Y - T)
(2)
I = 2 + .01Yt - 1
(3)
T = 0.2Y
(4)
The article is noteworthy
because is educated
economists on the new
applications of econometrics
made possible by advances
in computer technology
•The unkown variables are Y, C, I, and T
•The known variables are G and Yt - 1.
aDaniel
Suits.” Forecasting and Analysis with an
Econometric Model,” American Economic Review, March
1962: 104-132.
A simple national econometric model
a
Consider a closed economy with government
GDP = C + I + G
GDP is the dependent variable.
Hence, to get solution for GDP, we must
first specify and estimate models for C, I,
and G
The following is based on A. Migliario. “The National Econometric Model: A
Layman’s Guide,” Graceway Publishing, 1987.
a
The aggregate level specifications
GDP t + 1 = C t + 1 + I t + 1 + G t + 1
(2)
C t + 1 = 1 + 2DYt + et
(3)
I t + 1 =  3 +  4 i t + et
(4)
G t + 1 =  5 +  6 Gt
(5)
b
•Migliaro used OLS to estimated 1, 2, 3, 4, 5, and 6
•Having accomplished that, he substituted estimated equations
(3), (4), and (5) back into (2) to get a forecasted value of G t + 1.
•An example: I t + 1 = 11.567 - 0.419it
b
Migliaro used the trend component to forecast G.
Extending (disaggregating) the model
Let:
C t + 1 = DUR t + 1 + NONDUR t + 1 + SERVICES t + 1
Now let:
DUR t + 1 = AUTOS t + 1 + FURNITURE t + 1 + APPLIANCES
t+1+
Now let:
AUTOS t + 1 = Passenger Cars
t+1
+ Vans t + 1 + Trucks t + 1 + . . .
...
Trucks t + 1 = 1 + 2DYt + 3AGEt + 4PRICEt + et
•As we increase the level of disaggregation, we increase the
number of equations.That is, we could have equations for
different classes of trucks--midsize, etc.
•It is the disaggregate level forecasts which are most valuable
tobusiness decision-makers.
•Entities such as DRI-McGraw Hill and Chase econometrics sell
disaggregate-level forecasts to a high-powered client base.
f 1
f 1
f 1
f 1
dx1  ... 
dxn 
dy1  ... 
dyn  0
x1
xn
y1
yn
•The DRI-McGraw Hill Model has approximately
450 equations.
•The FRB-MIT-Wharton model has 669 equations.
•The Chase Econometrics modle has 350 equations
•The Kent model has 44,400 equations.