Simultaneous Equations Models
Source: Gujarati text
Simultaneous Equations Models
However, in some cases there may be a twoway flow of causality In such cases OLS is inappropriate as it assumes independent variables are either nonstochastic or if stochas

Topic 3: Deterministic Specificationfunctional form
The aim is to choose the appropriate set of
explanatory variables and the appropriate
functional form
The choice will be determined both from
economic theory and empirical application
There are econom

Functional form: Example 1
Example 1: Output, labour and capital (Maddala p 97). X-GNP index for USA 1929-67 L-labour input index K-capital input index Task is to estimate a regression of X on L and K Data indicate output has risen faster than inputs
700

Multiple Regression
(1)
Yt = + X t + Z t + Vt + t
More realistically, regression models contain more
than one independent variable eg demand equations
will typically have own price, cross price and an
income variable.
Multiple Regression
Note on R2 for

Multiple Regression cont.
Effect of correlations among regressors on OLS estimates (1)
Multiple Regression
It is only when X and Z are uncorrelated with each other that the parameter estimates will remain unchanged when either X or Z is excluded ie that

Multiple Regression: omitted variable bias
Specification problems :Omission of a relevant variable. When we omit a relevant variable, the effect can either turn up in the residuals or be picked up by the remaining variables. If the former happens, the res

Dummy Variables
Dummy variables can be used to test for structural
change, model seasonal effects
They work as on off switches
There are two types of dummy variable:
1. intercept or shift dummy
2. slope or interactive dummy
Dummy Variables
A model to tes

Violations of assumptions about error terms
Recall OLS assumes: E( t) = 0 Var E( t2) = Xt and
t t 2
Violations (cont)
HETEROSKEDASTICITY:
aka homoskedasticity
A violation of the assumption: Var E( t2) =
2
are independent are independent for all
t
aka hom

Violations of assumptions about error terms
Recall OLS assumes: E( t) = 0 Var E( t2) = Xt and
t t 2
Heteroskedasticity
Illustrative example: R&D expenditure and sales (source: text p395)
aka homoskedasticity
are independent are independent for all
t
RDi

Violations of assumptions about
error terms
Recall OLS assumes:
E( t) = 0
Var E( t2) =
Xt and
t
t-1
t
and
2
aka homoskedasticity
are independent
are independent for all
t
ie not
autocorrelated
Normality
Autocorrelation
This is a violation of the assu

Autocorrelation
Autocorrelation
(source: Studentmund)
Once autocorrelation is detected,
hypothesis test are invalid, so
something must be done to remove the
problem. The course of action depends
on the cause, and as noted in the last
lecture it can be due

Non-stationarity in time series
Recall the autoregressive model:
Yt = + X t + Yt -1 + t LR =
Non-stationarity
For the dynamic modelling procedure we Have already considered to be appropriate, the data must be stationary (have a constant mean and variance

Cointegration
Recall from last lecture, that nonstationarity in time series has consequences for forecasting, and spurious results. When variables are found to be non-stationary, (DF test) then it is necessary to consider the implications for model specif

wheat prices
200
Case study: relationship between
wheat prices in USA and
Australia
Consider two time series indices for
wheat prices in the US and in Australia.
Data are quarterly, 1965Q1 to 2005Q4
160
120
80
40
0
1965 1970 1975 1980 1985 1990 1995 2000

Basic regression (cont.)
90
Example:
Consider the relationship between the trade
weighted index (TWI) and Australias terms
of trade (TOT).
Quarterly data has been collected for the
period 1982-1999
80
70
60
50
40
5 10 15 20 25 30 35 40 45 50 55 60 65
T