chapter 14 Selected Topics in Single Equation Regression Models.ppt

Chapter 14
Selected Topics in Single Equation Regression Models
Restricted Least Squares(RLS)
1. OLS and RLS
(1)Unrestricted least squares(ULS):
When using the ordinary least square method(OLS) to estimate the parameters, we do not put any prior constraint(s)or restriction(s) on the parameters. So we can estimate the parameters without any restrictions. This is ULS.
(2)Restricted least squares(RLS)
In Yi=B1+B2X2i+B3X3i+ui
If we put any restrictions on the parameters, such as B2=2, or B2+ B3=1, we use RLS method to estimate.

The steps of RLS:
· transform the data to take into account the restrictions suggested by the relevant theory,
· apply the least squares method (OLS).
of the validity of the restriction(s):

Let
R2 =R2 from the unrestricted regression
R*2=R2 from the restricted regression
m =the number of linear restrictions imposed
k =the number of parameters estimated in
the unrestricted regression
n =the number of observations
H0: the restriction(s) is valid

()
· Estimate the ULS regression and obtain the R2
· Estimate the RLS regression and obtain R*2
· Find out the number of restrictions(m).
· Find out the coefficients estimated in the unrestricted regression(K)
· Compute F value
Hypothesis testing:
If F>Fc, refuse H0, the restriction(s) imposed by the theory is not valid(statistically speaking), reject the restricted least squares regression , use the standard OLS method.
If F<Fc, accept H0, the given restriction is valid, the RLS regression is preferred to ULS.
Dynamic Economic Models: Autoregressive and Distributed Lag Models
1. Definition
Dynamic models/ Distributed lag models:
--There is a non-contemporaneous, or lagged, relationship between Y and the Xs, for the effect of a unit change in the value of the explanatory variable is spread over, or distributed over, a number of time periods.
The reasons of the dependent variable respond to a unit change in the explanatory variable(s) with a