Estimation Problems—21
update. Using a named equation, or selecting Proc/Update Coefs from Equation, guarantees that you are using the correct coefficient values.
An alternative to referring to the coefficient vector is to reference the @coefs elements of your equation (see “Selected Keywords that Return Scalar Values” on page 16). For example, the examples above may be written as:
series cshat=eq1.@coefs(1)+eq1.@coefs(2)*gdp
EViews assigns an index to each coefficient in the order that it appears in the representations view. Thus, if you estimate the equation:
equation eq01.ls y=c(10)+b(5)*y(-1)+a(7)*inc
where B and A are also coefficient vectors, then:
•eq01.@coefs(1) contains C(10)
•eq01.@coefs(2) contains B(5)
•eq01.@coefs(3) contains A(7)
This method should prove useful in matching coefficients to standard errors derived from the @stderrs elements of the equation (see “Equation Data Members” on page 34 of the Object Reference). The @coefs elements allow you to refer to both the coefficients and the standard errors using a common index.
If you have used an alternative named coefficient vector in specifying your equation, you can also access the coefficient vector directly. For example, if you have used a coefficient vector named BETA, you can generate the fitted values by issuing the commands:
equation eq02.ls cs=beta(1)+beta(2)*gdp series cshat=beta(1)+beta(2)*gdp
where BETA is a coefficient vector. Again, however, we recommend that you use the @coefs elements to refer to the coefficients of EQ02. Alternatively, you can update the coefficients in BETA prior to use by selecting Proc/Update Coefs from Equation from the equation window. Note that EViews does not allow you to refer to the named equation coefficients EQ02.BETA(1) and EQ02.BETA(2). You must instead use the expressions, EQ02.@COEFS(1) and EQ02.@COEFS(2).
Estimation Problems
Exact Collinearity
If the regressors are very highly collinear, EViews may encounter difficulty in computing the regression estimates. In such cases, EViews will issue an error message “Near singular matrix.” When you get this error message, you should check to see whether the regressors are exactly collinear. The regressors are exactly collinear if one regressor can be written as a
22—Chapter 18. Basic Regression Analysis
linear combination of the other regressors. Under exact collinearity, the regressor matrix X does not have full column rank and the OLS estimator cannot be computed.
You should watch out for exact collinearity when you are using dummy variables in your regression. A set of mutually exclusive dummy variables and the constant term are exactly collinear. For example, suppose you have quarterly data and you try to run a regression with the specification:
y c x @seas(1) @seas(2) @seas(3) @seas(4)
EViews will return a “Near singular matrix” error message since the constant and the four quarterly dummy variables are exactly collinear through the relation:
c = @seas(1) + @seas(2) + @seas(3) + @seas(4)
In this case, simply drop either the constant term or one of the dummy variables.
The textbooks listed above provide extensive discussion of the issue of collinearity.
References
Davidson, Russell and James G. MacKinnon (1993). Estimation and Inference in Econometrics, Oxford: Oxford University Press.
Greene, William H. (2008). Econometric Analysis, 6th Edition, Upper Saddle River, NJ: Prentice-Hall.
Johnston, Jack and John Enrico DiNardo (1997). Econometric Methods, 4th Edition, New York: McGrawHill.
Pindyck, Robert S. and Daniel L. Rubinfeld (1998). Econometric Models and Economic Forecasts, 4th edition, New York: McGraw-Hill.
Wooldridge, Jeffrey M. (2000). Introductory Econometrics: A Modern Approach. Cincinnati, OH: SouthWestern College Publishing.