L25 - Heteroscedasticity[NOTE These notes draw heavily from Berry and Feldman and to a lesser extent Allison and Pindyck and Rubinfeld What

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Heteroscedasticity—Page 1 Heteroscedasticity [NOTE: These notes draw heavily from Berry and Feldman, and, to a lesser extent, Allison, and Pindyck and Rubinfeld.] What heteroscedasticity is. Recall that OLS makes the assumption that V j ( ) 2 for all j. That is, the variance of the error term is constant. (Homoscedasticity). If the error terms do not have constant variance, they are said to be heteroscedastic. When heteroscedasticity might occur. Errors may increase as the value of an IV increases. For example, consider a model in which annual family income is the IV and annual family expenditures on vacations is the DV. Families with low incomes will spend relatively little on vacations, and the variations in expenditures across such families will be small. But for families with large incomes, the amount of discretionary income will be higher. The mean amount spent on vacations will be higher, and there will also be greater variability among such families, resulting in heteroscedasticity. Note that, in this example, a high family income is a necessary but not sufficient condition for large vacation expenditures. Any time a high value for an IV is a necessary but not sufficient condition for an observation to have a high value on a DV, heteroscedasticity is likely. Similar examples: Error terms associated with very large firms might have larger variances than error terms associated with smaller firms. Sales of larger firms might be more volatile than sales of smaller firms. Errors may also increase as the values of an IV become more extreme in either direction, e.g. with attitudes that range from extremely negative to extremely positive. This will produce something that looks like an hourglass shape:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Heteroscedasticity—Page 2 Plot of X versus residuals -4 -3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 3 X variable Residuals Measurement error can cause heteroscedasticity. Some respondents might provide more accurate responses than others. (Note that this problem arises from the violation of another assumption, that variables are measured without error.) Heteroscedasticity can also occur if there are subpopulation differences or other interaction effects (e.g. the effect of income on expenditures differs for whites and blacks). (Again, the problem arises from violation of the assumption that no such differences exist or have already been incorporated into the model.) For example, in the following diagram suppose that Z stands for three different populations. At low values of X, the regression lines for each population are very close to each other. As X gets bigger, the regression lines get further and further apart. This means that the residual values will also get further and further apart. Other model misspecifications can produce heteroskedasticity. For example, it may be that
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/29/2012 for the course SOC 63993 taught by Professor Richardwilliams during the Spring '11 term at Notre Dame.

Page1 / 20

L25 - Heteroscedasticity[NOTE These notes draw heavily from Berry and Feldman and to a lesser extent Allison and Pindyck and Rubinfeld What

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online