ECONOMETRICS HKU

University of Hong Kong
Introductory Econometrics (ECON0701), Fall 2013
22 November 2013

Further Issues in Using OLS with Time Series Data
• Last time, we discussed the assumptions necessary for OLS parameter estimates to be consistent in a time series context.
• We also compared these assumptions with the assumptions necessary for OLS to be unbiased. • In general, the conditions are more restrictive for OLS to be unbiased than for OLS to be consistent, so in a time series context, it is fairly frequent to have OLS be biased but still consistent. Unbiasedness

Consistency

Model must be linear in parameters Yes

Yes

Model can include lagged independent variables (xt-1, xt-2, etc.)

Yes

Yes

Model can include lagged
No
dependent variables (yt-1, yt-2, etc.) x and y variables must be
No
stationary

Yes

x and y variables must be weakly No dependent Yes

Exogeneity of u

Contemporary

Strict

Multicollinearity of x variables Not Permitted

Yes

Not Permitted

Further Issues in Using OLS with Time Series Data
• Now we will discuss the additional assumptions necessary for standard errors, t statistics and F statistics in time series models to be asymptotically valid.
• Before, under the assumptions for unbiasedness, we required conditional homoskedasticity and no serial correlation.
• When these were true, the standard errors, t statistics and F statistics were exact.

Further Issues in Using OLS with Time Series Data
•
•

Unfortunately, in practice, the conditional homoskedasticity and no serial correlation assumptions we used are very strong and almost never satisfied.
Therefore, usually we must suffice with a weaker set of assumptions – contemporaneous homoskedasticity and a weaker version of the no serial correlation assumption. Further Issues in Using OLS with Time Series Data
• The conditional homoskedasticity assumption was:

Var  ut | X    2
• Contemporaneous