Econometry Gender Effect

CHAPTER 9: Serial Correlation

MODELLING SERIAL CORRELATION

Serial Correlation: Violation of [pic]for all [pic]

Often observed in time series data, not in cross-section, but also in panel data.

Hence, it is a rule rather than an exception

Sources: a) Intrinsic serial correlation

b) Model misspecification: Growth in variables (existence of a trend, omitted variables, non-linerarity, measurement errors etc.)

Example on Intrinsic serial correlation: Permanent Income Hypothesis

[pic] where [pic] is consumption and [pic]is unobserved permanent income. How to estimate [pic]?

Behavioral Assumption: [pic] where [pic]is current income and p is weight for past unobserved permanent income. Also, note [pic]and [pic]

Transformation: lag the model one period: [pic]and multiply by p and subtract from this equation.

One gets: [pic]

[pic]

Notice this is a function of observed current income, [pic] and hence, is estimable provided we know p. However, the residuals, say, [pic]has non-zero covariance:

[pic][pic]

[pic][pic][pic][pic]

Hence, the needed transformation to convert the model into an estimable form generates intrinsic SC in the residuals with [pic]

Diagnosis of Model Specification: a) Look at the residual plot ([pic]), this may tell you whether you have a non-linear model as a source of SC. Functional form of your model may not be linear, and this may cause SC in the residuals b) Explore if you may have omitted variables in your model, again it may create SC in the residuals.

Disturbances with AR(p) (autoregressive of order p) structure

Suppose SC is present in the following AR(1) form in the residuals such that

[pic]where [pic]and [pic]is white-noise [pic] with [pic]and [pic], and [pic]but

[pic]if [pic]then there is positive SC, if not negative SC.

In general, [pic]

Proofs that a) [pic], b) [pic] and...