Econ 399 Chapter10b

# Econ 399 Chapter10b - 10.3 Time Series Thus Far Whereas...

This preview shows pages 1–9. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 10.3 Time Series Thus Far Whereas cross sectional data needed 3 assumptions to make OLS unbiased, time series data needs only 2-Although the third assumption is much stronger-If we omit a valid variable, we cause biased as seen and calculated in Chapter 3-Now all that remains is to derive assumptions that allow us to test the significance of our OLS estimates Assumption TS.4 (Homoskedasticity) Conditional on X, the variance of u t is the same for all t: n. 1,2,..., t , ) ( ) | ( 2 = = = σ t t u Var X u Var Assumption TS.4 Notes-essentially, the variance of the error term cannot depend on X; it must be constant-it is sufficient if: 1) u t and X are independent 2) Var (u t ) is constant over time-ie: no trending-if TS.4 is violated we again have heteroskedasticity-Chapter 12 shows similar tests for Het as found in Chapter 8 Assumption TS.4 Violation Consider the regression: t t t t u politics tuition + + + = inflation 1 β β Unfortunately, tuition is often a political rather than an economic decision, leading to tuition freezes (=real tuition decreases) in an attempt to buy votes-This effect can span time periods-Since politics can affect the variability of tuition, this regression is heteroskedastic Assumption TS.5 (No Serial Correlation) Conditional on X, errors in two different time periods are uncorrelated: s t ) | , ( ≠ 2200 = X u u Cor s t Assumption TS.5 Notes If we assume that X is non-random, TS.5 simplifies to: (10.12) ) , ( s t ≠ 2200 = s t u u Cor-If this assumption is violated, we say that our time series errors suffer from AUTOCORRELATION, as they are correlated across time-note that TS.5 assumes nothing about intertemporal correlation among x variables-we didn’t need this assumption for cross- sectional data as random sampling ensured no connection between error terms Assumption TS.5 Violation Take the regression: t t t t u exercise weight + + + = calories 1 β β If actual weight is unexpectedly high one time period (high fat intake), then u t >0, and weight can be expected to be high in subsequent periods (u t+1 >0) Likewise if weight is unexpectedly low one time period (liposuction), then u t <0, and weight can be expected to be low in subsequent periods (u t+1 <0) 10.3 Gauss Markov Assumptions-Assumptions TS.1 through TS. 5 are our Gauss- Markov assumptions for time series data-They allow us to estimate OLS variance-If cross sectional data is not random, TS.1 through TS.5 can sometimes be used in cross sectional applications-with these 5 properties in time series data, we see variance calculated and the Gauss- Markov theorem holding the same as with...
View Full Document

{[ snackBarMessage ]}

### Page1 / 32

Econ 399 Chapter10b - 10.3 Time Series Thus Far Whereas...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online