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

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

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