Unit 10 ECONF16 (assignment)

# T test for ar1 serial correlation step 1 ho no

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t-test for AR(1) Serial Correlation Step #1 Ho : No SerialCorrelation, ρ = 0 Ha : Evidence of SerialCorrelation, ρ≠ 0 Step #2 This hypothesis test is based on the t- 5

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distribution with 128 degrees of freedom. α = 0.05 Reject the Ho if the t-test statistic is ≥ 1.98 or ≤ -1.98 and p-value < 0.05. EXCEL command for critical value: =F.INV.RT(0.05, 128) Step #3 t = 3.18 p-value = 0.002 Note: The p-value was found in STATA. Step #4 Since 3.18<2.17 AND 0.3002< 0.05 Reject Ho; there is evidence of Serial Correlation (ii) Using the same regression model, conduct a “four-step” Durbin-Watson test for serial correlation, described in your textbook pp. 418 - 419. You can use the STATA for Step #3 but will need this resource ( ) for the rejection criteria (Step #2) and for your conclusion (Step #4). As with the Chow test, you may find the Wikipedia entry for the Durbin-Watson test to be a good resource to describe this test and its implementation. Durbin-Watson test Step #1 Ho : No SerialCorrelation, ρ = 0 Ha : Evidence of SerialCorrelation , ρ > 0 Step #2 This hypothesis test is based on a Durbin- Watson test with K=2 and T=130. α = 0.05 6
Reject the Ho if the DW statistic is < 1.70 or > 1.73 and p-value < 0.05. Step #3 DW = 2.064 Step #4 Since 2.064>1.70 and 1.73 Fail to Reject Ho; there is no evidence of Serial Correlation according to the DW statistic. **Note that I don’t know why STATA is display a different result than the rough calculation, based on DW = 2 ( 1 ρ ) = ¿ 2 ( 1 .271 ) = 1.458 we would reject the null hypothesis. This is the same conclusion reached in part (i) of this problem. STATA tips: To inform STATA that your data should be considered “time series” (necessary for commands such as the Durbin-Watson test) there are two steps: (1) you should have a time variable in your data, for example a time trend called “t,” which provides a marker for STATA to track the time dimension. Note that if the data includes a variable such as “year” that can also be used. (2) use the command tsset to formally declare the data as “time series” using t (or a different time variable) as a marker: tsset t To run a Durbin-Watson test (post-estimation command): estat dwatson 7

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