Unit 10 ECONF16 (assignment)

# Iii please conduct a formal four step hypothesis test

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(iii) please conduct a formal “four-step hypothesis” test for this test of seasonality (i.e. an F-test for the joint significance of your “month dummies.”) Note that this data set already includes the monthly dummy variables, you do not have to report the results of this estimation but can directly run the F-test. STATA tips: To create a linear time trend, use the command: generate t = _n F-test Step #1 Ho : β lchempi = β lgas = β lrtwex = β befile 6 = β affile 6 = β afdec 6 = β feb = β march = β apr = β may = β jun = β jul = β aug = β sep = 2

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Ha : At least one≠ 0 Step #2 This hypothesis test is based on the F- distribution with 17, 112 degrees of freedom. α = 0.05 Reject the Ho if the F-test statistic is > 1.71 and p-value < 0.05. EXCEL command for critical value: =F.INV.RT(0.05,17,112) Step #3 F = 0.74 p-value = 0.7603 Note: The p-value was found in STATA using the test command Step #4 Since .74 <2.17 BUT 0.7603> 0.05 We Fail to Reject Ho; meaning that all other variables are jointly insignificant and that t is the only independent variable explaining lchnimp . It should also be noted that although the coefficients on the dependent variables did change they did not change in a significant or important way. #2. Chapter 10, C6 [p. 377] using the “fertility data set,” [called FERTIL3.RAW in the question]. Make sure you include all the necessary discussions, although your discussions may be brief. Notes for working this question: (i) Report your estimated model for gfrt on t and t2 before discussing the rest of the question. ^ gfr = 107.05 + .072 t .01 t 2 n = 72, R 2 = .314, ´ R 2 = .294 3
(ii) Report your estimated model before discussing the rest of the question. ^ gf t = 17.0 4 + .35 pe 35.88 ww 2 10.12 pill 2.60 t + .03 t 2 n = 72, R 2 = .602, ´ R 2 = .571 With the trend values removed the R-Squared is less than that of 10.35 mean that it explains less of the variation in the dependent variable, however, it is not too much less given that it is .602 vs. .727. (iii) You do not have to report your estimated model but in addition to discussing the significance of t3 , please discuss your overall impression of the contribution of “time” to this model The term t^3 is very statistically significant when re-estimating model 10.35. Time is pretty valuable in this model because it offers explanation in the general fertility rate at different points of time in the history of the US, without it there isn’t much context as to why the rates are fluctuating so wildly. We are better able to see the effects of war and the introduction of the birth control pill. #3. Chapter 11, C1 [p. 407] using the “earnings data set” [called HSEINV.RAW in the question]. Make sure you include all the necessary discussions, although your discussions may be brief.

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