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Econ 334: Practice Final Exam 7 1. Of the four assumptions for simple linear regression, which is most directly connected with estimating the slope coefﬁcient? EDA Klzo 2. Suppose you run a regression of student’s ﬁnal exam scores on their previous previous grades: f incl, = [30 + ﬁlmidtermlg + ,BzmidtermZg + 'u..; (a) How many points more would we expect you to do on the ﬁnal if you had scored 5 more points on midterm2?
5131 (b) Now suppose that students with lower midterm grades studied harder for the
ﬁnal. What does this do to our prediction of your ﬁnal grade? Is it too high or
too low? Be speciﬁc about what is correlated with what.
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er 3. You run a complex model to determine if cigarette prices (cigprice) determine mum
of cigarettes smoked per day (cigs). white is a dummy variable which is one if the person is white. Call:
lm(formula  cigs ” logIncome + age + ageSq + cigprice + educ +
white + white * educ, data = smoke) Residuals :
Min 10 Median 3Q Max
15.038 9.149 6.704 8.093 71.017 Coefficients:
Estimate Std. Error t value Pr(>tl)
(Intercept) 0.647517 10.839155 0.060 0.952 logIncome 0.676953 0.761178 0.889 0.374
age 0.734925 0.167618 4.385 1.33e—05 ***
ageSq 0.008627 0.001816 —4.751 2.43e—06 ***
cigprice —0 035384 0.106931 0.331 0.741
educ —0.650954 0.443422 1 468 0.143
white 2 432749 6.094492 —0.399 0.690
educzwhite 0.183638 0.473142 0.388 0.698 Residual standard error: 13.56 on 748 degrees of freedom
Multiple RSquared: 0.04161,Adjusted Rsquared: 0.03264
Fstatistic: 4.639 on 7 and 748 DF, pvalue: 4.246e05 1 (a) How many more or less cigarettes does a person smoke if they’re White? ZHﬁwM* (b) How many more or less cigarettes does 40—yearold smoke compared to a 39year “d" 043‘;  0. 008% 402—392) (c) How many more or less cigarettes does a white person with 10 years of education smoke compared with a white person with 9\years of education? ,:i;=~~r » ,\ \ K ' = \— 7/ —O.(o‘>l + o. l%& , o , ‘ I (d) Why did we include ageSq in the regression? What effect does it capture?
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(e) Interpret the coefﬁcient on logIncome. How does cigs change with income? As imam/mo. iimmases, ALL LLﬁL LILUL (Miami, MUMPHW
of; c'gmjﬁi‘es \“Wmsas. 4. ,31 in some regression is 3. Its standard error is estimated to be 1. (a) Is this enough information to conclude that the variable is stastically signiﬁcant? Write down the null and alternative hypotheses you’re testing. \ieS'. Re" 1350 Ml: IN #0
(b) Create 95% conﬁdence intervals for [31. (Use a rule of thumb for the math.) 3126 = [UK] (c) Do we know enough to conclude if the variable is economically signiﬁcant? What else would we need to know?
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+9,» Vax‘mloLas Lune ism ‘stcermdl ) 05k. 5. In the regression wage = ,60 + ,Blage + ﬁgage2 + [33educatz'on + u: (a) How can you test if education is a signiﬁcant variable? Specify the type of test you’d run and write out null and alternative hypotheses. gtW “0113,30 HI“. 123190 (b) How can you test that education is the only signiﬁcant variable? Specify the type of test you’d run and write out null and alternative hypotheses. F'l‘ag‘h DY LM'it—S‘l— Ho Ef‘Fz'tO, ’H‘: ‘3‘=fo bf ﬁﬁf D 6. You have data on wage, age, education, and firstJob (a dummy variable which is 1 if a person is on their ﬁrst fulltime job). (a) Write down a regression model that allows for people’s ﬁrsttime jobs to pay less,
all other things held equal. £00439. : ¥°4?\—&mtTok+ 1,10%; 4» 'Fgecﬂ 40L (b) Write down a regression model that allows for ﬁrsttime jobs to pay more for
additional education. way: 130 "‘3 QMJCSJO + 15103. + ”’33 ibivsgolokwﬂ i F1 0% “L“ 7. You run the regression model y = 50 + ﬁlm + u and ﬁnd out that u has a variance that’s proportional to 2:.
(a) What is this condition called? hie/WOSMAS‘HCCW (b) What are the consequences of this condition for 51? Be speciﬁc about bias and
testing (or conﬁdence intervals). (g‘ '1: S'ELL \Mloia [gmt 1’84; LmCich/lm micwols mlu Lie
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“a“ 7‘ (c) Write down a transformed model which doesn’t suffer from this condition. L6.— .._+\L lA “AMIB
ﬁ_rﬁbﬁ¥ﬁ+ (lamb. Pia.» (d) In three sentences (or equations), describe how you’d test for this condition using the residuals from the above regression. B_? 115%.. Squaw ‘l'Q—L realMS, ireTASS ‘l‘eau’v M X, ?ouao,rg D'Q’ K,
1? were. SiauiQLcm/ci cauaiucﬂk We. Micros Mag(1:111 8. You’re building a model of the 2008 election based on how people voted in the past
and their income. (There are two parties, “Elephant” and “Donkey”.) Consider the linear probability model: y = prob(voteDm1key2003) = [30 + ﬁlvotedDmkeygoM +
ﬂgincome + u. (a) A big problem with the linear probability model is that, as the probability gets nearer 0 or 1, its variance decreases. What is the name of this problem?
new SWSH Ll M!) (b) If you’re making a binary choice (like “elephant” or “donkey”), the variance of the
probability of choosing one or the other is var (prob(z)) = prob(z) (1 — prob(z)).
How could you solve the problem you named? Write down a transformed equa tion which doesn’t suffer from the ﬂaw above (Hint: you can use an estimated
value to make the math simpler.) 30 wt (kwouo lat x\ 1% L L — %\ g, :  . . L‘bt‘. 
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9. You’re interested in the Phillips curve. You have timeseries data for both inﬂation and unemployment. (a) Write down a model that allows you to estimate the percent change in inﬂation which arises from a. percent change in unemployment.
ﬁngc‘lwumﬁmw 3 ’Fo + F [63( MLDVW"\ + UL (b) If you think that the relationship between inﬂation and unemployment was signif—
icantly different during the 1970’s, what variable would you add to the regression? How would you test this? dz“) (3 a. CLUWLu/u/ Va«rioucaLL (‘0‘ ids (CTRB
ﬂogﬁmélaliab= “(3° a]; Olga—112,1 [03CUMPLik’wd\+ szgci £§(:MP\ (c) Now 1magine that you discover that unemployment 1s highly serially correlated in your monthly data. Write down in math what this means. \AAwwxs w) ‘ﬁw wﬁ'kﬂ/VLUL U‘MUMFioklmi/uti IS Cowelmétca ”OLA“ UWoﬁMLQA/Lfi 1 (d) Is the serial correlation 1n unemployment necessarily a problem for your regres sion? Not WSWLLV jig MLYSJLM SyriaL Watt/Chm in (e) Now suppose you ﬁnd serial correlation in your residuals. Is this a problem for Yes. “6M3 oor (F's WILL ice, fo‘camcﬂ. the regression? 10. You ﬁnd serial correlation in the regression residuals of your favorite timeseries re gression! (y; = Bo + 16113 + 10:) (a) What are the consequences for the coefﬁcient of interest, ﬁl? Be speciﬁc about bias and hypothesis testing. SUV £S~decﬁ A unik lop. uwkaiocbecg) Lei couccﬂwu‘ 1
\WL‘exwaLg coKLK +30 Swoik moQ wa‘kL [0.2, New; \‘twﬁ ”\‘0 (”DmiSeLtB rapt? +0“— VWLL \A‘IP06’L’ZSIS (b) You ﬁt an AR(1) model to the residuals: at = put_1 and ﬁnd fh/o = 0.5. Write
down a transformed model which does not suffer from serial correlation in the errors. %x*05‘ar~t = (Po +"F. (Xx —o.‘5 km} 4 (LI (c) Suppose I insisted that you didn’t have serial correlation in your errors. Propose a simple test to prove me wrong. Write down the null and alternative h otheses. J: H‘o .' A z: 0
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11. Write down the steps for conductlng a functionalform misspec1ﬁcation test of your " T" O choosing.
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M M [FFasi\ Ho' «909:0 Hg oméo Ur «Ho 12. You’re interested in modeling the elasticity of ice cream sales to price. However, you
notice a large seasonal component in the quantity of ice cream consumed which you’d like to account for in order to reﬁne your elasticity estimate. (a) Write down a model which relates the percent change in ice cream consumed
to a percent change in its price, accounting for seasonal effects. Describe any variables besides icecream and price that you choose to include in your model.
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WW midday, ﬂpv‘rus, SUI/1AM M 6001441447 vow “Ling (b) I claim that the seasonal patterns don’t matter. Propose a test (be speciﬁc about null, alternative, and test type) to prove me wrong. uoW>~L=a=7>«=~° 2*" ”FL?“ ”3*“ "MO "resi \Dl 9&ij av LWL +asi (c) Now suppose you think that ice cream consumption has been increasing over time
for nonprice reasons. Add something to your seasonal model in part (a) which allows for estimation of nonprice annual growth in ice cream consumption. [08 Cu”:— $°+F lESL—fvtu.\t 'F1, Unwicv —( F5 SFvwsdi ’F‘l SUM/MW
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13. In class we estimated the+ response of crime rates (crime) to additional spending on police forces (cops) using a crosssection of US cities, and found (surprisingly) that spending more on police was correlated with more crime! (a) Why did this happen? What was missing in the above regression? Explain this
carefully (what needs to be correlated with what?). Is WWW! lo! a Cops was MW03~ 1+ (£9me 15—“
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Cami; Tic—Ff; COPS: VFLC/rlmqvﬁ— (Lt (c) Now suppose we had a two—year panel dataset with both crime rates and expenses for each city. Write down the equation (or describe the procedure) that you would use to estimate the effect of increased police spending on crime rates. COM Jutoux dQQCuu/Lcn err Sulatmd' 04 +¢m Series away CWWLUthg CrlMQiiﬂ—Z "Best? (besii —— COPS). i1» +LL [CHM/ntli— Chm)» = 'Fo 4r Tn CCOnguc— COFSL +Lg
14. A pooled crosssection is made of two or more random samples taken at different times, often with dummyvariables for the time that the sample is taken. A panel dataset is similar but follows individual units over time. (a) What, does the panel dataset allow us to estimate that the pooled crosssection does not? F3)“; “aw(S 7 W mAMAwdl SPQCl'QlC
‘bm SQJHQS \‘M'Q’VCQflS (b) What old problem does this allow us to solve if we make the additional assump tion that something 1s constant over time? And how? EJ; M W\‘\' thvqw \féaLwawcl’ ’VMlal’ong, Lat V‘L
comml MRS ‘lww. ‘lbr WA (ﬂux/14ml we owe. wove «LL; +0 6,li 190v we (c) How would you remove the ﬁxed effects from the panel data so that you could
then use plain old leastsquares regression techniques? 1:614" SuLMc’l VLL ‘FlWJzSD.2¢‘\(L<5 M—é’w—aﬂﬂg
% Wt, \«Mmcﬂcwt Wisdohzs. 15. You’re interested in t e hypothesis that the Reaganera tax cuts spurred GDP growth.
You have data on GDPt. (a) Write a regression equation that allows you to test the hypothesis that the GDP
growth rate (the annual percent change in GDP) changed after 1984. Describe any additional variables you bring to the regression. ﬂ. (GDP): 0+ {Aquﬂ‘imsr 24km. +Lu
08 ' (F ”F [(6 «pin/K (in: is a ' «Io/violin b What kind of test would on use? S eciﬁ test e, null, and alternative h 
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variable. Below, describe the tests requested, being speciﬁc about test types, null and alternative hypotheses, test statistics, and critical values you’d look up. (a) Test if 22 is statistically signiﬁcant. 3% O .
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 Spring '09
 Woutersen
 Econometrics

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