ECON0019: QUANTITATIVE ECONOMICS AND ECONOMETRICS
report | 计量经济代写 | ECONOMETRICS代写 – 这是有一定代表意义的计量经济等代写方向
LATE SUMMER ASSESSMENTS 2022
CENTRALLY MANAGED ONLINE EXAMINATION
ECON0019: QUANTITATIVE ECONOMICS AND ECONOMETRICS
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Answer ALL TWO questions from Part A and answer ONE question from Part B.
Questions in Part A carry 60 per cent of the total mark and questions in Part B carry 40 per cent of the total. Tables for the normal and F-distribution are at the end of the examination paper.
In cases where a student answers more questions than requested by the examination rubric, the policy of the Economics Department is that the students first set of answers up to the required number will
ECON0019 LSA 1 TURN OVER
be the ones that count (not the best answers). All remaining answers will be ignored.
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PART A
Answer all questions from this section.
A.1 Consider the linear regression model:
y= 0 + 1 w+u,
where the error termu is fully independent of the regressor wand satisfies E[u] = 0 and
Var(u) =^2. We observe a random sample (yi,wi),i= 1,....,100, and compute the following
quantities:
1
100
X^100
i=
wi= 3,
1
100
X^100
i=
yi= 1,
1
100
X^100
i=
w^2 i= 10,
1
100
X^100
i=
yiwi= 3,
1
100
X^100
i=
yi^2 = 17.
(a) Use above information to compute the OLS estimates for 0 and 1. Include intermediate
calculations as part of your answer.
(b) Use above information to compute an estimator of^2. Include intermediate calculations as
part of your answer.
(c) Given the assumptions stated at the beginning of the question, report valid standard errors
of 0 and 1. Explain.
(d) You collect 100 more observations from the population of interest and obtain the following
regression fit based on the sample of 200 observations with standard errors reported in
parentheses:
y= 1. 2
(1.1)
0. 1
(0.3)
w
Use the above to answer the following questions. Test the hypothesisH 0 : 0 = 0 against
H 1 : 0 >0 at a 10% level. Conclude.
(e) Construct a 99% confidence interval for 1.
ECON0019 LSA 2 CONTINUED
(f) Consider the hypothesisH 0 : 1 =b 1 whereb 1 is a known number chosen by you. What
is the smallest value ofb 1 for which you wont rejectH 0 against a twosided alternative at
the 1% level?
A.2 In March 2021, State A in Gemany implemented a mandatory motivation programme for its
welfare recipients, requiring them to listen to a monthly afternoon motivation speech to inspire
them to search harder for work. Neighbouring State B did not change anything about its welfare
programme over the period considered. The average monthly earnings for a welfare recipient in
State A were 2,400 Euros in February 2021 and 2,200 Euros in June 2021. The average monthly
earnings for a welfare recipient in State B were 1,800 Euros in February 2021 and 1,500 Euros
in June 2021.
(a) What is the difference in difference estimate of the effect of the motivation programme on
earnings?
(b) Suppose you are given the individual earnings data for State A and State B. Provide the
regression equation for which the corresponding OLS estimator will deliver the estimate
you reported in (a).
(c) Which coefficient in this regression is estimated by the difference in difference estimator?
(d) One critic mentions that seasonal variation in jobs could cause a problem in the difference
in difference estimator. How would you respond?
(e) Another critic points out that the work force in State A is on average better educated than
the one in State B and that earnings growth lately has been higher for workers with high
levels of education. If this is true then what is the sign of the bias of the difference in
difference estimator?
(f) You decide to collect data on inviduals level of education in addition to their earnings.
Write up a new regression equation whose OLS estimator will not suffer from the potential
bias you discussed in (e).
ECON0019 LSA 3 TURN OVER
PART B
Answer ONE question from this section.
B.1 In The Oregon health insurance experiment: evidence from the first year (2012), Amy Finkelstein
and coauthors study the effects of having free health insurance via the Medicaid programme in
the United States on health and other outcomes of low-income residents of the state of Oregon.
Medicaid is a programme in the U.S. that helps with healthcare costs for some people with limited
income. In 2008, Oregon made eligibility to Medicaid more generous. However, because demand
for this programme exceeded available funding, the state ran a lottery among the applicants.
Simplifying some details, selected applicants were granted free Medicaid access for their entire
households conditionally on proving low income (which some applicants could and others could
not). Multiple members of the household could initially apply, and it was sufficient for just one
of them to win the lottery and prove low income. There were no other ways for the applicants to
receive Medicaid during the study period. Note that all analyses described below are performed
on the sample of applicants.
(a) The authors estimate the following regression by Ordinary Least Squares (OLS):
Li= 0 +Si+Ci+i,
whereLiequals one if at least one member of individualis household is selected in the
lottery,Siis a set of dummies for each household size (except household size of one used
as an omitted category) andCiareis characteristics in prior years, e.g. whetheriwas
admitted to a hospital in 2007. They find positive and stastistically significant, whileis
not significantly different from zero. The authors indicate that the results are as expected.
Explain why. Why did the authors estimate this specification in the first place?
(b) Consider estimating the following specification by OLS:
Hi= 0 + 1 Mi+ui,
whereHiis a self-reported dummy for good health in 2009 andMiis an indicator that the
person received Medicaid insurance. Explain why the estimate 1 may be biased for the
effect of having Medicaid on health. Provide at least one economic justification and explain
which direction of the bias it implies.
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(c) The authors focus on the Two-Stage Least Squares (2SLS) estimator 1 from the following
linear probability model:
Hi= 0 + 1 Mi+ 2 Si+ 3 Ci+ui, (*)
instrumentingMiwithLi. Describe precisely how 1 can be obtained.
(d) State the precise formal assumptions required for 1 to consistently estimate the causal
effect of having Medicaid insurance on health. Do you expect these assumptions to be
satisfied in this setting? For each assumption, explain why or why not. Why did the
authors includeSi? Why did they includeCi?
(e) The authors call 1 a local average treatment effect (LATE). If the effect of Medicaid on
the probability of having good (self-reported) health varies across individuals, explain what
kind of weighted average of treatment effects 1 estimates. That is, which groups receive
a higher weight compared to their size? (A careful verbal argument would suffice in this
part. Make sure to describe these groups in economic, and not only statistical, terms.)
B.2 In Valuation of New Goods under Perfect and Imperfect Competition (1996), Jerry Hausman
investigates the demand for ready to eat (RTE) cereal. In doing so, he uses several databases
where market shares and product characteristics for various brands (e.g., Special K, Trix,
Cheerios, Corn Flakes, etc.) are observed across space and time: The data used to estimate
the model are cash-register data collected on a weekly basis across a sample of stores in major
metropolitan areas of the United States over a two-year period. (This renders about 140 time
series observations per metropolitan area.)
(a) Let there beb= 1,...,Bbrands in each of them= 1,...,Mmarkets. (Note that the unit
of observation is the market, i.e. metropolitan region in a particular time period, not the
household.) Abstracting away from the time series dimension, one of the models estimated
in the study resembles the following specification:
sbm= 0 b+ 1 blogym+
XB
c=
bclogpcm+bm, (1)
where sbm is the market share for cereal brand b in metropolitan area m, ym is the
expenditure on cereals in marketm,pcmis the price for brandcin marketm. The cross-
price elasticity between brandsbandcis the relative change in (average) market share for
ECON0019 LSA 5 TURN OVER
brandbper relative change in price for brandc. Given estimates 0 b, 1 b, 1 b,...,Bbfor
the parameters above, propose an estimate for the cross-price elasticity between brandb
(say, Cheerios) and brandc(say, Corn Flakes) (i.e., the percent change inbs market share
for a small percent change in the price ofc). Explain your answer.
(b) If household consumption data were available, you could estimate a probit model with outcomeDirecording whether a householdibought (Di= 1) or not (Di= 0) a particular brandb(say, Cheerios) in a given week where this outcome is assumed to be dependent on that households income (say,yi) and the price for this cereal brand in that households market, pbi. (For simplicity, we omit the price of competing cereal products.) Suppose you obtain estimates for the coefficients in this probit model. How would you predict the change in the probability thatDi= 1 when there is a 20% discount relative topbi= 2 British pounds for a household withyi= 50,000 British pounds? (c) Consider again a situation where household consumption data is available. In particular, focus on one brand, say Cheerios. LetQirecord the number Cheer ios cereal boxes of a given size that householdipurchases in a given week. Suppose thatQican be modelled using a Poisson regression with households income (say,yi) and the price for this Cheerios box in that households market,pi, as independent variables. (For simplicity, we omit the price of competing cereal products.) Assume nonetheless that the quantity purchasedQi is censored and one only observes whether the household buys 0, 1 or 2 or more boxes. Write down the likelihood for this model if you hadi= 1,…,I independently sampled households in your sample. Explain your answer.
(d) In estimating equations like (1), Hausman instruments prices using factors which shift costs such as ingredients, packaging, and labor (p.218). Letting these IVs be denoted by a vectorZmvarying across markets and assuming that there are at least as many such variables as there are brandsB, explain how you would estimate equation (1) for brandb acrossMindependently sampled markets. Why do you need the number of IVs to be as large as the number of prices? Can you test whether the IVs are valid if there are as many instrumental variables as there are prices? Explain your answers. (e) Consider now equation (1) for a single market but across many periodstand suppose there are no endogeneity issues:
sbt= 0 t+ 1 tlogyt+
XB
c=
bclogpct+bt
Explain how you would test whether there is serial correlation inbt. Would serial correlation
imply that OLS is inconsistent? Explain your answer.
ECON0019 LSA 6 CONTINUED
5 % Critical values for theF 1 , 2 distribution
2 \ 1 1 2 3 4 5 6 7 8 10 12 15 20 30 50
1 161 199. 216. 225. 230. 234. 237. 239. 242. 244. 246. 248. 250. 252. 254.
2 18.5 19.0 19.2 19.2 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.5 19.5 19.
3 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.79 8.74 8.70 8.66 8.62 8.58 8.
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 5.96 5.91 5.86 5.80 5.75 5.70 5.
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.74 4.68 4.62 4.56 4.50 4.44 4.
10 4.96 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.38 2.31 2.23 2.16 2.07 2.00 1.
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.35 2.28 2.20 2.12 2.04 1.97 1.
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.16 2.09 2.01 1.93 1.84 1.76 1.
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 1.99 1.92 1.84 1.75 1.65 1.56 1.
80 3.97 3.11 2.72 2.49 2.33 2.21 2.13 2.06 1.95 1.88 1.79 1.70 1.60 1.51 1.
100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.93 1.85 1.77 1.68 1.57 1.48 1.
120 3.91 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.91 1.83 1.75 1.66 1.55 1.46 1.
3.85 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.83 1.75 1.67 1.57 1.46 1.35 1.
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NORMAL CUMULATIVE DISTRIBUTION FUNCTION (Prob(z < za) wherezN(0,1))
- za 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.
- 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.
- 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.
- 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.
- 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.
- 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.
- 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.
- 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.
- 0.7 0.7580 0.7611 0.7642 0.7673 0.7703 0.7734 0.7764 0.7794 0.7823 0.
- 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.
- 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.
- 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.
- 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.
- 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.
- 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.
- 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.
- 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.
- 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.
- 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.
- 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.
- 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.
- 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.
- 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.
- 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.
- 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.
- 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.
- 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.
- 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.
- 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.
- 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.
- 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.
- 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.
- 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.
- 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.