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## Applied Statistics and Econometrics Study Essay

Order ID:89JHGSJE83839Style:APA/MLA/Harvard/ChicagoPages:5-10

Instructions:Applied Statistics and Econometrics Study Essay

Applied Statistics and Econometrics II Bruce McNevin, Ph.D.

Fall 2021 bm76@nyu.edu

Final Examination

Please submit to NYUBrightspace no later than 4 PM on Monday., 12/20/2021.

Answer all questions (25 points each)

1) Let yi be a binary dependent variable that equals 1 or 0 for i = 1, . . . , n.

Let xi , i = 1, . . . , n, be k-element vectors of explanatory variables. Let β be a k-

element vector of unknown parameters.

- a) Write the functional form of E(yi |xi , β), the conditional mean function,
assuming a logit model.

- b) Derive the marginal effect, or partial derivative ∂E(yi |xi , β)/∂xij , where xij is the
j th element of the xi vector.

- c) Suppose logit model estimation produces the table:
(i) What is the predicted probability that y = 1 when X1 = 2 and X2 = 0.5?

(ii) Compute the change in the predicted probability when X2 increases by

one unit from X2 = 0.5 to X2 = 1.5, holding X1 at X1 = 2.

(iii) Using the derivative result from part (b) and the estimates in the above

table, compute the partial derivative ∂E(y|X1, X2, β)/∂X2 at the X values

given in part b.

2) In a study of the Canadian work force, we seek to predict marital status from x1 =

Age and x2 an indicator for Sex, with x2 = 1 meaning female and x2 = 0 meaning

male. Age is centered by subtracting off the mean for the entire sample, so that a

person of “average” age has x1 = 0. Marital status is coded as (1) Single and never

married, (2) Married, (3) Divorced or separated, and (4) Widowed, meaning the

husband or wife is dead.

- Write the estimation equations for a multinomial logit model. Make “Single
and never married” the reference category that goes in the denominator of

the generalized logit. (Hint: multinomial logit is a set of logit models so you

should have 3 linear equations, pi/pj = …, etc.)

- Define the πj symbols from your model so I know what they mean.
P(Single and never married) = ? P(Married) = ?

P(Divorced or separated) = ? P(Widowed) = ?

- In terms of the parameters from your model, what null hypothesis would you
test to determine whether being married (as opposed to single and never

married) is related to gender?

- Describe the IIA assumption and provide an example that illustrates why it
may be problematic.

3) Suppose that a true data generating process (DGP) is:

(c ) Are yt and xt cointegrated? Explain. If you believe that they are cointegrated

then provide the cointegrating vector.

4) a) Using matrix notation write a first order vector autoregession in structural form.

Can this model be estimated using OLS? Explain.

- b) Re-write the equation in reduced form. Describe the stability condition. Why is
the stability condition necessary?

- c) How would you estimate the model if the stability condition does not hold?
- d) What is Granger causality, and why is it useful?

RUBRIC

Excellent Quality95-100%

Introduction45-41 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Literature Support91-84 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Methodology58-53 points

Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.

Average Score50-85%

40-38 points

More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.

83-76 points

Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.

52-49 points

Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.

Poor Quality0-45%

37-1 points

The background and/or significance are missing. No search history information is provided.

75-1 points

Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.

48-1 points

There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met

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