代写125.785 Research and Analytics in Economics and Finance代写Java编程

日期：2024-04-29 11:32

125.785 Research and Analytics in Economics and Finance

Answer all 8 questions

At the end of the exam click 'Finish attempt', then confi rm by clicking 'Submit all and Finish'.

Optional you may use Excel to help answer the questions.You MUST provide the answer in the textbox below each individual question.

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Question 1

Please concisely answer the following: a. When starting an empirical exercise in Economics and Finance, we need to produce a table of basic statistics for the variables used in the study.

a. Briefl y describe the major purpose(s) of doing so.  [4 marks]

b. An assumption of the Classical Linear Regression Model (CLRM) is the normal distribution of the residuals. Briefl y discuss the major problem(s) if the assumption is violated.  [4 marks]

c. To conduct a study, you have collected annual data of the companies composing the S&P/NZX 50 Index over the period from 2019 to 2022. How will you assess whether the normality assumption holds? Explain why you will do so. [4 marks]

Question 2

In theory we have a model which explains a company’s expected stock return:

Stock Return = α+β1*RiskFactor1 + β2*RiskFactor2* + β3*RiskFactor3 +ε

Now we have run a time series OLS regression and our main interest is to test if the variable of RiskFactor1 has a beta value being greater than

1. The regression software produced these results in the default printout:

β1 equals 1.389, Standard Error=0.344, T-value equals 4.360, and P-values 0.0233 (Degree of Freedom=1389)

a. Describe in detail the null hypothesis and the alternative hypothesis.  [4 marks]

b. How do we conduct the statistical test to test whether the data is consistent with the null hypothesis? State all the assumptions.  [4 marks]

c. Using the data provided, conduct the test and state your conclusion.  [4 marks]

Question 3

Suppose we have a regression model:

For White’s general test for heteroskedasticity, we run the auxiliary regression:

a. State the hypothesis tested in the auxiliary regression.  [4 marks]

b. If the residual variance is proportional to the value of a variable of X4, which is not a variable in the regression model. Might there be any issue if you use this White test to identify the heteroskedasticity problem.  [4 marks]

c. Provide suggestions to address the potential issue (in your answer to part b)? (Explain why)  [5 marks]

Question 4

We have a linear regression model:  y= α + ß1 x1 + ß2 x2 + ε

a. Using data collected, we fi nd that the correlation coeffi cient between x1 and x2 is exactly negative 1. Describe what is the problem and discuss how to solve it.  [4 marks]

b. If the correlation coeffi cient is actually 0.62, how may we proceed to study the relations?  [4 marks]

c. What if the actual correlation coeffi cient between x2 and the residual ε is 0.42, how may we verify that it is the case and address the problem?  [5 marks]

Question 5

a.The table below shows the out-of-sample prediction performance of a default prediction model, in a number of borrowers.

The accuracy rate of a model is the ratio of the number of correct predictions to the total number of predictions.

i. Calculate the accuracy rate of the default prediction model.  [2 marks]

The naïve predictive model makes a prediction based on the default proportion of all the data.

ii. Does the default prediction model perform. better than the naïve predictive model? Explain.;  [2 marks]

b. Discuss the advantages and weaknesses of the logit model compared to the OLS linear probability model.  [5 marks]

c. Based on each of the two models below, calculate the probability of loan approval when the salary is 90,000 dollars per year.

Logit model: Y = 0.55 + 0.11*log(X)

OLS linear probability model: Y = 0.40 + 0.03*log(X)

Where Y is a binary variable that takes a value of 1 if the loan is approved and 0 otherwise; X is the annual salary in dollars; log(.) is a natural log function.

Note that the cumulative probability of the logistic function, F(Z), is 1/(1+exp(-Z)), where Z is the score from the logit model. [5 marks]

Question 6

a. Air pollution can adversely affect cognitive ability. You are researching whether an increase in air pollution causes an increase in the analyst forecast error. If you are using the two-stage-least-square (2SLS) approach and you consider to use the amount of rainfall as an instrumental variable, carefully discuss whether this instrumental variable is appropriate.  [4 marks]

b. The table below is Panel A of Table 5: Difference-in-differences analysis of the effect of stock liquidity on default risk in Brogaard, Li, and Xia (2017) Carefully discuss the meaning of the “Pre-match (1)” and the “Post-match (2)”. What can we conclude from Panel A of Table 5?  [5 marks]

c. Discuss the consequences of the regression estimation when the “dependent variable” has a measurement error problem.  [3 marks]

Question 7

a. You have estimated the following AR(1) model for the time-series data comprising stock returns: Rt = 0.89Rt-1 + ut . Check the model for stationarity. Show the work to support the conclusion.  [3 marks]

b. Consider AR and MA processes.

i. When is an AR model more appropriate?

ii. When is a MA model more suitable?   [4 marks]

c. Let Y1t, Y2t, Y3t are endogenous variables and X 1t, X2t, X3t are exogeneous variables. Given the system of equations below, write down the reduced-form. equations and determine whether the system of equations is identifi ed based on the order condition.

Equation 1: Y1t = a0 + a1Y3t + a2X3t + u1t

Equation 2: Y2t = b0 + b1Y1t + b2Y2t + b3X1t + b4X2t + u2t

Equation 3: Y3t = c0 + c1Y2t + c2X2t + c3X3t + u3t   [5 marks]

Question 8

a. Consider the three main approaches to regression analysis with panel data, pooled OLS regression, the fi xed effects model, and the random effects model.

i. When should the fi xed effects model be used?  [2 marks]

ii. What test can be done for determining the preferred model?  [1 mark]

iii. Which model should be used when the null hypothesis of the Hausman test is rejected? Which model should be used when the null hypothesis of the Hausman test is not rejected?  [1 mark]

b. Consider the Vector Auto-Regressive model (VAR).

i. Carefully explain when and how we should use the impulse response function (IRF). [2 marks]

ii. Discuss when we should use the variance decomposition analysis. [2 marks]

c. Carefully explain how to calculate the earning announcement CAAR(-1,+1) which is the cumulative average abnormal return from the period one day before to one day after the day in which the earning announcement is made. This CAAR(-1,+1) is based on all fi rms in the S&P500 index. [4 marks]