Stataistic

Answer all questions, all questions carry the same marks

Question 1 (20% Mark)

Suppose that a financial institution wishes to measure the relationship between the change in the interest

rate in a given period (it) and the change in the inflation rate in the previous period (INFt-1). Suppose that you gathered the data over the last 30 periods and the data are presented as follows:

Table 1 Data for selected macro-economic variables

Period (t) 1 2 3 4 5 6 7 8 9 10

it (%) 0.50 0.65 -0.70 0.60 0.40 -0.20 0.60 0.80 0.10 1.10

INFt-1 (%) 0.80 0.75 -1.20 0.15 0.60 -0.20 0.85 0.45 -0.05 1.30

Continued…

Period (t) 11 12 13 14 15 16 17 18 19 20

it (%) 0.90 -0.65 -0.10 0.40 0.30 0.60 0.05 1.28 -0.55 0.15

INFt-1 (%) 1.10 -0.80 -0.35 0.55 0.40 0.75 -0.10 1.50 -0.60 0.15

Continued…

Period (t) 21 22 23 24 25 26 27 28 29 30

it (%) 1.77 0.74 0.48 0.36 1.38 1.02 1.01 -0.15 0.23 1.58

INFt-1 (%) 2.10 1.20 1.02 0.12 1.75 1.30 1.21 -0.10 0.05 1.72

Assume that your line manager asked you to run the following regression model to the data:

ttt uINFi ++=

−110 

Where

it = change in the interest rate in period t; INFt-1 = change in the inflation rate in period t-1;

0 and 1 = regression coefficients to be estimated by regression analysis; and ut = error term.

a) Using the stata, generate descriptive statistics, scatter plot, run Pearson correlation test and discuss briefly your results. (5% Mark)

b) Using the same sample, generate regression results. (4% Mark) c) Evaluate the regression results taking into account section a) and b) with respect to its economic

meaning, overall fit, and the signs and significance of the individual coefficients. (3% Mark) d) What conclusion do you draw about the overall relationship between the response and explanatory

variables? (2% Mark) e) What econometric problems do these regressions have? Why do you think that these problems arise?

(3% Mark) ( f) Assume that last period’s change in inflation was 2%, what would be the expected effect on the

interest rate? Does the numerical value appear reasonable? What problems appear to exist in your

finding? Why? (3% Mark)

Question 2 (20% Mark)

i) Compare the uses of the independent samples and paired samples t tests. Explain clearly in which circumstances each method should be used in preference to the other, illustrating your answer with appropriate examples. State briefly the appropriate assumptions made in each case.

ii) In a particular population, it was of interest whether the male chief executive officer (CEO) was, on average, younger or older than their CEO female counterparts. A random sample of 15 firms was taken with the CEO age given in the table below.

Firm No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Male, age 39 38 73 54 24 57 49 63 48 44 26 64 42 45 61

Female, age 32 31 68 58 26 53 48 69 47 46 25 62 40 48 57

(a) Use the above data to calculate the mean and standard deviation of the differences between the ages of the male managers and their female counterparts. (10% Mark)

(b) Is there evidence that the mean difference in ages between male and female is non-zero? (5% Mark)

(c) Obtain a 95% confidence interval for the mean difference in ages of the male and their female colleagues. (5% Mark)

Question 3 (20% Mark)

In one or two paragraphs define and discuss the following concepts:

Part A

i. A standard “money demand” function used by researcher has the form

i uRGDPM +++=

210 lnln  , where M is the quantity of (real) money, GDP is the value

of (real) gross domestic product, and R is the value of the nominal interest rate measured in

percent per year. Suppose that 1 = 1 and 2 = -0.02. What will be happen to the value of M if GDP increases by 2%? What will happen to M if the interest rate increases from 4% to 5%? (3 % Mark)

ii. Over a period of one month, a survey was made on each of ten high street bank’s branch in a large urban area. Each branch operation was audited for a one-day period randomly chosen during the working week. For each branch, the mean money transaction flow, xi (in USD mil. per day), and the number of limit violations, yi, i = 1, 2, …, 10, were recorded. (3 % Mark)

Table 1

Transactions, x 5 5 5 10 10 15 25 25 30 50

Violations, y 2 1 1 4 2 5 8 2 5 10

Figure 1

Transactions, x

V io

la ti

o n

s ,

y

50403020100

10

8

6

4

2

0

Scatterplot of Violations, y vs Transactions, x

a. Comment on the data and graph above. What kind of model you would like to fit the data? Write down your model and explain briefly your model assumptions.

b. Without any further calculation comment on the suggestion that an intercept should be included in the model.

Part B

iii. Explain why two perfectly multicollinear regressors cannot be included in a linear multiple

regression. Give two examples of a pair of perfectly multicollinear regressors. (3 % Mark)

iv. While you were preparing your essay, your tutor mentioned to you “a stochastic error term must be added to your econometric model”. Do you agree with him? If yes or no – explain briefly and concisely your reasons. (3 % Mark)

v. Discuss the limitations of regression analysis. (3 % Mark)

vi. Financial and economic variables are often measured with error. Does this mean that the result

of regression analysis is unreliable? (3 % Mark)

vii. Why can’t we use empirical data to determine which variable is the independent variable and which is the dependent variable? (2 % Mark)