Estimate the above equation comment on your results and

Question

Question 1:

A well-known tool, which is employed by monetary authorities to track monetary policy, is the so-called Taylor rule. The aim of this exercise is to apply that tool to UK monetary policy. Data for this exercise are in Question_1.xlsx, where IR is the interest rate set by central bank, CPI is the consumer price index and GDP is the UK GDP volume, using 2005 as reference year. Data span from 1960q1 to 2004q4.

The Taylor rule can be represented as follows:

i_t = α + β₁inflation_t + β₂output_gap_t + ε_t

where i_t is the log of the interest rate, inflation_t is the inflation rate and output_gap_t is the difference between the actual level of output and the potential one.

a. Using the data contained in the dataset, construct the variables that you need in order to estimate eq. (1).

b. Estimate eq. (1), report the results and comment on them. Are the results consistent with Taylor's theory? Explain.

c. It is suggested that output_gap should weight half of inflation in determining the interest rate. Write correctly the null hypothesis and the alterative hypothesis of this test. Report the test and comment on its significance. Construct the test, report it and comment on its significance.

d. Someone suggests that if the coefficient associated to the inflation is equal to 0.8, output_gap is not relevant in explaining the variability of the dependent variable. Write down the correct null hypothesis and the alternative. Construct an appropriate test, report it and comment its significance.

e. A researcher suggests that the presence of heteroscedasticity in the residuals does not affect the results. Explain this fully and comment the result of such a test. Then, construct an appropriate test for detecting the presence of heteroscedasticity, explain it, report and comment the result of such a test.

f. A researcher suggests that the LM test should be always used to test for the presence of serial correlation. Do you agree? Suppose that you have a first order serial correlation. Explain two tests that you can use to detect the presence of serial correlation, report and comment their results.

g. If either serial correlation or heteroscedasticity is detected, apply the appropriate correction to your estimation. Report and explain your estimation results, by also commenting the difference with the estimations in point (b).

Question 2:

The Purchasing power parity (PPP hereafter) is based on the idea that two identical goods should be sold at the same price and at the same time. This implies that, taking into consideration the exchange rate between two countries, a good in country A should be sold at the same price in country B.

The aim of this exercise is to test whether PPP theory holds between Japan and US. The data for this exercise are contained in the file Question_2.xlsx, where CPIJPN is the Japanese Consumer Price Index, CPIUS is the US Consumer Price Index and YENUS is the US dollar to Japanese Yen nominal exchange rate (i.e. how many yen you need to by US$). Japan is the domestic country and US is the foreign country. Data have a monthly frequency and span from 1960 to 1995.

Let s_t be the log of the nominal exchange rate, p_t the log of CPIJPN and p_t* the log of CPIUS.

a. After inspecting the dataset, generate an appropriate Eviews workfile (pay attention to the frequency of the data).

b. Generate the real exchange rate, by applying the following formula:

q_t ≡ s_t -p_t +p_t*

Plot the variable q_t. Comment about the stationarity/non-stationarity of the variable.

c. Apply the appropriate unit root test for testing non-stationarity. State clearly which is your null hypothesis and briefly discuss the test, which you are going to apply. Report and explain the results from your test.

d. Suppose that you find that q_t is non-stationary. How many unit roots the series contains? Explain the procedure you implement to find the number unit of roots it contains. Based on your steps, if you believe that you need to implement some transformations, after each of them, plot the new series and run again the unit root test to check whether the variable is stationary or not.

e. Frenkel (1978) suggests that an alternative way to check for the validity of PPP theory consists of estimating the nominal exchange rate versus the differences in prices. More specifically, he suggests to estimate the following equation

s_t = α + β(p_t - p_t*) + ε_t

and then to test whether the parameter β is equal to 1.

1. Estimate the above equation, comment on your results and test the hypothesis that β = 1, specifying clearly which is your null hypothesis.

2. Apply the ADF test to check whether s_t and (p_t - p_t*) are stationary or non- stationary. Comment on your results [Hint: you may want to plot preliminarily the two variables to decide the specification of the test].

3. Are the results that you got from the estimation of equation at point 1 valid? Explain an appropriate approach to test whether s_t and (p_t -p_t*) are cointegrated or not. If necessary, carry out the test and comment on your results.

Question 3:

The competition in the banking industry has been debated extensively in the literature. Several approaches have been developed such as the Structure-Conduct-Performance paradigm (SCP), the Efficient-Structure hypothesis (ESH) and the New Economic Industrial Organization (NEIO). The Panzar and Rosse statistic belongs to the third line of research. Panzar and Rosse argue that the market power of a firm can be measured by the way in which the changes in the input prices affect the equilibrium revenues.

The objective of this exercise is to employ the Panzar and Rosse statistic to test the degree of competition in the Italian banking industry. The data are in the file named Question_3.xlsx. The dataset contains information for the 1066 banks over the period 1990-2010. The variables included in the dataset are:

1) name is the name of the bank;
2) year indicates the time period;
3) id is the identifier for each bank in the dataset;
4) ir is the net interest revenue;
5) deposit measures the deposits price;
6) labour is the labour cost;
7) capital is the capital cost;
8) loans is a proxy for the general level of credit risk faced by banks;
9) equity is a proxy for a general level of risk;
10) lnta, is the total asset, a proxy for the size of the bank. Notice that all the variables are in logs.

Let us consider the following model:

ir_it = α_i + β₁labour_it + β₂capital_it + β₃deposit_it + β₄loans_it + β₅equity_it + β₆lnta_it + μ_i + μ_t + ε_it

where μ_i and μ_t are the sets of bank specific and time effects, respectively. Note that the Panzar and Rosse statistics is calculated as the sum of the parameters β₁, β₂, and β₃ that the degree of competition is calculated as follows:

β₁ + β₂ + β₃ = 1 → Perfect competition

β₁ + β₂ + β₃ = 0 → Monoploy

β₁ + β₂ + β₃ ∈(0, 1) → Monopolistic competition

a. Generate an Eviews workfile and derive the summary statistics and the correlation matrix for the variables above.

b. Which estimator would you use to carry out your analysis? Is it more appropriate to use the OLS estimator or an alternative one? Discuss.

c. Estimate equation (1), report your results and comment.

d. In order to check the degree of competition in the banking sector test the following two null hypotheses:

H₀^A : β₁ + β₂ + β₃ = 1

H₀^A : β₁ + β₂ + β₃ = 0

Report your tests and comment. What is the degree of competition in the Italian banking system in the period you are considering? What can you argue if you reject both null hypotheses?

Since the degree of competition may be different according to the type of bank under investigation, it is better to split the sample in order to group banks according to a common characteristic. An idea could be to split the sample according to the size in order to have large and small banks.

e. Construct two sub-samples from your dataset, where the first subsample contains small banks and the second large banks. (Hint: using the summary statistics above generate two subsamples, one containing the banks with a total asset smaller than the mean value and one with a total asset larger than the mean value. The two subgroups will represent small and large banks, respectively) [Hint: you may find easier to this in Excel].

f. Generate the summary statistics of the mean variables for the two sub-samples.

g. Estimate equation (1) and tests hypotheses (2) and (3) for each sub-sample. Report and comment your results. Do you find any difference in the degree of banking competition between large and small banks? Discuss.

Question 4:

Firms usually desire to maintain financial flexibility in order to face the risk of high cost of external funds. This is the reason why they may want to keep sufficient cash reserve or spare debt capacity. The issue of financial conservatism has been studied from the point of view of both cash reserve and spare debt capacity. More specifically, some literature argues that if firms hold an amount of cash and cash equivalents not smaller than the 25% of their total asset, then they should be considered cash conservative. Some other literature arguments that if a firm holds total debt to total asset no greater than 20%, then this firm is leverage conservative.

The aim of this exercise is to evaluate, which variables affect the probability that a firm is either cash or leverage conservative. For this exercise, use the dataset named Question_4.xlsx. The dataset contains information about German firms. The variables included in the dataset are:

1. Capex is the ratio of capital expenditure to total asset;

2. Size is the log of total asset;

3. Sale is the log of net sales and it is employed as a proxy of firms revenues;

4. Mtb is firm's market to book;

5. Leverage is the amount of total debt to total asset;

6. Cf is the cashflow of eah firm to total asset;

7. Cashtoasset is the ration between cash and cash equivalents to total asset.

According to the main literature, we can model the probability of being cash conservative as follows:

Cash_coni = γ₀ + γ₁(CF/K)_i + y₂(leverage)_i + y₃(mtb)_i + y₄(capex)_i + y₅(size)_i + ε_i

a. Identify in the dataset the firms, which are cash conservative. Using Excel, the variable cashtoasset and the 25% threshold, identify them by constructing a dummy variable, which takes the value of 1 if cashtoasset is equal or greater than 0.25 and 0 otherwise. Import the data in Eviews, calculate and show the summary statistics for the variables above. Highlight the percentage of cash conservative firms. In addition, derive the correlation matrix for the main variables and discuss.

b. Now divide the sample between cash conservative and non-conservative firms and calculate the summary statistics for both sub-samples. Report, comment and compare the summary statistics for the two su-samples. [Hint: you may find easier to split the sample in Excel before importing the sub-samples in Eviews].

c. The dependent variable is a binary variable (equal to 1 if firm is conservative and 0 otherwise). Explain whether the OLS estimator is adequate to estimate the probability of being cash conservative. Explain this fully. Estimate the above equation, report and comment the results of your estimation.

Let us now consider which are the determinants of being leverage conservative. According to the literature, we can model that probability as follows:

Lev_coni = δ₀ + δ₁(size)_i + δ₂(cashtoasset)_i + δ₃(mtb)_i + δ₄(sale)_i + ε_i

where Lev_con is a dummy variable taking the variable of 1 is the firm is leverage conservative and 0 otherwise.

d. Repeat the same analysis you carried out in (a) to (c), after constructing the dummy variable Lev_con using the variable leverage and the 20% threshold. Notice that Lev_con takes the value of 1 if leverage is not greater than 0.20 and 0 otherwise.

A new approach points out that if a firm is cash conservative, it should be leverage conservative as well. In this case we refer to those firms as financially conservative. We verify this hypothesis by estimating the following equation:

Fin_con_i = μ + μ₁(size)_i + μ₂(sale)_i + μ₃(mtb)_i + ε_i

e. Repeat the same analysis in (a) to (c), once you constructed the variable Fin_con. Remind that the variable takes the value of 1 if a firm is both leverage and cash conservative and 0 otherwise.

Attachment:- Data.xlsx