Use the Stata data file thex.dta. The variables in the file are as follows:

1. Describe your data. Is your panel data balanced or unbalanced? Explain. Write down the number of firms and the number of years included in your sample. 9 marks

2. You want to estimate the model

CoEit  = ai  + b1ESGit  + b2sizeit  + b3MTBit  + b4levit  + uit                                                      (1)

where i identifies firms and t denotes the time period. What could the terms ai represent? Explain why it is important to control for individual specific effects in a panel data model.15 marks

3. Assume now ai = a0, a constant. Estimate the model using pooled OLS. Write down the fitted model. 5 marks

4. Test whether your assumption of a common intercept (used in point 3) is too strong. To this end, use the Breusch-Pagan LM test.

1.   a) Interpret the Stata results below. Explain in detail the test statistic performed.

35 marks

b) A study on financing terms reveals that some firms demand advance payment for the goods supplied to their customers. To assess which types of firms are likely to demand advance payments, a financial analyst uses OLS to estimate the model below:

AdvanceDi  = b0  + b1Agei +b2Profsi +b3Sizei + b4Ind1i + b5Ind2i  + ui

where

AdvanceD = 1 if a firm receives advance payments from its customers, 0 otherwise; Age = years since firm was established;

Profs = the ratio of firm profits to total sales;

Size = measured as the natural logarithm of firm’s total sales;

Ind1= 1 if the firm operates in industry 1, and 0 otherwise;

Ind2= 1 if the firm operates in industry 2, and 0 otherwise;

u = error term.

1) Demonstrate that the OLS error term is heteroskedastic. 20 marks

2) The firms in the sample operate in three different industries. Explain why only two industry dummies are included in the model. 10 marks

3) Using the logit estimator, the financial analyst obtains the estimated coefficients (estimated standard errors in brackets) below:

AdvanceDi  = -2.37 + 0.03Agei - 1.61 Profsi + 0.25Sizei + 0.66Ind1i + 1.06Ind2i

(0.56)   (0.01)        (0.48)            (0.02)         (0. 11)          (0. 10)

i) Do the logit results above provide support for the hypothesis that older firms are more likely to receive advance payments than younger firms? Explain. 10 marks

ii) Do the Logit estimates above suggest that the likelihood of receiving advance payments is 66% larger for firms in industry 1 relative to firms in industry 3, ceteris paribus? Explain. 10 marks

iii) Calculate the probability and the odds-ratio that a 20-year old firm operating in industry 3, with a 0.03 ratio of profits over sales, and of Size =12 is paid in advance by its customers. 15 marks

2. a) In line with the theory of the term structure of interest rates, you expect that when the Fed changes  the short-term rate on the government Treasury bill tbillyr1, the long-term government bond rate tbond30 eventually moves in the same direction. You know that both interest rates contain a unit root. Define stationarity and explain the concept of I(1) time series. 20 marks

b) You want to study the relationship between tbillyr1 and tbond30. Describe the test that helps you decide whether the relation between the two I(1) series is spurious. 30 marks

c) Define heteroskedasticity. What are the consequences of heteroskedasticity for the OLS estimator? In your answer, include formal notation and give an example to explain what heteroscedasticity means. 20 marks

d) You want to estimate the following model:

Yi    =  F0  +  F1X1i   +  F2X2i   +  ci

The variance of the error term is Var(ci)  =   X2(h)iG2 , where h is known. Explain why and how you would estimate the model above with generalised least squares. 30 marks

3. a) Define serial correlation. Explain the consequences of serially correlated errors for the OLS estimator. 20 marks

b) Explain how you would test the hypothesis β1 = 1 in the econometric model: Yt   =  F0   +  F1Yt−1   +  ct . 35 marks

c) A researcher builds a model in which a firm’s liquidity ratio depends on the firm’s profitability ratio and a dummy variable indicating whether the firm is listed on the stock exchange. In a second model, the researcher allows the firm’s listing status to influence the relation between its profitability and liquidity ratio. Explain how the researcher can build these two models. 25 marks

d) The estimates of the model Yi  = β0  + β1 X1i  + β2 X2i  + εi are presented below.