You are analyzing the cross-sectional variation in the number of financial analysts that follow a company (also the subject of Problems 3 and 8). You believe that there is less analyst following for companies with a greater debt-to-equity ratio and greater analyst following for companies included in the S&P 500 Index. Consistent with these beliefs, you estimate the following regression model.
(Analysts following) i = b0 + b1(D/E) i + b2(S&P) i + ε i
Where
(Analysts following) i = natural log of (1 + Number of analysts following company i)
(D/E) i = debt-to-equity ratio for company i
S&P i = inclusion of company i in the S&P 500 Index (1 if included; 0 if not included)
In the preceding specification, 1 is added to the number of analysts following a company because some companies are not followed by any analysts, and the natural log of 0 is indeterminate. The following table gives the coefficient estimates of the above regression model for a randomly selected sample of 500 companies. The data are for the year 2002.
Coefficient Estimates from Regressing Analyst Following on Debt-to-Equity Ratio and S&P 500
Membership, 2002

You discuss your results with a colleague. She suggests that this regression specification may be erroneous, because analyst following is likely to be also related to the size of the company.
A. What is this problem called, and what are its consequences for regression analysis?
B. To investigate the issue raised by your colleague, you decide to collect data on company size also. You then estimate the model after including an additional variable, Size
i, which is the natural log of the market capitalization of company i in millions of dollars. The following table gives the new coefficient estimates.
Coefficient Estimates from Regressing Analyst Following on Size, Debt-to-Equity Ratio, and S&P 500 Membership, 2002

What do you conclude about the existence of the problem mentioned by your colleague in the original regression model you had estimated?

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Standard Error 0.0582 Coefficient 1.5367 -0.1043 t-Statistic Intercept (D/E), S&P, 26.4038 -1.4649 14.5327 0.0712 0.0841 1.2222 n= 500 Coefficient -0.0075 0.2648 Standard Error t-Statistic -0.0616 Intercept Size; (D/E); 0.1218 13.8639 0.0191 0.0608 -0.1829 -3.0082 4.5898 S&P; 0.4218 0.0919 n= 500