On Dummy Independent and Dependent Variables; to Be Continued

FIN822 In Class Work 2

(On dummy independent and dependent variables; to be continued)

1. Question on dummy regressor

You are investigating ROA ratio in a sample of 100 firms. About 40 firms are in the pharmaceutical industry; other firms are in other industries. How could you define a dummy variable in a regression to test whether pharmaceutical firms tend to have higher or lower ROA ratios than firms in other industries?

2. Question on interactive dummy regressor

It was 1999. You are investigating the relationship between MB to ROA in a sample of internet stocks. About 40 firms have positive ROA while other firms report negative ROA. How would you define a dummy variable in a regression to test the relationship between MB to ROA for these internet stocks? Notice these two groups may behave differently.

3. Question on self-selection

To test the effectiveness of a job training program on the subsequent wages of workers, we specify the model:

where train is a dummy variable equal to 1 if a worker participated in the program.

Think of the error term u as containing unobserved worker ability. If less able workers have a greater chance of being selected for the program, and you use an OLS analysis, what can you say about the likely bias in the OLS estimator of ?

4. Question on interpretation of logit model coefficient

5. You are analyzing the relationship between one-year-ahead stock return (future one year return) and current year ROA (return on assets). The following regressions are run actually on the real data of over 5000 stocks. Dummy variable D takes value 0 if ROA>=0 and 1 if ROA<0. The output is listed below.

Parameter Estimates
Variable / Parameter / Standard / tValue / Pr|t|
Estimate / Error
Intercept / 0.025 / 0.005 / 5.09 / <.0001
ROA / 0.033 / 0.033 / 0.99 / 0.3201
D / -0.040 / 0.006 / -7.3 / <.0001
D*ROA / 0.107 / 0.034 / 3.11 / 0.0019

5(a) Please write down the regression models for non-negative ROA stocks and negative ROA stocks separately.

5(b) Explain your findings.

Answer:

1. You could define a dummy variable “D”. D=0 for pharmaceutical firms (base group) and 1 otherwise. The coefficient in regression will measure the difference between these two groups (mean ROA of non-pharmaceutical firm – mean ROA of pharmaceutical firms). The intercept (beta zero) gives the mean ROA for pharmaceutical firms.

Alternatively, you could define a dummy variable “D”. D=0 for non-pharmaceutical firms and 1 otherwise. The only difference is that you need to interpret the coefficient and intercept differently. Coefficient will measure mean ROA of pharmaceutical firm – mean ROA of non-pharmaceutical firms. Intercept: mean ROA of non-pharmaceutical firms.

2. You could define a dummy variable “D”. D=0 for firms with positive ROA while D=1 for firms with negative ROA. The coefficient in regression will tell the slope for positive ROA firms while the slope gives the slope for firms with negative earnings.

3. The estimator of is likely smaller than the true effect, i.e., the estimator is biased downward. This happens because less able workers, who likely will still have lower wages than more capable works after training, are more likely to participate in the program (more likely to have train=1).

5(a) Please write down the regression models for non-negative ROA stocks and negative ROA stocks separately.

For stocks with ROA>=0: One-year-ahead-return=0.025+0.033*ROA + error term

For stocks with ROA<0: One-year-ahead-return= -0.015+0.14*ROA + error term

5(b) Explain your findings.

For firms with profits, future one-year-ahead stock return is expected to be reliably/significantly positive, but the magnitude of ROA has no significant relationship with one-year-ahead return. (Because magnitude of t on ROA=0.99 <2)

For firms with loss, future one-year-ahead stock return is expected to be reliably/significantly negative. Moreover, the larger the loss, the lower will be one-year-ahead expected return. (Because magnitude of t on ROA =3.11>2)