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Solved: Corporate sustainability and firm characteristics.
Chapter 12, Problem 77E(choose chapter or problem)
Corporate sustainability and firm characteristics. Refer tothe Business and Society (March 2011) study on how firm size and firm type impact corporate sustainability behaviors,Exercise 9.7 (p. 492). Recall that Certified Public Accountants(CPAs) were surveyed on their firms’ likelihood of reporting sustainability policies (measured as a probability between 0and 1). The CPAs were divided into four groups depending on firm size (large or small) and firm type (public orprivate): large/public, large/private, small/public, and small/private. One goal of the analysis is to determine whether the mean likelihood of reporting sustainability policies differs depending on firm size and firm type.
a. Consider a single qualitative variable representingthe four size/type categories. Create the appropriatedummy variables for representing this qualitative variable as an independent variable in a regression modelfor predicting likelihood of reporting sustainabilitypolicies (y).
b. Give the equation of the model, part a, and interpreteach of the model parameters.
c. The global F-test for the model resulted in \(p \text {-value }<.001\).Give a practical interpretation of this result.
d. Now consider treating firm size and firm type as two different qualitative independent variables in a modelfor likelihood of reporting sustainability policies (y).Create the appropriate dummy variables for representing these qualitative variables in the model.
e. Refer to part d. Write a model for E(y) as a function of firm size and firm type, but do not includeinteraction. (This model is called the main effectsmodel.)
f. Refer to the model, part e. For each combination of firm size and firm type (e.g., large/public), write E(y) asa function of the model parameters.
g. Use the results, part f, to show that for the main effectsmodel, the difference between the mean likelihoodsfor large and small firms does not depend on firm type.
h. Write a model for E(y) as a function of firm size, firm type, and size \(\times\) type interaction.
i. Refer to the model, part h. For each combination of firm size and firm type (e.g., large/public), write E(y) asa function of the model parameters.
j. Use the results, part i, to show that for the interaction model, the difference between the mean likelihoods forlarge and small firms does depend on firm type.
Questions & Answers
QUESTION:
Corporate sustainability and firm characteristics. Refer tothe Business and Society (March 2011) study on how firm size and firm type impact corporate sustainability behaviors,Exercise 9.7 (p. 492). Recall that Certified Public Accountants(CPAs) were surveyed on their firms’ likelihood of reporting sustainability policies (measured as a probability between 0and 1). The CPAs were divided into four groups depending on firm size (large or small) and firm type (public orprivate): large/public, large/private, small/public, and small/private. One goal of the analysis is to determine whether the mean likelihood of reporting sustainability policies differs depending on firm size and firm type.
a. Consider a single qualitative variable representingthe four size/type categories. Create the appropriatedummy variables for representing this qualitative variable as an independent variable in a regression modelfor predicting likelihood of reporting sustainabilitypolicies (y).
b. Give the equation of the model, part a, and interpreteach of the model parameters.
c. The global F-test for the model resulted in \(p \text {-value }<.001\).Give a practical interpretation of this result.
d. Now consider treating firm size and firm type as two different qualitative independent variables in a modelfor likelihood of reporting sustainability policies (y).Create the appropriate dummy variables for representing these qualitative variables in the model.
e. Refer to part d. Write a model for E(y) as a function of firm size and firm type, but do not includeinteraction. (This model is called the main effectsmodel.)
f. Refer to the model, part e. For each combination of firm size and firm type (e.g., large/public), write E(y) asa function of the model parameters.
g. Use the results, part f, to show that for the main effectsmodel, the difference between the mean likelihoodsfor large and small firms does not depend on firm type.
h. Write a model for E(y) as a function of firm size, firm type, and size \(\times\) type interaction.
i. Refer to the model, part h. For each combination of firm size and firm type (e.g., large/public), write E(y) asa function of the model parameters.
j. Use the results, part i, to show that for the interaction model, the difference between the mean likelihoods forlarge and small firms does depend on firm type.
ANSWER:Step 1 of 11
(a)
The firms’ likelihood was surveyed and the sustainability policies were reported. Here, a qualitative variable represents the four size/type categories. Hence, the number of dummy variables required to represent the independent variables for predicting likelihood of reporting sustainability (y) for the regression model is three. The dummy variables are defined as given below:
\(\begin{array}{l}
x_{1}=\left\{\begin{array}{lc}
1 & \text { if large/private } \\
0 & \text { otherwise }
\end{array}\right. \\
x_{2}=\left\{\begin{array}{ll}
1 & \text { if } \text { small/public } \\
0 & \text { otherwise }
\end{array}\right. \\
x_{3}=\left\{\begin{array}{ll}
1 & \text { if } \text { small/private } \\
0 & \text { otherwise }
\end{array}\right.
\end{array}\)