Question

Question: Deferred tax allowance study. A study was conducted to identify accounting choice variables that influence a manager’s decision to change the level of the deferred tax asset allowance at the firm (The Engineering Economist, January/February 2004). Data were collected for a sample of 329 firms that reported deferred tax assets in 2000. The dependent variable of interest (DTVA) is measured as the change in the deferred tax asset valuation allowance divided by the deferred tax asset. The independent variables used as predictors of DTVA are listed as follows:

LEVERAGE: x₁= ratio of debt book value to shareholder’s equity

BONUS: x₂ = 1 if firm maintains a management bonus plan,

0 if not

MVALUE: x₃ = market value of common stock

BBATH: x₄ = 1 if operating earnings negative and lower than last year,

0 if not

EARN: x₅ = change in operating earnings divided by total assets

A first-order model was fit to the data with the following results (p-values in parentheses):

R_a² = .280

$\hat{\mathbf{y}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{044}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{006}{\mathit{x}}_{\mathbf{1}}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{035}{\mathit{x}}_{\mathbf{2}}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{001}{\mathit{x}}_{\mathbf{3}}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{296}{\mathit{x}}_{\mathbf{4}}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{010}{\mathit{x}}_{\mathbf{5}}$

(.070) (.228) (.157) (.678) (.001) (.869)

1. Interpret the estimate of the β coefficient for x₄.
2. The “Big Bath” theory proposed by the researchers’ states that the mean DTVA for firms with negative earnings and earnings lower than last year will exceed the mean DTVA of other firms. Is there evidence to support this theory? Test using α = .05.
3. Interpret the value of R_a².

Short answer

Answer

1. The value of coefficient of is 0.296 which is positive indicating a positive relation among DTVA and BBATH(x₄) .
2. 95% significance level, it can be concluded that .${\beta }_4\ne 0$Hence it can be concluded with enough evidence that is not statistically significant for the model.
3. The value of R²_ais 0.28 indicating about 28% of variation in the data is explained by the model. This value is very low indicating that the model fitted to the data is not a good fit or ideal fit for the data.

Step-by-step solution

Given Information 

The predicted model is given as:
$y=0.044+0.006x_1-0.035x_2-0.001x_3+0.296x_4+0.010x_5$

Where y is the dependent variable and x’s are the dependent variable. The standard error of y is givens as 0.070, the standard error for the constant term is 0.228 and the standard error for $x_1,x_{2,}{x}_3,x_4,x_5$_,are 0.157, 0.678, 0.001, and 0.869 respectively. The value for and we have to conduct the test at $\alpha =.05$.

Interpretation of  β4

a.

The value of coefficient of x₄ is 0.296 which is positive indicating a positive relation among DTVA and BBATH (x₄) . However, the lower value of the coefficient indicates that the changes in DTVA due to the variable might not be very high (slope of the line is very steep).

Significance of β4 

b.

$$\begin{gathered} H_0:{\beta }_4=0 \\ {H}_a:{\beta }_4\ne 0 \end{gathered}$$

Here, t-test statistic,

$$\begin{gathered} t=\frac{{\hat{\beta }}_4}{s{\hat{\beta }}_4} \\ =\frac{0.296}{0.001} \\ =296 \end{gathered}$$

Value of $t_{0.025,328}$is 1.96

H₀ is rejected if $t-statistic>t_{0.05,24,24}$. For $\alpha =0.025$, since,$\mathbf{t}\mathbf{>}{\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{,}\mathbf{31}}$ sufficient evidence to reject H₀ at 95% confidence interval.

Therefore,${\mathbf{\beta }}_{\mathbf{4}}\ne 0$.

Hence, it can be concluded with enough evidence thatis not statistically significant for the model.

Interpretation of  R2a

c.

The adjusted R squared is a modified version of R-squared.It is a corrected goodness of fit measures for linear models, here the value ofR²_a is 0.28 indicating about 28% of variation in the data is explained by the model. This value is very low indicating that the model fitted to the data is not a good fit or ideal fit for the data.