Conservatism Approaches

The Basu Model

This document compares three alternative approaches to conservatism. The first approach was formulated by Basu. Basu (1997) identifies conservatism as more timely recognition in earnings of bad news regarding future cash flows than good news and states that in efficient markets, stock returns symmetrically and quickly reflect all publicly available news. Since earnings is expected to be strongly associated with concurrent negative unexpected returns as a proxy for bad news than positive unexpected returns as a proxy for good news, his model employs stock return in order to measure news

where EPSi,t is the earnings per share of firm i at year t; Pi,t-1 is the price per share at the end of the three months after the previous fiscal year; DVi,t is a dummy variable that takes the value 1 if returns of firms i at year t are negative and 0 otherwise; Ri,t is the annually compounded stock returns of firm i at year t; and RDVi,t is the stock return of firm i at year t times the individual DV dummy variable. Thus, RDVi,t will be equal to Ri,t if returns are negative and zero otherwise.

We fitted a linear model (estimated using OLS) for our data to predict our dependent variable with dummy (formula: dv ~ dummy + return + dummy * return). The coefficients are as follows

model_basu$coefficients
##  (Intercept)        dummy       return dummy:return 
##    1.3118258   -0.7809083   -2.1131526    5.3378168

The model explains a statistically significant and substantial proportion of variance (R2 = 0.74, F(3, 1544) = 1447.03, p < .001, adj. R2 = 0.74). The model’s intercept, corresponding to dummy = 0, is at 1.31 (95% CI [0.83, 1.79], t(1544) = 5.39, p < .001). Within this model:

  • The effect of dummy is statistically non-significant and negative (beta = -0.78, 95% CI [-1.66, 0.10], t(1544) = -1.74, p = 0.082; Std. beta = 0.04, 95% CI [-0.02, 0.09])
  • The effect of return is statistically significant and negative (beta = -2.11, 95% CI [-2.18, -2.05], t(1544) = -65.78, p < .001; Std. beta = 0.31, 95% CI [-0.10, 0.72])
  • The interaction effect of return on dummy is statistically significant and positive (beta = 5.34, 95% CI [3.48, 7.20], t(1544) = 5.64, p < .001; Std. beta = 1.09, 95% CI [0.71, 1.47])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation. and We fitted a linear model (estimated using OLS) to predict dv with return (formula: dv ~ dummy + return + dummy * return). The model explains a statistically significant and substantial proportion of variance (R2 = 0.74, F(3, 1544) = 1447.03, p < .001, adj. R2 = 0.74). The model’s intercept, corresponding to return = 0, is at 1.31 (95% CI [0.83, 1.79], t(1544) = 5.39, p < .001). Within this model:

  • The effect of dummy is statistically non-significant and negative (beta = -0.78, 95% CI [-1.66, 0.10], t(1544) = -1.74, p = 0.082; Std. beta = 0.04, 95% CI [-0.02, 0.09])
  • The effect of return is statistically significant and negative (beta = -2.11, 95% CI [-2.18, -2.05], t(1544) = -65.78, p < .001; Std. beta = 0.31, 95% CI [-0.10, 0.72])
  • The interaction effect of return on dummy is statistically significant and positive (beta = 5.34, 95% CI [3.48, 7.20], t(1544) = 5.64, p < .001; Std. beta = 1.09, 95% CI [0.71, 1.47])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation.

The Ball and Shivakumar Model

On the other hand, the asymmetric accrual to cash-flow measure developed by Ball and Shivakumar (2005) is a non-stock-market version of the Basu measure and is based on the following regression:

where: ACCt : Accruals measured as ∆inventory + ∆debtors + ∆other current assets - ∆creditors - ∆other current liabilities – depreciation CFOt : cash-flow for period t DCFOt: dummy variable that takes the value 0 if CFOt ≥ 0 and 1 if CFOt < 0. The slope coefficients β3M and β3A in equations (1) and (2) are regarded as the measurement for the level of conditional conservatism. Therefore, both models follow the same underlying principle of asymmetric timeliness with a similar structure. However, they differ due to their choices of the proxies for economic news and earnings. Basu’s model uses stock return as the proxy for news, while the Ball and Shivakumar’s model employs operating cash-flow. Further, unlike the Basu model, accrual to cash-flow measure uses only the accrual component of earnings as it argues that accounting conservatism primarily affects the accruals component of earnings rather than the cash flows component.

We fitted a linear model (estimated using OLS) to predict ACCt with DCFOt (formula: ACCt ~ DCFOt + CFOt + DCFOt * CFOt). The coefficients are as follows

model_ball_shi$coefficients
## (Intercept)       DCFOt        CFOt  DCFOt:CFOt 
## -0.03097991 -0.09906661 -0.56344500  0.27184398

The model explains a statistically significant and weak proportion of variance (R2 = 0.06, F(3, 1545) = 34.08, p < .001, adj. R2 = 0.06). The model’s intercept, corresponding to DCFOt = 0, is at -0.03 (95% CI [-0.05, -0.01], t(1545) = -3.70, p < .001). Within this model:

  • The effect of DCFOt is statistically significant and negative (beta = -0.10, 95% CI [-0.13, -0.07], t(1545) = -6.24, p < .001; Std. beta = -0.16, 95% CI [-0.22, -0.10])
  • The effect of CFOt is statistically significant and negative (beta = -0.56, 95% CI [-0.70, -0.42], t(1545) = -7.90, p < .001; Std. beta = -0.41, 95% CI [-0.50, -0.31])
  • The interaction effect of CFOt on DCFOt is statistically significant and positive (beta = 0.27, 95% CI [0.11, 0.44], t(1545) = 3.20, p = 0.001; Std. beta = 0.08, 95% CI [0.03, 0.12])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation. and We fitted a linear model (estimated using OLS) to predict ACCt with CFOt (formula: ACCt ~ DCFOt + CFOt + DCFOt * CFOt). The model explains a statistically significant and weak proportion of variance (R2 = 0.06, F(3, 1545) = 34.08, p < .001, adj. R2 = 0.06). The model’s intercept, corresponding to CFOt = 0, is at -0.03 (95% CI [-0.05, -0.01], t(1545) = -3.70, p < .001). Within this model:

  • The effect of DCFOt is statistically significant and negative (beta = -0.10, 95% CI [-0.13, -0.07], t(1545) = -6.24, p < .001; Std. beta = -0.16, 95% CI [-0.22, -0.10])
  • The effect of CFOt is statistically significant and negative (beta = -0.56, 95% CI [-0.70, -0.42], t(1545) = -7.90, p < .001; Std. beta = -0.41, 95% CI [-0.50, -0.31])
  • The interaction effect of CFOt on DCFOt is statistically significant and positive (beta = 0.27, 95% CI [0.11, 0.44], t(1545) = 3.20, p = 0.001; Std. beta = 0.08, 95% CI [0.03, 0.12])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation.

Ozgecan Model

model_ozge <- lm(DV ~ dummy_ACCt_2 + ACCt_2 + d_ACCt,  data=ozge_step2)

We fitted a linear model (estimated using OLS) to predict DV with dummy_ACCt_2 (formula: DV ~ dummy_ACCt_2 + ACCt_2 + d_ACCt). The model explains a statistically significant and very weak proportion of variance (R2 = 0.01, F(3, 1545) = 7.25, p < .001, adj. R2 = 0.01). The model’s intercept, corresponding to dummy_ACCt_2 = 0, is at -2.37 (95% CI (-4.06, -0.69), t(1545) = -2.76, p = 0.006). Within this model:

The effect of dummy ACCt 2 is statistically significant and positive (beta = 2.76, 95% CI (0.90, 4.62), t(1545) = 2.91, p = 0.004; Std. beta = 0.08, 95% CI (0.03, 0.13)) The effect of ACCt 2 is statistically non-significant and positive (beta = 8.06, 95% CI (-11.27, 27.39), t(1545) = 0.82, p = 0.413; Std. beta = 0.08, 95% CI (-0.11, 0.26)) The effect of d ACCt is statistically non-significant and positive (beta = 3.98, 95% CI (-16.16, 24.12), t(1545) = 0.39, p = 0.698; Std. beta = 0.04, 95% CI (-0.15, 0.22)) Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation., We fitted a linear model (estimated using OLS) to predict DV with ACCt_2 (formula: DV ~ dummy_ACCt_2 + ACCt_2 + d_ACCt). The model explains a statistically significant and very weak proportion of variance (R2 = 0.01, F(3, 1545) = 7.25, p < .001, adj. R2 = 0.01). The model’s intercept, corresponding to ACCt_2 = 0, is at -2.37 (95% CI (-4.06, -0.69), t(1545) = -2.76, p = 0.006). Within this model:

The effect of dummy ACCt 2 is statistically significant and positive (beta = 2.76, 95% CI (0.90, 4.62), t(1545) = 2.91, p = 0.004; Std. beta = 0.08, 95% CI (0.03, 0.13)) The effect of ACCt 2 is statistically non-significant and positive (beta = 8.06, 95% CI (-11.27, 27.39), t(1545) = 0.82, p = 0.413; Std. beta = 0.08, 95% CI (-0.11, 0.26)) The effect of d ACCt is statistically non-significant and positive (beta = 3.98, 95% CI (-16.16, 24.12), t(1545) = 0.39, p = 0.698; Std. beta = 0.04, 95% CI (-0.15, 0.22)) Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation. and We fitted a linear model (estimated using OLS) to predict DV with d_ACCt (formula: DV ~ dummy_ACCt_2 + ACCt_2 + d_ACCt). The model explains a statistically significant and very weak proportion of variance (R2 = 0.01, F(3, 1545) = 7.25, p < .001, adj. R2 = 0.01). The model’s intercept, corresponding to d_ACCt = 0, is at -2.37 (95% CI (-4.06, -0.69), t(1545) = -2.76, p = 0.006). Within this model:

The effect of dummy ACCt 2 is statistically significant and positive (beta = 2.76, 95% CI (0.90, 4.62), t(1545) = 2.91, p = 0.004; Std. beta = 0.08, 95% CI (0.03, 0.13)) The effect of ACCt 2 is statistically non-significant and positive (beta = 8.06, 95% CI (-11.27, 27.39), t(1545) = 0.82, p = 0.413; Std. beta = 0.08, 95% CI (-0.11, 0.26)) The effect of d ACCt is statistically non-significant and positive (beta = 3.98, 95% CI (-16.16, 24.12), t(1545) = 0.39, p = 0.698; Std. beta = 0.04, 95% CI (-0.15, 0.22)) Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using a Wald t-distribution approximation.

The model explains a statistically significant and very weak proportion of variance (R2 = 0.01, F(3, 1545) = 7.25, p < .001, adj. R2 = 0.01)

Model 1Model 2Model 3
(Intercept)0.63 ** -0.06 ***-3.04 ***
(0.24)   (0.01)   (0.86)   
dummy0.93                  
(0.69)                 
return-10.86 ***              
(0.17)                 
dummy:return27.44 ***              
(4.87)                 
DCFOt       -0.08 ***       
       (0.02)          
CFOt       -0.08 ***       
       (0.01)          
DCFOt:CFOt       0.04 **        
       (0.01)          
dummy_ACCt_2              2.76 ** 
              (0.95)   
ACCt_2              0.97    
              (1.19)   
d_ACCt              0.45    
              (1.16)   
N1548       1549       1549       
R20.74    0.06    0.01    
All continuous predictors are mean-centered and scaled by 1 standard deviation. *** p < 0.001; ** p < 0.01; * p < 0.05.