4. The Role of Accounting, Market and Macroeconomic Variables for the
4.6.1. Marginal Effects and Changes in Predicted Probabilities
The parameters estimated from binary response models, unlike those estimated by linear models, cannot be directly interpreted because they do not provide useful information that fully describes the relationship between the independent variables and the outcome (Long and Freese, 2003). Previous financial distress and corporate failure prediction models constructed using binary response methodologies invariably focus on the overall discriminating and/or predictive accuracy of the models and very rarely do they provide an interpretation of the relationship between the predictor variables and the binary outcome. Such studies report solely the estimates obtained from binary response models and provide an interpretation of the direction of the relationship based on the sign of the estimate. Nevertheless, the basic output (the coefficient estimates) obtained by performing binary response models cannot explain the effects of the individual variables on the model’s outcomes because of their non-linear nature. Marginal effects and changes in predicted probabilities are appropriate tools to treat this issue.
This section presents results of the computation of marginal effects of individual regressors as well as graphic representations of predicted probabilities of failed companies.
This section intends to fill an important gap in the default/financial distress prediction literature, where the measurement of expected instantaneous changes in the response variable (corporate default in the present study) as a function of a change in a specific predictor variables while keeping all the other covariates constant, has been overlooked. As previously discussed, marginal effects measurements (defines as the computation of the partial derivative of the event probability with respect to the predictor of interest) are very useful to the interpretation of the individual effects of the regressors on the dependent variable in discrete dependent variable models, or binary response models (logit regression in the present study). With regard to their calculation, the present’s study’s methodology consists of outputting the marginal effects estimated at each observation in the dataset and then computing the sample average of individual marginal effects in order to obtain the overall marginal effects. SAS statistical software code was employed to generate the estimated marginal effects. Figures of changes in predicted probabilities were generated by plotting the vector reflecting the variations in the predicted probability of default (the predicted probability that the failure indicator, Corporate_Default = 1) when the change in an individual regressor ranges from its approximate minimum to its maximum observed value, keeping all the other covariates constant at their means113.
113 The SAS statistical package was also employed for this calculation.
Table 4-9 Marginal Effects
This table reports the marginal effects (in percentages) for the ‘accounting only’ model, the
‘accounting plus macroeconomic indicators’ model, the ‘full’ model including also market variables, or Model 1, Model 2 and Model 3 respectively. Additionally, marginal effects are generated for a
‘market only’ model and a ‘market plus macroeconomic variables,’ Model 4 and Model 5, for comparison purposes. n represents the number of observations. Marginal effects are intended to measure the expected instantaneous changes in the response variable (the corporate default indicator) as a function of a change in a specific predictor variable while keeping all the other covariates constant. The methodology used in the present study to generate the marginal effects consists of outputting the individual marginal effects estimated at each observation in the dataset and then calculating their sample average in order to obtain the overall marginal effect.
Variable Model 1 Model 2 Model 3 Model 4 Model 5
t-1 t-2 t-1 t-2 t-1 t-2 t-1 t-2 t-1 t-2 TFOTL -1.592 -1.438 -1.529 -1.431 -1.842 -1.537
TLTA 2.980 2.392 3.028 2.431 1.648 1.123 NOCREDINT -0.693 -0.511 -0.710 -0.532 -0.772 -0.361 COVERAGE -1.002 -0.772 -0.948 -0.737 -0.283 -0.023
RPI 0.035 0.012 0.020 -0.006 0.014 -0.008
SHTBRDEF 0.474 0.140 0.307 -0.112 0.276 -0.096
PRICE -0.441 -0.371 -0.483 -0.408 -0.500 -0.413
ABNRET -1.479 -1.750 -2.046 -1.810 -2.012 -1.813
IDYRISK 1.678 2.368 3.278 3.779 3.093 3.996
SIZE -0.153 -0.169 -0.339 -0.277 -0.334 -0.286
MCTD -2.074 -2.085 -2.577 -2.279 -2.497 -2.268
n 18,276 15,909 18,070 15,703 14,255 12,249 15,468 13,263 15,468 13,263
The marginal effects presented in Table 4-9 reflect a measure of the impact of the regressors on the response variable. Marginal effects were computed for all five models with information one and two years prior to the event of default, for comparison purposes.
The predictor variable with the largest absolute impact in Model 1 and Model 2 (the accounting-based models) is TLTA, followed by TFOTL, COVERAGE and CREDINT, in decreasing order of magnitude. The same analysis holds when the models are estimated in both t-1 and t-2, invariably. The macroeconomic variables RPI and SHTBRDEF yield the smallest impact on the expected instantaneous changes in the response variable while keeping all other covariates constant. A clear pattern is also observed for the market based models (Model 4 and Model 5); the regressor with the largest impact in absolute terms is IDYRISK, followed by MCTD, ABNRET and PRICE, in decreasing order of magnitude in both t-1 and t-2. Similar to the accounting-based models, the macroeconomic variables display the smallest individual impact on the expected instantaneous changes in the response variables corporate default while keeping all other covariates constant. Finally, from the overall marginal effects for the comprehensive model (Model 3), it can be observed that the regressor with the largest absolute impact is MCTD in t-1 and IDYRISK
in t-2, both market variables. The analysis of the relative effects of individual regressors included in the ‘full’ model reflects an important finding: when the model is estimated with information one year prior to the event of corporate default both market and accounting variable seem to have very similar individual effects on the response variable, however, when Model 3 is estimated with information two years prior to the event of default, market variables seem to have the largest absolute impact, suggesting that market variables perform better than accounting variables in t-2. In t-1, the decreasing order of magnitude (in absolute terms) of the regressors of Model 3 is as follows: MCTD, TFOTL, IDYRISK, TLTA, and ABNRET; whereas in t-2 the order is IDYRISK, MCTD, ABNRET, TFOTL, and TLTA. It can be therefore concluded that market variables do contain additional information (performing even better that accounting variables in t-2) that is relevant to the prediction of corporate failure and that they perform best when they are used as complements to financial ratios.
Presenting and analysing marginal effects for all the models in the study filled a gap in the default prediction literature that lacked a measure of the individual instantaneous contribution of a change of a specific variable on the response variable (the specific definition of corporate failure used in the present analysis), while keeping all other regressors constant. Additionally, the present study goes further by presenting the vector of predicted probabilities for all the individual variables’ specific minimum and maximum ranges where they have the most impact in the likelihood of corporate default, while keeping all the other covariates constant at their respective means. Thus, figures 3-4, 3-5, and 3-6 show the changes in predicted probabilities for accounting, macroeconomic and market variables, respectively, when the Corporate Default indicator is equal to 1. The importance of these figures is that they clearly show the magnitude as well as the directionality of each regressor reflected by the slope and inclination of the vectors, plotted at various levels of the independent variables.
Figure 4-5 Changes in Predicted Probabilities – Financial Statement Ratios
The figure plots the vectors reflecting changes in predicted probabilities (for Corporate Default
= 1) at different levels of the accounting independent variables Total Funds from Operations to Total Liabilities (TFOTL), Total Liabilities to Total Assets (TLTA), the No Credit Interval (NOCREDINT), and Interest Coverage (COVERAGE), keeping all the other covariates constant at their mean values (TFOTL = 0.09, TLTA = 0.495, NOCREDINT = -0.18, COVERAGE = 0.582, RPI = 178.4, SHTBRDEF = 2.058, PRICE = 4.409, ABNRET = -0.1, IDYRISK = 0.122, SIZE = -10.1, MCTD = 0.913). The computation was made taking into account all the variables included in the ‘Full’ model or Model 3 (financial statement ratios, macroeconomic indicators and market variables). Predicted probabilities are estimated employing an approximate value of the minimum and maximum ranges of the independent variables. In this way, the predicted probabilities for all levels of a variable can be observed. This figure reports the predicted probabilities for the ‘Full’ model estimated in period t-1, the vectors estimated using the full model in t-2 have very similar shapes, so they were not reported in the present study.
Figure 4-6 Changes in Predicted Probabilities – Market Variables
The figure plots the vectors reflecting changes in predicted probabilities (for Corporate Default
= 1) at different levels of the market independent variables Share Price (PRICE), Abnormal Returns (ABNRET), the relative Size of the company (SIZE), and the ratio Market Capitalisation to Total Debt (MCTD), keeping all the other covariates constant at their mean values (TFOTL = 0.09, TLTA = 0.495, NOCREDINT = -0.18, COVERAGE = 0.582, RPI = 178.4, SHTBRDEF = 2.058, PRICE = 4.409, ABNRET = -0.1, IDYRISK = 0.122, SIZE = - 10.1, MCTD = 0.913). The computation was made taking into account all the variables included in the ‘Full’ model or Model 3 (financial statement ratios, macroeconomic indicators and market variables). Predicted probabilities are estimated employing an approximate value of the minimum and maximum ranges of the independent variables. In this way, the predicted probabilities for all levels of a variable can be observed. This figure reports the predicted probabilities for the ‘Full’ model estimated in period t-1, the vectors estimated using the full model in t-2 have very similar shapes, so they were not reported in the present study.
Figure 4-7 Changes in Predicted Probabilities – Macroeconomic Indicators
The figure plots the vectors reflecting changes in predicted probabilities (for Corporate Default
= 1) at different levels of the macroeconomic independent variables Retail Price Index (RPI), and the proxy for interest rates, the Deflated Short Term Bill Rate (SHTBRDEF), keeping all the other covariates constant at their mean values (TFOTL = 0.09, TLTA = 0.495, NOCREDINT
= -0.18, COVERAGE = 0.582, RPI = 178.4, SHTBRDEF = 2.058, PRICE = 4.409, ABNRET
= -0.1, IDYRISK = 0.122, SIZE = -10.1, MCTD = 0.913). The computation was made taking into account all the variables included in the ‘Full’ model or Model 3 (financial statement ratios, macroeconomic indicators and market variables). Predicted probabilities are estimated employing an approximate value of the minimum and maximum ranges of the independent variables. In this way, the predicted probabilities for all levels of a variable can be observed. This figure reports the predicted probabilities for the ‘Full’ model estimated in period t-1, the vectors estimated using the full model in t-2 have very similar shapes, so they were not reported in the present study.
Figure 4-5 shows the behaviour of the predicted probabilities of corporate default at different values of each of the financial statement ratios. From the figure we can observe that the TFOTL variable displays the steepest slope relative to the other ratios, indicating that a given change in the level of this variable114 will have the largest impact on the predicted probability of corporate failure, when all other variables are kept constant at their means. The slope of the TFOTL vector also shows that there is a negative relationship between the predicted probability and the level of the variable: there is a considerable decrease of the predicted probabilities of corporate default as the TFOTL variable approaches its maximum value (1) after being transformed using the TANH function. The second variable in importance is TLTA: unlike TFOTL, there is a positive relationship between this ratio and the probability of corporate default. This analysis is consistent with the prediction of the present study, as TLTA is a measure of financial leverage: the higher the level of the variable, the greater the probability of failure. However, the impact is not as important as it is in the case of TFOTL as it can be observed that TLTA’s slope is less steep than the firm’s performance measure one. In other words, a change in its value produces a smaller effect than the one observed when there is a change in the magnitude of TFOTL, as shown by the slope of the vector. Changes in the magnitude of NOCREDINT, on the other hand, are negatively related to the probability of corporate default, an can be
114 Reflecting a measure of the firm’s performance.
considered as having the third most important impact among financial statement ratios, followed by COVERAGE, whose slope is almost flat, indicating a very small negative impact.
As posited, the market-based variables PRICE, ABNRET, SIZE, and MCTD display a negative relationship between variations in individual levels and predicted probabilities of corporate default. Also as expected, only the proxy for the firm’s volatility of returns is positively related to the likelihood of default. The covariate with the largest impact is PRICE, as its vector displays the steepest slope, meaning that a change in the level of this variable (relative to the other covariates) will produce the highest change in the probability of failure. It is followed by MCTD, ABNRET, SIZE, and IDYRISK.
Interestingly, the vectors’ slopes of the macroeconomic indicators RPI and SHTBRDEF are steeper than the financial statement ratios TLTA, NOCREDINT, and COVERAGE, which could lead us to conclude that the have a larger impact on the predicted probability of corporate failure than the estimates of marginal effects would suggest. Nevertheless, this is hardly the case, as the ranges used to plot the slopes of the macroeconomic indicators are larger in absolute terms than those of the three financial statement ratios, which might explain the observed phenomenon.