Corporate default probability (Logit)

This illustrates Logit for a binary outcome: predicting the probability of default ($Y=1$ if default) from financial ratios. Figures are illustrative.

Summary: regress the binary default on leverage, profitability and liquidity; interpret via odds ratios and marginal effects.

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Step 1 — Ideation

• Question: which financial ratios raise default probability, and by how much?

Step 2 — Literature Review

Early-warning credit-risk models (Altman Z-score, hazard models); clarify variables and threshold.

Step 3 — Data Collection

Variable	Symbol	Measurement	Source
Default	default	1 = default, 0 = not	listed-firm statements
Leverage	leverage	Debt/Total assets	financials
Profitability	roa	Net income/Total assets	financials
Liquidity	current	Current assets/Current liab.	financials

Step 4 — Modeling

Choose the Limited dependent variable family → Logit:

$$P(default_i = 1) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 leverage_i + \beta_2 roa_i + \beta_3 current_i)}}$$

Illustrative results (format — not real results):

Variable	Coefficient	Odds ratio	AME	p-value
leverage	1.45	4.26	0.21	0.000
roa	−3.10	0.045	−0.28	0.000
current	−0.60	0.55	−0.07	0.012
AUC	0.84

Sample interpretation: high leverage raises default odds (OR ≈ 4.3); higher ROA and liquidity reduce risk; AUC 0.84 indicates good classification.

Stata

* ===== Logit — Corporate default probability =====
* Estimate the logit model
logit default leverage roa current

* Odds ratios
logit default leverage roa current, or

* Average marginal effects (AME)
margins, dydx(*)

* Classification table
estat classification

* ROC curve and AUC
lroc
lsens

R

# ===== Logit — Corporate default probability =====
model <- glm(default ~ leverage + roa + current,
             data   = df,
             family = binomial(link = "logit"))

summary(model)

# Odds ratios
exp(coef(model))
exp(confint(model))

# Average marginal effects (AME)
library(margins)
summary(margins(model))

# ROC curve and AUC
library(pROC)
pred <- predict(model, type = "response")
roc_obj <- roc(df$default, pred)
auc(roc_obj)
plot(roc_obj, main = "ROC Curve — Default Logit")

Python

# ===== Logit — Corporate default probability =====
import statsmodels.api as sm
import numpy as np
from sklearn.metrics import roc_auc_score, roc_curve
import matplotlib.pyplot as plt

# Prepare data
X = sm.add_constant(df[["leverage", "roa", "current"]])
y = df["default"]

# Estimate the logit model
model = sm.Logit(y, X).fit()
print(model.summary())

# Odds ratios
print("Odds Ratios:")
print(np.exp(model.params))

# Average marginal effects
mfx = model.get_margeff()
print(mfx.summary())

# ROC curve and AUC
y_pred = model.predict(X)
print("AUC:", roc_auc_score(y, y_pred))

fpr, tpr, _ = roc_curve(y, y_pred)
plt.plot(fpr, tpr, label=f"AUC = {roc_auc_score(y, y_pred):.2f}")
plt.xlabel("False Positive Rate")
plt.ylabel("True Positive Rate")
plt.title("ROC Curve — Default Logit")
plt.legend()
plt.show()

Step 5 — Reporting

Export a report + replication code; include the classification table and ROC curve.

Video tutorial

Video Tutorial: Guide to running Logit for default prediction in EcoLab

See also

• Logit · Probit · Catalog