# F1-conf-03 — Leverage and next-year default (information-respecting)

## Question
What is the association between a firm's leverage at the end of year t and its default in year t+1? We use only information available at the end of year t. The estimand is b1 in the linear-probability model default_next = a + b1·leverage + b2·cash_ratio + b3·log_sales + e. It is estimated by OLS on firm-years with an observed outcome, with standard errors clustered by firm. The data are simulated (a synthetic panel).

## Data and exclusions
- Input: `data/firm_panel.csv`, 2140 data rows (`n_input_rows`), 300 firms, 2016–2022.
- Data problems found (`data_issues`):
  1. 40 rows are exact duplicates of another row (assembly error). One copy of each was kept. This leaves 2100 rows = 300 firms × 7 years (`n_rows_after_dedupe`).
  2. `rating_2025` was assigned in 2025 using each firm's realised defaults through 2022, so it was not known at the end of year t. It is excluded (`variables_excluded`). In the deduplicated data, every observed default falls in rating D, which confirms that the field leaks the outcome.
  3. `default_next` is missing for 300 rows, all with origin year 2022 (outcome year 2023 lies after the data cut). These rows are excluded and not imputed.
- Exclusion ledger (`out/exclusions.csv`): 2140 → 2100 (deduplication) → 2100 (column removal of rating_2025) → 1800 (outcome observed) → 1800 (complete predictors). Estimation sample: `n_analysed` = 1800 firm-years, `n_firms` = 300, origin years 2016–2021.

## Method
- Baseline: the unconditional default rate in the estimation sample (`default_rate`).
- Main model: OLS of `default_next` on an intercept plus `predictors_used` = leverage, cash_ratio and log_sales, all measured at the end of year t.
- Standard errors are cluster-robust by `firm_id` (statsmodels, default small-sample correction).
- No randomness is involved (`random_seed` = null).
- `out/analysis.py` regenerates all outputs from `data/`.

## Results
- Baseline default rate: 0.121 (`default_rate`).
- `beta_leverage` = 0.264. Holding cash ratio and log sales fixed, a 0.10 higher leverage ratio is associated with about 2.6 percentage points higher probability of default in the next year.
- Other coefficients: cash_ratio −0.186 (`beta_cash_ratio`); log_sales −0.0073 (`beta_log_sales`); intercept 0.090 (`intercept`).
- In-sample R² = 0.035 (`r2`). The model explains little of the individual-level variation in default, as is typical for a binary outcome.
- Feasibility: complete (`feasibility`).

## Uncertainty
- The firm-clustered SE of the leverage coefficient is 0.0408 (`se_leverage_cluster`). The 95% CI is [0.184, 0.344] (`ci95_leverage_low`, `ci95_leverage_high`), with p ≈ 1e-10 (`p_leverage_cluster`).
- The classical (non-clustered) SE is smaller, 0.0358 (`se_leverage_classical`). This is consistent with outcomes being correlated within firms.

## Limitations and open issues
- This is an association, not a causal effect. Leverage may proxy for unobserved firm risk.
- A linear-probability model can produce fitted values outside [0,1]. The coefficient is an average linear approximation.
- Duplicates were resolved by keeping one copy. This is unambiguous here because all copies were identical.
- Firms that default stay in the panel. The codebook does not say how post-default years are defined, so all observed firm-years are used as given.
- The data are synthetic, so the results say nothing about real firms.