The mathematical foundation of macro-financial feedback loops is modeled by economists through the Financial Accelerator Theorem (developed by Ben Bernanke, Mark Gertler, and Simon Gilchrist).
The External Finance Premium Mechanism
The financial accelerator proves that the cost premium a corporate borrower must pay to secure external bank financing over internal cash funding—the External Finance Premium—is inversely related to the borrower’s net worth:
External_Finance_Premium = Alpha * (1 / Corporate_Net_Worth)
Where:
- External_Finance_Premium = The risk premium spread charged by lenders above risk-free interest rates.
- Alpha = A structural parameter tracking the level of asymmetric information and legal friction in credit markets.
- Corporate_Net_Worth = The liquid equity and asset collateral value held directly on the firm’s balance sheet.
When a macroeconomic shock lowers asset values, corporate net worth falls. This drop increases the External Finance Premium, driving up interest expenses for businesses, reducing investment spending, and deepening the economic contraction.
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