Financial Accelerator Model

The financial accelerator grew out of the observation that standard DSGE models could not explain the severity of financial crises. Bernanke, Gertler, and Gilchrist (1999) - hereafter BGG - embedded a costly state verification (CSV) debt contract into a New Keynesian framework, building on Townsend (1979) and earlier work by Bernanke and Gertler (1989). The CSV setup gives rise to an external finance premium that is inversely related to borrower net worth, creating an endogenous wedge between the risk-free rate and the cost of external funds. The 2008 financial crisis made the model indispensable: it was the first DSGE framework that could rationalize how a moderate decline in housing prices could cascade into a near-depression through balance-sheet feedback.

The core mechanism works through three interlocking channels. First, entrepreneurs borrow to fund capital purchases, facing an optimal debt contract derived from costly state verification - the lender pays a monitoring cost mu when the borrower defaults, so the contract charges a spread above the risk-free rate to cover expected monitoring costs. Second, this external finance premium is a decreasing function of the entrepreneur's net worth relative to the capital stock: higher leverage means higher default probability, higher expected monitoring costs, and a wider spread. Third, the balance-sheet amplification loop closes the circle - when asset prices fall after an adverse shock, entrepreneurial net worth drops, the external finance premium rises, investment contracts, which further depresses asset prices and net worth. This positive feedback loop is the financial accelerator proper.

Central banks adopted financial accelerator models rapidly after 2008. The Federal Reserve's SIGMA model incorporates BGG-style financial frictions. The ECB's Christiano-Motto-Rostagno (2003, 2014) model extends the Smets-Wouters framework with an entrepreneurial sector and risk shocks. The Bank of England's COMPASS model includes a banking sector inspired by Gertler-Kiyotaki (2010). Iacoviello (2005) adapted the framework to housing markets with collateral constraints tied to property values, which became the standard for analyzing mortgage and housing policy. These models are now the workhorses for macroprudential stress testing, countercyclical capital buffer analysis, and quantitative easing evaluation.

The literature branched in several directions after BGG. Kiyotaki and Moore (1997) developed a parallel collateral-constraint tradition where borrowing limits are tied directly to asset values rather than derived from an optimal contract. Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) shifted the friction from the entrepreneur to the banking sector, creating models where bank leverage constraints drive credit supply. Jermann and Quadrini (2012) introduced financial shocks - disturbances to the borrowing constraint itself - and showed they account for a substantial share of business cycle variation. The debate between CSV-based and collateral-constraint-based approaches, and whether the friction belongs on the borrower or the intermediary side, remains active.

The model grafts an entrepreneurial sector with a CSV-based debt contract onto a New Keynesian core. The household side is standard: a representative household supplies labor, consumes, and saves in deposits at the risk-free rate. The firm side has two layers - competitive final goods producers and monopolistically competitive intermediate goods producers with Calvo pricing. The entrepreneurial sector is new: entrepreneurs purchase capital at the end of each period, fund the purchase with net worth and external borrowing, operate the capital next period subject to an idiosyncratic productivity shock, and then sell depreciated capital. The idiosyncratic shock creates default risk, which generates the CSV contract and the external finance premium.

The financial block links the entrepreneurial balance sheet to the macroeconomy through three equations. The net worth evolution equation tracks how entrepreneurial wealth accumulates from capital returns minus debt repayment and consumption, plus transfers from newly entering entrepreneurs. The external finance premium equation - the heart of the model - expresses the spread between the borrowing rate and the risk-free rate as a decreasing function of the net-worth-to-capital ratio (equivalently, an increasing function of leverage). The capital demand equation equates the expected return on capital to the risk-free rate plus the external finance premium, closing the loop between financial conditions and real investment.

The central bank follows a Taylor rule, and three types of structural shocks drive the system: standard NK shocks (technology, monetary policy, cost-push), financial shocks (net worth destruction, risk shocks to the idiosyncratic volatility), and asset price shocks. The model is solved by first-order perturbation around the deterministic steady state. The key amplification result shows up in the impulse responses: compared to the same NK model without financial frictions, output, investment, and consumption responses to any given shock are larger and more persistent because the balance-sheet feedback loop propagates the initial disturbance through the credit spread channel.

The Federal Reserve's SIGMA model and the ECB's CMR model use BGG-style financial frictions for stress testing and macroprudential policy analysis. After 2008, these models became the standard tool for evaluating countercyclical capital buffers, assessing how bank capital requirements interact with monetary policy, and quantifying the macro impact of credit crunches. The external finance premium in the model maps directly to observable credit spreads (e.g. BAA-AAA corporate bond spread, GZ spread), making the model empirically disciplined.

Iacoviello (2005) adapted the framework to housing markets, replacing business capital with housing as collateral. This variant became the workhorse for analyzing mortgage regulation, loan-to-value ratio policies, and the transmission of housing price shocks to aggregate consumption. Central banks in economies with large housing sectors (UK, Canada, Australia, Nordics) use Iacoviello-type models as a core component of their forecasting frameworks.

The model breaks down when the financial friction is on the intermediary side rather than the borrower side - bank runs, interbank freezes, and wholesale funding disruptions require the Gertler-Kiyotaki (2010) or Gertler-Karadi (2011) banking-sector extensions. It also struggles with the zero lower bound, where the monetary policy channel is disabled and the financial accelerator may interact with the ZLB in ways that first-order perturbation cannot capture. For distributional questions about heterogeneous borrower types, a HANK model with financial frictions is needed.

The financial accelerator framework is also used to evaluate unconventional monetary policy. Gertler and Karadi (2011) showed how central bank asset purchases work by absorbing credit risk from the private sector, effectively compressing the external finance premium directly rather than through the policy rate. This provided the theoretical backbone for QE analysis at the Fed, ECB, and Bank of Japan.