The model they use is a combination of two existing models: 1) the famous and popular Smets-Wouters (2007) New Keynesian model that I discussed in my last post, and 2) the "financial accelerator" model of Bernanke, Gertler, and Gilchrist (1999). They find that this hybrid financial New Keynesian model is able to predict the recession pretty well as of 2008Q4. Importantly, the forecasts (of the current version) are based on parameter estimates using data available December 2008, so not including 4th quarter 2008 GDP but including the differential between Baa corporate bonds and the Treasury 10 year rate. The model correctly forecasts a deep recession followed by a sluggish recovery. I want to raise a quibble mostly with Smets and Wouters (SW) . In Smets and Wouters (2007) (SW 2007) they assert that they have already considered financial frictions as in Bernanke, Gertler, and Gilchrist (1999)
Finally, the disturbance term [epsilon^b] represents a wedge between the interest rate controlled by the central bank and the return on assets held by the households. A positive shock to this wedge increases the required return on assets and reduces current consumption. At the same time, it also increases the cost of capital and reduces the value of capital and investment, as shown below.3 This shock has similar effects as so-called net-worth shocks in Ben S. Bernanke, Gertler, and Simon Gilchrist (1999) and Christiano, Roberto Motto, and Massimo Rostagno (2003), which explicitly model the external finance premium.The paragraph explains a FOC for optimal consumption (an Euler equation). It it the real interest rate considered by consumers is the federal funds rate minus the expected inflation rate plus this disturbance term epsilon^b. That would be correct if this were a safe real interest rate. A risk premium which has something to do with risk would not appear in the Euler equation that way. IIRC the risk premium in Bernanke Gertler and Gilchrist doesn't affect consumption at all -- it is the difference between interest charged on loans to firms and interest paid to consumers (consumers get the risk free rate). In fact, consumers do not need to bear the risk of possible bankruptcy of firms. Optimization implies that the Euler equation holds for all assets including Treasury bills or, once they were introduced TIPS. It implies expected return differentials on all assets via the consumption CAPM. The SW 2007 risk premium is also paid by firms as in Bernanke, Gertler, and Gilchrist (1999). But if SW already consider a risk premium motivated by reference to Bernanke, Gertler, and Gilchirst (1999) what do Del Negro, Giannoni, and Schorfheide write about the epsilon^b disturbance in SW 2007 which also appears in their model relabeled simply "b"
The exogenous process [b_t] drives a wedge between the intertemporal ratio of the marginal utility of consumption and the riskless real return [R_t - Et[ pi_(t+1)]], and follows an AR(1) process with parameters [rho_ b] and [ sigma_b].This is in section "2.1.1 The SW Model" the term b_t is justified simply because it appears in SW 2007. No explanation for whey there is such a wedge is given (nor is it easy to imagine one when presenting a model with a non-liquidity constrained representative consumer). In contrast the interest rate paid by firms includes a term which really does correspond to the external finance premium in Bernanke Gertler and Gilchrist (1999). I can't manage the notation with plain ascci it is The expected nominal interest rate paid by firms minus the safe interest rate is equal to b_t plus a constant times the (debt+equity) to equity ratio plus the dispersion of ability across entrepreneurs. Or in other words the differential is equal to a log linear approximation of the external finance premium as modelled in Bernanke Gertler and Gilchrist (1999) plus the disturbance term which Del Negro, Giannoni, and Schorfheide call b and which SW call epsilon^b and which SW justify with a reference to Bernanke, Gertler and Ghilchrist (1999). There is still no explanation of why it appears in the Euler equation. OK I trust no one has read this far [text deleted] update: Mark Thoma did it again. I am no longer confident that no one will read this far. I deleted the rest of of this post because it wasn't polite.