During the financial crisis, life insurers sold long-term policies at deep discounts relative to actuarial value. The average markup was as low as -19 percent for annuities and -57 percent for life insurance. This extraordinary pricing behavior was due to financial and product market frictions,...

The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state space system for a vector of observables. An associated state space system (A,ˆB,C,ˆD) determines a vector autoregression for those same...