We describe how to adapt a first-order perturbation approach and apply it in a piecewise fashion to handle occasionally binding constraints in dynamic models. Our examples include a real business cycle model with a constraint on the level of investment and a New Keynesian model subject to the zero lower bound on nominal interest rates. We compare the piecewise linear perturbation solution with a high-quality numerical solution that can be taken to be virtually exact. The piecewise linear perturbation method can adequately capture key properties of the models we consider. A key advantage of this method is its applicability to models with a large number of state variables.

This paper investigates how oil price shocks affect the trade balance and terms of trade in a two country DSGE model. We show that the response of the external sector depends critically on the structure of financial market risk-sharing. Under incomplete markets, higher oil prices reduce the relative wealth of an oil-importing country, and induce its nonoil terms of trade to deteriorate, and its nonoil trade balance to improve. The magnitude of the nonoil terms of trade response hinges on structural parameters that affect the divergence in wealth effects across oil importers and exporters, including the elasticity of substitution between oil and other inputs in production, and the discount factor. By contrast, cross-country wealth differences effectively disappear under complete markets, with the implication that oil shocks have essentially no effect on the nonoil terms of trade or the nonoil trade balance.

Galí's innovative approach of imposing long-run restrictions on a vector autoregression (VAR) to identify the effects of a technology shock has become widely utilized. In this paper, we investigate its reliability through Monte Carlo simulations of several relatively standard business cycle models. We find it encouraging that the impulse responses derived from applying the Galí methodology to the artificial data generally have the same sign and qualitative pattern as the true responses. However, we highlight the importance of small-sample bias in the estimated impulse responses and show that the magnitude and sign of this bias depend on the model structure. Accordingly, we caution against interpreting responses derived from this approach as "model-independent" stylized facts. Moreover, we find considerable estimation uncertainty about the quantitative impact of a technology shock on macroeconomic variables, and a corresponding level of uncertainty about the contribution of technology shocks to the business cycle.

A model with collateral constraints displays asymmetric responses to house price changes. When housing wealth is high, collateral constraints become slack, and the response of consumption and hours to shocks that move house prices is positive yet small.When housing wealth is low, collateral constraints become tight, and the response of consumption and hours to house price changes is negative and large. This finding is corroborated using evidence from national, state-level, and MSA-level data. Wealth effects computed in normal times may underestimate the response to large house price declines.Debt-relief policies may be far more effective during protracted housing slumps.