The last decade has seen a burst of micro price studies. Many studies analyze data underlying national CPIs and PPIs. Others focus on more granular sub-national grocery store data. We review these studies with an eye toward the role of price setting in business cycles. We summarize with ten stylized facts: Prices change at least once a year, with temporary price discounts and product turnover often playing an important role. After excluding many short-lived prices, prices change closer to once a year. The frequency of price changes differs widely across goods, however, with more cyclical goods exhibiting greater price flexibility. The timing of price changes is little synchronized across sellers. The hazard (and size) of price changes does not increase with the age of the price. The cross-sectional distribution of price changes is thick-tailed, but contains many small price changes too. Finally, strong linkages exist between price changes and wage changes.

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a b s t r a c tWe compare the performance of perturbation, projection, and stochastic simulation algorithms for solving the multi-country RBC model described in Den Haan et al.(this issue). The main challenge of solving this model comes from its large number of continuous-valued state variables, ranging between four and 20 in the specifications we consider. The algorithms differ substantially in terms of speed and accuracy, and a clear trade-off exists between the two. Perturbation methods are very fast but invoke large approximation errors except at points close to the steady state; the projection methods considered are accurate on a large area of the state space but are very slow for specifications with many state variables; stochastic simulation methods have lower accuracy than projection methods, but their computational cost increases only moderately with the state-space dimension. Simulated series generated by different methods can differ noticeably, but only small differences are found in unconditional moments of simulated variables. On the basis of our comparison, we identify the factors that account for differences in accuracy and speed across methods, and we suggest directions for further improvement of some approaches.

We describe a sparse-grid collocation method to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method can be in applications by computing the non-linear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy, the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with up to 10 countries (i.e., up to 20 continuous-valued state variables). AbstractWe describe a sparse-grid collocation method to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method can be in applications by computing the nonlinear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international We thank Ken Judd for clarifying discussions about the scope and focus of this paper. We also wish to thanks seminar participants at the 2006 Cleveland FED conference on international macroeconomics, the 2007 Heterogeneity and Macrodynamics conference in Paris, and the 2009 conference on computational economics in Zurich, as well as Wouter Denhaan, Karl Schmedders, Paul Pichler, Michael Reiter and an anonymous referee for helpful comments. Krueger and Kubler gratefully acknowledge …nancial support under NSF grant SES-0004376. The views expressed in this paper are solely our own and should not be interpreted as re ‡ecting those of the Board of Governors or the sta¤ of the Federal Reserve System. 1 capital ‡ows. In this economy, the aggregate state vector includes the distribution of world capital across di¤erent countries as well as the exogenous country-speci…c technology shocks. We use the algorithm to e¢ ciently solve models with up to 10 countries (i.e., up to 20 continuous-valued state variables).