In the first chapter of this dissertation, I propose a methodology to conduct counterfactual analysis in a way that is robust to specific assumptions about primitives of linear models of dynamic stochastic economies. Then, I apply the methodology to quantify how fiscal unions contribute to regional stabilization. I start by showing how to identify a set of models that yield the same counterfactual equilibrium after a policy change by imposing restrictions directly on equilibrium equations. Next, I describe how to construct this counterfactual equilibrium using data under a benchmark policy. The methodology allows obtaining quantitative predictions with respect to policy changes with minimal a-priori structural assumptions while being immune to Lucas critique, enhancing credibility of the analysis. In the application to fiscal unions, I focus on models where the federal government redistributes resources via a transfer policy rule, which is a function of local variables, in order to smooth local shocks. Using US state-level data, I construct a counterfactual US economy without the rule in place. This counterfactual is identical in many fiscal union models with rich features, such as nominal rigidities and asset market incompleteness. My primary finding is that during the Great Recession fiscal integration significantly reduced cross-state employment differences by redistributing resources from states that were doing relatively well to states that were doing relatively poorly. Finally, I discuss how the methodology can further be used to falsify a set of models, provided data before and after a policy change are available. In the second chapter of this dissertation (joint with Erik Hurst and Juan Ospina), we study the aggregate implications of regional business cycles. We argue that it is difficult to make inferences about the drivers of aggregate business cycles using regional variation alone because (i) the local and aggregate elasticities to the same type of shock are quantitatively different and (ii) purely aggregate shocks are differenced out when using cross-region variation. Then, we highlight the importance of these issues in a monetary union model, and by contrasting the behavior of US aggregate time-series and cross-state patterns during the Great Recession. In particular, using household and retail scanner data for the US, we document a strong relationship across states between local employment growth and local nominal and real wage growth. These relationships are much weaker in US aggregates. Finally, in order to identify the shocks driving aggregate (and regional) business cycles, we develop a methodology that combines regional and aggregate data. The methodology uses theoretical restrictions implied by a wage setting equation that holds in many monetary union models with nominal wage stickiness. We show how to estimate this equation using cross-state variation-- thus linking particular regional patterns to particular aggregate shock decompositions. Applying the methodology to the US, we find that a combination of both ``demand" and ``supply" shocks are necessary to account for the joint dynamics of aggregate prices, wages and employment during the 2007-2012 period while only ``demand" shocks are necessary to explain most of the observed cross-state variation. We conclude that the wage stickiness necessary for demand shocks to be the primary cause of aggregate employment decline during the Great Recession is inconsistent with the flexibility of wages estimated from cross-state variation. In the third and last chapter of this dissertation (joint with Fernando Alvarez, Martin Gonzalez-Rozada, and Pablo Andres Neumeyer), we analyze how inflation affects firms' price setting behavior. In a class of menu cost models, we derive several predictions about how price setting changes with inflation at very high and near-zero inflation rates. Then, we present evidence supporting these predictions using firm-level-data underlying Argentina's consumer price index from 1988 to 1997-- a unique experience where monthly inflation ranged from almost $200$ percent to less than zero. First, we show that the frequency of price changes, the dispersion of relative prices, and the absolute size of price changes do not change with inflation when inflation is low. Second, we find that the frequency and size of price increases and decreases are symmetric around zero inflation. Third, we find that inflation changes near zero-inflation are mostly accounted for by changes in the difference between the frequency of price increases and decreases. Finally, we show that, when inflation is high, the frequency of price changes across different products becomes similar and the relation between the frequency of price changes, the dispersion of relative prices, and the absolute size of price changes are consistent with those predicted by menu cost models with no idiosyncratic shocks. Our findings reflect how inflation swamps idiosyncratic firm shocks as a motive for changing prices in high inflation economies whereas the opposite is true in low inflation economies. Moreover, they confirm and extend available evidence for countries that experienced either very high or near-zero inflation.