Abstract
This thesis is composed of three chapters. Chapter 1 introduces a statistical framework to study dynamic (S,s) economies. The proposed framework enables researchers to estimate unit level cumulated changes in frictionless variables based on a panel of variables for which changes are intermittent and lumpy. Formally, the estimates are grounded on an exact closed-form solution for the smoothing problem associated with a nonlinear and non-Gaussian state-space representation of an economy composed of microeconomic unit pursuing two-sided (S,s) policies subject to costless adjustment opportunities. This state-space representation is semi-structural and can accommodate some classic problems that have been analysed through the lens of (S,s) models such as pricing subject to menu costs, cash withdrawals and plant-level investment and hiring and firing decisions. The resulting unit level estimates can be used to construct estimates of frictionless aggregate variables and of the cross-sectional distribution of state gaps for any time period. Chapter 2 applies the theoretical results developed in chapter 1 to a large micro price dataset underlying the United Kingdom Consumer Price Index to produce a novel measure of in inflation which I label frictionless in ation. This measure is theoretically grounded on a random menu cost model and it should be interpreted as the in ation that would have been observed in a counterfactual world where menu costs of price adjustment did not exist. I use this measure to answer four questions. First, what is the importance of menu costs for the aggregate in inflation dynamics? Second, what is the importance of menu costs for the transmission of monetary policy shocks? Third, what is the relationship between frictionless in ation and the movements in the output gap? Fourth, can frictionless in inflation be used as a leading indicator for headline in inflation? Chapter 3 studies the estimation of impulse responses functions (IRFs) of different individuals to an aggregate shock. The commonplace approach to this 3 problem involves first grouping individuals according to some external classification or observable explanatory variables and subsequently estimating the associated group-specific IRFs. This chapter starts by showing that the IRF estimates based on this approach are subject a misclassification bias that arises whenever the grouping of individuals imposed by the researcher groups together individuals that do not react in the same way to aggregate shocks. Motivated by this results, this chapter introduces an alternative methodology to estimate disaggregated IRFs using the C-Lasso framework which asymptotically eliminates the misclassification bias without the need for the researcher to take a stance on individual group membership. The proposed estimator is used to revisit the dynamic responses of firm-level debt to an aggregate investment specific technology shock.
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