The asymptotic theory of the gauge of the step-indicator saturation estimator and its application to study the effect of deindustrialisation on real rates

Thesis

This thesis is about Step-indicator Saturation, an algorithm that identifies and models location shifts which are changes in the intercept of time series regression models. It contributes both to the asymptotic theory as well as applications of the algorithm. On theory, we develop asymptotic results about the empirical gauge of Step-indicator Saturation which is the frequency of false positives. The ability to control the empirical gauge is essential to have confidence that the location shifts identified by Step-indicator Saturation are not statistical artifacts. On applications, we use Step-indicator Saturation to study the empirical relationship between deindustrialisation and the real interest rate.

Chapter 1. We set out the mathematical framework for the asymptotic theory of Step-indicator Saturation. We establish empirical process results for differenced residuals, which introduce a specific timeseries dependence between the indicator functions. We develop techniques to handle the time-series dependence within the traditional chaining argument that is used to show uniform convergence of empirical processes.

Chapter 2. We derive asymptotic results of the empirical gauge of a stylized version of Step-indicator Saturation that uses the split-half algorithm. We prove that the empirical gauge converges in probability to the population gauge which depends on the distribution of the error terms. Moreover, asymptotic distribution results of the empirical gauge are derived. We show that the asymptotic distribution the empirical gauge of Step-indicator Saturation is larger than for Impulseindicator Saturation.

Chapter 3. We present two new ways to use Step-indicator Saturation in an empirical study. We first show that location shifts can hide an empirical relationship between two macroeconomic variables, in our case the relationship between deindustrialisation and the real interest rate. Step-indicator Saturation identifies two step-indicators that suffice to uncover a highly significant empirical relationship. Second, we apply the catalyst method to study the causal transmission of terms of trade shocks which first hit the manufacturing sector before they transmit into the real interest rate. Step-indicator Saturation is used to construct the catalyst from the location shifts in the Britsh terms of trade. We estimate that deindustrialisation can explain a 419 basis point reduction of the real interest rate from 1990 to 2017.

Authors: Qian, M

• DOI: 10.5287/ora-rdxmv7ng4
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English