Boundary limit theory for functional local to unity regression

This paper studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multi-directional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its $t$ statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the paper

Is Productivity Diverging in the EU? Evidence from 11 Member States

An argument that received a lot of attention in the political and economic discussion surrounding the recent crisis in the EU is that diverging trends in productivity across member countries will undermine the viability of the common currency. This article examines the issue of convergence in multifactor productivity using sector-level data from 11 EU Member States. A state-space model is developed and formal Bayesian model comparisons are performed to infer whether productivity is diverging, both at the aggregate level and at a sector-by-sector basis. The data point towards diverging productivity at the aggregate level, but suggest the opposite for many individual sectors

International Financial Aggregation and Index Number Theory: A Chronological Half-Century Empirical Overview

This paper comprises a survey of a half century of research on international monetary aggregate data. We argue that since monetary assets began yielding interest, the simple sum monetary aggregates have had no foundations in economic theory and have sequentially produced one source of misunderstanding after another. The bad data produced by simple sum aggregation have contaminated research in monetary economics, have resulted in needless “paradoxes,” and have produced decades of misunderstandings in international monetary economics research and policy. While better data, based correctly on index number theory and aggregation theory, now exist, the official central bank data most commonly used have not improved in most parts of the world. While aggregation theoretic monetary aggregates exist for internal use at the European Central Bank, the Bank of Japan, and many other central banks throughout the world, the only central banks that currently make aggregation theoretic monetary aggregates available to the public are the Bank of England and the St. Louis Federal Reserve Bank. No other area of economics has been so seriously damaged by data unrelated to valid index number and aggregation theory. In this paper we chronologically review the past research in this area and connect the data errors with the resulting policy and inference errors. Future research on monetary aggregation and policy can most advantageously focus on extensions to exchange rate risk and its implications for multilateral aggregation over monetary asset portfolios containing assets denominated in more than one currency. The relevant theory for multilateral aggregation with exchange rate risk has been derived by Barnett (2007) and Barnett and Wu (2005)