An Invariance Property of the Common Trends under Linear Transformations of the Data

It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis of the term structure of interest rates.cointegration vectors; common trends; prediction errors

Extracting Information from the Data: A Popperian View on Empirical Macro

The cointegrated VAR model is proposed as an empirically coherent framework for analyzing macroeconomic phenomena within a dynamic system of pulling and pushing forces. As an illustration we show how an economic theory for inflation and money demand gives rise to a number of hypotheses formulated as testable parameter restrictions on cointegrating relations and common trends. The procedure not only allows us to test prior theoretical hypotheses in a valid maximum likelihood framework but also provides additional empirical results suggesting how to modify or improve our theoretical understanding. The latter is important when theoretical implications fail to hold in the data.cointegrated VAR; inflation; money growth; empirical methodology

Controlling Inflation in a Cointegrated Vector Autoregressive Model with an Application to US Data

The notions of instrument, intermediate target and final target are defined in the context of the cointegrated VAR. A target variable is said to be controllable if it can be made stationary around a desired target value by using the instrument. This can be expressed as a condition on the long-run impact matrix. Applying a control rule to intervene in the market changes the dynamics of the process and the properties of the new controlled process have to be derived. The theoretical results are applied to US monetary data on a daily and monthly basis. The empirical results do not provide support for the widely held belief that the Federal Reserve Bank can bring US CPI inflation down by increasing the federal funds rate.Inflation Target; Monetary Instruments; Control Rules

Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate

This paper discusses a number of likelihood ratio tests on long-run relations and common trends in the I(2) model and provide new results on the test of overidentifying restrictions on β’xt and the asymptotic variance for the stochastic trends parameters, α⊥1: How to specify deterministic components in the I(2) model is discussed at some length. Model specification and tests are illustrated with an empirical analysis of long and persistent swings in the foreign exchange market between Germany and USA. The data analyzed consist of nominal exchange rates, relative prices, US inflation rate, two long-term interest rates and two short-term interest rates over the 1975-1999 period. One important aim of the paper is to demonstrate that by structuring the data with the help of the I(2) model one can achieve a better understanding of the empirical regularities underlying the persistent swings in nominal exchange rates, typical in periods of floating exchange ratesPPP puzzle; forward premium puzzle; cointegrated VAR; likelihood inference

A Resolution of the Purchasing Power Parity Puzzle: Imperfect Knowledge and Long Swings

Asset prices undergo long swings that revolve around benchmark levels. In currency markets, fluctuations involve real exchange rates that are highly persistent and that move in near-parallel fashion with nominal rates. The inability to explain these two regularities with one model has been called the "Purchasing Power Parity puzzle". In this paper, we trace the puzzle to exchange rate modelers' use of the "Rational Expectations Hypothesis". We show that once imperfect knowledge is recognized, a monetary model is able to account for the puzzle, as well as other salient features of the data, including the long-swings behavior of exchange rates.PPP puzzle; long swings; imperfect knowledge; rational expectations hypothesis