By Dennis L. Hoffman
The econometric outcomes of nonstationary facts have extensive ranging im plications for empirical examine in economics. in particular, those matters have implications for the examine of empirical relatives comparable to a cash call for func tion that hyperlinks macroeconomic aggregates: actual cash balances, genuine source of revenue and a nominal rate of interest. conventional financial idea predicts that those nonsta tionary sequence shape a cointegrating relation and as a result, that the dynamics of a vector strategy constructed from those variables generates unique styles. Re cent econometric advancements designed to deal with nonstationarities have replaced the process empirical study within the zone, yet many basic demanding situations, for instance the problem of identity, stay. This booklet represents the efforts undertaken via the authors in recent times with a purpose to confirm the results that nonstationarity has for the research of mixture cash call for family members. we've introduced jointly an empirical technique that we discover worthwhile in accomplishing empirical examine. a number of the paintings was once undertaken in the course of the authors' sabbatical classes and we want to recognize the beneficiant aid of Arizona nation collage and Michigan nation collage respectively. Professor Hoffman needs to recognize the help of the Fulbright-Hays starting place that supported sabbattical examine in Europe and separate aid of the Council of a hundred summer season examine software at Arizona kingdom University.
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Additional resources for Aggregate Money Demand Functions: Empirical Applications in Cointegrated Systems
3. IDENTIFICATION OF LONG-RUN PARAMETERS 43 useful in cases where (3 is not identified. Let ml denote the number of independent (3 restrictions while m2 denotes the number of independent a restrictions pertinent to (3 identification. When a restrictions exist, a generalized order condition ml + m2 ~ r - 1 is applicable. 13 When identification is obtained using this standard linear ''vector-by-vector'' approach, matrix normalizations can play a useful role in cointegration vector identification.
In practice, time series variables are assumed to be stationary or are simply integrated (differenced) until they exhibit the characteristics of stationarity. 6) are equal to 1, the univariate process is integrated of order d; Zti '" 1(d). In contrast to variables that are covariance stationary, the higher moments of integrated time series depend upon t. 9) 2Some applications have focused on models that exhibit higher orders of integration (see Johansen (1992a)) while others have examined "fractionally integrated" systems(see Hamilton (1994)).
2 Examples of Long-Run Parameter Identification A simple example illustrates the basic principles of long-run parameter identification. King, Plosser, Stock, and Watson (1991) specify a simple three variable log-linear model consisting of consumption; c, investment; i, and output; y (lower case denotes natural logs ). KPSW argue that the nonstationary behavior 13See Pesaran and Shin for a detailed discussion of nonlinear and "cross-vector" identification restrictions. The conditions for long-run parameter identification in Pesaran and Shin are perfectly comparable to those in our simple example after accounting for the r (one in each vector)normalization restrictions.
Aggregate Money Demand Functions: Empirical Applications in Cointegrated Systems by Dennis L. Hoffman