Working Papers 1998 – Abstracts

7/98
Nonparametric seemingly unrelated regression
Michael Smith and Robert Kohn

This paper presents a method for simultaneously estimating a system of nonparametric multiple regressions which may seem unrelated, but where the errors are potentially correlated between equations. We show that the prime advantage of estimating such a `seemingly unrelated' system of nonparametric regressions is that substantially less observations can be required to obtain reliable function estimates than if each of the regression equations was estimated separately and the correlation ignored. This increase in efficiency is investigated empirically using both simulated and real data. The method suggested here develops a Bayesian hierarchical framework where the regression function is represented as a linear combination of a large number of basis terms, the number of which is typically greater than the sample size. All the regression coefficients, and the variance matrix of the errors, are estimated simultaneously using their posterior means. The computation is carried out using a Markov chain Monte Carlo sampling scheme that employs a `focused sampling' step to combat the high dimensional representation of the function and a Metropolis-Hastings step to correctly account for the distribution of the covariance matrix. The methodology is also easily extended to other nonparametric multivariate regression models.

8/98
A new approach to model GNP functions: An application of non-separable two-stage technologies
Gary K.K. Wong

This paper shows that two-stage technologies can provide a general procedure for combining profit and value-added functions to obtain new specifications of import demand and output supply systems. In such technologies, we assume that imports interact with other exogenous variables to produce intermediate inputs, which are in turn used to produce final outputs. To show the utility of this new approach, we use it to specify and estimate the Australian GNP functions. As will be seen, our proposed framework has an attractive property: the capability of incorporating exogenous effects such as labour and capital endowments within a strong theoretical underpinning. We investigate a new GNP function for which the demand and supply systems are effectively globally regular. Our results demonstrate that the new approach is feasible and promising while the estimated elasticities are not significantly different from those of the traditional models.

9/98
Bayesian estimation of the reduced rank regression model without ordering restrictions
Rodney W. Strachan

Estimation of the parameters of the reduced rank regression model in a Bayesian method required the solution of two identification problems: global or strong identification and local identification. Traditionally Bayesians, and to a large extent frequentists, have relied on zero-one identifying restrictions which require the researcher to impose an order on the variables to achieve global identification. Examples of this approach include Geweke (1996), Bauwens and Lubrano (1993), Kleibergen (1997), Kleibergen and Paap (1997), and Kleibergen and van Dijk (1994). This ordering relies on a priori knowledge of which variables enter the reduced rank relations. For example, the cointegrating error correction model requires knowledge of which variables are I(0) or cointegrate. Incorrect ordering may result in an estimated space for the cointegrating vectors that does not have the true cointegrating space as a subset, effectively misspecifying the model. In this paper, we present an estimation method which does not require a priori ordering by using restrictions similar to those used in maximum likelihood estimation by Anderson (1951) of the reduced rank regression model generally, and by Johansen (1988) in an error correction model specifically. As with much of the recent work, we focus on the cointegrating error correction model to show our approach.
Local identification is achieved by nesting the reduced rank model within a full rank model with a well behaved posterior distribution. This approach is due to Kleibergen (1997) and is consistent with the principle of a "data-translated likelihood" suggested by Box and Tiao (1973). In nesting the reduced rank model in a full rank model, we use a transformation from the potentially reduced rank matrix Π to the matrices α , β and λ where λ = 0 restricts Π to a lower rank. Results from Roy (1952) enable us to derive the Jacobian for this transformation.

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