Estimation of Parameters of Econometric Models

Abstract

Econometric relations are often simultaneous in the sense that some of their variables are connected by a system of such equations. These variables are called endogenous in the system and the others, the values of which are supposed to be determined outside the system, exogenous. If the statistical analysis of such relations is based on time series, a distinction is also made between lagged and current variables.¹ Lagged endogenous and all exogenous variables are called predetermined, the former being predetermined in a temporal and the latter in a logical sense. Current endogenous variables are called jointly dependent, they are considered to be simultaneously determined by the predetermined variables and random disturbances, in a way prescribed by the system. This requires that the system is complete, i.e. that the number of jointly dependent variables equals the number of equations. When supposing that the system is linear, we may write it as

$$\Gamma y\left( t \right) + Bx\left( t \right) + A + U\left( t \right) = 0{\text{ }}\left( {t = 1,...,T} \right),$$

(1.1)

where y is the column vector of M jointly dependent variables y ₁ , … y _M and x that of Λ predetermined variables. Γ and B are matrices of unknown parameters, Γ being square. A is the vector of constant terms and U( _t ) that of the disturbances; t should be interpreted as time

This article first appeared in Bulletin de l’Institut International de Statistique, 34 (1954), 122-129. Reprinted by permission of the International Statistical Institute, Voorburg, The Netherlands.