Microeconometrics in Business Management

2 Multiple-equation econometric models

2.1 Classification of multiple-equation models

A multiple-equation model is a system of equations consisting of many (at least two) equations, which describe a given economic system or its part called a subsystem. The model contains a G of endogenous variables: Y₁, …, Y_g, …, Y_G with statistical observations y_1t, …, y_gt, …, y_Gt. The endogenous variable is characterized by the fact that in one of the model’s equations it acts as a dependable variable; however, it can also act as an explanatory variable. This type of a model also contains exogenous variables X₁, …, X_j, …, X_k with observations x_t1, …, x_tj, …, x_tk. Exogenous variables in the equations act solely as explanatory variables. Endogenous variables without anytime-delays will be called the model’s total interdependent variables. An alternative group of predetermined variables Z₁, …, Z_j, …, Z_K (with observations z_t1, …, z_tj, …, z_tK) is formed by exogenous variables and delayed endogenous variables, which in the model’s equations appear as explanatory variables.

A system of G equations in a multiple-equation model in a structural form¹ can be written as follows:

(2.1)

In the above G equations, some random components as well as structural parameters associated with the total interdependent variables have appeared. Additionally, the parameters α_gj (g = 1, …, G; j = 0, 1, …, K), associated ...