Tashkent institute of finance “Statistics and econometrics” department subject of econometrics phd jumayev Akbar Makhmudovich

Consumption function:

Income identity:

Therefore, once again the classical least-squares method is inapplicable to Eq. (2). If applied, the estimators thus obtained will be inconsistent, as we shall show later.

The structural and reduced-form of model

(1)

The equations appearing in (1) are known as the structural, or behavioral, equations because they may portray the structure (of an economic model) of an economy or the behavior of an economic agent (e.g., consumer or producer). The β’s and γ’s are known as the structural parameters or coefficients.

The structural and reduced-form of model

A reduced form equation is one that expresses an endogenous variable solely in terms of the predetermined variables and the stochastic disturbances.

The structural and reduced-form of model

• To illustrate, consider the Keynesian model of income determination:
• If Eq. (3) is substituted into Eq. (2), or conversely we obtain, after simple algebraic manipulation,

The structural and reduced-form of model

Equations (4) and (5) are reduced-form equations; they express the endogenous variable Y solely as a function of the exogenous (or predetermined) variable I and the stochastic disturbanceterm u.

β0’ and β1’ are the associated reduced-form coefficients. Notice that these reduced-form coefficients are nonlinear combinations of the structural coefficient(s).

The identification problem

• By the identification problem we mean whether numerical estimates of the parameters of a structural equation can be obtained from the estimated reduced-form coefficients.
• From the position of identifiability, structural models can be divided into three types:

1. Exactly or just identified

2. Underidentified

3. Overidentified