Notations of endogenous and exogenous variables:

To  facilitate our discussion, we introduce the  following example of hie  different notations: 

Let us consider a SEM with M  endogenous and K  exogenous  variables.

The general M  equations model  in  M  endogenous, jointly dependent,  variables may be written as equation given below, which is a time dependent SEM:  

As  equation  shows,  both  endogenous  and  exogenous  variables enter a simultaneous equation model. First, we have endogenous variables, whose values are determined within  the model. Next, we have predetermined variables, whose values are determined outside the model. Finally, we have the  stochastic error terms. The endogenous  variables are regarded as stochastic whereas the predetermined variables are non-stochastic in nature.

The predetermined variables are divided into two categories: i) exogenous variables, exogenous variables  may be  current  as  well  as  lagged;  ii)  lagged  endogenous variables. Thus, X_1t is a current (present-time) exogenous variable, whereas X_1(t-1) is a  lagged  exogenous variable. With  a  lag of one time period,  on  the other hand, Y_(t-1)  is a 'lagged endogenous variable' with a lag of one time period. Since  the value of Y_1(t-1) is known at the current  time  t ,  it is regarded as non-stochastic. Hence, it  is considered as a predetermined  variable.  In  short, current exogenous,  lagged exogenous, and  lagged  endogenous  variables are  considered  as  predetermined variables, as their values are not determined by the model in the current time period.

At  this point  a question may  be  taking shape  in  your mind, how  do we  construct econometric models? What are the variables that should be  included in  an equation? In  fact, these questions are answered by  economic theory. In some cases, which are not established theory as yet, the equations  depend upon the logic that the researcher puts forth. Thus behind the inclusion of a variable in an equation,-there  is some logic.

Secondly,  it  is  up  to the  concepts of  economic theory  and  the model  builder  to specifL  which variables are  endogenous and which are predetermined. Although non-economic variables (variables not determined by  any of the economic  theory), such as  temperature  and  rainfall,  are  clearly  exogenous or predetermined, the  model building must be  exercised with great care while classifiing economic variables as endogenous or predetermined.  One  must  be  in  a  position  to  defend  i)  the classification  of variables into  endogenous and  exogenous, and  ii)  inclusion of a particular variable in an  equation.