This paper attempts to clarify the connection between simple economic theory models and the approach of the Cointegrated Vector-Auto-Regressive model (CVAR). By considering (stylized) examples of simple static equilibrium models, it is illustrated in detail, how the theoretical model and its structure and assumptions can be translated into a CVAR. We also see how the CVAR allows for explicit hypotheses about transitory dynamics, that could be relevant for assessing price rigidity, and hence, "the length of the short run" - a controversial issue in traditional macroeconomics. Moreover, it is demonstrated how other controversial hypotheses such as Rational Expectations can be formulated directly as restrictions on the CVAR-parameters. A simple example of a "Neoclassical synthetic" AS-AD model is also formulated. Finally, the partial- general equilibrium distinction is related to the CVAR as well. Further fundamental extensions and advances to more sophisticated theory models, such as those related to dynamics and expectations (in the structural relations) are left for future papers