Contents of model equations


When we optimise with respect to a set of constraints, should we include those constraints as a part of model equations.


In general yes, since most of the times constraint include information about the relationship between controls and states, e.g. capital accumulation process: k_{t}=I_t+(1-\delta)k_{t-1} or household budget constraint. Nevertheless they have to be compatible with certain characteristics of the model, for example the budget constraint has to be compatible with the resource constraint of the economy, which could be Y_t=C_t+I_t in closed economy case. This specification of the resource constraint may change depending on whether you include other aspects as some type of adjustment cost or open the economy.

The constraints are first order conditions (the derivative with respect to the Lagrange multiplier). They are need for a complete model.

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Indeed @jpfeifer. We often miss that we need to optimise wrt to the langramge multiplier as well. Thanks.

But then we do not include budget constraints in the model block because we aggregate them to include in the market clearing condition. Budget constraint are derivatives wrt to langrange multipliers. If we do not include them in model block, the model will always be short of number of equations.

I am not sure what you are after. You can only “aggregate” them by replacing a variable. That way, you would be getting rid of a variable and an equation.