I’m working on a model with irreversible investment and I have a question regarding its implementation in Dynare. I’ve attached a .mod file that uses two alternative approaches:
The MCP functionality (mcp).
The max operator.
My questions are:
Is the implementation of MCP in the attached file correct? The idea is to enforce that the accumulated capital cannot decrease below a certain threshold.
What would be the equivalent way to correctly implement this using the max operator without relying on MCP? I want to ensure that both approaches are consistent because MCP is unavailable for extended_path (here).
I’d appreciate any feedback on the proper formulation of the equations and best practices for these cases.
The model is the simplest possible one with irreversible capital investment. There is a representative household that consumes c and invests in capital k. There is a firm with a production function y = Z* (k)^alpha. The idea is that capital investment is irreversible so investment ( ivt = k-(1-ddelta) * k(-1) ) cannot be negative, ivt>0.
Thank you very much in advance for any potential insight.
Sorry for the misunderstanding. The model considers 3 multipliers:
mu1; marginal utility of consumption
mu2; the shadow value of capital accumulation
mu3; this multiplier is associated with the Kuhn-Tucker condition for the irreversibility of investment.
mu3 = 0 when investment is positive, as the irreversibility constraint does not bind.
mu3 > 0 when investment hits the zero lower bound (ivt=0), reflecting the shadow cost of being unable to reduce investment further.
These multipliers are linked by the stationarity condition:
-mu1+mu2+mu3=0
which ensures that the household’s optimization balances the marginal utility of consumption, the shadow value of capital accumulation and the impact of the irreversibility constraint.
I am not sure if this is the proper way to consider occasinally binding constraints with the MCP and how the equivalent formulation using the max operator would look.