to interpret the policy function

[superztt]

I am curious about the interpretation of the coefficients in the policy function.

If it is a second order approximation, there are some cross product terms of different state variables and shocks. Can I take them as the indication of state-dependent influence?

For example, I have bond as a state variable and productivity shock. So is the coefficient of (b(-1), shock) the difference of impact of the shock between high debt agents and low- debt agents?

[jpfeifer]

It is a partial derivative and your interpretation is mostly correct. However, it usually describes the aggregate law of motion. You cannot take it in isolation for some agent in the economy and conduct counterfactuals the way you seem to do it in your question.

The coefficient of (b(-1), shock) on total consumption gives you the differential impact of the shock for a particular level of debt on total consumption.