# ConsIndShockFastModel

In this post I will go over my latest PR on econ-ark/HARK.

The goal of this PR is to create a mirror to ConsIndShockModel.py, but that implements faster solutions using numba just-in-time compiling and optimization.

### PerfForesightSolution

The first step is to create a solution object called PerfForesightSolution that contains only python primitives and numba arrays. This object takes the place of ConsumerSolution, which creates additional HARK objects and can lead to unnecessary time overhead in the solution iteration. The distance_criteria for this solution is ["cNrm", "mNrm"], which is identical to the distance_criteria for ConsumerSolution but more straight forward. This ConsumerSolution replacement is faster because instead of having to create HARK objects such as cFunc, vFunc, etc. as LinearInterpolators for every solution iteration, the solution method or algorithm only really needs the primitives that compose these objects. Below I will describe in more detail how this object is used in the solver.

### ConsPerfForesightFastSolver

The next step is to create a solver that replaces ConsPerfForesightSolver, aptly called ConsPerfForesightFastSolver. The object uses a numba-optimized helper function called solveConsPerfForesightNumba. In this implementation, the outputs of this helper method are packaged into a PerfForesightSolution object instead of a ConsumerSolution object. As I mentioned, this avoids the needless creation of other HARK objects in the iteration, leaving the creation of a proper HARK solution to the end of the iteration. An additional feature that has been removed from the solution iteration is the searching of steady-state normalized market resources with addSSmNrm(). As the iteration does not depend on this result as an intermediate input, this can be safely moved to the end of the solution method, or rather to postSolve().

### PerfForesightFastConsumerType

Finally, I create an agent that can use the above solution method called PerfForesightFastConsumerType. Since now the solution iteration uses PerfForesightSolution, I first override solution_terminal_ = PerfForesightSolution(). Then, on __init__, I override solveOnePeriod to ConsPerfForesightFastSolver. Since I am overriding the solution_terminal_, I might still need a ConsumerSolution terminal in the case of a non-infinite problem. So, I override the method updateSolutionTerminal() to save an internal ConsumerSolution version of the solution_terminal. The final step is to implement a postSolve() method to wrap every PerfForesightSolution parameter into a HARK object and to run addSSmNrmNumba() only on the final solution. As I had mentioned, there is no need to create these objects at every iteration step of the solution, and it is thus more efficient to leave them to postSolve(). Now, ideally, the output of solve() is the same between the standard HARK approach and the fast approach, a list of ConsumerSolution objects with cFunc, vFunc, etc. as HARK LinearInterpolators.

### Checking for Equality

Having proposed a new agent type and solution that should be equivalent, or ideally identical, I then focus on implementing __eq__ methods for == comparison. In the class definition of ConsumerSolution in ConsIndShockModel.py, I add this method. The logic is that if the solution is a subclass of a HARKobject (which I presume all solutions should be), and if one of the solutions is a subclass of the other (for the two solutions being compared), and if the other solution has an attribute called "tolerance", then if the distance between both solutions is smaller than the tolerance of both solutions, then the solutions are equal, otherwise they are not. For this, I had to create a dummy attribute for ConsumerSolution as tolerance = 0.000001, although I argue that the solution should inherit “solution method parameters” such as tolerance, solution_distance, and completed_cycles. Although this works for comparing standard HARK approach and fast approach, there might be other cases where this should be revised.

For comparing whether two models are the same, I added an __eq__ method to PerfForesightConsumerType. The logic is that if the corresponding agent being compared to is a subclass of AgentType, and if one of the models is a subclass of the other (for the two models being compared), and if the other agent has an attribute called "params", then the models are equal if the params dictionaries are the same, where equality between dictionaries is built in. For this, I had to make params an attribute of PerfForesightConsumerType, and additionally I had to add cycles to params, to differentiate between finite and infinite horizon models with otherwise identical parameters.

##### Alan Lujan
###### PhD Candidate in Economics

My research interests include poverty and inequality, household finance, and computational economics.