Aggregating heterogeneous-agent models with permanent income shocks

I introduce a method for simulating aggregate dynamics of heterogeneous-agent models where log permanent income follows random walk. The idea is to simulate the model using counterfactual permanent-income-neutral measure which incorporates effect that shocks have on macroeconomic aggregates. With measure, one does not need keep track permanent-income distribution. both useful analytical characterization consumption-savings behavior and numerical models. Furthermore, it trivial implement with few lines code.