In this paper we look at the PBC problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the NKPC model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton- Jacobi-Bellman (HJB) equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.
Prof. Gopal Basak did his early education in Indian Statistical Institute, Kolkata, and his Ph.D. from Indiana University, USA. He has held positions in Indian Institute of Science, Hong Kong Uni. of Science and Technology and Uni. of Bristol, UK, before joining the Indian Statistical Institute, Kolkata. His research interests are in stochastic processes, stochastic control, stochastic algorithms, urn models, and mathematical finance, among other things.