This paper is about a now classic question in macroeconomics and public finance. A government needs to finance an exogenously given stochastic process of purchases. How do the optimal taxes behave over dates and states?
There is a large literature on this question that uses what I will term the Ramsey approach. Under this approach, the government is restricted to use linear taxes on current variables like capital and labor income. The government's main goal is then to minimize the social distortions associated with linearity.
The main weakness in the Ramsey approach is obvious: there is no explicit motivation for the restrictions that drive the analysis. Why should the government be restricted to using linear taxes? Virtually all real-world labor income tax codes display nontrivial amounts of nonlinearity. Why should the government be restricted to using functions of current variables? At least in the United States, federal taxes depend in complicated ways on the full history of assetholdings (through the use of basis calculations) and federal (social security) transfers depend in complicated ways on the history of labor incomes.
This weakness in the Ramsey approach has led to a new literature about the optimal taxation question. Under the new approach, instead of specifying an arbitrary set of tax instruments, the investigator first specifies the informational and/or enforcement frictions that limit the government's ability to extract revenue. Then, the investigator designs a tax system that implements a constrained Pareto optimal allocation given these frictions.