Part V Recursive contracts Chapter 18 Dynamic Stackelberg problems . History dependence Previous chapters described decision problems that are recursive in what we can call ‘natural’ state variables, ., state variables that describe stocks of capital, wealth, and information that helps forecast future values of prices and quantities | Part V Recursive contracts Chapter 18 Dynamic Stackelberg problems . History dependence Previous chapters described decision problems that are recursive in what we can call natural state variables . state variables that describe stocks of capital wealth and information that helps forecast future values of prices and quantities that impinge on future utilities or profits. In problems that are recursive in the natural state variables optimal decision rules are functions of the natural state variables. This chapter is our first encounter with a class of problems that are not recursive in the natural state variables. Kydland and Prescott 1977 Prescott 1977 and Calvo 1978 gave macroeconomic examples of decision problems whose solutions exhibited time-inconsistency because they are not recursive in the natural state variables. Those authors studied the decision problem of a large agent the government facing a competitive market composed of many small private agents whose decisions are influenced by their forecasts of the government s future actions. In such settings the natural state variables of private agents at time t reflect their earlier decisions that had been influenced by their earlier forecasts of the government s action at time t. In a rational expectations equilibrium the government on average confirms private agents earlier expectations about the government s time t actions. This need to confirm prior forecasts puts constraints on the government s time t decisions that prevent its problem from being recursive in the natural state variables. These additional constraints make the government s decision rule at t depend on the entire history of the state from time 0 to time t. Prescott 1977 asserted that optimal control theory does not apply to problems with this structure. This chapter and chapters 19 and 22 show how Prescott s pessimism about the inapplicability of optimal control theory has been overturned by more recent An important finding is .
