The dynamic inconsistency of a government's preferred policy implies that delivering the `optimal' welfare level in the initial period constrains the economy to `low' levels in the future. In Discussion Paper No. 536, Research Fellow Daniel Cohen and Philippe Michel assume that policy-makers unequivocally implement ex post a fixed policy rule chosen ex ante and focus on which rule should be chosen. They argue that such a rule must satisfy the `Generalized Bellman equation' (GBE), in which the `best' policy rule is constrained always to deliver in the future at least the level of welfare which it offers to deliver in equilibrium today, but solving such an equation requires additional restrictions on the set of eligible policies.

Cohen and Michel derive a simple model of capital accumulation to examine the effects of `simple' tax policies, which they restrict to be linear, constant or kinked linear. They find surprisingly that linear tax policies provide no solution to the specified equation: `simple' rules must be more or less sophisticated. By restricting the strategies to be `simpler', i.e. constant, they find a unique solution to the GBE; while by allowing the policies to be more sophisticated, i.e. kinked linear, they find a range of `politically credible' policies, which all converge towards the same policy as the discount factor approaches one. Subject to some technical conditions, all such policies may be characterized by two simple necessary and sufficient criteria: they must always outperform the `standstill' policy of stabilizing the economy at whichever point it has reached; and they must also outperform the subset of policies that lead to the stationary state they aim to reach.

In Discussion Paper No. 537, Cohen and Michel again assume that policy-makers implement ex post the policies they announce ex ante and focus on whether voters who are not bound by their previous choices can be trusted to re-elect committed policy-makers in a democracy. The first-best (`time- inconsistent') policy on capital taxation is usually to tax all capital installed today and promise a more moderate tax for the entire future. In `industrial organization' models, in which policy-makers deviating from an announced policy are `punished' by a shift of private sector expectations away from the announced policy towards memoryless (`time-consistent') expectations, setting the rate of time preference low enough to make any deviation very costly will suffice to make such a policy credible.

Cohen and Michel argue, however, that if a democracy ever elects a politician on such a policy, any other politician who promises at the next election (with fresh credibility) to re-start the same programme will emerge as the victor. This critique of `time- inconsistent' policy need not imply that the `time-consistent' policy must be chosen, however, since even with continual elections a more moderate politician may successfully argue for a lower tax on capital both today and `tomorrow' (the date of the next election). Such a `moderate' politician must also show, however, that no superior option can or will be offered, today or tomorrow, by opponents making the same claim. But if politicians are free to announce anything they like, then no moderate politician can face the (rhetorical) competition of `free-riding' opponents who offer to postpone by one election the implementation of the moderate policy while offering to deviate optimally from it today. And such a `free-riding' policy can only be implemented today if it will not itself be subject to `free-riding' tomorrow. All politicians must therefore restrict their policy announcements to ensure that their message is not outweighed by the rhetoric of others.

Cohen and Michel adopt an axiomatic approach to assess which policy may emerge from such a political debate. Assuming the existence of a subset of policy announcements within which policy-makers agree to limit their announcements, they impose that this set be big enough to include all constant policies and that all policies must be self-consistent in the stationary state they aim to attain, i.e. they do not `free-ride' upon themselves. If politicians agree to restrict their announcements to offering a time-invariant tax rate for the infinite future, there is a single optimal tax rate for each level of capital accumulation, which changes continually over time.

In the literature of the industrial organization type, the optimal (constant) tax rate is the initial optimal rate. In Cohen and Michel's model, however, a democracy chooses the rate that is optimal last, i.e. once the economy has reached its stationary state. In the general case, this time-invariant policy has the unique property that it also dominates all other policies, once they have driven the economy to their own stationary states. Cohen and Michel therefore argue that all `politically credible' time-variant challengers to this policy must have the same stationary state, which corresponds simply to a `modified golden rule'.

Which `Simple' Rules Rather than Discretion?
Which Rules Rather than Discretion in a Democracy? An Axiomatic Approach
Daniel Cohen and Philippe Michel

Discussion Paper Nos. 536-7, March and April 1991 (IM)