Partial Credibility: A Solution Technique for Econometric Models

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This paper examines the optimal policy design problem for a government facing a private sector with forward-looking agents. As is well known, the optimal policy will be time-inconsistent in the sense that governments will have an incentive to re-optimise, period by period, even in the absence of shocks. Only if a government has established full credibility will the private sector believe that it will sustain its original policy announcement.Previous work has suggested that this a game-theoretic problem where the government is competing with the private sector. Thus, in a situation where the government has zero credibility, the situation degenerates to a Nash game and the time-consistent solution results. This paper argues that this usual conclusion is misleading in one important respect. The game does not directly involve the private sector since they display no strategic behaviour. Instead, the situation is analagous to a game between successive governments in each period. The time-inconsistent or full-credibility solution is thus the outcome which results when governments agree ex ante to minimise the same cost function which applies to all periods. By contrast, the time-consistent or zero-credibility solution is that which emerges when each successive government attempts to minimise its own cost function which ignores the cost incurred in previous periods.The implication of this interpretation is striking. It allows us to exploit standard solution techniques from game theory in a novel way. Since each player in the game has only a single vector of policy instruments, the size of the problem is no larger than for standard optimisation problems. Moreover, the technique can cope with a continuum of possibilities between zero and full credibility by varying a single parameter; this parameter may be interpreted as the ex ante probability that a government will re-optimise with respect to its own restricted cost function. As such, the time-inconsistent and time-consistent solutions emerge as special cases (with the parameter set at 1 and 0 respectively).This new solution technique is applied to the National Institute model of the U.K. economy, a large non-linear model, for varying degrees of credibility. A number of possible future applications for this technique are suggested.