Time Inconsistency As Well As Debt

For macroeconomists

In recent posts I’ve talked nearly empirical work I did a decade agone on telephone commutation rates, a non-technical piece on policy I wrote a few years ago, as well as closed to recent microfounded analysis undertaken yesteryear others. So for completeness, hither is something on a pretty technical, thoroughly microfounded article that I wrote amongst Campbell Leith that late came out inward the JMCB.

The house to start is a upshot that is relatively familiar. When governments tin commit as well as follow an optimal policy, steady dry ground debt follows a random walk. If nosotros start out from a seat where the debt stock is at its optimal level, as well as and so at that topographic point is a daze that causes debt to rise, the optimal response is to permit debt remain permanently higher. This is essentially a variant of the taxation smoothing idea. Taxes could rising to convey debt dorsum downwards to its pre-shock level, but that incurs electrical current costs (higher distortionary taxes) for futurity benefits (less debt, so less debt interest, so lower taxes). If the existent involvement charge per unit of measurement equals the charge per unit of measurement of fourth dimension preference, as well as so taxation smoothing implies it is improve to smoothen taxes, which inward plow implies it is improve to permit debt remain higher.

I discussed this upshot inward this post based an before EJ article written amongst Tatiana Kirsanova. That newspaper focused on uncomplicated financial rules combined amongst optimal monetary policy. This JMCB newspaper simply looks at optimal policy, where the authorities jointly controls monetary as well as financial instruments, inward a really conventional New Keynesian model.

In this sort of model the description inward a higher house of the optimal response to a debt daze is non quite complete. In the initial period, governments volition deed to cut down debt yesteryear a minor amount. It is optimal to engineer a minor outburst of surprise inflation to cut down debt. This solely occurs inward the initial period, as well as it has a hardly noticeable comport on on debt. However 1 time that catamenia has passed, the same incentive exists to generate a flake of surprise inflation inward the novel electrical current catamenia to farther cut down debt. So the policy is fourth dimension inconsistent for this reason.

The fourth dimension inconsistency employment is like to the familiar inflation bias illustration for monetary policy. There, the optimal policy would endure to accomplish the inflation target, but if the natural charge per unit of measurement of output is inefficiently depression at that topographic point is an incentive to generate an initial outburst of surprise inflation. The solely means of removing this temptation inward futurity periods is to run inflation good inward a higher house target, which is inflation bias.

So how create nosotros take the incentive to snuff it on cutting debt a picayune bit? The answer is obvious 1 time y'all dry ground it, but it is unfortunately non-trivial to prove, which is what the newspaper does. The incentive to initiate a minor amount of surprise inflation to cut down excess debt exists equally long equally at that topographic point is excess debt. To take the incentive to cutting debt yesteryear a little, y'all receive got to cutting debt yesteryear a lot. The discretionary, fourth dimension consistent response to a positive daze to debt is to convey debt really rapidly dorsum to the pre-shock level.

 

So the root best policy, if the authorities tin commit, is to permit debt remain higher. The inferior policy that results from a lack of commitment is that debt is brought dorsum downwards really quickly. If this upshot seems strange, it may endure because nosotros receive got inward the dorsum of our minds the existent the world employment of deficit bias as well as potential default. However neither is acquaint inward this model: the authorities is benevolent, as well as at that topographic point is nix inward the model to brand high levels of debt problematic. 

The newspaper calculates welfare inward both the commitment as well as discretionary cases. The welfare costs of whatever daze to the world finances are much greater nether discretion, equally y'all mightiness approximate for a policy that straight off brings debt dorsum downwards to its master copy level. Finally the newspaper looks at ‘quasi-commitment’, which puts closed to probability on plans beingness revised.

The newspaper takes an idealised set-up (benevolent governments) inward a simple, idealised model (e.g. agents alive forever), so it is a long means from practical policy concerns. (If y'all desire something along those lines, meet this paper I wrote amongst Lars Calmfors.) However what this newspaper does demo is that at that topographic point is no necessary linkage betwixt the employment of fourth dimension inconsistency as well as the lack of debt control. In a uncomplicated New Keynesian model lack of credibility tin Pb to excessive command of debt.