Can International Monetary Policy Cooperation Be Counterproductive?

Rogoff states the paper “demonstrates that increased international monetary cooperation may actually be counterproductive,” because “cooperation between central banks may exacerbate the credibility problem of central banks vis-a-vis the private sector” (Abstract). The mechanism: coordinated monetary expansion produces a better output/inflation trade-off than unilateral expansion precisely because it does not induce exchange-rate depreciation; wage setters recognize that the incentive to inflate is therefore greater under a cooperative regime, so time-consistent nominal wages – and hence mean inflation – end up higher. Cooperation does still improve the response to disturbances, so “a cooperative regime which contains institutional constraints on systematic inflation is definitely superior” to a noncooperative one – the paper’s point is about unconstrained cooperation specifically, not cooperation as such.

Each central bank minimizes a social loss function (eq. 1a-b) quadratic in deviations of own-country employment n from its socially-desired level n-tilde and CPI inflation pi_I from its target pi_I-tilde, with chi the relative weight on inflation versus employment stabilization. Substituting the model’s structural equations, the loss can be written as a function of the productivity shock z, the real exchange rate q, and the gap between society’s and wage-setters’ employment targets (eq. 2a-b); the real exchange rate enters because wages are partially indexed to the CPI (which includes the foreign good) and the paper notes a similar term would arise if the foreign good entered the home production function. The paper stresses that although central banks are modeled as trying to stabilize employment and inflation around their socially preferred values, in time-consistent equilibrium they end up behaving as if stabilizing around the market-determined mean values instead – a consequence of the quadratic objective’s structure.

In equilibrium, wage setters set base nominal wages high enough that, absent disturbances, the central bank will not choose to inflate beyond the point consistent with wage setters’ desired real wage, because at that point the marginal benefit of further inflation to the bank is fully offset by the marginal disutility of the added inflation (Sec. 3) – the standard Barro-Gordon/Kydland-Prescott logic, cited explicitly. A second-best equilibrium could be reached if the central bank could credibly commit not to inflate systematically, but the paper frames the open question as how to design such a commitment device without sacrificing the bank’s ability to respond to genuine unanticipated shocks – the question the paper returns to in Section 8.

In the rational-expectations Mundell-Fleming macro model of Appendix A, each country produces a differentiated good; demand for each depends on relative prices, the real interest rate, and incomes, while only home (foreign) residents hold home (foreign) money and residents of both countries hold both countries’ bonds as perfect substitutes. The key structural link: any unilateral effort by either central bank to inflate causes its own real exchange rate to depreciate (except under complete wage indexation), and this depreciation directly raises CPI inflation while (given partial CPI wage indexation, or if the foreign good enters the home production function) tending to lower domestic employment – so the real exchange rate is “the key link between the two central bank objective functions.”

The mechanism, stated at its simplest for the no-disturbance, symmetric case: once base wage rates are set, any unilateral attempt by a central bank to inflate depreciates its real exchange rate, which raises CPI inflation and can lower employment – a “tempering influence” that wage setters factor into their nominal wage demands. Under cooperation, each central bank can count on the other to match any money-supply increase, so this tempering influence disappears – the real exchange rate stays fixed under coordinated expansion – and wage setters must therefore set a higher nominal wage growth rate to secure their target real wage, since the central banks will in fact ratify it. Since monetary policy has no systematic effect on mean employment in either regime (by the standard time-consistency logic), “the only thing accomplished by central bank to central bank cooperation is to raise inflation.” Rogoff is explicit that this is a specific result, not a general law: “one can construct counterexamples to this counterexample: cooperation can also be productive” (Sec. 5).

Solving the Nash first-order conditions (eqs. 3a-b, with the key term Psi defined as the ratio of partial derivatives of q and p with respect to money-supply surprises), the paper derives the mean Nash inflation rate pi_I^N (eq. 4) and shows that, because of the symmetric productivity shock assumption, the real exchange rate is always exactly zero in Nash equilibrium (q^N = 0), regardless of shock realizations (Sec. 6). The cooperative counterpart (eqs. 9-11) yields pi_I^C = pi_I-tilde + gamma*(n-tilde - n-bar)/chi, which the paper shows is strictly higher than the Nash mean inflation rate (comparison of eq. 9 vs. eq. 4) — “the mean rate of CPI inflation is indeed higher under the cooperative regime than under the noncooperative regime,” for exactly the reason discussed in Q5. Separately, comparing the magnitude of the price-level response to supply shocks, |dp_t^C| > |dp_t^N| (comparing eqs. 10 and 5) – the Nash regime lets supply shocks move employment more and inflation less than the cooperative regime does. The paper proves formally (via the comparative loss functions Gamma^N and Gamma^C, eqs. 7 and 11) that the cooperative response to disturbances is always weakly superior, Gamma^C < Gamma^N – cooperation improves stabilization of employment and inflation around their market-determined means even while raising the systematic inflation rate.

If the central banks’ objective functions instead depend on employment and money-supply growth (rather than employment and inflation directly) – the Canzoneri-Gray (1985) specification – the cooperative regime has a lower time-consistent inflation rate provided that, holding base wages constant, an unanticipated foreign money-supply increase lowers domestic employment, which holds when the expenditure-switching effect of the resulting real depreciation outweighs the expenditure-increasing effect of lower world real interest rates (absent wage indexation); if the expenditure-increasing effect dominates instead, cooperation remains more inflationary (Sec. 5, discussing Canzoneri and Gray 1985). The paper notes this ambiguity did not arise under the employment-inflation objective functions used in its main analysis, since there joint money growth always produces a better employment/inflation trade-off than unilateral growth.

The paper argues the central lesson is not that cooperation should be avoided but that an “optimally-designed cooperative regime is superior to any noncooperative scheme” – if central banks could credibly commit not to try to systematically raise employment, using monetary policy only to offset genuine disturbances, a strictly superior, “truly cooperative” outcome becomes available. The paper sketches one institutional channel: each country could pass a binding law fixing the future path of its money supply except for prespecified responses to specific disturbances (citing Buiter 1981 on optimal contingent rules); designing such prespecified responses jointly, rather than independently, could move the system from the Nash-like outcome toward the cooperative one without sacrificing the credibility gain. The paper flags this as suggestive rather than fully modeled – a direction for institutional design, not a worked-out mechanism.

The paper states its main result “has been expressed in a rational expectations cum wage contracting model” but argues “it clearly can arise in models with alternative non-neutralities and different sources of time-consistency problems,” giving as an example a flexible-price currency-substitution model in which each central bank maximizes seigniorage (Sec. 9, Conclusions) – explicitly offered as an illustrative extension, not a result derived in the paper. The paper’s own emphasized general point is methodological: “it can be misleading to model the strategic interactions of two governments without also modeling the game between the governments and the private sector” – i.e., analyses of international policy coordination that ignore the domestic credibility problem can reach the wrong sign on the welfare effects of cooperation.