New directions for stochastic open economy models
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
This sequel to "Redux" switches the friction from sticky goods prices to sticky nominal wages, solved exactly (not linearized) under uncertainty -- a choice the authors motivate by showing that the rival pricing-to-market/local-currency-pricing literature's prediction (that depreciation worsens a country's terms of trade) is "decidedly counterfactual" in the data. The exact solution reveals that uncertainty affects expected output and welfare levels directly, not just their variances; the resulting efficient monetary rule is procyclical, and welfare ranks an optimal float above an optimal fix above a fixed money-supply-ratio regime.
What this paper finds — and why it matters
This 2000 Journal of International Economics paper by Maurice Obstfeld and Kenneth Rogoff extends the “Redux” sticky-price approach to a genuinely stochastic setting with an exact closed-form solution – not a linear approximation – built around sticky nominal WAGES, rather than sticky goods prices, set one period in advance under log-normal uncertainty, with both traded- and nontraded-goods prices remaining fully flexible markups over those preset wages. The paper first motivates this modeling choice empirically: it shows that the pricing-to-market/local-currency-pricing (PTM-LCP) literature’s prediction – that an unexpected currency depreciation should IMPROVE a country’s manufacturing terms of trade, since import prices are preset in the importer’s own currency – is “decidedly counterfactual,” since correlations between nominal effective exchange-rate changes and multilateral terms-of-trade changes are mostly positive across twenty-one industrial countries, matching the traditional assumption that exporters invoice largely in their own (the exporter’s) currency rather than the buyer’s. Having settled on sticky wages and flexible goods prices, the paper derives closed-form expressions for expected output, the terms of trade, and welfare that depend directly on the VARIANCES and COVARIANCES of underlying shocks (productivity, money, exchange rates) – a channel invisible to linearized models, which collapse uncertainty into a certainty-equivalent mean. The paper then characterizes globally efficient monetary policy: a particular policy rule that replicates the flexible-wage allocation is shown to be constrained-efficient (Proposition 1) despite the interaction between nominal wage stickiness and monopoly distortions, and the implied optimal rule is procyclical, with a positive productivity shock calling for an expansionary monetary response. Finally, comparing three monetary regimes restricted to productivity shocks, the paper ranks expected welfare as optimal float greater than optimal fix greater than world monetarism (a fixed ratio of the two countries’ money supplies), with the fix-versus-float welfare gap collapsing to zero only in the special cases of no traded goods or unit consumption-elasticity of money demand.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What gap in the existing new-open-economy-macroeconomics literature motivates this paper?
“There has been an explosion of academic literature on the ’new open economy macroeconomics’ in the last several years… very recent contributions have sought to understand more deeply the positive macroeconomic effects of uncertainty as well as the normative implications for alternative international monetary regimes. As we showed in Obstfeld and Rogoff (1998), important effects of uncertainty… can compound or offset the more obvious welfare effects of variability. These effects are central to accurate regime evaluation, yet they are masked by the linearization techniques commonly used to solve dynamic stochastic models” (Abstract / Introduction, p. 1). The paper’s response is to present a simplified sticky-wage model with an exact closed-form solution that captures uncertainty’s effects on levels, not just variances.
Q2. What empirical evidence does the paper present against the pricing-to-market/local-currency-pricing (PTM-LCP) view, and why does this matter for the modeling choice?
Under PTM-LCP, an unanticipated home currency depreciation should IMPROVE the home manufacturing terms of trade, since import prices are preset in the importer’s own currency and do not move with the exchange rate; the paper tests this by correlating quarterly changes in each of 21 industrial countries’ nominal effective exchange rate with changes in its multilateral terms-of-trade index, 1982-1998 (Sec. 2.4.1, Table 1, p. 8). The correlations are overwhelmingly positive (e.g., 0.51 for Australia, 0.31 for the US, 0.42 for the UK, with only Netherlands and Portugal slightly negative), which is “decidedly counterfactual” for PTM-LCP and instead matches “a traditional framework in which exporters largely invoice in home currency.” A second test using monthly bilateral exchange-rate and relative-export-price data across six industrial countries (Table 2, Sec. 2.4.2) finds correlations “typically 0.70 or higher,” again inconsistent with LCP’s prediction of a near-zero or negative covariance.
Q3. What is the basic structure of the stochastic sticky-wage model, and what is “preset” versus flexible?
Two equal-sized countries each produce a continuum of differentiated tradable and nontradable goods; workers are monopolistic suppliers of differentiated labor who preset next period’s NOMINAL WAGE one period in advance of observing money and productivity shocks, but all GOODS prices (traded and nontraded) remain fully flexible markups over the (predetermined) wage (Sec. 3, pp. 12-16). This is the reverse of the Redux/sticky-price convention: “the most crucial assumption in our model is that workers set next period’s nominal wages… in advance of production and consumption of realized economic shocks.”
Q4. What is the closed-form wage-setting equation, and how does uncertainty enter it directly?
The optimal preset nominal wage can be written (under lognormality) as W = (phi/(phi-1)) times (E{K}(E{L})^(nu-1)) / ((E{C})^(-rho) E{1/P}) times exp(xi), where xi – “entirely due to uncertainty” – is a function of the variances of labor supply, consumption, and the covariances of consumption with labor supply and the price level (eq. 14, Sec. 4.1, p. 18). Because xi depends on variances and covariances of the underlying shocks, “uncertainty affects the expected LEVELS of expenditure and other macroeconomic aggregates… invisible to crude linear approximations to models such as ours that ignore variance terms” – for example, a positive covariance between consumption and labor supply raises the expected marginal utility of consumption when labor supply is high, inducing workers to set a HIGHER wage ex ante.
Q5. What does the paper establish about efficient monetary policy under sticky wages (Proposition 1)?
“A global monetary policy that gives the same real allocation as under flexible wages is efficient” (Sec. 6.1.2, Proposition 1, p. 29). The proof shows that although two distortions are present – nominal wage stickiness and monopoly power in both labor and goods markets – the monopoly distortions can be eliminated by standard proportional wage and production subsidies that have no bearing on the terms that enter the model’s welfare-variance expression (Omega, Omega); given these subsidies in place, any monetary policy rule that replicates the flexible-wage allocation is Pareto efficient, since it is impossible to make one country better off without hurting the other.* The paper further shows such flexible-wage-replicating rules exist and are achievable, in the special case where a single productivity shock symmetrically moves both the traded and nontraded sectors.
Q6. What is the qualitative character of the optimal monetary policy rule derived in the paper?
The optimal rule is, “in a sense, procyclical”: a negative productivity shock (a fall in K) would, absent any response, elicit greater labor supply and output under flexible wages, so optimally home monetary policy responds expansively to offset the shortfall, while the foreign monetary response is simultaneously contractionary when epsilon is greater than 1 – yet “the net global monetary response… is always positive,” taking the explicit form m + m = E m + E m - (1/(nu times epsilon)) times [(kappa minus E kappa) + (kappa* minus E kappa*)]** (Sec. 6.1.2, pp. 30-31). “Notice that only when gamma=0 (no goods traded) or epsilon=1 (no over/under-shooting) is it optimal for a country’s monetary policy to respond exclusively to the domestic productivity shock” – in general, efficient policy requires cross-country coordination of the exchange-rate response, not simply each country stabilizing its own shocks.
Q7. How does the paper rank welfare across the optimal float, optimal fix, and “world monetarism” regimes?
Restricting to productivity shocks alone (no monetary shocks), expected utility under an optimal float equals a baseline expression (eq. 25, Sec. 6.2); “world monetarism” (fixing the exchange-rate-weighted average of the two countries’ money supplies rather than letting policy respond to shocks) delivers strictly lower welfare, EU^World monetarism = EU^Optimal float minus (1/(2 nu)) times sigma_kappa^2; an optimal FIXED exchange rate, which still allows monetary policy to offset shocks subject to the exchange-rate constraint, achieves EU^Optimal fix = EU^Optimal float minus (1/(4 nu)) times sigma_kappa^2, which is strictly HIGHER than world monetarism but still strictly below the (unconstrained) optimal float (Sec. 6.2, pp. 31-32). The ranking is therefore optimal float greater than optimal fix greater than world monetarism, with the fix-float welfare gap vanishing only in the special cases already noted (gamma=0 or epsilon=1).
Q8. What does the paper’s conclusion identify as the contribution and the remaining research agenda?
“In this paper we have developed a remarkably simple and tractable stochastic model… that can be used to answer a variety of theoretical and policy questions, including questions about welfare under alternative monetary regimes. Thanks to the model’s log-linearity, we are able to get not only exact closed form solutions for levels and variances of all the endogenous variables in the model, but we are also able to derive exact welfare results despite the complication that there are two sources of market imperfection: monopoly and wage stickiness” (Sec. 7, Conclusion, pp. 32-33). The paper explicitly frames its approach as complementary to, not a replacement for, the contemporaneous PTM-LCP literature: “we do not necessarily view our model as ‘better’ than the plethora of interesting new open economy macroeconomic models built on the assumption that all prices… are equally rigid in domestic-currency terms,” while maintaining that its own empirical findings on terms-of-trade/exchange-rate comovement are “not worse than” those of the PTM-LCP alternative.
Key terms in this paper
Definitions below follow the paper's own usage.
- Sticky-wage closed-form model (versus sticky-price models)
- The paper's central modeling choice (Sec. 3): rather than the Redux convention of preset goods prices, workers preset next period's nominal wage one period in advance under uncertainty, while all traded- and nontraded-goods prices remain fully flexible markups over that wage; this delivers an exact (not log-linearized) stochastic solution in which the level, not merely the variance, of expected output, terms of trade, and welfare depends on the underlying shocks' second moments.
- Terms-of-trade/exchange-rate comovement evidence against PTM-LCP
- The paper's empirical motivation (Sec. 2.4, Table 1): quarterly correlations between nominal effective exchange-rate changes and multilateral terms-of-trade changes across 21 industrial countries, 1982-1998, are overwhelmingly positive, directly contradicting the pricing-to-market/local-currency-pricing literature's prediction that a depreciation should improve the manufacturing terms of trade, and instead matching the traditional assumption that exporters invoice predominantly in their own currency.
- Procyclical optimal monetary rule and the float-fix-monetarism welfare ranking
- The paper's policy results (Sec. 6): the globally efficient monetary rule responds expansively to a negative home productivity shock while the net global money supply always moves procyclically with shocks; restricting to productivity shocks, expected welfare ranks an optimal float above an optimal fixed exchange rate, which in turn ranks above 'world monetarism' (a fixed money-supply ratio), with the fix-float gap closing only when there are no traded goods or when the consumption elasticity of money demand equals one.