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It is believed that a common monetary policy in a monetary union will have identical effects on different countries as long as these countries have identical fundamentals. We show that, when there is specialization in production, the terms of trade react to the shock. The transmission mechanism of a monetary shock has in this case an additional channel, the terms of trade. This is the case even if state contingent assets can be traded across countries. For a reasonable parametrization, the differential on the transmission across countries is quantitatively significant when compared with the effect on the union's aggregates. Monetary shocks create cycles with higher volatility in “poor” countries than in “richer” ones.

The widespread view in the profession is that homogeneous shocks in a set of countries or regions have no idiosyncratic effects if these countries or regions are identical. The standard hypotheses in the international macroeconomic literature imply that aggregate shocks do not affect the terms of trade when countries are identical. Therefore, relative consumptions, relative incomes and the current accounts do not change in response to such a shock. Instead, in this paper we want to stress the effects of common shocks in identical countries, by not closing the potential role of the terms of trade and of the current account in the transmission of common shocks, and therefore allowing for different outcomes across similar countries. Countries in this paper are similar in the sense that they have identical preferences and technologies, but they are specialized in the production of aggregate tradable goods with different income elasticities. We do not explain formally how identical countries specialize in goods with different income elasticities to keep the model simple. But it is not difficult to devise setups that could originate such an outcome. A simple paradigm of such a situation would be equal production technologies for the goods, with increasing returns to scale, or with constant returns to scale and an initial sunk entry cost for each firm. Each country specializes in the production of a set of the goods, and the aggregate tradable goods, in which the countries specialize, will have in general different income elasticities. The number of firms in each of the countries, and the pattern of trade and specialization across countries would be indeterminate as in Krugman (1980). The main result of this paper conveys more importance to monetary policy in a monetary union because – by impacting on the terms of trade and on relative allocations – it is more powerful than in the traditional view where a common monetary policy cannot affect similar countries differently. In this sense, this paper represents a step forward in trying to understand the transmission mechanism of monetary policy in a monetary union. We evaluate numerically the idiosyncratic effects of a monetary policy shock, in a simple model where countries have an identical nominal rigidity, and conclude that the asymmetric effects have the potential to be quantitatively significant. We focus on a monetary shock in a monetary union, but the conclusions extend to any other common shock. Market completeness is an important assumption in the open macroeconomics literature. The effects of idiosyncratic shocks may change substantially when this hypothesis is dropped, and therefore the non-existence of markets has non-trivial implications. The empirical plausibility of this assumption, is associated with the importance of changes in the current account in the transmission of shocks across countries. Although this assumption is clearly identified as determinant in the analysis of idiosyncratic shocks, or different exogenous transmission mechanisms, its importance for common shocks and identical transmissions mechanisms has not yet been explored in the literature.1 Typically to avoid the indeterminacy of the aggregates in the steady-state when markets are incomplete, and the associated non-stationarity in the dynamics, it is necessary to introduce a modification to the standard models (see Schmitt-Grohé and Uribe, 2003 and Correia et al., 1995 for further details). In this paper, even with incomplete asset markets, we maintain simplicity and tractability, because we consider a model that has well defined aggregates and is stationary at the union level, while it is non-stationary at the country level. That is, we have a particular form of aggregation even when asset markets are incomplete.2 The existence of state-contingent asset markets across countries is qualitatively unimportant for our results. The crucial market incompleteness is the labor immobility across countries. It is interesting that here the so much publicized role of the terms of trade as an insurance mechanism is reversed. It is exactly the endogenous response of the terms of trade to the common shock that leads to the asymmetric responses of the various economic variables across countries to the common shocks when labor is immobile. Usually, in response to an idiosyncratic productivity shock, the country whose productivity increased the most will produce relatively more but the relative price of the bundle of goods it produces will decrease also. Thus, the terms of trade reaction in response to idiosyncratic shocks will determine a smaller dispersion of the relative income of the countries. In the context of a simple model, Cole and Obstfeld (1991) demonstrated that the gains from completing the markets can be modest, as the terms of trade are a good insurance scheme for countries without state contingent asset markets. Even though, they provide full insurance only for a very small set of parameters, for a larger set of other realistic parameters they provide almost full insurance. Therefore, Cole and Obstfeld (1991) conclude that ”the terms of trade may play an important role by automatically pooling national economic risks”. More recently Ghironi (2006) showed these results may not be robust. The terms of trade can be a poor substitute for a full insurance scheme since, in more complex models, the transmission of idiosyncratic shocks has effects in an incomplete market framework that can be quantitatively fairly different from the ones obtained in a complete market setup. Our analysis is just on aggregate shocks, and in an environment where the insurance provided by the terms of trade, to idiosyncratic shocks, would not be enough to replicate complete markets. We show that, due to labor immobility, the terms of trade react to the common shock and therefore the outcomes of the shock differ across countries. To develop the intuition for the change in the terms of trade, and to introduce the aggregation results, we consider first an economy where firms have no restrictions on the way they choose prices. For the monetary shock to have real effects in the flexible price economy we assume that money has a role in transactions. Latter, to get an idea of the quantitative importance of this effect, we consider an alternative environment where firms set prices according to a Calvo (1983) mechanism. In this environment the model is solved numerically with log-linearization of the equilibrium equations. Unlike what happens in most closed economy models, where with the first order approximation the behavior of relative prices is lost, here there is a change in the terms of trade. This occurs because we impose labor immobility across countries and non-homothetic preferences. These are our crucial assumptions. If instead we had assumed homothetic preferences for the households, the same result could be obtained if government expenditures were introduced, identical across countries but whose composition across goods did not coincide with the one of the households. In this way total demand (private and public) would be again non-homothetic, and the result would be preserved. The assumption of identical income elasticities across goods is clearly rejected by empirical microstudies. For example, Blundell et al. (1993) state that “In our sample of UK survey data for 15 years we find strong evidence of (…) the presence of nonlinearity in the micro-level Engel curves”. Another example, Banks et al. (1997) establish that Engel curves differ across goods, and that they depend on higher order income terms through coefficients which are price dependent. These empirical facts are not relevant for macro-models if the assumption of homogeneity/nonhomotheticity is not central for the issues under study. Therefore, for convenience and tractability most macro-models use homogeneous momentary preferences. However, there is a large literature that shows that this assumption is not harmless for the understanding of some facts, which under homogeneity turn into puzzles. For instance in growth models, when markets are open to international capital, it is very difficult to explain both the direction of capital flows and the cross section growth rates, when preferences are homogeneous. In Rebelo (1992) it is shown that the introduction of nonhomothetic preferences can solve both questions. Another example in growth is when aggregate consumption has to be disaggregated due to the question under scrutiny. To study the sectorial structural transformation associated with development, the different income elasticities across agriculture, manufacture and service goods play a fundamental role. This is shown in Kongsamut et al. (2001). In trade, the general equilibrium models used have consumption goods disaggregation as a main modeling assumption. Again here nonhomothetic preferences are fundamental. Examples are studies that explain trade determinants (e.g. Markusen, 1986 and Hunter, 1991) or the factor content of trade, e.g. Davis and Weinstein (2003), Trefler (1995) and Chung (2005). Thus, in models with a positive degree of disaggregation, like those used to understand the transmission of monetary policy through countries that trade, the abstraction of homogeneity should be used cautiously. If the individual goods that compose an aggregate traded good have different income elasticities then it should be expected that different aggregate traded goods would also have different income elasticities. This possibility is typically ignored as this literature of monetary policy transmission assumes homogeneity of preferences. Our paper explores this concern. To our knowledge Ravn et al. (2008) were the first to explore in a closed economy with flexible prices the effects of preference, government and technological shocks when households have Stone-Geary preferences. In contrast our paper studies the interaction between Stone-Geary preferences and labor immobility in the transmission of monetary shocks across countries. Ravn et al. (2008) stress the countercyclicity of the mark ups, while we use instruments to maintain the mark ups constant. How is an aggregate shock transmitted across countries? In a closed economy an aggregate shock does not affect the relative price of goods. However, this result does not extend to economies with more than one country. Aggregate shocks with asymmetric subsistence levels will have identical effects in all countries if and only if labor is perfectly mobile across countries. In this paper we want to stress that when there is less than perfect mobility of labor across countries then aggregate shocks will have asymmetric effects if countries are specialized in goods with different subsistence levels. It is the interaction of labor immobility and the specialization of countries in goods with different income elasticities that originate the asymmetric effects of aggregate shocks. The intuition behind the main result of the paper is straightforward. Since goods have different income elasticities, an aggregate shock, which can be a monetary shock or any other aggregate shock, changes the relative demands for the goods. Because countries are specialized in goods with different income elasticities some countries become relatively better off or worse off, depending on the sign of the shock and the goods in which they specialize. The countries that specialize in the goods with higher income elasticity benefit relatively more with a positive aggregate shock than the countries that specialize in goods with lower income elasticity. The opposite occurs with a negative aggregate shock; all countries are worse off but the countries that specialize in the goods with lower income elasticity are relatively better off than the countries that specialize in goods with higher income elasticity. The paper proceeds as follows. In Section 2 we describe the basic two-country monetary union when firms have no price setting restrictions. In Section 3 we show how the equilibrium can be computed analytically. The solution for the terms of trade is explored to identify how the common shock can create heterogeneous outcomes. In Section 3 we use an environment with price-setting frictions a la Calvo, where the degree of stickiness is the same for every firm independently of the country, and we show numerically that the idiosyncratic effects are significative when compared with the union's wide effects of the monetary shock. Section 4 contains concluding remarks.

The conventional wisdom is that common shocks should be transmitted identically in a set of countries connected by trade and with no differences in fundamentals. Therefore, a monetary shock in a monetary union composed by identical countries would not have idiosyncratic effects. In this paper we show that this conventional wisdom is not a general result. The crucial assumptions are segmented labor markets and non-unitary income elasticities of total demand for the goods. The first is the standard one in international economics. The second is not the usual one in macroeconomics when the focus is on one aggregate consumption per date and state. It is a well documented fact that different goods have different income elasticities and is reasonable to assume that the aggregate traded consumption goods inherit this property. We described the effects of a common monetary shock but it is trivial to verify that these results can be extended to other aggregate shocks, like common technology shocks. Since monetary policy should be used primarily for stabilization policy, i.e. in response to technological or other shocks, it is crucial to understand not only the monetary transmission but also the transmission of these other shocks. Controlling for country-specific shocks, our result is that richer countries exhibit less volatile cycles. This is not in conflict with the empirical evidence. During most of the last 50 years, less developed countries tend to have higher output volatility. The plot of the standard deviation of annual (per capita) growth rates against the level of real GDP per capita, for a large cross section of countries, has a quite pronounced negative slope (see Koren and Tenreyro, 2007 and Lucas, 1988). There are some explanations in the literature for this result, our paper proposes an additional one. This result can be regarded as complementary to the well known result that changes in the terms of trade, originated from country specific shocks, can replicate, partially or totally, state complete markets. This automatic insurance mechanism of the terms of trade that occurs with idiosyncratic shocks, is reversed when shocks are common. As we showed the change in the terms of trade is the mechanism that makes the common shock have asymmetric country specific outcomes.