## Abstract

This paper extends the efficiency wages/partially adaptive expectations Phillips curve, otherwise known as the price-price Phillips curve, from a closed economy context to an open economy one with both commodity trade and capital mobility. We also consider the case of a monetary union (a country) with two member states (regions). The theoretical results are *a priori* ambiguous. However, in the first place, on resorting to plausible numerical simulations, economic openness increases the reactiveness of inflation to the unemployment rate. In regard to a monetary union, the national unemployment multiplier in the aggregate Phillips curve decreases with the weight of the member state in aggregate employment and increases with that in output. Secondly, we show in two empirical applications that our calibration can provide informative priors for models to be estimated thanks to the Kalman filter.

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## Notes

Also to distinguish it from the wage-wage Phillips curve proposed by Campbell (2010a) as well. In this further model, it is wage and not price inflation that is connected to unemployment within an efficiency wages/imperfect information framework.

We identify the long-run structural values with steady state ones as done for instance by Aghion and Howitt (1998, p. 9).

From an empirical point of view, the sacrifice ratio is defined, after Ball (1994), as the ratio of the sum of the differences between trend output and actual output in logs, at the numerator, and the change in trend inflation during a disinflationary period, at the denominator. This variable–considering the differential between actual and potential output–is also interesting for short-run analyses. This is not so for the variable adopted in Bowdler (2009) and Daniels and VanHoose (2013) where reductions in trend output are considered. The former study found, in a sample of 41 countries running from 1981 to 1998, a weak negative correlation of sacrifice ratios with openness, which is not affected by the kind of exchange rate regime in place. In the latter study the marginal effect of trade openness at the average value of their CBI index is very close to zero. Furthermore, when accounting not only for CBI, but also for exchange rate pass-through, greater openness has an ambiguous effect on the sacrifice ratio. However, these results, given their long-run nature, cannot be considered as directly relevant to our analysis, which is concerned with the short-run.

*L*_{ t+i }(*h*) is the fraction of employed individuals within household*h*, not the working time of an individual agent.This implies that, using the symbology of Campbell (2010a),

*ψ*=0, where*ψ*is the steady state value of the short-run elasticity of labor supply. We also assume parameters to be chosen so that excess labour supply exists.Equation 6 does not imply rational expectations. To obtain this equation, one only has to leave unspecified the expectation operator in the first order conditions for bond and money holdings.

The reasons for not simply assuming either rational or adaptive expectations are reviewed in Campbell (2011b). Many studies have found that expectations are neither completely rational (Evans and Gulamani 1984; Batchelor and Dua 1989; Roberts 1997; Thomas 1999; Mankiw et al. 2003) nor purely adapative (Mullineaux 1980; Gramlich 1983; Baghestani and Noori 1988). The results obtained by Fuhrer (1997) and Roberts (1998) support a mixture of rational and adaptive expectations.

This is also consistent with Obstfeld and Rogoff (1996, Chapter 1).

This result of ours is broadly consistent with empircal findings by Çenesiz and Pierdzioch (2010), who showed that capital mobility has small effects on labour market magnitudes.

To facilitate the economic interpretation of our results, consider that unemployment rates were not multiplied by 100. Therefore, in the North a one point increase in the unemployment rate translates into a −0.07 % deviation of output from its long-run value. In the South, this deviation is about −0.02 %.

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## Acknowledgments

We wish to thank Carl M. Campbell and three anonymous referees for insightful comments. The usual disclaimer applies.

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## Appendix: Deriving the efficiency wages Phillips curve upon opening the trade account of the economy

### Appendix: Deriving the efficiency wages Phillips curve upon opening the trade account of the economy

The present appendix focuses on an economy with a closed capital account and an open trade one, given that a completely open economy is a special case of what follows. The procedure below is a generalization and a simplification of the one proposed by Campbell (2010b).

Consider Eq. 12 and substitute into it Eqs. 13, 16 and the condition \(\tilde {e}\tilde {e}_{W}^{-1}=\frac {W_{ss}}{P_{ss}^{e}}\) to obtain

Further make explicit \(\hat {L}_{t}+\hat {W}_{t}\) in Eq. 38 and substitute it with \(\frac {\hat {y}_{t}^{H}}{\phi }-\hat {A}_{t}+\hat {P}_{t}^{e}-e^{-1}e_{u}du_{t}\) from Eq. 16 to obtain

Combine Eqs. 13, 14 and 16 to obtain

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Vaona, A. The price-price Phillips curve in small open economies and monetary unions: theory and empirics.
*Int Econ Econ Policy* **12**, 281–307 (2015). https://doi.org/10.1007/s10368-014-0270-2

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DOI: https://doi.org/10.1007/s10368-014-0270-2