## 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.

This is a preview of subscription content, access via your institution.

## 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 %.

## References

Aghion P, Howitt P (1998) Endogenous growth theory. MIT Press, Cambridge

Alexopoulos M (2004) Unemployment and the business cycle. J Monet Econ 51:277–298

Alexopoulos M (2006) Shirking in a monetary business cycle model. Can J Econ 39:689–718

Alexopoulos M (2007) A monetary business cycle model with unemployment. J Econ Dyn Control 31:3904–3940

Badinger H (2009) Globalization, the output-inflation trade-off and inflation. Eur Econ Rev 53:888–907

Baghestani H, Noori E (1988) On the rationality of the Michigan monthly survey of inflationary expectations. Econ Lett 27:333–335

Ball L (1994) What determines the sacrifice ratio? In: Mankiw G (ed) Monetary policy. NBER, Cambridge, pp 155–193

Ball L (2006) Has globalization changed inflation? Working Paper 12687. NBER, Cambridge

Baltagi BH (2005) Econometric analysis of panel data, 8th edn. Wiley, Chichester

Batchelor RA, Dua P (1989) Household versus economist forecasts of inflation: a reassessment. J Money Credit Bank 21:252–257

Beetsma RMWJ, Jensen H (2005) Monetary and fiscal policy interactions in a micro-founded model of a monetary union. J Int Econ 67:320–352

Benigno P (2004) Optimal monetary policy in a currency area. J Int Econ 63:293–320

Blanchard O, Galì J (2010) Labor markets and monetary policy: a new Keynesian model with unemployment. Am Econ J Macroecon 2:1–30

Bleaney M (1999) The disappearing openness-inflation relationship: a cross-country analysis of inflation rates. Working Paper WP/99/161. International Monetary Fund, Washington DC

Bowdler C (2009) Openness, exchange rate regimes and the Phillips curve. J Int Money Finance 28:148–160

Campbell CM (2006) A model of the determinants of effort. Econ Model 23:215–237

Campbell CM (2008a) An efficiency wage approach to reconciling the wage curve and the Phillips curve. Labour Econ 15:1388–1415

Campbell CM (2008b) An efficiency wage—imperfect information model of the Phillips curve. Northern Illinois University, Dekalb. http://nzae.org.nz/wp-content/uploads/2011/08/nr1215477105.pdf

Campbell CM (2010a) Deriving the wage-wage and price-price Phillips curves from a model with efficiency wages and imperfect information. Econ Lett 107:242–245

Campbell CM (2010b) Appendix to “Deriving the wage-wage and price-price Phillips curves from a model with efficiency wages and imperfect information”. http://www.niu.edu/econ/Directory/Campbell/PhillipsPaperELAppendix.pdf. Accessed 8 March 2011

Campbell CM (2011a) Efficiency wage setting, labour demand, and Phillips curve microfoundations. http://mpra.ub.uni-muenchen.de/49196/

Campbell CM (2011b) The formation of wage expectations in the effort and quit decisions of workers. http://mpra.ub.uni-muenchen.de/31590/

Canova F (1998) Detrending and business cycle facts. J Monet Econ 41: 475–512

Caraballo MÁ, Efthimiadis T (2012) Is 2 % the optimal inflation rate for the Euro area?Int Econ Econ Policy 9: 235–243

Cavelaars P (2009) Does globalization discipline monetary policymakers?J Int Money Finance 28: 392–405

Çenesiz MA, Pierdzioch C (2010) Capital mobility and labor market volatility. Int Econ Econ Policy 7: 391–409

Chinn MD, Ito H (2008) A new measure of financial openness. J Comp Policy Anal 10: 309–322

Chari VV, Kehoe PJ, McGrattan ER (2000) Sticky price models of the business cycle: can the contract multiplier solve the persistence problem?Econometrica 68: 1151–1180

Cragg JG, Donald SG (1993) Testing identifiability and specification in instrumental variable models. Econ Theory 9: 222–240

Daniels J, VanHoose D (2006) Openness, the sacrifice ratio, and inflation: is there a puzzle?J Int Money Finance 25: 1336–1347

Daniels JP, VanHoose DD (2009) Trade openness, capital mobility and the sacrifice ratio. Open Econ Rev 20: 473–487

Daniels JP, VanHoose DD (2013) Exchange rate pass through, openness, and the sacrifice ratio. J Int Money Finance 36: 131–150

Daniels JP, Nouzard F, VanHoose DD (2005) Openness, central bank independence, and the sacrifice ratio. J Money Credit Bank 37: 371–379

Danthine JP, Kurmann A (2004) Fair wages in a new Keynesian model of the business cycle. Rev Econ Dynamics 7: 107–142

Danthine JP, Kurmann A (2010) The business cycle implications of reciprocity in labor relations. J Monet Econ 57: 837–850

De Grauwe P (2011) The Eurozone as a morality play. Interecon 46: 230–231

Duca J, VanHoose D (2000) Has greater competition restrained inflation?South Econ J 66: 479–491

Edge RM (2002) The equivalence of wage and price staggering in monetary business cycle models. Rev Econ Dyn 5: 559–585

Evans G, Gulamani R (1984) Tests for rationality of the Carlson-Parkin inflation expectations data. Oxf Bull Econ Stat 46: 1–19

Fuhrer JC (1997) The (un)importance of forward-looking behavior in price specifications. J Money Credit Bank 29: 338–350

Gibson HD, Palivos T, Tavlas GS (2013) The crisis in the Euro area: an analytic overview. J Macroecon, forthcoming. doi:10.1016/j.jmacro.2013.09.014

Gouveia S, Correia L (2013) Labour costs dynamics in the Euro area: some empirical evidence. Int Econ Econ Policy 10: 323–347

Gramlich EM (1983) Models of inflation expectations formation. J Money Credit Bank 15: 155–173

Gruben W, McLeod D (2002) Capital account liberalization and inflation. Econ Lett 77: 221–225

Gruben W, McLeod D (2004) Capital market liberalization, disinflation, and commitment. Federal Reserve Bank of Dallas, Dallas

Guiso L, Sapienza P, Zingales L (2004) Does local financial development matter?Q J Econ 119: 929–969

Hamilton J (1994) Time series analysis. Princeton University Press, Princeton

Honkapohja S (2013) The euro area crisis: a view from the North. J Macroecon, forthcoming. doi:10.1016/j.jmacro.2013.08.004

Hughes Hallett A, Richter C (2008) Have the Eurozone economies converged on a common European cycle?Int Econ Econ Policy 5: 71–101

Karras G (1999) Openness and the effects of monetary policy. J Int Money Finance 19: 13–26

Koronowski A (2009) Divergent business cycles as an effect of a monetary union. Int Econ Econ Policy 6: 103–113

Lane P (1997) Inflation in open economies. J Int Econ 42: 327–247

Lombardo G (2006) Inflation targeting rules and welfare in an asymmetric currency area. J Int Econ 68: 424–442

Loungani P, Razin A, Yuen CW (2001) Capital mobility and the output-inflation trade-off. J Dev Econ 64: 255–274

Mankiw NG, Reis R, Wolfers J (2003) Disagreement about Inflation Expectations. NBER Macroecon Annu 18: 209–248

Mullineaux DJ (1980) Inflation expectations and money growth in the United States. Am Econ Rev 70: 149–161

Obstfeld M, Rogoff K (1996) Foundations of international macroeconomics. MIT, Cambridge

Pedregal DJ, Young PC (2002) Statistical approaches to modelling and forecasting time series. In: Clements MP, Hendry DA (eds) A companion to economic forecasting. Blackwell, Oxford, pp 69–104

Razin A, Loungani P (2005) Globalization and inflation-output tradeoffs. Working Paper 11641. NBER, Cambridge

Razin A, Yuen C (2002) The ‘New Keynesian’ Phillips curve: closed economy versus open economy. Econ Lett 75: 1–9

Roberts JM (1997) Is inflation sticky. J Monet Econ 39: 173–196

Roberts JM (1998) Inflation Expectations and the transmission of monetary policy. Board of Governors of the Federal Reserve System, Finance and Economics Discussion, Washington DC

Romer D (1993) Openness and inflation: theory and evidence. Q J Econ 108: 869–903

Sögner L, Stiassny A (2010) An analysis on the structural stability of Okun’s law—a cross-country study. Appl Econ 34: 1775–1787

Staiger D, Stock JH (1997) Instrumental variables regression with weak instruments. Econometrica 65: 557–586

Stock J, Watson MW (1999) Forecasting inflation. J Monet Econ 44: 293–335

Stock JH, Yogo M (2005) Testing for weak instruments in linear IV regression. In: Andrews DWK, Stock JH (eds) Identification and inference for econometric models: essays in honor of Thomas Rothenberg. Cambridge University Press, Cambridge, pp 80–108

Temple J (2002) Openness, inflation, and the Phillips curve: a puzzle. J Money Credit Bank 34: 450–468

Terra C (1998) Openness and inflation: a new assessment. Q J Econ 113: 641–648

Thomas LB (1999) Survey measures of expected U.S. inflation. J Econ Perspect 13: 125–144

Vaona A (2007) Merging the purchasing power parity and the Phillips curve literatures: regional panel data evidence from Italy. Int Reg Sci Rev 30: 152–172

Vaona A (2013a) The most beautiful variations on fair wages and the Phillips curve. J Money Credit Bank 45: 1069–1084

Vaona A (2013b) Inflation gifts and endogenous growth through learning-by-doing. Working Papers 09/2013. University of Verona, Department of Economics, Verona

Walsh C (2003) Monetary theory and policy. MIT Press, Cambridge

Woodford M (2003) Interest and prices: foundations of a theory of monetary policy. Princeton University Press, Princeton

## Acknowledgments

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

## Author information

### Authors and Affiliations

### Corresponding author

## 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

## Rights and permissions

## About this article

### Cite this article

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

Published:

Issue Date:

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

### Keywords

- Efficiency wages
- Unemployment
- Phillips curve
- Inflation
- Adaptive expectations
- Kalman filter

### JEL Classifications

- E3
- E20
- E40
- E50
- F15
- F41
- C22
- C26