Sophie Piton
email: sophie.piton@psemail.eu.

Valérie Mignon

Dramane Coulibaly

A European Disease? Non-tradable ination and real interest rate divergence

Keywords: Non-tradable prices, Balassa-Samuelson eect, Real interest rate Secteur abrité, eet Balassa-Samuelson, taux d'intérêt réel F41, F45, E43

, it shows that the real interest rate fall in the Euro Area (EA) periphery following the single currency's inception induced an increase in the relative price of non-tradable goods. Using a new dataset, it documents the dynamics of the tradable and the non-tradable sectors over 1995-2013 and the expansion of the non-tradable sector in the periphery before the euro crisis. It then carries out an econometric estimation for 11 EA countries over 1995-2013 and quanties the contribution of the pure Balassa-Samuelson eect and the impact of the interest rate on non-tradable relative prices. Diverging evolution in the interest rate impacted greatly the evolution of non-tradable relative prices within the euro area over the period. In Greece, the fall in the real interest rate over 1995-2008 could explain almost half of the non-tradable price increase relative to the EA average, while in Germany the increase in the real interest rate might have contributed up to 7% of the decrease of the non-tradable price relative to the average of the EA.

Introduction

When the euro was introduced, conditions for economic convergence the process of narrowing income gaps between lower and higher income countries seemed to be present. 1 Nominal interest rates between higher and lower income countries had converged rapidly2 and capital was owing from the richer (the "core") to the poorer (the "periphery") countries of the area. This convergence process was supposed to be the main reason behind the strong macroeconomic divergence between the core and the periphery, and the imbalances were supposed to be reduced as countries would converge. The 2010 euro crisis has challenged this view, with macroeconomic divergence among countries pointed to as reecting bad imbalances. In particular, debates have emerged to reassess the mechanisms behind the divergence in ination rates across countries and behind substantial price dierentials between tradable and non-tradable goods in some countries. Even though there is evidence of a convergence of tradable prices across Europe and higher productivity growth in the tradable sectors of catching-up economies, there seems to be a growing consensus that the Balassa-Samuelson (BS) eect3 cannot be the sole explanation to the steep rise in the non-tradable relative to the tradable price in the Euro Area (EA) periphery before the crisis [START_REF] Estrada | Patterns of convergence and divergence in the euro area[END_REF].

This paper further investigates the mechanisms behind the divergence of relative (non-tradable to tradable) prices across Europe. The starting point is Figure 1 which shows the evolution of relative prices and real interest rates in the periphery compared to core countries over 1995-2013. The periphery, facing a steep increase in relative prices, also faced a strong decrease in real interest rates up to 2008. Introducing two factors of production in the BS framework, the paper shows that the real interest rate fall in the EA periphery following the single currency's inception induced an increase in the relative price of non-tradable goods. Using a new dataset, it then documents the dynamics of the tradable relative to the non-tradable sector over 1995-2013 and highlights the expansion of the non-tradable sector in the periphery before the euro crisis. Finally, it carries out an econometric estimation for 11 EA countries over 1995-2013 to quantify the contribution of the pure BS eect and that of the interest rate reduction on non-tradable relative prices.

A growing literature has analyzed the impact of falling interest rates on the increase in relative prices of non-tradables. In 1983 already, [START_REF] Dornbusch | Real interest rates, home goods, and optimal external borrowing[END_REF] showed how an exogenous disturbance in the real interest rate can aect the price of non-traded goods by fueling a demand boom. This argument has also been suggested more recently by [START_REF] Fagan | Adjusting to the euro[END_REF]. Other papers analyze the impact of the interest rate on the supply side rather than on the demand-side of the economy: [START_REF] Reis | The Portugese slump and crash and the euro crisis[END_REF], studying the case of Portugal, suggests that capital inows were misallocated within the non-tradable sector due to nancial frictions, fueling transitory price increases in this sector. Other authors look at the impact of such misallocation on the sustainability of the current account and the probability of a balance of payment crisis [START_REF] Giavazzi | Why the current account may matter in a monetary union: Lessons from the nancial crisis in the euro area[END_REF][START_REF] Kalantzis | Financial fragility in small open economies: rm balance sheets and the sectoral structure[END_REF]. This paper departs from these analyses in the way that it studies the impact of interest rate variations in a BS framework. The BS framework has already been subject to various extensions to explain the permanent drift in non-tradable prices. Among others, De Gregorio et al. (1994) suggest that it could be explained by an exogenous demand-shift towards non-tradable goods.

More recently Bénassy-Quéré and Coulibaly (2014) suggest that ination dierentials in Europe also originate in heterogeneous market regulations. This paper shows that in the long term, a permanent and exogenous decrease in the interest rate will lead to a permanent drift in nontradable prices as long as the non-tradable sector is labor-intensive. This is, to our knowledge, the rst attempt to analyze the impact of the interest rate in a BS framework.

The remainder of the paper is organized as follows. Section 2 extends the usual BS theoretical framework to analyze the impact of a fall in the real interest rate on the non-tradable relative price. Section 3 describes the dataset and the construction of a tradability indicator, and then documents the dynamics of the non-tradable and tradable sectors over 1995-2013 in 11 countries of the EA. Section 4 presents the econometric strategy, reports empirical estimation results and robustness tests. Section 5 concludes.

Conceptual framework

The workhorse model to analyze the evolution of non-tradable prices in an open economy is the framework set by [START_REF] Balassa | The purchasing-power parity doctrine: a reappraisal[END_REF] and by [START_REF] Samuelson | Theoretical notes on trade problems[END_REF]. Their model features a small open economy with a perfectly competitive tradable sector (the price being determined by the world market), and a non-tradable sector (the price being determined domestically). Labor is the only factor of production. They show that, assuming the law of one price holds for tradable goods, productivity growth in this sector pushes real wages up both in the tradable sector and in the non-tradable one. This results in an increase in the relative price of non-tradable goods and thus in a real-exchange rate appreciation, which is commonly known as the BS eect. Several theoretical extensions have been proposed in the literature.4 Some of them consider two factors of production (labor and capital), or examine the implications of incorporating a demand-side in the BS framework (see, among others, De Gregorio et al., 1994;[START_REF] Obstfeld | Foundations of International Macroeconomics[END_REF][START_REF] Bénassy-Quéré | The impact of market regulations on intra-European real exchange rates[END_REF]. 5 This paper is the rst attempt to look at the impact of an exogenous change in the interest rate on the evolution of the non-tradable relative price. It focuses on the supply-side and builds on the framework set by De [START_REF] De Gregorio | International evidence on tradables and nontradables ination[END_REF] to show the impact of both faster productivity growth in the tradable sector and an exogenous and permanent fall in the interest rate on the relative price of non-tradable goods.

The model features a small open economy with two goods: a tradable, the numeraire, whose market is perfectly competitive and subject to the law of one price; a non-tradable good, which price is set domestically. Production takes place using two inputs: capital (mobile internationally and between sectors) and labor (mobile between sectors but not internationally). Labor sectoral mobility ensures that workers earn the same wage in either sector whereas capital international mobility ensures that the interest rate is given internationally.

Representative rms in each sector face a Cobb Douglas production function with two factors of production, of the form:

Y T = A T K T T L 1 T T (1) Y N = A N K N N L 1 N N (2)
where the subscripts T and N denote the tradable and non-tradable goods, Y denotes real output, L labor inputs and K capital. T ; N represent capital intensity in each sector ( T ; N P ]0; 1[ ).

Given that the tradable good acts as a numeraire, and given that the interest rate r is exogenous, combining rst order conditions in the tradable sector yields the equation for the real wage (nominal wage deated by the numeraire T ), !:

! = r T 1 T A 1 1 T T T 1 T T (1 T ) (3)
Combining rst order conditions in the non-tradable sector, given r and !, yields the equation for the non-tradable relative price p:

p = 1 A N ! 1 N (1 N ) r N N (4)
Plugging (3) into (4), we get that the non-tradable relative price is determined entirely by technological conditions and is independent of demand conditions. The relative price depends on the rate of interest (r ) and on the tradable and non-tradable sector productivities (A T ; A N ) and capital intensities ( T ; N ):

p = r N T 1 T A T (1 T ) 1 T T T 1 N 1 T A N (1 N ) 1 N N T (5)
The BS eect postulating a positive link between faster productivity growth in the tradable sector and the relative price of the non-tradable good is straightforward. Other things constant, a rise in the productivity of the tradable sector (A T ) decreases the price of this sector relative the non- tradable one. This BS eect goes through the impact of A T on !:

d! dA T = 1 1 T A T 1 T T r T 1 T T 1 T T (1 T ) > 0
This wage increase ensures that the marginal cost of tradables remains constant but it increases the marginal cost, and hence the relative price, of the non-tradable good:

dp dA T = 1 N 1 T A T N 1 T T r N T 1 T 1 A N 1 T 1 N 1 N T (1 N ) 1 T T N N > 0
In turn, the impact of an exogenous and permanent fall in the interest rate on the relative nontradable price depends on the capital intensity of the non-tradable relatively to the tradable sector ( N T ). Indeed, a fall in the interest rate all other variables remaining constant is matched by a wage increase ensuring that the marginal cost of tradables remains constant:

d! dr = T 1 T r 1 1 T A 1 1 T T T 1 T T (1 T ) < 0
If the non-tradable sector is relatively more (less) labor intensive, this rise in wages will increase (decrease) the marginal cost, and hence the relative price, of the non-tradable good:

dp dr = N T 1 T r 1 N 1 T A 1 N 1 T T A N 1 T 1 N 1 N T (1 N ) 1 T T N N < 0 if N < T
Expressing all variables relative to the Euro area (EA) average, assuming the law of one price holds in the tradable sector (p T = p EA T ), and assuming, as in the literature, that productivity grows faster in the tradable sector than in the non-tradable sector, the empirically testable model is given by:

p N p EA N = f A T A EA T ; r r EA (6)
where A T stands for productivity in the tradable sector, r the real interest rate, and EA subscripts stand for euro area averages. For similar productivity growth in the non-tradable sector, the country should experience a relative increase in its non-tradable price if its productivity growth in the tradable sector is stronger than the average productivity growth of the T sector in the euro area: we expect a positive coecient on the rst variable. Similarly, the country is expected to experience a non-tradable price increase if its real interest rate (expressed in terms of tradables) decreases more than it does, on average, in the EA, given that the non-tradable sector is more labor intensive than the tradable one. There seems to be evidence supporting this assumption that the non-tradable sector is more labor-intensive than the tradable sector. van [START_REF] Van Riet | Competition, productivity and prices in the euro area services sector[END_REF] show that services sectors are less capital intensive than the manufacturing sectors in the euro area at the beginning of the 2000s. Moreover, they show that Southern European countries tend to be characterized by a smaller average rm size than the Euro area aggregate, and have a larger share of self-employment in the service sector, making this sector even more labor intensive than in the rest of the EA. This assumption is also conrmed in the dataset used here. These results will be tested empirically after describing the dataset used and documenting patterns in the non-tradable sector ination across Europe over 1995-2013. All databases are converted into a 21-level NACE revision 2 classication, to get an unbalanced database6 providing data on gross value added at current and constant prices, production at current and constant prices, labor compensation at current prices, employment and the value of trade in goods and services and goods export for up to 11 EA countries (EA11)7 over 1995-2013. It is then possible to measure gross value added deators (chained linked indices, using 1995 as the reference year) and labor apparent productivity (value added in volume per hour worked) as a proxy for total factor productivity. Finally, series on annual real8 long-term interest rates come from Ameco.

Dening tradability

The tradability of a good or a service sector is dened as the capacity to trade its output internationally. As in De [START_REF] De Gregorio | International evidence on tradables and nontradables ination[END_REF] and most of the empirical literature, the extent to which a good or a service is actually traded with a foreign country is used as a proxy for its tradability. Therefore, the tradability of each sector at the euro area (EA11) level depends on its openness ratio the ratio of total trade (imports + exports) of the EA11 to total production in the EA11. As in De [START_REF] De Gregorio | International evidence on tradables and nontradables ination[END_REF] we use a threshold of 10%, so a sector is considered as being tradable if the average of its openness ratio over 2000-2013 is higher than 10% (the openness ratio for the period 1995-1999 cannot be measured since data on trade in services are not available for this period).

Figure 2 reports the openness ratio by sector on average over 2000-2013 (see Table A.1 in Appendix for more details). Unsurprisingly, agriculture, the manufacturing and mining and quarrying sectors are in the tradable sector. Concerning services, four industries are considered as tradable: accommodation and food service activities; transportation and storage; information and communication, and administrative and support service activities. The tradable sector accounts for 47% of total production, 36% of GVA (both at current prices) and 39% of employment.

A European Disease? Non-tradable ination and real interest rate divergence Inevitably, the threshold of 10% is arbitrary. One possibility could be to apply dierent tradability criteria for dierent countries, but applying the same criterion for all countries leads to more clearcut results.9 Using a threshold of 15% would exclude administrative and support service activities from the tradable sector. The tradable sector would then account for 43% of total production and 32% of GVA (at current prices), and 33% of employment. Using a threshold of 5% would include 2 other sectors in the tradable sector, and more particularly nancial and insurance activities. The tradable sector would then account for 57% of total production and 47% of GVA (at current prices), and 47% of employment.

However, for nancial and insurance activities for example, recent empirical work [START_REF] Jensen | Tradable services: Understanding the scope and impact of services outsourcing[END_REF][START_REF] Gervais | The tradability of services: Geographic concentration and trade costs[END_REF] shows that nancial and insurance activities are heterogenous and contain both tradable and non-tradable activities. 10 Therefore, labeling this sector as tradable or non-tradable is not straightforward. A few authors show the deep linkages between the non-tradable sector expansion and the banking and nancial activity (see, for example, [START_REF] Sy | Overborrowing and balance of payments imbalances in a monetary union[END_REF], supporting the assumption of considering nancial and insurance activities as non-tradable. As the choice of a 10% threshold is arbitrary, the 15% and 5% thresholds will be used to check the robustness of the empirical results.

3.3. Stylized facts: the drift from the tradable to the non-tradable sector

Figure 3 describes the evolution of gross value added, employment and prices in the non-tradable sector relative to the tradable sector, for each country of the EA11, for two subperiods: 1995-2008 and 2008-2013. 11 The 10% threshold is used to classify each sector as tradable or not, but similar gures using other thresholds are reported in Appendix. Relative prices are measured as the ratio of non-tradable to the tradable price in the EA11. 12Figures 4 and 5 report the contribution of each sector to the average price and employment growth over the two sub-periods: 1995-2008 and 2008-2013. Contributions to price growth are measured as the average ination over the period in the considered sector weighted by its share in total GVA in volume at the initial year (1995 or 2008). Contributions to employment growth are measured as the average employment growth in the considered sector weighted by its share in total employment in thousands of hours at the initial year (1995 or 2008).

Figure 3, for the rst sub-period (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008), highlights the similar pattern in all peripheral countries: the hypertrophy of the non-tradable sector. This pattern is also striking when using other thresholds for the measurement of tradability. Prices in the non-tradable sector relative to the tradable sector rose sharply between 1995 and 2008 in Ireland, Italy, Portugal, Spain and Greece.

The rise in relative prices and the growing share of the non-tradable sector led to a strong rise in overall prices and wages. However, some dierences remain among the peripheral countries.

As [START_REF] Giavazzi | Why the current account may matter in a monetary union: Lessons from the nancial crisis in the euro area[END_REF] have noted already, relative employment in Greece rose faster than relative GVA at current prices. The country faced a relatively smaller bubble in the housing sector (F-L) than Spain, with the housing sector contributing to 6p.p. of the average ination over 1995-2008 (Figure 4). The main contributor to ination and employment growth over 1995-2008 was the public, education and health sector (O_Q), contributing to respectively 4p.p. of the average employment growth (Figure 5) and 9p.p. of the average GVA deator growth.

In Portugal, the non-tradable price increase was also led by both the housing and the public, education and health sectors, contributing respectively to 8p.p. and 9p.p. of the average ination and 1p.p. and 3p.p. of average employment growth over 1995-2008. Employment decreased on 10 These authors use the geographic concentration of activity as a proxy for the tradability of the industry. The more concentrated the activity, the higher its tradability. Applying this methodology on data on U.S. establishments, Gervais and Jensen show that the nancial and business services sector has industries in both the top 5 most concentrated and least concentrated manufacturing and business services industries.

A European Disease? Non-tradable ination and real interest rate divergence average in the tradable sector and especially for the industrial and agricultural activities (A_C) which had a negative contribution of -6p.p. to total employment growth.

Ireland and Spain were the two countries with the fastest employment growth over 1995-2008, both experiencing a housing bubble: the housing sector contribution to the average growth employment over the period reached 5p.p. and 6p.p. respectively. In Ireland, employment growth was also led by the expansion of the public, education and health sector. In Spain, the housing sector also contributed to a 8p.p. increase in the average ination, and was by far the main contributor to price growth over 1995-2008. A European Disease? Non-tradable ination and real interest rate divergence

The evolution of the relative price of non-tradables seems to be well correlated to current account decits: countries facing the steepest increase in prices have the largest decits over 1995-2008. Since capital inows did not serve to expand the tradable sector, however, when facing sudden stops, countries were forced to readjust and reallocate their factors of production to the tradable sector in order to produce the tradable surplus necessary to reimburse foreign liabilities previously accumulated. As we see in Figure 3, relative prices decreased in the peripheral countries relatively more than in the rest of the EA11 over 2008-2013. These adjustments happened at a high social cost. In Spain and Greece, in particular, the readjustment resulted in a steep increase in unemployment. Wages fell by 16% in Greece, 5% in Ireland, remained stable in Portugal and slowed down in Spain between 2008 and 2013.

Determinants of the relative price of non-tradables

This section presents empirical evidence supporting the theoretical result that the real interest rate, together with the traditional BS eect, impact the evolution of non-tradable prices. To do so, it uses the data gathered on the evolution of non-tradable relative prices, apparent labor productivity in the tradable sector and real interest rates. 13 All variables are expressed in deviations from the EA11 average. The choice of a reference here is neutral since all estimations are performed in logarithms.

The Figure 6 displays non-tradable prices, real interest rates and apparent labor productivity in the tradable sector, over 1995-2013, in core and periphery countries (weighted averages; the gures for each countries are presented in Appendix). The gures highlight both the BS eect and the real interest rate eects analyzed earlier: in the periphery for example, real interest rates declined by about 1.0% over 1995-2008 compared to the EA average, while non-tradable relative prices increase by 12.2% and productivity in the tradable sector increased (25.0%) compared to the EA average. In core countries, real interest rates increased by 0.3% over 1995-2008 relatively to the EA average, while non-tradable prices and tradable productivity decreased by 17.6% and 13.3% respectively, relatively to the EA average (numbers are also given in Table 6).

To deal with data limitations, panel techniques are used to estimate equation ( 6). With nonstationary series, equation ( 6) needs to be a cointegration relationship, as is usually the case in the BS framework. Therefore, before estimating equation ( 6), panel unit root tests and tests for the existence of a cointegration relationship are performed. 14 The presence of structural breaks will be tested, as the sample covers both the adoption of the common currency and the 2010 euro crisis.

For robustness, all tests and estimations are performed using the 5% and 15% thresholds value for the measure of tradability. Estimates will also be provided for a sample covering the shorter Finally, OLS estimates for variables in rst dierence will be presented for the four samples (the three using dierent thresholds and the one with the shorter time period).

Panel unit root and cointegration tests

The presence of unit roots in the series is studied using the third generation panel unit root test of [START_REF] Bai | Structural changes, common stochastic trends, and unit roots in panel data[END_REF], allowing for heterogeneous panels with cross-section dependence and multiple structural breaks. The case for cross-section dependence is especially relevant here since real interest rate divergence resulted from nominal interest rate convergence in the euro area around the euro's inception. This test allows also the presence of multiple structural breaks, which number and dates are unknown and heterogeneous across countries. These shifts can aect both the level and the slope of each time series. Allowing for structural breaks is important in the analysis since the sample covers both the adoption of the common currency and the 2010 euro crisis.

This test has a null hypothesis of a unit root. More precisely, after identifying and taking into account the number and locations of structural breaks for each series (identied using the sequential procedure in [START_REF] Bai | Estimating and testing linear models with multiple structural changes[END_REF] and the common factors (estimated using the BIC criterion), this test pools modied Sargan-Bhargava (MSB) tests for individuals series. Three dierent pooling methods are used resulting in three dierent test statistics: Z, a standardization of individual statistics, and P and P m combining their p-values. When shifts in trends are present, a simplied MSB test is also performed on individual series, adding three other pooled statistics : Z £ , P £ and P £ m . Monte Carlo simulations conrm the good performance of the tests in nite samples (see Bai Up to two structural breaks are found for each country time series, and one on average for each of the 3 variables (relative price, productivity in the tradable sector and real interest rate). 15 Results are presented in Table 1. It can be concluded that at conventional levels of signicance, all series are non-stationary.

Cointegration tests are then performed. We use the third generation test proposed by [START_REF] Westerlund | A simple test for cointegration in dependent panels with structural breaks[END_REF], which allows for heterogeneous specications in both the long and short run parts of the error correction model, based on the data. It also takes into account crosssection dependence and unknown structural breaks in both the mean and slope of the cointegrated regression. The authors suggest two simple tests for the null hypothesis of no cointegration derived from the Lagrange multiplier (LM) based unit root tests: the coecient version ( N ) and the t-test version ( N ). Three dierent options are presented: the case with no break, the case with a shift in level only, and the case with a shift in level and trend. The tests generally perform well even in small samples.

Table 2 give the results of the tests: the two statistics reject the null hypothesis of no cointegration at the 10% level of signicance in every case, expect the N statistic in the model with no shift.

Estimation of the long-run relationship

The long-run relationship is estimated using panel Dynamic OLS (DOLS) techniques. Two main approaches have been proposed in the literature that both deal with serial correlation and the endogeneity of the regressors: the fulled modied ordinary least squares (FMOLS) and the dynamic ordinary least squares (DOLS). The DOLS procedure consists in estimating a long-run relationship by instrumental variables using leads and lags of the dierenced endogenous variables as instruments. [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] show that DOLS outperform both OLS and FMOLS estimators in estimating cointegrated panel regressions. We use the extension to the DOLS framework suggested by Mark and Sul (2003), which allows for individual heterogeneity through dierent short-run dynamics, individual-specic xed eects and individual-specic time trends.

The empirical model corresponding to equation ( 6

where i and i t are country-specic xed eects and trends, t is a common-time eect, and " i;t is the idiosyncratic error.

Table 3 report the estimation for the single BS eect (columns 1 and 3), and of the BS and real interest rate eects (columns 2 and 4). For robustness, a rst estimation is implemented with country-specic xed eects and trends (columns 1 and 2), while the second also includes a common-time eect (columns 3 and 4).

It appears that both explanatory variables (tradable productivity and real interest rate, in deviations from the EA average) are signicant at the 1% level and have the expected sign. A +1% dierential in the tradable sector productivity raises the non-tradable price by 0.36% to 0.66% relative to the A European Disease? Non-tradable ination and real interest rate divergence EA average. Introducing the real interest rate tends to depress the coecient of the BS eect using the samples covering the 1995-2013 period.

A +1% dierential in the real interest rate reduces the non-tradable price by 1.19% to 1.29% relative to the EA average. It thus seems that diverging evolution in the interest rate impacted greatly the evolution of non-tradable relative prices within the euro area over the period.

Robustness tests

For robustness, all tests and estimations are now performed using the 5% and 15% thresholds value for the measure of tradability. We rst test for the presence of unit roots in the series using the third generation panel unit root test of [START_REF] Bai | Structural changes, common stochastic trends, and unit roots in panel data[END_REF]. Structural breaks are found again for every variable. There are up to two structural breaks for each time series, and one on average. Results for the tests are presented in Appendix (Table A.2). It can be concluded that at conventional levels of signicance, all series are non-stationary. 16The stationarity of series in rst dierence are also tested, and it results that at conventional levels of signicance, all series in rst dierence are stationary. The stationarity of variables in rst dierence is conrmed using the second-generation panel unit root test of [START_REF] Pesaran | A simple panel unit root test in the presence of cross-section dependence[END_REF]. This test allows for cross-section dependence but does not allow the presence of structural breaks. Simulations made by [START_REF] Pesaran | A simple panel unit root test in the presence of cross-section dependence[END_REF] show that this cross-sectional augmented panel unit root test have satisfactory size and power even for relatively small samples (T = N = 10). Results

of the panel unit root tests are presented also in Appendix (Table A.2). They conrm that, at conventional levels of signicance, all series are stationary in rst dierence.

Cointegration tests are then performed for series that are non-stationary using test proposed by [START_REF] Westerlund | A simple test for cointegration in dependent panels with structural breaks[END_REF]. Three dierent options are presented: the case with no break, the case with a shift in level only, and the case with a shift in level and trend. cointegration at the 10% level of signicance in every case, expect the N statistic in the model with a regime shift for the 5% threshold, and with no shift for the 15% threshold.

As all three series, measured using dierent thresholds (5% and 15%), are non-stationary and cointegrated, panel DOLS estimations of equation are performed to estimate equation ( 6). Table 4 reports the estimation for the single BS eect (columns 1 and 3), and of the BS and real interest rate eects (columns 2 and 4). For robustness, a rst estimation is implemented with countryspecic xed eects and trends (columns 1 and 2), while the second also includes a common-time eect (columns 3 and 4). Estimates are also provided for a sample covering the shorter period 1995-2009 to see if results are relevant when not taking into account the 2010 euro crisis.

It appears that both explanatory variables (tradable productivity and real interest rate, in deviations from the EA average) are signicant at the 1% level and have the expected sign using the two samples with dierent thresholds for the measure of tradability (5% and 15%). In the sample covering a shorter time period, tradable productivity is not signicant when introduced alone. We can see that the impact of a +1% dierential in the tradable sector productivity raises the non- This paper has analyzed how the real interest rate inuences the dynamics of non-tradable relative prices. The theoretical framework, incorporating two factors of production in the traditional Balassa-Samuelson model, shows that the real interest rate fall in the euro area periphery following the single currency's inception induced an increase in the relative price of non-tradable goods. The paper then documents the dynamics of the tradable to the non-tradable sector over 1995-2013 using a new dataset and carries out an econometric estimation for 11 EA countries to quantify the contribution of the pure Balassa-Samuelson eect and the impact of the interest rate on non-tradable relative prices.

The results conrm that, together with the traditional BS eect, diverging evolutions in real interest rates seem to have contributed to the evolution of non-tradable relative prices within the euro area over the period. In Greece, the fall in the real interest rate over 1995-2008 could explain almost half of the non-tradable price increase relative to the EA average, while in Germany the increase in the real interest rate might have contributed up to 7% of the decrease of the non-tradable price relative to the average of the EA.

This result is especially important in the context of the debate on the relative price adjustment and the subsequent surveillance within Europe. Divergence across euro area members challenges greatly the eciency of a single monetary policy. This divergence was translated, before the crisis, in strong ination dierentials as we have seen. While the introduction of the euro should have fostered a real convergence as capital ew towards so-called "catching-up" economies, these capital ows were indeed mainly allocated in the less innovative non-tradable sectors and fueled strong price increases. Since the 2008 nancial crisis, in the EA periphery, increased interest rates may have contributed to internal rebalancing but labor reallocation happens at a high social cost as the non-tradable sector is more labor-intensive than the tradable sector. The divergence thus now takes the form of strong heterogeneities in how economies reacted to the nancial crisis, and through high dierentials in unemployment rates across countries.

A European Disease? Non-tradable ination and real interest rate divergence Source: author's calculations using Eurostat, BACI and UN ServiceTrade and Ameco. Note: non-tradable prices and productivity in the tradable sector are measured using the 10% threshold for tradability. The real interest rate is a 2-year moving average.

Figure 1

 1 Figure 1 Relative prices and real interest rates in the periphery vs. core countries, 1995-2013 indices 1995=100 Relative (non-tradable to tradable) prices Real interest rates

Figure 2

 2 Figure 2 Openness ratio and tradability by sector, EA11 Average 2000-2013, in %

Figure 3

 3 Figure 3 Evolution of the non-tradable relative to the tradable sector, % (a) 2008/1995 (b) 2013/2008

Figure 4

 4 Figure4GVA deators: contributions of each sector to average growth over1995-2008 and 2008- 2013, by country 1995-2008

Figure 5

 5 Figure5Employment: contributions of each sector to average growth over1995-2008 and 2008- 2013, by country 1995-2008

  sample ranges from 1995 to 2013 and covers N = 11 EA countries, which amounts to T = 19 observations per country. In terms of size, the sample is close to previous studies of the BS eect, for instance De Gregorio et al. (1994) use data for 14 OECD countries over 1970-1985 (16 observations per country), or Bénassy-Quéré and Coulibaly (2014) use a dataset including 12 European countries over 1985-2006 (21 observations per country).

Figure 6

 6 Figure 6 Non-tradable prices, productivity in the tradable sector and long-term real interest rate in core and periphery countries 1995-2013, log deviations from the EA11 average Core countries Periphery

  period 1995-2009 to see if results are relevant when not taking into account the 2010 euro crisis.

Figure A. 2

 2 Figure A.2 Evolution of the non-tradable relative to the tradable sector 5% threshold for the measurement of tradability. (a) 2008/1995 (b) 2013/2008

Figure A. 3

 3 Figure A.3 Non-tradable prices, productivity in the tradable sector and long-term real interest rate 1995-2013, log deviations from the EA11 average Austria Belgium Germany

A

  European Disease? Non-tradable ination and real interest rate divergence Most studies label the manufacturing sector as tradable and consider services sectors as nontradable. However, services represent an increasing share of advanced economies' exports. To reassess the tradability of both goods and services, one needs to construct a database allowing to compare trade in goods and services, and national accounts data at a sectoral level. Eurostat provides data for national accounts for up to 64 sectors in the NACE revision 2 classication. It provides detailed information on Gross Value Added (GVA) in current and constant prices, production at current and constant prices, employment and labor compensation for European countries. For data on trade in goods, BACI, CEPII's database based on COMTRADE, provides a harmonized world trade matrix for values at the 6-digit level of the Harmonized System of 1992. Data are available from 1989 to 2013 for 253 countries and 5 699 products. Finally, for trade in services, UN ServiceTrade database provides data on services exports and imports in the BPM5 classication over2000-2013.

	3.	Data
		3.1. Data sources

Table 3

 3 Panel cointegration estimates of the Balassa-Samuelson and real interest rate eects

	Dependent variable : ln@ p N p N;EA A, 1995-2013
	No common time eect ( t ) Common time eect ( t )
	(1)	(2)	(3)	(4)
	ln@ A T A T ;EA A 0.611***	0.360***	0.659***	0.410***
	(0.126)	(0.130)	(0.132)	(0.135)
	ln@ 1+r 1+r EA A	-1.287***		-1.186***
		(0.360)		(0.376)
	Note: standard errors, in parentheses, are based on Andrews and Monathan (1992) pre-whitening
	method. *, ** and *** denote signicance at 10%, 5% and 1% levels respectively.
	Source: author's calculations.

  Table A.3 in the Appendix gives the results of the tests: the two statistics reject the null hypothesis of no A European Disease? Non-tradable ination and real interest rate divergence

Table 4

 4 Panel cointegration estimates of the Balassa-Samuelson and real interest rate eects

			Dependent variable : ln@ p N p N;EA A
	No common time eect ( t ) Common time eect ( t )
		(1)	(2)	(3)	(4)
			5% threshold
	ln@ A T A T ;EA A 0.650***	0.404***	0.722***	0.458***
	(0.125)	(0.106)	(0.137)	(0.113)
	ln@ 1+r 1+r EA A		-1.181***		-0.994***
			(0.353)		(0.360)
			15% threshold
	ln@ A T A T ;EA A 0.550***	0.406***	0.605***	0.461***
	(0.179)	(0.130)	(0.195)	(0.138)
	ln@ 1+r 1+r EA A		-1.260***		-1.135***
			(0.357)		(0.373)
			10% threshold, 1995-2009
	ln@ A T A T ;EA A	0.127	0.259***	0.147	0.284***
	(0.162)	(0.054)	(0.189)	(0.054)
	ln@ 1+r 1+r EA A		-1.521***		-1.494***
			(0.282)		(0.271)
	Note: standard errors, in parentheses, are based on Andrews and Monathan (1992) pre-whitening
	method. *, ** and *** denote signicance at 10%, 5% and 1% levels respectively.
	Source: author's calculations.

Table 6

 6 Contributions of the Balassa Samuelson (BS) and the real interest rate eects to the non-

	tradable price growth 1995-2008, deviations from the EA average
			Growth		Contributions to non-tradable price growth
		Non-tradable prices	Productivity in the tradable sector	Real interest rates	BS eect	Real interest rate eect
	AT	-20.2%	-15.3%	0.4%	-4.0%	-0.6%
	BE	-12.4%	-7.3%	-0.4%	-1.9%	0.6%
	DE	-30.9%	-21.9%	1.4%	-5.7%	-2.1%
	EL	7.6%	9.3%	-2.3%	2.4%	3.5%
	ES	7.6%	31.5%	-1.0%	8.1%	1.5%
	FI	-0.4%	-21.0%	0.3%	-5.4%	-0.5%
	FR	-6.0%	-4.7%	-1.1%	-1.2%	1.7%
	IE	31.7%	-23.6%	3.4%	-6.1%	-5.2%
	IT	14.1%	27.4%	-1.4%	7.1%	2.1%
	NL	-7.3%	0.9%	0.6%	0.2%	-0.9%
	PT	9.2%	22.0%	0.0%	5.7%	0.0%
	Core*	-17.6%	-13.3%	0.3%	-3.4%	-0.5%
	Periphery*	12.2%	25.0%	-1.0%	6.5%	1.6%
	*weighted averages, weight: gross value added at current prices.
	Source: author's calculations.
	Note: contributions are measured using the coecients resulting from panel DOLS estimates with no
	common time eect on the sample covering the 1995-2009 periods and using the 10% threshold for
	the measure of tradability, see Table 4, 3rd estimate, column (2). For example, in Greece (EL), the
	real interest rate contribution to the non-tradable price increase is: (-2.3)*(-1.521) = 3.5%. Therefore,
	the real interest rate fall in Greece could explain 3.5/7.6 = 46% of the non-tradable price increase over
	1995-2008 relative to the EA11.

21

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Sorbonne -2016.44

Table A .

 A 1 Openness ratio by sector, EA11 2000 and 2000-2013 average in %, 2013/2000 growth in p.p.Source: author's calculations using Eurostat, BACI and UN ServiceTrade. Note: the red lines indicate the 15%, 10% and 5% thresholds. The openness ratio is the ratio of total trade (imports+exports) to total production.

	Sector	2000 (%)	growth (%) 2013-2000	average (p.p.) 2000-2013
	B Mining and quarrying	184.1	179.0	249.4
	C Manufacturing	44.0	10.1	48.4
	I	Accommodation and food service activities	9.4	17.4	23.7
	H Transportation and storage	26.1	-4.1	22.8
	A Agriculture, forestry and shing	19.0	8.2	22.8
	J	Information and communication	12.5	10.3	15.8
	N Administrative and support service activities	11.0	6.3	13.7
	M Professional, scientic and technical activities	9.0	3.7	9.0
	K Financial and insurance activities	6.8	2.2	7.8
	G Wholesale and retail trade; repair of motor vehicles and motorcycles	3.0	0.4	3.1
	D Electricity, gas, steam and air conditioning supply	1.5	1.9	3.0
	F Construction	1.9	0.0	1.7
	R Arts, entertainment and recreation	2.1	-0.5	1.5
	O Public administration and defence; compulsory social security	1.9	-0.8	1.4
	S Other service activities	0.5	1.1	0.9
	P Education	0.3	0.5	0.7
	E Water supply; sewerage, waste management and remediation activities	0.0	0.2	0.2
	Q Human health and social work activities	0.0	0.1	0.2
	L Real estate activities	0.0	0.0	0.0
	TOTAL	33.1	6.3	34.8

à la dynamique du prix des biens non échangeables en zone euro. Partant d'un modèle proposé par De[START_REF] De Gregorio | International evidence on tradables and nontradables ination[END_REF], il montre que la baisse du taux d'intérêt réel dans les pays périphériques de la zone euro (ZE) après l'adoption de la monnaie unique a induit une augmentation du prix relatif des biens non échangeables. L'utilisation d'une nouvelle base de données permet de documenter la dynamique des secteurs abrités et ouverts sur la période 1995-2013 et de montrer l'expansion du secteur abrité dans les pays périphériques avant la crise de l'euro. Une estimation économétrique est menée pour 11 pays de la ZE sur la période 1995-2013 pour quantier la contribution de l'eet Balassa-Samuelson et l'impact du taux d'intérêt sur les prix relatifs des biens non échangeables. Il semble que la divergence dans l'évolution des taux d'intérêt a fortement impacté l'évolution des prix des biens non échangeables dans la zone euro sur la période. En Grèce, la baisse du taux d'intérêt réel sur la période 1995-2008 pourrait expliquer près de la moitié de l'augmentation des prix des biens non échangeables par rapport à la moyenne de la ZE, alors qu'en Allemagne, l'augmentation du taux d'intérêt réel pourrait expliquer 7 % de la diminution du prix des biens non échangeables par rapport à la moyenne de la ZE.

Documents de travail du Centre d'Economie de laSorbonne -2016.44

[START_REF] Blanchard | Current account decits in the euro area: the end of the Feldstein Horioka puzzle?[END_REF] suggested that current account decits in the periphery after the euro's inception reected mainly a catch-up and convergence process.

The periphery faced, on average between 2001-2008, a real rate of 0.26% against 1.4% for the rest of the euro area as a whole(Ameco, February 2016.)

[START_REF] Balassa | The purchasing-power parity doctrine: a reappraisal[END_REF] and[START_REF] Samuelson | Theoretical notes on trade problems[END_REF] suggested that higher ination rates in catching-up economies could reect a process of real convergence: assuming the law of one price holds for tradable goods, productivity growth in this sector pushes real wages up both in the tradable sector and the non-tradable one; it results in an increase in the relative price of non-tradable goods and thus in a real exchange rate appreciation in catching-up economies.3 Documents de travail du Centre d'Economie de laSorbonne -2016.44

Documents de travail du Centre d'Economie de laSorbonne -2016.44

See Bahmani-Oskooee and Nasir (2005) for a review.

In all cases, demand shocks appear unable to move the real exchange rate in the long run. 5 Documents de travail du Centre d'Economie de la Sorbonne -2016.44

Documents de travail du Centre d'Economie de laSorbonne -2016.44

Information on disaggregated trade in services is available only for the period 2000-2013.

The 11 EA countries are: AT: Austria; BE: Belgium; DE: Germany; EL: Greece; ES: Spain; FI: Finland; FR: France; IE: Ireland; IT: Italy; NL: Netherlands; PT: Portugal.

Long-term interest rate deated by GDP deators. 7 Documents de travail du Centre d'Economie de la Sorbonne -2016.44

At country-level, tradability could be aected by market regulations or market structure, which should not matter for the EA11 since tradable sectors are well integrated in Europe[START_REF] Estrada | Patterns of convergence and divergence in the euro area[END_REF]. 8 Documents de travail du Centre d'Economie de laSorbonne -2016.44

As seen on Figure1, the trends of relative prices and real interest rates started to reverse after the 2008-crisis. We thus use the year 2008 as a break point for the stylized facts presented in this section.

Like in the model and the following empirical analysis, the law of one price is assumed to hold in the tradable sector of the EA and the same tradable EA price is used as the numeraire for the 11 countries. The database used does not inform on price levels, but recent work show empirical evidence of a substantial convergence in price levels in the case of tradable goods (see[START_REF] Estrada | Patterns of convergence and divergence in the euro area[END_REF]. As the main focus of the paper is on the dynamics of the non-tradable sector, we assume the LOP holds and exclude from the analysis the dynamics specic to the tradable sectors.

Documents de travail du Centre d'Economie de laSorbonne -2016.44

Documents de travail du Centre d'Economie de laSorbonne -2016.44

A 2-year moving average (average of the value in t and t 1) for the interest rate is used to capture the inertia of capital adjustment and its consecutive eect on the relative price.

The tests are performed with GAUSS, using the codes provided by J. Westerlund, J.L. Carrion-i-Silvestre and N.C. Mark & D. Sul. OLS estimates for variables in rst dierence are performed using Stata.13 Documents de travail du Centre d'Economie de laSorbonne -2016.44

The break is most recurrent in 2010 for the relative price, 1998 for the productivity in the tradable sector and 2007 for the real interest rate.

Only the Z statistic for the tests driven for non-tradable prices present mixed results.

Documents de travail du Centre d'Economie de laSorbonne -2016.44

Documents de travail du Centre d'Economie de laSorbonne -2016.44

I am especially thankful for Agnès Bénassy-Quéré's extensive advice and support.

A European Disease? Non-tradable ination and real interest rate divergence The number of common factors are estimated using the panel Bayesian information criterion proposed by [START_REF] Bai | Determining the number of factors in approximate factor models[END_REF], and the test was estimated with a maximum number of breaks of 3. Source: author's calculations. tradable price by 0.26% to 0.72% relative to the EA average. Introducing the real interest rate tends to depress the coecient of the BS eect using the samples covering the 1995-2013 period, but increase the coecient using the sample covering the 1995-2009 period. A +1% real interest rate dierential reduces the non-tradable price by 0.99% to 1.52% relative to the EA average.

Finally, OLS estimates for variables in rst dierence are presented in table 5 for the four samples (the three using dierent thresholds and the one with the shorter time period). The two variables are signicant at the 1% level using all four samples. The impact of a 1% increase in the tradable productivity ranges from a 0.17% to a 0.22% increase in non-tradable ination. A 1% real interest rate growth ranges from a 0.91% to 2.03% decrease in non-tradable ination.

Overall, the impact of a +1% dierential in the real interest rate reduces the non-tradable price by 0.99% to 1.52% relative to the EA. It thus seems that diverging evolution in the interest rate impacted greatly the evolution of non-tradable relative prices within the euro area over the period.

In periphery countries, over 1995-2008, changes in the interest rate could explain up to 13% of the changes in relative prices. In Greece, the fall in the real interest rate over 1995-2008 could explain almost half of the non-tradable price increase relative to the EA average, while in Germany the increase in the real interest rate might have contributed up to 7% of the decrease of the non-tradable price relative to the average of the EA (Table 6).

A European Disease? Non-tradable ination and real interest rate divergence 10% threshold 5% threshold 15% threshold ln@ 1+r 1+r EA A ln@ p N p N;EA A ln@ A T A T ;EA A ln@ p N p N;EA A ln@ A T A T ;EA A ln@ p N p N;EA A ln@ A T A T ;EA A