Absolute inflation convergence in the euro area
Master Thesis
MSc Economics – Macroeconomic Theory and Policy
Details student Bart Rutjesa
Faculty of Economics and Business University of Groningen
Details supervisor prof. dr. J.M. Berk
Faculty of Economics and Business University of Groningen
Details co-assessor dr. J.P.A.M. Jacobs
Faculty of Economics and Business University of Groningen
January 2019
JEL classification: C33, E31, E58, F45
Keywords: inflation convergence, euro area, panel unit root tests, monetary unions ABSTRACT
This study explores economic theory on inflation convergence in monetary unions, with focus on the euro area. Inflation convergence is both a criterion to adopt the euro and a desirable process among member states of the euro area. To investigate the occurrence of inflation convergence in the euro area, a panel unit root test allowing for cross-sectional dependence is employed. Convergence is found for a group of sample countries against a cross-sectional benchmark. Results are robust to the use of two alternative benchmarks, a different econometric framework, and a core inflation measure. The creation of two subsamples uncovers sensitivities of the results to the sample period. The results indicate the success of the EMU project from a price stability perspective and may pave the way to eventual enlargement of the euro area.
1. Introduction and motivation
The Maastricht Treaty1 concerns the coordination of economic and fiscal policies of member states of the
European Union (EU) and the adoption of a common currency and monetary policy (Karanasos et al., 2016). The Treaty established the Economic and Monetary Union (EMU) and the euro, an important step in the
process of monetary integration of the EU (Brož and Kočenda, 2018). The euro was introduced on 1 January 1999, replacing the national currencies as the at-parity successor of the European Currency Unit.2 At its inception, eleven EMU member states formed a monetary union with the euro as its currency, i.e. the euro area. Greece joined the monetary union two years later – one year before notes and coins were introduced.
Inflation convergence is both a criterion to adopt the euro (Siklos, 2010) and a desirable process among the member states of the euro area (Giannellis, 2013). Hence, it is not surprising that the occurrence of inflation convergence in the euro area has received considerable attention in the literature. This study differs from the current body of literature in two ways. First, the literature on inflation convergence is often saturated with econometric digression while underexposing the economic rationale behind methodologies and results. This study uses economic phenomena to motivate choices and clarify results throughout. Second, a thorough robustness analysis of the results is performed, which might expose sensitivities in the results that could declare the heterogeneous results reported in the literature.3
To investigate the occurrence of inflation convergence in the euro area, an empirical analysis is performed using monthly data on the Harmonised Index of Consumer Prices (HICP). Ten countries are included in the sample after applying two inclusion criteria, which are motivated in Section 5.1. A series of year-on-year inflation rates is constructed for the sample countries. Next, differentials are calculated with respect to a cross-sectional benchmark that excludes the country of interest.4 The empirical analysis is performed by employing a unit root test that addresses cross-sectional dependence. The results answer the question whether there is evidence to support the presumption that inflation rates in the euro area have been in the process of convergence since the inception of the common currency.
The topic of inflation convergence can be approached from a number of angles. A distinction is made between relative and absolute convergence. The former refers to the case in which inflation differentials converge to an equilibrium unequal to zero in the long run, while the latter refers to inflation differentials converging to an equilibrium equal to zero in the long run (Busetti et al., 2006). This study tests for absolute convergence of the inflation rates of a sample of countries in the euro area. The choice to test for absolute rather than relative convergence is motivated fourfold. First, in the long run absolute convergence of inflation rates among members of a monetary union is a more desirable situation than relative convergence of inflation rates. Convergence clustering (or the forming of convergence clubs) is a common type of relative convergence in which only countries that share similar characteristics converge, which could exacerbate a divide between groups of countries in a monetary union (e.g. Northern and Southern Europe). The existence of convergence clustering in the euro area is confirmed in the literature (see footnote 13). Furthermore, inflation differentials
2 The European Currency Unit was a weighted basket of the currencies of the member states of the European Community, created to prepare member states for the adoption of the common currency (Works Jr., 1986).
3 The heterogeneity in the results reported in the literature is explored in Section 3.
converging to zero ensure maximum effectivity of the ECB’s monetary policies, since these target the euro area as a whole. Second, Brož and Kočenda (2018) focus on relative inflation convergence and leave absolute convergence open as an interesting research opportunity. Next, two more technical reasons motivate the choice to test for absolute rather than relative convergence. Busetti et al. (2006) show that unit root tests are best run without an intercept (i.e. test for absolute convergence). Unit root tests suffer from low power and might provide false confirmation of the null hypothesis of no convergence when intercept terms are included. Finally, one of the primary reasons Brož and Kočenda (2018) include an intercept (i.e. test for relative convergence) is the possibility to add specification dummy variables in their regressions. This is not relevant in this study.
Brož and Kočenda (2018) find that relative inflation convergence was not set back by economic shocks such as the global financial crisis (GFC). When testing for absolute rather than relative convergence, the power of unit root tests is increased. It is therefore expected that the null hypothesis of no inflation convergence can be rejected more easily, leading to the following hypothesis: inflation rates in the euro area have been in the process of absolute convergence since the inception of the common currency.
The remainder of the paper is organized as follows. The next section provides an economic digression on inflation convergence in monetary unions. Section 3 provides an overview of the related literature. In Section 4, the econometric framework is discussed. The dataset is described in Section 5. Section 6 presents the results and provides robustness checks. Section 7 discusses the results and proposes policy implications. Section 8 concludes.
2. Monetary unions and inflation convergence
2.1 The Optimum Currency Area (OCA), Purchasing Power Parity (PPP) and inflation differentials
Mundell’s (1961) OCA theory has been the cradle of extensive literature on monetary unions and their prerequisites. Several seminal contributions, notably McKinnon (1963) and Kenen (1969), have led to OCA properties that supposedly pave the way to optimality, i.e. the situation in which the benefits of being part of a currency area most strongly outweigh the associated costs. The United States is often regarded as a primary example of a geographic area that approaches optimality in this sense.5 The EMU has attracted attention in this regard as well. In the period before the inception of the euro, a body of literature arose (concisely summarized in Bayoumi and Eichengreen (1997)) that evaluated the extent to which the EMU could be regarded as an OCA, and the topic is still central in debate today.6
An OCA is a geographical area, not bounded by national borders, that would benefit from the adoption of a common currency (Mundell, 1961). Reduced transaction costs are the foremost benefit of a monetary union. The costs of adopting a common currency originate from the effects of the abandonment of the exchange rate. The exchange rate functions as a mechanism that ensures PPP holds and as such absorbs asymmetric shocks between areas that have an own currency. When the exchange rate is abandoned, asymmetric shocks are transferred via price or output/employment levels to restore PPP.
To better understand the link between inflation and PPP (convergence) and the OCA theory, PPP is briefly explained and illustrated with an example. The PPP doctrine is an economic theory that concerns price levels and exchange rates between countries and/or regions.7 It is based on the law of one price, which states that identical goods should have identical prices, regardless of the currency (Dixon, 2009). Several interpretations of the PPP theory exist. A distinction is made between absolute and relative PPP.8 The former asserts that the exchange rate equals the ratio of the purchasing power of the respective currencies, i.e. a constant real exchange rate equal to one (Widodo, 2015). The latter requires that the growth in the exchange rate offsets inflation differentials (Rogoff, 1996). PPP is not a short-run phenomenon, attributed to stickiness in nominal prices while exchange rates are volatile. Convergence toward PPP in the long run is often reported in the literature, but usually at slow rates (half-life times typically range from three to five years, see for example Rogoff (1996)).9 As an example of a situation in which asymmetric shocks are transferred to restore PPP, consider two countries that both produce one good and consumer taste shifts from country 1’s good to country 2’s good. The price of country 2’s good rises, causing a general price level increase in country 2; the output of country 1’s good decreases, causing unemployment in country 1. To restore PPP, an exchange rate adjustment would be appropriate. Now consider the case in which the same two countries coexist in a monetary union and thus exchange rate adjustment is impossible. A situation could arise in which country 1 faces staggering unemployment levels, while country 2 has to bear severe inflationary pressure. To prevent this situation, Mundell (1961) argues, principal criteria for a monetary union to function properly are (i) mobility of factors of production (primarily labor, to a lesser extent also capital) between the members of the monetary union and (ii) price and wage flexibility, to accommodate for the necessary adjustments.
2.2 Debate on the inflation convergence criterion
The Maastricht Treaty for the first time established explicit convergence criteria to further European
7 In its modern form the doctrine stems from Cassel (1918), but the economic idea is older. See for example Haberler and Blumenthal (1961) for an overview of the history of PPP.
8 For example in Balassa (1964).
integration toward adopting a common currency. One of the criteria for accession is related to inflation and is defined in the Treaty as “the achievement of a high degree of price stability; this will be apparent from a rate of inflation which is close to that of, at most, the three best performing Member States in terms of price stability.” (Treaty on European Union, 1992). Remarkably, inflation convergence is not a prerequisite in the OCA literature. In this light, the inflation convergence criterion has been topic of debate. De Grauwe (1996) argues that prior convergence of inflation rates is neither necessary nor sufficient for a potential currency union to function properly. If countries are similar in economic terms and face symmetric shocks, prior discrepancy in inflation rates will disappear after forming a monetary union, at least insofar the discrepancy stems from prior monetary institutional differences. Conversely, countries facing equal inflation rates may have disparate economies, causing shocks to transfer highly asymmetrically and rendering a monetary union suboptimal (De Grauwe, 1996). Apart from doubts on the inflation convergence criterion itself, incompatibility with the exchange rate stability criterion is recognized in the literature (e.g. in De Broeck and Sløk (2006)). The exchange rate stability criterion requires successful participation in the Exchange Rate Regime (ERM II) for at least two years (Buiter and Grafe, 2002). The so-called exchange rate regime dilemma can now be explained as follows. Convergence of price levels when adopting a common currency is a natural phenomenon (Diaz del Hoyo et al., 2017). By fixing the exchange rate at least two years prior to accession, real convergence adjustments create inflationary pressure that endangers meeting the inflation convergence criterion. The inflationary pressure is caused by inflation differentials taking over as an adjustment mechanism, since exchange rate flexibility can no longer perform this function. Meeting both criteria simultaneously thus may bring the accession country into a forced recession. As a phenomenon in a monetary union, price level adjustment is regarded one of the most important sources of inflationary pressure, especially in catching-up economies (Lein-Rupprecht et al., 2007). Therefore, temporary inflation rate variations among member states are not inherently malicious. Some level of price flexibility is desired to enable the necessary adjustments. If prices are inflexible, adjustment must take place through quantities, i.e. through output/unemployment, which can be painful for the country at hand. Alternatives for the inflation criterion have been proposed, for example excluding productivity-driven inflation from the definition of the criterion (Buiter and Grafe, 2002). Even so, in its current form the inflation convergence criterion has had implications for countries that wanted to join the euro area: by not complying to the inflation criterion (and due to its staggering debt levels, violating one of the other convergence criteria), Greece was disallowed to join the euro at its inception.
heterogeneities in wage rigidities, the size of the output gap10, exposure to extra-union trade, consumer confidence, institutional differences, oil dependence, and several other factors (European Central Bank, 2003). Country heterogeneities and its implications for the euro area are discussed next.
2.3 The situation in the euro area
Heterogeneities are common – and to some extent inevitable – in a monetary union. However, euro area heterogeneities are particularly strong compared to other currency unions such as the United States. The euro area, for example, lacks strong inter-union migration and has a relatively weak federal fiscal system. This may cause inflation differentials to gain persistence rather than functioning as a mere adjustment mechanism, which can pose serious problems (Honohan and Lane, 2003). First and foremost, there is the potential of sustained high inflation in certain member countries. This causes concerns about the respective country’s residents’ purchasing power, especially since countries in a currency union lack the monetary instruments to single-handedly address inflationary pressure. This may, eventually, put political pressure on remaining part of the euro area. Furthermore, sustained inflation differentials lead to inequalities in real interest rates (Busetti et al., 2006). Since the nominal interest rate is equal for all euro area countries, real interest rates are relatively low for countries facing persistent above-average (expected) inflation rates.11 In turn, this may cause rising local asset prices (i.e. bubbles, especially in times of abundant global liquidity), wealth transfers from creditors to debtors (debts decrease relatively fast in real value) and balance sheet adjustments, mainly excessive debt accumulation by the private sector (Estrada et al., 2013). This type of procyclicality risks to affect individual countries in the euro area asymmetrically. As noted in Diaz del Hoyo et al. (2017), catching-up economies in the euro area are disproportionally hit by boom-bust cycles, which directly conflicts with one of the main OCA characteristics discussed above. Finally, among others Giannellis (2013) argues that convergence of macroeconomic factors such as inflation is undoubtedly a desirable path in the euro area considering the egalitarian nature of ECB’s monetary policies. Indeed, ECB’s uniform policy is not effective when economy-specific boom-bust cycles must be countered.
3. Literature review
Price and inflation convergence in monetary unions have been intensely investigated. Focus in the literature is mainly on the two primary monetary unions, the United States and the euro area. Cecchetti et al.
10 The output gap is defined as the difference between actual and potential output, and is considered an important cause of inflationary pressure (Gonzalez-Astudillo, 2017). Rogers (2002) reports a significant positive correlation between the output gap and inflation in the euro area.
(2002) investigate the dynamics of price levels in large U.S. cities. City price levels are found to be persistent, given the half-life time of approximately nine years against three years for cross-national estimates. Half-life times found in related studies on U.S. cities vary substantially and range from 2.5 years (Papell, 1997) to 7.5 years (Nath and Sarkar, 2009). Rogoff (1996) gives a characterization of three to five years. These results are relevant for the case of inflation convergence in the euro area. Cecchetti et al. (2002) argue that, considering the many similarities between the EMU and the United States, studying price level convergence in U.S. cities helps to understand the pattern of inflation convergence in the euro area. This was especially true due to the lack of available data on the euro area at the time of writing. Currently, the euro area has been in place for twenty years. This provides a substantial amount of data that enables researchers to directly investigate inflation convergence in the euro area, rather than relying on derived conclusions from US data. Consequently, the body of literature analyzing the euro area directly has been growing rapidly in the past two decades.
The literature on inflation convergence in the EMU differs substantially across multiple dimensions. Varieties are mainly found along the following lines: (i) the type of convergence investigated; (ii) the target group of countries and/or regions; (iii) the sample period and subsamples, (iv) the benchmark against which convergence is tested, and (v) the results. Apart from these dimensions, several econometric frameworks can be applied to test for inflation convergence. Suitable frameworks are discussed in Section 4.1.
As argued in the first section, absolute inflation convergence is tested in this study. Brož and Kočenda (2018) and Lopez and Papell (2012) take another approach by exclusively focusing on relative convergence, while Karanasos et al. (2016) treat both relative and absolute convergence. Kočenda and Papell (1997) and Busetti et al. (2006) focus on absolute convergence, the latter even arguing to only use the concept of absolute convergence when inflation is concerned.12
Brož and Kočenda (2018) take a broad approach by including all EU countries in the analysis on the assumption that most member states will adopt the euro. Kočenda and Papell (1997) also consider all EU member states and include several non-EU countries as comparison. Giannellis (2013) and Busetti et al. (2006) include all EMU member states. Other researchers include countries that have had a similar pathway leading up to their present membership, for example by including the twelve initial member states of the EMU as in Lopez and Papell (2012) and Karanasos et al. (2016).
Most researchers choose a significant economic event as starting point of their dataset. Lopez and Papell (2012), Karanasos et al. (2016) and Busetti et al. (2006) use the introduction of the European Exchange Rate Mechanism (ERM), while Giannellis (2013) and Brož and Kočenda (2018) use the adoption of the common currency as starting point. Most researchers employ two subsamples that naturally correspond with their
research objective. In Brož and Kočenda (2018), for example, the sample is split at the onset of the GFC to investigate its effects on inflation convergence. Lopez and Papell (2012) use an eight-year rolling window to isolate smaller estimation periods and deal with potential structural breaks in the data.
Most of the related literature employs a benchmark based on the cross-sectional mean. Notable exceptions include Siklos (2010), who focuses exclusively on the Maastricht inflation criterion, and Brož and Kočenda (2018), who employ three benchmarks to gain robustness in their results. Busetti et al. (2006) mainly use single benchmark countries, noting that their multivariate unit root tests are invariant to the benchmark country chosen.
The results in the literature are heterogeneous. There is no apparent trend: applying a similar econometric framework or choosing similar sample periods, for example, does not lead to consistent results. Lopez and Papell (2012) find evidence for inflation convergence when their window rolls past the adoption of the euro, while only sporadic evidence is found pre-euro. This contrasts with the results found in Busetti et al. (2006), who primarily find inflation convergence pre-euro. Results are further diversified by Karanasos et al. (2016), who find stationarity both pre- and post-euro, and in some cases even diverging behavior. Other contradictory post-euro results are reported in Brož and Kočenda (2018), who find convergence despite the GFC, and in Giannellis (2013), who finds monotonically persistent inflation differentials and thus clear evidence against convergence. Results in Kočenda and Papell (1997) are supportive of convergence, but find that the convergence rate is substantially higher for countries that participated in ERM.13
Table 1 provides a concise overview of the diversity in approaches and results in related literature.
4. Econometric framework
4.1 Tests for inflation convergence
Multiple econometric frameworks are appropriate to test for inflation convergence. Most studies rely on either panel unit root tests or cointegration tests.14 In panel unit root tests, inflation differentials are calculated with respect to a certain benchmark. The series of inflation differentials is then tested for the presence of a unit root. If the null hypothesis of a unit root is rejected, the differentials are not persistent and inflation convergence is confirmed.15
13 There is more consensus regarding convergence clustering. Some level of convergence clustering is found in Lopez and Papell (2012), Karanasos et al. (2016) and Busetti et al. (2006), among others. For example, Karanasos et al. (2016) identify three subgroups (convergence clubs) among early accession countries that appeared to move homogeneously. Convergence clustering is not a topic in this study.
14 A notable exception is Cavallero (2011), who relies on a “mixed time series/cross-section approach” or distribution dynamics approach, as proposed in Quah (1996).
Table 1
Concise overview of the literature on inflation convergence in the EU/EMU.
Study Results Sample period Target group Conv. type Method Benchmark
Kočenda and Papell (1997) Convergence found 1959-1994, split at adoption of ERM Group of non-ERM countries Absolute convergence Panel unit root Cross-sectional mean Busetti et al. (2006) Convergence pre-euro; clustering post-euro 1980-2004, split at adoption of euro EMU (2004) Absolute convergence Panel unit root, stationarity Benchmark countries Lopez and Papell (2012) Convergence post-euro; clustering 1979-2010, eight-year rolling window Twelve initial EMU countries Relative convergence ADF-SUR Cross-sectional mean Giannellis (2013) Persistent differentials 1998-2009 EMU (2009) Inflation differentials persistence Linear unit root; TAR unit root Cross-sectional mean Karanasos et al. (2016) Convergence clustering; divergence 1980-2013, split at adoption of euro Twelve initial EMU countries Relative and absolute convergence Panel unit root EMU average inflation Brož and Kočenda (2018) No weakening of convergence post-GFC 1999-2017; split at start GFC EU (in 2018) Relative convergence
ADF-SUR (i) Cross-sectional mean; (ii) ECB inflation rate; (iii) Maastricht criterion
In the realm of unit root testing, commonly used tests include the (Augmented) Dickey-Fuller (ADF) test and the Phillips-Perron (PP) test. Many unit root tests suitable for panel data are adaptations of these two tests. The body of literature on panel unit root tests is extensive – powerful tests are proposed in Choi (2001), Levin et al. (2002) and Im et al. (2003), for example. The major drawback of these tests is their reliance on the assumption of no cross-sectional dependence, a condition unlikely satisfied for most macroeconomic variables (Busetti et al., 2006).A number of panel unit root tests allowing for cross dependence are proposed as well, for example in Demetrescu et al. (2006), Pesaran (2007) and Costantini and Lupi (2013).
The designs of the panel unit root tests applied in the inflation convergence literature differ substantially. A basic version is used in Kočenda and Papell (1997), who employ a standard ADF framework and use a common lag selection method proposed by Ng and Perron (1995). Monte Carlo simulations are run to derive the critical values. Lopez and Papell (2012) use a more advanced model, specifically an ADF-SUR model, which is an extension of the panel unit root test proposed in Levin et al. (2002).16 A bootstrap procedure is used to derive the critical values. Brož and Kočenda (2018) consider an extension of Lopez and Papell (2012) by adding dummy variables to the specification. Several other adaptations of the original ADF test are found in the literature. Giannellis (2013), for example, employs a threshold autoregressive (TAR) model to investigate the presumption that inflation differentials switch from persistent to transitory and vice versa.17
Next to unit root tests, cointegration techniques can be applied to investigate inflation convergence. Examples of papers that use cointegration techniques include Siklos and Wohar (1997) and Siklos (2010). Beliu and Higgins (2004) rely on fractional cointegration techniques.18 Cointegration tests and unit root tests are related, i.e. unit root processes can be shown to be a special case of cointegration. As stated above, in unit root testing inflation differentials are calculated with respect to a benchmark by simply subtracting the benchmark from the inflation rate, i.e. 𝑑 = 𝜋 − 𝑏, with 𝜋 inflation, b the benchmark, and d the resulting inflation differential. This implies a one-on-one relation between 𝜋 and b. By employing cointegration techniques, a long-term relation between integrated series 𝜋 and b is assumed that is not necessarily one-on-one. In this case, 𝑑 = 𝜋 − 𝛼𝑏, with 𝛼 a coefficient that specifies the relation between the two series. Indeed, unit root testing can now be recognized as a special case of cointegration by setting 𝛼 = 1.
4.2 Econometric framework
This study employs a unit root test that addresses cross-sectional dependence. The choice to use a unit root test follows from the hypothesis that a convergence process is underway in the euro area. As Busetti et al. (2006) point out, if interest lies in testing whether countries are in the process of convergence, unit root tests are particularly useful.19 Furthermore, Busetti et al. (2006) argue the power of the unit root test is increased if no intercept is added to the regression, which is the case since interest lies in absolute convergence testing.
A general, simple model for convergence satisfies:
𝑙𝑖𝑚
𝑠→∞𝐸(𝑑𝑡+𝑠|𝑌𝑡) = 𝛼 (1)
with d the difference between the variable of interest y and a specified benchmark b, i.e. d ≡ 𝑦 − 𝑏, 𝑌𝑡 the information set at time t and 𝛼 the mean to which the difference converges. As noted before, 𝛼 = 0 refers to absolute convergence and 𝛼 ≠ 0 to relative convergence. Since focus lies on absolute convergence, the simplest representation of this convergence model is an AR(1) model in error-correction form that does not feature an intercept (Busetti et al., 2006):
𝛥𝑑𝑡 = 𝜙𝑑𝑡−1+ 𝜖𝑡 (2)
with Δ𝑑𝑡 ≡ 𝑑𝑡− 𝑑𝑡−1 the first difference of 𝑑𝑡, 𝜙 the estimated coefficient on its first lag, and 𝜖𝑡 the error term. Defining 𝜌 ≡ 𝜙 + 1 allows to test for convergence with null hypothesis 𝐻0∶ 𝜌 = 1 (no convergence) against alternative hypothesis 𝐻1∶ 𝜌 < 1 (convergence).
This study uses Pesaran’s (2007) cross-sectionally augmented Dickey-Fuller (CADF) test, a panel unit root test that addresses cross-sectional dependence.20 The standard ADF specification is augmented with the cross-sectional means of the first lag and the first difference of the variable of interest to deal with cross-cross-sectional dependence. Pesaran (2007) shows this specification tends to outperform other panel unit root tests allowing for cross-sectional dependence. The CADF specification applied in this study is defined as follows21:
𝛥𝑑𝑖𝑡 = 𝜙𝑖𝑑𝑖,𝑡−1+ 𝛽𝑖𝑑̅𝑡−1+ 𝛾𝑖𝛥𝑑̅𝑡+ 𝜖𝑖𝑡 (3)
with 𝑑𝑖𝑡 the inflation differential with respect to the benchmark for country i at time t, bar variables representing the respective cross-sectional means and 𝜖𝑖𝑡 the idiosyncratic error term.22 Eq. (3) is fitted by ordinary least squares (OLS) for the individual countries. The test statistic 𝐶𝐴𝐷𝐹𝑖 (following notation) concerns the t-ratio of the coefficient on 𝑑𝑖,𝑡−1, i.e. of 𝜙𝑖 with 𝜌𝑖 ≡ 𝜙𝑖+ 1 the country-specific convergence coefficient. The test statistic for the group of countries is simply calculated as the arithmetic mean of the test statistics of the individual countries, i.e.:
𝐶𝐴𝐷𝐹 ̅̅̅̅̅̅̅̅ ≡ 𝑁−1∑ 𝐶𝐴𝐷𝐹 𝑖 𝑁 𝑖=1 (4)
Critical values for test statistics 𝐶𝐴𝐷𝐹𝑖 and 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ are reported in Tables I(a) and II(a), Pesaran (2007), respectively.
5. Data
5.1 Sample of countries
The sample of countries is selected based on (i) membership of the EU at entry into force of the first stage
20 In Section 6.3, an alternative econometric framework is employed to check for robustness of the results.
21This specification makes the rather unrealistic assumption of serially uncorrelated errors, which can be regarded as a limitation to this study. Pesaran (2007) also considers specifications that simultaneously account for cross-sectional dependence and serially correlated errors, but restricts attention to cases in which the convergence coefficients are homogeneous across panel units because “the mathematical details become much more complicated if 𝜌𝑖 [𝜙𝑖] is allowed to differ across 𝑖”. Assuming homogeneous convergence coefficients across countries would tremendously restrict the possibilities of this analysis.
of EMU, and (ii) adoption of the euro. Inclusion criteria are less strict in the related literature. For example, Brož and Kočenda (2018) include all member states of the EU on the assumption that most member states will adopt the euro. The Maastricht Treaty indeed does not leave adoption of the euro as a choice, but countries that gained EU membership at a later point in time will have experienced different convergence pressures than countries obliged to follow the Maastricht Treaty from the start, and hence exclusion from the sample is argued. The same reasoning applies to the three EU member states that will not adopt the euro, at least in the near future.23 By applying the criteria, ten countries are included in the sample: Belgium, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal and Spain.
5.2 Dataset
Data is derived from the Eurostat statistical database, which provides the official statistical information used by the EU’s institutions. The dataset consists of monthly observations of the annual rate of change in the national HICP for the aforementioned ten euro area countries. Annualized inflation rates are used because the official EU reference inflation rate is based on annual inflation rates. The HICP rather than the Consumer Price Index (CPI) is used since the EU considers the HICP the official measure for the assessment of inflation convergence under the Maastricht Treaty.24 Furthermore, since its methodology is harmonised across the EU, it can be confidently applied for direct comparison.
The inflation rate of country i at time t is defined as:
𝜋𝑖𝑡= ln(𝑃𝑖𝑡) − ln(𝑃𝑖,𝑡−12) (5)
with the first term on the right-hand side the natural logarithm of the price level (as measured by HICP) of country i at time t and the second term on the right-hand side the natural logarithm of the price level of country i one year ago. The sample period is 1997M1-2018M9, which amounts to 261 observations per country. The dataset includes data from just before the inception of the common currency up to the present day, which is in line with Giannellis (2013) and Brož and Kočenda (2018). There are no missing values.
5.3 Benchmark
This study employs a benchmark based on the cross-sectional mean of the inflation rates of the sample
23 Great Britain negotiated an opt-out for adoption of the euro and is currently in the process of leaving the EU. Denmark negotiated an opt-out for adoption of the euro as well. Sweden deliberately never joined ERM-II and thus does not qualify for adoption of the euro.
countries. The benchmark is calculated as the cross-sectional mean of inflation rates of the countries in the sample excluding the country of interest, at time t. Differentials with respect to each country’s benchmark are calculated. This inflation differential 𝑑𝑖𝑡 is defined as country i’s inflation rate at time t, 𝜋𝑖𝑡, minus the country’s benchmark inflation rate at time t, 𝜋̅𝑖𝑡, i.e.
𝑑𝑖𝑡 = 𝜋𝑖𝑡− 𝜋̅𝑖𝑡 (6) with 𝜋̅𝑖𝑡 ≡ (𝑁 − 1)−1∑ 𝜋𝑗𝑡 𝑁−1 𝑗=1 for 𝑗 ≠ 𝑖 (7)
Summary statistics on the data are presented in the Appendix, specifically in Table A1 and Figures A1-2.
6. Results and robustness checks
The cross-sectional means of the first lag and the first difference of the inflation differentials with respect to the cross-sectional benchmark are calculated and regressions are run using Eq. (3). The main results of the analysis are reported in Table 2. The size of the convergence coefficient 𝜌 and the associated test statistic are reported. The size of the convergence coefficient is interpreted as the rate of convergence, i.e. the lower the value of the convergence coefficient, the stronger inflation convergence (Brož and Kočenda, 2018). Absolute inflation convergence is found in seven out of ten countries at the 5% level. Convergence coefficients range from 0.9553 (Greece) to 0.8398 (Italy).25 The test statistic for the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ equals -3.15, which rejects the null of no convergence at the 1% level, i.e. absolute inflation convergence is found for the group of sample countries.26
The main results are thoroughly checked for robustness in several ways. To aid this process, an inflation rate benchmark is introduced that is independent of the sample countries’ inflation rates. This benchmark is based on the ECB’s price stability objective established by the Governing Council of the EU in 2003: inflation rates below, but close to, 2% over the medium term. The inflation rate benchmark is of equal magnitude throughout the sample period for all countries and is set to an annual rate of inflation of 𝜋̿ = 1.9.27 Inflation differentials for this benchmark are calculated according to (with the variables having their usual meaning):
𝑑𝑖𝑡 = 𝜋𝑖𝑡− 𝜋̿ (8)
25Only convergence coefficients that are significant at the 5% level are reported in the text.
Table 2
Convergence toward the cross-sectional benchmark.
Country ρi CADFi Belgium 0.9174*** -3.29 Germany 0.9639 -2.24 Spain 0.9188*** -3.29 France 0.9638 -2.24 Greece 0.9553** -2.87 Ireland 0.9756 -1.80 Italy 0.8398*** -4.70 Luxembourg 0.8704*** -4.29 Netherlands 0.9385** -2.85 Portugal 0.8890*** -3.90
Notes: This table reports convergence coefficient ρi≡ ϕi+ 1 and test statistic CADFi for convergence toward the cross-sectional benchmark. Results are based on the CADF-framework as in Pesaran (2007), who also reports critical values. Inflation differentials are based on the HICP measure. The cross-sectional benchmark is equal to the mean of inflation differentials of all countries in the sample, excluding the country of interest. The sample period is 1997M1-2018M9. ***, **, and * denote statistical significance at 1% (-3.21), 5% (-2.60), and 10% (-2.26) levels, respectively, with critical values in parentheses. The test statistic for the group of countries 𝐶𝐴𝐷𝐹
̅̅̅̅̅̅̅̅, simply calculated as the arithmetic mean of the test statistics of the individual countries, equals -3.15, which is significant at the 1% level (critical value -1.95).
The rest of this section is organized as follows. Section 6.1 applies the inflation rate benchmark to check for robustness of the results when using a different benchmark. In Section 6.2, an alternative cross-sectional benchmark is constructed in a way that is common in related literature. Results for both alternative benchmarks are reported in Table 3. In Section 6.3, an alternative econometric framework is applied that does not address cross-sectional dependence. Results are reported in Table 4. In Section 6.4, the sample is divided in two subsamples and regressions are separately run on the subsamples. Results are reported in Table 5. Finally, in Section 6.5 a core inflation measure is used. Results are reported in Table 6.
6.1 Inflation rate benchmark
Table 3
Convergence toward the inflation rate benchmark and the alternative cross-sectional benchmark.
Country Inflation rate benchmark Alternative cross-sectional benchmark
ρi CADFi ρi CADFi Belgium 0.9097*** -3.49 0.9171*** -3.31 Germany 0.9477** -2.75 0.9631* -2.30 Spain 0.8984*** -3.70 0.9184*** -3.31 France 0.9578* -2.41 0.9646 -2.21 Greece 0.9549** -2.79 0.9540** -2.95 Ireland 0.9658* -2.42 0.9758 -1.78 Italy 0.8110*** -5.67 0.8383*** -4.75 Luxembourg 0.8639*** -4.87 0.8700*** -4.31 Netherlands 0.9321** -3.15 0.9372** -2.90 Portugal 0.8835*** -3.97 0.8881*** -3.92
Notes: This table reports convergence coefficient ρi≡ ϕi+ 1 and test statistic CADFi for convergence toward the inflation rate benchmark and the alternative cross-sectional benchmark. Results are based on the CADF-framework as in Pesaran (2007), who also reports critical values. Inflation differentials are based on the HICP measure. The inflation rate benchmark is of equal magnitude (𝜋̿ = 1.9) for all countries and periods. The alternative cross-sectional benchmark is equal to the mean of inflation differentials of all countries in the sample. The sample period is 1997M1-2018M9. ***, **, and * denote statistical significance at the 1% 3.21), 5% (-2.60), and 10% (-2.26) levels, respectively, with critical values in parentheses. The test statistic for the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅, simply calculated as the arithmetic mean of the test statistics of the individual countries, equals 3.52 for the inflation rate benchmark and -3.17 for the alternative cross-sectional benchmark, which is both significant at the 1% level (critical value -1.95).
6.2 Alternative cross-sectional benchmark
In related studies that apply unit root tests, it is common practice to compute the cross-sectional benchmark without excluding the country of interest.28 In that case, the benchmark is the mean of the inflation rates of all sample countries at a particular point in time, and is thus equal for all countries. Inflation differentials are calculated according to (with the variables having their usual meaning):
𝑑𝑖𝑡 = 𝜋𝑖𝑡− 𝜋̅𝑡 (9) with 𝜋̅𝑡≡ 𝑁−1∑ 𝜋𝑖𝑡 𝑁 𝑖=1 (10)
By construction, the inflation differentials have zero mean for the group of countries, which leaves a simple specification in Eq. (3). The regressions are rerun using this alternative cross-sectional benchmark. Results are reported in Table 3. The largest change is seen in Germany. As opposed to the standard case, for Germany the null of no convergence is rejected at the 10% level. There are no other significant changes. Convergence is still found for (the same) seven out of ten countries at the 5% level. Convergence coefficients range from 0.9540 (Greece) to 0.8383 (Italy). The test statistic for convergence of the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ changes from
3.15 to -3.17 compared to the original case. Hence, the null of no group convergence is still rejected at the 1% level. The results are robust to the use of an alternative cross-sectional benchmark.
The alternative benchmark created in this section is not applied in any of the subsequent sections.
6.3 Alternative econometric framework
A univariate ADF specification is employed that allows for higher-order serial correlation but does not address cross-sectional dependence. Inflation differentials with respect to the inflation rate benchmark are calculated, i.e. Eq. (8) is used. The ADF test performs well under the current circumstances, as confirmed in Harvey and Bates (2003). Furthermore, Busetti et al. (2006) argue the ADF test performs well in the case of no intercept. A general ADF specification is as follows, allowing for serial correlation of order k:
𝛥𝑦𝑡 = 𝜙𝑦𝑡−1+ ∑ 𝛽𝑠 𝑘
𝑠=1
𝛥𝑦𝑡−𝑠+ 𝜖𝑡 (11)
The ADF test can be used to test for convergence in case of higher-order serial correlation with the same null
and alternative hypotheses as stated in Section 4.2, i.e. it allows to test for convergence with null hypothesis 𝐻0∶ 𝜌 = 1 (no convergence) against the alternative 𝐻1∶ 𝜌 < 1 (convergence). Eq. (11) is rewritten to:
𝛥𝑑𝑖𝑡 = 𝜙𝑖𝑑𝑖,𝑡−1+ ∑ 𝛽𝑖𝑠 𝑘𝑖
𝑠=1
𝛥𝑑𝑖,𝑡−𝑠+ 𝜖𝑖𝑡 (12)
with 𝜌𝑖 ≡ 𝜙𝑖+ 1 the country-specific rate of convergence, 𝑘𝑖 the optimal number of lags for country 𝑖 and 𝜖𝑖𝑡 the idiosyncratic error term. The optimal number of lags to include in Eq. (12) is determined by minimizing the Akaike Information Criterion (AIC). This is the preferred choice under these circumstances (Siklos, 2010). The maximum number of lags to include is set by using a common rule of thumb introduced by Schwert (1989), i.e. 𝑘max= 12 ∙ ( 𝑇 100) 1 4 (13)
Table 4
Convergence toward the inflation rate benchmark using an alternative econometric framework.
Country ρi Test statistic Lags
Belgium 0.8888*** -3.35 12 Germany 0.9363*** -2.68 12 Spain 0.9649* -1.85 14 France 0.9584** -2.17 12 Greece 0.9685** -2.05 12 Ireland 0.9797* -1.77 12 Italy 0.9583** -2.09 12 Luxembourg 0.9321** -2.42 12 Netherlands 0.9486*** -2.61 12 Portugal 0.9561** -2.22 12
Notes: This table reports convergence coefficient ρi≡ ϕi+ 1, the ADF test statistic and the optimal number of lags. The optimal number of lags is determined by minimization of the Akaike Information Criterion. Results are based on the standard ADF-framework. Inflation differentials are based on the HICP measure. The inflation rate benchmark is of equal magnitude (𝜋̿ = 1.9) for all countries and periods. The sample period is 1997M1-2018M9. ***, **, and * denote statistical significance at the 1% (-2.58), 5% (-1.95), and 10% (-1.61) levels, respectively, with critical values in parentheses. The twelfth lag is significant for all countries due to the use of annual inflation rates, as defined in equation (1).
and without a drift, for reasons argued above. The results are reported in Table 4. The null hypothesis of the presence of a unit root is rejected (i.e. absolute inflation convergence is confirmed) for eight out of ten countries at the 5% level. Convergence coefficients range from 0.9685 (Greece) to 0.8888 (Belgium). The results are robust to the use of an alternative econometric framework.
This alternative econometric framework is not used in any of the subsequent sections.
6.4 Two subsamples
The sample is divided in two parts and regressions are run on each subsample separately using Eq. (3). The onset of the GFC is chosen as point in time to divide the sample. This is an appealing point in time to divide the sample since (i) the GFC had a fierce (yet not necessarily asymmetric) impact on inflation rates and differentials in the euro area29, and (ii) the onset of the GFC is roughly halfway the series, leaving a sufficient amount of observations per subsample to employ the unit root test. The first subsample runs from 1997M1-2008M8, the second subsample from 2008M9-2018M9, for a total of 140 and 121 observations per country, respectively.30 As an additional robustness check, the subsamples are tested by employing both the cross-sectional and the inflation rate benchmark. Results are reported in Table 5. Due to the smaller sample sizes, critical values are adjusted following Pesaran (2007) and reported in the notes of Table 5.
29 This can be roughly verified in Figures A1-2, Appendix.
Table 5
Convergence toward the cross-sectional benchmark and the inflation rate benchmark after dividing the sample in two subsamples.
Pre-crisis period Post-crisis period
Cross-sectional benchmark Inflation rate benchmark Cross-sectional benchmark Inflation rate benchmark
Country ρi CADFi ρi CADFi ρi CADFi ρi CADFi
Belgium 0.8947** -2.63 0.8813** -2.88 0.9429 -2.01 0.9275* -2.44 Germany 0.9766 -1.29 0.9453 -2.24 0.8687** -3.11 0.8110*** -3.68 Spain 0.9574 -1.68 0.9384 -1.90 0.8619** -2.99 0.8413*** -3.27 France 0.9781 -1.34 0.9684 -1.56 0.8745** -2.71 0.9077 -1.99 Greece 0.9511* -2.58 0.9361** -3.24 0.9608 -1.53 0.9669 -1.24 Ireland 0.9716 -1.36 0.9755 -0.99 0.9799 -1.09 0.9653 -1.98 Italy 0.7985*** -3.90 0.7372*** -4.35 0.8668** -2.96 0.8415*** -3.55 Luxembourg 0.8487*** -3.42 0.8364*** -3.85 0.9077* -2.40 0.8917** -3.21 Netherlands 0.9568 -1.67 0.9537 -1.87 0.8951** -2.69 0.8815** -2.83 Portugal 0.9034* -2.53 0.8772** -3.18 0.8783** -2.80 0.8611** -3.07
Notes: This table reports convergence coefficient ρi≡ ϕi+ 1 and test statistic CADFi in the pre-crisis and post-crisis periods for both the cross-sectional benchmark and the inflation rate benchmark. Results are based on the CADF-framework as in Pesaran (2007), who also reports critical values. Inflation differentials are calculated based on the HICP measure. The cross-sectional benchmark is equal to the mean of inflation differentials of all countries in the sample, excluding the country of interest. The inflation rate benchmark is of equal magnitude (𝜋̿ = 1.9) for all countries and periods. The sample periods are 1997M1-2008M8 (pre-crisis) and 2008M9-2018M9 (post-crisis). ***, **, and * denote statistical significance at the 1% (-3.26), 5% (-2.60), and 10% (-2.26) levels, respectively, with critical values in parentheses. In the pre-crisis period, the test statistic for the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅, simply calculated as the arithmetic mean of the test statistics of the individual countries, equals -2.24 for the cross-sectional benchmark and -2.61 for the inflation rate benchmark, which is both significant at the 1% level (critical value -1.94). In the post-crisis period, the test statistic for the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ equals -2.43 for the cross-sectional benchmark and -2.73 for the inflation rate benchmark, which is both significant at the 1% level.
In the pre-crisis period, for the cross-sectional benchmark absolute inflation convergence is found in three out of ten countries; for the inflation rate benchmark, absolute inflation convergence is found in five out of ten countries, both at the 5% level. This is less than the original case, which reported seven out of ten countries converging for the cross-sectional benchmark and eight out of ten countries for the inflation rate benchmark, both at the 5% level. Convergence coefficients range from 0.8947 (Belgium) to 0.7985 (Italy) for the cross-sectional benchmark and from 0.9361 (Greece) to 0.7372 (Italy) for the inflation rate benchmark. The group test statistic 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ for the two benchmarks equals -2.24 and -2.61, respectively. Hence, with both benchmarks the null of no convergence for the group of countries is still rejected at the 1% level.31
In the post-crisis period, for both benchmarks absolute inflation convergence is found in six out of ten countries at the 5% level. This is, again, less than the original case. Convergence coefficients range from 0.8951 (Netherlands) to 0.8619 (Spain) for the cross-sectional benchmark and from 0.8917 (Luxembourg) to 0.8110 (Germany) for the inflation rate benchmark. The group test statistic 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ for the two benchmarks equals -2.43 and -2.73, respectively. Hence, for both benchmarks the null of no convergence for the group of countries is still rejected at the 1% level.
Remarkably, the number of countries displaying convergence behavior is lower for both subsamples than for the original sample. Furthermore, the test statistic for the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ is higher for both subsamples than for the original sample, i.e. convergence for the group of countries is less significant for the subsamples compared to the original sample. This finding indicates sensitivity of the results to the choice of the sample period, a notion also reported in related literature. Lopez and Papell (2012), for example, employ an eight-year rolling window and report period-specific rejection of the null hypothesis of a unit root.
6.5 Core inflation measure
Core inflation is a frequently used measure of inflation in which HICP price levels are calculated excluding goods with highly volatile price levels (Vega and Wynne, 2001). As such, it provides a more stable measure of inflation and an arguably better indicator for the evolution of inflation in the medium and long term.32 The ECB calculates core inflation by including all HICP price levels except energy and unprocessed food (Hubrich, 2003). The subsamples created in Section 6.4 apply: the regressions are only run on the post-crisis subsample since pre-crisis data on the core inflation measure is largely unavailable.33 Results are reported in Table 6. For the cross-sectional benchmark, absolute inflation convergence is found in five out of ten countries at the 5% level with convergence coefficients ranging from 0.8727 (France) to 0.8191 (Portugal). Using the inflation rate benchmark, absolute inflation convergence is found in six out of ten countries at the 5% level with convergence coefficients ranging from 0.8774 (France) to 0.7790 (Portugal). For the cross-sectional benchmark, this is less than the original case in which regressions were run on the post-crisis sample, which reported six out of ten countries converging at the 5% level. For the inflation rate benchmark, this is equal to the original case in which regressions were run on the post-crisis sample. The group test statistic 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅ for the cross-sectional and inflation rate benchmarks equals -2.48 and -2.99, respectively. Hence, the null of no convergence for the group of countries is still rejected at the 1% level. This confirms robustness of the results to a core inflation measure.
7. Discussion
Absolute inflation convergence is found for the group of sample countries. The results are confirmed to be robust to two alternative benchmarks. Furthermore, the results are robust to an alternative econometric framework and a core inflation measure. Dividing the original sample in two subsamples uncovered
32 The statement that the core inflation measure is less volatile than the standard inflation measure can be verified in Table A1, Appendix. The standard deviation of the core inflation measure is lower for all countries than the standard deviation of the standard inflation measure.
Table 6
Convergence of core inflation toward the cross-sectional benchmark and the inflation rate benchmark.
Cross-sectional benchmark Inflation rate benchmark
Country ρi CADFi ρi CADFi
Belgium 0.9496 -1.75 0.7774*** -3.86 Germany 0.8553** -3.23 0.7849*** -4.03 Spain 0.8243*** -3.44 0.8082*** -3.59 France 0.8727** -2.89 0.8774** -3.04 Greece 0.9548 -1.71 0.9538 -1.65 Ireland 0.9780 -1.20 0.9680 -1.43 Italy 0.8457** -3.15 0.8440** -3.12 Luxembourg 0.9695 -1.46 0.9267* -2.30 Netherlands 0.9049* -2.49 0.8971* -2.54 Portugal 0.8191*** -3.47 0.7790*** -4.27
Notes: This table reports convergence coefficient ρi≡ ϕi+ 1 and test statistic CADFi for convergence toward the cross-sectional and the inflation rate benchmark. Results are based on the CADF-framework as in Pesaran (2007), who also reports critical values. Inflation differentials are based on the HICP measure excluding unprocessed food and energy, which represents the core inflation rate. The cross-sectional benchmark is equal to the mean of inflation differentials of all countries in the sample, excluding the country of interest. The inflation rate benchmark is of equal magnitude for all countries and all periods. The sample period is 2008M9-2018M9. ***, **, and * denote statistical significance at the 1% (-3.26), 5% (-2.60), and 10% (-2.26) levels, respectively, with critical values in parentheses. The test statistic for the group of countries 𝐶𝐴𝐷𝐹̅̅̅̅̅̅̅̅, simply calculated as the arithmetic mean of the test statistics of the individual countries, equals -2.48 for the cross-sectional benchmark and -2.99 for the inflation rate benchmark, which is both significant at the 1% level (critical value -1.95).
sensitivities in the results. For both subsamples, group convergence was reported to be less significant compared to the total sample. Sensitivity to the sample period is a common issue in unit root testing, and its effects should be kept in mind when investigating inflation convergence.
create additional costs in terms of severe adjustments, while the net benefits of membership of a monetary union may change over time (Aizenman, 2016). Second, ECB’s definition of price stability should be evaluated at regular intervals in light of ongoing absolute inflation convergence. This is motivated as follows. ECB’s definition of price stability is set at a positive inflation rate in the medium run for several reasons, i.e. (i) it aims to prevent the undesirable situation in which the nominal interest rate reaches its lower boundary, since this impairs monetary policy instruments and possibly causes a liquidity trap, (ii) it provides a safety net against the risk of deflation for the euro area, and (iii) it accommodates for inter-country inflation differentials, preventing the undesirable situation in which a single country has to bear deflation while price stability is achieved euro-area wide.34 The third point is endorsed by Sinn and Reutter (2001), among others. However, it must be noted that the ECB’s current definition of price stability is set by the Governing Council of the ECB over fifteen years ago, in May 2003. Since then, as found in this study, there has been absolute inflation convergence among the members of the euro area, which implies that accommodation for inter-country inflation differentials is a less valid reason to define price stability as it is. Furthermore, if enlargement of the euro area materializes, new entrants will, by definition of the Maastricht inflation criterion, lower the euro area average inflation rate.
Future research should focus on the concept of absolute inflation convergence. Busetti et al. (2006), for econometric reasons explained above, argue to test the hypothesis of absolute inflation convergence rather than relative convergence. It may provide an interesting research opportunity to employ a similar econometric framework35 to a dataset including all countries in the euro area, rather than using a selection of countries based on inclusion criteria. This can be regarded a limitation to this study. If absolute inflation convergence is confirmed for a broader dataset, the suggestion for possible enlargement of the euro area is substantially strengthened. Furthermore, this result would provide additional strength to the argument that the occurrence of absolute inflation convergence should be a serious factor in decisions regarding ECB’s definition of price stability. Second, future research should focus on the distinction between structural and cyclical causes of inflation differentials.36 Different causes of inflation differentials in a monetary union imply using a different set of policy measures by both the central bank and national governments. This distinction is currently underexposed in the literature. Cavallero (2011) is a notable exception. He analyzes convergence properties of structural and cyclical components in inflation series separately and finds divergent behavior mainly due to cyclical factors. In this way, the distinction between cyclical and structural factors of persistent inflation differentials or even diverging behavior can render the findings less troublesome if the main troublemaker is the business cycle. Third, it would be interesting to perform a thorough sensitivity analysis of the results
34 The possibility of a small but positive bias in the HICP measurement is also part of the rationale, but this is of minor importance (and presumably decreasingly so due to measurement improvements) in the current discussion.
35 Or, preferably, an econometric framework that simultaneously accounts for both cross-sectional dependence and serially correlated errors.
reported in the literature to the use of different sample periods. Finally, this study focuses on the occurrence of inflation convergence for the group of sample countries rather than the rate at which convergence occurs. The country-specific rates of inflation convergence found in this study differ substantially across countries and frameworks, with values ranging between 0.9685 and 0.7372. It may be interesting to further explore the economic rationale behind the difference in convergence rates of countries in a monetary union.
8. Conclusion
This study has found clear evidence in favor of the hypothesis that inflation rates in the euro area have been in the process of absolute convergence since the inception of the common currency. This result is attained by employing a panel unit root test developed in Pesaran (2007), which allows for cross-sectional dependence between panel units, a necessary attribute when testing among members of a monetary union. Convergence is tested against a cross-sectional benchmark that excludes the country of interest. Results are confirmed to be robust in several ways. First, an inflation rate benchmark based on ECB’s price stability objective was applied. Second, an alternative cross-sectional benchmark was created in which the country of interest is not excluded from the cross-sectional mean. Third, a different econometric framework was employed. A univariate ADF specification that does not address cross-sectional dependence was created for this purpose. This framework was applied to test for country-by-country convergence toward a benchmark that does not suffer from cross-sectional dependence (i.e. the inflation rate benchmark). Fourth, the sample was divided into two subsamples to check for sensitivity of the results to the sample period applied, which was confirmed to be the case. Finally, the results were confirmed to be robust against a core inflation measure.
The results largely complement earlier findings of Lopez and Papell (2012), who report evidence strongly in favor of inflation convergence after the introduction of the euro, and Brož and Kočenda (2018), who find that inflation convergence was not disturbed by significant economic shocks such as the GFC. This study contributes to the literature by testing the concept of absolute inflation convergence, which for reasons explained above is of particular interest when investigating inflation convergence in a monetary union. Finally, as opposed to a large body of related literature, this study emphasized the economic concepts and relevance of inflation convergence in a monetary union.
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Appendix
Table A1
Summary statistics on inflation and core inflation.
Inflation Core inflation
Full sample Pre-crisis Post-crisis Post-crisis
Country 𝜇 med. 𝜎 𝜇 med. 𝜎 𝜇 med. 𝜎 𝜇 med. 𝜎
Belgium 1.9 1.8 1.14 2.0 1.8 1.01 1.7 1.8 1.25 1.8 1.7 0.40 Germany 1.4 1.4 0.81 1.6 1.5 0.72 1.3 1.3 0.87 1.3 1.3 0.35 Spain 2.2 2.4 1.49 3.0 3.0 0.87 1.2 1.5 1.48 1.0 1.0 0.76 France 1.5 1.6 0.88 1.7 1.8 0.76 1.2 1.1 0.92 1.0 0.9 0.49 Greece 2.4 2.9 2.02 3.6 3.5 0.97 1.0 0.7 2.00 0.7 0.6 1.60 Ireland 1.8 1.9 1.91 3.1 2.9 1.22 0.2 0.3 1.25 0.1 0.4 1.18 Italy 1.9 2.0 1.03 2.3 2.3 0.53 1.3 1.2 1.20 1.3 1.2 0.72 Luxembourg 2.1 2.2 1.42 2.6 2.5 1.27 1.6 1.7 1.43 1.9 1.9 0.54 Netherlands 1.9 1.7 1.21 2.3 1.9 1.13 1.4 1.4 1.09 1.4 1.2 0.79 Portugal 2.0 2.2 1.39 2.8 2.7 0.86 1.1 0.8 1.35 0.9 0.8 0.79
Figure A1. Inflation rates and benchmarks. The solid line represents the evolution of the respective country’s inflation
