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The global financial crisis and stochastic convergence in the Euro area.

Abstract This paper analyzes the issue of convergence in the original Euro Area countries, and assesses the effect of the global financial crisis on the process of convergence. In particular, we consider whether the global financial crisis pulled the 12 economies of the Euro Area together or pushed them apart. We investigate the dynamics of stochastic convergence of the original Euro Area countries for inflation rates, nominal interest rates, and real interest rates. We test for convergence relative to Germany, taken as the benchmark for core EU standards, using monthly data over the period January 2001 to September 2010. We examine, in a time-series framework, three different profiles of the convergence process: linear convergence, nonlinear convergence, and linear segmented convergence. Our findings both contradict and support convergence. Stochastic convergence implies the rejection of a unit root in the inflation rate, nominal interest rate, and real interest rate differentials. We find that the differentials are consistent with a unit-root hypothesis when the alternative hypothesis is a stationary process with a linear trend. We frequently, but not always, reject the unit-root hypothesis when the alternative is a stationary process with a broken trend. We also note that the current financial crisis plays a significant role in dating the breaks.

Keywords Stochastic convergence * Nonlinearity * Unit-root tests * Structural breaks

JEL F36 * F42 * C20 * C50

Introduction

In January 1999, 11 countries of the European Union (EU) formed an economic and monetary union (EMU) that officially became known as the Euro Area or Euro Zone. They abandoned their respective national currencies and relinquished their monetary independence to adopt a common currency, the euro These countries are Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxemburg, the Netherlands, Portugal, and Spain. Greece adopted the euro in January 2001. Since 1999, the European Central Bank (ECB) conducts monetary policy. Denmark, Sweden, and the United Kingdom maintain their own currencies and monetary independence.

The EU, as we know it today, was born out of the Maastricht Treaty (1992), which created the legal, institutional, monetary, and fiscal framework of the EMU (see Eichengreen and "Wyplosz 1993 for more details). The Maastricht Treaty requires that the countries in the Euro Zone achieve real and financial integration. After the inception of the euro, however, we witness a growing number of apparent divergences, especially in connection with the current financial crisis. The relevant literature, however, does not y1193-8308-139001-25011024et determine whether these divergences constitute temporary events or represent the manifestation of more structural phenomena.

This paper analyzes the issue of convergence in the original Euro Area countries, and assesses the effect of the global financial crisis on the process of convergence. (1) In particular, we consider whether the global financial crisis pulled the 12 economies of the Euro Area together or pushed them apart.

We analyze three aspects of convergence. First, we consider whether inflation differentials persist in the Euro Area. (2) Persistent inflation differences complicate the ECB's monetary policy, as the common interest rate policy may prove too lax for some countries and too strict for others. As such, a single monetary policy, one size fits all, cannot efficiently fight inflation within the Euro Area. Countries with slow growth, high unemployment, and a large trade deficit, such as Greece, Italy, and Portugal, may want to leave the Euro Area to ease monetary conditions and devalue their currencies. Similarly, other countries, such as Germany that prefer tougher monetary policy, may want to leave the Euro Area to pursue a tighter policy. Alternatively, regional inflation differentials may only reflect differences in productivity growth, the well-known Balassa-Samuelson effect. Alberola (2000) provides a full discussion of the potential sources of regional inflation differentials, making a distinction between a benign view of inflation differentials when caused by productivity-related convergence and a more worrying view when inflation differentials result from structural rigidities. In this regard, Duarte and Wolman (2002) show that productivity shocks can account for a significant portion of inflation variation across European countries. (3)

Second, we consider whether nominal interest rate differentials also persist in the Euro Area. (4) Since the Euro Area countries share a common currency, exchange-related premium differentials can no longer exist in theory, and nominal interest rates on assets with similar characteristics cannot diverge significantly in the Euro Area. Persistence in yield differentials suggests that investors do not regard bonds issued in different Euro Area countries as close substitutes, which, in turn, delivers the financial markets' assessment of the sustainability of the government's fiscal policy, and implies that the real economies of these countries do not follow convergent paths.

Haugh et al. (2009) analyze the recent large movements in the yield spread for sovereign bonds between Germany and other Euro Area countries and conclude that differing fiscal policies, especially their effects on future deficits, and debt service ratios explain significant portions of bond yield spreads in the Euro Area. (5) The important policy making implications of this analysis becomes especially relevant, given the massive expansionary fiscal policies undertaken by Euro Area countries in response to the 2008 recession. The profound deterioration of public finances raises significant red flags regarding the possible negative effect on interest rates. Particularly, a widespread concern exists in the EMU that the increase in yields on the capital markets, driven by the deterioration of national fiscal conditions, will damage the ability to implement the common monetary policy In early 2010, concerns about fiscal solvency of some Euro Area countries, such as Portugal, Ireland, Greece, and Spain, with the widening of government bond yield spreads and talk of possible bail-outs, disturbed the Euro Area's financial stability. For example, the spread of the Greek 10-year government bond to the 10-year German bond reached a maximum of 329 basis points in February 2010. Similarly, the maximum spread of the Irish 10-year government bond saw 274 basis points in March 2009. Conversely the spread of the French 10-year government bond peaked in March 2009 at 63 basis points. These differentials reflect the countries' fiscal weaknesses and are especially important in the Euro Area, where member countries can no longer monetize their debt. At the same time, however, the absence of these differentials may only reflect the financial markets' anticipation that the ECB or other member countries will bail out distressed member countries.

Third, we analyze whether real interest rate differentials persist in the Euro Area. Convergence of real interest rates implies that capital flows move to close real interest rate spreads across the Euro Area, and provides a measure to assess the degree of integration in capital markets. (6)

The concept of convergence inherently relates to economic growth. That is, definitions and methodological approaches to convergence come from the empirical growth literature, pioneered by Baumol (1986), Bairo (1991), and Barro and Sala-i-Martin (1991, 1992). In contrast to the cross-section notion of convergence, the extant literature also examines a time-series notion of convergence. In two seminal contributions, Bernard and Durlauf (1995, 1996), drawing on Carlino and Mills (1993), develop a stochastic approach to convergence, which uses the property of stationarity to evaluate convergence. A stationary series reverts back to its equilibrium value after being disturbed by external shocks. Within this context, the time-series properties of inflation, and nominal and real interest rate differentials are most relevant. A finding that we can characterize these series by unit-root behavior indicates stochastic divergence, with shocks affecting the series on a permanent basis.

Bernard and Durlauf (1996) introduce two definitions of convergence--catching up (Definition 1) and equality of long-term forecasts (Definition 2). They demonstrate that countries i and j do not conform to Definition 2 of convergence when the time-series difference between an economic variable in the two countries contains a non-zero mean or a unit root. That is, absolute stochastic convergence implies that long-run forecasts of the differential between any pair of countries converge to zero, as the forecast interval increases (Oxley and Greasley 1997). Absolute stochastic convergence exists only if the difference between two time-series conforms to a zero mean stationary process. This can only occur if the paths of the two series coincide. From this viewpoint, the presence of a deterministic trend or a drift impedes the realization of long-run stochastic convergence.

Second, catching up or conditional convergence, which automatically holds if we can establish the equality of long-term forecasts, focuses on identifying movement toward complete convergence, although it is not yet achieved. Bernard and Durlauf (1996) state that this definition of convergence is violated when history matters or when differences persist into the future. In other words, catching up implies that the differential narrows, but does not necessarily disappear, as the series moves through time. This definition also requires that the difference between two time-series is stationary, but does not preclude the presence of a non-zero mean or a deterministic time trend (Carlino and Mills 1993). Since the concept of convergence underlying the Maastricht Treaty reflects a gradual process of real and financial integration, we use the second characterization of stochastic convergence (i.e., conditional convergence) and model the bilateral behavior of the inflation rates, nominal interest rates, and real interest rates of the countries in the Euro Area against Germany as a unit-root problem. (7)

We examine three different representations of the convergence process: linear convergence, nonlinear convergence, and linear segmented convergence. First, we apply the efficient version of linear unit-root tests proposed by Ng and Perron (2001). Second, we allow nonlinearities in the convergence process and apply the Kapetanios et al. (2003) unit-root test. Finally, to permit up to two endogenously determined structural breaks, we apply the Perron and Rodriguez (2003) and Lee and Strazicich (2003) unit-root tests. (8)

Data

We use monthly data on interest rates and consumer prices for the original 12 EMU countries that adopted the euro and, thus, a common monetary policy: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxemburg, the Netherlands, Portugal, and Spain. As noted above, Greece adopted the Euro in 2001, while the remaining countries adopted the euro in 1999. To use a common sample, the raw monthly data cover the period from January 2001 to September 2010, and come from the Eurostat databank of the European Central Bank. The data are harmonized to conform to the Maastricht Treaty. The sample consists of 117 observations for each country. (9)

We compute the inflation rate, [p.sub.t] as the percentage change of the monthly Harmonized Consumer Price Index (HCPI) over a 12-month period, and the nominal interest rate, it is the Harmonized 10-Year Government Bond Yield (HGBY). (10) We construct the real interest rate [r.sub.t] using the ex post version of the Fisher equation. That is,

[r.sub.t] = [i.sub.t] - [p.sub.t] (1)

where [i.sub.t] is the nominal interest rate at time t. We use these three measures to construct the series of bilateral inflation differentials ([[p.sup.i].sub.t] - [[p.sup.G].sub.t]), bilateral nominal interest rate differentials ([[[i.sup.i].sub.t] - [[i.sup.G].sub.t]), and bilateral real interest rate differentials ([[r.sup.i].sub.t] - [[r.sup.G].sub.t]), where [[p.sup.G].sub.t], [[i.sup.G].sub.t]and [[r.sup.G].sub.t] are, respectively, the benchmark measures of the German inflation rate, nominal interest rate, and real interest rate.

Convergence Methodology

As emphasized in the introduction, the existence of stochastic convergence relates to the unit-root hypothesis. Stationarity relates to shock persistence in the sense that for a stationary series, shocks only exert temporary effects. On the other hand, for a non-stationary series, shocks possess permanent effects. Thus, if the series of differentials do not possess a unit root, we conclude that evidence exists to support stochastic convergence. In this context, failure to reject the unit-root hypothesis corresponds to failure to provide evidence of stochastic convergence. In this section, we briefly review the methods employed to test stochastic convergence. In what follows, we consider the series {[d.sub.t]} where [d.sub.t,] denotes nominal interest rate differentials, inflation differentials, and real interest rate differentials at time t.

First, we examine the convergence of [d.sub.t] using the linear tests M[Z.sub.t] and M[P.sub.T] developed by Ng and Perron (2001). The tests are constructed using local-to-unity GLS detrended data and possess good size and power properties. Most conventional unit-root tests suffer from at least three problems. First, they exhibit low power when the root of the autoregressive polynomial is close to, but less than unity (DeJong et al. 1992). Second, most of the tests suffer severe size distortions, when the moving average MA polynomial of the first-differenced series comes with a large negative autoregressive root (Schwert 1989). Third, size distortions and loss of power associate with the selection of the number of lags (Ng and Perron 1995). Ng and Perron (2001) address these three issues with the M-class of tests, which is robust to these issues. The M[Z.sub.t] statistic modifies the [Z.sub.t] statistic of Phillips and Perron (1988), while the M[P.sub.T] statistic modifies the [P.sub.T]statistic of Elliott et al. (1996). These statistics are defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

And

M[P.sub.T] = ([[bar.a].sup.2][kappa] + (1- [bar.a])[T.sup.-1][[~.d].sup.2.sub.T])/[f.sub.0] (3)

Where [[~.d].sub.t] is the locally detrended data, [bar.a] = -13.5a, [f.sub.0] is the residual spectrum at frequency zero, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Next, we examine nonlinear stationarity using the Kapetanios et al. (2003) unit-root test, a nonlinear version of the Augmented Dickey-Fuller test, based on an exponentially smooth-transition autoregressive model (ESTAR). The Ng and Perron (2001) tests assume that the adjustment toward equilibrium follows linear dynamics. Many situations exist, however, where nonlinear adjustments may occur. For example, policy actions may differ depending on the direction of the deviations from equilibrium, or may take place only when the deviation from equilibrium exceeds a threshold. Kapetanios et al. (2003) argue that nonlinear data generation processes (DGP) can severely affect the power of linear unit-root tests and may prevent the tests to reject the null hypothesis of unit root. Kapetanios et al. (2003) propose the following univariate ESTAR model:

[DELTA][d.sub.t] = [beta][[bar.d].sub.t-1] + [1 + exp(-[theta][[d.sup.2].sub.t-1])] + [[epsilon].sub.t] (4)

The test focuses on the parameter 0 which equals zero under the null and is positive under the alternative. Since 7 is not identified under the joint null hypothesis of linearity and a unit-root, testing the null hypothesis of Ho: [theta] = 0 against the alternative hypothesis of H1: [theta] > 0 is not feasible. Thus, Kapetanios et al. (2003) reparameterize Eq. 4 using a Taylor series approximation to obtain:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where [[bar.d].sub.t] is the OLS detrended series [d.sub.t] and k is the number of lags used to correct for serially correlated errors. Equation 5 tests the null of a unit root against the alternative of a nonlinear, but globally stationary, process using the OLS t-statistic corresponding to [beta].

Finally, we explicitly address the issue of structural breaks. The unit-root literature (see Perron 1989; Zivot and Andrews 1992; Perron 1997) shows that conventional unit-root tests suffer from a loss of power in the presence of structural breaks and may fail to reject the null hypothesis of a unit root when the series is stationary around a segmented trend function. (11) We employ tests that allow up to two structural breaks, which are determined endogenously from the data, so as to capture the possible changes in the convergence path. Not only do important statistical reasons exist for structural breaks in the data generation process of the differential series, but also important economic reasons exist as well. The financial markets of the Euro Area countries experienced significant structural changes from January 2001 to September 2010, where the global financial and economic crisis, when the subprime crisis hit global financial markets in the third week of July 2007, provided the biggest effect. Until then, analysts viewed the stability and convergence of nominal and real interest rates and inflation differentials as the hallmark of successful financial integration within the Euro Area.

We employ several testing procedures for unit roots that permit structural breaks in the data generating process (DGP). The Perron and Rodriguez (2003) test extends the GLS detrending approach of Elliott et al. (1996) and Ng and Perron (2001) in the context of one unknown structural change. We also consider the possible existence of two breaks under the alternative hypothesis of stationarity. Lumsdaine and Papell (1997) provide a frequently used test based on the ADF statistic. ADF-typs tests suffer a drawback that the presence of structural breaks under the null affects their size properties. Furthermore, these statistics experience divergence under the null hypothesis. To overcome this issue, we use a two-break minimum-LM statistic proposed by Lee and Strazicich (2003), which is related to the one-break LM unit-root test developed by Amsler and Lee (1995). Unlike conventional unit-root statistics, the minimum-LM statistic does not suffer from bias and spurious rejection in the presence of structural breaks under null.

Perron and Rodriguez (2003) extend the tests for a unit root developed by Ng and Perron (2001) to consider an endogenous change in the trend function. The Ng and Perron (2001) test modifies a version of the Phillips and Perron (1988) test that corrects the size distortions (as suggested by Perron and Ng 1996) and improves the power (as suggested by Elliott et al. 1996). The Perron-Rodriguez test is based on the following regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where [d.sub.t] represents the detrended series, which come from the local-to-unity GLS detrending and k is selected using the Modified Akaike Information Criterion (MAIC). Under the unit-root hypothesis, [beta] = 0 The test statistics employed is the [[MZ.sup.GLS].sub.t ]([delta]) statistic, defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [delta] = [T.SUB.B]/T, [delta] [member of] (0,1) is the relative position of the timing of the break, and s is an autoregressive spectral density estimator of the long-term variance. We estimate the break point by minimizing [[MZ.sup.GLS].sub.t] ([delta]).

Lee and Strazicich (2003) develop a version of the LM unit-root test to accommodate two structural breaks. The two-break test reduces the potential loss of power to reject the unit root when two breaks occur instead of one. The test includes the two breaks under both the null and the alternative hypotheses, and the rejection of the null unambiguously implies stationarity. Lee and Strazicich (2003) analyze two alternative models, which they call Model A and Model C. We consider Model C, (12) which allows for two shifts in the level and the trend of [d.sub.t] so that [Z.sub.t] = [1, t, [D.sub.1t], [D.sub.2t,] [DT.sub.1t] [DT.sub.2t]]'. [D.sub.jt] and [DT.sub.jt], j=1, 2, are dummy variables that denote mean and trend shifts, respectively. [D.sub.jt] = 1 for t [greater than or equal to] [T.sub.bj] + l,j = 1, 2 and 0 otherwise, and [DT.sub.jt] = t - [T.sub.Bj] for t [greater than or equal to] [T.sub.Bj] + 1, j = 1, 2, and 0 otherwise. [T.sub.B] represents the time period when a break occurs. In Model C, Eqs. 8 and 9 give the null and alternative hypotheses as follows:

[d.sub.t] = [u.sub.0] + [[c.sub.1]B.sub.1t] + [[c.sub.2]B.sub.2t] + [[e.sub.1]D.sub.1t] + [[e.sub.2]D.sub.2t] + [d.sub.t-1] + [[[v.sub.1t] (8)

and:

[d.sub.t]=u.sub.1] + [r.sub.t] + [[c.sub.1]B.sub.1t] + [[c.sub.2]B.sub.2t] + [[e.sub.1]DT.sub.1t] + [[e.sub.2]DT.sub.2t] + [v.sub.1t] (9)

where the error terms [v.sub.1t] and [v.sub.1t] are stationary processes, and Bjt = l for t = [T.sub.bj] + 1, j = 1, 2, and zero otherwise. The test assumes the following DGP:

[d.sub.t] = [delta]'[Z.SUB.T] + [[eta].sub.t], [[eta].sub.t] = [beta][[eta].sub.t-1] + [[epsilon].sub.t] (10)

where Zt is a vector of exogenous variables and [[epsilon].sub.t] ~iid (0. [[delta].sup.2]). The LM unit-root test statistic comes from the following regression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where the detrended series [[~.S].sub.t] is defined as follows: [[~.S].sub.t] = [d.sub.t] - [[~.[psi]].sub.x] - [Z.sub.1][~.[delta]], t=2, ..., T; [~.[delta]] equals the coefficient vector in the regression of [DELTA] [d.sub.t] onto [DELTA] [Z.sub.t]; [[psi].sub.x] equals [d.sub.1] - [Z.sub.1[delta]], where [d.sub.1] and [Z.sub.1] correspond to the first observations of [d.sub.t] and [Z.sub.t], respectively. We include the lags [[DELTA]S.sub.t-i] to correct for serial correlation. Under the null hypothesis of a unit root, [empty set] = 0, and under the alternative, [empty set] < 0. The LM test statistic equals the t-statistic [~.[tau]] for testing the null hypothesis [empty set] = 0. We find the two breaks [[lambda].sub.j] = [T.sub.bj]/T,J = 1, 2 by a grid search [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] that minimizes [~.[tau]].

We complement the univariate analysis with a panel unit-root approach, which significantly increases the power of the test against the null. We first apply two common panel unit-root tests. The first test, suggested by Levin et al. (2002), uses the following model:

[DELTA][d.sub.it] = [[rho].sub.i][d.sub.it-1] + [Z'.sub.it][gamma] + [u.sub.it], i=1, ..., N; t=1, ..., T, (12)

where [Z.sub.it] is the deterministic component and [u.sub.it] is a stationary process. The test assumes that [p.sub.i] = p for all i and the panel statistics is a t-statistic calculated under the null as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [[~.d].sub.it] and [[~.u].sub.it] are, respectively, [d.sub.it] and [u.sub.it] corrected for the deterministic component.

The second test, developed by Im et al. (2003), allows [p.sub.i] to vary across the different panel units and uses the average of the individual unit-root test statistics obtained from Augmented Dickey-Fuller regressions. That is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

where [t.sub.pi] is the individual t-statistic for testing the unit-root hypothesis. Im et al. (2003) show that t is normally distributed under the null hypothesis, and use estimates of its mean and variance to convert t into a standard normal statistic so that conventional critical values can evaluate its significance. The two panel tests also differ in how they treat the alternative hypothesis. In Levin et al. (2002), the alternative hypothesis assumes that all of the series are trend stationary, while in Im et al. (2003), the alternative hypothesis assumes that at least one, rather than all, of the series are trend stationary.

Finally, we apply the panel LM unit-root test recently proposed by Im et al. (2005). In contrast to conventional panel unit-root tests, the distribution of the panel LM test statistic proves invariant to break-point nuisance parameters. As such, the critical values that apply to the panel LM unit-root test without breaks are also valid for the panel LM unit-root test with breaks, regardless of the location and number of breaks in each cross-section. The panel LM test statistic comes by averaging the optimal univariate LM test statistics estimated for each series. That is, define:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

to equal the mean of the individual LM statistics obtained from Eq. 11, where N is the number of series. Im et al. (2005) compute the following standardized panel LM test statistic:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

where [E(L.sub.T]) and [V(L.sub.T]) denote the expected value and the variance of [LM.sub.i] respectively, under the null hypothesis that all [empty set] are zero. The numerical values for [E(L.sub.T]) and [V(L.sub.T]) appear in Im et al. (2005, Table 1). The asymptotic distribution of [T.sub.LM] depends only on AT and T9 and follows the standard normal distribution.

Empirical Results

Table 1 displays the results of linear unit-root tests without structural breaks. We select the lag order using the modified Akaike information criteria (MAIC), assuming an upper bound of k* = 12. Using the 5-percent significance level, we find poor evidence for convergence, since the tests cannot reject the presence of a unit root in favor of the trend stationary alternative. We reject nominal and real interest rate convergence in 10 out of 11 cases (Austria is the only exception), while we reject inflation convergence in all 11 cases. In addition, for Greece, the test results suggest the possibility that nominal interest rate differentials follow an explosive process.

Well-known power gains exist in unit-root tests using panel techniques. Our panel results, however, do not differ from the univariate estimates. The Levin et al. (2002, LLC) and Im et al. (2003, IPS) panel unit-root tests yield test statistics that cannot reject the unit-root hypothesis for the nominal interest rate, inflation rate, and real interest rate differentials. In addition, we uncover the same findings when we exclude those countries identified in the popular press as experiencing significant issues with their sovereign debt -- Greece, Ireland, Portugal, and Spain. To complete the analysis, we also ran a test for just Greece, Ireland, Portugal, and Spain. Once again, the panel tests still cannot reject the unit-root hypothesis, using the LLC and the IPS tests.

We note that the panel unit-root tests improve the power of the tests. Moreover, since both tests cannot reject the null, these rejections call into question our limited finding of convergence for the nominal and real interest rate differentials in Austria.13 In addition, we uncover the same findings when we exclude those countries identified in the popular press as experiencing significant issues with their sovereign debt -- Greece, Ireland, Portugal, and Spain or when consider these countries by themselves.
Table 1 Linear unit-root tests with no structural break

Country         Nominal                           Inflation rate
             intcrcst rate                        differentials
             differentials

              M[Z.sub.t]      M[P.sub.T]    k     M[Z.sub.t]

Austria           -3.028 **     5.011 **      11     -1.220
Belgium            -1.587      14.961         11     -0.927
Finland            -2.381       8.030          2     -1.478
France             -1.511      18.310         11     -1.882
Greece              2.175      73.671         12     -1.027
Ireland           -2.670f       7.039          3     -1.650
Italy              -0.501      35.033         10     -2.205
Luxembourg         -1.169      32.921          4   -2.81 Of
Netherlands        -2.432       7.701          7     -1.360
Portugal           -1.930      10.155          6     -2.175
Spain              -0.655      23.703         11     -2.205
Panel tests          Test    p- value       Test   /7-valuc
LLC(ll)             6.409       1.000      2.179      0.985
IPS(ll)             4.131       1.000      0.417      0.662
LLC(7)              0.727       0.766      0.963      0.832
IPS(7)              0.518       0.697     -0.417      0.338
LLC(4)             10.476       1.000      2.365      0.991
IPS(4)              6.200       1.000      1.257      0.895

Country                            Real interest rate
                                       differentials

             M[P.sub.T]      k     M[Z.sub.t]  M[P.sub.t]   k

Austria         25.914        12   -3.147 **    4.653 **    1
Belgium         30.564        12   -2.278       8.648       0
Finland         20.647        12   -1.356      24.482      12
France          12.718        12   -1.673      16.189      12
Greece          19.554         1   -0.913      17.481       1
Ireland         16.323             -0.898      26.310       0
Italy            9.363             -2.235       8.989       1
Luxembourg      5.791|             -2.015      11.197      12
Netherlands     20.307             -1.510      16.872       0
Portugal         9.118             -2.485       7.379       2
Spain            9.355             -1.821      13.071       0
Panel tests       Test   p-va\uc
LLC(ll)          2.619     0.995
IPS(ll)          0.096     0.538
LLC(7)           1.124     0.869
IPS(7)          -1.066     0.143
LLC(4)           2.684     0.996
IPS(4)           1.585     0.943

The Ng and Perron (2001) M-class of tests include the MZ, statistic and
the M[P.sub.T]statistic. The 1 %, 5%, and 10% asymptotic critical values
for M[Z.sub.t] arc -3.42, -2.91, and -2.62, respectively, and for
M[P.sub.T]arc 4.03, 5.48, and 6.67, respectively. The LLC and IPS are
the panel unit-root tests of Levin ct al. (2002) and Im ct al. (2003),
respectively. The 11 in parentheses after LLC and IPS refers to tests
for all countries, 7 refers to tests for all countries except Greece,
Ireland, Portugal and Spain, and 4 refers to only tests for Greece,
Ireland, Portugal and Spain. The symbols *, **, and f mean significantly
different from zero at the 1-. 5-. and 10-pcrccnt levels, respectively.


Table 2 reports the results of the Kapetanios et al (2003) nonlinear unit-root test, with the number of lags k determined using the Akaike information criterion (AIC), assuming an upper bound of k* = 12. When accounting for nonlinearity, the test adds three more rejections of the null hypothesis of unit root at the 5-percent level, while losing the two cases for Austria identified by the linear unit-root tests in Table 1. We find nonlinear convergence of nominal interest rate differentials for Belgium and Finland and of real interest rate differentials for Greece. The nonlinear tests provide a marginal increase in support for convergence when compared to the linear tests.
Table 2 Kapetanios nonlinear unit-root test

Country         Nominal            Inflation             Real
             interest rate           rate          interest rate
             differential        differential      differential
             t-statistic     k   t-statistic   k   t-statistic     k

Austria             -0.531   12        -0.408  12          0.701   12
Belgium            -6.695 *  12        -2.051  12         -1.890   12
Finland            -4.000 *   1        -0.740  11         -1.117   12
France              -1.465   12        -0.103  11          0.213   11
Greece               2.890   12        -2.185  11       -3.690 **   2
Ireland             -2.716    2        -0.905  11          0.089   11
Italy               -0.050   12        -1.264  11         -1.751    n
Luxembourg          -0.396    8        -0.498  11         -0.915    n
Netherlands         -0.962    5         0.451  11          0.268    n
Portugal            -2.920    5        -2.065  12         -1.608   12
Spain               -3.072   12        -0.028   5         -0.375    5

The 1%, 5%, and 10% asymptotic critical values (case 3) are -3.93,
-3.40, and -3.13, respectively. The symbols *, **, and [dagger] mean
significantly different from zero at the 1-. 5-. and 10-percent levels,
respectively.


Table 3 reports the results of using the two-break LM unit-root test. In all cases, the maximum number of lags is k* = 12. We reject nominal interest rate convergence in only 1 of the 11 series using a 5-percent level of significance -- Luxemburg. We also reject inflation rate convergence at the 5-percent level in 7 of 11 countries--Austria, Belgium, Finland, Ireland, Italy, Portugal, and Spain. For four of these countries, Finland, Ireland, Portugal, and Spain, we can accept convergence by rejecting the unit-root hypothesis, but only at the 10 percent significance level. We can accept real interest rate convergence at the 5-percent level in only two cases--France and the Netherlands -- and at the 10-percent level in two other cases--Finland and Spain. For nominal interest rate differentials, the most frequently identified period of break occurs in the years 2008 to 2009. Similarly, in case of inflation differentials, the highest frequency occurs in 2008, while for real interest rate differentials the breaks most frequently occm from 2006 to 2008.
Table 3 Two-break minimum LM unit-root tests, January 2001
-September 2010

Country           Nominal                     Inflation rate
               interest rate                  differentials
               differentials

               [T.sub.B1]      Test       k      [T.sub.B1]
               [T.sub.B2]     Statistic         [T.sub.B2]


Austria        May-06 Sep-08    -7.256 *  12  Nov-04 Mar-06

Belgium        Mar-07 Dec-08    -6.466 *  12  Mar-08 Aug-09

Finland        May-06 Aug-08   -5.757 **  11  Jan-04 Aug-08

France         Apr-06 Sep-08   -6.249 **  12  Feb-03

Greece         Jul-07 Jan-09    -9.561 *  10  Jan-04 Oct-08

Ireland        Oct-07 Feb-09    -9.568 *  11  Oct-04 Oct-08

Italy          Apr-08 Feb-09    -6.542 *  11  Jan-03 Aug-05

Luxembourg     Apr-04 Jan-09      -4.369   3  Jun-03 Jun-06

Netherlands    Jun-05 Aug-08   -5.943 **  11  Feb-04 Mar-06

Portugal       Feb-08 Mar-09   -11.267 *   5  May-04 Nov-08

Spain          Oct-07 Mar-09    -6.731 *   8  Dec-06 Aug-08

Panel Test     Test                              Test
               statistic                      statistic

F.sub.lM(11)]  -30.054 *                       -21.040 *

FYm(7)         -18.774 *                       -16.265 *

F.sub.LM](4)   -25.006 *                       -13.381 *

Country                       Real interest
                                 rate
                              differentials

               Test       k    [T.sub.B1]      Test
               Statistic       [T.sub.B2]     Statistic  k

Austria          -4.726   12  Oct-07 Oct-08      -4.261  12

Belgium          -3.948   12  Nov-02 Aug-06      -3.943  12

Finland          -5.689   12  Jan-04 Dec-08     -5.510t  12
               [dagger]

France         -6.373 *   11  Dec-02 Apr       -5.906 *  11

Greece         -6.352 *   11  Sep-07 Mar-09      -5.167   4

Ireland          -5.688   11  Oct-04 Oct-08      -4.862  11
               [dagger]

Italy            -4.865   12  Jan-03 Sep-04      -4.781  12

Luxembourg     -6.424 *   11  May-03 Apr-06      -4.314  12

Netherlands    -6.627 *   11  Jan-04 Mar-06   -6.043 **  11

Portugal         -5.665   11  Mat-04 Jun-06      -4.575  12
               [dagger]

Spain            -5.668   11  Aug-03 Apr-06      -5.483   8
               [dagger]                        [dagger]

Panel Test                       Test
                                statistic

F.sub.lM(11)]                 -17.385 *

FYm(7)                        -13.381 *

F.sub.LM](4)                  -10.601 *

Critical values for the LM two-break unit-root test statistic in Model C
depend on the location of the break. The 1%, 5%, and 10% critical values
for different values of [T.sub.BJ]/Tand [T.sub.B2]/Tcomc from Table 2 in
Lee and Strazicich (2003). [T.sub.LM] is the Im et al. (2005) panel LM
unit-root test. The II in parentheses after Flm refers to tests for all
countries, 7 refers to tests for all countries except Greece, Ireland,
Portugal and Spain, and 4 refers to only tests for Greece, Ireland,
Portugal and Spain. The symbols *, **, and f mean significantly
different from zero at the 1-. 5-. and 10-percent levels, respectively.


The inclusion of endogenously determined structural breaks in the data generating process leads to slightly different findings. Now, we generally find convergence for nominal interest rates, but limited evidence of convergence for inflation rate and real interest rate differentials, employing the 5-percent significance level. When we relax the significance level to the 10-percent level, we find much more evidence of convergence of inflation rate differentials (i.e., eight rather than four countries) as well as more evidence of real interest rate differential convergence (i.e., four rather than two countries).

Further examination of these results reveals that the two structural breaks do not prove significant at the 5-percent level in all cases. The inclusion of two breaks when only one actually occurs affects the power to reject the null. For nominal interest rate differentials, the one-break test is appropriate for five countries -- Austria, France, Greece, Ireland, and Luxemburg. For inflation differentials, one structural break is appropriate for four countries--Belgium, France, Portugal, Spain, and for real interest rate differentials it is appropriate only for Greece.

Tables 4 and 5 present the one-break unit-root tests. While we focus on the series that failed to satisfy the two-break test, we report the test results for all series. Table 4 reports the results of the Perron and Rodriguez (2003) unit-root test based on Model II, while Table 5 reports the Lee and Strazicich (2004) results based on Model C. Both test results support nominal interest rate convergence for Austria and Ireland, but not for France and Luxemburg. They do not identify, however, the break dates at the same time, since for Austria the Lee and Strazicich test dates the break in 2008 and the Perron and Rodriguez test dates the break in 2005.14 Greece provides mixed evidence with the Perron-Rodriguez results supporting convergence and the Lee-Strazicich results not supporting convergence. Furthermore, in no instances do the one-break Perron-Rodriguez or Lee-Strazicich results support inflation convergence for Belgium, France, Portugal, and Spain or real interest rate convergence for Greece.

Combining the results from Tables 3, 4 and 5 gives the following conclusions. While Table 3 identifies only the nominal interest rate differential of Luxembourg as exhibiting non-stationarity, the consideration of the Perron-Rodriguez and Lee-Strazicich one-break unit-root tests adds France to this non-stationary list while the Lee-Strazicich test alone suggests that Greece exhibits a non-stationary nominal interest rate differential. For the tests of inflation rate differentials, the Perron-Rodriguez and Lee-Strazicich one-break unit-root tests remove France, Portugal, and Spain from the list of stationary series. (15) Finally, the Perron-Rodriguez and Lee-Strazicich one-break unit-root tests do not alter the findings for real interest rate differentials in Table 3.

The panel LM results provide further significant evidence of convergence (see Table 3). The TLM statistics rejects the null hypothesis of a unit root for nominal interest rate differentials, inflation rate differentials, and real interest rate differentials. Dichotomizing the sample does not affect the results. When we exclude Greece, Ireland, Portugal, and Spain, we also can reject the null hypothesis for all three differentials. Using only Greece, Ireland, Portugal, and Spain, we still can reject the null hypothesis in each case. This panel unit-root test that incorporates different structural breaks uses the alternative hypothesis that at least one panel unit exhibits stationary series. Given that we find at least one country for each differential series that exhibits convergence, the panel unit-root tests confirm the country-by-country findings.
Table 4 Perron Rodriguez one-break unit-root tests
Country         Nominal                   Inflation rate
               Interest                    differentials
                 rate
             differentials

             [MZ,.SUP.GLS]  k  Break   [M[Z.sub.t].SUP.GLS]  k  Break
                               date                             date

Austria           -4.468 *  5  Aug-05             -3.705 **  1  Aug-05
Belgium             -2.704  0  Jun-06                -2.476  0  Jun-09
Finland             -2.985  3  Jun-04                -2.530  0  Jan-04
France              -3.057  5  Jun-06                -2.451  1  Mar-04
Greece            -8.596 *  2  Jan-08                -2.663  2  Aug-09
Ireland           -8.216 *  3  Jan-09                -2.154  0  Jun-09
Italy            -3.569 **  1  Mar-08                -2.561  1  Apr-04
Luxembourg          -2.115  4  Dec-04                -3.066  0  Jul-06
Netherlands        -3.381t  6  Nov-08                -2.913  0  Jul-04
Portugal          -9.810 *  6  Mar-05                -2.803  2  Jun-09
Spain               -3.103  2  Sep-07                -2.526  0  Apr-03

Country          Real intersst
              rate differentials

             [M[Z.sub.t].SUP.GLS]  k   Break
                                        date

Austria                 -3.564 **  1  Oct-08
Belgium                    -2.666  0  Mar-09
Finland                    -2.786  0  Jan-04
France                     -2.623  1  Mar-04
Greece                     -2.848  0  Mar-09
Ireland                    -2.431  0  Jan-08
Italy                      -3.055  1  Jan-04
Luxembourg                 -2.500  0  Oct-06
Netherlands                -3.059  0  Dec-04
Portugal                   -3.186  2  Mar-06
Spain                      -2.518  0  Nov-06

The 1%, 5% and 10% asymptotic critical values (Model II) are -3.93,
-3.56, and -3.36, respectively, and come from Table 1 in Perron and
Rodriguez (2003). The symbols *, **, and [dagger] mean significantly
different from zero at the 1-. 5-. and 10-percent levels, respectively.

Table 5 Lee and Strazicich one-break unit-root [[tests

Country         Nominal                          Inflation
               interest                            rate
                 rate                          differentials
             differentials

                [T.suB. B1]  [S.sub.t-1]   k     [T.sub.B1]  [S.sub.m]

Austria             Jun-08     -4.511 **  11         Jan-08     -3.955
Belgium             Jun-08        -3.940  11         Apr-08     -3.762
Finland             Feb-08        -3.764   6         Sep-05     -3.000
France              Jul-08        -4.121  12         Apr-05     -3.276
Greece              Feb-09        -3.997  12         Jan-08     -3.601
Ireland             Aug-08      -5.637 *  11         Jan-09     -3.544
Italy               Jun-09     -4.553 **  11         Aug-05     -3.850
Luxembourg          Apr-06        -3.330   9         Oct-05     -3.655
Netherlands         Aug-08        -3.930  11         Jun-04     -3.573
Portugal            Dec-08      -5.910 *   4         May-04     -3.907
Spain               May-08        -3.898  11         Oct-09     -4.043

Country          Real interest
                     rate
                 differentials

              k     [T.sub.B1]  [S.sub.t-1]   k

Austria      12         Oct-06       -3.602  12
Belgium      12         Apr-08       -3.553  12
Finland      12         Sep-05       -2.985  12
France       12         Mar-05       -3.476  12
Greece       11         Jun-09       -2.744   6
Ireland      11         Oct-08       -3.931  11
Italy        12         Sep-04       -3.606  12
Luxembourg   12         Apr-06       -3.389  12
Netherlands  12         Mar-04       -3.569  12
Portugal     12         Dec-05       -3.068  12
Spain        12         Oct-08       -3.715  12

Critical values for the LM one-break unit-root test statistic in Model C
depend somewhat on the location of the break. The 1%, 5%, and 10%
critical values for different values of [T.sub.B]j/Tcome from Table 1 in
Lee and Strazicich (2004). The symbols *, **, and f mean significantly
different from zero at the 1-. 5-. and 10-percent levels, respectively.


Conclusions

We investigate whether the time series of the inflation rate, the nominal interest rate, and the real interest rate differentials (with respect to Germany taken as the benchmark to represent core EU standards) in the original Euro Area countries converge stochastically. The methodological framework builds on the literature on growth convergence and brings together several econometric techniques to address the unit-root properties of these variables. In particular, we employ three modeling paradigms. The first paradigm relies on the linear unit-root tests that do not permit structural breaks to exist in the deterministic component of the trend function. The second relies on unit-root tests that allow for nonlinear adjustment. The third relies on unit-root tests that endogenously determine structural breaks. The use of the structural break approach in this context is novel and provides results that generate new insights into the convergence process.

The study covers the period January 2001 to September 2010. This data set extends the sample used in previous empirical analyses and at the same time, highlights the effects of the current crisis. We find significant evidence of structural breaks using the two-break LM test of Lee and Strazicich (2003). If less than two breaks are significant, we use the one break unit-root tests of Perron and Rodriguez (2003) and Lee and Strazicich (2004). The findings of the univariate one- and two-break unit-root tests overturn the results of the linear and nonlinear tests that do not allow for structural breaks, whereas the results of the Im et al. (2005) panel unit-root test that allow for structural breaks overturn the findings of Levin et al. (2002) as well as Im et al. (2003) that do not allow for structural breaks.

Given that we find strong evidence of structural breaks in the inflation, nominal interest, and real interest rate differential series, we cannot place much confidence in our linear unit root tests without structural breaks. Focusing on the findings reported in Tables 3, 4, and 5, we draw the following conclusions at the 5-percent significance level. We find that for the real interest rate differential, only two countries exhibit convergence--France and the Netherlands. For the inflation rate differentials, three countries show convergence--Greece, Luxembourg, and the Netherlands. Finally nine countries display convergence for the nominal interest rate differentials. France and Luxembourg provide the exceptions. In sum, we discover little evidence of convergence for inflation rate and real interest rate differentials, but much evidence of convergence for nominal interest rate differentials.

What conclusions can we draw from our findings? The primary objective of the ECB has been to achieve and maintain price stability. Previous empirical evidence (e.g., Gali 2003; Rodriguez-Fuentes and Olivera-Herrera 2003; Angeloni and Dedola 1999; and Batini 2002, among others) show that this objective was fulfilled in the 1990s. The new empirical evidence presented in this paper reveals mixed support for the hypothesis that inflation and interest rate differentials have stochastically converged in the period January 2001 to September 2010. The implementation of a single monetary policy did not eliminate these differentials in all countries. This finding, however, does not break new ground, as researches find persistence of inflation differentials in both the Spanish regions and the US (Rodriguez-Fuentes et al. 2004).

Our findings, however, highlight the immediacy of the current debate in the Euro Area between Euro-supporters and Euro-skeptics as Greece, Ireland, Portugal, and Spain face mounting sovereign debt problems. Although the European Central Bank implements monetary policy, individual countries remain sovereign over fiscal policy. And therein lies the problem. Unlike most states in the U.S., individual countries in the Euro Area can run fiscal deficits to stimulate their local economies. As a result, the policies of the Southern tier countries (Greece, Ireland, Italy, Portugal, and Spain) caused them to become less competitive with the Northern tier countries (Germany, France, the Netherlands, and Belgium) over time. Tied to a common currency, the Southern tier countries cannot devalue their currencies to regain their competitive position. Thus, either fiscal austerity and lower prices in the Southern tier or fiscal expansion and higher prices in the Northern tier provide the basic options to rebalance the competitive positions of the Southern tier countries. Of course, the Northern tier countries do not want to inflate their economies, leaving it to the Southern tier countries to contemplate austerity and recession. The Euro-skeptics see the potential breakup of the Euro Area and a withdrawal of the weaker Southern tier countries from the Euro.

Do these findings imply that the ECB failed to achieve its goal? Do they imply that restrictive monetary policy cannot alone support convergence and that convergence also requires fiscal restraint? Or do they imply that these differentials reflect diverging degrees of nominal rigidities observed across the countries of the Euro Area? Many factors may explain such rigidities, such as wage dynamics not linked to productivity developments, structural inefficiencies and market rigidities as well as misaligned fiscal policies. While the Northern tier countries possess broadly similar economic structures, the Southern tier present substantial structural differences. Obviously, the solution of these problems does not fall within the domain of monetary policy. Our findings that shocks permanently affect inflation and real interest rate differentials suggest that fiscal policy measures may prove significant. National fiscal policies can react to shocks in such a way as to counteract the emergence of differentials. From this perspective, a sound control of public spending may prove an essential element of economic stability. Substantial research on these issues is needed.

(1.) Following Schuknecht et al. (2010), we distinguish between two phases of the current crisis, a period of market turmoil starting in August 2007 and lasting until August 2008, and the period of the acute crisis starting with the collapse of Lehman Brothers in September 2008.

(2.) Empirical evidence on the persistence of inflation differentials appears in Cecchetti et al. (2002) for US cities, Rogers (2001), Berk and Swank (2002), and Ortega (2003) for European countries, Alberola and Marques (1999) and Eijffinger and De Haan (2000) for Spanish provinces. Gregoriou et al. (2007) examine the time-series properties of inflation differentials in 12 EMU countries. A number of papers apply various unit-root and cointegration tests to analyze the persistence of inflation differentials in the Euro Area. Siklos and Wohar (1997) find evidence of convergence for the time period 1974 to 1995. Kocenda and Papell (1997) and Weber and Beck (2005) also report evidence of inflation convergence during the pre-euro period using panel unit-root tests. Busetti et a). (2006) discover convergence during the pre-euro period, but divergence following the introduction of the euro. Rodriguez-Fuentes and Olivera-Herrera (2003), contrary to previous studies, identify persistence in inflation differentials in the pre-euro period in eight out of 11 EMU countries. Lopez and Papell (2010), using a new panel-data procedure, uncover strong evidence of convergence among the inflation rates soon after the implementation of the Maastricht treaty and a dramatic decrease in the persistence of the differential after the occurrence of the single currency.

(3.) A recent ECB (2003) study acknowledges that the monetary policy of the ECB must incorporate the size and persistence of differences in inflation rates, and specifically mentions the possibility that high inflation in some regions could push inflation rates towards deflationary levels elsewhere, which in the presence of downward nominal rigidity may adversely affect economic and eventually even political outcomes.

(4.) Several studies provided empirical evidence about nominal interest rate convergence. Karfakis and Moschos (1990), Katsimbris and Miller (1993), and Kirchgassner and Wolters (1995), using a bivariate cointegration approach, find no evidence of interest rate convergence within the European Monetary System (EMS). Katsimbris and Miller (1993) do report evidence of cointegration between the nominal interest rates of some EMS countries and the US. Conversely, Hafer and Kutan (1994), as well as Haug et al. (2000), using a multivariate cointegration approach, find evidence of partial convergence.

(5.) In one ECB (2004) study, Italy, France, and Germany issue 70% of the sovereign debt outstanding in the Euro Area, while Spain, Belgium, and the Netherlands issue another 20%, and Austria, Finland, Portugal, Greece, Luxemburg, and Ireland issue the remaining 10%.

(6.) Jenkins and Madzharova (2008), using cointegration techniques, find no evidence of real interest rate convergence, using a sample of 15 EU countries during the period 1999 to 2004. Fountas and Wu (1999) using cointegration tests that allow for an endogenously determined regime shift, however, find strong evidence in favor of bilateral real interest rate convergence between several countries in the EU and Germany over 1979 to 1993. Wu and Fountas (2000) also provide strong evidence in favor of bilateral real interest rate convergence between the US and Germany and France. Arghyrou et al. (2009), using time series techniques that allow for endogenously determined structural breaks, report evidence of convergence of real interest rates towards the EMU average.

(7.) The ECB and numerous papers analyze convergence in the EMU before or after the onset of the euro (e.g., Fountas and Wu 1999; Camarero et al. 2002; Duarte 2003). According to ECB (2004), we use Germany as the benchmark. Germany's large share in the long-term Euro Area government bond market as well as its achievement of the lowest harmonized long-term German government bond yield at the start of EMU justifies its use as the benchmark.

(8.) Existing endogenous structural-break tests can identify at most two breaks.

(9.) A longer version of this paper provides descriptive statistics, charts, and discussion of our sample data. See http://ideas.repec.Org/p/nlv/wpaper/l 004.html

(10.) The yield equals the monthly average of the secondary market daily yields of government bonds with maturities of close to 10 years. Since Luxembourg does not issue long-term debt securities with a residual maturity of close to 10 years, we use a basket of long-term bonds, which exhibits an average residual maturity of close to 10 years. Since a private credit institution issues the bonds, this indicator is, thus, not fully harmonized.

(11.) The seminal work of Perron (i9891989) demonstrates that the unit-root and structural-break issues are intertwined. Perron shows how the presence of a structural break at a known break date biases standard unit-root tests toward non rejection of the null hypothesis of a unit root. Researchers now call this the Perron phenomenon.

(12.) Sen (2003) provides Monte Carlo evidence that Model C yields more reliable estimates of the brrak dares than Model A, when the break data are treated as unknown.

(13.) Remember that the LLC alternative hypothesis is that all panel units exhibit stationary series whereas the IPS alternative hypothesis only requires that one unit exhibit stationary series. See the discussions in the previous section.

(14.) No a priori reason exists to expect the break dates estimated using the Lee-Strazicich and Perron-Rodriguez procedures to coincide.

(15.) Table 3 reports that the inflation rate differential in France rejects the unit toot hypothesis at the 5-percent level whereas this differential for both Portugal and Spain reject the unit-root hypothesis at the 10-percent level.

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G. Canarella * S. M. Miller University of Nevada, Las Vegas, Las Vegas, NV 89154-6005, USA e-mail: stephen.miller@unlv.edu

G. Canarella e-mail: gcanare@calstatela.edu e-mail: giorgio.canarella@unlv.edu

S. K. Pollard e-mail: spollar2@calstatela.edu

G. Canarella * S. K. Pollard California State University, Los Angeles, Los Angeles, CA 90032, USA

Published online: 11 June 2011 [C] International Atlantic Economic Society 2011

DOI 10.1007/s11294-011-9308-1
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Author:Canarella, Giorgio; Miller, Stephen M.; Pollard, Stephen K.
Publication:International Advances in Economic Research
Date:Aug 1, 2011
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