ESTUDIOS SOBRE LA ECONOMIA ESPAÑOLA

Juncal Cuñado

Fernando Pérez de Gracia

EEE 70

September, 2000

http://www.fedea.es/hojas/publicado.html

Juncal Cuñado Fernando Pérez de Gracia

Version: September, 2000

ABSTRACT

This paper estimates the sacrifice ratio for the EMU countries for the period 1960-1998. It also considers whether there is enough cross-country similarity in the relationship between inflation and unemployment to assume that a common sacrifice ratio exists for these countries, since this would help in the implementation of the unique monetary policy. It further analyses the stability of this ratio for the whole period, which encompasses years of both high and low inflation rates, as those observed after the European integration. This stability analysis is related to a new research line on the non-linearity of the Phillips curve.

Keywords: Phillips curve, sacrifice ratio, unemployment rate, inflation rate.

JEL: E31, E52, F15.

Address: Juncal Cuñado, Department of Quantitative Methods, University of Navarra, Campus Universitario, 31080 Pamplona, jcunado@unav.es

1 INTRODUCTION

Although the Phillips curve is a standard subject in macroeconomics textbooks (see, for example, Abel and Bernanke, 1998; Dornbusch, Fisher and Startz, 1998; and Mankiw, 1999; Blanchard, 2000), it is difficult to find a consensus view about the relationship between unemployment and inflation among economists. It played a prominent role in empirical macroeconomics and it was widely regarded as stable, reliable and accurate in the fifties and sixties. However, at the end of the seventies, it was attacked by Friedman (1968) and Phelps (1968) for its prediction of a long-run trade-off between inflation and unemployment.¹ Both the supply shocks (specially, unexpected increases in oil prices) and the change in the way agents form expectations are considered to be the main causes of the empirical failure of the Phillips curve in the seventies. In the last years, the macroeconomics analysis has witnessed a revival of the interest on this curve (Sargent, 1999; Haldane and Quah,1999; Galí and Gertler, 1999; Cooley and Quadrini, 1999; Gruen, Pagan and Thompson, 1999; Ireland, 1999; and DiNardo and Moore, 1999; Galí, 2000, among others).² The estimation of the sacrifice ratios, commonly defined as the unemployment cost (or benefit) associated with a one percentage point reduction (increase) in inflation, carried out in this paper are thus based on the Phillips curve.

The relevance of estimating the sacrifice ratios is evident for its implications for the conduct of the monetary policy. For instance, and in the context of the European Monetary Union (EMU), the estimates of these indicators allow us to calculate the different efforts in real terms that each of the countries has overcome in order to gain nominal convergence. Furthermore, the differences in this indicator among the EMU countries will reveal us the difficulties of implementing a common monetary policy. Additionally, the significant progress made in reducing inflation rates in the last years has led to new concerns about the effectiveness of the monetary policy in an environment of price stability, since more credible monetary policies may have reinforced inflation inertia, increasing, therefore the sacrifice ratios (Anderson and Washer, 1999; Jordan, 1999). There is empirical evidence that suggests that the Phillips curve has suffered an structural break in the eighties, at least in some countries, as it is also the case for the United Kingdom (Haldane and Quah, 1999). These authors explain this change due to the greater credibility of the monetary authorities. In this context, the analysis of the potential changes of the sacrifice ratios over time, leading to nonlinearities in the Phillips curve, may shed some light on this issue.

We wish to thank participants at seminars at the Foundation of Applied Economic Studies (April, 2000), the University of Navarra (June, 2000), III Meeting of Spanish Applied Economics (June, 2000) and the Annual Conference of the Money, Macro and Finance Study Group (September, 2000) for their helpful comments.

¹ The empirical failure of the original Phillips curve is also documented in Lucas (1973) and Sargent and Wallace (1974).

² See the special issue on The return of the Phillips curve in the Journal of Monetary Economics, 1999.

The purpose of this paper is to estimate the sacrifice ratio for each of the EMU countries for the period 1960-1998. It also considers whether there is enough crosscountry similarity in the relationship between inflation and unemployment to assume that a common sacrifice ratio exists for all EMU countries. It further analyses the stability of this ratio for the whole period, which encompasses years of both high and low inflation rates, as those we have observed after the European integration. The main contribution of this paper is to compare the sacrifice ratio among the EMU countries over a long period, which will allow us to analyse the differences both across countries and over time.

The plan of the paper is the following. Section 2 reviews the literature concerning the estimation of the sacrifice ratio and the model. In Section 3, the empirical analysis is carried out in three steps. First, an estimation of this ratio is pursued for each of the EMU countries based on a Phillips curve. Then, and by means of specifying a simultaneous system of equations, we test whether or not each of these countries face a common sacrifice ratio. Thirdly, a stability analysis is provided estimating different threshold models. Section 4 concludes.

See Debelle and Laxton (1996) for a detailed analysis. In the non-linearity case, the deviation of unemployment rate from the natural rate of unemployment will depend on the success or failure of past economic policies.

2 SOME PRELIMINARY CONSIDERATIONS ON THE SACRIFICE RATIO

This Section reviews the literature concerning the sacrifice ratio, and then we present the theoretical framework on the Phillips curve, since the empirical analysis we carry out in the next Section is based on this curve.

2.1 Sacrifice Ratios: a Review

It is generally believed that attempts of a monetary authority to lower the inflation rate will lead to a period of increased unemployment and reduced output. These disinflationary episodes have a real impact on the economy, since the inflation behaves in an inertial or persistent manner.

The variety of techniques used in the literature to estimate sacrifice ratios may be classified in three groups.

The first methodology, followed by Gordon (1982), Kiley (1997), Filardo (1998), Hutchison and Walsh (1998) and Andersen and Washer (1999), among others, estimate the sacrifice ratio based on the Phillips curve. In this case, the sacrifice ratio is measured as the inverse of the slope of the Phillips curve.

Alternatively, the sacrifice ratio may be estimated using structural equations on wage and price determinants. This approach is used by King and Watson (1994), Ceccheti (1994), Andersen and Washer (1999) and Ceccheti and Rich (1999), and the obtained estimator depends on the restrictions imposed on the structural model.

Thirdly, an appropiate methodology used to calculate the sacrifice ratio is based on the analysis of disinflationary episodes. Mankiw (1999) considers the US-disinflation in the early 1980s. This decade began with tight monetary policies pursued by Paul Volcker. His estimation of the sacrifice ratio from the Volcker disinflation is 2.8 percentage points. Ball (1994) examines disinflation from 1960 to 1991 in moderateinflation countries of the OECD. He develops a method for estimating the sacrifice ratio for each episode. In this case, the sacrifice ratio is defined as the ratio of the total output losses to the change in trend inflation. He obtains estimates that vary from 1.8 to 3.3 percentage points. However, this approach presents some drawbacks as those mentioned by Ceccehetti, 1994 and Cecchetti and Rich, 1999): first, it does not take into account the correlation between unemployment and inflation rates in different phases of the economic cycle; second, it associates disinflationary episodes with those of a restrictive monetary policy; furthermore, the rigidity in prices and wages is not considered in the estimation.

2.2 Theoretical Framework

In this Section, we present the theoretical framework on the Phillips curve. As we noted before, the estimation of the sacrifice ratios carried out in this paper is based on this curve.

The linear expectations-augmented short-run Phillips curve is assumed to have a constant slope 4

\[\pi_ {t} = \pi_ {t} ^ {\mathrm{e}} + \gamma (u _ {t} - u ^ {*}) + \varepsilon_ {t}\tag{1}\]

where is the inflation rate at t, is the expected inflation at is the unemployment rate at is the natural rate of unemployment, and is the error term.

There are two main difficulties when estimating this model empirically. They are due to measurement problems regarding inflation expectations and the natural rate of unemployment. Neither of these variables is directly observable and has to be approximated. In some studies inflation expectations are modelled as a simple weighted average of the past inflation rates. Following Galí and Gertler (1999), this can be viewed as a mixture between the traditional and the new Phillips curve:

\[\pi_ {\mathrm{t}} ^ {\mathrm{e}} = \lambda_ {1} \pi_ {\mathrm{t}} ^ {\mathrm{f}} + \lambda_ {2} \pi_ {\mathrm{t}} ^ {\mathrm{i}} + (1 - \lambda_ {1} - \lambda_ {2}) \mathrm{A(L)} \pi_ {\mathrm{t-i}}\tag{2}\]

where is the forward looking component and A(L) is a lag polynomial. The backward-looking component reflects the inertia in the inflation process and forwardlooking components indicate agents’ expectations. Equation (2) is extended to include inflation in imported goods, , which may be an influential component in open economies.

As far as the assumption about the natural rate of unemployment, some models presume that is constant, so that equation (1) can be rewritten as:

\[\pi_ {t} = \alpha + \pi_ {t} ^ {\mathrm{e}} + \gamma u _ {t} + \varepsilon_ {t}\tag{3}\]

where . However, there is some empirical evidence suggesting that the natural rate of unemployment is not stable over time (see for example Apel and Jansson, 1997;

Laxton et al., 1998; Gruen et al., 1999). Hence, the characteristics of the natural rate of unemployment will be an important point in the estimation of the Phillips curve for the EMU countries.

Following Gordon (1997), the specification of the Phillips curve incorporate supply shocks and no long run trade-off as the “triangle” model of inflation whereby inflation depends on three basic determinants: inertia, demand and supply. The specification of the model is:

\[\pi = a (L) \pi_ {- 1} + b (L) D + c (L) z + e\tag{4}\]

where the dependent variable is the inflation rate, inertia is captured by the lags of inflation, D is a measure of excess demand, z is a vector of supply shocks variables, a(.), b(.) and c(.) are polynomials in the lag operator L, subscripts denote lags and e is the error term. The restriction that the sum of the coefficients on lagged inflation values equals unity is imposed to ensure there is no long run trade off between inflation and excess demand.

3 EMPIRICAL ANALYSIS

This Section estimates the sacrifice ratio of the EMU countries for the period 1960- 1998. We use annual data⁵, measured in percentage terms, from the Data Basis EUROSTAT. The variables are: inflation rates, unemployment rates and the imported inflation rates.⁶

It may prove useful, at this stage, to have a look at the evolution of the variables we employ in this paper, by means of a graphic analysis and reporting their basic statistics. Secondly, an univariate analysis of the variables is carried out, followed by cointegration and Granger type causality tests. This analysis shall help us to specify the model to estimate the sacrifice ratios. Later on, we shall test if the EMU countries face the same sacrifice ratio. Finally, we shall test the stability of this ratio for the whole period.

⁴ See King and Watson (1994) for a review of the economic and econometric literature on the Phillips curve.

⁵ The reason of using annual data is that quarterly data on unemployment rates are not available for all the analysed countries.

⁶ Gruen et al. (1999) and Turner and Seghezza (1999), among others, employ the imported inflation rates as a proxy variable of supply shocks. For these authors, the imported inflation rate is the main supply shock.

3.1 A First Look at the Data

Table 1 displays the basic statistics of the inflation, unemployment and imported inflation rates. Figure 1 complements these data by illustrating the pattern over time of the first two variables for each of the EMU countries during the period 1960-1998. As we can see, EMU is characterised by a diverse evolution of the inflation and unemployment data. Both variables take low values at the beginning of the sample period until the first oil price shock. Then, all countries experience a period of rising inflation and unemployment rates until mid-eighties. From this period, the unemployment rate carries on rising while since the ‘90s the inflation rates decline in all EMU countries, except in Holland⁷.

Furthermore, we also detect significant differences across countries. For instance, the average inflation rate takes values from 3.38% in the German case to 11.13% in Portugal, that is, three times higher. These differences are even more pronounced for the unemployment rate, with a range of values from 1.43% in Luxembourg to 11.39% in the Spanish case.

(Insert Table 1)

(Insert Figure 1)

3.1 An Estimation of the Sacrifice Ratios

We test for non stationarity, by means of applying the Phillips-Perron test (see Table 2). As both inflation and unemployment rates exhibit a unit root, we tested for cointegration using the Phillips Ouliaris (1990) test based on the analysis of the stationarity of the residuals of the long-run relationship between the two variables. The results shown in Table 3 suggest that the series do not cointegrate, suggesting that there is no evidence that a long-run Phillips curve trade-off exists. From now on, we shall be interested in the short-run trade-off between these two variables.

(Insert Tables 2 and 3)

Based on the previous results, and in order to justify the use of a Phillips curve for the estimation of the sacrifice ratios, we apply Granger-type causality tests in order to detect the causality direction between inflation and unemployment rates. That is, we can define the next bivariate VAR model, in which the variables are differentiated and we do not include an error correction term since they do not cointegrate:

⁷ This could be associated with the coordinated actions that took place in Holland at that time.

\[\left[ \begin{array}{c} \Delta \pi_ {t} \\ (u _ {t} - u _ {t} ^ {*}) \end{array} \right] = \left[ \begin{array}{c c} \delta_ {1} & \gamma_ {1} \\ \theta_ {2 1, 1} & \theta_ {2 2, 1} \end{array} \right] \left[ \begin{array}{c} \Delta \pi_ {t - 1} \\ (u _ {t - 1} - u _ {t - 1} ^ {*}) \end{array} \right] +... + \left[ \begin{array}{c c} \delta_ {p} & \gamma_ {p} \\ \theta_ {2 1, p} & \theta_ {2 2, p} \end{array} \right] \left[ \begin{array}{c} \Delta \pi_ {t - p} \\ (u _ {t - p} - u _ {t - p} ^ {*}) \end{array} \right] + \left[ \begin{array}{c} v _ {1 t} \\ v _ {2 t} \end{array} \right]\tag{5}\]

Following Cecchetti (1994), the first equation may be associated with a Phillips curve, while the second one describes a supply curve. Based on this model, we shall say that the unemployment rate do not cause the inflation rate if the next condition is satisfied:

\[\gamma_ {1} = \gamma_ {2} = \dots = \gamma_ {p} = 0\tag{6}\]

Similarly, the inflation rate do not cause the unemployment rate, if:

\[\theta_ {2 1, 1} = \theta_ {2 2, 2} = \dots = \theta_ {2 2, p} = 0\tag{7}\]

Based on the Granger type causality tests carried out in this Section (see Tables 4 and 5) we cannot reject that the coefficient that measures the impact of past inflation on the unemployment gap is equal to zero for any of the countries. On the other hand, the impact of past unemployment fluctuations on inflation is significantly different from zero in most countries, which suggests that the direction of the inflation-unemployment relationship is in favour of unemployment fluctuations being an indicator of demand tensions. In any case, we also find evidence that inflation depends on imported inflation rates.

\[(\text { Insert Tables 4 and 5 })\]

Thus, following Gordon (1997), the equation has been estimated for each of the EMU countries:

\[\Delta \pi_ {t} = \sum_ {j = 1} ^ {p} \delta_ {j} \pi_ {t - j} + \sum_ {j = 0} ^ {q} \gamma_ {j} (u _ {t - j} - u _ {t - j} ^ {*}) + \lambda s _ {t} + \varepsilon_ {t}\tag{8}\]

in which as a proxy variable of the supply shocks , the imported inflation rate is used, the estimation of the natural rate of unemployment is carried out by means of applying the Hodrick-Prescott and Kalman⁹ filters. The coefficients measure the inflation inertia and the tightness in the labour market. From (8), we can define the sacrifice ratio as:

In this case, the natural rate of unemployment, u*, is obtained solving the following minimization u*, problem:

\[S R = \frac {1 - \sum_ {j = 1} ^ {p} \delta_ {j}}{\sum_ {j = 0} ^ {q} \gamma_ {j}}\tag{9}\]

(Insert Tables 6 and 7) ¹⁰

The results suggest that the relationship between these variables is not significant for the cases of France, Italy and Luxembourg, which may imply that the Phillips curve is in these cases horizontal.¹¹ For the rest of the countries, the values of the sacrifice ratios vary from 0.48% in the case of Portugal to 2.02% in the case of Finland.¹²

3.3 Asymmetries across EMU countries

This Section analyses if the EMU countries face a common sacrifice ratio. Following Turner and Seghezza (1999), we shall test if the sacrifice ratios defined by (9) are equal for all EMU countries. More precisely, we estimate the following simultaneous equation system:

T T Min ∑ (u_t-u_t*)2 + λ ∑ ((u_t+1* - u_t*) - (u_t* - u_t-1*))2 t 1= t 2=

⁹ See Gruen et al. (1999), Laxton et al. (1998) and Apel and Jansson (1997) for an estimation of the natural rate of unemployment using the Kalman filter. In our case, the sacrifice ratio is tested estimating the following equations:

_{t t}^e _{t t}u u− = − +*

_{t t}u u= + ₋* * ₁

That is, allowing the constant term in the first equation (a simple version of the Phillips curve) to be time varying or, more particularly, a random walk, we allow u* to be time varying. For a detailed analysis of u* this methodology, see Harvey (1981).

¹⁰ The estimation carried out using the Hodrick-Prescott filter fits the data better, so that from now on, we shall display the results obtained using this filter. However, those obtained using the Kalman filter to estimate the natural rate of unemployment are very similar.

¹¹ This result is similar to that obtained for most of the EMU countries in low inflation periods (see Section 3.4) and to that obtained by Haldane and Quah (1999) for the UK case from the eighties.

¹² These results are similar to those found in the literature for other countries (see for example, Ball 1994).

\[\Delta \pi_ {t, 1} = \sum_ {j = 1} ^ {p} \delta_ {j, 1} \Delta \pi_ {t - j, 1} + \sum_ {j = 0} ^ {p} \gamma_ {j, 1} (u _ {t - j, 1} - u _ {t - j, 1} ^ {*}) + \lambda s _ {t, 1} + \varepsilon_ {t, 1}\]

\[\Delta \pi_ {t, 2} = \sum_ {j = 1} ^ {p} \delta_ {j, 2} \Delta \pi_ {t - j, 2} + \sum_ {j = 0} ^ {p} \gamma_ {j, 2} (u _ {t - j, 2} - u _ {t - j, 2} ^ {*}) + \lambda s _ {t, 2} + \varepsilon_ {t, 2}\tag{10}\]

\[\Delta \pi_ {t, n} = \sum_ {j = 1} ^ {p} \delta_ {j, n} \Delta \pi_ {t - j, n} + \sum_ {j = 0} ^ {p} \gamma_ {j, n} (u _ {t - j, n} - u _ {t - j, n} ^ {*}) + \lambda s _ {t, n} + \varepsilon_ {t, n}\]

In order to test this hypothesis, we shall obtain SURE (Seemingly unrelated regression) estimates of the previous system, since we need the variance and covariance matrix of the coefficients to test the hypothesis that these coefficients are equal for every country. That is, we shall obtain the following estimation vector:

\[\hat {\beta} _ {S U R E} = \left[ Z ^ {\prime} (\hat {\Sigma} ^ {- 1} \otimes I _ {N}) Z \right] ^ {- 1} \left[ Z ^ {\prime} (\hat {\Sigma} ^ {- 1} \otimes I _ {N}) y \right]\tag{11}\]

in which Z is the matrix of explanatory variables in the model (unemployment and imported inflation rates, in this case) and is the variance and covariance matrix of the errors of the different equations. The results displayed in Table 8 suggest that there is evidence enough to reject the null hypothesis that all EMU countries face the same sacrifice ratio.

If we assume that this ratio is the same for all countries, the restricted estimation of this indicator takes the value of 1.89, that is, each 1 percentage point decline in the inflation rate is followed by a 1.89 percentage point increase in the unemployment rate.

(Insert Table 8)

Based on the previous result, the group of EMU countries is divided into two subgroups on the basis of their average unemployment rate¹³. If their average unemployment rate lies below the median average-unemployment rate across countries, the country is placed in the ‘low-average-unemployment’ group. If it is above the median, it is placed in the ‘high-average-unemployment’ group. Based on this criteria, the second group contents the following countries: Belgium, Spain, France, Ireland, Italy, Finland. When we estimate the previous Simultaneous Equation System (SES) imposing the restrictions that each country within the same group faces the same sacrifice ratio, we cannot reject this hypothesis, and obtain the following values for the ratios: 1.11% for low-average unemployment group, and 3.57% for high-averageunemployment group.

13 We use average unemployment rates as a measure of the rigidities of the labour markets, which according to the literature (Andersen and Wascher, 1999) is one of the main factors explaining the differences in sacrifice ratios.

3.4 Stability of the Sacrifice Ratios over time

This Section studies the stability of the sacrifice ratio over the analysed period, which encompasses years of both high and low inflation rates, as those we have observed after the European integration. This stability analysis is related to a new research line on the non-linearity of the Phillips curve. The implications concerning economic policy decisions are relevant since in the context of non-linearities, the deviations of the unemployment rate from the natural rate of unemployment (cyclical unemployment) will depend on the success of previous stabilisation policies (Debelle and Laxton, 1996).

The methodological approach we employ in this Section is based on the Threshold models.¹⁴ The simplest model is the assumption that the relationship between our variables may be characterised by the following equations:

\[\begin{array}{l} \Delta \pi_ {t 1} = \sum_ {j = 1} ^ {p} \delta_ {j 1} \Delta \pi_ {t - j} + \sum_ {j = 0} ^ {q} \gamma_ {j 1} (u _ {t - j} - u _ {t - j} ^ {*}) + \lambda_ {1} s _ {t} + \varepsilon_ {t 1} \quad x \leq h \\ \Delta \pi_ {t 2} = \sum_ {j = 1} ^ {p} \delta_ {j 2} \Delta \pi_ {t - j} + \sum_ {j = 0} ^ {q} \gamma_ {j 2} (u _ {t - j} - u _ {t - j} ^ {*}) + \lambda_ {2} s _ {t} + \varepsilon_ {t 2} \quad x > h \end{array}\tag{12}\]

in which x is the threshold variable, so that the relationship between the two variables changes when it reaches the value of h, and and are the coefficients for each of the two regimes¹⁵. The estimation of the previous model has been carried out in two steps, since the threshold variable is assumed to be both time and inflation rate. The choice of δ for each of the countries in the sample has been carried out by means of the stability Chow tests calculating in a recursive way and choosing that value for which the previous statistic takes the greater value. The main results are displayed in Tables 9 and 10, and suggest the following:

\[(\text {Insert Tables 9 and 10})\]

¹⁴ See Hansen (1996) for a detailed analysis.

15 Note that taken ∆π as the threshold variable and h equal to zero, we could test the null hypothesis that the sacrifice ratio is equal to the benefit ratio leading to asymmetries in the Phillips curve. However, the results indicate that we cannot reject this hypothesis

First, we obtain that the sacrifice ratios have experienced, in general, a significant increase in the seventies and eighties, being in these moments higher than before in the cases of Belgium, Germany, Spain, Luxembourg and Holland. Second, and according to the results displayed in Table 10, we obtain that the sacrifice ratios are lower in periods of high inflation rates (as in the cases of Belgium, Germany, France, Holland, Portugal and Finland), a result which is consistent to those presented in Table 9. On the contrary, in periods of low inflation rates, the relationship between the inflation and unemployment rates is no longer significant in many cases. Haldane and Quah (1999) interpret this results, noticing that the monetary policy decisions are more credible in the present, which might explain why the Phillips curve may present an horizontal shape.

4 CONCLUDING REMARKS

In this paper we estimated the sacrifice ratio for the EMU countries in the period 1960- 1998, based on a Phillips curve in which different assumptions on the natural rate of unemployment are employed. The main contribution of the paper is to analyze the temporal evolution of this indicator and its stability over the whole period in order to asses if its value and its differences among the analysed countries have changed in the last decades, which are characterised by lower inflation rates. The main results may be summarised as follows.

First, and as documented in other papers, the relationship between inflation and unemployment is limited to low frequency data; that is, we observed a significant relationship when the variables are defined in differences and not in levels. That suggests that there is no evidence of long-run, but short run trade-off between these variables.

The values of the estimated sacrifice ratios of the EMU countries range from 0.48% in the case of Portugal to 2.02% in the case of Finland, a credible range of values according to previous results obtained in the literature for other countries (Ball, 1994).

Based on the estimation of a simultaneous system of equations, the hypothesis that all the EMU countries face a common sacrifice ratio is tested, and we find evidence enough to reject that this indicator takes the same value for all the countries. This result may complicate the unique monetary policy decisions.

As the sacrifice ratio is commonly related to the rigidities in the labour markets, the group of EMU countries is divided into two subgroups on the basis of their average unemployment rate, obtaining that the sacrifice ratio takes the value of 1.1 for low average unemployment group (Germany, Luxembourg, Holland, Austria and Portugal) and 3.57 for the high average unemployment group (Belgium, Spain, France, Ireland, Italy and Finland). That is, a 1% fall in inflation rates will be followed by a 1.1% increase in the unemployment rate in the first group of countries, whereas this rate will increase in a 3.57% in the other group.

Finally, we analyse the stability of the sacrifice ratio over the period, and the results suggest that this ratio takes higher values in periods of low inflation rates, as those we observe nowadays. In fact, in many cases, the estimation of a Phillips curve in periods of low inflation rates yields non significant coefficients, which may be associated with more horizontal Phillips curves at low inflation rates, suggesting a possible non-linearity in this curve. The specification and estimation of a non-linear functional form of the Phillips curve constitutes one of the objectives of future research.

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Turner, D. and E. Seghezza (1999): “Testing for a common OECD Phillips Curve”, OECD Working Paper 9911.
Yates, A. and B. Chapple (1996): “What determines the short-run output-inflation tradeoff?” Bank of England working paper, No. 53.

TABLE 1 BASIC STATISTICS

	Inflation rate		Unemployment rate		Imported inflation rate
	Mean	Std. Deviat.	Mean	Std. Deviat.	Mean	Std. Deviat.
Belgium	4.42	2.81	6.12	3.53	3.75	6.26
Germany	3.38	1.75	4.06	3.10	2.22	5.75
Spain	8.94	5.33	11.39	8.27	7.27	10.73
France	5.79	3.84	6.41	3.99	5.12	9.45
Ireland	7.45	5.83	10.03	4.22	6.36	9.26
Italy	8.50	5.85	7.50	2.51	7.65	11.64
Luxembourg	4.23	2.80	1.43	1.41	4.04	4.86
Holland	4.17	2.73	4.87	3.15	2.61	7.19
Austria	4.06	2.01	2.63	1.06	2.74	3.68
Portugal	11.13	8.65	5.08	2.35	9.85	12.44
Finland	6.52	4.37	5.87	4.81	6.17	8.18

Own elaboration from EUROSTAT.

HOLLAND FIGURE 1. UNEMPLOYMENT AND INFLATION RATES (1960-1998) BELGIUM SPAIN

GERMANY

IRELAND

FRANCE

ITALY

AUSTRIA

Own elaboration from EUROSTAT. The continuous and discontinuous lines show the evolution of the unemployment and inflation rates, respectively.

TABLE 2 UNIT ROOT TESTS

	Inflation rate	Unemployment rate	Imported inflation rate
Belgium	-1.19 (a)	-0.45 (a)	-3.50*(b)
Germany	-1.17 (a)	-0.19 (a)	-4.25*(b)
Spain	-0.74 (a)	-0.13 (a)	-3.74*(b)
France	-0.86 (a)	-0.24 (a)	-4.43*(b)
Ireland	-0.92 (a)	-0.53 (a)	-3.10*(b)
Italy	-0.78 (a)	2.11 (a)	-3.41*(b)
Luxembourg	-1.00 (a)	1.00 (a)	-3.15*(b)
Holland	-0.95 (a)	-0.24 (a)	-4.29*(b)
Austria	-1.10 (a)	0.81 (a)	-4.15*(b)
Portugal	-0.91 (a)	-0.44 (a)	-2.75*(b)
Finland	-1.05 (a)	-1.19 (a)	-4.14*(b)

Own elaboration. (a) indicates that the unit root test has been carried out based on a model without deterministic trend and constant. The critical value of this statistic at 10% is -1.64. (b) indicates that the unit root test has been carried out with a constant but without a determinist trend. The critical value of this statistic at 10% is -2.57. * means that the null hypothesis of unit root is rejected at a significativity level of 10%. The same unit root tests have been applied to the first differences of inflation and unemployment rates and in all cases we rejected the null hypothesis of unit root. Therefore, these two variables are I(1).

TABLE 3 COINTEGRATION TESTS

	Phillips-Ouliaris
Belgium	-2.25
Germany	-2.11
Spain	-1.76
France	-1.32
Ireland	-1.76
Italy	-1.65
Luxembourg	-1.88
Holland	-2.03
Austria	-1.49
Portugal	-0.71
Finland	-2.02

Own elaboration. The critical value of this statistic at 10% is -3.04, so that we do not reject the null hypothesis in any of the cases.

TABLE 4 GRANGER TYPE CAUSALITY TESTS

	Belgium	Germany	Spain	France	Ireland	Italy
$\Delta\pi_{t-1}$	0.05(1.15)	-0.10(-1.22)	0.002(0.05)	-0.01(-0.33)	-0.04(-1.03)	-0.03(-1.49)
$\Delta\pi_{t-2}$	-0.02(-0.60)	-0.06(-0.79)	-0.02(-0.31)		0.05(1.39)	0.02(1.01)
(u-u*)t-1	0.99(6.26)**	0.75(4.25)**	0.93(5.97)**	0.36(2.09)**	0.76(5.14)**	0.68(4.39)**
(u-u*)t-2	-0.68(-4.14)**	-0.70(-3.79)**	-0.59(-3.80)**		-0.55(-3.58)**	-0.49(-3.28)**
INT	-0.01(-0.13)**	-0.013(-0.21)	-0.01(-0.01)	-0.01(-0.13)	-0.01(-0.10)	0.004(0.07)
Adj. R2	0.52	0.51	0.50	0.08	0.48	0.44
	Luxembourg	Holland	Austria	Portugal	Finland
$\Delta\pi_{t-1}$	-0.02(-0.67)	0.003(0.04)	-0.03(-0.85)	0.03(1.70)	-0.04(-0.63)
$\Delta\pi_{t-2}$		0.05(0.61)	-0.01(-0.34)	0.01(0.66)
(u-u*)t-1	0.28(1.69)	0.50(2.98)**	0.25(1.45)	0.96(5.77)**	0.62(4.31)**
(u-u*)t-2		-0.43(-2.42)**	-0.46(-2.71)**	-0.54(-3.26)**
INT	0.4E-3(0.01)	0.001(0.10)	-0.004(-0.10)	-0.001(-0.02)	-0.03(-0.19)
Adj. R2	0.03	0.22	0.15	0.48	0.36

Own elaboration. When the Hodrick-Prescott filter is applied to estimate the expected inflation, the results are very similar. The t-statistics are shown in parenthesis. * and ** mean significant at 10 and 5%, respectively. INT stands for intercept.

TABLE 5 GRANGER TYPE CAUSALITY TESTS

	Belgium	Germany	Spain	France	Ireland	Italy
$(u-u^{*})_{t-1}$	-1.19(-2.37)**	-1.29(-2.76)**	-0.71(-2.35)**	-0.14(-0.18)	-1.51(-2.15)**	1.65(1.49)
$(u-u^{*})_{t-2}$		0.74(1.56)		-0.012(-0.02)	0.73(1.00)	-0.29(-0.27)
$\Delta \pi_{t-1}$	-0.25(-1.70)	0.09(0.45)	-0.19(-1.23)	-0.06(-0.45)	0.07(0.37)	-0.09(-0.57)
$\Delta \pi_{t-2}$	-0.22(-1.66)			-0.26(-1.81)*	-0.24(-1.40)	-0.16(-1.07)
INT	-0.80(-2.62)	-0.11(-0.63)	-0.44(-0.89)	-0.87(-2.84)**	-0.46(-0.77)	-1.41(-3.03)**
Adj. $R^2$	0.41	0.29	0.14	0.34	0.15	0.43
	Luxembourg	Holland	Austria	Portugal	Finland
$(u-u^{*})_{t-1}$	1.01(0.92)	-0.75(-1.94)*	-0.65(-1.79)*	-0.58(-1.75)*	-0.91(-2.40)**
$(u-u^{*})_{t-2}$	-0.38(-0.34)				0.71(1.89)*
$\Delta \pi_{t-1}$	0.09(0.53)	-0.26(-1.54)	-0.29(-1.97)*	-0.29(-2.02)**	-0.29(-0.87)
$\Delta \pi_{t-2}$	-0.15(-0.93)				-0.30(-2.13)**
INT	-0.77(-2.12)**	-0.12(-0.45)	-0.74(-3.01)**	-0.70(-2.83)**	-1.33(-2.75)**
Adj. $R^2$	0.20	0.10	0.33	0.34	0.28

Own elaboration. The t-statistics are shown in parenthesis. * and ** mean significant at 10 and 5%, respectively. INT stands for intercept.

TABLE 6 SACRIFICE RATIOS (HODRICK-PRESCOTT FILTER)

Dependent variable: Δπt
	Belgium	Germany	Spain	France	Ireland	Italy
(u-u*)t	-1.07(-2.36)**	-1.36(-5.03)**	-0.54(-1.79)*	-0.45(-0.65)	-1.15(-1.93)**	0.38(0.40)
St	0.16(3.84)**	0.03(1.20)	0.06(1.08)	0.11(3.92)**	0.07(1.46)	0.13(3.89)**
INT	-0.65(-2.15)**	-0.12(-0.81)	-0.44(-0.84)	-0.64(-2.18)**	-0.46(-0.81)	-1.02(-2.18)**
SR	0.93	0.74	1.85		0.87
LLF	-67.93	-43.88	-85.87	-67.30	-88.67	-82.56
	Luxembourg	Holland	Austria	Portugal	Finland
(u-u*)t	0.42(0.40)	-0.63(-1.73)*	-1.11(-1.74)*	-2.07(-2.00)**	-0.49(-2.70)**
St	0.17(3.09)**	0.03(0.91)	0.19(5.10)**	0.13(2.53)**	0.17(6.45)**
INT	-0.65(-1.92)**	-0.09(-0.35)	-0.58(-2.60)**	-1.28(-1.56)*	-1.08(-2.46)**
SR		1.58	0.91	0.48	2.02
LLF	-67.78	-66.45	-56.52	-100.62	-82.12

Own elaboration. The t-statistics are shown in parenthesis. SR stands for sacrifice ratio. The SR is not reported for the cases of Italy, France and Luxembourg, since the relationship obtained in this cases is not significant and the sign of the estimated γ coefficient is positive. LLF stands for the log of the likelihood function. * and ** means significant at 10 and 5%, respectively. INT stands for intercept.

TABLE 7 SACRIFICE RATIOS (KALMAN FILTER)

Dependent Variable: $\Delta\pi_t$
	Belgium	Germany	Spain	France	Ireland	Italy
$u_t$	-0.44(-1.54)	-0.59(-3.10)**	-0.28(-1.13)	-0.06(-0.17)	-0.46(-1.15)	0.45(0.70)
$S_t$	0.26(5.09)**	0.07(2.71)**	0.10(2.07)**	0.16(5.58)**	0.13(1.78)*	0.19(4.68)**
$\gamma u^*$	3.06(1.13)	5.35(2.83)**	4.93(0.93)	0.31(0.07)	5.11(1.24)	-6.35(-0.80)
SR	1.70
LLF	-74.70	-54.16	-94.51	-71.55	-96.93	-85.19
	Luxembourg	Holland	Austria	Portugal	Finland
$u_t$	-0.19(-1.02)	-0.37(-1.25)	-1.35(-2.50)**	-0.63(-2.00)**	-1.06(-3.70)**
$S_t$	0.16(3.05)**	0.048(1.08)	0.50(1.73)*	0.23(1.60)	0.59(1.81)*
$\gamma u^*$	-0.36(-0.81)	1.92(1.09)	1.49(0.36)	3.04(1.50)	2.85(1.04)
SR			0.74	1.59	0.94
LLF	-73.97	-76.09	-82.80	-79.04	-56.04

Own elaboration. The t-statistics are shown in parenthesis. SR stands for sacrifice ratio. The SR is not reported for the case of Italy, Belgium, Spain, France, Ireland, Luxembourg and Holland. since the relationship obtained in this cases is not significant and the sign of the estimated coefficient is positive. LLF stands for the log of the likelihood function. * and ** means significant at 10 and 5%, respectively.

TABLE 8 SURE ESTIMATIONS

Non restricted estimation
	Belgium	Germany	Spain	France	Ireland	Italy
$(u-u^{*})_{t}$	-0.44(-1.37)*	-1.10(-4.85)**	-0.43(-1.51)*	0.43(0.88)	-0.47(-0.94)	0.53(0.92)
$S_{t}$	0.16(4.54)**	0.02(1.01)	0.04(1.29)	0.11(4.65)**	0.10(2.24)**	0.11(4.53)**
SR	2.19	0.95	2.13	--	2.13	--
	Luxembourg	Holland	Austria	Portugal	Finland
$(u-u^{*})_{t}$	-0.99(-1.31)	-0.20(-0.63)	-0.80(-1.10)	-1.47(-1.85)*	-0.32(-1.32)
$S_{t}$	0.20(4.21)**	0.03(0.98)	0.18(3.57)**	0.15(3.41)**	0.15(3.74)**
SR	--	2.93	1.29	0.56	2.44
System $R^2$ : 0.88
Restricted estimation 1(common SR for each country)
	Belgium	Germany	Spain	France	Ireland	Italy
$(u-u^{*})_{t}$	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**
$S_{t}$	0.16(4.76)**	0.03(1.54)	0.04(1.38)	0.10(4.56)**	0.11(2.51)**	0.12(4.47)**
SR	1.89	1.89	1.89	1.89	1.89	1.89
	Luxembourg	Holland	Austria	Portugal	Finland
$(u-u^{*})_{t}$	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**	-0.53(-4.67)**
$S_{t}$	0.21(4.69)**	0.03(0.91)	0.18(3.86)**	0.17(3.79)**	0.15(3.67)**
SR	1.89	1.89	1.89	1.89	1.89
Equal SR test (Wald) 17.4**System $R^2$ : 0.80
Restricted estimation 2(different SR for each group of countries)
	Belgium	Germany	Spain	France	Ireland	Italy
$(u-u^{*})_{t}$	-0.28(-1.92)*	-0.90(-5.76)**	-0.28(-1.92)*	-0.28(-1.92)*	-0.28(-1.92)*	-0.28(-1.92)*
$S_{t}$	0.16(4.55)**	0.03(1.17)	0.05(1.42)	0.10(4.89)**	0.11(2.57)**	0.12(4.38)**
SR	3.57	1.11	3.57	3.57	3.57	3.57
	Luxembourg	Holland	Austria	Portugal	Finland
$(u-u^{*})_{t}$	-0.90(-5.76)**	-0.90(-5.76)**	-0.90(-5.76)**	-0.90(-5.76)**	-0.28(-1.92)*
$S_{t}$	0.21(4.54)**	0.02(0.56)	0.17(3.62)**	0.16(3.78)**	0.15(3.60)**
SR	1.11	1.11	1.11	1.11	3.57
System $R^2$ : 0.84Equal SR test for each group (Wald): 9.25**

Own elaboration. The t-statistics are shown in parenthesis. SR is the sacrifice ratio. * and ** mean significant at 10 and 5%, respectively.

TABLE 9 STABILITY TESTS AND TRESHOLD MODELS

	h=t	SRt ≤ h	SRt > h		h=t	SRt ≤ h	SRt > h
Belgium	1986	0.51(8.94)**	-20.00(0.01)	Luxembourg	1981	-0.28(9.76)**	0.32(5.34)**
Germany	1971	0.33(11.38)**	0.76(23.32)**	Holland	1969	0.85(0.11)	1.85(2.93)**
Spain	1977	0.38(3.95)**	4.17(0.65)	Austria	--	0.91(3.02)*	0.91(3.02)*
France	--	2.22(0.42)	2.22(0.42)	Portugal	--	0.48(4.01)**	0.48(4.01)**
Ireland	--	0.87(3.74)*	0.87(3.74)*	Finland	--	2.02(3.05)*	2.02(3.05)*
Italy	--	-2.63(0.16)	-2.63(0.16)

Own elaboration. h is the value of the threshold variable (time) which maximises the probability of rejection of the null hypothesis that no structural break occurs in that point. -- indicates that the stability test does not reject the previous null hypothesis. The chi-square statistic for the test of the null hypothesis that the inverse of the Phillips curve slope is equal to zero is presented in parenthesis. * and ** mean significant at 10 and 5%, respectively.

TABLE 10 STABILITY TESTS AND TRESHOLD MODELS

	h=π	SR π ≤ h	SR π > h		h=π	SR π ≤ h	SR π > h
Belgium	3.3	-50.00(0.001)	1.14(5.55)**	Luxembourg	5.1	2.17(0.10)	-1.23(0.20)
Germany	2.8	0.97(2.04)	0.67(24.49)**	Holland	4.4	0.95(3.42)*	1.49(1.54)
Spain	--	1.85(2.97)*	1.85(2.97)*	Austria	--	0.91(3.02)*	0.91(3.02)*
France	5	-2.77(0.67)	0.56(0.92)	Portugal	7	1.23(0.34)	0.41(3.12)*
Ireland	--	0.87(3.74)*	0.87(3.74)*	Finland	6	2.63(1.19)	1.52(1.40)
Italy	7	8.33(0.03)	-2.5(0.03)

Own elaboration. h is the value of the threshold variable (inflation) which maximises the probability of rejection of the null hypothesis that no structural break occurs in that point. -- indicates that the stability test does not reject the previous null hypothesis. The chi-square statistic for the test of the null hypothesis that the inverse of the Phillips curve slope is equal to zero is presented in parenthesis. * and ** mean significant at 10 and 5%, respectively.