A. Introduction and Summary

82. This chapter provides estimates of the tradeoff between inflation and cyclical measures of real activity in Switzerland. Traditionally, the short-run tradeoff is estimated using data on unemployment and inflation—an expectations-augmented Phillips curve. In the Swiss case, however, this approach has proved largely unsuccessful in the past. For example, in a recent extension of the Fund’s MULTIMOD (multi-region econometric model) to Switzerland, initial estimations using Swiss data yielded such poor results that pooled data from the major industrial countries had to be employed to obtain a plausible relationship.⁵² However, given the well-documented differences between labor markets in Switzerland and other industrialized countries, it is unlikely folly satisfactory parameters were obtained.⁵³ Moreover, Faruqee (1997)⁵⁴ estimated country-specific parameters for Phillips’ curves of various industrial countries, excluding however Switzerland. He found substantial differences in these parameters across countries.

83. A principal obstacle to estimating a short-run Phillips curve for Switzerland has been the limited variability of its unemployment rate (Figure III-1). Until the 1990s, the Swiss unemployment rate has been very low—below 1 percent—for both institutional and statistical reasons. Changes in the labor market that took place during the 1980s had their consequences revealed during the economic slowdown of the 1990s, and the unemployment rate rose to record levels for Switzerland.

Switzerland: Inflation and Real Activity, 1977-96

(In percent)

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Sources: Swiss Institute for Business Cycle Research, data tape; IMF, World Economic Outlook.

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Switzerland: Inflation and Real Activity, 1977-96

(In percent)

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Sources: Swiss Institute for Business Cycle Research, data tape; IMF, World Economic Outlook.

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Switzerland: Inflation and Real Activity, 1977-96

(In percent)

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Sources: Swiss Institute for Business Cycle Research, data tape; IMF, World Economic Outlook.

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Switzerland: Seasonally Adjusted Consumer Price Index Inflation (CPIS) and Unemployment

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Swiss Institute for Business Cycle Research, data tape.

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Switzerland: Seasonally Adjusted Consumer Price Index Inflation (CPIS) and Unemployment

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Swiss Institute for Business Cycle Research, data tape.

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Switzerland: Seasonally Adjusted Consumer Price Index Inflation (CPIS) and Unemployment

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Swiss Institute for Business Cycle Research, data tape.

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84. Confronted with this statistical challenge to estimating a standard Phillips curve, two extensions are undertaken in this paper. One, in addition to the unemployment rate, employment and the output gap series are used as measures of real activity. As expected, the relationship between wage inflation and the employment/output gap is closer than the relationship between wage inflation and the unemployment rate (Figure III-1). Thus, greater success should be anticipated in uncovering the tradeoff between inflation and real activity based on output gap series than based on the unemployment rate. The second innovation is to estimate a non-linear relationship between various measures of real activity and inflation, instead of relying only on a linear specification. As in Laxton and Prasad (1997) and Debelle and Laxton (1996)⁵⁵, the estimates obtained in this paper for Switzerland suggest that a non-linear (convex) specification could be more appropriate than a linear one.⁵⁶

85. A non-linear Phillips curve has important implications for the appropriate conduct of macroeconomic policy. Given a non-linear Phillips curve, the tradeoff (the sacrifice ratio) varies depending on the level of activity. Thus, the tradeoff is time dependent, varying with the current economic conditions. This contrasts with a linear Phillips curve, where the same tradeoff exists regardless of prevailing economic conditions. Policy miscues in a linear world have identical costs. However, with a non-linear Phillips curve, the costs associated with policy miscues depend on prevailing economic conditions. For instance, the further output is below potential, the smaller would be the increase in inflation—a lower sacrifice ratio—in response to higher aggregate demand. On the other hand, when the economy operates near or above full capacity, increased aggregate demand could result in sharply higher inflation—a high sacrifice ratio. Wide swings in aggregate demand can, therefore, prove costly both in terms of inflation and unemployment. An even moderately convex Phillips curve, thus, places a premium on the successful implementation of stabilization policies if the economy is subject to significant aggregate demand shocks.

86. The estimates obtained in this chapter appear robust to the various measures of cyclical activity and suggest that a non-linear specification appears to be marginally superior to a linear specification. Both specifications indicate that the “Phillips curve” faced by Switzerland was relatively flat at the end of the sample period—the fourth quarter of 1996. Higher aggregate demand would, thus, primarily produce increases in economic activity with only minor increases in inflation. This low sacrifice ratio contrasts with the very high sacrifice ratio that existed in the late 1980s.

87. This chapter focuses mainly on the short-run trade-off between inflation and real activity. However, the possible existence of a long-run tradeoff between inflation and economic activity would also have important implications for the conduct of macroeconomic policies and the inflation target of the Swiss National Bank. To examine this issue more rigorously, statistical tests for a long-run tradeoff between inflation and economic activity are carried out in section D. These statistical tests did not support the existence of a long-term non-vertical Phillips curve in Switzerland. This result, however, may not hold for all inflation levels, in particular, the number of observations of very low inflation (below 1 percent) are very limited.

B. A Framework for Estimating Short-Run “Phillips Curve” Tradeoffs

88. From the interaction of wage- and price-setting behavior, a reduced form relation between price adjustments and the level of real activity can be derived.⁵⁷ This relationship is commonly expressed as an expectations-augmented short-run Phillips curve. It relates price or wage inflation to the unemployment gap—the departure of actual unemployment from the non-accelerating inflation rate of unemployment or NAIRU. Equivalent relationships can be derived between consumer (or wage) inflation and employment or the output gap. In general, a short-run relation between inflation and real activity can be expressed in the following reduced form:

Here, π_t is observed inflation, ${\pi }_t^a$ is anticipated inflation, and x_t - $x_t^{*}$ is a “real activity gap” such as the output gap, employment gap, or the unemployment gap. For example, when x_t stands for output and $x_t^{*}$ for potential output, then x_t - $x_t^{*}$ is the output gap. The condition that f(0)=0 ensures that unanticipated inflation is zero when the “real activity gap” is closed. Hence, this specification implies that there is no long-term trade-off between real activity and inflation. The validity of this restriction is examined in section D.

89. As in Debelle and Laxton (1996) and Fuhrer (1995),⁵⁸ anticipated inflation is based on a combination of forward- and backward looking information. Specifically,

The first term on the right hand side is the backward-looking component and is assumed to depend only on previous period inflation. The second term is the forward-looking component, and depends on expected inflation in the following period, ${\pi }_{t+1}^e$. Anticipated inflation is the weighted average of these two components. The weight placed on the forward-looking component is δ. Inflationary expectations are assumed to be rational, so expected future inflation will only differ from realized future inflation by a random error term,

The error term ε_t+1 is assumed to have a zero mean governed by a serially uncorrected white noise process with standard deviation as. This specification implies that inflationary expectations will be correct on average. Combining equations (1)-(3) leads to the following equation which will be used in the estimations below,

where Δπ_t = π_t - π_t-1 The original model parameters can be recovered from the estimated coefficients in (4) using,

90. The model is estimated below using quarterly data. Three measures of real activity—the unemployment rate, employment, and the output gap—are utilized. Several measures of inflation are employed, including the Consumer Price Index (CPI) inflation and wage inflation (LWI). These inflation series are filtered using the Hodrick-Prescott (HP) technique (e.g. HP-CPI, and HP-LWI) to remove very high frequency components. (The HP filter smoothing parameter was 10.) In addition, several functions, f(.), will be used below, including both linear and non-linear forms.

Estimates Based on Unemployment Data

91. As a staring point, the following Phillips line is considered:

$\begin{array}{cc}{\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{\gamma }\left(U_t-U_t^{*}\right)& \left(6\right)\end{array}$

Here, U_t is the unemployment rate and $U_t^{*}$ is the time-varying NAIRU. Under the natural rate hypothesis, an unemployment rate of $U_t^{*}$ is consistent with zero unanticipated inflation. In this linear specification, the parameter γ equals the time-invariant short-run trade-off between inflation and unemployment, and is the inverse of the “sacrifice ratio”.

92. Measurement issues in Switzerland are very important for institutional and statistical reasons. The most important institutional factor would seem to be the role of foreigner workers in the labor market. Prior to the economic slowdown of the 1990s, the labor force had a high degree of cyclical responsiveness (OECD Economic Survey-Switzerland, 1996), owing in large part to swings in foreign employment. Foreign workers by leaving Switzerland acted as an unemployment buffer and were not be recorded as unemployed in Switzerland. According to the OECD (1996), for example, about 80 percent of the employment loss during the 1974-76 recession was absorbed by a shrinking foreign labor force; most of the decrease came from foreigners holding annual work permits. The restrictiveness of work permit rules declines with the cumulated time spent in Switzerland, however. The share of foreign workers with permanent resident status has, thus, risen from about 20 percent in 1970 to close to 60 percent in 1996. Consequently, the cyclical responsiveness of the labor force has declined over time.

93. Another reason for a declining cyclical responsiveness of the registered labor force was the introduction of compulsory unemployment insurance in 1977 and the subsequent increase in coverage and generosity. These changes have enhanced the economic incentives for the unemployed to register at labor offices. Data on unemployed are based on the number of persons who register for unemployment benefits at the cantonal employment offices. This measurement practice is subject to both under-and over-estimation problems. Actual unemployment could be underestimated because people fail to register when unemployed since prior to 1997 they would not receive benefits. (The 1990 census data found the number of unemployed individuals to be three-times higher than the number of registered unemployed, suggesting hidden unemployment.) Unemployment could be overstated because individuals who are not actively seeking employment remain registered in order to obtain unemployment benefits. (During 1994-95, survey-based unemployment rates have been well below the registered unemployment rates (0.9 percentage points) suggesting that unemployment benefits have boosted registered unemployment.)

94. Finally, the measurement of unemployment changed in 1991. Prior to 1991, unemployment was given by the number of unemployed workers registered with regional labor offices. From 1991 onwards, the unemployment rate has been calculated from the annual Labor Force Survey. However, the measured labor force has not been updated since the 1990 survey. Using the sum of employed and unemployed persons as an alternative measure of the labor force, the unemployment rate would be about ½ percentage point below the official figure. These various problems with the unemployment data have hampered the estimation of the short-run Phillips curve for Switzerland, and suggest that the Swiss unemployment series may not correspond closely to real economic activity or inflation.

95. The model is expressed in state-space form before estimation. The measurement equation is obtained by substituting equation (6) in (4) to give,

$\begin{array}{cc}{\mathrm{\Delta \pi }}_t={\mathrm{\phi \Delta \pi }}_{t-1}+\mathrm{\gamma }\left(U_{t-1}-U_{t-1}^{*}\right)+{\mathrm{\epsilon }}_t& \left(7\right)\end{array}$

or, in vector form,

$\begin{array}{cc}{\mathrm{\Delta \pi }}_t=\left[\begin{array}{cccc}-\mathrm{\gamma }& \mathrm{\gamma }{U}_{t-1}& {\mathrm{\Delta \pi }}_{t-1}& 0\end{array}\right]·\left[\begin{array}{c}{U}_{t-1}^{*}\\ 1\\ \mathrm{\phi }\\ \mathrm{\beta }\end{array}\right]+{\mathrm{\epsilon }}_t& \left(8\right)\end{array}$

The 4 × 1 period-t state vector is: [$U_{t-1}^{*}$ 1 φ β]′. As mentioned above, the error term et is assumed to be a zero mean serially uncorrected white noise process with standard deviation σ_ε. The parameter β does not enter into the data equation, (8), but is needed in the state equation below.

96. The evolution of the state variable $U_{t-1}^{*}$ is assumed to follow a random walk process with a structural break in 1992,

$\begin{array}{cc}{U}_t^{*}=U_{t-1}^{*}+\mathrm{\beta }{d}_t+{\mathrm{\eta }}_t& \left(9\right)\end{array}$

Here, the variable d_t is a dummy which equals zero for all quarters before the first quarter in 1992 and equals one for all quarters after that. Thus, d_t is used to separate the two regimes in the unemployment series. The year 1992 was chosen as the break point because it was the first year after the change in unemployment definition that an output gap emerged.

97. The error term η_t in (9) is assumed to be a zero mean and serially uncorrected white noise process with standard deviation σ_η. Using equation (9), the evolution of the state vector is described by the state transition equation:

$\begin{array}{cc}\left[\begin{array}{c}{U}_t^{*}\\ 1\\ \mathrm{\phi }\\ \mathrm{\beta }\end{array}\right]=\left[\begin{array}{cccc}1& 0& 0& d_t\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\cdot \left[\begin{array}{c}{U}_{t-1}^{*}\\ 1\\ \mathrm{\phi }\\ \mathrm{\beta }\end{array}\right]+\left[\begin{array}{c}{\mathrm{\eta }}_t\\ 0\\ 0\\ 0\end{array}\right]& \left(10\right)\end{array}$

where, the error vector, [η_t 0 0 0]′, is normally distributed with mean [0 0 0 0]′ and a variance-covariance matrix:

$\begin{array}{cc}Q=\left[\begin{array}{cccc}{\mathrm{\sigma }}_{\mathrm{\eta }}^{\mathrm{2}}& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]& \left(11\right)\end{array}$

The state-space formulation of the model consists of the measurement equation, (8), the state transition equation, (10), and the stochastic assumptions for the shocks η_t and ε_t.

98. The model parameters σ_ε, σ_η, γ, φ, and β, and the series $U_t^{*}$ are unknown. To identify the model, an a priori restriction on the variability of $U_t^{*}$ was used to fix the value of σ_η Since $U_t^{*}$ is the natural unemployment rate, and this rate is expected to be less volatile than the observed unemployment rate, a value for σ_η was chosen so that the $U_t^{*}$ series was less volatile than the unemployment rate. For this purpose the value of σ_η is set to 0.03. This value was chosen by estimating the model for different values of σ_η and comparing the variability of the estimated $U_t^{*}$ series and that of unemployment. Several values for σ_η were found that guaranteed that the $U_t^{*}$ series is smoother than the unemployment rate. However, the results reported here did not change substantially with these different values for σ_η. Therefore, the results reported here are based on σ_η=0.03. With σ_η given, the model was estimated by maximum likelihood using the Kalman filter.⁵⁹

99. The estimated parameters are shown in Table III-1a. Using equation (5), these estimates imply a value for δ of 0.53 and θ=-0.0017. The estimated natural rate is shown in Figure III-3. The estimated value of U* was 3.8 percent in 1996 with a standard error of 1.2 percent. In light of the results of Debelle and Laxton (1996) and Faruqee (1997), which support a non-linear relation over a linear one, the following nonlinear specification replaced (6),

$\begin{array}{cc}{\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{\gamma }\frac{U_t-U_t^{*}}{U_t}& \left(12\right)\end{array}$

Table III-1.

Parameter Estimates Allowing for a Regime Shift in 1992 Sample: 1976 (Q3) - 1996 (Q4)

Table III-1.

Parameter Estimates Allowing for a Regime Shift in 1992 Sample: 1976 (Q3) - 1996 (Q4)

Table III-1a. Linear Phillips Curve
Set: ση = 0.03
Estimated Parameters (standard errors)				Implied Model Parameters		Log-Likelihood
σε	γ	φ	β	δ	θ
0.17	0.03	0.88	3.36	0.53	-0.00	-4.55
(0.00)	(0.00)	(0.05)	(1.39)
Table III-1b. Nonlinear Phillips Curve
Set: ση = 0.03
Estimated Parameters (standard errors)				Implied Model Parameters		Log-Likelihood
σε	γ	φ	β	δ	θ
0.16	0.049	0.91	1.76	0.52	-0.03	-4.13
(0.00)	(0.00)	(0.05)	(2.20)

View Table

Table III-1.

Parameter Estimates Allowing for a Regime Shift in 1992 Sample: 1976 (Q3) - 1996 (Q4)

Table III-1a. Linear Phillips Curve
Set: ση = 0.03
Estimated Parameters (standard errors)				Implied Model Parameters		Log-Likelihood
σε	γ	φ	β	δ	θ
0.17	0.03	0.88	3.36	0.53	-0.00	-4.55
(0.00)	(0.00)	(0.05)	(1.39)
Table III-1b. Nonlinear Phillips Curve
Set: ση = 0.03
Estimated Parameters (standard errors)				Implied Model Parameters		Log-Likelihood
σε	γ	φ	β	δ	θ
0.16	0.049	0.91	1.76	0.52	-0.03	-4.13
(0.00)	(0.00)	(0.05)	(2.20)

Switzerland: Estimated NAIRU Using a Linear Model

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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Switzerland: Estimated NAIRU Using a Linear Model

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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Switzerland: Estimated NAIRU Using a Linear Model

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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In this non-linear specification, $U_t^{*}$ is the deterministic NAIRU or D-NAIRU. This specification is motivated by a traditional upward sloping supply function: as the economy approaches its capacity constraint, and the unemployment rate is below the NAIRU rate, excess demand only raises inflation without any output or employment gains. The differences between the D-NAIRU and the NAIRU are shown in Figure III-4, The D-NAIRU is the unemployment rate consistent with zero unexpected inflation (π_t - π_t^e = 0); whereas the NAIRU is the expected value of the unemployment rate in the stochastic steady state. Given the range of variability of the unemployment rate in Figure III-4 (i.e. symmetric shocks about the NAIRU), the convexity of the curve (which implies that excess demand is more inflationary than excess supply), implies that the NAIRU will exceed the D-NAIRU, $U_t^{*}$. In the linear model, on the other hand, $U_t^{*}$ and the NAIRU are equal.

Switzerland: The Convex Phillips Curve

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

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Switzerland: The Convex Phillips Curve

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

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Switzerland: The Convex Phillips Curve

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

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100. The non-linear model is expressed in state-space form prior to estimation. This involves replacing equation (8) by:

$\begin{array}{cc}{\mathrm{\Delta \pi }}_t=\left[\begin{array}{cccc}\frac{-\mathrm{\gamma }}{U_{t-1}}& U_{t-1}& {\mathrm{\Delta \pi }}_{t-1}& 0\end{array}\right]\cdot \left[\begin{array}{c}{U}_{t-1}^{*}\\ 1\\ \mathrm{\phi }\\ \mathrm{\beta }\end{array}\right]+{\mathrm{ϵ}}_t& \left(13\right)\end{array}$

The state vector is still assumed to evolve according to (10). The Kalman filter was used to obtain the Maximum Likelihood estimates for the parameters as well as the time-varying D-NAIRU, $U_t^{*}$, with a regime shift in 1992. The estimated parameter values are presented in Table III-1b. The estimated D-NAIRU is shown in Figure III-5. The non-linear specification improves somewhat the fit compared with the linear specification, judging by the log-likelihood values. Also, the NAIRU (obtained by filtering U_t) never dips below the D-NAIRU plus one standard error (Figure III-5). Thus, the estimation results agree with the theoretical specification for a convex Phillips curve. The standard errors for the non-linear specification are smaller than those for the linear specification during the period 1976-91 (0.2 vs 0.7). However, the standard errors for the non-linear specification are significantly larger after the series break in 1992 (2.2) compared with their earlier values and compared with the standard errors for linear model for the period 1992-96 (1.2). The relatively poor performance of the non-linear model since 1991 casts doubts on the specification despite its superior performance over the entire sample period.

Switzerland: Estimated D-NAIRU Using a Non-linear Model

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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Switzerland: Estimated D-NAIRU Using a Non-linear Model

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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Switzerland: Estimated D-NAIRU Using a Non-linear Model

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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101. Moreover, the estimated value of γ for Switzerland is 0.05 and is substantially lower than the estimated values for other industrial countries (see the results in Debelle and Laxton (1996) or in Farquee (1997)), also casting doubt on the plausibility of the empirical results. The exceptionally low value of γ for Switzerland would imply that the Swiss Phillips curve is much flatter than in other countries—that is, a one percentage point change in the unemployment rate would have almost no impact on inflation over a wide range of the Phillips curve (Figure III-6)—an empirical result at odds with the observation that the flexibility of nominal wage setting in Switzerland appears to be higher than in most other industrial countries in Europe. The parameter 5 is estimated at 0.52. This estimate implies that wage and price setters place a weight of about 52 percent on forward-looking inflation expectations. This estimate is not out of line with estimates for G-7 countries reported by Farquee (1997) and indeed were almost identical to the values for Germany and Canada. Finally, the D-NAIRU, U*, was estimated at 2.2 percent in 1996. For comparison, OECD estimates of the NAIRU cluster around 3 percent. This value falls between the estimated average annual D-NAIRU and NAIRU for 1996 (2.2 percent and 3.9 percent, respectively).

Switzerland: The Short-run Trade-off Between Inflation and Unemployment in 1996

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

1/ The standard error reflects uncertainty in the estimate of U* only. Parameter uncertainty is not reflected in this chart.

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Switzerland: The Short-run Trade-off Between Inflation and Unemployment in 1996

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

1/ The standard error reflects uncertainty in the estimate of U* only. Parameter uncertainty is not reflected in this chart.

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Switzerland: The Short-run Trade-off Between Inflation and Unemployment in 1996

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

1/ The standard error reflects uncertainty in the estimate of U* only. Parameter uncertainty is not reflected in this chart.

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Estimates Based on Output Gap Data

102. In this section, the output gap replaces the unemployment rate as the relevant activity measure. One disadvantage of the output gap is that it is not an observable variable, and its magnitude is subject to dispute. For example, the estimated output gap in 1996 ranged from about 2 ½ percent (Economic Policy Commission) to 3½ percent (Fund staff), to 4½ percent (SNB), to close to 5 percent (OECD).

103. In order to check the robustness of the previous results to the expectations model, unanticipated inflation is now modeled as,

$\begin{array}{cc}{\mathrm{\pi }}_t^a=\left(1-\mathrm{\delta }\right){\mathrm{\pi }}_{t-1}+\mathrm{\delta }{\mathrm{\pi }}_t^{\mathit{LTE}}\mathit{where}\mathrm{\delta }\mathrm{ϵ}\left(0,1\right)& \left(14\right)\end{array}$

instead of equation (2). In this specification, the forward looking component of anticipated inflation depends on long-term inflation expectations, ${\mathrm{\pi }}_t^{\mathit{LTE}}$, as in Debelle and Laxton (1996). This ${\mathrm{\pi }}_t^{\mathit{LTE}}$ term is the difference between long-term interest rates and a measure of the world interest rate:⁶⁰

$\begin{array}{cc}{\mathrm{\pi }}_t^{\mathit{LTE}}=r_t^{\mathit{LR}}-r_t^{\mathit{WORLD}}& \left(15\right)\end{array}$

This model was estimated below using quarterly data and several measures of inflation, the CPI and wages. The version of equation (1) used is:

$\begin{array}{cc}{\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{\gamma }{\mathit{YGAP}}_t& \left(16\right)\end{array}$

where YGAP_t is the output gap and is defined as:

$\begin{array}{cc}{\mathit{YGAP}}_t=\left[\frac{Y_t-Y_t^{*}}{Y_t^{*}}\right]\cdot 100& \left(17\right)\end{array}$

Here, Y_t is GDP in constant prices and Y* is potential GDP. Equations (14) and (15) are substituted into (16), and the resulting equation is estimated using OLS, The estimation results are shown in Table III-2. The estimated coefficient γ has the anticipated sign and is statistically significant. The adjusted R squared is 0.97 and the F-statistic is highly significant.

Table III-2.

Linear Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Table III-2.

Linear Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Regression: ${\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{C}{\left(2\right)}^{*}\mathrm{YGAP}$
Inflation: HP-CPIS
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.03	0.02	1.37	0.18
C(2)	0.09	0.02	4.49	0.00
R-squared		0.97	Mean dependent var		3.18
Adjusted R-squared		0.97	S.D. dependent var		1.81
Durbin-Watson stat		0.23	Prob (F-statistic)		0.00
Inflation: HP-LWI
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.03	0.01	1.78	0.08
C(2)	0.09	0.02	4.50	0.00
R-squared		0.97	Mean dependent var		3.80
Adjusted R-squared		0.97	S.D. dependent var		1.89
Durbin-Watson stat		0.14	Prob (F-statistic)		0.00
Variables:
CPIS = CPI inflation, seasonally adjusted
LWI = wage index inflation

View Table

Table III-2.

Linear Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Regression: ${\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{C}{\left(2\right)}^{*}\mathrm{YGAP}$
Inflation: HP-CPIS
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.03	0.02	1.37	0.18
C(2)	0.09	0.02	4.49	0.00
R-squared		0.97	Mean dependent var		3.18
Adjusted R-squared		0.97	S.D. dependent var		1.81
Durbin-Watson stat		0.23	Prob (F-statistic)		0.00
Inflation: HP-LWI
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.03	0.01	1.78	0.08
C(2)	0.09	0.02	4.50	0.00
R-squared		0.97	Mean dependent var		3.80
Adjusted R-squared		0.97	S.D. dependent var		1.89
Durbin-Watson stat		0.14	Prob (F-statistic)		0.00
Variables:
CPIS = CPI inflation, seasonally adjusted
LWI = wage index inflation

104. Next, a quadratic specification is estimated instead of (16). The quadratic specification imposes a positive relation between inflation and the output gap when output is below potential, and a negative relation when output is above potential.

$\begin{array}{cc}{\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{\gamma }{\mathit{YGAP}}_t+\mathrm{\eta }{\mathit{YGAP}}_t^2& \left(18\right)\end{array}$

The estimation results for equation 18 are given in Table III-3. Both coefficients had a positive coefficient that were statistically significantly different from zero. The adjusted R squared is about 0.97 or virtually unchanged from the linear specification. However, the quadratic specification has a marginally better fit using other criteria such as standard error of the regression, log likelihood, and F statistic. This suggest that the relation between inflation and the output gap may be somewhat non-linear. However, a quadratic specification may be too restrictive and appears to imply anomalous behavior for unanticipated inflation when the output gap is high.

Table III-3.

Quadratic Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Table III-3.

Quadratic Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Regression: ${\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{C}{\left(2\right)}^{*}\mathrm{YGAP}+\mathrm{C}{\left(3\right)}^{*}\left(\mathrm{YGAP}\stackrel{}{^}2\right)$
Inflation: HP-CPIS
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.08	0.02	3.58	0.00
C(2)	0.10	0.02	5.39	0.00
C(3)	0.03	0.01	3.80	0.00
R-squared		0.98	Mean dependent var		3.18
Adjusted R-squared		0.97	S.D. dependent var		1.81
Durbin-Watson stat		0.27	Prob (F-statistic)		0.00
Inflation: HP-LWI
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.07	0.02	4.04	0.00
C(2)	0.12	0.02	5.72	0.00
C(3)	0.03	0.01	3.98	0.00
R-squared		0.98	Mean dependent var		3.80
Durbin-Watson stat		0.18	Prob (F-statistic)		0.00
Variables:
CPIS = CPI inflation, seasonally adjusted
LWI = wage index inflation

View Table

Table III-3.

Quadratic Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Regression: ${\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{C}{\left(2\right)}^{*}\mathrm{YGAP}+\mathrm{C}{\left(3\right)}^{*}\left(\mathrm{YGAP}\stackrel{}{^}2\right)$
Inflation: HP-CPIS
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.08	0.02	3.58	0.00
C(2)	0.10	0.02	5.39	0.00
C(3)	0.03	0.01	3.80	0.00
R-squared		0.98	Mean dependent var		3.18
Adjusted R-squared		0.97	S.D. dependent var		1.81
Durbin-Watson stat		0.27	Prob (F-statistic)		0.00
Inflation: HP-LWI
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.07	0.02	4.04	0.00
C(2)	0.12	0.02	5.72	0.00
C(3)	0.03	0.01	3.98	0.00
R-squared		0.98	Mean dependent var		3.80
Durbin-Watson stat		0.18	Prob (F-statistic)		0.00
Variables:
CPIS = CPI inflation, seasonally adjusted
LWI = wage index inflation

105. An alternative non-linear specification (19), which does not impose this relation, was also estimated:

$\begin{array}{cc}{\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{\gamma }\frac{\mathit{YGAP}}{\hat{Y}-{\mathit{YGAP}}_t}& \left(19\right)\end{array}$

Ŷ can be interpreted as the maximum possible output gap. Equation (19) was estimated using ordinary least squares for different values of Ŷ, selecting the value of Ŷ that produced the best fit. The estimates are given in Table III-4.

Table III-4.

Non-Linear Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Table III-4.

Non-Linear Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Regression: ${\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{C}{\left(2\right)}^{*}\mathrm{YGAP}/\left(\mathrm{YHAT}-\mathrm{YGAP}\right)$
Inflation: HP-CPIS
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.06	0.02	3.01	0.00
C(2)	0.48	0.09	5.60	0.00
R-squared		0.97	Mean dependent var		3.18
Durbin-Watson stat		0.27	Prob (F-statistic)		0.00
Inflation: HP-LWI
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.05	0.01	3.44	0.00
C(2)	0.47	0.08	5.84	0.00
R-squared		0.98	Mean dependent var		3.80
Durbin-Watson stat		0.18	Prob (F-statistic)		0.00
Variables:
CPIS = CPI inflation, seasonally adjusted
LWI = wage index inflation

View Table

Table III-4.

Non-Linear Relation Between Inflation and the Output Gap Sample: 1980 (Q1) to 1996 (Q4)

Regression: ${\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a=\mathrm{C}{\left(2\right)}^{*}\mathrm{YGAP}/\left(\mathrm{YHAT}-\mathrm{YGAP}\right)$
Inflation: HP-CPIS
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.06	0.02	3.01	0.00
C(2)	0.48	0.09	5.60	0.00
R-squared		0.97	Mean dependent var		3.18
Durbin-Watson stat		0.27	Prob (F-statistic)		0.00
Inflation: HP-LWI
	Coefficient	Std. Error	T-Statistic	Prob.
C(1)	0.05	0.01	3.44	0.00
C(2)	0.47	0.08	5.84	0.00
R-squared		0.98	Mean dependent var		3.80
Durbin-Watson stat		0.18	Prob (F-statistic)		0.00
Variables:
CPIS = CPI inflation, seasonally adjusted
LWI = wage index inflation

106. The adjusted R squared is about 0.97 as in the previous two specifications. Based on some goodness-of-fit indicators (i.e., standard error of the regression and log-likelihood) the quadratic specification out performs this non-linear specification, while the non-linear specification has a higher F-statistic than does the linear specification. The non-linear specification has a slightly better fit than the linear specification based on all these goodness-of-fit indicators. Again, this suggests that the relationship between inflation and the output gap may be somewhat non-linear. The trade-offs between unanticipated inflation (HP-CPIS) and the output gap for all three specifications are shown in Figure III-7. Given the output gap estimated to prevail in 1996, the tradeoffs are similar. For the nonlinear specification, the estimated trade-off remains fairly flat and linear until the economy moves into a region of excess demand.

Switzerland: The Short-run Trade-off Between Inflation and the Output Gap in 1996

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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Switzerland: The Short-run Trade-off Between Inflation and the Output Gap in 1996

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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Switzerland: The Short-run Trade-off Between Inflation and the Output Gap in 1996

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.

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C. Policy Implications of a Non-Linear Short-Run Phillips Curve

107. To examine how the trade-off between inflation and unemployment has changed with the level of unemployment, the expression in (19) was solved for its slope,

Unanticipated inflation is given by ${\mathrm{\pi }}_t^u={\mathrm{\pi }}_t-{\mathrm{\pi }}_t^a$. This expression was used to compute the trade-off between inflation and the output gap (Figure III-8).⁶¹ As the figure shows, the inflation cost of reducing the unemployment rate has varied. As the economy moved along the Phillips curve from a flat region to an increasingly upward sloping region, the sacrifice ratio has increased sharply. Thus, the conduct of macroeconomic policies must bear in mind the economy’s current and prospective tradeoffs between inflation and growth. The convexity of the Phillips curve also places a premium on the successful conduct of stabilization policies.

Switzerland: Short-run Trade-off Between Inflation and Output Gap ^1/

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.^1/ Increase in unexpected inflation for each year that would have resulted from a 1 percentage point lower output gap in that year.

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Switzerland: Short-run Trade-off Between Inflation and Output Gap ^1/

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.^1/ Increase in unexpected inflation for each year that would have resulted from a 1 percentage point lower output gap in that year.

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Switzerland: Short-run Trade-off Between Inflation and Output Gap ^1/

Citation: IMF Staff Country Reports 1998, 043; 10.5089/9781451807158.002.A003

Source: Staff estimates.^1/ Increase in unexpected inflation for each year that would have resulted from a 1 percentage point lower output gap in that year.

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D. The Long-Run Tradeoff Between Inflation and Real Activity

108. The analysis in previous sections was based on the reduced-form relation of equation (1) which imposed long-run neutrality. However, evidence of a long-run trade-off between high inflation and growth has been found in cross-country studies. For example, Sarel (1996)⁶² reported that when inflation was high (above about 8 percent), there was a strong and statistically significant negative correlation between inflation and growth. At low inflation levels, on the other hand, inflation appeared to have no effect, or it may have a small positive effect, on real growth. Others have reported that the welfare costs in terms of lost output of even low inflation (2-3 percent) can be high mainly due to tax distortions.⁶³ On the other hand, Fischer (1994)⁶⁴ and Akerlof et.al.(1996)⁶⁵ have argued that some low inflation may be needed in order for the economy to operate efficiently in light of nominal rigidities, particularly for wages.

109. As for Switzerland, annual inflation averaged almost 4 percent during 1960-96, while real GDP growth averaged close to 3 percent. However, periods with below average inflation have been associated with below average real growth rates, while periods of above average inflation have also been associated with below average real growth rates. Sorting real GDP growth rates by inflation rates that are above or below (by one standard deviation) the average annual inflation rate for 1960-96 (see tabulation), yields a suggestive pattern. Periods of relatively high inflation experienced below average growth rates, while periods of relatively low inflation also recorded below average growth rates. This calculation can only be regarded as illustrative for several reasons including inter alia that the direction of causation was not specified. In this section, formal tests for a long-run vertical Phillips’ curve are carried out.

CPI Inflation and Real GDP Growth, 1960-96

^1/Mean inflation was 3.7 percent with a standard deviation of 2.2 percentage points.

CPI Inflation and Real GDP Growth, 1960-96

Average Inflation Rates1/	Average Real GDP Growth Rate
Periods when inflation was:	Average real growth was:
Less than 1.5 percent	1.7 percent
Between 1.5 percent and 5.9 percent	2.9 percent
More than 5.9 percent	1.2 percent

^1/Mean inflation was 3.7 percent with a standard deviation of 2.2 percentage points.

View Table

CPI Inflation and Real GDP Growth, 1960-96

Average Inflation Rates1/	Average Real GDP Growth Rate
Periods when inflation was:	Average real growth was:
Less than 1.5 percent	1.7 percent
Between 1.5 percent and 5.9 percent	2.9 percent
More than 5.9 percent	1.2 percent

^1/Mean inflation was 3.7 percent with a standard deviation of 2.2 percentage points.

110. The testing procedure utilized is based on a procedure developed by Pesaran et. al.⁶⁶ and Pesaran and Pesaran (1996).⁶⁷ In contrast to the test procedure for long-run relations proposed by King and Watson (1992),⁶⁸ this estimation strategy can be applied when variables are integrated of order zero or one. The first step in the procedure is to test for the existence of a long-term relation between inflation and real activity. If there is evidence for such a relation, then the coefficients of the long-run relation are estimated using an error correction model.

111. The test for a long-run relationship employs a standard F-statistic for testing the significance of the lagged levels of the variables in a first-difference regression, Specifically, the following error correction relation is estimated:

Here, the β_i and η_i coefficients capture the short-run effects, and the δ₁ and δ₂ coefficients are used to test the long-run relation between π_t and x_t—because, if δ₁ ≠ 0 and δ₂ ≠ 0, then there exists a long-run relation between the levels of π_t and x_t The parameters p and q allow lags to vary. The test in (14) is undertaken under the assumption that the variable π is the “long-run forcing variable,” explaining x Replacing Δπ_t on the left hand side of equation (14) by Δx_t allows for a test of the existence of a long term relation when the forcing variable is x.

112. This statistical test:

is equivalent to testing the hypothesis: “there is no long term relation between π_t and x_t” (when the variable π is the “long-run forcing variable” for the explanation of x).

113. The alternative hypothesis is:

The relevant test statistic is an F-statistic for the joint significance of δ₁ and δ₂. If the computed F-statistic exceeds the confidence bounds provided in Pesaran and Pesaran (1997), then the null hypothesis is rejected regardless of the order of integration.

114. The results of tests for a long-run relationship between real activity and inflation are given in Table III-5. The measure of inflation is HP-filtered seasonally adjusted CPI (HP-CPIS). Three different lag specifications of the model in (14) were employed (p=q=3, p=q=4, and p=q=5). Alternate tests were carried out using inflation and the measure of real activity as the forcing variables for each of the lag specifications. The F-statistics of each test are presented in the third column of Table III-5. These F-statistics are compared with the confidence bands at the bottom of this Table. It is found that, in four of the specifications tested, the null of “no long-run relation” is rejected at the 95 percent confidence level—insufficient evidence for the existence of a long-run relation between output and inflation. However, there may be a long-run relation between unemployment and inflation and between employment and inflation.

Table III-5.

The Long Run Relation Between Inflation and Real Activity Inflation measured by HP-PCPIS Sample Period: 1970 (Q2) to 1993 (Q4)

^*means rejection of the null at the 90% level.

^**means rejection of the null at the 95% level.

^***means rejection of the null at the 99% level.

(The null hypothesis is the absence of a long-run relation. For the specification used, the confidence intervals are: 90% confidence band: 4.042 to 4.788, 95% confidence band: 4.934 to 5.764,99% confidence band: 7.057 to 7.815).

Table III-5.

The Long Run Relation Between Inflation and Real Activity Inflation measured by HP-PCPIS Sample Period: 1970 (Q2) to 1993 (Q4)

Test of the Long Run Relation between Inflation and Real Activity
Measure of real activity	Forcing Variable	F-statistic
p=q=3
Unemployment	Unemployment	0.45
	Inflation	6.00	**
Employment	Employment	6.32	**
	Inflation	2.50
Output	Output	2.38
	Inflation	3.99
p=q=4
Unemployment	Unemployment	0.73
	Inflation	3.99
Employment	Employment	6.48	**
	Inflation	1.71
Output	Output	3.21
	Inflation	3.57
p=q=5
Unemployment	Unemployment	0.90
	Inflation	6.60	**
Employment	Employment	4.23
	Inflation	2.39
Output	Output	2.74
	Inflation	4.75

^*means rejection of the null at the 90% level.

^**means rejection of the null at the 95% level.

^***means rejection of the null at the 99% level.

(The null hypothesis is the absence of a long-run relation. For the specification used, the confidence intervals are: 90% confidence band: 4.042 to 4.788, 95% confidence band: 4.934 to 5.764,99% confidence band: 7.057 to 7.815).

View Table

Table III-5.

The Long Run Relation Between Inflation and Real Activity Inflation measured by HP-PCPIS Sample Period: 1970 (Q2) to 1993 (Q4)

Test of the Long Run Relation between Inflation and Real Activity
Measure of real activity	Forcing Variable	F-statistic
p=q=3
Unemployment	Unemployment	0.45
	Inflation	6.00	**
Employment	Employment	6.32	**
	Inflation	2.50
Output	Output	2.38
	Inflation	3.99
p=q=4
Unemployment	Unemployment	0.73
	Inflation	3.99
Employment	Employment	6.48	**
	Inflation	1.71
Output	Output	3.21
	Inflation	3.57
p=q=5
Unemployment	Unemployment	0.90
	Inflation	6.60	**
Employment	Employment	4.23
	Inflation	2.39
Output	Output	2.74
	Inflation	4.75

^*means rejection of the null at the 90% level.

^**means rejection of the null at the 95% level.

^***means rejection of the null at the 99% level.

(The null hypothesis is the absence of a long-run relation. For the specification used, the confidence intervals are: 90% confidence band: 4.042 to 4.788, 95% confidence band: 4.934 to 5.764,99% confidence band: 7.057 to 7.815).

115. In the next step, these latter two relationships were estimated. First the relation between unemployment and inflation was estimated using inflation as the forcing variable (Table III-6a). For three different lag specifications, the equation was estimated according to the Schwarz Bayesian Criterion (SBC) and the Akaike Information Criterion (AIC) (see Pesaran and Pesaran (1997)).⁶⁹ The one with the highest goodness-of-fit (for the AB and AI criteria) were selected and reported in Table III-6a. The long-run coefficients were not statistically significant different from zero for any of the specifications. Furthermore, the error correction coefficient had the wrong sign and was not significant. This suggests that the long-run Phillips curve for Switzerland is vertical.

Table III-6.

Estimate of the Long Run Relation between Inflation and Real Activity

Table III-6.

Estimate of the Long Run Relation between Inflation and Real Activity

(a) Measure of Real Activity: Unemployment. Forcing Variable: Inflation
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	-0.22 (-0.95)	-0.13 (-1.98)	0.15 (0.85)	0.04 (2.04)	0.82	0.83
4	-0.35 (-0.50)	-0.22 (-1.05)	0.08 (0.40)	0.02 (0.85)	0.83	0.84
5	-0.35 (-0.48)	-0.22 (-1.05)	0.01 (0.40)	0.02 (0.86)	0.83	0.84
(b) Measure of Real Activity: Employment. Forcing Variable: Employment
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	0.67 (2.37)	0.67 (2.37)	-0.14 (-1.61)	-0.14 (-1.61)	0.96	0.96
4	0.37 (2.89)	0.42 (2.44)	-0.03 (-3.58)	-0.02 (-2.30)	0.96	0.97
5	0.38 (2.93)	0.43 (2.52)	-0.03 (-3.57)	-0.02 (-2.31)	0.96	0.97
(SBC = Schwarz Bayesian Criterion, AIC = Akaike Information Criterion)

View Table

Table III-6.

Estimate of the Long Run Relation between Inflation and Real Activity

(a) Measure of Real Activity: Unemployment. Forcing Variable: Inflation
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	-0.22 (-0.95)	-0.13 (-1.98)	0.15 (0.85)	0.04 (2.04)	0.82	0.83
4	-0.35 (-0.50)	-0.22 (-1.05)	0.08 (0.40)	0.02 (0.85)	0.83	0.84
5	-0.35 (-0.48)	-0.22 (-1.05)	0.01 (0.40)	0.02 (0.86)	0.83	0.84
(b) Measure of Real Activity: Employment. Forcing Variable: Employment
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	0.67 (2.37)	0.67 (2.37)	-0.14 (-1.61)	-0.14 (-1.61)	0.96	0.96
4	0.37 (2.89)	0.42 (2.44)	-0.03 (-3.58)	-0.02 (-2.30)	0.96	0.97
5	0.38 (2.93)	0.43 (2.52)	-0.03 (-3.57)	-0.02 (-2.31)	0.96	0.97
(SBC = Schwarz Bayesian Criterion, AIC = Akaike Information Criterion)

116. The employment-inflation relationship was then estimated as above, using employment as the forcing variable (Table III-6b). In this case, the long-run coefficient was found to be significantly different from zero in all three lag specifications. Moreover, the error correction coefficient was properly signed (i.e., negative) and significant in two of the three estimations. The long-run coefficients ranged from 0.37 to 0.67 (Table III-7b), implying that a 1 percentage point increase in employment would be associated with a 0.37 to 0.67 percentage points increase in long-run inflation. Moreover, while employment affects inflation, inflation does not affect employment. These results support the conventional view that an economy operating at, or above, potential on a sustained basis will tend to higher long-run inflation. However, the absence of a long-run inflation impact on long-run employment is interpreted as a consistent with vertical long-run Phillips curve.

Table III-7.

The Long Run Relation Between Inflation and Real Activity Inflation measured by LWI Sample Period: 1970 (Q2) to 1993 (Q4)

^*means rejection of the null at the 90% level.

^**means rejection of the null at the 95% level.

^***means rejection of the null at the 99% level.

(The null hypothesis is the absence of a long-run relation. For the specification used, the confidence intervals are: 90% confidence band: 4.042 to 4.788,95% confidence band: 4.934 to 5.764, 99% confidence band: 7.057 to 7.815).

Table III-7.

The Long Run Relation Between Inflation and Real Activity Inflation measured by LWI Sample Period: 1970 (Q2) to 1993 (Q4)

Test of the Long Run Relation between Inflation and Real Activity
Measure of real activity	Forcing Variable	F-statistic
p=q=3
Unemployment	Unemployment	1.96
	Inflation	3.60
Employment	Employment	6.98	**
	Inflation	3.99
Output	Output	1.70
	Inflation	9.00	***
p=q=4
Unemployment	Unemployment	L97
	Inflation	2.74
Employment	Employment	4.94	*
	Inflation	4.44
Output	Output	1.08
	Inflation	4.12
p=q=5
Unemployment	Unemployment	0.38
	Inflation	2.51
Employment	Employment	3.75
	Inflation	1.81
Output	Output	1.01
	Inflation	2.92

^*means rejection of the null at the 90% level.

^**means rejection of the null at the 95% level.

^***means rejection of the null at the 99% level.

(The null hypothesis is the absence of a long-run relation. For the specification used, the confidence intervals are: 90% confidence band: 4.042 to 4.788,95% confidence band: 4.934 to 5.764, 99% confidence band: 7.057 to 7.815).

View Table

Table III-7.

The Long Run Relation Between Inflation and Real Activity Inflation measured by LWI Sample Period: 1970 (Q2) to 1993 (Q4)

Test of the Long Run Relation between Inflation and Real Activity
Measure of real activity	Forcing Variable	F-statistic
p=q=3
Unemployment	Unemployment	1.96
	Inflation	3.60
Employment	Employment	6.98	**
	Inflation	3.99
Output	Output	1.70
	Inflation	9.00	***
p=q=4
Unemployment	Unemployment	L97
	Inflation	2.74
Employment	Employment	4.94	*
	Inflation	4.44
Output	Output	1.08
	Inflation	4.12
p=q=5
Unemployment	Unemployment	0.38
	Inflation	2.51
Employment	Employment	3.75
	Inflation	1.81
Output	Output	1.01
	Inflation	2.92

^*means rejection of the null at the 90% level.

^**means rejection of the null at the 95% level.

^***means rejection of the null at the 99% level.

(The null hypothesis is the absence of a long-run relation. For the specification used, the confidence intervals are: 90% confidence band: 4.042 to 4.788,95% confidence band: 4.934 to 5.764, 99% confidence band: 7.057 to 7.815).

117. To check the robustness of these results to the choice of inflation data, the previous procedure was repeated using data on wage inflation (LWI). The results are presented in Table III-7. In three cases, the hypothesis of no long-run relation was rejected—inflation and output, and inflation and employment. Selected statistics for these two relations are presented in Table III-8a and Table III-8b, respectively. The conclusion is as above, namely, that the only long-run relation is between employment and inflation, with employment as the forcing variable. On the other hand, long-run inflation has no impact on long-run employment.

Table III-8.

Estimate of the Long-Run Relation between Inflation and Real Activity

Table III-8.

Estimate of the Long-Run Relation between Inflation and Real Activity

(a) Measure of Real Activity: Output. Forcing Variable: Inflation
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	-5.60 (-0.64)	-7.60 (-0.86)	-0.01 (-0.76)	-0.01 (-0.90)	0.33	0.36
4	-3.70 (-0.30)	-8.37 (-0.83)	-0.00 (-0.46)	-0.01 (-0.87)	0.30	0.35
5	-8.60 (-1.30)	-7.60 (-0.93)	-0.01 (-1.44)	-0.01 (-0.98)	0.50	0.55
(b) Measure of Real Activity: Employment. Forcing Variable: Employment
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	0.76 (8.21)	0.76 (7.03)	-0.57 (-6.27)	-0.48 (-4.79)	0.31	0.34
4	0.90 (4.11)	0.90 (4.11)	-0.25 (-2.15)	-0.25 (-2.15)	0.46	0.46
5	0.54 (2.08)	0.54 (2.08)	-0.21 (-1.97)	-0.21 (-1.97)	0.59	0.59
(SBC = Schwarz Bayesian Criterion, AIC = Akaike Information Criterion)

View Table

Table III-8.

Estimate of the Long-Run Relation between Inflation and Real Activity

(a) Measure of Real Activity: Output. Forcing Variable: Inflation
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	-5.60 (-0.64)	-7.60 (-0.86)	-0.01 (-0.76)	-0.01 (-0.90)	0.33	0.36
4	-3.70 (-0.30)	-8.37 (-0.83)	-0.00 (-0.46)	-0.01 (-0.87)	0.30	0.35
5	-8.60 (-1.30)	-7.60 (-0.93)	-0.01 (-1.44)	-0.01 (-0.98)	0.50	0.55
(b) Measure of Real Activity: Employment. Forcing Variable: Employment
Max. Lags	Long-Run Coefficient		Error-Correction Coefficient		R2 of Error-correction equation
	SBC	AIC	SBC	AIC	SBC	AIC
3	0.76 (8.21)	0.76 (7.03)	-0.57 (-6.27)	-0.48 (-4.79)	0.31	0.34
4	0.90 (4.11)	0.90 (4.11)	-0.25 (-2.15)	-0.25 (-2.15)	0.46	0.46
5	0.54 (2.08)	0.54 (2.08)	-0.21 (-1.97)	-0.21 (-1.97)	0.59	0.59
(SBC = Schwarz Bayesian Criterion, AIC = Akaike Information Criterion)