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Filling the gap--an international comparison of the cyclical adjustment of budget balances.

INTRODUCTION

The potential output of an economy is widely used by both policymakers and analysts to evaluate economic conditions. The difference between actual and potential GDP yields the aggregate output gap, but the concept of potential level and sap or cyclical position can be extended to any macroeconomic variable. For instance, the unemployment rate fluctuates around an equilibrium level, the non-accelerating inflation rate of unemployment (NAIRU). The cyclical adjustment of the budget balance also represents an application of this idea by attempting to remove the cyclical effects from budget revenues and expenditures in order to estimate the cyclically adjusted budget balance (CAB). Formally, CAB equals the budget balance minus the cyclical component.

Although economists generally agree on the intuitive concept of the cyclical component, there is less consensus on how to measure it, given that it is unobservable. Of the various econometric techniques proposed to solve this problem, two have emerged as the most widely used: the aggregated approach, advocated by the International Monetary Fund (IMF), the Organisation for Economic Co-operation and Development (OECD) and the European Commission (EC), and the unconstrained disaggregated approach, used by the European Central Bank (ECB).

While several studies discuss the problems of the CAB from the point of view of fiscal issues in great detail, for instance see Van den Noord (2000) or Chalk (2002), they do not identify the potential problems arising from the estimation of output gaps. Neither the aggregate nor the ECB-type disaggregated approach has been tested to establish whether they meet the economic requirements, such as the usage of appropriate macroeconomic variable and theory, that are indispensable in order to obtain relevant and accurate gap estimations. The unobservable nature of cyclical component requires a special approach to evaluate and compare the different methods. Since the true value of the output gap is unknown, the simple concepts of econometric error or bias are not applicable. Therefore, the estimations of different methods should be ranked by the validity of their theoretical foundation and information they require. Consequently, if there is discrepancy between two estimations, then this discrepancy is considered as bias if one method is superior to the other on the theoretical and/or professional ground.

This paper seeks to provide a more thorough assessment of cyclical position estimates. It examines the cyclical position of the US, Japan and 25 EU Member States, and finds that both the aggregated and disaggregated approaches have significant shortcomings. The aggregated approach cannot cope with different shocks, that is, provides the same fiscal indication regardless to the source of economic disturbancy, whereas the unconstrained disaggregated method suffers from systematic bias and fails to exploit theoretical consideration. To overcome these limitations, we introduce a methodology that is free of these distortions.

The remainder of the paper is structured as follows. The following section examines the approaches advocated by the above-mentioned international institutions in detail. The next section proposes a new methodology for measuring the cyclical position. Then the succeeding section estimates the compositional effects. The penultimate section shows the importance of the composition effect by means of three case studies of the Finnish, Hungarian and Italian budget balances. Finally, the last section provides some overall conclusions.

PROBLEMS WITH RECENT APPROACHES

The aggregated approach proposed by the EC, IMF and OECD assumes that a single number, the output gap, is sufficient to evaluate the effect of business cycle fluctuations on the budget balance. The ECB, recognising that this could be misleading in certain cases, advocates the disaggregated approach. Nevertheless, the ECB's disaggregation method raises two problems: (1) the sum of the sub-aggregates should add up to the total and (2) different deflators are used in the case for different variables, which leads to bias.

Aggregation versus disaggregation bias

The aggregated method assumes that the aggregate output gap describes the cyclical position of the budget balance. Provided that we have the output gap in hand, the only question is the elasticity that defines the relationship between the output gap and each budget element (Figure 1).

[FIGURE 1 OMITTED]

To estimate the output gap, Denis et al. (2002) apply a Cobb-Douglas production function with neutral technological progress to estimate potential output:

[Y.sup.*.sub.t] = TF[P.sub.t][[[L.sub.t](1 - [U.sup.*.sub.t])].sup.[alpha]][K.sup.1 - [alpha].sub.t] (1)

where [Y.sup.*], L, K, [U.sup.*] and TFP denote output, labour input, capital stock, the trend unemployment rate and total factor productivity, respectively. The trend unemployment rate is considered as the NAIRU and estimated by a state-space model (see Denis et al., 2002), while TFP is computed as a Solow residual. Instead of estimating labour ([alpha]) and capital (1 - [alpha]) shares, the EC suggests using national accounts to calibrate them. The output gap is computed in the usual way, namely O[G.sub.t] = [Y.sup.t]/[Y.sub.t.sup.*]. The aggregated approach applies simple elasticities to compute the cyclical position of the relevant GDP components, such as private wages, consumption, corporate profits, etc. These elasticities are derived by estimating the co-movement between output and the corresponding variables.

Unfortunately, this method has four key drawbacks. First, it does not take into account and exploit the consequences of choosing the Cobb-Douglas production form, namely its parameters [alpha] and 1 - [alpha] determine not only the labour and capital share in level, but also the relative weight of disaggregated gaps. That is, the sum of the labour and capital income gap, weighted by labour's and capital's shares, should be equal to the aggregated output gap. In addition, labour and capital shares cannot be assumed to be constant even in the case of developed economies, not to mention transition ones. Second, given that the unemployment rates in transition economies have been influenced by several shocks, the standard relations and state-space estimation therefore yield inappropriate results for elasticities. Third, capital stock and/or TFP are not available for some countries. Moreover, even where they are available, their values are already the result of an estimation process, as they are not observable variables. Fourth, and most important, in certain circumstances the disaggregated approach is a more appropriate method of cyclical adjustment because the aggregate output gap and its elements, such as consumption, profit, etc, can move in opposing directions. The significantly different budgetary implications of these 'atypical' circumstances have been taken into account in some ad hoc analyses (such as EC, 2000), and a few new methods have been proposed (Bouthevillain et al., 2001; Kiss, 2002; Braconier and Forsfalt, 2004).

Given these atypical cases, Boije (2004) argues that the aggregate output gap hides underlying developments. The same output gap can be made up of different gaps in its components, and thus the same aggregate gaps will have a different effect on the economy and the budget. However, the aggregated approach calculates the same effect based on any given aggregate output gap no matter what the values of the sub-aggregates may be. (1) This may explain Cronin and McCoy's result (1999) that the elasticities of budgetary revenue and spending with respect to aggregate output are not constant, although their results may be attributable to the above-mentioned composition effect. Even if elasticities were stable, the elasticity in the aggregate differs if the shares of disaggregated gaps are not constant, which is likely to be true for all countries.

Violation of the aggregation constraint

Since the aggregated approach is appropriate only under very restrictive assumptions, that is, every GDP component is at the same cyclical position, the ECB proposes using a disaggregated method (see Figure 2). In an application of the ECB's method, Bouthevillain et al. (2001) estimate numerous gaps in private wages, employment, consumption, corporate profit and unemployment gaps by using a univariate Hodrick-Prescott (HP) filter. Although this method helps to identify the cyclical positions of the relevant economic factors and is extremely easy to use, there are some problems that limit its usefulness.

[FIGURE 2 OMITTED]

The most important and relevant objection to univariate HP filtering is that it makes no use of theoretical relationship among variables. Bouthevillain et al. (2001) and Mohr (2003) argue that the linear nature of the HP filter ensures theoretical consistency among variables, as the weighted sum of disaggregated HP-filtered gaps equals the aggregate gap. Even though the HP filter is linear, this characteristic cannot be exploited in the field of economic time series because economic time series should be log-transformed in the HP filter (2) and, as a consequence, the aggregation constraint is not satisfied. (3) The section 'Demonstration of the composition effects' estimates the distortion created by the violation of the aggregation constraint.

Another problem is that using only one univariate method may result in an extreme estimation. The inaccuracy of the estimation cannot be realised since the estimation is not controlled by either other reference method or theory. If only univariate methods are applicable, Darvas and Vadas (2005) prove that better results can be achieved by using the combination of several univariate methods. They argue that, from the point of view of policymaking, the stability of the output gap estimate is crucial. Methods that yield extensive revision in the estimated past output gap cannot be used in policy decisionmaking because they may frequently render previous decisions inadequate. (4) Using a revision-based weighting scheme, Darvas and Vadas (2005) find that a multiple-method approach provides more stable output gap estimation than any single univariate method.

Despite the problems with the univariate HP-filtered approach, we do agree that aggregate relying on an output gap leads to the loss of valuable information. Consequently, we also argue for the importance of the disaggregated approach; however, at the same time we seek a method that exploits theoretical relationship among the cyclical components that satisfies the aggregation constraint.

Effect of different deflators

Hitherto, we have considered variables in real terms; however, both tax bases and tax revenues are observed in nominal terms. As a result, real and nominal cyclical positions may have different signs, with one above trend, the other below. Therefore, prices and nominal variables are used. To make the argument more transparent, suppose that the real consumption gap determines the real cyclical position of indirect taxes. Nominal consumption is obtained by multiplying real consumption by the consumer price index (CPI), while indirect taxes are multiplied by the GDP deflator. If the CPI is higher than the GDP deflator, then nominal indirect taxes based on nominal consumption would be higher than indirect taxes based on real consumption. Consider the Hungarian economy in the mid-1990s. Owing to the high inflation rate and tight fiscal policy, the consumption gap was negative in real terms, while the CPI was higher than the GDP deflator. As a result, despite the negative consumption gap, the nominal cyclical position of budget revenues was relatively favourable.

A NEW METHOD FOR MEASURING THE CYCLICAL POSITIONS

In line with the ECB, we agree that the aggregate output gap hides the true state of the underlying processes. However, in the process of disaggregation we insist on respecting the theoretical foundation of the output gap, the existence of a theoretical relationship among cyclical components, and on satisfying the aggregation constraint using time-varying labour and capital income shares (see Figure 3).

[FIGURE 3 OMITTED]

In addition, we also suggest taking into account the effect of different deflators in the disaggregated method.

Deriving the cyclical position

We propose a tractable method capable of decomposing the output gap. Contrary to univariate methods the production function is favourable, since it is based on various factors that define the aggregate gap. The main drawback of the application of the 'full-form' of production function, as in equation (1), is that it involves several estimated variables, such as capital stock and TFP. Note that, since we need only the output gap, these variables are not necessary. The ratio of actual output to potential can be computed by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where CU denotes the level of capacity utilisation; here we apply the Cobb-Douglas form with labour-augmenting technical progress. (6)

There are two important deviations from the IMF, OECD and EC approaches. First, we apply a more realistic time-varying capital share, which can be obtained from either estimation (7) or from national accounts. This specification allows us to avoid the assumption of constant labour and capital income shares. It should also be kept in mind that these shares determine how the aggregate output gap should be decomposed into its components. Second, we argue against the HP-filtered Solow-residual on both theoretical and practical grounds. If TFP is an explanatory variable in the production function, then estimating equation (1) without it results in an omitted variable problem and mis-specification. Using the estimated parameters of this regression and incorporating an HP-filtered residual into the computation of potential GDP cannot, however, be justified. More importantly, in this case the smoothness of potential GDP simply comes from the smoothed disturbance term. Recall that TFP is an unobservable variable. Explaining output gap by the deviation of an unobservable variable from its unobserved potential level can be problematic. Because the CAB plays an important role in policy debates, the use of the TFP variable as a key explanatory variable could yield inappropriate policy decisions. (8)

After simplifying and log-transforming equation (2), we obtain:

[y.sub.t] - [y.sup.*.sub.t] = (1 - [[alpha].sub.t])[c[u.sub.t] - c[u.sup.*.sub.t]] + [[alpha].sub.t][ln(1 - [U.sub.t]) - ln(1 - [U.sup.*.sub.t])] + [[epsilon].sub.gap,t] (3)

where small letters denote the logarithm of corresponding variables. Although equation (3) can be used to estimate potential GDP, the level of capacity utilisation is not available for every country, as is the case with capital stock. Basu and Fernald (2001) show that working hours per worker contain information about capacity utilisation. Firms adjust their capital stock more slowly than their labour input; therefore, higher working hours per worker clearly indicate the more intensive use of capital. Obviously, where capacity utilisation time series are available, this approximation is not necessary.

The parameters of the production function also identify the relationship among the output (y-[y.sup.*]), labour (w-[w.sup.*]) and the capital income ([pi]-[[pi].sup.*]) gaps. The aggregate output gap equals the weighted sum of labour and capital income gaps, where weights are wage ([alpha]) and capital shares (1-[alpha]). As a consequence, the output gap can be decomposed in the following way:

[y.sub.t] - [y.sup.*.sub.t] = [[alpha].sub.t]([w.sub.t] - [w.sup.*.sub.t]) + (1 - [[alpha].sub.t])([[pi].sub.t] - [[pi].sup.*.sub.t]) (4)

where variables with superscript stars denote the potential or trend values of the corresponding variables. (9)

The above-mentioned criteria identify only the share of labour compensation and profit income gaps, not the magnitude of these gaps. Moreover, other real variables and their cyclical components should be determined. In order to achieve this, we have to incorporate a behavioural equation to derive the necessary cyclical component that is not determined by the parameters of the production function.

Obviously, several behavioural equations can be included. However, because the labour-compensation gap determines the direct tax on households, social security contributions and pensions; and the profit gap determines direct tax on corporations, there are only two potential budgetary elements left: unemployment benefits and indirect taxes on household consumption.

As far as unemployment benefits are concerned, the trend unemployment rate is estimated in line with the output gap (see equation (3)). Indirect taxes on households' expenditures are among the most important budget revenues, and, therefore, we incorporate a consumption function, which ensures that the potential value of wages and consumption are connected by theoretical considerations:

[DELTA]c[e.sup.*.sub.t] = [[theta].sub.1] + [[theta].sub.2] (c[e.sup.*.sub.t-1] + [rho][w.sup.*.sub.t-1]) + [[theta].sub.3][DELTA]c[e.sup.*.sub.t-1] + [[theta].sub.4][DELTA][w.sup.*.sub.t] + [[epsilon].sub.ce,t] (5)

where ce denotes the log of private consumption expenditure, and superscript stars again denote the potential of corresponding variables.

In order to incorporate the above equations into our decomposition and to keep our approach tractable and easily reproducible, we develop an alternative framework. Extending the ideas of Laxton and Tetlow (1992), Butler (1996) and St-Amant and van Norden (1997), we apply a multivariate HP filter. The potential values of the wage and profit shares are constrained by equation (4), and the entire system is influenced by equations (3) and (5). To achieve this, we embed the above-mentioned equations into the multivariate HP filter: (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

subject to

[y.sub.t] - [y.sup.*.sub.t] = [[alpha].sub.t]([w.sub.t] - [w.sup.*.sub.t]) + (1 - [[alpha].sub.t])([[pi].sub.t] - [[pi].sup.*.sub.t]

Only one question remains: how to weight ([[omega].sub.i]) the different terms in the optimisation. In fact, there are two possible weighting schemes that do not involve an arbitrary assumption. First, we let every variable have its own scale, that is, [[omega].sub.i] = [[omega].sub.j], [for all] i,j. Second, every variable is normalised, which implies equivalent volatility. Instead of normalising every variable, we set [[omega].sub.i] as [[omega].sub.i] = 1/[[sigma].sub.i.sup.2], where [[sigma].sub.i.sup.2] denotes the variance of ith variable. (11)

The solution to problem (6) provides the potential values of variables and the gaps.

Correcting the effect of different deflators

Although several methods have been proposed for capturing the trend or potential price level, the actual concept of the potential price level is more difficult to interpret. (12) In this paper, we do not address the issue of potential price levels. However, another problem was identified that resembles the composition effect of real variables. We capture this composition effect by recording the difference between the CPI and GDP deflators. In order to understand the basic idea behind our method, it should be noted that nominal variables are first deflated; however, the corresponding deflators differ, variable by variable. For instance, corporate profit is usually deflated by the GDP deflator, while private wages and consumption are deflated by the CPI. As the budget deficit is compared to GDP, the GDP deflator is therefore the relevant one for the budget.

To make the above more explicit, consider BU[D.sub.R,i] = BAS[E.sub.R,i.sup.[beta]] where BUD, BASE, R and [beta] denote ith budgetary revenue or expenditure, its corresponding base, for example personal income tax and wages, variables in real terms, and the elasticity of budgetary revenue or expenditure to its base, respectively. Note that the cyclical component is expressed relative to the output, so that the cyclical component in real terms (C[C.sub.R]) can be obtained by

C[C.sub.R] = BU[D.sub.R,i] / [Y.sub.R] = BAS[E.sup.[beta].sub.R,i] / [Y.sub.R] (7)

Since the budget is evaluated in nominal terms, equation (7) has to be reformulated. Assume that the tax base is deflated by the CPI. In this case BU[D.sub.R,i][P.sub.Y]=BU[D.sub.N,i], BAS[E.sub.R,i][P.sub.CPI]=BAS[E.sub.N,i], where N denotes variables in nominal terms. The cyclical component in nominal terms (C[C.sub.N]) takes the following form:

C[C.sub.N] = BU[D.sub.N,i] / [Y.sub.N] = [(BAS[E.sub.R,i][P.sub.CPI]).sup.[beta]] / [Y.sub.R][P.sub.Y] = C[C.sub.R] [P.sup.[beta]]CPI / [P.sub.Y] (8)

Equation (8) shows that the real cyclical component has to be corrected to obtain the nominal cyclical component if the deflators, in our case GDP and CPI, are different.

Finally, those budget items that are influenced by this gap should be identified, that is, those that are determined by private wages and consumption, namely direct taxes on households, pension and social security contributions, and indirect taxes on households' consumption. Like the cyclical position of the real economy and budget deficit, the whole price gap effect is the weighted average of individual elements deflated by the CPI.

DEMONSTRATION OF THE COMPOSITION EFFECTS

In previous sections, we have identified the theoretical sources of distortions in the aggregate and ECB's disaggregated approaches. In order to demonstrate their magnitude, we estimate cyclical components using aggregated, ECB-type disaggregated and our own approaches to estimate the effect of business cycle fluctuation on the budgets of the US, Japan and the 25 EU Member States. (13) Instead of the production function-based aggregated approach, we apply an earlier technique, namely where potential GDP is derived using an HP filter. (14) This allows us to protect our results from estimation issues, such as the specification of state-space representation, and to emphasise the fundamental problems that these approaches entail.

As for aggregation versus disaggregation bias concerns, we examine the composition effect of aggregation and disaggregation. The main problem of using an aggregated approach is the possibility of leading incorrect policy steps. For instance, a negative output gap automatically generates a negative cyclical component and suggests a tax reduction. However, some relevant GDP components, such as profits, could be above their trend, implying a positive cyclical component and tax increase.

To estimate the size of the composition effect of disaggregation, we compute cyclical budget components based on the aggregated and disaggregated methods. The third column of Table 1 reveals that the difference between two cyclical components is at times sizeable. The maximum difference between two cyclical components is higher than 4% in the case of Luxembourg. Similar considerable discrepancies can be found in other countries. The third to last column of Table 1 shows the frequencies of moderate bias, that is, where the discrepancy between the two cyclical component estimations is at least 0.1% of GDP. Excluding the US, this moderate bias occurs in almost the entire sample. The serious bias, that is, where the bias is more than 0.5% of GDP, occurs in roughly half the sample. The distortion becomes more policy related if we consider the frequency of those cases when the two methods yield different signs, that is, provide a misleading cyclical indication for fiscal tightening or loosening. In the case of France, the aggregated method provides a wrong indication in 33% of all cases (see the last column). This cannot even be considered an extreme result, as the average of 27 countries is 15%. Another noteworthy result is that these differences are positively auto-correlated, which means that an aggregated approach results in persistent bias. This is not surprising if we recall the stylised fact that consumption and wages, which are the most important components of fiscal revenue, exhibit less variance than GDP. (15) In addition, due to the so-called habit formation, consumption adjusts sluggishly to changes in income. (16)

As for violation of the aggregation constraint, the proposed ECB method does not satisfy the aggregation constraint, which generates another form of bias. Here we computed the aggregate output gap and the weighted sum of the gaps of GDP components. One should note that the disaggregated approach tends to provide higher output gap estimation than the aggregate one does (see the third to fifth columns of Table 2). Owing to the non-linear logarithmic transformation, it is not surprising that we obtain a fairly asymmetric bias. As a consequence, if one uses an unconstrained HP filter on log-linearised time series, systematic bias, which derives from the violation of the aggregation constraint, is likely to occur. According to our estimation, the maximum effect of this bias on the cyclical component could be as high as 2% of GDP in the case of Greece and Portugal (see seventh column of Table 2). The next to last column of Table 2 shows the frequency of moderate bias, that is, where the discrepancy between the two cyclical component estimations is at least 0.1% of GDP. Apart from the US and the 10 new EU Member States, where the samples are quite short, the violation of the aggregation constraint causes moderate bias in 16%-84% of the sample. The last column of Table 2 shows the frequency of serious bias, that is, where distortion is more than 0.5% of GDP, which is between 2% (Estonia) and 45% (Portugal) of the sample. In short, unconstrained decomposition could be a considerable source of bias.

To evaluate the distortion coming from aggregation versus disaggregation and the violation of aggregation constraint simultaneously, we decompose the maximum differences between the aggregated approach and our constrained disaggregated method to these two sources (see Table 3). In line with our expectations, fourth column reveals that much of the distortion comes from the lack of disaggregated information, namely the varying cyclical structure behind the same aggregate output gap. Of course, this does not mean that the lack of satisfied aggregation constraint plays a negligible role. In some cases they do amplify each other, see for instance Ireland and Luxembourg among the others. However, in other cases the two biases work against each other, and thus the entire bias is smaller, for example Finland and France. If one uses a univariate disaggregated approach without taking into account the aggregation constraint, the bias presented in Table 2 occurs.

As for the effect of different deflators concerns, Table 4 provides some estimation results about the price effect caused by using a different GDP deflator and CPI. Obviously, its long effect equals zero; however, it could have a considerable impact in certain periods. For instance, in Portugal the price effect caused real and nominal CAB to differ by approximately 6 percentage points.

CASE STUDIES (17)

Our results demonstrated that aggregated cyclical positions can differ from the disaggregated cyclical positions corrected by deflators--in other words, that these so called 'atypical' circumstances are in fact rather common (EC, 2000). According to one possible explanation, the fiscal adjustments or expansions can affect various GDP components differently, and this composition effect remains hidden in the standard measures of the aggregated cyclical positions. This effect could be partially removed if internationally comparable data were available on the tax contents of public spending. (18) Another possible explanation is that labour market developments can also explain sizeable composition effects. Employment and wages can on the one hand respond to external shocks with significant lags, while on the other hand macroeconomic adjustments often rely on wage agreements to restore competitiveness and the share of capital income.

In the following sections we present three periods in three countries (Finland, Hungary and Italy), which have been chosen because they exhibit sizeable differences between their aggregated cyclical positions and the disaggregated cyclical positions, corrected by deflators. A more precise calculation of cyclical positions becomes extremely relevant if policymakers rely on CABs when evaluating how far current fiscal positions are from medium-term objectives. If the aggregated approach distorts CABs, the orientation of fiscal policy could be either tighter or looser than targeted.

Finland 1988-1992

One example of atypical circumstances can be illustrated in the case of Finland, where changes in the aggregate output gap and changes in its composition have differed considerably. Figure 4 displays how these developments affect the estimation of cyclical components. One reason is the occurrence of different shocks at the same time. Another is the response lag, for example in the case of employment.

[FIGURE 4 OMITTED]

Our results show that the disaggregated cyclical component corrected by deflators indicates a much higher cyclically adjusted deficit than the aggregated cyclical component in 1992. (19) This would have called for a smaller fiscal loosening in 1992 or at least a tighter fiscal stance in 1993-1994.

During the 1980s, Finland experienced a significant increase in household debt supported by tax incentives and financial deregulation. Fiscal policy was also expansionary, and therefore domestic demand was relatively strong. Exports were supported by the favourable terms of trade. As a consequence, the economy was booming, and unemployment was unusually low.

This situation changed dramatically in the period 1990-1992, when external conditions deteriorated following the abolition of the bilateral trade agreement with the former Soviet Union. At the same time, a number of export goods were negatively affected by falling world market prices. These initial shocks were followed by a rapid recovery in exports in 1992. The fall of domestic demand was less severe, but more prolonged; household consumption and housing investment declined following an interest shock to household debt and a large increase in the average unemployment rate.

The composition effect of GDP became important, because the capital income share decreased. The effects of the decline in demand were accompanied by a financial crisis in the banking sector. This profit squeeze was more severe than the drop in the wage bill, partly because employment responded to the decline in production with a significant lag.

The deceleration of wage inflation was insufficient to restore the competitiveness of exports, and capital outflows accelerated, necessitating exchange rate depreciation. (20) Following the devaluation of the currency, the labour market partners accepted a two-year centralised wage agreement, freezing nominal wages in 1992.

The composition of the deflators has also changed considerably. In 1988 the GDP deflator was significantly higher than the CPI because of higher deflators for exports, capital formation and government final expenditures. In 1991-1992, the GDP deflator turned out to be lower than the CPI because of the lower deflator for exports and capital formation. In 1992 the deflator for government final expenditures also fell lower than the CPI; however, until then it had been significantly higher. This was achieved by targeting zero growth for total central government expenditures in real terms.

Hungary 1995-2003

In the case of Hungary, the sample period covers two episodes. The first is an example of an inflationary adjustment of the wage share and private consumption in a period when economic growth was determined by export performance. The second is an example of the expansion of domestic demand in a period of weak external demand. Figure 5 displays the cyclical component estimations of different methods.

[FIGURE 5 OMITTED]

The situation in the early 1990s resembles the Finnish experience. After the collapse of trade with Eastern Europe, production fell dramatically. With significant lags, unemployment grew rapidly, some firms went bankrupt and the banking sector experienced a crisis. At the same time, market wages, public expenditure and household consumption did not adjust to this crisis and these delays in macroeconomic adjustment caused the external balance to deteriorate. (21) Confidence in the currency was shaken, and, after the Mexican crisis, capital outflows intensified.

In March 1995 a stabilisation programme was launched in order to reverse the growing level of external indebtedness and to avert the risk of an external crisis. (22) Since wages in the public and private sector were set prior to the devaluation and indirect tax increases and were not adjusted afterwards, this unexpected inflation sharply reduced real wages. The higher level of inflation was not compensated for in the following year either, causing real wages to fall by 17% in the period 1995-1996. The distributional consequences of the surprise inflation were a significant decrease in the wage share and an increase in capital's share in income and in competitiveness. The disaggregated approach in this case would clearly show the different budgetary implications of this change. However, it would only capture effects in real terms. Actually, the effects on the nominal deficit were less significant, and this distortion can be partially corrected by taking into account the price gap. Full correction would only be achieved by defining the price gap as the size of the surprise inflation. (23)

Following this adjustment, growth of wages and consumption remained moderate for a couple of years. Real wage growth accelerated from 2000 to 2003, and consumption also did with a one-year lag. Domestic demand was boosted by higher private wages, plus a sharp increase in minimum wages, expansionary fiscal policy, including higher public wages, and a significant increase in household debt supported by tax incentives and changes in the financial system. From the end of 2000, the growth of external demand and investment was below their corresponding trends. As a consequence, a twin-deficit problem re-emerged.

The composition of deflators also changed markedly, mainly reflecting government policy. In 1995-1996 the GDP deflator was significantly lower than the CPI because the surprise inflation was not compensated for in the public sector; therefore the deflator of government final expenditures increased only moderately. The opposite happened in 2001-2003, when the exchange rate appreciated, but the growth of the CPI was muted. In this period, the growth of the GDP deflator did not decrease owing to a higher deflator for government final expenditures caused by a significant wage increase in the public sector. Regulated prices also had a significant impact on the CPI in the period 1995-1999; their growth exceeded that of non-regulated consumer prices by 8.5% in 1995-1996. This can be attributed to the fact that utility charges had been kept low earlier and a gradual adjustment became necessary after the privatisation of public utilities. However, this adjustment was suspended in 2000-2003 when regulated prices were increased in line with non-regulated prices.

Our results show that a disaggregated cyclical component corrected by deflators indicates a higher cyclically adjusted deficit in 2003 than the aggregated method does. On the one hand, it reveals that the underlying deficit became more unsustainable. On the other hand, it implies that the short-term fiscal costs of a necessary adjustment of wages and consumption could be sizeable, since positive cyclical components of taxes can disappear.

Italy 1991-1998

Italy is an example of a switch from wages to capital incomes and shows correspondingly weak private consumption in a period when economic growth was determined by export performance. The effect of these developments can be seen at Figure 6.

[FIGURE 6 OMITTED]

On the external side, continued losses in competitiveness caused exports to fall during 1991. However, domestic demand, mainly private consumption, remained relatively strong. In any case, real profits and investments were squeezed in the private sector against a background of high interest rates, deteriorating net exports and accelerating wage inflation.

In 1992, after the financial crisis and the lira's exit from the Exchange Rate Mechanism (ERM), the currency depreciated significantly, after which the export sector became a more important factor in economic growth. In 1992-1993, losses in aggregate output were dampened by a surge in net exports. The economic expansion of 1994-1995 was also linked to strong exports and investment activity. Net exports declined, however, in the period 1996-1998 because of several factors, for example a currency appreciation and the crisis in Asia.

Real wage moderation and higher labour productivity combined to contain the inflationary effects of the depreciation. The automatic indexation of wages was replaced by indexation to the official inflation target in 1993, with the possibility of adjustments from 1996. As a consequence, purchasing power decreased during the inflation 'overshoot' in 1994-1995, but this was followed by exceptional wage moderation. Nominal wage increases stayed below the inflation rate in 1993-1995, although real wages ceased to decline in 1996. The rate of unemployment increased quickly, both after the first crisis in 1992 and after the drop in net exports in 1996. These developments resulted in a switch from wage to capital income and correspondingly weak private consumption. From 1997, a gradual recovery began for both wages and consumption.

The price gap was not affected by surprise inflation because the inflation overshoot was not sizeable and was realised as an overshoot of the official target rather than a surprise compared to the expectations. Despite some fluctuation, Italy's performance in terms of inflation was surprisingly good. In 1992-1995 the price gap was positive, which means that the fiscal situation seemed to be more unfavourable than it actually was; this situation reversed in 1996-1998 when the price gap turned negative, making the deficit apparently more favourable than the actual underlying deficit. The explanation was that the CPI, which is the deflator of the major revenues, was lower than the GDP deflator. (24) Regulated prices, with the exception of 1995-1996, increased more than the other non-discretionary components of the CPI. (25) Without these discretionary effects, the price gap would have been less positive in 1992-1994 and even more negative in 1997-1998.

Our results show that a disaggregated cyclical component corrected by deflators indicates a lower cyclically adjusted deficit than the other estimations of cyclical component in 1998. Other analyses also find that tax developments cannot be fully explained by cyclical and discretionary factors (Kremer et al., 2006). In fact, this unexplained residual, which is calculated by employing the disaggregated cyclical adjustment of the ECB, would disappear if our method was employed. Of course, none of the estimations would have justified the fiscal loosening that was implemented in 1998. Further cuts in the deficit, however, could have been postponed by misclassifying cyclical improvements in the following years as reductions of the structural deficit. The disaggregated cyclical component corrected by deflators improved by 1.1% of GDP in 1998-2000, while the aggregated cyclical component remained broadly unchanged. If the temporary nature of this improvement had already been identified, then consolidation measures could have been implemented in 1999-2000, possibly avoiding the deficit overshoots starting in 2001. (26)

Summary

In this paper we have surveyed the two main official cyclical adjustment methods, namely the aggregated approach as adopted by the EC, IMF and OECD, and the unconstrained disaggregated approach championed by the ECB.

The main advantage of the aggregated approach is that it uses the production function and hence, incorporates a theoretical background into cyclical adjustment. However, it assumes that any other GDP components that are relevant in terms of budget revenue and expenditure are in the same cyclical position as GDP, which is obviously rarely the case. Moreover, aggregated approaches do not exploit the information content of wage and capital shares, which are used to estimate the production function.

The ECB's disaggregated approach is designed to take into consideration the possibility of the different cyclical positions of real variables. It filters each relevant variable, one by one, using the univariate HP filter. However, this procedure can be criticised for its lack of theoretical considerations. In addition, there are serious implications implied by the application of the univariate HP filter. Since economic variables, due to their exponential nature, are log-transformed, the ECB-type disaggregation cannot fulfill the aggregation criterion.

The above-mentioned drawbacks, namely the lack of disaggregation or theory and the violation of the aggregation constraint, produce considerable bias in the estimation of cyclical components. While the first one involves the possibility of wrong policy implications, the latter, due to its non-linear transformation, causes systematic bias.

Since both a theoretical foundation and disaggregation are essential when seeking to obtain appropriate cyclical components, we introduce a method that is able to meet these requirements. First, we insist on the production function-based output gap; however, this implies difficulties owing to the availability of data. Fortunately, since we are only interested in the output gap rather than the full form of the production function, the capital stock and TFP data are not needed in our method. Another important implication of the production function is that the aggregation constraint should not only be satisfied, but also that the constraint is set by the capital and labour income share. In our approach, we restrict the estimation procedure by using these shares. Finally, to derive the remaining cyclical component, we apply another behavioural equation, namely a consumption function. The system is estimated by a multivariate HP filter. We also showed that if the deflators of variables are different then the real and nominal cyclical component can differ significantly. This paper provides a method that corrects this difference.

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Braconier, H and Forsfalt, T. 2004: A new method for constructing a cyclically adjusted budget balance: The case of Sweden. National Institute of Economic Research Working Paper No. 90, April.

Brunila, A, Hukkinen, J and Tujula, M. 1999: Indicators of the cyclically adjusted budget balance: The Bank of Finland's experience. Bank of Finland discussion Papers No 1/99.

Boije, R. 2004: The general government structural budget balance. Sveriges Riksbank Economic Review 1/2004, Sveriges Riksbank.

Bouthevillain, C, Cour-Thimann, P, van den Dool, G, Cos, PH, Langenus, G, Mohr, M, Momigliano, S and Tujula, M. 2001: Cyclically adjusted budget balances: Art alternative approach. Working paper No. 77, European Central Bank, September 2001.

Buti, M and van den Noord, P. 2003: Discretionary fiscal and policy and elections: The experience of the early years of EMU. Economics Department Working paper No. 351, OECD.

Butler, L. 1996: A semi-structural method to estimate potential output: Combining economic theory with a time-series filter. The Bank of Canada's New Quarterly Projection Model' Part 4, Technical Report No. 77, Bank of Canada.

Carroll, CD, Overland, JR and Well, DN. 2000: Saving and growth with habit formation. American Economic Review 90(3): 1-15.

Chalk, NA. 2002: Structural balances and all that: Which indicators to use in assessing Fiscal policy. IMF Working paper No. 102/101.

Coricelli, F and Ercolani, V. 2002: Cyclical and structural deficits on the road to accession: Fiscal rules for an enlarged European Union. Discussion paper No. 3672, December 2002, Centre for Economic Policy Research.

Cronin, D and McCoy, D. 1999: Measuring structural budget balances in a fast growing economy: The case of Ireland. Technical paper No. 4/RT/99, Central Bank of Ireland.

Darvas, ZS and Vadas, g. 2005: A new method for combining detrending techniques with application to business cycle synchronization of the new EU members. MNB Working paper No. 5/2005, Magyar Nemzeti Bank, August 2005.

Denis, C, Mc Morrou, K and Roger, W. 2002: Production function approach to calculating potential growth and output gaps--Estimates for the EU member states and the US. Economic papers No. 176, European Commission, Directorate-general for Economic and Financial Affairs, September 2002.

European Commission. 2000: Public finances in EMU--2000. Report of the Directorate for Economic and Financial Affairs, Reports and Studies, No. 3, May 2000.

Kremer, J, Rodrigues Braz, C, Brosens, T, Langenus, G, Momigliano, S and Tujula, M. 2006: A disaggregated framework for the analysis of the structural developments in public finances. ECB working paper No. 579, January.

Kiss, GP. 2002: A fiskalis jelzoszamok uj megkozelitesben. Kozgazdasagi Szemle, 2002/4 in Hungarian.

Kiss, GP. and Vadas, G. 2004: Mind the gap--Watch the ways of cyclical adjustment of the budget balance. MNB Working paper No. 7/2004, Magyar Nemzeti Bank, June 2004.

Laxton, D and Tetlow, R. 1992: A simple multivariate Jilter for the measurement of potential output. Technical Report No. 59, Bank of Canada.

Mohr, M. 2003: Presentation at Frankfurt University, 3 June 2003.

Orban, G and Szapary, GY. 2004: The stability and growth pact from the perspective of the new member states. MNB Working paper No. 4/2004, May 2004.

St-Amant, P and van Norden, S. 1997: Measurement of the output gap: A discussion of recent research at the Bank of Canada. Technical Report No. 79, Bank of Canada.

Stock, JH and Watson, MW. 1998: Business cycle fluctuation in U.S. macroeconomic time series. NBER Working paper series 6528, April 1998.

Van den Noord, P. 2000: The size and the role of automatic fiscal stabilizers in the 1990s and beyond. OECD Working paper.

(1) For instance, suppose a fictive example in which the first economy is hit by a foreign demand shock, that is, has a negative export gap, while the second economy faces a negative consumption shock. Since exports have a smaller direct effect on the budget position than consumption, the cyclical effect on the budget is smaller in the first economy. Meanwhile, the aggregate approach reports the same cyclical effect.

(2) The general form of the univariate HP filter is min[[summation][(x - [x.sup.*]).sup.2] + [lambda][summation][([DELTA]x - [DELTA][x.sub.-1.sup.*]).sup.2]]. Note that economic time series generally grow exponentially, which means that [DELTA][x.sub.t] also increases over time. As a consequence, the second smoothness term in the HP filter would give higher importance to the end of the sample. Log transformation renders the economic time series to I(1) series, implying that [DELTA][x.sub.t] becomes constant and thus avoids over-weighting.

(3) It is apparent if X + Y = Z and HP(X) + HP(Y) = HP(Z) then x + y > z, when X, Y > 1 thus HP(x) + HP(y) > HP(z), where small letters denote the logarithm of variables.

(4) Consider the case when the output gap estimation for period t at period t is positive, implying fiscal tightening, while the estimation for the same period at period t + k becomes negative, indicating that the fiscal tightening was inadequate policy decision.

(5) The Gauss code for the two official approaches and our method is available as QM&RBC Codes 159 at www.repec.org or http://vadasg.extra.hu.

(6) Neutral technological progress is not justified by empirical work.

(7) For a Kalman filter estimation of the time-varying capital share, see Kiss and Vadas (2004).

(8) Nevertheless, if incorporating TFP is desired, then this can be done by simply replacing TFP with TF[P.sup.*] in the denominator and extending equation (3) with an additional [[alpha].sub.t](ln TF[P.sub.t] - ln TF[P.sup.*.sub.t]) term.

(9) To understand the derivation of this constraint, divide [Y.sub.t.sup.*] = [W.sub.t.sup.*] + [[PI].sub.t.sup.*] by [Y.sub.t] and rearrange the right-hand side to obtain

[Y.sup.*.sub.t] / [Y.sub.t] = [W.sub.t] / [Y.sub.t] [W.sup.*.sub.t] / [W.sub.t] + [[PI].sub.t] / [Y.sub.t] [[PI].sup.*.sub.t] / [[PI].sub.t]

Note that labour and capital income shares then enter into the constraint, namely [W.sub.t]/[Y.sub.t] = [[alpha].sub.t] and [[PI].sub.t]/[Y.sub.t] = 1 - [[alpha].sub.t]. If [x.sub.t] - [x.sub.t.sup.*] is small then [X.sub.t] - [X.sub.t.sup.*] - 1 [approximately equal to] [x.sub.t] - [x.sub.t.sup.*], we obtain equation (4).

(10) Based on the empirical literature, we restrict the cointegration vector to [1 -1] in the consumption equation. Note that other cointegration vectors would imply 100% or minus infinity saving rate, which is unacceptable from both a theoretical and an empirical point of view. However, it is technically possible to assume other cointegration vectors and to estimate [rho] in line with the other parameters.

(11) To understand why this weighting scheme provides the same result as the normalisation, consider the normalised [x.sub.t]

[x.sub.t] = [x.sub.t] - [[bar.x].sub.t] / [[sigma].sub.x]

Now the minimisation problem has the following form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Note that [x.sub.t.sup.*] can be estimated by [x.sub.t.sup.*] = [[sigma].sub.x][x.sub.t.sup.*] + [[bar.x].sub.t.sup.*], which results

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(12) For instance, Buti and Van den Noord (2003), Kiss (2002) and Denmark in the annex of Bouthevillain et al. (2001). Based on their results, the Danish price gap from 1999 to 2000 could lift the cyclical component by 0.3% of GDP.

(13) We use GDP, private consumption and labour income share data taken from the EC's AMECO database. The fiscal elasticities of the 15 existing EU Member States plus the 10 new Member States are borrowed from Bouthevillain et al. (2001) and Orban and Szapary (2004), which are fairly close to the estimate of Coricelli and Ercolani (2002). In the case of Japan and the US, we apply unit elasticities to items and multiply them by the proportion of relevant fiscal revenues in the budget.

(14) Moreover, at present some EU Member States are allowed to compute the output gap using an HP filter.

(15) See, for instance, Stock and Watson (1998).

(16) See Carroll et al. (2000).

(17) Our aim is to display the difference between methodologies and not to reproduce exactly the numbers of any institutions. Thus cyclical components presented in case studies are our estimation.

(18) If data on public taxes are not available, then one can focus on the main items, namely personal income tax and social security contributions paid by public employers and employees. The cyclical component can be adjusted by the effects of public wage shocks by calculating a public wage gap between public and private wage indexes. This public wage gap should be subtracted from or added to the cyclical wage gap as estimated using our disaggregated methodology.

(19) Significant differences in aggregated cyclical components can also be recognised when comparing the estimations of the EC, the IMF, and the OECD with the alternative estimations of the Bank of Finland. (see Brunila et al., 1999.)

(20) The markka was devalued by 12.3% in relation to the ECU on 15 November 1991.

(21) In 1994, the external debt service burden reached 42% of exports.

(22) The first step was a 9% depreciation of the currency, followed by the adoption of a pre-announced crawling peg system with a relatively narrow band. This was accompanied by the introduction of a temporary surcharge on imports of consumer goods.

(23) This concept is closer to the inflation gap as defined in Buti and Van den Noord (2003).

(24) The reason behind the higher GDP deflator was the higher deflators of government consumption, which is by definition outside the paper's scope.

(25) The driving force behind this higher increase was the high regulated price increase of goods and rents, rather than the increase in utility charges.

(26) The deficit exceeded the 3% of GDP reference value in 2001-2005 except for 2002, when it was 2.9% of GDP. This overshooting was revealed by statistical revisions of fiscal data in 2005.

GABOR P KISS (1) AND GABOR VADAS (1,2)

(1) Economics Department, Magyar Nemzeti Bank, H-1850, Szabadsag ter 8/9, Budapest, Hungary. E-mail: vadasg@mnb.hu

(2) Department of Economics, Central European University, H-1051, Nador 9, Budapest, Hungary
Table 1: Aggregation versus disaggregation bias

Country Trimmed sample Cyclical components (b)
 (a)
 Max. Avg. Var.
 [DELTA]CC [DELTA]CC [DELTA]CC

USA 1962-2001 0.5 0.1 0.11
Japan 1962-2001 1.0 0.3 0.24
Austria 1962-2001 0.6 0.2 0.14
Belgium 1962-2001 1.3 0.5 0.34
Cyprus 1992-2001 1.4 0.9 0.54
Czech Rep. 1992-2001 0.6 0.3 0.15
Denmark 1962-2001 0.8 0.3 0.19
Estonia 1995-2001 1.0 0.7 0.38
Finland 1962-2001 2.3 0.8 0.65
France 1962-2001 1.4 0.5 0.41
Germany 1967-2001 1.8 0.4 0.40
Greece 1962-2001 2.6 0.5 0.44
Hungary 1992-2001 1.6 0.9 0.30
Ireland 1962-2001 1.6 0.4 0.32
Italy 1962-2001 1.3 0.4 0.26
Latvia 1997-2001 0.9 0.8 0.17
Lithuania 1997-2001 1.9 1.0 0.75
Luxembourg 1962-2001 4.2 1.0 0.95
Malta 1997-2001 0.9 0.3 0.29
Netherlands 1962-2001 1.3 0.4 0.27
Poland 1992-2001 1.5 0.5 0.44
Portugal 1962-2001 2.7 0.5 0.61
Slovakia 1995-2001 0.6 0.2 0.24
Slovenia 1992-2001 1.6 0.9 0.45
Spain 1962-2001 0.9 0.3 0.26
Sweden 1962-2001 2.2 0.8 0.59
UK 1962-2001 1.2 0.4 0.34

Country Cyclical components (b)

 Autocorr. Moderate Serious Opposite CC
 of [DELTA]CC bias 0.1< bias 0.5< sign (%)
 [DELTA]CC [DELTA]CC
 (%) (%)

USA Positive 47 0 7
Japan Positive 71 16 7
Austria Positive 56 2 9
Belgium Positive 87 31 24
Cyprus No 55 45 27
Czech Rep. No 80 7 7
Denmark Positive 78 9 7
Estonia No 67 42 25
Finland Positive 80 53 16
France Positive 82 40 33
Germany Positive 70 30 3
Greece Positive 80 33 18
Hungary Positive 80 60 7
Ireland Positive 78 24 29
Italy Positive 80 33 9
Latvia Positive 70 40 20
Lithuania No 70 50 10
Luxembourg Positive 91 62 13
Malta No 70 50 30
Netherlands Positive 87 29 7
Poland No 73 47 7
Portugal Positive 71 24 16
Slovakia No 42 8 0
Slovenia Positive 80 47 7
Spain Positive 73 22 13
Sweden Positive 82 60 20
UK Positive 71 33 24

Abbreviations: CC, cyclical component; agg., aggregate approach; disagg,
disaggregated approach; agg. const., aggregation constraint; opp.,
opposite.

(a) Due to the endpoint problem of HP filter, we ignore 2 years from
both ends of samples (eg every sample ends at 2003).

(b) max., avg. and var. denote the maximum, average and standard
deviation of difference in cyclical components as a percentage of GDP.
The significance of auto-correlation of cyclical component differences
is tested by Ljung-Box Q-statistics. Moderate bias indicates the
frequency when the difference between cyclical components is at least
0.1% of GDP. Serious bias indicates the frequency when the difference
between cyclical components is at least 0.5% of GDP. While opp. CC sign
denotes the frequency of those cases when two methods provide different
signs, that is, misleading cyclical indication of aggregated approach.

Table 2: Violation of aggregation constraint

Country Trimmed sample (a) Difference between output gaps (b)

 Min. Max. Avg. Var.

USA 1962-2001 -0.1 0.0 0.0 0.0
Japan 1962-2001 -0.7 0.0 -0.2 0.0
Austria 1962-2001 -0.2 0.0 -0.1 0.0
Belgium 1962-2001 -0.3 0.0 -0.1 0.0
Cyprus 1992-2001 -2.0 0.2 -0.9 0.2
Czech Rep. 1992-2001 -0.1 0.0 0.0 0.0
Denmark 1962-2001 -0.3 0.0 -0.1 0.0
Estonia 1995-2001 -0.4 -0.1 -0.3 -0.1
Finland 1962-2001 -1.1 0.1 -0.2 0.1
France 1962-2001 -1.1 0.1 -0.2 0.1
Germany 1967-2001 -0.2 0.0 -0.1 0.0
Greece 1962-2001 -4.7 0.9 -0.5 0.9
Hungary 1992-2001 -2.0 0.7 -1.0 0.7
Ireland 1962-2001 -1.0 0.1 -0.2 0.1
Italy 1962-2001 -0.4 0.0 -0.1 0.0
Latvia 1997-2001 -0.7 -0.3 -0.6 -0.3
Lithuania 1997-2001 -1.9 -0.4 -0.8 -0.4
Luxembourg 1962-2001 -2.1 0.1 -0.4 0.1
Malta 1997-2001 -0.1 0.0 -0.1 0.0
Netherlands 1962-2001 -0.3 0.0 -0.1 0.0
Poland 1992-2001 -1.7 0.0 -0.5 0.0
Portugal 1962-2001 -6.2 0.4 -1.0 0.4
Slovakia 1995-2001 -0.1 0.0 0.0 0.0
Slovenia 1992-2001 -0.5 -0.1 -0.3 -0.1
Spain 1962-2001 -0.3 0.0 -0.1 0.0
Sweden 1962-2001 -0.5 0.0 -0.1 0.0
UK 1962-2001 -0.5 0.0 -0.1 0.0

Country Cyclical components (c)

 Max Moderate Serious
 [DELTA]CC bias 0.1 < bias 0.5 <
 [DELTA]CC (%) [DELTA]CC (%)

USA 0.0 2 0
Japan 0.2 68 11
Austria 0.1 16 0
Belgium 0.2 30 0
Cyprus 0.8 23 16
Czech Rep. 0.0 0 0
Denmark 0.2 41 0
Estonia 0.2 23 2
Finland 0.7 68 11
France 0.4 68 11
Germany 0.1 11 0
Greece 1.9 82 36
Hungary 0.7 32 25
Ireland 0.3 61 9
Italy 0.2 27 0
Latvia 0.2 20 11
Lithuania 0.6 20 9
Luxembourg 1.3 73 23
Malta 0.1 7 0
Netherlands 0.2 32 0
Poland 0.8 27 7
Portugal 2.2 84 45
Slovakia 0.0 0 0
Slovenia 0.2 23 2
Spain 0.1 39 0
Sweden 0.4 50 2
UK 0.2 34 0

(a) Due to the endpoint problem of HP filter, we ignore 2 years from
both ends of samples (eg every sample ends at 2003).

(b) Violation of aggregation constraint displays the effect of
unsatisfied constraint. Min and max denote the minimum and maximum
differences between the aggregate output gap and the sum of
disaggregate gaps as a percentage of GDP. avg. and var. denote the
average and standard deviation of this difference.

(c) Max [DELTA] CC denotes the maximum difference between two cyclical
components as a percentage of GDP. Moderate bias indicates the
frequency when the difference between cyclical components is at least
0.1% of GDP. Serious bias indicates the frequency when the difference
between cyclical components is at least 0.5% of GDP.

Table 3: Maximum bias between aggregate approach and CMHP

Country Trimmed Maximum entire bias in cyclical components
 sample (b)
 (a)
 Date Bias comes Bias comes Entire
 from agg. from bias
 approach violation
 of agg.
 const.

USA 1962-2001 1982 0.5 0.0 0.5
Japan 1962-2001 1970 -0.9 -0.1 -1.0
Austria 1962-2001 1970 -0.6 -0.1 -0.7
Belgium 1962-2001 1973 -1.2 -0.1 -1.3
Cyprus 1992-2001 1996 -1.1 -0.3 -1.4
Czech Rep. 1992-2001 2000 -0.5 -0.1 -0.6
Denmark 1962-2001 1988 -0.6 -0.2 -0.8
Estonia 1995-2001 1999 1.2 -0.1 1.0
Finland 1962-2001 1992 2.7 -0.4 2.3
France 1962-2001 1991 1.8 -0.4 1.4
Germany 1967-2001 1991 -1.8 0.0 -1.8
Greece 1962-2001 1973 -2.7 0.1 -2.6
Hungary 1992-2001 1999 -1.0 -0.2 -1.2
Ireland 1962-2001 1978 -1.3 -0.3 -1.6
Italy 1962-2001 1969 -1.2 -0.1 -1.3
Latvia 1997-2001 1997 0.9 -0.1 0.9
Lithuania 1997-2001 1999 2.6 -0.7 1.9
Luxembourg 1962-2001 1974 -3.4 -0.8 -4.2
Malta 1997-2001 2000 -0.8 0.0 -0.8
Netherlands 1962-2001 2000 -1.1 0.0 -1.1
Poland 1992-2001 2000 -1.2 -0.3 -1.5
Portugal 1962-2001 1973 -1.4 -1.3 -2.7
Slovakia 1995-2001 1998 0.6 0.0 0.6
Slovenia 1992-2001 1999 -1.4 -0.2 -1.6
Spain 1962-2001 1989 -0.9 -0.1 -0.9
Sweden 1962-2001 1977 2.4 -0.2 2.2
UK 1962-2001 1973 -1.2 -0.1 -1.2

(a) Due to the endpoint problem, we ignore 2 years from both ends of
samples (eg every sample ends at 2003).

(b) As a percentage of GDP.

Table 4: Effects of different deflators

Country Period Price effect (a)

 Min CC Max CC Average CC Var CC

USA 1960-2003 0.2 0.7 0.1 0.2
Japan 1960-2003 1.5 0.6 0.0 0.3
Austria 1960-2003 -0.7 0.4 0.0 0.2
Belgium 1960-2003 -0.5 2.0 0.1 0.4
Cyprus 1994-2003 0.3 0.3 0.0 0.2
Czech Rep. 1990-2003 1.3 0.7 -0.2 0.5
Denmark 1960-2003 2.1 1.9 -0.1 0.8
Estonia 1993-2003 -0.6 1.9 -0.1 0.7
Finland 1960-2003 -2.2 1.2 -0.1 0.7
France 1960-2003 -1.3 0.8 0.0 0.4
Germany 1965-2003 1.0 0.5 0.0 0.3
Greece 1960-2003 7.1 1.9 -0.2 1.3
Hungary 1990-2003 0.9 0.8 0.1 0.5
Ireland 1960-2003 -1.3 3.3 -0.1 0.8
Italy 1960-2003 -5.9 4.3 -0.2 1.2
Latvia 1995-2003 0.8 2.8 0.2 1.1
Lithuania 1995-2003 1.4 1.1 0.1 0.7
Luxembourg 1960-2003 NA NA NA NA
Malta 1995-2003 0.8 0.7 0.0 0.5
Netherlands 1960-2003 -2.7 3.1 0.0 0.8
Poland 1990-2003 -1.2 6.1 1.1 2.1
Portugal 1960-2003 6.5 1.1 -0.3 1.4
Slovakia 1993-2003 0.2 1.2 0.5 0.5
Slovenia 1990-2003 2.7 1.0 -0.6 1.3
Spain 1960-2003 2.4 0.8 -0.1 0.5
Sweden 1960-2003 -2.8 3.4 -0.1 0.9
UK 1960-2003 -1.0 0.7 0.0 0.4

(a) Price effect denotes the minimum, maximum and average effects on
cyclical component resulting from different deflators.
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Date:Jun 1, 2007
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