THE POTENTIAL OUTPUT ESTIMATION AND THE PROBLEM OF REVISIONS

The use of univariate statistical techniques (such as the Hodrick Prescott filter, thereafter HP) to derive measures of the level of potential output (and of the output gap) have been recognized to have at least two serious drawbacks, see in particular Kuttner (1994). First, potential output measures generated with these techniques lack a substantive economic foundation. Second, such techniques generally allow for identifying turning points in the potential output trajectory only with a considerable lag and can thus lead to large ex-post revisions. This can substantially exacerbate the uncertainty associated with real-time potential output estimates.

Commission services is based on the so called Cobb-Douglas production function approach. (63₎

This approach relates potential output to the capital stock, hours worked, the Non-Accelerating Inflation Rate of Unemployment (NAIRU) and the permanent component of Total Factor Productivity (TFP). It is hence better grounded in economic theory than a univariate type of approach. However, the NAIRU and TFP are themselves unobservable and have to be estimated. The introduction of a bivariate procedure linking unemployment and inflation in a Phillips curve relationship to disentangle the permanent and cyclical components of labour has allowed enhancing the reliability of the NAIRU estimates so far. Yet, the permanent and cyclical components of TFP have been extracted with the Hodrick- Prescott filter, and hence can be argued to be themselves susceptible to Kuttner's critiques. In particular, the fact that the method utilizes only limited information, see Baxter and King (1995) and D'Auria et al. (2010) for a discussion of these issues in the recent EU context.

A direct consequence of the high uncertainty around the estimates of TFP components at the end of the sample is that the estimates of potential output and of the cyclically adjusted budget balances (CAB) are frequently revised. This makes real-time fiscal policy assessment, especially in the vicinity of business cycle turning points difficult. Taking these factors into considerations, the European Commission has proposed to replace the HP method of the TFP components extraction with a new bivariate model that exploits the theoretical link between TFP cycle and capacity utilisation that arises in the Cobb-Douglas production framework. The new method has been applied officially applied for the first time in parallel to the HP filter in the 2010 Spring forecast round. (64₎

The general structure of the new model is presented in Box II.5.1. A more detailed technical description of the method can be found in D'Auria et al. (2010, forthcoming).

(63_{) See Denis et al. (2006) for a description of this method.} (64_{) The definitive move to the new method will take place in}

the autumn 2010 forecast round as endorsed by the Economic and Financial Committee.

the x-axis correspond to the different time horizon considered to calculate the standard deviations. (68₎

As can be seen, the average standard deviation of the revisions of the CAB estimates based on TFP cycle estimates obtained with the bivariate method is in general smaller than the average standard deviation of revisions on HP filter for every time- horizon considered in nine out of eleven Member States. (69_{) Only for two Member States (Spain and}

UK) the result is ambiguous and depends on the time horizon. It is also worth noting that for a number of Member States (Denmark, Germany, Ireland, Italy and Portugal), the bivariate method produced standard deviation of the revisions which are smaller by at least 20% across all time horizons. This result therefore provides supporting evidence in favour of the use of the capacity utilisation as this method significantly reduces the ex-post CAB revisions compared to the HP method. Ongoing work in this area by the Commission services will allow to extend the method to other Member States once data availability becomes sufficient for this purpose.

CAB revision analysis

The usefulness of capacity utilisation data for disentangling TFP components is justified on two grounds: first, capacity utilisation is measured with acceptable precision and, crucially, without revisions. This can be expected to be helpful in reducing TFP trend estimate revisions due to the updates of the underlying series. (65_{) Second,}

capacity utilisation indicators have been found to strongly co-move with the unobserved cyclical component of TFP, hence enabling unbiased extraction of the TFP cycle even at the end of the sample. (66_{) Mechanically, one should expect a}

similar effect of the new method on the real-time estimates of national CABs, since their construction requires the TFP cycle estimates as one of the input arguments.

Following Planas et al. (2010) the two different methods used here, i.e. the HP and capacity- utilisation affect all years of estimation of the CAB. One can exploit this feature to measure the sensitivity of CAB estimates to ex-post revisions. Graph II.5.1 does this by reporting the standard deviations of revisions of CAB measurement recorded for 11 EU Member States calculated over the period 2000-2008. (67_{) The revisions are}

computed on CAB estimates using the different autumn vintages of DG ECFIN Ameco database running from the autumn 2000 to the autumn 2009 vintages over four different time horizons. The number of time horizons considered is conditioned by the data needed to compute meaningful statistics (i.e. standard deviations are used here) over sufficiently long time span to calculate differences in the CAB estimates recursively for years 2008 till 2000 using the different autumn vintages of the Ameco database. The numbers on

(65_{) It should however be understood that such revisions will} never be completely eliminated.

(66_{) The positive impact of the new method on decreasing the} size of TFP cycle revisions in real time has also been documented for a sample EU Member States in Planas et al. (2010).

(67_{) The period 2000 -2008 is determined by the availability of} previous Ameco vintages from the autumn 2000 till the autumn 2009, i.e., the first year for which the estimate of the CAB can be compared using the HP and capacity utilisation method is 2008 using the autumn 2008 and the autumn 2009 Ameco vintages. The countries covered are Belgium, Denmark, Germany, Greece, Spain, France, Ireland, Italy, the Netherlands, Portugal and United Kingdom. Due to lack of data the new method is not yet applicable for the Austria, Finland, Luxemburg and Sweden and the 12 New Member States.

(68_{) For instance, the first measure of the size of revisions} reported in Graph II.5.1 covers eight years, i.e., from 2008 till 2000 and for each of these years the difference between two different estimates are calculated the following way: The time horizons in the x-axis correspond to the years considered to calculate the standard deviation in the revisions of the CAB estimates. For instance, the standard deviation of the CAB estimate corresponding to the time horizon 1 covers the differences in the CAB estimated for the years 2008 (using the autumn 2009 and the autumn 2008 forecast), the year 2007 (using the autumn 2008 forecast and the autumn 2007 forecast), etc. till the year 2000 (using the autumn 2001 forecast and the autumn 2000) forecast. Time horizon 2 covers the years 2007 (using the autumn 2008 forecast and the autumn 2007 forecast), etc. till the year 2001 (using the autumn 2002 forecast and the autumn 2001) forecast. By doing these calculations recursively (i.e. moving down from year 2008 to year 2000) one obtains four standard deviations values measuring the size of the revisions in the CAB estimate. (69_{) It can also be observed that the size of revisions tends to}

grow when moving from the first time horizon to the fourth time horizon which might simply reflect the smaller number of years that is considered each time.

Box II.5.1: A joint model for TFP and capacity utilisation

The basic structure of the new bivariate method is similar to the Phillips-curve augmented unobserved component model proposed by Kuttner (1994) for estimating potential output and output gap in the US. In the Cobb-Douglas production function framework TFP can be related to the labour efficiency (E_L) and capital efficiency (E_K) levels of the available technology and to labour and capital capacity utilisation (U_L and U_K respectively) according to:

(1) ₌( α 1−α)( α 1−α) K L K LE U U E TFP

where the constant α represents the labour share of income. Since efficiency is a persistent process whereas capacity utilisation depends on the current economic condition, equation (1) suggests a TFP-decomposition into a trend P and a cycle C such that TFP = P × C with:

α α α α − ₌ − = 1 1 K L K LE C U U E P

The first relationship has no empirical relevance since efficiency is not measured. Capacity utilisation measures are instead available, although so far without discriminating between the different production factors. It follows that only aggregate capacity utilisation series (U) can be readily obtained. By construction we expect UL and UK to be significantly correlated. Given that average hours worked per employee already

contain some cyclical movements, the link with labour utilisation should be somewhat looser. But if there are fluctuations in the degree of labour hoarding that are not captured by the number of hours variable, a correlation between labour and capital utilisation may nevertheless be present. It is thus assumed that:

1 0< < + =

γ

ε

γ

where lowercase letters denote logarithms and ε is a random shock. Hence log-TFP is related to capacity utilisation through:

ε

α

αγ

α

This link is exploited to detrend TFP through the following bivariate model: (2) 1 ) - (1 - 1 1 e c u c p tfp Ut t U t t t t > = + + = + = γ α β β μ

where the small-case letters indicate log-levels of their large-case letter counterparts. Given that both α and γ lie in the (0,1)-interval, the loading coefficient β should be greater than one. The value of β can be considered a formal quantitative measure of the link between the capacity utilisation and TFP. The term eUt

in the second equation of system (2) stands for a random shock. System (X.2) must be completed with assumptions about the unobserved components dynamics. Their general structure as well as specific assumptions made for every Member States are discussed in D'Auria et al. (2010, forthcoming).

Construction of the capacity utilisation composite indicator

Data on capacity utilisation for the EU can be obtained from: the Capacity Utilisation Indicator (CUI), which is available for manufacturing only, and the Business Survey Capacity Indicator (BS) collected for both manufacturing and services as a part of the EC Business and Consumer Survey Programme, see the European Economy Special Report 5/2006. Due to its wider scope, BS is thought to be a superior measure of capacity utilisation for the total economy. It has the disadvantage however that data on the Service sector has been collected only since years 1995-1998 for most Member States. For this reason, CUI, suitably rescaled,

Box (continued)

is used for the period when BS is not available, while BS is used for the remaining years. Only CUI is used for Luxemburg as business surveys are not conducted for this country. Ireland has interrupted business surveys in 2009.

Model estimation

The model can be estimated using the standard maximum likelihood method or applying a Bayesian approach. The latter is preferred as it overcomes a stability problem that can occur with maximum likelihood estimation whereby 0-coefficient estimates are obtained for structural shock variances. Another advantage of Bayesian approach is that the additional information possessed by modellers and policy makers that is not captured in the data can be easily incorporated into the analysis. For instance, some information is a priori available about the periodicity of the TFP cycle or the inertia of its trend. In the Bayesian framework all parameters are considered as random variables with an initial distribution that reflects the prior knowledge. The estimation procedure aims at delivering posterior distributions of all unobserved quantities given both prior assumptions and observations. The likelihood is evaluated by casting model (2) into a state space format in order to apply the Kalman filter. More details about the methodology and the prior distributions are given in D'Auria et al. (2010, forthcoming). (1₎

(1_{) All computations are made by programme GAP developed in the Joint Research Centre and downloadable from}

CIRCA website

Graph II.5.1: One to four-step ahead revision standard deviations (x 100) for four different time horizons (1) Belgium 0 0.2 0.4 0.6 0.8 1 1 2 3 4 BE HP BE KF Denmark 0 0.2 0.4 0.6 0.8 1 1 2 3 4 DK HP DK KF Germany 0 0.2 0.4 0.6 0.8 1 1 2 3 4 DE HP DE KF Greece 0 0.2 0.4 0.6 0.8 1 1 2 3 4 EL HP EL KF Spain 0 0.2 0.4 0.6 0.8 1 1 2 3 4 ES HP ES KF France 0 0.2 0.4 0.6 0.8 1 1 2 3 4 FR HP FR KF Ireland 0 0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 IE HP IE KF Italy 0 0.2 0.4 0.6 0.8 1 1 2 3 4 IT HP IT KF The Netherlands 0 0.2 0.4 0.6 0.8 1 1 2 3 4 NL HP NL KF Portugal 0 0.2 0.4 0.6 0.8 1 1 2 3 4 PT HP PT KF United Kingdom 0 0.2 0.4 0.6 0.8 1 1 2 3 4 UK HP UK KF

(1) The time horizons in the x-axis correspond to the years considered to calculate the standard deviation in the revisions of the CAB estimates reported in the y-axis. For instance, the standard deviation of the CAB estimate corresponding to the time horizon 1 covers the differences in the CAB estimated for the years 2008 (using the autumn 2009 and the autumn 2008 forecast), the year 2007 (using the autumn 2008 forecast and the autumn 2007 forecast), etc. till the year 2000 (using the autumn 2001 forecast and the autumn 2000) forecast. Time horizon 2 covers the years 2007 (using the autumn 2008 forecast and the autumn 2007 forecast), etc. till the year 2001 (using the autumn 2002 forecast and the autumn 2001) forecast.

5.2. THE PRO-CYCLICAL NATURE OF