Procyclicality of Trend TFP Reduces Revisions of Potential Output in the EC estimation
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1 Procyclicality of Trend TFP Reduces Revisions of Potential Output in the EC estimation Susanne Maidorn * Vienna, March 31, 2015 Abstract The EC estimates for potential growth have considerably decreased in 2009, with little recovery since. In Austria, Finland, Sweden and the UK the decline is mainly due to a sharp decrease in the contribution of TFP to potential growth as a result of a TFP trend that is highly procyclical or even overshooting the decline in actual TFP growth rates according to EC estimates. The correlation between TFP trend and the capacity utilisation indicator, used by the EC approach to determine the TFP cycle component, is accordingly high. The EC employs a Kalman filter model together with a Bayesian approach to estimate TFP trend and cycle. The smoothness of the TFP trend depends on the prior assumptions for the residual variance of the TFP cycle equation. Exploiting this, simulations over increasing values of the residual variance of the TFP cycle equation are run, leading to increasing smoothness of TFP trend estimates. This paper presents the results regarding the extent of revisions on TFP trend levels and growth rates. Increasing smoothness of TFP trend estimates increases the extent of revisions, thus the EC sets prior assumptions such that revisions are minimised. Keywords: Potential Output, Procyclicality, TFP, Revisions JEL Classification: C53, D24, E32, E62 * Office of the Austrian Fiscal Advisory Council c/o Oesterreichsiche Nationalbank, Vienna, susanne.maidorn@oenb.at.
2 1 Introduction Potential Output denotes an output level at the maximum of durably sustainable production without tensions in the economy, especially without inflationary pressure. The output gap is the amount that actual output is below or above potential output. The European Commission (EC) follows a production function approach in order to estimate potential output and the output gap. Potential output is determined by the two input factors, capital and the trend of labour, and by the trend of total factor productivity (TFP). TFP is decomposed into a trend entering potential output and a cycle. The cycle component of TFP is modelled to depend on an indicator of capacity utilisation. Emphasis is put on a smooth TFP trend, with the cycle component fluctuating around it 1. But among existing estimations of potential output and of trend TFP 2 ) the EC estimate is the most procyclical. The EC replaced the earlier HP filter methodology for estimating potential output by the production function approach in the year One of the key objectives of replacing the earlier HP filter methodology for estimating potenitial output was for the EC to reduce the degree of cyclicality of the trend growth estimates in order to avoid an overly optimistic picture of the degree of budgetary improvement in the upswing phase of economic cycles. Still, cyclicality is a source of concern in the view of the EC itself. 3. Potential growth rates have considerably decreased after the financial crisis according to EC estimates, with little recovery since. This is mainly due to a sharp decrease in the contribution of TFP to potential growth in some countries. The reduction of the growth rate of actual TFP fully translated into a decline of the TFP trend and hence the contribution of TFP to potential growth, in some cases the latter overshooted the overall decline. Reasons for a secular decline of TFP trend growth are seen in a reduced share of the manufacturing sector in favour of the IT sector, which has weaker macroeconomic productivity effects. Other arguments are declining growth rates of skill acquisiton and skill mismatches in the labour force. While adverse effects of the crisis on productivity are evident in the OECD estimates of potential output, the size of the negative effect is much more pronounced in the EC estimates. A high correlation between the capacity utilisation indicator (CUBS) used in the EC estimation approach and TFP trend for some countries can be seen as a further indicator of 1 see D Auria et al. (2010), p Compared to OECD and IMF estimates, s. European Central Bank (2014), p see Havik et al. (2014) p. 6 1
3 procyclicality of the TFP trend. As a result, increased volatility of the CUBS indicator in the recent years, which is supposed to translate into the TFP cycle entailed procyclicality of the TFP trend. Smoothness of TFP trend estimates depends on the residual variance in the TFP cycle equation of the EC estimation model. Furthermore, the EC estimates are very sensitive to the prior assumptions on the corresponding variance parameters in the Bayesian estimation approach. Increasing the prior specifications for the cycle residual variance, starting from the rather low levels assumed by the EC, increases the smoothness of TFP trend, comparable to the parameter λ in the Hodrick Prescott filter. A second issue about EC estimates of TFP trend and hence poential output is the extent of revisions, which are a special concern for policy makers because of the revisions they entail on the output gap and the cyclical adjustment of the headline government deficit. Hers and Suyker (2014) empahsise the volatility of potential output and output gap estimates leading to wrong conclusions for policy makers. Substantial adjustments can occur even if fiscal policy does not change or, conversely, signigicant policy changes can be offset by output gap revisions. 4 This paper shows that procyclicality of TFP trend reduces revisions for recent vintages. 5 Looking at real time estimates of the years 2011 to 2014 compared to the most recent estimats of Autumn 2014, the extent of revisions increases with increasing smoothness of TFP trend estimates. Thus the EC sets prior assumptions so as to minimise the extent of revisions 2 Empirical Evidence The concept of TFP results from growth accounting, an approach to measure the contribution of input factors to economic growth. TFP constitutes the unexplained residual of output growth. Table 1 shows average potential growth rates according to EC estimates in the years 2004 to 2008 compared to after the crises 2010 to 2014 for eight Euro area countries. Average potential growth rates have considerably decreased in 2009 with little recovery since, Germany being the only exception 6. In Austria, Finland, Sweden and the 4 see Hers and Suyker (2014) 5 The EC comes to the same conclusion when comparing revisions to output gap estimates of the EC, the OECD and the IMF. 6 The financial crisis is estimated to have no adverse effect on potential output in Germany by Ollivaud and Turner (2014), see p. 6. 2
4 UK the decline of potential growth is mainly due to a sharp decrease in the contribution of TFP to potential growth. As pointed out in section 3 TFP trend estimation depends on actual TFP and capacity utilisation. But whereas the growth rate of total TFP determines both, trend growth and the cycle of TFP, underutilitsation of production capacity is expected to flow into the TFP cycle. Table 1: TFP Contribution to Potential Growth, in % Potential Growth TFP Contribution TFP Growth AT DE DK FI FR IE SE UK EA Source: EC 2014 Autumn Forecast Columns 6 and 7 of Table 1 show that the pronounced decline in actual TFP growth rates was translated into a decline of the contribution of TFP to potential growth of the same size (Austria and Finland) or even stronger (Sweden and UK). The reduction of actual TFP growth rates is thus expected to persist in the medium to long run in Austria and Finland and is expected to lead to even larger decreases in trend growth rates in Sweden and the UK according to the EC estimates. TFP trend is definitively procyclical or even overshooting the cycle in this group of countries. In the second group of countries selected in Table 1, i.e. Germany, Denmark and France, TFP growth reached its pre-crisis extent or even recoverd from negative rates in the case of Ireland. The contribution of TFP to potential growth was still reduced on average in 2010 to 2014, but the reduction was moderate and therefore not the main source of the slow-down of potential growth. The EC itself argues that a secular decline of TFP trend can be explained by the fact that recent innovations mostly came from the IT sector and have as such weaker macroeconomic productivity effects than innovations of the industrial revolution, even more so in European countries with smaller IT sectors than the US. 7 Similarily, Anderton et al. 7 see European Commission (2014), p
5 (2014) state that trend TFP has been affected by the change in the economic structure brought about by the crisis. A decline in the share of manufacturing, a sector with high TFP growth rates could have had a negative impact on TFP growth. But the authors see that the decline in the share of construction, a sector with low TFP growth rates, suggests that TFP is likely to increase following the crisis. The higher share of services is difficult to estimate because of its heterogeneity with respect to TFP intensity. Other arguments for a secular decline of TFP brought about by the EC are declining growth rates of skill acquisition and skill mismatches in the labour force. 8 Ollivaud and Turner (2014) estimate the effect of the global financial crises on potential output in the medium run. They compute, among others, the effect on TFP in % of a hypothetical counterfactual potential output assuming pre-crisis productivity trends. Their calculations based on OECD potential output estimates give an effect of -1.5 % for Austria, -9.7 % for Finland, -5.3 % for Sweden and -7.4 % for the UK 9. Thus, while adverse effects of the crisis on productivity are evident in OECD potential output, and e.g.rawdanowicz et al. (2014) are concerned about permanent hits of the crisis on potential output based on OECD estimates 10, the size of the negative effect is by far more pronounced in EC estimates. Applying the approach of Ollivaud and Turner (2014) to the EC estimates of TFP gives an effect of -4.7 % for Austria, % for Finland, % for Sweden and % for the UK. The extent of the slowdown of the EC TFP trend growth is large compared to the OECD estimates. Table 2: Correlation between Capacity Utilisation and TFP Trend and Cycle, 2005 to 2013 TFP Trend TFP Cycle AT DE DK FI FR SE UK Recessions generally tend to have only a temporary effect on potential growth, but a prolonged recession may have long-lasting effects. Papell and Prodan (2012) find empirical 8 see European Commission (2014), p see Ollivaud and Turner (2014), p see Rawdanowicz et al. (2014) 4
6 evidence that most severe recessions associated with financial crisis in advanced countries do not cause permanent reductions in potential output, but the return to potential output takes on average nine years and is much longer than the return following other recessions. Benati (2015) estimates sizeable but temporary effects of financial crisis on potential output dynamics, but without impact on potential output growth after the crisis. According to the theoretical concept of the EC production function approach, as described in section 3, correlation between capacity utilisation and TFP cycle is supposed to be and is indeed high, see Table 2. Correlation between the 1st differences of TFP trend and capacity utilisation as an indicator of procyclicality of potential output, is given in Table 2, too. Correlation is high in Austria, Finland, France and UK, and is still pronounced in Germany 11. Figure 1 plots the 1st differences of trend TFP, TFP cycle and capacity utilisation (CUBS) as estimated in the EC autumn 2014 forecast. In Austira, an increased volatility of the CUBS indicator from 2005 on did not translate into an increase of volatility of TFP cycle. This entailed more procyclicity and volatility of TFP trend. In France and UK, the variance of TFP cycle seems to be restricted, too, an increase of the volatility of the CUBS indicator from 2007 onwards left the range of the TFP cycle unchanged. In Denmark, on the other hand, the TFP cycle matches the CUBS indicator much closer. 3 The Production Function Approach of the EC Reproducing the EC production function approach as in Havik et al. (2014) 12, actual output, Y, can be represented by a combination of factor inputs (labour, L and capital stock, K), corrected for the degree of excess capacity, U L and U K, and adjusted for the level of efficiency, E L and E K. Assuming a Cobb Douglas specification, output is given by so that T F P is equal to Y = (U L LE L ) α (U K KE K ) (1 α) = L α K 1 α T F P, (1) T F P = (E α LE 1 α K )(U LU α 1 α K ), (2) including both the degree of utilisation of factor inputs as well as their technological level. 11 Capacity utilisation is only available up to 2008 for Ireland 12 see Havik et al. (2014), p. 10ff 5
7 Figure 1: TFP and Capacity Utilisation AT TFP Trend (1.Diff, right scale) TFP Cycle CUBS DK TFP Trend (1.Diff, right scale) TFP Cycle CUBS DE TFP Trend (1.Diff, right scale) TFP Cycle CUBS FI TFP Trend (1.Diff, right scale) TFP Cycle CUBS FR IE TFP Trend (1.Diff, right scale) TFP Cycle CUBS TFP Trend (1.Diff, right scale) TFP Cycle CUBS SE UK TFP Trend (1.Diff, right scale) TFP Cycle CUBS TFP Trend (1.Diff, right scale) TFP Cycle CUBS In order to compute potential output, the maximum contribution of capital is given by full utilisation of the existing capital stock in an economy, so that K enters the potential output production function. The potential of labour, defined in terms of hours, is determined by the trends of the participation rate, of unemployment (as in the concept of a non-accelerating wage rate of unemployment - NAWRU) and of hours worked. 6
8 In Autumn 2010 the EC replaced the previously used Hodrick-Prescott method of detrending TFP with a Kalman filter based approach which exploits the link between TFP and capacity utilisation. Efficiency of the input factors, as given in equation 2 is a persistent process whereas capacity utilisation depends on current economic conditions. TFP is thus decomposed into a trend P and a cycle C so that T F P = P C with P = E α LE 1 α K C = U α LU 1 α K. (3) Aggregate capacity utilisation, U, is constructed from the Capacity Utilisation indicator and a set of Economic Sentiment indicators surveyed in the EC s Business and Consumer Survey Programme. Assuming U and U K to be significantly correlated and that the average hours worked per employee contains cyclical movements, leads to the bivariate model in log-levels tfp t = p t + c t u t = µ U + βc t + e Ut β > 0, (4) where lower case indicate log-levels and e Ut is a White Noise random shock 13. It represents the observation equations of the Kalman filter model. The unobserved components dynamics are modeled as p t = µ t 1 µ t = ω(1 ρ) + ρµ t 1 + a µt V (a µt ) = V µ (5) c t = 2A cos(2π/τ)c t 1 A 2 c t 2 + a ct V (a ct ) = V c. The tfp mean growth rate is equal to ω with dampening coefficient ρ. The autoregressive coefficients of the cycle, c t are parameterised in order to use polar coordinates A and τ capturing the business cycle. 7
9 Figure 2: Smoothness of TFP Trend depending on V c.014 AT DE diffvc diffv c diffv c 0663 diffv c diffvc 0.05 diffvc diffv c diffv c 0663 diffv c diffvc DK.016 FI diffvc diffv c diffv c 0663 diffv c diffvc 0.05 diffvc diffv c diffv c 0663 diffv c diffvc FR.016 IE diffvc diffv c diffv c 0663 diffv c diffvc 0.05 diffvc diffv c diffv c 0663 diffv c diffvc SE UK diffvc diffv c diffv c 0663 diffv c diffvc 0.05 diffvc diffv c diffv c 0663 diffv c diffvc
10 4 Sensitivity of Results to priors of V c The EC employs a Bayesian approach to estimate the Kalman filter model in equations (4) and (5). The prior assumptions are given in Havik et al. (2014) 14. As indicated in section 2, the variance of the TFP cycle is crucial for the procyclicality of trend TFP. The EC assumes inverted gamma (IG) distributions for the residual variances, a common approach in Bayesian estimation 15. As will be shown below, the posterior distribution of V c, the variance of the error term in the cycle equation in (5), depends on the prior specifications of the IG distribution. In contrast to the other prior settings in the Bayesian estimation model, the estimation results for V c are determined by the prior assumptions. As V c in turn influences the procyclicality of trend TFP, the prior assumptions for V c determine the smoothness of TFP trend. As discussed in section 2, this procyclicality or smoothness is passed through to potential growth. Put the other way round, the procyclical behaviour of potential output and the pronounced reduction in potential growth after the financial crisis in some countries are a result of rather restrictive prior settings for V 16 c that led to a small residual variance of the TFP cycle and hence to procyclicality of TFP trend. Figure 2 shows the sensitivity of the estimation outcome to prior settings of V c. Increasing V c results in higher smoothness of trend TFP. Denmark is an exception because of a low and negative correlation between capacity utilisation and TFP, and a correlation between capacity utilisation and the TFP cycle of above 0.99, as seen in table 2. Thus the smoothness of Trend TFP does not increase with V c. 5 Method In order to test the effects of increasing values of V c and thus increasing smoothness of TFP trend on the extent of revisions of TFP estimations, the estimations are repeated for increasing values of V c, that are governed by the prior assumptions, leaving all other prior assumptions at the official values given by the EC. An input file to the EC bgap43.exe estimation procedure is changed in consecutive steps according to the parameters of the IG distribution assumed for V c. An IG distribution with 6 degrees of freedom is selected in accordance with the EC approach so as to set the mean and the standard deviation equal a priori. The mean and 13 For Finland, France and Sovenia an AR(1) random shock is modeld with e Ut = δ U e Ut 1 + a Ut and δ U < 1 14 p.59ff 15 see Bauwens et al. (1999), p The author thanks Alessandro Rossi and Christophe Planas for the clarification that the EC prior settings are chosen such that the marginal likelihood of the Bayesian estimation are at the highest value. 9
11 the standard deviation start at and are increased on an logarithmic scale 17 in 100 grid points to V c is therefore used in a way comparable to λ within the Hodrick Prescott filter. The simulations are run for the vintages of the EC estimation of Spring 2011 to Autumn 2014, where the respective original prior settings ure used, except for V c. The results for the revisions in Autumn 2014 of the estimates at earlier vintages are presented in this paper. The mean squared revision of the TFP trend level and growth in Autumn 2014 are given for t 0 : Estimates in year t for year t t +1 : Estimates in year t for year t +1 Other results are have been computed, too, but are not repeated, because they are very similar to the results presented. 6 Results Figures 3 to 6 show the mean squared revisions depending on V c in Autumn 2014 of estimates for t and t +1 at the seven vintages from Spring 2011 to Spring The vertical lines mark the official prior settings of the European Commission for each country. It can be assumed that increasing smoothness (associated with lower values of V c ) leads to more stable predictions of TFP trend levels and growth rates and lower revisions. At the extreme, if prediction of TFP trend growth were fixed at, say 1 per cent, there would be no revisions. But it can be assumed, on the contrary, that increasing procyclicality of TFP trend with increasing correlation between TFP trend and actual TFP (associated with lower values of V c ) leads to more stable predictions of TFP trend levels and growth rates and lower revisions. At the extreme, if TFP trend growth would equal actual TFP growth, the only source of revisions would lie in revisions of GDP, of the capital stock or total hours of labour supplied. TFP trend estimation would not add any uncertainty. An inverse U-shape in terms of increasing values of V c results with both effects at work. The results show that the inverse U-shape is visible for the mean squared revision of TFP trend growth for all countries considered. The prior settings of the EC are in favour of a low extent of revisions and high procyclicality of the trend growth rate at the left corner 17 The logarithmic scale is used because of the exponentially increasing effects of parameter settings on smoothness in filter methods like the Kalman filter and Hodrick Prescott filter 10
12 of the graphs. The EC estimates reduce the extent of revisions through a high correlation between TFP trend growth and actual TFP growth. Only very high levels of smoothness would reduce the mean squared revision after a peak when moving to the right corner of the graphs. In the estimation of TFP trend levels, the mean squared revision increases with the smoothness of the estimate over the whole range of prior settings considered for the most countries. Germany and Denmark are exceptions, the extent of revisions would be reduced with higher smoothness. The results for the other countries show, that prior settings are again set so as to minimise the extent of revisions. 11
13 Figure 3: Mean Squared Revisions of TFP Trend Level at t to Autumn 14, depending on V c AT DE DK.0018 FI FR.0018 IE SE UK
14 Figure 4: Mean Squared Revisions of TFP Trend Growth at t to Autumn 14, depending on V c AT DE DK FI FR IE SE UK
15 Figure 5: Mean Squared Revisions of TFP Trend Level at t+1 to Autumn 14, depending on V c AT DE DK FI FR IE SE UK
16 Figure 6: Mean Squared Revisions of TFP Trend Growth at t + 1 to Autumn 14, depending on V c AT DE DK FI FR IE SE UK Conclusions Actual TFP, that results out of a production function approach, is decomposed into a TFP trend and a TFP cycle estimate by the EC on the basis of a Kalman filter model using a Bayesian approach. Exploiting the sensitivity of the results on the prior assumptions concerning the residual variance of the cycle equation, the smoothness of the TFP trend estimates is increased by increasing values of this residual variance of the cycle equation. The results show that the revisions are decreased with increasing procyclicality of the 15
17 TFP trend level and growth estimates. The EC estimates reduce the extent of revisions through a high correlation between TFP trend growth and actual TFP growth. Only very high levels of smoothness would reduce the mean squared revision after a peak when moving to the right corner of the graphs. A reduction of the mean squared revision by , which is within the range of the considered increased procyclicality of the estimated TFP trend, c.p. decreases revisions of potential output and the output gap by approximately 1 percent in terms of potential output, i.e. approximately 0.5 percent of the cyclical adjustment of the budget balance. 16
18 References Anderton, R., T. Aranki, A. Dieppe, C. Elding, S. Haroutunian, P. Jacquinot, V. Jarvis, V. Labhard, D. Rusinova, and B. Szrfi (2014): Potential Output from Euro Area Perspective, ECB Occasional Paper Series, No 156. Bauwens, L., M. Lubrano, and J. F. Richard (1999): Bayesian Inference in Dynamic Econometric Models, Oxford University Press. Benati, L. (2015): Why Are Recessions Associated With Financial Crises Different? Journal of Applied Econometrics, forthcoming. D Auria, F., C. Denis, and K. H. et al. (2010): The production function methodology for calculating potential growth rates and output gaps, Economic Papers, European Commission, 420. European Central Bank (2014): Monthly Bulletin April 2014,. European Commission (2014): Quarterly Report on the Euro Area, 13 No 4. Havik, K., K. M. Morrow, and F. O. et al. (2014): The Production Function Methodology fr Calculating Potential Growth Rates and Output Gaps, Economic Papers, 535. Hers, J. and W. Suyker (2014): Structural Balance. A love at first sight turned sour. CPB Policy Brief, 07. Ollivaud, P. and D. Turner (2014): The Effect of the Global Financial Crisis on OECD Potential Output, OECD Economics Department Working Papers, No Papell, D. H. and R. Prodan (2012): The Statistical Behavior of GDP after Financial Crises and Servere Recessions, The B.E. Journal of Macroeconomics, Vol. 12, Iss. 3. Rawdanowicz, L., R. Bouis, K.-I. Inaba, and A. K. Christensen (2014): Secular Stagnation: Evidence and Implications for Economic Policy, OECD, No
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