A Practitioner’s Guide to Potential Output and the Output Gap Definition ∙ Estimation ∙ Validation www.euifis.eu Potential output and the output gap Abstract This paper provides a comprehensive literature review of potential output and output gap estimates from the perspective of a fiscal authority and, by extension, an independent fiscal institution tasked with assessing cyclically adjusted fiscal indicators. Considering the mandate of these institutions, the focus is often broader in the sense that more sources of imbalances and longer horizons are considered. Yet it is similar to other institutions in terms of the methods used to assess the unobserved potential output and the output gap. The paper reviews univariate and multivariate trend-cycle decomposition methods that are actually used within the Network of European Union’s independent fiscal institutions. It summarizes their salient features and provides a critical review of commonly used methods. This literature review preludes the back-testing exercise assessing the quality of output gap estimates and the discussion of their real-time applied issues in the context of cyclically adjusted fiscal indicators. JEL references: C50, E27, E32, E62. Keywords: output gap, growth cycle, potential output, uncertainty, unobserved component, fiscal authority, independent fiscal institution, production function, trend-cycle decomposition. The paper has been prepared by the Network’s Output Gap Working Group coordinated by Dmitrij Celov from the Lithuanian IFI. Special thanks to Eddie Casey of the Irish IFI for providing a thorough review of the document in addition to contributing to it. The document is not an official position document of the Network. Views, if any, expressed in the paper reflect the views of the technical experts working on the document and do not necessarily represent the views of the individual IFIs of the Network or the collective views of the Network. 2 Potential output and the output gap Table of Contents List of Abbreviations .............................................................................................................................. 4 Introduction ............................................................................................................................................. 6 Conceptual issues .................................................................................................................................... 7 Minding the gap .............................................................................................................................. 7 Prospecting the future ................................................................................................................... 10 Requiring data ............................................................................................................................... 12 Accommodating uncertainty ......................................................................................................... 13 Assessing performance.................................................................................................................. 15 Computing without pain ................................................................................................................ 18 Estimating the Output Gap .................................................................................................................... 19 Going alone ................................................................................................................................... 20 Hodrick-Prescott filter ............................................................................................................. 20 Prior-Consistent filter............................................................................................................... 26 Band-pass filters: ideal and approximations ............................................................................ 28 Beveridge-Nelson decomposition ............................................................................................ 29 Univariate unobserved components model and trend-cycle filter ............................................ 31 Seeking refinement........................................................................................................................ 34 Bivariate filters ........................................................................................................................ 35 Multivariate unobserved components models .......................................................................... 38 Principal Components Analysis ............................................................................................... 39 Accounting for production ............................................................................................................ 40 Problems with commonly agreed methodology ....................................................................... 45 Best practices of the network ................................................................................................... 48 Mixing things up ........................................................................................................................... 51 Nominating the winner .................................................................................................................. 53 Concluding remarks .............................................................................................................................. 55 References ............................................................................................................................................. 57 Annexes ................................................................................................................................................ 62 Appendix A. Data collection ......................................................................................................... 62 Appendix B. Kalman filter and Kalman smoother ........................................................................ 64 One-sided (concurrent) estimates of the state vector ............................................................... 66 Two-sided (historical, smoothed) estimates of the state vector ............................................... 66 3 Potential output and the output gap List of Abbreviations Abbreviation Full Form A Autumn forecast AMECO Annual macro-economic database of the European Commission ARIMA Autoregressive Integrated Moving Average model BK Baxter-King filter BN Beveridge-Nelson decomposition/filter CAB Current account balance CAM Commonly agreed methodology CD Cobb-Douglas CEE Central and Eastern Europe countries CES Constant elasticity of substitution CF Christiano-Fitzgerald filter CIRCABC Communication and Information Resource Centre for Administrations, Businesses and Citizens CPI Consumer price index CUBS Capacity utilization and business surveys indicator D Downturn point DSGE Dynamic stochastic general equilibrium EC European Commission ECB European central bank ESA 2010 European System of National and Regional Accounts 2010 EU European Union GDP Gross domestic product GG General government GNI Gross national income GVA Gross value-added HP Hodrick-Prescott filter IBP Ideal band-pass filter IFI Independent fiscal institution IMF International Monetary Fund KF Kalman filter L Latest known forecast M1 Narrow money M3 Broad money MAR Mean Absolute Revision MIMIC Multiple indicators and multiple causes model MLE Maximum likelihood estimation MR Maximal Revision MS Microsoft MUC Multivariate unobserved components model MUF Multivariate filter NAIRU Non-accelerating inflation rate of unemployment NAWRU Non-accelerating wage rate of unemployment 4 Potential output and the output gap Ni Necessary condition i NKPC New Keynesian Philips Curve OECD Organisation for Economic Co-operation and Development OG Output gap P Peak point PC Prior consistent filter PCA Principal components analysis PF Production function PIM Perpetual inventory method S Spring forecast SEATS Signal Extraction in ARIMA Time Series Si Sufficient condition i STS Structural time series model T Trough point TC Trend-cycle decomposition/filter TFP Total factor productivity TRAMO Time series Regression with ARIMA noise, Missing values and Outliers U Upturn point UC Unobserved components model UF Univariate filter UK United Kingdom VBA Visual Basic VCV Variance-covariance matrix 5 Potential output and the output gap Introduction Actual General Government (GG) budget balances are imperfect indicators for assessing public finances and the fiscal policy stance as they are affected by a number of temporary and cyclical factors that are beyond the direct control of fiscal authorities. In implementing their functions, Independent Fiscal Institutions (IFIs) strive to understand the dynamics of the output gap and reveal its specific location as it decisively determines the current budgetary stance and its sustainability (Cuerpo, Cuevas and Quilis 2018, Casey 2018). It is also important to have a medium-term view as to economic growth projections in the context of expenditure planning and GG debt sustainability assessments – something that estimates of potential output can help to assess (Casey 2018). Therefore, plausible real-time potential output and output gap estimates become an essential prerequisite to timely implement required countercyclical fiscal policy measures. The source of substantial uncertainty