German macroeconomic forecasting – institutions, performance, perspectives Ullrich Heilemann Universität Leipzig, Germany George Washington University, Washington, DC August 29, 2013 A: Deeply honored B: Enjoyed very much & benefitted from the most friendly & productive atmosphere at the center C: The topic was chosen 2 weeks ago: necessarily incomplete and, of course, it is a personal view D: Something New? – at this center and in the presence of Herman no such claims can reasonably be made E. 2: Lyndhurst House, Upper Norwood, Surrey, England, Sonntag, 30. April 1865. Captain Robert FitzRoy, Reisegefährte von Charles Darwin auf der zweiten Fahrt der HMS Beagle, Träger zahlreicher Auszeichnungen, Würden und Ämter und seit 1854 der erste Leiter des eben gegründeten, staatlichen britischen Wetterdienstes, bereitet sich auf den Kirchgang vor. Plötzlich greift er zu seinem Rasiermesser und schneidet sich mit einem festen, sauberen Schnitt die Kehle durch. Was war geschehen? Der Admiral sah sich angesichts einer Fülle eklatanter prognostischer Fehlleistungen des mit hohen Erwartungen gegründeten Wetterdienstes einer wachsenden, zunehmend spöttischen Kritik der Fachöffentlichkeit, der Presse und des Publikums an der Institution und an seiner Person ausgesetzt, die der ohnehin depressive Admiral nicht mehr ertragen konnte und der er mit seinem Schnitt ein Ende machte (Brookes 2003, S. 134). 17.09.2018 Ullrich Heilemann

Macroeconomic forecasting in Germany Forecast performance Perspectives Disposition Introduction Macroeconomic forecasting in Germany Forecast performance Perspectives General: Two views on forecasting: the view of the producer and that of the consumer of the forecast. Here usually no clear distinction is made, though both views to some extent would have different consequences Academic interests are on both sides, however, forecast analysis is often much user oriented – as in many fields, starting with medicine, our diagnostic capabilities are often very far ahead of our therapeutic possibilities. Interestingly: no national comparative studies/reports on forecasting practice – are there no national differences? Here no rerences to particular methods such as indicators macroeconometric models etc. Here only short-term macroeconomic forecasting – mid-term forecasting somewhat better/more accurate 17.09.2018 Ullrich Heilemann

I. Introduction Why looking from the US at German macroeconomic forecasting? Institutional characteristics of supply & demand of the German market for forecasting Material characteristics of Germany‘ s macroeconomic short-term development Preferences of economic policy? Ad A: Not much of a subject of international studies. Not of much importance for the US economy, not on the methodical forefront. The industrialization of short-term forecasting started in the US already in early 20th century (Babson, Harvard Service etc.) (Friedmann 2007, Heilemann 2011) – Germany: still today artisan style Ad B: Mixed supply, mixed demand – so in the last 20 years a shift to government on both sides of the market. Ad C: No traditional cycles of boom & bust since the early 1970s – but US-crises spreading over the world (2001. 2007ff. Or international crisis OPEC I/ II, consoliditaion crisisis, unification crisis ... no „credi crunch“-phase in the cycle, in general not much attention to credit availability Ad D: Does government always want to know the truth as we assume in our policy preference functions – internally or externally? (Arrow in the early 1960s raised the point of much more spending for forecasts given the cost of recessions (recently Blinder (2013, p...). Much more is spent for environment research or to make the NA a diagnostic tool for counting a nation‘swealth – in deed the short-term diagnostic of NA data seems to be decreasing 17.09.2018 Ullrich Heilemann

II. The market for macroeconomic forecasting I Supply & demand for macroeconomic forecasts 2 principal forms of supply: the private sector (US), the government (France) & many mixed systems (Germany, Netherlands, UK) A brief history of German „Konjunkturforschung“ The present situation: 1. About 50 regulary (quarterly) macroeconomic forecasts (Consensus forecasts) 2. Government sponsored forecasting: Macroeconomic forecasting in 5 large research institutes (about 200 000 Euro each) „Gemeinschaftsdiagnose“ (Joint Diagnosis (JD)) (bi-annual forecasts. government contract) (about ......) Council of Economic Experts (CEE)(now bi-annual forecasts) Ad A: An open market (France survey “certification”, government monopole of forecasting in the 6th century a. C. in the Roman Empire …) Good reasons for each alternative – Reasons for government supply external effects, non-exclusion principle, difficulties of information markets, Institutes have now limited (4 years) contracts, 2 years forecast horizons – Policy conclusions!! CEE – an academic group (similar CEA) – is basically not much interest in forecasting! (In 1967: 10 % of its report, in 2012: 2 %) Ad B: Starts after WW I, DIW leading institution, spring off of the Statistical Reichsamt – later much decentralized (Kulla 1996, no profit orientation, methods: symptomatic; not much change by the Weltwirtschaftskrise. Considerable progress on the data side by the Nazis The Keynesian revolution had its greatest influence in the 1950s when there was no need for it … - Ordnungspolitik believed not in business cycles …. Ad C: Continuity after WWII – decentralized (now: large institutes in Hamburg, Berlin, Halle, Essen, Munich, Mannheim) informal GDP model 17.09.2018 Ullrich Heilemann

II. The market for macroeconomic forecasting II 3. Government forecasts: „Jahreswirtschaftsbericht“ (Government annual economic report (GAER)) (annual forecast). Deutsche Bundesbank (bi-annual) 4. Private forecasts: large banks. national trade associations. employer associations, for profit research institutes (DRI/Global Insights) – hardly play a sizable role 5. International instutions/organizations (EU-commission. ECB. IMF. World Bank) D. Some characteristics of German macroeconomic forecasts 1. Method: Informal GDP-model – macroeconometric models are used as alibi 2. Strong correlations of GDP growth forecasts (R2 > 0.9) 3. Not surprising: same data, same theories, same methods – same general macroeconomic/policy orientation 4. JD kind of „Star of Bethlehem“ since – as CEE forecasts – for free avaliable 5. Despite government funding, no political bias of JD Ad C 3: Supposed to deliver listings of planned economic policies became just another forecast. Ad C 5: Much seen as politically influenced forecasts and being not very actual Ad D 1: Though the hypotheses of the models hardly differ from the ones used by the informal GDP models. Ad D 3: Freiburger Schule, competition policy, purgation effect of crisis – however 4 of the 6 postwar crisis were imported – no signs of overriding boom … Ad D 4: detailed reports (JD: 70 pp., CEE: 600 pp. – what made the German market for model shops like DRI so difficult. 17.09.2018 Ullrich Heilemann

II. The market for macroeconomic forecasting III Why no larger role for macroeconometric models in Germany? Requirements Macroeconomic theory No superiority in forecasting accuracy – add-factoring The difficulties of new techniques in an old setting Ad E 1: Econometrics, technical possibilities, transportability Ad E 2: Changes in macroeconomic theory in mid 1970s – Lucas-critique, Sims-critique, rise of monetarism (simple models!) Ad E 3: Harvard-Conference 1968 & model forecasting accuracy – no evidence in Germany – if properly done why less accurate, but more efficient Ad 4: New techniques need new institutions – telecommunication, photography, automobiles, steam ships … Are there institutes exclusively basing there forecasts on time series? 17.09.2018 Ullrich Heilemann

III. Forecast performance I A. Average accuracy of growth & inflation forecasts – as good as everywhere (Fildes, Stekler 1992)(Table 1) 1967 to 2012 (Heilemann, Stekler 2013) autumn for next year a. Real growth – MAE: autumn1.0, spring 0.5 (Table 2) b. Inflation rate (GDP-deflator) – MAE: autumn 0.5 c. Bias, Theil‘ coefficient d. Turning Points 2. Improving? – Accuracy by decades (by cycles …) Real growth – constant RMSE/ Inflation rate – slight improvements (the 1970s creeping out) 3. Accuracy & forecast utility functions Note: Forecast accuracy is not forecast quality as a Popperian derivative: forecast quality improves with information content, theoretical foundation, accuracy but is reduced by conditionality, (Wild 1972) Ad 1d: Clear tendencies to overestimation – basically all turning points are missed (however more generous ..) No detailed error-analysis – government/monetary policy, internationals disturbances, 17.09.2018 Ullrich Heilemann

III. Forecast Performance II Table 1: Accuracy of selected growth and inflation forecasts. 1967–2010. rates of changes against previous year in %   Real GDP GDP-deflator JD CEE OECD GAER 1967 - 2010 MAE 1.5 1.3 1.2 0.7 0.6 BIAS 0.3 0.2 -0.0 -0.1 U 0.5 RMSE/σ 0.9 0.8 0.4 1970 - 1979 1.9 1.4 -0.7 -0.8 -0.4 -0.9 1980 - 1989 1.1 1.0 0.1 -0.2 Forecast ./. Actual Differences for growth & inflation forecasts between forecasters are small & may be attributed to the date of forecast production the 1 % rule for autumn forecasts Small positive bias of growth forecasts Growth forecasts not terribly better than no-change forecasts (though past change is not yet known) Theil had expected 0.4 Basically no improvement over the decades – prices? 17.09.2018 Ullrich Heilemann

III. Forecast Performance II Table 1, cont.   Real GDP GDP deflator JD CEE OECD GAER 1990 - 1999 MAE 1.0 0.9 0.8 0.5 0.4 BIAS 0.3 0.1 U 0.2 RMSE/σ 0.7 0.6 2000 - 2010 1.7 1.5 1.2 1.1 Source: Heilemann/ Stekler 2013. – Forecasts in autumn (Januar) for the comming (current) year (GAER). MAE: Mean average error; BIAS: bias; U: Theil’s inequality coefficient; RMSE/σ: Root mean square error standardized by variance. 17.09.2018 Ullrich Heilemann

III. Forecast performance III B. Forecast accuracy by demand aggregates 1967 to 2012 (Table 2) 1. Forecasts in spring (I) & autumn (II) forecasts for (t) & t+1 2. The usual results … 3. The problems … 4. By decades a. The standard b. The problems C. Crisis forecasting (GDP-growth) Not much influence on the figures Ad B: Caution isolated view – errors are linked – the consumers view (says nothing about the „scientific“ value) Ad B 1. : CP > GC > Construction > Machinery > Imports > Exports t: autumn > spring, but high!, t+1: autumn > spring Ad 3: hardly sizeable improvements over time 17.09.2018 Ullrich Heilemann

III. Forecast performance IV Table 2: MAE for JD forecasts of demand ggregates. real. 1967 to 2012 Are exports the problem? Domestic demand vs. GDP Qualitative analysis: nearly all (4) phases of the cycle identified with multivariate discriminant analysis (Heilemann, Münch, Schuhr 2010) are correctly met 17.09.2018 Ullrich Heilemann

III. Forecast performance V D. An international perspective (Table 3) 1. Different forecasting markets – supply side! 2. Accuracy a.1967-2001 (bias, Theil’s U. etc.) of growth (inflation) forecasts 1967-2001 – MAE vs. RMSPE/σ b. Development 1967 – 2001 17.09.2018 Ullrich Heilemann

III. Forecast Performance VI Rather large MAE differences, much smaller RMSE/σ Germany at the upper limit – large changes Italy! No trend towards improvment (even > 2001!) G 7, OECD forecasts seem to have benefitted from aggregations gains 17.09.2018 Ullrich Heilemann

III Forecast performance VII Forecasting recessions 1. Six recessions 1967 to 2002/03 Since 1967 all lower turning points were recessions – duration 2 to 3 quarters Four of these recessions came from abroad. None of the recessions was seen by JD. CEE. OECD. GAER in their autumn forecasts for the next year; better for the spring forecasts (JD. OECD) but not perfect (Table A4). MAER 1967-2010: 1.3, for recession years 3.1 17.09.2018 Ullrich Heilemann

The second oil-crisis 1981/82 Table 4: Growth forecasts by mayor institutions in six crises 1967-2009 Year Date JD CEE OECD GAER Actual The crisis 1966/67 1967 At-1 2.5 3.0 3.5 2.0 -   St -0.5 At 0.0 -1.0 The oil-crisis 1974/75 1974 1.0 1.5 0.5 1975 -2.0 -4.0 -3.5 The second oil-crisis 1981/82 1980 1981 -1.5 1982 Autumn t-1, Spring t, Autumn t Hardly differences between forecasters – OECD/ JD? Preceding year? Type of crisis does not seem to matter (REH?) 17.09.2018 Ullrich Heilemann

The unification-crisis 1993 Table 1: continued The unification-crisis 1993 1992 At-1 2.0 -   St 1.0 1.5 At 1993 0.5 0.0 -0.5 -2.0 -1.5 -2.5 The high-tech crisis 2001/02 2001 2.5 3.0 2002 The crisis 2008ff 2008 2009 -1.0 -6.0 -5.0 Sources: Heilemann. Stekler 2012, all figures rounded. Till ….GNP. since then GDP. – 1 At-1: autumn forecast for the coming year; St: Spring forecast for the current present year; At : Autumn forecast for the current year. 17.09.2018 Ullrich Heilemann

III Forecast performance VIII F. The recent recession (2008/09)Forecasting recessions (Table 5, Figure1) Again seen only when already amidst (November 2008), while it had started in 2nd quarter 2008 Many signals by official statistics & indicators had been ignored Slight adaption of declining real economy Reluctancy to forecast recessions – a reluctant Minister of Finance even after Lehman Brothers) 17.09.2018 Ullrich Heilemann

Table 5:. Forecasts of real GDP growth in Germany for 2008 - 2009 Table 5: Forecasts of real GDP growth in Germany for 2008 - 2009. rates of change against previous year. 2008 Date Institution 2008 2009 Actual (Spring each year National Statistical Office 1.3 5.0 April 2. DIW 2.0 1.6 April 8 IMF 1.4 1.0 April 17 JD 1.8 April 24 EU-Commission 1.5   June 5 IfW Kiel 2.1 June 12 RWI 2.2 June 20 OECD 1.9 1.1 Deutsche Bundesbank 2.3 June 24 Ifo 2.4 June 26 IMK 0.9 July 1 2.7 1.2 September 9 IWH Halle September 11 0.2 September 16 1.7 0.7 0.4 17.09.2018 Ullrich Heilemann

Table 6:. Forecasts of real GDP growth in Germany for 2008 - 2009 Table 6: Forecasts of real GDP growth in Germany for 2008 - 2009. rates of change against previous year. 2008 (continued) Date Institution 2008 2009 Actual (Spring e. year) National Statistical Office 1.3 5.0 October 7 IMF 1.8 0.0 October 8 DIW 1.9 1.0 October 14 JD 0.2   November 6 1.7 -0.8 November 12 CEE November 25 OECD 1.4 December 5 Deutsche Bundesbank 1.6 December 10 RWI 1.5 -2.0 December 11 Ifo -2.2 December 18 IWH -1.9 IMK -1.8 December 22 IfW -2.7 January 7 -1.1 Source: Institutions listed. 17.09.2018 Ullrich Heilemann

Figure 1: Forecasts of real GDP growth 2008 and 2009. April to December 2008 Stekler/Carnow 2013, the Conference Board 2011, similar for the US No error analysis of the forecast errors so far – assumptions: World trade, interest rates, etc. or expectations …. The JD in early October would probably have cried “Recession” – but August data for orders and for manufacturing that came in in early October The CEE called in its summary for extensive fiscal stimulus, but not in the full text and saw also only stagnation for 2009 Sources: see Table 1 and Federal Statistical Office. 17.09.2018 Ullrich Heilemann

III. Forecast performance VIII Forecasts presented in the 2nd & 3rd quarter 2008 did not fully take up the information of national & international statistics given by various surveys (on this & the following Heilemann, Schnorr-Bäcker 2012 The data available to forecasters do not seem to have been ambiguous or erroneous It is difficult to decide to which degree the forecast process itself contributed to these errors. alternative explanations than reported here are hard to see Forecasts for Germany seem to have low priors to forecast recessions The results point at a sticky or noisy processing of information (Clements 2012) at the onset of the crisis 2008/09 – a general feature or at work only in crises? (Fintzen/Stekler 1999) “Better data” (nor “methods”) will not necessarily help! 17.09.2018 Ullrich Heilemann

IV. Perspectives I The difficult object – the „imported“ crises National forecasters International forecasters B. The difficult subject – „The Great Dichotomie widens“ Dichotomy between theory and forecasting practice widens – indicators – a cyclical phenomen or a lasting reversal (trend) given the increasing supply of data and possibilities to analyse and use them? Who is starting monthly NA? … flash estimates? Using the internet? The supplemented (eclectic) informal GDP-model Increasing division of labour: decoupling of theory, data production, methods & forecasting The rise of symptomatic techniques & the decline of analytical techniques a. Indicators. barometers etc. – but widely ignoring the financial sphere that played a large role in the Harvard Barometer b. 250 indicators for Germany – but who can use them (we do make „sticky“ use of the data available (Clements, Mankiw etc.) Ad B 3: What theory anyway – the around-1978 macro-theory (Gordon 2009) Ad B 4: macro forecasting is 4 x 4 weeks business 17.09.2018 Ullrich Heilemann

IV. Perspectives II C. The difficulties of learning from past performance Only since a few years the JD is required to look back & not much detailed (assumptions/hypotheses/ „adds“?) Limits of the informal GDP-model to learn Nobody writes the minutes of the forecast production (as the FED, ECB & rating agencies are required to do?) The personal factor & collective memory The reluctance of the „Ordnungspolitik“-based forecasters to forecast crisis Institutional changes in the German forecast organisation – more (CEE, Bundesbank) & less (JD)? Ad C 1: The JD – CEE/OECD/etc say nothing about accuracy - bandwidth Dante hell & forecasters … Ad C 2b: So of limited leeway in a competitive environment – 0.5 % - a little bit here & there, inventories … Ad D. 4 to 5: large JD-institutions could be reduced to 2 without loss of accuracy and without difficulties to select them (in general: the number of forecasters does not increase the accuracy of foecasts …. 17.09.2018 Ullrich Heilemann

IV. Perspectives III D. Modest expectations as to further improvements of the accuray of the analytical approach 1. More theory, data, better methods, techniques? 2. Now a truism: integrating monetary sector & real economy 3. More competition? 4. Modest expectations a. the national & international experience so far – despite so many efforts b. time series analysis c. Analytical studies with macroeconometric models: the villain is the one period solution E. A different culture of forecasting and of forecasting analysis, most of all in the government sector D 1: not just forecasts of GDP of DDP-deflator Ad D2 : Germany not a particulier important demand: no financial crisis & no housing crisis Ad E: CBO, expert evaluation of forecasts, publishing forecasts 17.09.2018 Ullrich Heilemann

IV. Perspectives IV E. An optimistic view on the future of forecasting: The Taylor from Ulm (ca. 1592) “The bells ring out in praise That man is not a bird It was a wicked, foolish lie, Mankind will never fly, Said the Bishop to the People.” Bertolt Brecht 1934 17.09.2018 Ullrich Heilemann

Literature I 17.09.2018 Ullrich Heilemann Antholz, B. (2005), Zur Treffsicherheit von Wachstumsprognosen. Münsteraner Dissertation. Münster. Arrow, K. (1962), Economic welfare and the allocation of resources for invention. In: National Bureau of Economic Research (ed.), The rate and direction of inventive activity: economic and social factors. Princeton, N.J. : Princeton Univ. Press, S. 609-626. Barabas, G. (2009), Immer wieder aus Prognosefehlern lernen. In: Adolf Wagner (Hrsg.). Empirische Wirtschaftsforschung heute. Stuttgart (Poeschel). S. 183-193. Blix, M., Wadefjord, J., Wienecke, U., Ådahl, M. (2001), How good is the forecasting performance of major institutions? Sveriges Riksbank Economic Review,.., S. 38-68. Brookes, M. (2004), Extreme measures – the dark visions and bright ideas of Francis Galton. New York: Bloomsbury. Conference Board (2010), The Conference Board Leading Economic Index for the United States in the 2007 recession. In: Business Cycle Indicators, 15, no. 2. Clements, M. P. (2012). Do professional forecasters pay attention to data releases? International Journal of Forecasters 28. S. 297-308. Döhrn. R., Kitlinski, T., Münch, H. J. (2006). Zur Prognosegenauigkleit des RWI-Konjunkturmodells im Vergleich zu Zeitreihenmodellen. In: Adolf Wagner (Hrsg.). Empirische Wirtschaftsforschung heute. 2. Aufl.. Marburg (Metropolis). S. 171-181. Fair, Ray C. (2000). Structural macroeconometric modeling and the ‘modern’ view of macroeconomics. (Cowles Foundation and International Center for finance). New Haven. CT (Yale University). mimeo. Fildes, R. and Stekler, H. O. (2002), The state of macroeconomic forecasting, Journal of Macroeconomics 24, 435-468. Friedman, Walter A. (2007): The rise of business forecasting agencies in the United States, Harvard Business School Working Paper 07-045, Cambridge, MA. Fritsche, U.,Heilemann, U. (2010). Too many cooks? The German Joint Diagnosis and its production. (Universität Hamburg Department of Economics and Politics Discussion Papers Macroeconomics and Finance Series 1/2010.). Hamburg (Universität Hamburg). Gordon, R. F. (2009), Is modern macro or 1978-era macro more relevant to the understanding of the current economic crisis? Northwestern University. September 12, 2009. 17.09.2018 Ullrich Heilemann

Literature II Heilemann, U. (2012), Anwendungs-. Geltungs- und Reflexivitätsprobleme von Prognosen – Empirische Befunde und Probleme. In: C. Müller. F. Trosky. M. Weber (Hrsg.). Ökonomik als allgemeine Theorie menschlichen Verhaltens – Grundlagen und Anwendungen. Stuttgart (Lucius & Lucius), pp. 40-58. Heilemann. U., Klinger. S. (2006), Zu wenig Wettbewerb? Zu Stand und Entwicklung der Genauigkeit makroökonomischer Prognosen. In: W. Schäfer (Hrsg.). Wirtschaftspolitik im Systemwettbwerb. (Schriften des Vereins für Socialpolitik. 309.) Berlin (Duncker & Humblot). pp.. 225–257. Heilemann, U., Stekler, H. (2007), The future of forecasting – Introduction to ”The future of macroeconomic forecasting”. International Journal of Forecasting 23, pp.159-165. Heilemann, U., Schnorr-Bäcker, S. (2013), The 2008/09 recession in Germany: could it have been foreseen? Universität Leipzig/Statistisches Bundesamt Wiesbaden 2013 Heilemann. U., Stekler. H. (2012), Has the accuracy of macroeconomic forecasts for Germany improved? German Economic Review 14, 2, pp. 215-253. Johnston, J. (1991), Econometrics: retrospect and prospect. The Economic Journal 101, pp. 51-56. (Reprinted in H. Hanusch. H. C. Recktenwald (Hrsg.), Ökonomische Wissenschaft in der Zukunft - Ansichten führender Ökonomen. Düsseldorf (Verlag Wirtschaft und Finanzen), pp. 204-213. Koopmans. T. C. (1947), Measurement without theory, Review of Economic Statistics, August, pp. 161-172. Krugman. P. (2009). A dark age of macroeconomics (wonkish). New York Times. 27. Januar 2009. Kulla, B. (1996), Die Anfänge der empirischen Konjunkturforschung in Deutschland 1925–1933, Volkswirtschaftliche Schriften, Heft 464. Berlin 1996 Lucas. R. E. (2003). Macroeconomic priorities. Presidential address to the American Economic Association. American Economic Review. 93. S. 1-14. Nierhaus. W.. Sturm. J.-E. (2003). Methoden der Konjunkturprognose. Ifo-Schnelldienst. 56, Nr. 4, pp. 7-23. 17.09.2018 Ullrich Heilemann

Literature III 17.09.2018 Ullrich Heilemann Osterloh, S. (2008), Accuracy and properties of German business cycle forecasts. Applied Economics Quarterly. vol. 54. S. 27-57. Schips, B. (2012), Gedanken zur aktuellen Rolle der empirischen Forschung in den Wirtschaftswissenschaften. In diesem Band. S..-.. Seidler, H. (1975). Das für die Konjunkturdiagnose von den Instituten angewandte Ver­fahren. In: G. Fürst (Hrsg.). Konjunktur- Indikatoren. (Sonderheft zum AStA. 7.) Göttingen u.a. . S. 101-1 14. Sinai, A. (1992), Criteria for judging macroeconomic forecasting, Cato Journal 12, 161-165. Sinclair, T. M., Stekler. H. O., Kitzinger, L. (2010). Directional Forecasts of GDP and Inflation: A Joint Evaluation with an Application to Federal Reserve Predictions. Applied Economics 42. S. 2289-2297. Stekler, H. O. (2011), Was wissen wir über die makroökonomischen Vorhersagen für die G7? in: In: Adolf Wagner (Hrsg.). Empirische Wirtschaftsforschung heute, 2. Aufl.. Marburg (Metropolis), S. 207-211. Tichy, G. (1994). Konjunktur. Stilisierte Fakten. Theorie. Prognose. Berlin u. a. (Springer). Wagemann, E. (1928). Konjunkturlehre. Berlin (Reimar Hobbing). Wallis, K. F.. (ed.) with Andrews. M. J.. Fisher. P. G.. Longbottom. J. A. Whitley. J. D. (1986). Mo­dels of the UK Economy. A Third Review by the ESRC Macroeconomic Modelling Bureau. Oxford (Oxford University Press). Wild, J. (1974). Grundlagen der Unternehmensplanung. (rororo-Studium. 26.) Reinbek bei Hamburg (Rowohlt). 17.09.2018 Ullrich Heilemann