Long-term GDP forecasts and the prospects for …

1 Long-term GDP forecasts and the prospects for growthTheodore Modis ,1 growth Dynamics, Via Selva 8, 6900 Massagno, Lugano, Switzerlandarticle infoabstractArticle history:Received 13 August 2012 Received in revised form 4 February 2013 Accepted 20 February 2013 Available online 13 March 2013 The growth of GDP is considered as a natural- growth process amenable to description by thelogistic- growth equation. The S-shaped logistic pattern provides good descriptions and forecastsfor both nominal and real GDP per capita in the US over the last 80 years. This enables thecalculation of a Long-term forecast for inflation, which is to enter a declining trend not so far in thefuture. The two logistics are well advanced, more so for nominal GDP. The assumption for logisticgrowth works even better for Japan whose nominal GDP per capita has already completed tracingout an entire logistic trajectory.

2 The economic woes of industrialized countries could be attributedto the saturation of growth there, as if a niche in nature had been filled to capacity. In contrast,GDP growth in China and India is in the very early stages of logistic growth still indistinguishablefrom exponential patterns. The ceiling of these logistics can be anywhere between 5 and 10 timestoday's levels. 2013 Elsevier Inc. All rights :Logistic growthNatural growthS-curveGDPI nflationSaturationLogistic versus exponential1. IntroductionThe growth of Gross Domestic Product (GDP) is consideredto be an essential ingredient of a healthy economy. A plethora ofnear-future forecasts typically projects a constant percentageover several years in the future invariably promising growth [1].But longer-range forecasts are also often based on more or lessexponentially growing patterns[2]. And yet there have beenvoices advocating that days of diminishing growth areapproaching.

3 These voices began in 1972 with the publicationofThe Limits to Growthby the Club of Rome[3].Buttheyincreased in numbers recently with such works as Tim Jackson'sProsperity Without growth [4],SergeLatouche'sFarewell toGrowth[5], and Peter Victor'sManaging Without growth : Slowerby Design, Not Disaster[6]. Richard Heinberg has a ratherextensive compilation of publications on this subject in his bookThe End of growth [7].Complementary to the works mentioned, which aregenerally based on economic arguments, I want to addressin this article the growth of GDP as a natural- growth in competition is an appropriate eyepiece herebecause there is abundant competition in the processesthat contribute to the formation of GDP and the issue oflimited resources cannot be denied. Competition and limitedresources are the ingredients of logistic growth that de-scribes growth in competition of species populating ecologicalniches.

4 But my ultimate argument for using a logisticapproach is an a posteriori one, namely the goodness of theway logistic growth describes the evolution of GDP over growth implies a cap, a final ceiling, in sharpcontradiction to forecasts based on linear and exponentialpatterns, which are unlimited. I will present actual data onGDP growth demonstrating that such a cap is altogetherrealistic. Once at the ceiling there can be no more growth ,none unless catastrophes and disasters of unseen-beforemagnitude create new niches for growth or the species undergoes a major mutation effectively transforming itselfinto a different species, through war and conquest ofnew Forecasting & Social Change 80 (2013) 1557 1562 Tel.: +41 91 9212054; fax: +41 801 Modis is the founder of growth Dynamics, an organiza-tion specializing in strategic forecasting and management consulting: $ see front matter 2013 Elsevier Inc.

5 All rights lists available atScienceDirectTechnological Forecasting & Social Change2. Logistic-growthfits on the US GDPThe historical data on the US GDP per capita come from theUS Department of Commerce, Bureau of Economic Analysis,and the USCensus Bureau[8] . Theyconsist of yearlydata pointsup to and including reliable estimates for year 2012. Thelogistic equation used is Eq.(1) . The fitting procedure involvedthe minimization of a Chi Square using EXCEL's M1 e t to C 1 whereMis the ceiling level of the logistic S-shaped pattern, the steepness of the curve,tothe midpoint of the entire growthprocess, andCan eventual pedestal (positive or negative) onwhich the logistic may be sitting, often associated with missingearly with the dilemma of studying the nominal GDPexpressed in current dollars or the real GDP correctedfor inflation expressed in constant (chained) dollars, Idecided to study them both.

6 Furthermore, I chose to look atGDPper capita, because the growth of population may maskor modulate the growth of GDP. To my surprise both sets ofdata resulted in excellent logistic 1shows nominalGDP per capita andFig. 2shows real GDP per capita. Thelower graphs show the rate of change in annual increments, the life cycle of each process; they are derived from thecurves at the top ofFigs. 1 and 2. The emerging imagesindicate that the inflection points centers of the life-cyclecurves are behind us, particularly for nominal, and thatthere is about a 7-year lead by nominal goodness of the fits can be visually appreciated by theway the data points closely follow the logistic patterns (thickgray lines) over 80 years despite many world-shaking eventsand varying inflation over this period of time. The fitparameters are tabulated inTable further surprise was that whereas the nominal GDP nearscompletion of the growth process, the curve was by the end of 2012, the real GDP has still considerableremaining growth potential, its curve was only respective midpoints inflection points of the logistics were in mid 1998 for nominal GDP and late 2005 for real black lines delimit 90% confidence-level bands, in otherwords, where we should expect future GDP values to fallnine times out of ten.

7 Such bands were established usinglook-up tables in Reference[9] and taking into account theerror per data point (approximated here by the meanabsolute deviation). The 90% confidence-level intervals forthe two inflection points are 1995 2000 and 1991 $US Nominal GDP per Capita in Current $Annual IncrementsFig. , nominal GDP per capita (black dots) and logistic fit (thick grayline). Below, the rate of growth in annual increments. The open circles areIMF forecasts . The thin black lines delimit 90% confidence-level $US Real GDP per Capita in Chained 2005 $Annual IncrementsFig. , real GDP per capita (black dots) and logistic fit (thick grayline). Below, the rate of growth in annual increments. The open circles areIMF forecasts . The thin black lines delimit 90% confidence-level bands. Thebig black dot is a Long-term forecast by Agnus Maddison[11].Table 1 Results for the logistic fits on nominal and real US GDP per toCMean Modis / Technological Forecasting & Social Change 80 (2013) 1557 1562 The open circles shown for the period 2013 2017 areforecasts by the International Monetary Fund (IMF) made intraditional economists' ways, most frequently consisting oflinear and exponential extrapolations[10].

8 For nominal GDPthey indicate a more optimistic trend progressively deviatingfrom the logistic course (outside the 90% confidence-levelband). The big black dot inFig. 2is a Long-term forecast byAgnus Maddison[11].There is a rather limited amount of growth potentialahead of us in nominal GDP but a significant amount ofgrowth potential in real GDP, which economists prefer to talkabout more often than not. But what good is it for us to knowthat somewhere there is much growth while all we see ineveryday life in current dollars is little growth ? The real GDPseems to have little relevance to the people on the inflation has eaten up all our growth given that both nominal and real GDP constitutenatural- growth processes follow logistic trajectories inflation, which is linking these two must also have somenaturalorigin rather than its usual attribution to frivoloushuman behavior!

9 In fact, the decline of nominal GDP's rate of growth inpercentage termsbegan already in the late 1970s, as can beseen inFig. 3. The data fluctuate considerably particularlyduring early 20th century because of the small absolutevalues of GDP (which is in the denominator). Nevertheless,the thick gray line, derived from the logistic curve inFig. 1,provides a good description for what happened during thelast 80 years. The trend indicated by the IMF forecasts seemsto be in sharp InflationFrom the logistic curves for nominal and real GDP we canextract an overall trend for inflation, shown inFig. 4. Thethick gray line is not a fit to the data here. It is calculated fromthe ratio of the gray logistic curves inFigs. 1 and 2, and seemsto be a fair description of the trend of the consumer priceindex over the past 80 years. It provides a Long-term forecastfor inflation something of a Holy Grail quest for heralds deflationary times in the GDP growth in other parts of the worldIt is of interest to also examine the Long-term prospects ofGDP growth from a logistic point of view in other parts of 5shows that the nominal GDP per capita in Japanhas completed its logistic curve twenty years ago!

10 No un-certainties around this logistic fit. The fit parameters are givenin Table has been no growth in Japan for twenty years and thetraditional forecast from IMF for years 2013 2017 shownhere with the open circles does not contradict our logisticdescription unless its rising trend continues well beyond in developing countries the story is 6 and 7show the nominal GDP per capita and logisticfits for China and India respectively. The data come fromEconStats[12]. Both growth processes are in the very earlystages of logistic growth , a region where it is difficult to-5%0%5%10%15%20%1930 1938 1946 1954 1962 1970 1978 1986 1994 2002 2010 2018 2026 2034 2042 2050 PercentageNominal GDP per Capita % Annual Rate of ChangeFig. percent rate of growth of nominal GDP per capita (black dots) and of the logistic fit (thick gray line). The open circles are IMF Price Index1982-84 = 100 Fig.