Australia's Population Future: Probabilistic Forecasts Incorporating Expert Judgement

Australia’s Population Future: ProbabilisticForecasts Incorporating Expert Judgementgeor_702 261..275

MARTIN BELL*, TOM WILSON and ELIN CHARLES-EDWARDSQueensland Centre for Population Research, School of Geography, Planning and EnvironmentalManagement, Chamberlain Building, The University of Queensland, Brisbane Qld 4072, Australia.*Corresponding author. Email: [email protected]

Received 30 November 2010; Revised 24 April 2011; Accepted 1 May 2011

AbstractProjections of future population are essential for planning in both the public andprivate sectors but conventional approaches provide little guidance as to theuncertainties associated with published projections. Moreover, history suggeststhat forecasters are generally slow in responding to new trends in key demo-graphic processes. These limitations come into sharp relief at times of high publicinterest, such as occasioned by the unprecedented increase in Australia’s netoverseas migration over the past decade. How reliable is the recent upwardsrevision which raises Australia’s projected population from 28 million to 35million by mid-century? If projections are to be of more value to users, progressis required on two fronts: (i) more effective processes for setting assumptions, and(ii) greater clarity as to the uncertainty of the resulting projections. We addressthese challenges by combining a more systematic, theoretically guided approachto the formulation of projection assumptions using a structured questionnaire toelicit the views of experts on the future of net overseas migration to Australia, andharness the results in a new, probabilistic projection framework which explicitlyidentifies confidence intervals within which Australia’s future population growthis likely to fall. We present probabilistic projections for Australia from 2010 to2051 and compare the results with the 2006-based Australian Bureau of Statisticsprojections. We show how forecast uncertainty grows, and how it varies betweendemographic variables.

KEY WORDS population projections; forecasts; migration; probabilistic;expert judgement; Australia

ACRONYMNOM net overseas migration

IntroductionThe growth and distribution of population hasbeen a recurrent theme in Australia since the daysof first European settlement, but concern withdemographic issues intensifies at times of crisis,and one result is that population projections tendto proliferate. Triggered by concern about thefalling birth rate, the earliest projections datefrom the turn of the last century, and were based

on simple extrapolation of contemporary growthrates (see, e.g. Coghlan, 1903; Johnston, 1906;Bell, 1992). Similar concerns underpinned pro-jections prepared by the National Health andMedical Research Council (1944) in the early1940s as fertility hovered at historic lows, andagain in the 1970s as the National PopulationInquiry (1975; 1978) was established against abackground of declining fertility, reaction to

261Geographical Research • August 2011 • 49(3):261–275doi: 10.1111/j.1745-5871.2011.00702.x

high post-war immigration and increasingdebate about desirable population futures. Fromthe 1930s, most projections were made usingthe cohort-component approach, now widelyadopted as the standard methodology, and fromthe mid-1970s the Australian Bureau of Statistics(ABS) began to produce national projectionson a regular basis, every 2 to 3 years. These weresubsequently extended to the states and territo-ries, and then to capital cities, and now underpinan extensive state-based system of demographicforecasting aimed at providing a basis forinformed planning from the national to the locallevel (Bell, 1992; 1997).

How well have these projections performed interms of correctly anticipating future populationchange? As the American demographer NathanKeyfitz once observed, demographers haveshown surprisingly little interest in examiningthe performance of their forecasts (Keyfitz,1981). In Australia, the available evidence sug-gests only limited improvements in forecast per-formance over several decades (Adam, 1992;Bell and Skinner, 1992; Wilson, 2007). Accuracyis not the only goal of demographic projections;they can also serve to illustrate alternative popu-lation futures, or to describe the pathway to apreferred population target (Isserman, 1984).However, the utility and credibility of projectionsis not well served by a proliferation of alternativeprojection series, nor by radical changes in pro-jection assumptions from one series to the next.The effective doubling of projected growth from7 to 14 million between the 2004- and 2006-based ABS projections, taking Australia’s popu-lation from its 2010 level of 22 million to either28 million (ABS, 2006) or 35 million (ABS,2008a) by mid-century, does little to inspire con-fidence in forecast reliability, although it doesperhaps help to underline the uncertainties asso-ciated with forecasting future population growth(ABS, 2006; 2008a).

In this paper, we present a new projectionfor the population of Australia in a way thataddresses both these concerns of inherent uncer-tainty and the selection of appropriate assump-tions. We do this by using a probabilisticapproach to making projections, coupled with asurvey that aimed to elicit expert opinion as tolikely future trends in overseas migration, thesingle most volatile component of populationchange. By way of background, the followingsection first provides a brief overview of recentAustralian population trends. Next, we outlinekey elements of the probabilistic approach to

projections and the methods used to set assump-tions. Results from the survey of experts follow,and we describe how these are integrated into theprojection process. Based on these assumptionswe report the probable trajectory of Australia’spopulation through to the year 2051 and identifythe envelope of uncertainty.

Trends in population growthAt the turn of the millennium, Australia’s popu-lation stood at a little over 19 million, more thandouble of the 8.2 million attained in mid-century, and a fivefold increase on the 3.8million at the time of Federation. From 1950 to2000, the population grew at an average of 1.7%per annum, with a net addition of some 220 000people each year, two-fifths of which was duedirectly to overseas migration. Growth ratesfluctuated sharply over the 50 year period, aver-aging 2.2% during the baby boom and the surgeof post-war immigration, then falling to just1.3% in the 1970s as fertility dipped belowreplacement level and net overseas migration(NOM) fell to a historic low of just 21 000.While the birth rate remained depressed, surgesof immigration sustained growth in the 1980s,as NOM climbed above 100 000 per annum in1981–1982, and again from 1986 to 1990, inter-rupted by sharp cutbacks in response to domes-tic economic conditions. The early 1990srepeated the pattern, with net gains dipping tojust 30 000 in 1993, then climbing to 104 000three years on as the total fertility rate (TFR)resumed its downwards trend. At the same time,a sustained fall in mortality, after a brief hiatusin the 1960s, contributed to the steady ageing ofthe country’s population. By 2000, the TFR washovering at 1.75, life expectancy for men stoodat 77.4 (5 years below that of women), andNOM was again on the rise, registering just107 000 for the year.

Embedded firmly in these trends, populationprojections prepared since the 1970s have beencharacterised by a large measure of assumptiondrag – the tendency to shape assumptions basedon attachment to outdated information or expec-tations, and a disregard for new developments(Ascher, 1979) – although there is evidence tooof some recency bias – a tendency to be exces-sively influenced by the very latest trends. Thus,it was not until 1987 that ABS projections movedaway from an expectation that fertility wouldreturn to replacement level, although once abelief in low fertility had set in, that soon becamethe conventional wisdom. The 1997 projections

262 Geographical Research • August 2011 • 49(3):261–275

© 2011 The AuthorsGeographical Research © 2011 Institute of Australian Geographers

set one fertility assumption at a TFR of 1.6 andby 2002 this had become the medium assumption– even though actual fertility never fell below1.7. In a similar way, the hiatus in mortalityimprovement in the 1960s underpinned a lastingbelief that contemporary gains in life expectancycould surely not be sustained, so that it was notuntil the 2002 ABS projections that a low mor-tality assumption emerged. As Oeppen andVaupel (2002) observed worldwide, and Wilson(2007) demonstrated for Australia, forecastershave consistently underestimated gains in lon-gevity. Overseas migration assumptions, too,have proven remarkably sticky, with net gainsranging from 75 000 to 110 000 persistent inABS projection assumptions throughout the1980s and 1990s. It therefore came as a remark-able shock when the 2006 projections radicallyrevised expectations about future levels of over-seas migration. Compared with the projectionsreleased just 2 years earlier, the medium assump-tion rose from 110 000 to 180 000 per annum,and yesterday’s high (140 000) became today’slow, while the new high was re-drawn at amassive net gain of 220 000 per annum – a figurenever before approached in Australian migrationhistory.

It was this sharp jump in the assumed level ofNOM, coupled with a small increase in mediumfertility, that underpinned the stark jump in theABS projection for 2050. Mirrored in the ThirdIntergenerational Report (Department of Trea-sury, 2010), the shift from 28 million to 35million triggered a subsequent frenzy of debateduring early 2010 about the merits of a ‘BigAustralia’ (Henry, 2009; Rudd, 2009; Betts,2010a). In the short term, the projections haveproven prophetic, at least for migration, with aclear vindication for recency bias in projectionassumptions. NOM hovered around 120 000 perannum for the first 5 years of the new decade,then rose sharply to 182 000 in 2006, 244 000 in2007, and 316 000 in 2008, falling dramaticallyto 216 000 in 2009–2010. Triggered largely byan unprecedented gain from various forms oftemporary migration – students, skilled labour,tourists, working holiday makers, and others –this spike has proven to be short-lived, althougha concurrent rise in the permanent skilled migra-tion programme foreshadows at least someratcheting up of net gains from overseas com-pared with the 1990s. At the same time, Austra-lian fertility has risen unexpectedly beyond thehigh–low bounds anticipated in recent projec-tions, with the TFR reaching 1.93 in 2008–2009,

a level not seen since the 1970s. As Morrison(1975) once observed, there is perhaps no moredifficult nor dangerous task in demography thanto try to distinguish a trend from a fluctuationwhen one is still in the middle of it. These varia-tions do, however, have the singular merit ofunderlining the volatility of population trendsand the uncertainty associated with attempting topredict them.

Probabilistic projection modeland assumptions

Why projections should be probabilisticConventionally, demographers have attempted towarn users about forecast uncertainty by produc-ing several alternative projections, often ‘high’,‘medium’, and ‘low’ variants. The high–lowrange is understandably construed by many usersas a kind of prediction interval, but unfortunatelyinterpreting it in this way is problematic (Lee,1999; Keilman et al., 2002).

• First, the likelihood of future population lyingwithin this high–low range is generally notspecified. What is the chance that future popu-lation will be within the range? Is it 50%, 67%,80%, 95%, 100%? It is unclear.

• Even if the high–low range were assigned acertain prediction interval, the proportion ofpossible demographic futures between the highand low variants would almost certainly varyover the course of the projection horizon. Thehigh–low range is inconsistent over time. Infact, it has been shown that a high–low rangeoften covers a smaller proportion of possibledemographic futures in the first few years of aprojection horizon compared with later on(Keilman, 2008).

• Similarly, the high–low range covers largeintervals for some projected demographic vari-ables (e.g. total population) but fairly smallranges for other variables (e.g. the elderlydependency ratio). High and low projectionvariants are often specified with high and lowfertility and migration. Projected variableswhich are affected significantly by mortality(such as deaths) will therefore possess a smallhigh–low range. For any particular forecastyear the high–low range cannot possibly coverthe same proportion of future outcomes for allvariables: it is probabilistically inconsistentacross variables.

In addition to the invalidity of the high–lowrange as a prediction interval, there are further

M. Bell et al.: Australia’s Population Future 263


problems with the traditional variants approach.For example, if there is a choice of projections,users will tend to select whichever variant alignswith their vested interests (Keilman, 2008).Property developers are likely to argue that thehigh fertility–high migration variant is the mostlikely outcome. Government transport depart-ments might decide that a low growth scenario ismore probable.

Probabilistic population projections – projec-tions comprised of a distribution of possibledemographic futures – overcome these problems.They are created by running thousands of simu-lations with randomly varying fertility, mortality,and migration rates or flows. The results of allthese simulations are then ranked from highest tolowest for every projection year. User-definedprediction intervals covering a certain percentageof the distribution (e.g. 20%, 67%, 95%) can thenbe calculated. For example, if 5000 simulationsare produced, the 95% prediction interval rangesfrom the 125th ordered value to the 4875th.Commonly, probabilistic projections are illus-trated by ‘fan diagrams’ with selected predictionintervals marked out. Several of the graphs pre-sented in this paper are of this form.

The advantage of probabilistic projections tousers is that they indicate how much uncertaintyexists for a particular demographic variable andhow this changes the further we look into thefuture. For some variables there may be littleuncertainty over a selected time frame; for othersuncertainty may be very considerable. Planners,policy makers and other users of projections canincorporate this information on uncertainty intotheir planning and decision-making (Lee andTuljapurkar, 2007). For example, if there wasconsiderable uncertainty about the future annualnumber of births then plans could be formulatedwhich allow some flexibility in hospital mater-nity service provision. On the other hand, a morepermanent course of action could be applied to aservice which depends on a demographic vari-able, such as the number of deaths, for whichthere is relatively little uncertainty.

The many advantages of probabilistic methodshave been accepted by demographic researchers,and probabilistic population projections havenow been produced for many countries andglobal regions. Contributions over the last fewyears include those for Australia (Wilson andBell, 2004; Hyndman and Booth, 2008), China(Li et al., 2009), Germany (Härdle andMysickova, 2009), Japan (Okita et al., 2009),New Zealand (Wilson, 2005), and Poland (Maty-

siak and Nowok, 2007). In addition, the Uncer-tain Population of Europe project produced a setof probabilistic forecasts for 18 European coun-tries using a consistent method and correlationsin demographic processes between countries(Statistics Netherlands, 2005). The challengeremains to convince national and state statis-tical offices, naturally conservative and cautiousorganisations, to embrace these methods. TheUS, UK, and New Zealand statistical offices haveundertaken some experimental work on probabi-listic population projections, but such projectionshave yet to become part of these organisations’regular statistical output (Long and Hollmann,2004; Rowan and Wright, 2010).

While probabilistic projections offer manyadvantages over conventional deterministic pro-jections, they are not a panacea for all demo-graphic forecasting problems. They quantifyuncertainty in a statistically consistent way, butthey do not necessarily provide more accurateprojections. In addition, predictive distributionsare themselves estimates. Probabilistic projec-tions are also a little more complex andtime-consuming to produce than deterministicprojections and the models are currently onlyfully developed for national-level applications.Nonetheless, we hope this paper demonstratesthat the advantages of probabilistic projectionsfar outweigh these relatively minor drawbacks.

The PROBPOP modelPopulation projections reported in this paperwere produced by the PROBPOP (PROBabilisticPOpulation Projections) model developed by theQueensland Centre for Population Research.This incorporates a cohort-component modelwhere the population is disaggregated by sexand single years of age up to 110+, and whereemigration is modelled as age-specific ratesconstrained to a total flow, and immigration asage-specific flows. Constraining emigration inthis way simplifies the setting of assumptions interms of NOM numbers. The probabilistic natureof the model is obtained by running 5000 simu-lations with randomly varying demographic ratesand flows generated by time series models. Themodel is operationalised in Fortran 95 and linkedto a Microsoft Excel front end for ease of use anddata input. The projections begin with the 30June 2010 Estimated Resident Population andextend out to 30 June 2051.

Projection output from PROBPOP is obtainedin a two-stage process. First, projections arewritten in detail to several files, effectively



creating a large database of ‘raw’ projectionoutput (as advocated by Alho and Spencer,1991). Second, distributions for any of the statis-tics in the database (e.g. total population, elderlydependency ratio, births) are obtained througha separate program which extracts the variablesof interest and sorts the 5000 values from highestto lowest for every projection year. Values atselected points on the distribution are thenwritten to a summary output file. This two-stageprocess allows users to quickly obtain new pre-dictive distributions from the database withouthaving to wait 15 minutes while the probabilisticmodel is rerun.

Projection assumptionsIn probabilistic population projections predictivedistributions of fertility, mortality, and migrationare commonly produced using a combination oftime series models, expert judgement, and analy-ses of historical forecast errors (Keilman et al.,2002); sometimes error distributions of naiveforecasts – those which assume no change or nochange from an obvious trend – are also takeninto account (Alho, 1990). In our projections wefitted Autoregressive Integrated Moving Average(ARIMA) models to the TFR and female andmale life expectancy at birth. To represent totalimmigration and total emigration we also usedARIMA models but selected the model andparameters to align with the findings of ourexpert survey. Equations and parameters of thesemodels are presented in the Appendix.

In identifying a suitable model to represent theTFR we examined data from 1976 to 2009, aperiod of below-replacement fertility which ismost relevant to the current and future social andeconomic context within which childbearingoccurs. A random walk with drift model wasfound to be appropriate. We adjusted the medianof the distribution to match the most recentABS medium series fertility projection, whichassumes the TFR slowly declines from recentvalues until it levels off at 1.80 from 2020 to2021 onwards (ABS, 2008a). The 95% predic-tion interval for the TFR spans 2.33 to 1.29 by2051.

For life expectancy at birth we fitted models todata spanning 1971 to 2009. This period waschosen because of a discontinuity in trend in thelate 1960s marking the turning point from littleimprovement in life expectancy to sustainedincreases ever since (Australian Institute ofHealth and Welfare, 2000; ABS, 2010a). Randomwalk with drift models were found to represent

the 1971–2009 trends satisfactorily. The mediansof female and male life expectancy were adjustedto align to our own deterministic mortality pro-jections, which were calculated through expo-nential extrapolations of age-specific death ratesand life tables. By 2050–2051, these projectionsput female life expectancy in Australia at 90.8years and that of males at 87.8 years, rather moreoptimistic than the equivalent medium seriesABS assumptions of 87.8 and 84.6 for femalesand males, respectively (ABS, 2008a). The 95%prediction intervals of our projections span 94.5to 87.0 years for females and 91.7 to 84.1 yearsfor males by 2051.

For migration we took a slightly differentapproach. As mentioned earlier, given the radicalchange in overseas migration trends in Australiaover the past decade, together with changes in themethod of measuring overseas migration in2006, we felt past data would not provide a reli-able guide to uncertainty. Instead we chose anARIMA model with selected parameters basedon the findings of our survey of migrationexperts.

Net overseas migration – whatthe experts thinkPopulation projections are commonly preparedby analysts working in-house, but most statisticalagencies consult with experts to assist in formu-lating assumptions. Lutz (2009) found that three-quarters of 21 European Union members hadinvolved external experts in assumption-setting.However, the number of experts involved, themechanisms employed for consultation and thesignificance attached to the expert views variedwidely. Eliciting expert views, reconciling differ-ences, and incorporating them into assumptionsis by no means straightforward. Wisniowski andBijak (2009) used a two-round Delphi approachto explore expert opinion on future levels ofinternational migration for eight Europeancountries. The most systematic assault on theproblem to date, however, is due to Lutz andcolleagues who have pioneered an ‘argument-based’ approach to incorporating expert views,which attempts to systematically assess both thevalidity of particular arguments about forceslikely to influence future trends in a demographicprocess (e.g. migration), and the significance ofthose force in determining future trends (Lutz,2009). Lutz (2009) established an extensive,spreadsheet-based questionnaire identifying themultiple forces acting on each of the componentsof population change – fertility, mortality, and



migration. Although ultimately intended tounderpin a new global set of projections, the firstapplication of this approach was by the UKOffice of National Statistics who piloted anadapted version to seek the views of their smallNational Population Projections Expert AdvisoryGroup in 2007 (Shaw, 2008).

Our approach to eliciting expert opinion fol-lowed in the same tradition but confined attentionsolely to international migration. Implemented asa web-based instrument using Survey Monkey,we asked respondents how a series of specifiedfactors would impact on future levels of migra-tion under nine distinct categories of visa entry.These included both permanent and temporarymigration, each of which are arguably subject tosomewhat different sets of international anddomestic forces. Following Lutz (2009) we alsoasked the experts to identify the most likelyoverall level of NOM to Australia 10 and 20years into the future, and to qualify the probablebounds of their estimates by expressing 67%confidence intervals. Comprehensive results ofthe survey are reported elsewhere (Wilson et al.,2011). Here we confine attention to reporting themajor characteristics and survey results.

The survey was distributed to 38 individualsidentified by the authors as having expertise onAustralia’s overseas migration, of whom 24responded. More than half of respondents wereacademics (13), nine worked in Government orthe Private sector and two did not identify theiraffiliation or background. The majority werelocated in Australia (19), while three were over-seas. Individuals were asked to nominate thelength of time they had been involved in demo-graphic research. Eleven indicated they had morethan 20 years experience, seven had between 10and 20 years experience, while four had beenworking in the field for less than 10 years.Respondents were also asked to self-rate theirexpertise with respect to Australia’s overseasmigration. Five rated their knowledge as Excel-lent, 14 as Good, and three as Average.

The key purpose of the survey was to elicitopinions on the likely level of NOM to Australiain 2020 and 2030. Information was sought withrespect to total NOM, as well as the individualcategories of movement which make up thistotal. Table 1 reports the mean of the estimatesgiven by respondents, classified according toemployment sector and level of expertise.

Combining all responses, our group of 24experts expected that NOM would be sustained atlevels well above the recent long term average of

170 000 per annum, although considerably belowthe peak reached in the spike of 2007–2009. By2020, their collective wisdom puts NOM at187 000 per annum, on an upward trend to a littleunder 200 000 per annum by 2030. Predictedlevels vary according to respondent backgrounds.Experts working in Government and the Privatesector anticipate net migration levels that are con-sistently 25–30% higher than their counterparts inacademia. Predictions also vary with self-assessed expertise. Respondents who classifiedtheir knowledge of overseas migration to Austra-lia as Average (the lowest of the three categoriesselected) cited the lowest values of NOM, andwere the only group anticipating a declinebetween 2020 and 2030. Those professing Goodknowledge of the field predicted significantlylarger net gains, especially by 2030, with thefigure of 208 000 almost 40% above that pre-dicted by the ‘Average’ group. The experts withthe highest self-ratings fell midway between thesetwo extremes, with predictions that are remark-ably close to the NOM of 180 000 assumed inSeries B of the 2006-based ABS population pro-jections. Perhaps bullish views intensify, thenmoderate, as knowledge and experience evolve?Our results certainly point to more conservativeexpectations among experts with longer experi-ence in the field, although this might reflectassumption drag, rather than greater expertise.

Underpinning these global predictions, thesample of experts was asked which visa categoriesthey thought would be the key drivers of future

Table 1 Predicted net overseas migration, Australia(Source: authors’ survey of experts).

2020(Thousands)

2030(Thousands)

Employment sector1

Academic 169 178Public/private 214 228

Self-rated expertiseAverage 162 150Good 195 208Excellent 178 195

Length of experience working in migration0 to 10 years 208 25010 to 20 years 181 195More than 20 years 183 189

Total 187 197

1 Two respondents did not identify their background and didnot provide net overseas migration predictions.



change. Table 2 summarises the distribution ofresponses relative to average values for the period2004 to 2008. Most components of NOM arepredicted to be higher in 2020 and 2030 than inrecent years. For permanent skilled migration,family migration, temporary labour migration,and working holiday makers there is close tounanimous agreement that levels will be higher in2020 and 2030. Consensus is weaker on futurelevels of migration by New Zealand citizens andinternational students, but again most respondentssaw an increase on current levels as the mostlikely result. Movement by Australian citizensand humanitarian migration are the only catego-ries for which a stabilisation at current levels isseen as the most likely future.

What were the forces that would shape futurechange across the various categories of migra-tion? The experts identified skill shortages, unmetdemand for labour, and concerns about populationageing as key factors likely to drive future growthin labour migration – both permanent and tempo-rary – including movements under the WorkingHoliday Maker programme. Increased globalmobility and liberalisation of migration flowswere also seen as influential, raising both labourand family-related migration to Australia. On theother hand, the experts thought that growingpublic concern about a ‘big Australia’, coupledwith changes to government regulation, wouldconstrain flows in several categories of move-ment. International student migration has been thebiggest contributor to NOM in recent years, butthe collective wisdom from our survey suggestedthat increased competition for international stu-dents, rising tuition and living costs, coupled withreduced opportunities for permanent residencywould lead to a fall in future levels of student

migration, counterbalanced in part by growth inthe global international student market.

Extending this inquiry into causes and condi-tions, we also asked each respondent to speculateon the societal conditions that would be needed toraise or lower their predicted NOM 20 years intothe future by 100 000 or more. A fall of thismagnitude was considered unlikely, but mightpotentially be initiated by environmental con-cerns, economic collapse precipitated by the endof the resources boom, or a public backlashagainst high immigration underpinned by ethnicor racial tension. A corresponding increase wasthought to require a confluence of favourableconditions, including public acceptance of a ‘bigAustralia’ supported by development of appropri-ate infrastructure, continued skill shortages andsustained growth of temporary migration gains,particularly from the international student market.

As experts well-versed in the volatile nature ofinternational migration, we also asked respon-dents to quantify the level of uncertainty associ-ated with their predictions, by nominating theupper and lower bounds around their forecastNOM for 2020 and 2030. Figure 1 presents theindividual expert views on the most likely levelof NOM in 2020 and the extent of the 67% pre-diction interval. Underpinning the averages citedin Table 1, it is clear that opinions differ widely,both about the future level of migration and thedegree of uncertainty. Most likely values for2020 vary from 100 000 to 280 000; the lowerbound of the 67% interval ranges from 70 000 to220 000 while the upper bound varies from130 000 to 350 000.

The literature provides little guidance onmechanisms for translating expert views intopredictive distributions. The approach adopted

Table 2 Predicted future trends in net overseas migration by visa category (Source: authors’ survey of experts).

Visa Category 2020 2030

Lower Same Higher Lower Same Higher

Permanent skilled migration 3 0 21 3 2 18Family migration 1 2 20 1 2 20Temporary labour migration 1 1 19 1 1 19Working holiday makers 2 1 19 2 0 19New Zealand citizens 2 6 14 3 5 13International Students 3 8 11 4 5 12Australian citizens 2 10 10 5 9 7Humanitarian visas 2 14 6 1 11 9

Note: Totals vary due to non-response.



here aims to take account of the considerableuncertainty and variability about future migra-tion expressed by our group of experts. We com-bined the experts’ upper and lower boundpredictions into a single distribution and set the67% predictive interval of NOM for 2020 tocover 67% of this new distribution. Applying thismethod to the expert views in Figure 1 delivers anet migration range of 156 851, spanning from121 043 to 277 894. The result is shown as thedarker bar at the right-hand side of Figure 1. Thesame process applied to expert opinions for 2030resulted in a most likely value of 195 952 and a67% interval spanning from 107 746 to 303 914.

These expert-based prediction intervals couldnot be used directly because immigrationand emigration are modelled separately inPROBPOP to avoid the practical and conceptuallimitations of net migration (Rogers, 1990;Wilson and Bell, 2007). Our solution was to usethe expert opinions to adjust the parameters ofthe immigration and emigration time seriesmodels, such that (i) the median of the NOMdistribution produced as part of the model outputapproximately matched the mean of the expertopinions in 2020 and 2030, and (ii) the predictivedistribution approximately equalled the expert-based 67% prediction interval in 2020. It was notpossible to obtain 67% prediction intervals in themodel output to match both the 2020 and 2030expert-based intervals. Given that uncertainty is

greater further into the future we opted to privi-lege the 2020 expert-based prediction interval.NOM projections are illustrated in Figure 2.

Australia’s demographic futures

Total populationFigure 3 presents the results of the probabilisticprojections of Australia’s total population outto 2051. From a jump-off population of 22.3million in 2010, the median of the distributionincreases to 29.5 million by 2031, 32.8 millionby 2041, and 36.1 million by the end of theprojection horizon in 2051. This trajectory tracksabove the 2006-based ABS Series B projectiondue to a higher starting population, more opti-mistic life expectancy assumptions and margin-ally higher NOM. Under the ABS Series Bassumptions Australia’s population is projectedto reach 28.8 million by 2031, 31.6 million by2041, and 34.2 million by 2051 (ABS, 2008a).

The extent to which uncertainty about thedemographic future increases over time is clearlyillustrated by the prediction intervals. We can berelatively certain about the size of Australia’spopulation in the near future. By 2016, forexample, we estimate there is a 67% chance, or 2to 1 odds, that the total population will lie withinthe range 24.2 million to 24.7 million. By 2031the 67% prediction interval has expanded to 28.1

Figure 1 Expert opinions on the most likely value and 67% prediction intervals for net overseas migration in 2020. (a) Final67% prediction interval based on expert responses (see text) (Source: authors’ survey). Note: Only 21 of the 24 surveyparticipants provided answers to the questions on total net overseas migration and 67% prediction intervals.



million to 31.0 million, and by 2051 it spans therange from 32.7 million to 39.6 million.

Despite uncertainty about the size of thenation’s population over the next four decades,the projections clearly show the certainty of popu-lation increase. The lower limit of the 95% pre-diction interval in 2051 is 29.4 million, about 7million higher than the 2010 jump-off population.In fact, even the lowest of the 5000 simulations isseveral million higher than the 2010 population.

This predictive distribution provides a usefulframework to assess the plausibility of variousaspirational targets. The newly created StablePopulation Party of Australia, for example, wouldlike to ‘stabilise Australia’s population at around23–26 million through to 2050’ (Stable Popula-

tion Party of Australia, 2010). However, accord-ing to these projections, the chance of Australia’spopulation lying within this range by 2050 isnegligible: the lower bound of our 99% predictioninterval for 2050 is 27.2 million. On the otherhand, former Prime Minister Malcolm Fraser sup-ports a population of 45 million to 50 million bymid-century (Weekend Australian, quoted inMcdonald and Kippen, 1999). The chance of thenation’s population reaching 45 million or moreby 2050 is also very slim: less than 1% of oursimulations exceeded 45 million by this date.

The problems of interpreting high–low rangesas prediction intervals were mentioned earlier.It is instructive therefore to compare our predic-tive distribution with the high–low range of

Figure 2 Observed trends and probabilistic projections of net overseas migration, Australia, 1970–1971 to 2050–2051(Sources: ABS, 2008b; 2009; 2010a; 2010b). Note: Net overseas migration figures before and after 2006 are not strictlycomparable due to a change in measurement by ABS (2010c).

Figure 3 Observed trends and probabilistic projections of the total population of Australia, 1971–2051 (Sources: ABS, 2008b;2009; 2010a; 2010b).



conventional population projections forAustralia.We select the most recently produced ABS SeriesA and C projections which, while not explicitlylabelled as high and low variants by ABS, aregenerally interpreted as such. This implies nocriticism of ABS, but rather of the high–low vari-ants approach to demographic uncertainty. SeriesA assumes a long-run TFR of 2.00, annual NOMof 220 000 and large gains in life expectancy;Series C assumes a long-run TFR of 1.60, annualNOM of 140 000 and moderate gains in lifeexpectancy. Comparing results, we find that theproportion of our predictive distribution coveredby the Series A–C range varies markedly overtime: it covers 70% of the distribution in 2021,77% in 2031, 79% in 2041, and 82% in 2051. Inother words, the probabilistic approach indicatesthat there is one chance in five that Australia’spopulation will outside the range described by theABS in 2051, and for 2021, just 10 years out, thisrises to roughly one chance in three.

Population ageingAs well as registering substantial overall growth,Australia’s population is certain to experiencefurther population ageing – defined as an increasein the proportion of the population aged 65 andabove (Figure 4). According to the median of thedistribution the proportion aged 65 and above willincrease from 13.5% in 2010 to 20.3% in 2031and 23.8% by 2051. The relatively rapid increaseover the next two decades will be driven by theshift of the baby boom generation into this agegroup. The share of population aged 65 and aboveis relatively certain for the next decade or so. By2021, there is a 67% chance that the percentagewill be between 16.7% and 17.5%. By 2051, we

are much less certain: the 67% interval rangesfrom 22.1% to 25.8%. We note that, despite thissubstantial age structural shift, Australia’s popu-lation is likely to have a smaller proportion of itspopulation in the elderly ages compared to Euro-pean and east Asian countries (Scherbov et al.,2008; UN Population Division, 2009).

How does the predictive distribution compareto a conventional high–low range? Again, we usethe ABS 2006-based projections (ABS, 2008a).By 2021, Series A projects 16.8% aged 65 yearsand above while Series C gives 17.7% – a rangeof 0.9%. This range increases to 1.4% by 2031,remains at 1.4% in 2041 and falls to 1.1% by2051. This range covers a relatively narrow bandof our predictive distribution. In fact, the differ-ence between the series A and C projections doesnot consistently provide the widest range of theA, B, and C series. By the late 2030s the Series Bprojection moves from its middle position toproject the lowest percentage aged 65 and aboveof the three series.

Variability in uncertaintyUsing high–low ranges to represent uncertaintyprovides inconsistent results for different seg-ments of the population. Probabilistic projectionsavoid this problem and deliver a more reliablepicture of the extent to which uncertainty variesbetween different demographic measures. Whilesome aspects of Australia’s future demographycan be predicted with considerable confidencefor the next couple of decades; others are lesscertain. Table 3 reports some examples. To stan-dardise for different units we use the RelativeInterdecile Range (RIDR), defined as the 80%prediction interval (i.e. the difference between

Figure 4 Observed trends and probabilistic projections of the percentage of the population aged 65 years and above, Australia,1971–2051 (Source: ABS, 2009).



the ninth and first deciles of the predictive distri-bution) divided by the median (Lutz et al., 2004).A value of 0.5, for example, signifies that the80% prediction interval spans half the value ofthe median. Table 3 presents the RIDR forselected variables. Of births, deaths and NOM,the RIDR for migration is by far the greatestfollowed by births and then deaths. Notice howthe RIDR for deaths and NOM stops wideningafter some years, while that for births continuesto increase. Births are affected by growing uncer-tainty over both fertility rates and the femalepopulation at risk. The latter becomes especiallyuncertain after 2030 when some children arebeing born to mothers who themselves were notyet alive at the start of the projection period, andwhose cohort sizes are therefore uncertain.

Age-sex structureHow does the uncertainty of fertility, mortalityand migration interact with the population age-sex structure? Figure 5 presents probabilisticpopulation pyramids for selected years. Thepyramid for 2016 shows a modest degree ofuncertainty emerging in the childhood ages,because of uncertainty over the number of births,and across the late teenage years to late 30s wheremigration rates are highest. Further into the futureuncertainty increases and propagates to higherages as cohorts get older. By 2026, uncertaintyover the number of teenagers starts to showbecause some have been born during the projec-tion interval. At older ages, the future is attendedby much greater clarity because those aged 65 andover are already alive, and most are resident inAustralia. Future numbers are influenced princi-

pally by mortality, where variations impact prima-rily among the elderly. Only towards the end of theprojection horizon does uncertainty start tobecome significant at the elderly ages.

ConclusionsAustralia’s population, like that of other devel-oped countries, is in the midst of a fundamentaldemographic transition, from a young, rapidlygrowing population, to one with a markedlyolder age structure recording slower growth. Thefuture trajectories of Australian child-bearingand life expectancy may yet hold some surprises,but it is overseas migration that now representsthe major unknown in Australia’s populationfuture. While levels of immigration have fluctu-ated markedly over the past century, the upsurgein net migration gains over the past decadeappears to represent the dawning of a new era, atleast to judge by the revision of official projec-tions, which now put the nation’s populationabove 35 million by mid-century. To borrowfrom the language of Geoffrey Blainey (1994), itseems that calls for ‘A Big Australia’ may beahead of public opinion (see Betts, 2010b), butthe burgeoning public debate underlines thediversity of views on Australia’s most probable,as well as its most desirable, population future.

We aimed to inform this discussion by can-vassing expert views on future levels of NOM,and by using stochastic methods to establishthe statistical bounds within which future popu-lation growth will probably lie. Our surveyresults reveal that even among experts, there isconsiderable diversity of views as to likely futuretrends in migration. While three-quarters of

Table 3 The Relative Interdecile Range1 of selected projection variables

Year/Projection Interval2

2021 2031 2041 2051

Net overseas migration 1.10 1.16 1.14 1.16Births 0.23 0.35 0.44 0.54% aged 85+ 0.10 0.20 0.29 0.36Baby boom generation 0.02 0.05 0.15 0.33Total population 0.06 0.13 0.19 0.25Elderly dependency ratio 0.07 0.14 0.19 0.23Deaths 0.18 0.21 0.22 0.21% aged 65+ 0.06 0.12 0.17 0.20Median age 0.03 0.06 0.09 0.11

1 The Relative Interdecile Range is the difference between the ninth and first deciles of the distribution divided by the median.2 30 June for stock variables; 1 year projection interval ending 30 June for flow variables.



2016 2021

2031

2041

2026

2036

Figure 5 Selected predictive intervals of the Australian population’s age-sex structure, 2016–2041.



respondents anticipated net migration gains 10years from now to lie between 150 000 and220 000, a small minority expected the figure tobe substantially above or below these levels.Nevertheless, on their collective judgement, themedian for the next decade will lie well aboverecent history, and they were all but unanimousin foreshadowing an upwards trend. Eliciting andharnessing expert opinion is a hazardous busi-ness (Lutz et al., 1998), but focusing on the rangeof forces which drive particular types of move-ment does appear to provide for a more rigorousprocess of assessment. While consensus may beout of reach in work of this type, even usingDelphi-style techniques, the range of viewsexpressed is itself highly informative. We usedthe median and 67% predictive interval from theexpert survey to set the migration assumptionsfor our probabilistic forecast.

The forecast reported here clearly demon-strates the value of a probabilistic approach overconventional methods which simply report a low,medium, and high projection. Our results indi-cate a 95% probability that Australia’s popula-tion in 2051 will lie in the range 29.4 million to43.0 million, and a 67% chance that the popula-tion will fall between 32.7 million and 39.6million. The median forecast (36.1 million) isclose to the 2006-based ABS Series B projection(34.3 million in 2051), but the ABS range issignificantly narrower than our predictive distri-bution, particularly in the early years of the pro-jection interval. A key benefit of the probabilisticapproach, then, is in quantifying the degree ofuncertainty about future population growth, ina form that is simply not available from con-ventional projections. Predictive distributionstherefore have direct application to planning,investment, and risk management by showing theprobability of reaching a particular populationthreshold by a specified date.

We have confined attention here to the nationalpicture, but probabilistic forecasts can also bemade for subnational areas, although dealing withinternal migration adds significant complexity(see Wilson and Bell, 2007). Of course, the accu-racy of any forecast is fundamentally contingenton the assumptions which are made, and it is wellestablished that forecast errors propagate as hori-zons lengthen and spatial scales reduce. Neverthe-less, the twin advances proposed in this paper,coupling probabilistic methods with more rigor-ous processes for assumption setting, offer theprospect of greater utility and transparency indemographic projections, as well as improve-

ments in projection accuracy. The challengenow is to promote wider acceptance of theseapproaches, both among the users and the produc-ers of demographic projections.

ACKNOWLEDGMENTSThe authors would like to thank those individuals whoresponded to the Expert Survey, the results of which arereported here. The interpretation of responses is of course thesole responsibility of the authors. Helpful referee commentson an earlier version of the paper are gratefully acknowledged.

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Appendix: Time series modelsThe Box-Jenkins approach to time series model-ling was applied to the total fertility rate and lifeexpectancy at birth (Makridakis et al., 1998,chapter 7). The total fertility rate was modelledusing a random walk with drift model:

TFR y TFR y y c yTFR TFR( ) = −( ) + ( ) + ( )1 ε

where y denotes the projection interval, e repre-sents normally distributed random errors with amean of zero, and c is an adjustment to shift themedian of the distribution to a predefined mostlikely assumption.

We set the standard deviation of random errorsto 0.0414, the value obtained from fitting themodel to 1976–2009 data. For the predefinedmost likely level of fertility we used the latestAustralian Bureau of Statistics (ABS) mediumfertility assumption which has the total fertilityrate at 1.80 from 2021–2021 onwards (ABS,2008a).

Female and male life expectancy at birth, e0,were also modelled using random walk with driftmodels:

e y e y y c ye e0 0 10 0

( ) = −( ) + ( ) + ( )ε .

The standard deviation of εe0was set at 0.2989

for both males and females. This is the valueobtained from fitting the model to female lifeexpectancy data for the period 1971–2009. Thestandard deviation of male life expectancy errorswas judged a little small (giving a 95% predic-tion interval by 2051 of 6.9 years), so for projec-tion purposes we applied the slightly largerstandard deviation of females (increasing the95% prediction interval by 2051 to 7.8 years).Correlated random errors to ensure realisticcovariance between male and female e0 samplepaths were generated via Cholesky decomposi-

tion (Press et al., 2001) of the historicalvariance–covariance matrix of the differenced e0

series, which implies a correlation of r = 0.719.For total immigration and emigration we

chose models based on judgement rather thanfitting, as mentioned in the main text. We optedto use an Autoregressive Integrated MovingAverage (1,0,0) model because it provides pre-dictive distributions which open up rapidly in theearly years of a projection and more slowlyfurther into the future. It therefore allows suddenspikes in net overseas migration, like that ofrecent years, to occur again. The model for immi-gration, I, may be written as:

I y I y y c yI I I( ) = −( ) + ( ) + ( )ϕ ε1

where j refers to the autoregressive parameter.The emigration model is identical. Autoregres-

sive parameters of 0.95 for immigration and 0.92for emigration were used, while the standarddeviation of random errors was set at 49 941 forimmigration and 51 500 for emigration. Theseare twice the historical values of the de-trendedimmigration and emigration series for 1971–2009, chosen on the assumption that there will bemuch greater variability in migration in thefuture. A variance–covariance matrix incorporat-ing a correlation of 0.80 between immigrationand emigration errors was employed. This waschosen to give a predictive distribution of netoverseas migration which matched the 67% pre-diction interval for 2020 based on the experts’survey. (By 2030, the Autoregressive IntegratedMoving Average models produced a net over-seas migration 67% prediction interval of179 000, smaller than the interval suggested bythe experts [196 000]. We decided to privilegethe experts’ interval for 2020 over that for 2030and produce projections with the aforementionedparameters.)



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Australia's Population Future: Probabilistic Forecasts Incorporating Expert Judgement