of
Vol. 10, 371-398 (1991)
NlCO KEILMAN
Netherlands Interdisciplinary Demographic Institute, The Hague,
The Netherlands
TOMAS K U ~ E R A
Charles University, Prague, Czechoslovakia
ABSTRACT
This study considers the accuracy of national population forecasts o f the
Netherlands and the Czechoslovak Socialist Republic (CSSR) produced by the statistical agencies of these countries after World War 11. Attempts are made to link patterns of ex-post errors to changes in forecasting methodology. We look at the demographic components employed in each forecast, the procedure to extrapolate fertility and the level at which assumptions for each component are formulated. Errors in total population size, fertility, mortality and foreign migration, and age structure are considered. We discuss trends in errors and methodology since 1950 and compare the situations in the two countries. The findings suggest that methodology has only a very limited impact on the accuracy of national population forecasts.
K E Y WORDS Accuracy Population Forecasts ex-post errors
Forecasting methodology The Netherlands CSSR
INTRODUCTION
In 1965 the population of the Netherlands was expected to reach 16.5 million in 1985 and almost 21 million in the year 2000. We know that Dutch demographers were inaccurate. The population numbered no more than 14.5 million in 1985, and for the year 2000 the Netherlands
Central Bureau of Statistics (NCBS) recently put the total population at 15.3-16.1 million.
Hence, in 1965, the 1985 population was overestimated by 2 million or some 1407'0. The 1965 forecast for Czechoslovakia resulted in an estimate of the 1986 population of 16 million.
Twenty years later this was found to be 4% too high.
These examples for the Netherlands and Czechoslovakia raise a number of questions. Why were Dutch forecasts in the 1960s so much more inaccurate than those of Czechoslovakia? Is
0277-6693/91/04037 1 -28$14.00
0 by John Wiley & Sons, Ltd.
Received October 1989
Revised March 1990

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Vol. IO, Iss.
4 this due to a difference in methodology? Or is the accuracy of population forecasts a matter of luck rather than of methodology?
These general questions will be dealt with here. In particular, we try to assess the impact of population forecasting methodology on the accuracy of these forecasts. We analyse the changes over time in forecasting methodology in the Netherlands and in Czechoslovakia since
World War 11, and at the same time study changes in in that period. This is our
forecast errors in each country
perspective. Our
perspective consists of a comparison of the methodology of demographic forecasts in the two countries, in reltion to a comparison of demographic forecast errors.
Although agreement exists in demographic journals about the distinction between a
and a
of the population of a certain region, the current practice of statistical agencies is not generally in conformity with the usual interpretation of these concepts. We shall adopt throughout the following definition:
Population projections are calculations which show the future development of a population when certain assumptions are made about the future course of population change, usually with respect to fertility, mortality and migration. A population forecast is a projection in which the assumptions are considered to yield a realistic picture of the probable future development of a population.
From this definition it follows that projections are
developing the consequences of the assumptions that are made. A forecast is
based on current scientific insights, a forecaster gives a best guess of what the future population will be. Thus population forecasts, like weather forecasts, have a limited reliability and a limited life (Tennekes, 1984, p. 17).
The general practice of statistical agencies deviates from these definitions. For instance, the
Netherlands Central Bureau of Statistics (NCBS) wrote about its 1970 forecast: ‘A forecast is
... in no way a prediction, but merely the determination of the consequences of certain assumptions’ (NCBS, 1971, p. 13; our translation). This is illustrative for what statistical agencies generally do: they produce forecasts, but they call their products projections. It is left to the user to judge the plausibility of the assumptions. Most agencies do not clearly state whether their assumptions are realistic or not. The reluctance of official forecasters to admit that they aim at providing a realistic picture of the future population is understandable, given the relatively poor record of population forecasting (Ascher, 1978). Nevertheless, it is not justified for two reasons. First, forecasters are in a much better position t o judge the plausibility of a given set of assumptions than is the average user. If the forecaster is not able to tell whether his or her calculations paint a realistic picture of future demographic numbers, who else could? Second, the average user simply acts as if the statistical agency had produced a forecast in the sense defined earlier. He cannot assume that the agency based its calculations on a set of assumptions which d o not make sense.
In the 1980s some statistical agencies shifted the interpretation of what they produce towards the accepted definition of a forecast: examples are the Netherlands Central Bureau of Statistics
(NCBS) and the Chechoslovak statistical agencies (NCBS, 1982, p. 16, 1985, p. 32; CSU, 1982, p. 11; FSU, 1987, p. 1).
The discussion above shows why we prefer to speak of a forecast, unless it is explicitly assumed that the calculations do not show a realistic picture of the future population (for instance, because currently observed demographic indicators are kept constant for the future, or because it is assumed that fertility will reach a level of two children per woman within 10 years). An additional reason is that evaluating the accuracy of conditional projections is not

N . Keilrnan and T. Kuhra National Population Forecasts 373 very useful. Unless errors were made in the calculations, a projection is accurate by definition.
Only the conditions can be evaluated, but this does not provide much insight.
In the first three decades after World War I1 forecasters were more cautious than was strictly necessary. However, from the early 1980s, forecasters in some countries have shown more interest in the accuracy of population forecasts. Since 1984, the United States Bureau of the
Census (USBC) analyzes systematically ex-post observed errors of their forecasts (USBC,
1984; Long and McMillen, 1984; Long, 1987; USBC, 1989). The NCBS uses the average of ex-post observed errors in live births in historical forecasts to set the margin between the high and the low fertility variant in the forecast of 1984 and 1988, and it investigates the pattern of errors in age structures (NCBS, 1985, pp. 19, 33, 1989, pp. 17, 31). Statistics Sweden devotes a section to errors in historical forecasts in its publication concerning the 1986-based national forecast (SCB, 1986, pp. 76-81). Bretz (1986) investigates ex-post observed errors of national demographic forecasts in the Federal Republic of Germany.
An important issue is to what extent the methodology used in population forecasts contributes to the accuracy, as compared to the contribution made by general social and more specific demographic circumstances. When forecast errors turn out to be influenced mainly by actual trends in demographic indicators that are observed after the forecast was produced (and much less so by a choice for more advanced forecast methodologies), then monitoring the observed trends should have a much higher priority for forecasters than the construction of more sophisticated models and methods.
The structure of this paper is as follows. In the next section we give a description of trends in the methodology which has been used to produce national population forecasts in the
Netherlands and the CSSR after World War 11. Turning points in the history of post-war population forecasting for the two countries are identified. The third section contains a discussion of sources of forecast errors, and we describe briefly the error measures which are used in this paper. Errors in population size and age structure are presented in the fourth section. As errors at young ages depend on fertility, and those at high ages mainly on mortality, error patterns in these demographic components are discussed in the fifth section.
In the sixth section we discuss whether forecast errors in the Netherlands and the CSSR are comparable. The final section contains the main conclusions of this paper and the findings are placed in a wider context.
POST-WORLD WAR 11 TRENDS IN POPULATION FORECASTING
METHODOLOGY
In this section we try to discover trends and changes in the methodology of population forecasting in the Netherlands and the CSSR which have taken place after World War 11. In view of the disruption of social trends in both countries during the war and in the early post- war years, the 1950s are a natural starting point.
The Netherlands
The overview presented here starts with the 1950 NCBS forecast, that is, with the forecast which took the observed population of January 1950 as its starting point (NCBS, 1951). Table
I presents the demographic characteristics used in the NCBS forecasts since 1950, their components, the way in which the major component of change (fertility) is modelled, the manner in which assumptions are formulated, and the number of variants which can be distinguished for each forecast.

N . Keilman and T. K u k r a National Population Forecasts 375
Several trends can be distinguished from 1950. First, the number of demographic components used in the NCBS forecasts has increased. With the introduction in 1970 of marriage and marriage dissolution for females, and the same demographic phenomena for males in the 1980 forecast, the most recent forecasts draw up assumptions for seven demographic phenomena; in 1950 only two were included. Second, the level at which the assumptions are formulated is gradually rising. Until the forecast of 1967, ,Fertility was described at the most detailed level, that is, the level of age-specific marital fertility rates. From
1970, summarizing indicators, such as the average number of children per woman, have been used. The year 1975 was the first in which the NCBS formulated fertility assumptions at the general level. Future fertility trends were viewed from a socio-demographic and social point of view, and the psychological, cultural and socio-economic factors influencing these trends were taken into account. In doing so, the NCBS supported the findings of the then State
Committee for Population Issues, which formulated expectations for future fertility, mortality and nuptiality trends. For mortality, age-specific rates were aggregated in the life expectancy at birth as early as 1950, using the life-table method. Since 1980, the influence on mortality of preventive medicine, hygiene, nutrition and socio-economic, cultural and technological trends has been taken into account.
Third, the cohort approach to formulating assumptions is becoming increasingly popular at the expense of the period approach. In a period approach, the behaviour of individuals of various ages is investigated for a certain calendar year or period. These persons belong to different birth cohorts. In a cohort approach, the behaviour of individuals of various ages who belong to the same birth cohort is analysed. Such an analysis covers several calendar years.
Instead of birth cohorts, one may also study marriage cohorts (e.g. with respect to marital fertility). In that case, age is replaced by marriage duration. In the cohort approach to formulating, say, assumptions for fertility, the childbearing behaviour of women in a series of birth cohorts (or marriage cohorts) is analyzed, and next extrapolated into the future.
Similarly, in the period approach to formulating fertility, analysis and extrapolation of period fertility is pursued.
In the entire post-war period, mortality assumptions have been drawn up by period analysis.
However, for fertility there was a change from a period to a cohort approach between 1967 and 1970. This change was stimulated in particular by the Working Group for Population
Forecasting Methodology. This was instituted in 1967 and included, besides the NCBS forecasters, staff of the National Physical Planning Agency and the Central Planning Bureau, as well as prominent academic demographers. Prompted by the poor results of the 1965 forecast, this working group examined the advantages and disadvantages of a period methodology and of a cohort approach to the analysis and extrapolation of fertility. The advice given, and incorporated into the 1970 forecast, was two-fold. Do not follow the usual period approach, in which the results are influenced in particular by short-term effects.
Instead, apply a cohort analysis which produces a better picture of the actual, more structural trends. Do not use birth cohorts (and age-specific fertility trends), but instead use marriage cohorts (and a marriage duration-specific analysis). The introduction in 1970 of marriage duration-specific fertility, from a cohort point of view, may be considered to be one of the most important methodological changes in national population forecasting methods in the
Netherlands since World War 11.
Fourth, as from 1975, foreign migration was incorporated into the forecasts. Earlier forecasts did have one (1950) or two (1951, 1956, 1965) forecasting variants which included international migration, but the publications clearly show that less importance was attached to these variants than to the basic variant which did not include migration (NCBS, 1951, 1954,

376 Journal of Forecasting Vol. 10, Iss. No. 4
1961, 1965). Even as late as 1975, the publication of the forecast had a separate section on international migration; this component had not yet been fully incorporated into the forecast
(NCBS, 1976). However, between 1975 and 1980 the interpretation shifted. In two articles about the accuracy of the 1975 forecast the results including international migration are seen as the forecasting results (Kregting, 1979, 1980).
From 1980 onwards, international migration was fully incorporated into forecasting methodology (NCBS, 1982). Thus the wishes expressed by the Scientific Council for the
Government Policy (WRR) in 1974 were finally fulfilled (WRR, 1974, p. 34).
To summarize, we can say that there were t w o important turning points in the history of post-war population forecasting in the Netherlands. The first was the year 1970, in which the period age-specific approach to fertility was replaced by a cohort marriage duration-specific method. The second turning point was in 1975, when international migration was introduced into the population forecasting process and more attention was given to the social scientific basis for forecasting assumptions.
CZECHOSLOVAKIA
Table I1 presents a summary of the main aspects of forecasting methodology in the CSSR since the early 1950s. The coherent series of the Czechoslovak official population forecasts was established in the early 1950s, further to the first post-war census held in 1950. Taking this year as the starting point, their history may be dated from then.
In comparison with the Dutch forecasting history, changes in Czechoslovakia have not been as fundamental. The only major difference in approach took place in the way in which the national results were calculated.
The future population of Czechoslovakia has always been estimated by aggregating the results for the two national republics, the main reason being the existing regional fertility differences. Until the 1970.2 forecast (i.e. the second forecast with starting year 1970, made in 1973; the 1970.1 forecast became available t w o years earlier) the assumptions about future demographic reproduction were the same for the two national republics. Since the 1972 forecast, the assumptions have differed by region.
The basis for the assumption-making process has usually been the outcome of a time-series analysis of observed demographic trends. Most assumptions have corresponded to the most detailed level of age-specific parameters and have only exceptionally referred to the level of their aggregates.
For fertility, we can observe a transition from the use of general rates (1950) t o age-specific rates (since 1955), and from five-year age groups (until 1977) t o one-year age groups (since
1978). The assumptions about future fertility have always been expressed in terms of age- specific rates. Where other indicators (e.g. average number of live births per woman, parity age-specific fertility, etc.) have been considered, they were used to check the consistency between assumptions formulated at the detailed level and general concepts referring to higher levels. In all analyses, the period perspective was applied, and only in the last case (1985) were some fundamental results of cohort analysis taken into account. Intended population policy measures are only sporadically mentioned in official forecasting because they were usually not known at the time the forecasts were produced. There are only two such forecasts (1955 and
1965.2) which explicitly took such policy measures into account (KuEera, 1958, p. 399, 1969, p. 368).

In
2
x x x x x x x
--- v, n n o.
2 x
2 x x x x x x x
--N N =-zz n
377 x x x x x
N- N
ZZ a x x x x x x x x x x x x x x
- - N n n n

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The assumptions about future
have been formulated in a manner similar to that for fertility. Only age and sex were used to disaggregate the mortality process. For the forecasts made immediately after the censuses (1950 and 1960) and since the 1972 forecast, the one-year age detail has been used. For the remaining forecasts the five-year age groups were the basic units. Life expectancies were used to check the plausibility of the detailed assumptions. Apart from the above-mentioned changes from one- to five-year age groups, the departure from time- constant age-specific mortality for ages above 0 as from the 1960 forecast was probably the most important methodological shift.
As to
this component’s position changed continuously until the early 1980s. The opinions regarding the place of, migration especially its internal component, varied from practically every forecast to the next. In the forecasts of 1955, 1960, 1965.2, 1970.1, 1970.2 and 1978 migration was not considered. In those of 1965.1, 1980 and 1985, along with internal migration, external migration (more exactly, its registered part) was also included. During the whole period in question, migration was forecasted solely through the concept of net migration, without any reference to the direction of flow and predicted age structure.
Furthermore, the starting-point populations deserve further comment. First, all age-sex structures of the population prior to the year 1961 were derived from the 1950 census, when the
population was enumerated, as well as from the current registration of demographic events based on the
population. Second, during the whole period studied here, the accuracy of these age-sex structures decreased with a growing lapse of time from the last census, due t o unregistered migration.
Finally, a change of approach took place with the 1985 forecast, in which, for the first time, forecast assumptions were discussed outside the Federal Statistical Office (FSU, 1987, p. 1).
Before the forecast was released, the authorities consulted the Czechoslovak Demographic
Society about the assumptions to be used.
If we look for comparable turning points as identified for the Dutch forecasting history in the previous section, only one such point can be found. It is the 1955 forecast, when general fertility rates were replaced by age-specific rates. The remaining methodological changes, including the treatment of migration, may be considered less important in the given context.
ERRORS IN POPULATION FORECASTING
What are the sources of error of population forecasts? Hoem (1973) and Keyfitz (1977, p. 227) were among the first authors to discuss this issue. Berk and Cooley (1987, p. 257) review sources of errors in forecasting social phenomena in general. Based on these analyses, we distinguish seven types of errors:
(1)
(2)
Due to the difference between the
and the
population, population registers (and thus the demographic data derived from these) do not accurately reflect actual behaviour. Moreover, if registration is not complete, basic data used in forecasts may have been derived from sample surveys. This is likely to create sampling arA non-response errors, etc.
The production of population statistics based on population registration is never 100% accurate. Therefore, with time, the population numbers determined by the statistical bureau will increasingly deviate from the figures given in the population registers.

N .
T.
379
(3)
Observed birth rates, death rates, etc. are composed of a trend plus a random fluctuation. Population forecasts, however, are based on an extrapolation of the (supposed) trend, whereby randomness is not taken into account.
(4)
Rounding errors are made in observed demographic rates as well as in the results of population forecasts.
( 5 )
in
analyses may show that the extrapolation of exogenous variables (birth rates, death rates, etc.) has resulted in an
( 6 ) over- or underestimation of observed trends.
in
External circumstances such as war, disasters, serious economic depression, etc. as well as sudden changes in legislation can significantly
(7) influence the course of demographic parameters.
The population model used may not be entirely valid.
When simulating population trends over a given period with the aid of such a model the model results should, ideally, be exactly the same as the observed trends. However, this is not always the case.
Errors in observed trends (category 1) and errors in the starting-point population (category
2) are related to the quality of population registration. In most developed countries this does not give rise to serious problems, although it should be noted that the quality of the starting- point population gradually deteriorates as the time at which the last census was taken (or any other independent check) lies in the more distant past. In countries where registration is substandard or even absent, one must resort t o data from surveys, in addition to censuses.
Indirect estimation techniques can then give rise to unreliable estimates for the basic demographic trends. Various studies have shown that randomness in parameters (category 3) does not lead to serious forecast errors (Sykes, 1969; Schweder, 1971; Cruijsen and Van
Hoorn, 1983; Brunborg, 1984). The same applies to rounding errors (category 4).
The most common forecast errors arise because of a misspecification of the values of exogenous variables (category 5 ) . Sudden shifts in parameters (category 6) can create large forecast errors, but they are not very common. For example, if it has been proven that an economic recession encourages women to postpone childbirth, and if such an economic slump does indeed occur, and persists, then the resultant errors are usually classified under the fifth category of errors. In the past, model specification errors (category 7) were caused in particular by the fact that international migration was not included. For small countries this resulted in forecast errors which were quite important for migration-sensitive ages (up t o about 40 years), as compared to the errors made for other age groups.
I f we want to determine the magnitude of forecast errors made in the past, we must first answer two questions. First, we must determine the forecast variable for which we wish to measure an error. There are a large range of possibilities: total population size, annual population growth, the annual number of births, deaths, migrants, marriages and marriage dissolutions, or the age structure of the population. In general,
are pleased to have information about errors in population size and structure and the absolute numbers of births, deaths and migrants. However, if one is interested in the
one will want to know more, and descend from the level of forecasting results to the level of assumptions. It is not possible to make an error analysis at the most detailed level, namely the level of age-specific assumption parameters, since this information is usually no longer available for forecasts made in the past. Moreover, one may expect t o find the major patterns in forecast errors in the next highest level, that is, the level of summary variables, such

380
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4 as the total fertility rate, life expectancy, etc. These and other summary variables bring together in one figure the separate age-specific rates.
Once we have determined for which forecasting variables the errors need t o be quantified, the question remains as t o which measure is most appropriate. The literature gives a large number of measures, and Steece (1982), Ahlburg (1982) and Armstrong (1985) discuss several.
We use three: the mean percentage error (MPE); the root mean square percentage error
(RMSPE); and a modification of Theil’s U2, defined as
J[E
-
o ~ ) ~ I
In this expression,
and
represent the forecast value and the observed value at a certain point in time, respectively. evaluated.
N is the total number of forecast or observed values which is
is an alternative ‘forecast’ or benchmark ‘forecast’, the quality of which is compared with the actual forecast, because much of the accuracy may be due to persistence and inertia in demographic trends (Keyfitz, 1977, p. 230).
For the alternative ‘forecast’ one can take the results of a naive extrapolation in which the relevant variable is kept constant at the level which was recently observed. When one, then the alternative ‘forecast’ was more accurate than the actual forecast.
U exceeds in the opposite case, and U = indicates a perfect forecast. U as defined here differs from
Theil’s U2 in two respects (Armstrong, 1985). First, the alternative ‘forecast’ Ai is not contained in the definition of
1 7 2 .
Second, 0 and F (and A ) refer to
here, whereas they represent
in Theil’s U2. U2 compares the root mean squared error (RMSE) of the forecast to that of a no-change ‘forecast’, when 0 is taken t o denote actual change and
F forecast change. U2 may very well be used for the evaluation of a forecast of stock variables
(for instance, total population size). However,
in stock variables as such are seldom analyzed by demographers. Rather, they investigate
of
births, deaths, and migrations. In the following sections we study the accuracy of these components, and therefore we need an explicit assumption on the value of an alternative ‘forecast’. This explains why
is used in the definition of U.
In this paper the alternative ‘forecast’ for a certain variable is the value as it is observed in the year prior to the starting year of the relevant forecast. This rule is applied to the evaluation of forecasts for the number of live births, the crude birth rate, and the crude death rate. For the number of deaths this would be a forecast which is ‘too naive’: a constant annual number of deaths would not be a very realistic assumption in a growing population. Therefore, the naive forecast consists in this case of a crude death rate which is constant over time. Numbers of deaths were derived after multiplication with the forecasted population size.
FIRST RESULTS: ERRORS IN POPULATION SIZE AND AGE STRUCTURE
Table 111 presents the percentage error (PE) of post-war forecasts of the total population for the Netherlands. The forecasts of the 1950s generally underestimated actual population size, which is indicated by a negative PE. The 1956 forecast is, in the short run, a slight overestimate of actual trends, but in the long run it is an underestimate. The overestimations in the forecast of 1965 are by far the largest of the Dutch forecasts studied.
Figure 1 shows the MPE for the age structure of the population. As in Table 111, the errors per age group and per forecast have been calculated for a forecasting period of exactly 5, 10 and 15 years. We took per age group the mean of the different forecasts: all 13 forecasts for a 5-year period given in Table 111, the 10 forecasts prior to and including that in 1975 for 10

T.
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Y k
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Vol. 10, Zss. No. 4 years ahead and the eight forecasts before 1975 for a 15-year period. Figure 1 clearly shows the magnitude of overestimation for the youngest age group: up to 25% for 0- to 4-year-olds for the 15-year forecasts. We will see later that this may be attributed mainly to an overestimation of fertility in the Dutch forecasts made between 1965 and 1972. The underestimation of the elderly female population results from a too-pessimistic evaluation
30
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--
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14
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24
30-
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40-
44
50-
54
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70-
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Figure 1 . Mean percentage error by age, the Netherlands

N . Keilman and T. Kutera National Population Forecasts 383
2
W
B
.-
Y
Q
- z
-c,
0
3
8
2
P ul

384
of
Vof. 10, Zss.
4 regarding mortality. As the length of forecasting period rises, so do the forecast errors.
However, for ages between 10 and 74 years, the over- or underestimation is less than 5 % . At more advanced ages, forecast errors become larger, especially if the forecasting period exceeds
10 years. Similar forecast errors for the elderly population have been found for Denmark and
Norway (Leeson, 1981, p. 77; Brunborg, 1984, p. 14). This shows that for ages over 75, it is
H A L E S
FEMALES
?
5
15
I
0-4 10-
14
20-
24
30-
34
40-
44
50-
54
60-
64
70-
74 ae-as+
04
Figure 2. Mean percentage error by age, CSSR
Forecast horizon
... 5 years
10 years
.- 15 years

385 relatively difficult t o make an accurate forecast. Figure 1 prompts us to analyse in greater detail, fertility and mortality trends. This will be done in the next section of this paper.
International migration, which takes place primarily between the ages of 20 and 40 years, is much less important for the accuracy of population forecasts in the Netherlands.
We now turn to a first analysis of errors in national population forecasts in the CSSR. Table
IV shows some results for total population size. The 1965.1 forecast overestimated real population trends more than the average forecast, as did the 1960 forecast for a horizon of
10 years or longer. The 1970.1 forecast shows a relatively large underestimation which resulted from pronatalist measures, the effects of which were not foreseen by forecasters. The changes in fertility methodology (age-specific fertility rates were introduced in the 1955 forecast and rates for single years in the 1978 forecast) are
reflected in the error patterns of Table IV.
For instance, after 5 years, the 1955 forecast of total population showed an error of 0.1%, whereas its predecessor, the 1950 forecast, virtually had no error in its population size after
5 years. Again, after 5 years, the 1978 forecast was worse than the 1977 forecast produced one year earlier. For periods of 10 or 15 years analogous conclusions can be drawn. Similarly, the shift from time-constant mortality rates to varying rates since the 1960 forecast could not prevent this forecast from showing the largest errors in population size among all forecasts with lead times of 10 or 15 years. If there were some changes in forecast accuracy connected with changes in methodology, they have been concealed by the effects of pronatalist measures and unregistered migration. The latter effects can only be monitored by census taking.
Mean percentage errors in the age structure of Czechoslovak forecasts are shown in Figure 2.
The general pattern is the same as for the Netherlands: relatively high errors at low and at high ages, and errors that increase as the forecast horizon becomes further removed from the starting year. A notable difference between the two countries is that CSSR errors at low ages and (for females only) also at high ages seem t o be smaller than in the Netherlands, at least when these errors are measured by the MPE. For females at high ages, this is caused by compensation effects: RMSPEs of the two countries are of comparable magnitude. However, the errors at lower ages remain relatively small, when the RMSPE is considered. This suggests that fertility trends were forecast quite accurately in the CSSR. Also, note the relatively large errors in CSSR forecasts for males above age 45. This suggests an underestimation of male mortality levels. The next section presents a more detailed discussion.
ERRORS IN FERTILITY, MORTALITY AND EXTERNAL MIGRATION
Table V shows that in 1965 the Dutch short-term (up to 5 years) fertility forecast was better than those made in 1970 and 1972. That of 1967 was very accurate, because the birth decline in the Netherlands which began in 1964 was interrupted in 1969 by a substantial increase in the birth rate (see Figure 3). In 1970, the birth rate in the Netherlands started to drop significantly. The 1967 fertility forecast was, on average, fairly accurate for the first 5 years, since the first 3 years had been underestimated and the last 2 years overestimated. However,
Theil’s I/ shows that a naive short-term forecast would have been better, both in 1967 and in
1970. Since the observed birth decline between 1964 and 1970 was much less significant than that after 1970, the 1965 short-term fertility forecast contained smaller errors than the 1970 and 1972 forecasts. For the ten-year forecasting period (Table VI) the 1965 fertility forecast was again better than the 1970 forecast. Only when we forecast 15 years ahead (Table VII) does the 1970 fertility forecast become more accurate. As shown above, the fertility forecast of 1967 measured by the MPE and the RMSPE is still significantly better than the 1970 forecast. The

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0
0
0
0
0
0
0
0
0 o o
0 0
0
0 o o o o
+
1950 Forecast
XI
1951 and 1956
Forecast
1965 Forecast
+ + + + +
1967 Forecast
350
'I
Figure 3. Births, forecasts and observations, the Netherlands

400
-
350
--
300--
1
0
0
0 2 5 0 - -
381
-
O b s e r v e d
+
1975 High
Forecast
1975 Low
Forecast
O
1980 Hiah
Forecast x 1980 L-
Forecast
Figure 3. (continued)
Table V. Accuracy of fertility and mortality forecasts, 5-year forecasting period, the Netherlands
1950 1951 1956 1965 1967 1970 1972H 1972L 1975H 1975L 1980H 1980M 1980L Total
Number of live births
MPE (YO) -9.0 1.3 -6.4 13.0 0.6 20.5 19.2 13.0 3.0 -3.4 8.3 6.1 3.9 5.4
RMSPE (Vo) 9.7 1.6 6.7 13.7 4.3 25.6 25.5 16.0 3.6 4.3 10.2 7.6 5.2 12.8
U 3.1 2.3 1.8 3.3 1.5 1.2 1.1 0.7 0.6 0.7 4.3 3.2 2.2 1.2
Crude birth rate
MPE ("70) -9.0 0.7 -6.4 12.7 0.9 20.7 19.5 13.3 3.0 -3.3 8.0 5.9 3.8 5.4
RMSPE (Yo) 9.6 1.0 6.7 13.5 4.5 25.6 25.8 16.4 3.6
I/
4.2 9.9 7.3 5.1 12.8
1.2 0.2 4.9 1.6 0.8 1.0 1.0 0.6 0.4 0.5 2.8 2.1 1.4 1.0
Number of deaths
MPE(V0) 7.1 8.1 -5.1 -1.6-3.2 2.7 4.7 4.6 5.8
RMSPE (Vo) 7.4 8.6 5.9 2.0 3.8 4.5 5.4 5.3 6.7
U 0.9 4.4 1.7 0.4 1.2 2.0 2.5 2.5 2.7
5.6 0.9 0.6 0.6 2.4
6.5 1.2 1.0 1.0 5.2
2.7 0.7 0.5 0.5 1.5
Crude death rate
MPE (YO) 7.2 7.3 -5.1 - 1.8 -2.8 2.9 5.0 4.9 5.8
RMSPE ('70) 7.5 7.6 5.8 2.2 3.5 4.5 5.7 5.6 6.7
5.8 0.7 0.4 0.4 2.3
6.7 0.9 0.8 0.8 5.1
U 0.9 3.4 1.7 0.4 1.1 2.2 2.8 2.7 3.0 3.0 0.4 0.4 0.4 1.5

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Table VI. Accuracy of fertility and mortality forecasts, 10-year forecasting period, the Netherlands
1950 1951 1956 1965 1967 1970 1972H 1972L 1975H 1975L Total
Number of live births
MPE (TO) - 11.7
RMSPE (To) 12.4
U
Crude birth rate
4.8
MPE (TO) - 11.4
RMSPE (To) 11.9
U
Number of deaths
1.2
MPE (To)
RMSPE (To)
U
Crude death rate
MPE(To)
9.0
9.5
1.3
9.5
RMSPE (To) 10.1
U 1.3
-0.5 - 5 . 5 31.8 18.6 37.7
2.4 6.1 39.5 27.4 42.9
1.0 1.8 2.5 1.4 1.3
1.2 -5.2
2.7 5.9 37.4 27.5 41.9
0.4 0.9
8.8
8.7 8.9 3.1 3.5 8.3
6.3 1.8 0.6
7.9
8.1
4.7
-8.0
-7.7
8.6
1.9
30.4
1.5
-
-2.8
3.6
0.6
18.9 37.0
1.0
-2.5
1.1
-2.2
3.3
1.1
1.0
6.4
2.3
5.8
7.4
2.7
30.6
34.9
1.4
30.4
34.7
1.1
9.1
10.3
3.0
9.0
10.1
3.2
18.4
20.3
0.8
18.8 9.5 -3.9 12.3
20.8 12.7 5.1 24.3
0.6
8.8
10.0
3.5
9.2
10.5
3.3
9.3 -4.5 12.4
12.5
2.0
1.2
7.8
8.4
4.1
8.0
8.6
4.5
5.6
0.9 1.4
0.5 1.1
7.6
8.2
3.3
24.8
4.5
8.2
2.1
8.3 4.5
9.0 8.3
4.7 2.0
Table VII. Accuracy of fertility and mortality forecasts, 15-year forecasting period, the Netherlands
1950 1951 1956 1965 1967 1970 1972H 1972L Total
Number of live births
MPE (To)
RMSPE (To)
U
- 14.3
15.1
4.4
Crude birth rate
MPE (To) - 13.2
13.8
1.2
RMSPE (To)
U
Number of deaths
MPE (To)
RMSPE (To)
U
Crude death rate
MPE(To)
RMSPE (To)
U
10.0
10.5
1.8
11.4
12.1
1.7
4.9
1.1
5.1
0.6
7.5
8.1
2.1
7.1
7.3
2.0
10.0
-
1.5
10.2
0.6
-11.4
12.8
1.8
11.0
12.3
1.8
53.5
64.7
2.3
49.2
58.7
1.4
3.5
0.7
3.7
0.6
30.8
39.0
1.5
30.2
37.9
1 .o
3.5
1.2
3.0
1.2
44.2
48.2
1.3
42.3
45.8
1 .o
9.4
11.1
2.6
8.0
9.3
3.4
32.9
35.9
1.3
32.1
35.0
1 .o
10.9
11.9
3.9
10.3
11.1
4.0
20.4
21.8
0.8
20.8
22.3
0.6
10.7
11.6
4.7
11.0
12.0
4.3
20.5
35.6
1.6
19.7
33.6
1 .o
4.5
9.8
2.2
4.1
9.6
2.0
Table VIII. Percentage error of forecasts of live births, Czechoslovakia
Forecast horizon 1960 1965.1 1970.1 1972*
5 years
10 years
15 years
-2.8
5.1
3.8
8.4
4.7
3.3
1965.2
-
1.7
-
- 4.1
1975
1.8
5.7 aAfter 5 , 8 and 13 years.
1980
-3.1
Row average
-
1.3

389
150
1401
130--
120--
110-- lee--
90--
+
+
+
: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : t
1958 1955 1960 1965 1978 1975 1980 1985
---
Observed
+
1958 Forecast
*
1951 Forecast
1956 Forecast
1965 and 1967
Forecast
158-
140--
130--
X
120--
8 lee--
90--
I
I
X I
* *
0
* *
0 0 y
* *
* o o
+ +
+/ o
+
1965 and 1967
/ / 1 ; % 1 7
+
+
Forecast
*
1970 and 1972
Forecast
O
1975 Forecast f +
1988 Forecast
Figure 4. Deaths, forecasts and observations, the Netherlands

390
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10, Zss. No. 4
RMSPE found for 5-year fertility forecasts in the Netherlands, which fluctuated between
1070 and 26%, is of the same magnitude as the corresponding RMSPE that Ahlburg (1982, p. 368) found for post-war fertility forecasts in the United States: a minimum RMSPE of 2% for the
1967 US forecast and a maximum of 21% for that of 1970. For the forecasts with a lead time of 10 and 15 years the RMSPEs for fertility in the Netherlands are also comparable to those in the United States. The 5-year mean percentage forecast errors for Dutch live births are of the same order as the errors after 5 years for the Norwegian forecasts of live births made since
1969 (Brunborg, 1984, p. 91).
For mortality, fluctuations in accuracy of the Dutch forecasts also accompany changes in the observed trends in the Netherlands. In the 1960s male life expectancy dropped temporarily, resulting in an accelerated growth of the annual number of deaths (Figure 4). Since 1970, the decline in the life expectancy of males has halted and the growth of the number of deaths has slowed. The forecasts of 1965 and 1967 (in which the mortality assumptions were identical) were too optimistic for the first 5-10 years, resulting in an underestimation of mortality (see
Table V). In the long term the average outcome was quite accurate, due to compensation effects after a period of 10 years (see also Van Poppel, 1984). The mortality forecasts of 1970,
1972 and 1975 were based partly on an extrapolation of the declining life expectancy of males experienced in the 1960s. This meant that mortality was overestimated in those forecasts. It was not until the forecast of 1980 that forecasters had (almost perfectly) forecasted the improved mortality situation.
External migration errors for the Netherlands will only briefly be dealt with here, since migration was not formally included in Dutch forecasts until 1975 (see Figure 5). Given our definition of a population forecast, it will be clear that we shall assume that external migration
‘forecasts’ made before 1975 were implicitly put at zero. An analysis by Schreurs (1988, p. 27) shows that Theil’s U is slightly below 1 (0.92) for 10-year external migration forecasts

N.
39 1 produced in 1975. The average U-value (over nine 10-year migration ‘forecasts’ produced between 1950 and 1975) is 1.29, and the ‘forecasts’ produced in the 1950s were better than average: 1.12 for the 1950 forecast, 0.57 for that of 1951, and 0.94 for that of 1956. Hence, the formal introduction since 1975 of external migration as a component of change in Dutch population forecasts generally improved their accuracy, although an assumption of zero net immigration implicitly contained in the forecasts produced in the 1950s did not yield less accurate results.
We now turn to the case of Czechoslovakia. Because it was rather difficult to retrieve detailed information from historical forecasts, the tables t o be discussed here are not as detailed as those for the Netherlands. However, the general pattern that emerges from them is quite clear.
Table VIII presents percentage errors in live births cumulated over 5, 10 and 15 years. Due to missing information for single calendar years we were not able to compute
percentage errors, as in Tables V-VII. Two patterns are striking. First, and again, the shift in fertility methodology from 5-year age groups to single ages is not reflected in smaller errors: compare the underestimation of 3.1% in the 1980 forecast with the average 5-year forecast error of
-2.3%. Second, fertility extrapolations carried out in the second half of the 1960s do
deteriorate with increasing time horizon. The reason is that observed fertility shows relatively large fluctuations, meaning that a short-run extrapolation which starts from some ‘average’ value (i.e. not from a peak or a trough) would often result in larger errors than a long-run extrapolation (cf. Figure 6).
Mortality shows an even stronger effect than fertility: percentage errors in absolute numbers of deaths generally
with longer lead times (see Table IX). The effect is particularly strong for the 1965.1 forecast, where the percentage error diminishes by roughly one third every five years. Figure 7 shows that Czechoslovak forecasters foresaw mortality trends after
1960 quite accurately. Because the 1965.1 forecast is the only one for which we have data on migration errors we were not able to formulate general conclusions for that component.
OVERALL COMPARISON
Our spatial perspective may be highlighted by drawing up tables for the Netherlands similar to Tables VIII and IX for the CSSR. To answer the question formulated above for fertility, we summarize the results in Table X. We computed for both countries the MPE and RMSPE by length of forecasting period, averaging over forecasts. The differences between the two countries are striking. Whereas in the case of Czechoslovakia the MPE fluctuates around
- 2 % , the Dutch MPE increases regularly from 7 % after 5 years to 21% after 15 years. A comparison of RMSPE values between the two countries reveals the same pattern. Dutch
Table 1X. Percentage error of forecasts of deaths, Czechoslavakia
Forecast horizon
5
10
15 years years years
‘After 5 , 8 and 13 years.
1965.1
-
12.2
-9.1
1970.1
- 1.3
1972a
1.3
2.0
0.6
1975
- 1.4
1980
Row average
- 3 . 1

392
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Vol. 10, Iss. No. 4
320-
300-
+
+
+
+
X
0
0
280-- t
260--
240--
+
1950 Forecast
1959 L o w
Forecast
.* 1959 High
Forecast
1961 Forecast
220-- z e e ! : : : : ~ : : l ~ : : ~ ~ ~ ~ : : I : ~ : ~ ~ ~ : : I : : : : : : : : I
1950 1955 1960 1965 1970 1975 1988 1985
320-
300--
X
280--
/
0
0 t
260--
240--
+
+
+
1965.1
Forecast
1965.2
Forecast o o o o o
O
1970.1
Forecast
\
*
1972 Forecast
220--
0 0 0 0 0
200
1950 1955 1960 1965 1970 1975 1980 1985

T.
288--
X
8
B
268-
248--
228--
+ a + + +
0 0 0
--- Observed
+
1975 Forecast
* 1977 Forecast
O
1978 Forecast
1988 Forecast
X
X
Figure 6. (confinued)
Table X. Average accuracy of forecasts of live births
Forecast horizon
5 years
10 years
15 years
The Netherlands
MPE RMSPE
6.5
13.1
20.8
10.6
21.1
31.0
Czechoslovakia
MPE RMSPE
6.9
8.2
7.8
Table XI. Average accuracy of forecasts of deaths
Forecast horizon
5
10
15 years years years
The Netherlands
MPE RMSPE
3.1
6.7
8.2
4.1
1.6
9.3
Czechoslovakia
MPE
- 3 . 1
RMSPE
8.8
6.2
5.3
393

394
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+
+
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ZOOT me-- I
Figure 7 . Deaths, forecasts and observations, CSSR

395
-*-
Observed
+
1977 Forecast
1978 Forecast
O
1980 Forecast errors not only take off at a much higher initial level, they also grow steadily, whereas
Czechoslovak errors show small fluctuations around a relatively low level. Hence, the relatively high level of sophistication of fertility forecasting methodology in the Netherlands, as shown in Table I, has not resulted in small errors. Observed fertility trends, which showed a major decline between 1964 and 1975, have almost entirely dominated error patterns. With mortality,
Table XI leads t o the same conclusion as the one for fertility, although the differences in mortality forecasts between the two countries are not as large as those of live births.
CONCLUSIONS
When we assume that the findings of this case study for the Netherlands and Czechoslovakia may be generalized to other counlries, then the general conclusion is clear: the accuracy of national population forecasts is more closely linked to the nature of underlying trends than to forecasting methodology. The transition from a period age-specific approach to a cohort marriage duration-specific approach to fertility in the Netherlands, which took place between
1967 and 1970, has not resulted in a reduction in forecast errors. Nor did the introduction of age-specific fertility rates in the CSSR in the 1955 forecast, instead of general fertility rates, reduce errors. Also, a comparison of errors in forecasts of births between the two countries shows clearly that a relatively detailed treatment of a certain component in the national forecast (fertility, mortality) does
accompany relatively small errors.
Ascher (1978) analyses errors in forecasts of total population in the United States and comes to similar conclusions. However, Ahlburg (1982) shows in a more detailed analysis that in the
United States the transition in 1964 from a period approach t o a cohort approach significantly reduced forecast errors for fertility. Our data are more detailed than those of Ahlburg, as we investigate errors in fertility and mortality (and, to some extent, also in migration) both in

396
Vol. 10, Iss. No. 4 terms of absolute numbers and crude rates. The findings of this paper for the Netherlands and the CSSR support and complement those of Ascher.
Ascher explains the low accuracy of population forecasts mainly by a psychological factor which he calls ‘assumption drag’; forecasters continue t o use assumptions which have long been refuted by actual trends. Ascher (1978, p. 53) attributes this assumption drag to a number of factors. First, it is often difficult to distinguish temporary fluctuations from the start of a new trend. We generally need information covering a longer period in order to be able to distinguish between these two phenomena. Moreover, careful construction of a population forecast is a lengthy process, in which the initial assumptions may have been superseded by the time the forecast is published.
Do these pessimistic conclusions mean that the accuracy of population forecasts can in no way be improved? We believe not. Improvement is possible, but hardly through changes in the technical approach. We can, however, counteract the assumption drag by releasing forecasts more frequently. Therefore the annual revisions of the population forecasts which the NCBS has carried out since 1984 will most probably increase their accuracy. Moreover, the assumption drag could be reduced by setting up a multidisciplinary forecasting team, whose members each interpret the historical developments in their own way, and who consequently contribute to a more balanced forecast. In an article on the accuracy of population forecasts in a large number of countries Keyfitz (1981) compares forecasters with marksmen having to hit a target. The conclusion must be drawn that the individual marksman must
try to increase his chances of a good shot by using a more sophisticated weapon. Instead, several marksmen should work together to fire the single shot.
ACKNOWLEDGEMENTS
Part of this research was carried out during a three-month stay at the NIDI by TomaS Kueera, who is affiliated with the Faculty of Sciences, Charles University, Prague. We are indebted to the Netherlands Central Bureau of Statistics and the Federal Statistical Office of the CSSR who generously provided us with unpublished results of post-World War I1 population forecasts.
The computational assistance offered by Rudi Schreurs is gratefully acknowledged. Thanks are due to Willemien Kneppelhout for assistance with the English translation and to Tonny
Nieuwstraten for accurately typing the manuscript.
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Authors ’ biographies:
Nico Keilman is a research associate at the Netherlands Interdisciplinary Demographic Institute. His current fields of interest are uncertainty in population forecasting and the modelling of household formation and dissolution.
TomaS Kurera is a research associate at the Faculty of Sciences, Charles University, Prague. His research includes methods of population forecasts and projections at the national and regional level.
Authors ’ addresses:
Nico Keilman, Netherlands Interdisciplinary Demographic Institute, PO Box 11650,2502 AR The Hague,
The Netherlands.
TomaS Kuiera, Faculty of Sciences, Charles University, Albertov 6, 12843 Prague 2, Czechoslovakia.