2.1 Mexico. A largely rural country at the turn of the 20th century, Mexico began its rapid urbanization following the Mexican Revolution (1910-1921).
WORKING PAPER
Inferring Migration Flows From the Migration Propensities of Infants: Mexico and Indonesia Andrei Rogers Bryan Jones Virgilio Partida Salut Muhidin May 2006
Population Program POP2006-05 ___________________________________________________________________________
Inferring Migration Flows From the Migration Propensities of Infants: Mexico and Indonesia Andrei Rogers Bryan Jones Virgilio Partida Salut Muhidin May 2006
Acknowledgments: This research is supported by grants from the National Science Foundation (SES0240808) and the National Institute for Child Health and Human Development (HSS-R03HD048561). This is a revised version of a paper presented at the Annual Meeting of the Western Regional Science Association convened in Santa Fe, New Mexico on 22-25, February 2006. The authors are grateful to Lisa Jordan, Megan Lea and Jonathan Rafaelson for contributions to earlier versions of this paper. Andrei Rogers, Professor of Geography, and Bryan Jones, graduate student, are both members of the Population Program, Institute of Behavioral Science, University of Colorado, Boulder. Virgilio Partida is Director of Research at CONAPO, the National Population Council of Mexico. Salut Muhidin is a staff member at the Queensland Centre of Population Research at the University of Queensland in Brisbane, Australia.
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Abstract The need for methods of indirectly estimating migration flows is particularly important in developing countries, where migration data are often incomplete and inaccurate. This paper focuses on the use of an indirect internal migration estimation method applied to Mexican and Indonesian census data. It shows that the mobility propensities of infants can be used to infer the corresponding propensities of all other age groups. However, the promise of this method is reduced in instances of inadequate data, and great care must be taken to identify outlying values in the data and to correct obviously erroneous patterns. Future work increasingly will be directed to this issue. Keywords: migration, indirect estimation, Mexico, Indonesia
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Contents 1
Introduction
2
Context and Data
3
4
5
6
2.1
Mexico
2.2
Indonesia
Method 3.1
Age-specific Regularities
3.2
The Linear Relationship
3.3
Outlying Observations
3.4
The Cubic Spline and the Model Schedule Fit
Analysis 4.1
Measuring Error
4.2
Predicting Inter-regional Migration Using Observed Data: Mexico 1990 and 2000 Censuses
4.3
Predicting Inter-regional Migration Using Observed Data: Indonesia 1980, 1990, and 2000 Censuses
4.4
Applying Confidence Intervals to the Data: Mexico and Indonesia
4.5
Applying Cubic Spline and Model Schedule Fit to the Data: Mexico and Indonesia
Prediction 5.1
Predicting 2000 Migration Flows Using 1990 Data: Mexico
5.2
Predicting 1990 Migration Flows Using 1980 Data: Indonesia
5.3
Predicting 2000 Migration Flows Using 1990 Data: Indonesia
Conclusion References 4
Inferring Migration Flows from the Migration Propensities of Infants: Mexico and Indonesia 1. Introduction In much of the developing world adequate and accurate data on inter-regional migration flows are not readily available. In some places information concerning inter-regional migration is derived from population censuses by comparing place of residence five years ago (origin) with the current place of residence (destination). Those with a destination residence in a region other than that of their origin region are considered to be migrants. In the absence of such data, researchers often turn to residual methods of estimation, in which the difference in a regional population that is unaccounted for by natural increase, is attributed to net migration, which provides no information concerning directional inand out-migration flows. Past studies of migration have identified a very consistent migration profile with respect to age. The model migration schedule (Rogers and Castro, 1981), which captures this profile, reflects the changing migration propensities exhibited by the various age cohorts (Figure 1A). However, unlike mortality and fertility schedules, migration schedules have not yet been used to develop adequate techniques for estimating age-specific migration propensities in nations with incomplete or inaccurate data. Figure 1B contains an example of one specific inter-regional directional flow that deviates significantly from the expected migration age-profile, and is likely the result of inadequate data. To adequately develop and test such methods requires the availability of adequate migration data, thus largely restricting, until now, the application of model migration schedules to developed countries with sufficiently accurate data (e.g., Rogers and Castro, 1981). This study uses a method (successfully tested on United States data) that allows one to infer agespecific directional migration propensities at the regional level in Mexico and Indonesia. The method
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uses birthplace-specific infant population data to predict infant migration propensities, and from these to infer the migration propensities for all other ages. Using Mexico and Indonesia as our examples of countries with inadequate data concerning inter-regional migration, this study will test the model’s usefulness in such nations.
A method for successfully inferring migration data would allow for
improved analyses of regional demographic processes that are essential in planning exercises. Additionally, by using such an inferential model to derive historical migration patterns, researchers could identify trends in past migration flows. (Insert Figure 1 here) Section Two of this paper frames the context of the study in both Mexico and Indonesia, using existing demographic data. Section Three reviews the infant migration method used by Rogers and Jordan (2004), and discusses two alterations in such a model, designed to improve its performance: namely, the use of confidence intervals to remove outlying observations, and the application of model schedules to smooth irregular age profiles. Section Four contains the analysis of two “test” runs, in which data from several censuses, 1990 and 2000 in Mexico, and 1980, 1990, and 2000 in Indonesia, are used to infer age-specific migration propensities during those periods.
Section Five contains an
examination of the model’s predictive capability, when 1990 data are used to predict migration patterns around the year 2000 in Mexico, and when 1980 and 1990 data are used to predict 1990 and 2000 migration patterns in Indonesia. Finally, Section Six summarizes the results and comments on future research. 2. Context and Data 2.1 Mexico A largely rural country at the turn of the 20th century, Mexico began its rapid urbanization following the Mexican Revolution (1910-1921). Post-revolution development occurred in two stages. During the first stage, which lasted into 1960s, the country’s economic policies were focused on 6
developing domestic industry and production for domestic consumption. As a result, Mexico’s principal cities enjoyed advantages associated with economies of scale, making them the primary destinations for rural out-migrants. From the 1960s onward, the second stage, the Mexican economy was increasingly influenced by global interactions, which led to a decline in the domestic power and influence of Mexico’s largest cities, and enlarged the range of potential destinations for rural out-migrants. Subsequently, in the past 40 years there has been a more even spatial distribution of the population as a result. However, despite socioeconomic changes in Mexico over the past 90 years, rural out-migration remains a significant force, and urbanization continues. Since 1900 the portion of the Mexican population residing in urban areas has increased from 10% to more than 66%. Fertility and the rate of natural increase in Mexico have dropped considerably in the past halfcentury, increasing the importance of inter-regional migration in Mexican population growth and distribution. Internal migration is now the largest determining factor of the demographic characteristics of many regional populations. To understand the socioeconomic ramifications of internal migration it is imperative that the process be adequately recorded and modeled. Planning and decision making efforts may suffer if data are incomplete. In these situations, the model discussed in this paper may prove to be useful. This paper uses data from the 1990 and 2000 Mexican national censuses. These data sets offer the most useful and reliable available information on Mexican migration, inasmuch as the 1980 census had serious undercount problems (Partida, 1993), and prior censuses excluded tables included age, place of previous residence, and place of current residence, preventing construction of our infant migration model. Data for this paper are classified by region (see Figure 2). There is no official regional division in Mexico therefore, the four regions in Figure 2 were chosen by the investigators to reflect different economic and historical zones. The Border region contains most of the nation’s formal-sector 7
employment. The North Central region has an economy focused on manufacturing and export agriculture. The Central region, home to Mexico City, and formerly the most dynamic area in Mexico, is still today the core of finance and politics. The South region, the nation’s poorest, has an economy based on tourism and petroleum. (Insert Figure 2 here) 2.2 Indonesia Due to both its extensive geography and diverse ethnicity, Indonesia presents a complex study in population mobility and internal migration patterns. Indonesians have traditionally been rather mobile. Certain ethnic groups within the nation are known to be highly mobile, such as the Minangkabau and Batak in Sumatra, Bugis and Makassarese in Sulawesi, Banjarese in Kalimantan, and Madurese in Java. Historical population policies in Indonesia are responsible for several involuntary waves of migration that took place both in colonial and post-colonial times. Through a powerful transmigration policy, many Indonesian families who resided in the densely settled regions (in particular Java and Bali) were resettled to lower population density regions (i.e., the islands of Sumatra, Kalimantan, Sulawesi, Papua and other islands). More recent trends in internal migration reflect those of a nation undergoing demographic transition. Between 1980 and 2000, the total fertility rate in Indonesia dropped from 4.6 to 2.6 children per woman. Over the same period, infant mortality dropped from 109 to 46 deaths per thousand live births. The total population grew by over 50 million persons (from 147.5 to 206.3 million); however, the annual population growth rate dropped from 2.3% to 1.4%. Consequences of the change include a shift in the age-structure of the population. For example, the portion of the total population under age 15 will continue to shrink as birth rates decline. Furthermore, a lower rate of natural increase elevates the importance of internal migration as a component of regional population change. The volume of internal migration tends to increase as development occurs in a country, due to 8
new opportunities in urban areas and the increased ability of the population to move. This pattern is evident in Indonesia, where according to the 1971 census, nearly 5% of the total population lived in provinces other than their place of birth. This figure increased to 10% in the 1995 inter-censal survey (ICBS, 1997b). Additionally the general pattern of regional migration changed during the last two decades. Between the 1960s and the mid-1980s, migration from Java to other islands in Indonesia was the prevailing trend. This situation, however, has shifted since the mid-1980s; the net out-migration from Java to other islands, between the periods 1970-1980 and 1980-1990, declined markedly from 137% to only 16% (Hugo, 1997). Tirtosudarmo (2000) argues that the change reflects the increasing role of pull factors in Java, such as urban job opportunities, and the decreasing role of the transmigration policy as a major push factor behind out-migration from Java. Like Mexico, much of the recent change in Indonesia is related to urbanization and rural to urban migration. Indonesian rural out-migrants, in general, target the largest cities as destinations. As a result, the rural population in Indonesia has declined in absolute terms, and between 1980 and 2000 the percentage of the population living in urban areas rose from 22% to nearly 42%. At the regional level, however, levels of population mobility vary strikingly. Some regions are already in the relatively late stages of demographic transition, while others are still in the early stages. For example, Jakarta has emerged as one of the world’s mega-cities and has shown characteristics similar to many advanced western cities, cities characterized by slowing rural to urban movement and urbanization rates. In contrast, many of the more remote islands are just beginning to experience changes associated with fertility, mortality, and economic structure that will lead to development and the increased importance of internal migration. In short, the geography of migration within Indonesia is just as complex as the ethnic and political geographies of the nation. This study uses data from the 1980 and 1990 Indonesian population censuses. All data sets were prepared initially from census data. The time periods do not match those chosen for Mexico because of 9
problems with the 2000 census in Indonesia. In the preliminary report of the 2000 census, data from 3 of the 27 provinces included in the 1980 and 1990 censuses were not available due to security reasons. These were the provinces of Aceh (in Sumatra) and of Maluku (between Sulawesi and Papua), where political and ethnic turbulences occurred in 2000, and East Timor (neighbor to Bali) a region that became an independent nation in 1999. Nevertheless, a few results obtained with the 2000 census data are included for purposes of comparison. Ideally, each of Indonesia’s 27 provinces would be considered in this study. But, once the data were disaggregated by age (i.e., into 5-year age groups) and sex, problems appeared because of small sample sizes. Some regional flows contained zero values, others exhibited strange patterns in age profiles. In response to these problems, the provinces in this study were classified into five macro regions: (1) Sumatra Island, (2) Western Java Island, (3) Eastern Java and Bali Islands, (4) Central Indonesia Islands, and (5) the Eastern Indonesia Islands (see Figure 3). (Insert Figure 3 here) 3. Method This study attempts to indirectly estimate patterns of inter-regional migration in Mexico and Indonesia by using information on the migration propensities of infants to predict the corresponding propensities for all other age groups. This infant migration method (Rogers et al., 2003; Rogers and Jordan, 2004), relies on the observed regularities in empirical age patterns of migration propensities. To carry out this analysis, we employ three strategies: (1) the identification of age-specific regularities, including the detection of outliers, (2) the use of the seven-parameter model migration schedule to smooth data irregularities, and (3) the subsequent prediction of the migration flows from regularities observed in past data.
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3.1 Age-specific Regularities Observed age patterns of migration probabilities generally exhibit strong regularities. The highest probabilities occur in the early adult years, when individuals leave their parental home to attend college, enter the military, marry, or enter the labor force. This is reflected in a “labor” peak in the proto-typical empirical migration schedule set out in Figure 4 (Rogers and Castro, 1981). The lowest probabilities occur in late adolescence and toward the end of the working ages.
The migration
probabilities of children mirror those of their parents, and because young adults migrate more than older adults, the migration rates of infants exceed those of adolescents. In some instances, particularly in the developed world, the migration probabilities of those reaching retirement age show a sudden increase and exhibit a retirement peak around age 65. (Insert Figure 4 here) In some cases, certain regional migration flows in both the Mexican and Indonesian data have exhibited irregularities in the age-specific pattern of migration. It may thus prove useful to employ the age-specific model migration schedule to smooth out these irregularities. This application should not only eliminate the irregularities, but also enforce a profile that is consistent with commonly observed data. The complete model migration schedule has four components: (1) the pre-labor force stage (children), (2) the labor force stage (adults), (3) the post-labor force stage (elderly), and (4) a constant curve. The model can be expressed as: m( x ) = N 1 ( x ) + N 2 ( x ) + N 3 ( x ) + c m( x) = a1 exp(−α 1x) + a 2 exp{−α 2 ( x − µ 2 ) − exp[−λ 2 ( x − µ 2 )]} + a3 exp{−α 3( x − µ 3 ) − exp[−λ 3 ( x − µ 3 )]} +c Where: m(x) = migration probability at age x N1 = pre labor force (child), N2 = labor force stage (adult) N3 = post-labor force stage (elderly), c = constant 11
(1)
α and µ = parameters, and x = age
3.2 The Linear Relationship Observed regularities in patterns of age-specific migration probabilities suggest that information on the probabilities of infant migration can be linked to the corresponding probabilities in each of the subsequent age groups by means of regression equations (Rogers and Jordan, 2004). The use of the infant migration propensity as a starting point is advantageous in that, in the absence of reported migration data, it’s level can be approximated by the birthplace-specific population count of children who are 0-4 years old and residing in region j at the time of the census, and who were born in region i, within the past five years, and therefore must have migrated during the immediately preceding 5-year interval. Since they were, on average, born some 2-1/2 years ago, it is unlikely that they moved more than once. Hence, back-casting their numbers to their region of birth, as well as all those of other infants born in the same region, one is then able to divide each i to j migration number by the total (“survivingto-census”) births in i, to obtain an estimate of each of the infant “conditional-on-survival” migration probabilities, Sij(-5). We, therefore, can consider a linear regression that links Sij(x) with Sij(-5) (see Figure 4).
S ij ( x) = a + b S ij (−5) + error term
(2)
Using this simple linear regression equation, estimated migration propensities for each of the subsequent five-year age cohorts can be determined, as well as for the corresponding propensity of all ages combined, Sij(+). (Insert Figure 5 here)
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3.3 Outlying Observations
Migration data in developing countries often display the common age-specific pattern; but some do not. When plotting the S ij (x) values against the Sij (−5) value, and fitting a regression line to the resulting scatter of points, several points may fall significantly above or below the regression line. These points, labeled “outliers,” skew the estimated S ij (x) values further away from the common age-specific pattern
of observed values, reducing the accuracy of the model. Because these points probably reflect errors in the data set, removing them should improve the fit of the regression line and yield improved estimated values. The points can be removed by statistical means, so that their deletion is not arbitrary. To do so, confidence intervals may be used. A 90% confidence interval, for example, defines a range of values that in general will capture the observed data points 90% of the time. To remove outlying data points, an interval first must be obtained such that the predicted value (in this case each S ij (x) ), lies between a lower and upper bound a certain percentage of the time. This study applies both 90% and 80% confidence intervals to the data sets. A migration propensity that lies outside of the appropriately calculated range is deleted (see Figure 6). The following equation is used to determine confidence intervals in this study: 1 ( X i − X )2 Yˆi ± t n − 2,α / 2 + n S xx
(3)
such that if the following is not satisfied: 1 (X i − X )2 1 ( X i − X )2 Yˆi − t n − 2,α / 2 + < Yi < Yˆi + t n − 2,α / 2 + n S xx n S xx then the observation is removed from the equation. (Insert Figure 6 here)
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(4)
3.4 The Cubic Spline and the Model Schedule Fit
In many cases there are specific migration flows, or data points within certain flows, that deviate markedly from the model migration schedule. In the case of Mexico and Indonesia this is likely the result of incomplete or inaccurate data. Including these data points into the regression model will skew the predicted migration propensities and increase error.
In the previous section, a method using
confidence intervals to select and remove outlying observations was described. In this section, an alternative method to deal with outlying observations is presented: fitting the model migration schedule to observed data, after first using cubic spline on the data, and inserting the resulting curves into TableCurve 2D, a commercially available curve – fitting software package. (Insert Figure 7 here) A cubic spline is constructed of third-order polynomials that pass through a set of pre-defined control points. The five-year data points serve as control points in this model, and one-year migration propensities are obtained by interpolations using the cubic spline. One-year data are preferred to fiveyear data because they provide significantly more data points to which the model schedule can be fitted. Using TableCurve 2D, the seven parameter model migration schedule is fitted to the splined data. Fiveyear data resulting from the model fit are then used in place of the observed data in the simple linear regression described in Section 3.2. In cases where the observed data are accurate, there will be few deviations between the fitted and observed data. But in cases where the observed age-profile exhibits irregularities, the fitted data will deviate substantially from the observed data, thereby correcting what are likely erroneous data points, and thereby improve the associated predictions.
4 Analysis 4.1 Measuring Error
It is convenient to use a measure of goodness-of-fit to better evaluate the results of the 14
estimations. We draw on the widely used mean absolute percentage error (MAPE) statistic, for a particular flow:
∑ MAPE =
Sˆij ( x) − S ij ( x) S ij ( x)
x
N
× 100
(5)
where N is the total number of age groups, and for all the flows use: n
Sˆij ( x) − S ij ( x)
i =1 j ≠i x
S ij ( x )
n
∑∑∑ MAPEij =
n(n − 1) N
× 100
(6)
4.2 Predicting Inter-regional Migration Using Observed Data: Mexico 1990 and 2000 Censuses
The infant migration model was “tested” in Mexico using population stock data from the 1990 and 2000 national censuses. In the initial trial, 1990 and 2000 infant migration propensities were used to estimate 1990 and 2000 age-specific migration probabilities for all age cohorts, respectively. The R² results (see Table 1) for the entire model are close to 0.70 for both periods. When examining each age cohort individually, the R² results range from highs of 0.81 in 1990 (0-4) and 0.85 (0-4) in 2000, to lows of 0.48 (10-14) in 1990 and 0.41 (15-19) in 2000. However, the standard errors for the 2000 data are lower, indicating the likelihood that less variability in error among regional flows exist for the 2000 data. The MAPE ranges vary from 19.17% (0-4 in 2000) to 70.49% (10-14 in 1990) and are 42.05% and 34.53% for all flows, 1990 and 2000, respectively. (Insert Table 1 here) Table 2A presents the MAPEs associated with regional flows in the 1990 census data. The highest errors are associated with flows out of the Border Region, the lowest errors with flows both out of the Central Region and into the Border Region. The model predicts total inter-regional migration
15
quite accurately; however, the MAPE statistic of 42.05% indicates that a larger degree of error exists in specific regional flows. Not surprisingly, the MAPE of flows from the Border Region was the largest at 86.91%. The MAPE for flows into the Border Region was 18.96%. (Insert Table 2A & B here) Table 2B presents the MAPEs associated with regional flows in the 2000 census data. The highest errors are again associated with flows out of the Border Region, and the lowest errors with flows both out of the Central Region and into the Border Region. As in the previous period, total interregional migration was predicted very accurately; however, the associated MAPE (34.53%) once again indicates that a larger degree of error exists in direction-specific regional flows. Note that the range of MAPE values is significantly narrower in 2000. As in 1990, the MAPE of flows from the Border Region was the largest at 63.94%. The MAPE for flows from the Central Region was the lowest (17.65%).
4.3 Predicting Inter-regional Migration Using Observed Data: Indonesia 1980, 1990, and 2000 Censuses
The infant migration model was also “tested” using Indonesian population data from the 1980, 1990, and 2000 national censuses. The R² results (see Table 3) for the entire model are much higher than those from the Mexican data, nearly 0.90 for all periods. However, note that MAPE values are also significantly higher than observed in the Mexican data, particularly in 2000. In contrast to the Mexican data, the R² results were strongest for the younger age cohorts and weaker in the older age groups. Note the very low R² results for the five oldest age cohorts in 2000. The 2000 census data contain several zero values that we believe to be incorrect because the 2000 census was incomplete. Consequently, the MAPE for the 2000 census was very high, but the results are included here, because the 2000 census data are an example of officially acknowledged inadequate data. 16
(Insert Table 3 here) Table 4 presents observed and predicted migration levels and MAPE associated with regional flows using the 1980 and 1990 census data sets, respectively, leading us to ignore those data. The highest errors are associated with flows out of Sumatra, largely due to very high errors in flows to the Central and Eastern Indonesian Islands. Additionally, flows into the Central Indonesian Islands, largely due to errors associated with in-migration from Sumatra, also exhibit large error values. This is not surprising, given the acknowledged inadequacies in the data. But, as was the case with the Mexican data, total inter-regional migration was predicted quite well, even in 2000. But larger MAPE values indicate again that a larger degree of error exists in direction-specific regional flows. The very high R² values and associated larger MAPE values (in relation to Mexico) indicate that these alternative goodness-of-fit measures do not necessarily work in parallel. A high R² does not necessarily indicate a low MAPE. This is potentially problematic when it comes to assessing the adequacy of the model. (Insert Table 4 here)
4.4 Applying Confidence Intervals to the Data: Mexico and Indonesia
Table 5 contains the R² results for the Mexican and Indonesian data sets for the total population and also when 90% and 80% confidence intervals are used to remove outliers. Note the very high numbers for all three Indonesian censuses, and the dramatic improvements that come with the use of 90% and 80% confidence intervals in the Mexican data. (Insert Table 5 here) The removal of outliers using confidence intervals for the Mexican (1990 and 2000) data led to a dramatic improvement in MAPE values for all flows, and for the entire model.
Using an 80%
confidence interval to remove outliers, the MAPE value for the entire model dropped to 20.25% and 17
15.32% for 1990 and 2000 data sets, respectively. MAPE values from Indonesian data from 1980, 1990, and 2000 (following the removal of outliers using 80% and 90% confidence intervals) improve markedly as the confidence intervals tighten. Total error for the model was reduced to 22.43%, 25.27%, and 36.01% for 1980, 1990, and 2000, respectively, when applying 80% confidence intervals. These figures are again higher than those from the Mexican data. The highest errors remained associated with flows out of Sumatra, and the aggregate error for the 2000 data was, as expected, higher than the ones associated with the 1980 and 1990 data. Table 6 reviews the MAPE results for the 100%, 90%, and 80% samples. Improvement is observed in all cases when outliers are removed. The large error for the 2000 census data in Indonesia is, again, likely due to incorrect or missing data points. In Section 5 of this paper, the infant migration model is used to predict migration propensities for all five-year age cohorts (for a subsequent census) using regression parameters derived from a previous census. Because the 2000 census data in Indonesia are incomplete, our methodology may prove to be very useful for improving, or “correcting” it. (Insert Table 6 here)
4.5 Applying Cubic Spline and Model Schedule Fits to the Data: Mexico and Indonesia
The Mexican observed profiles are well represented by the smoothed profiles. Most of the Indonesian observed profiles also were well fitted; however, there are more irregularities in these flows, some of which are significant. For example, the observed age profile of the flow from Sumatra to the East Indonesia Islands in 1980 was not well-fitted by the smoothed age profile. The regression results for both the Mexican and Indonesian migration schedules using the smoothed data and the infant migration model (Equation 2) are similar to those observed when using the 100% sample of observed (non-smoothed) data. However, for the fitted Mexican data, the standard error is noticeably lower, suggesting less deviation between the various inter-regional flows. This is not 18
surprising given the process of smoothing the data. It is somewhat surprising, therefore, that this was not the case for the fitted Indonesian data. MAPE values for inter-regional flows reflect the error associated with the predicted migration propensities (from the infant migration model) using the fitted data in place of the observed data. Values are again very similar to those observed in Sections 4.2 and 4.3, which reported on performance with the 100% sample observed data. However, an extremely high error appeared in many of the 2000 census Indonesian flows. These MAPE values are again indicative of a situation where the specific ageprofiles are very inconsistent. In this case, even smoothing the data did not improve the results. However, the source of error must be considered before judging this outcome. Are the results poor because the model does not work, or because the data are incorrect? Even in this case, in which the observed data were fitted by the model schedule, sufficient variation existed between individual flows to skew the overall results. Because we know the 2000 census contains errors and missing data points, we do not interpret high MAPE values as indicating flaws in the model. The next section of this paper will discuss the use of the infant migration model to predict migration propensities using regression parameters derived from a past instead of a current period, and applying them on infant migration propensities from the current period. The results of this exercise may prove useful in a case such as the 2000 Indonesian census data, where we are aware of acknowledged inadequacies in the data.
5. Prediction
To assess the predictive power of the model, infant migration propensities derived from the 2000 census in Mexico were used as an independent variable, with regression parameters derived from the 1990 observed data, to predict the 2000 migration schedule (the dependent variables) for all ages. Infant migration propensities from the 2000 and 1990 censuses in Indonesia were used with derived 1990 and 19
1980 regression parameters in Indonesia for the same sort of assessment. These assessments will test the consistency of the correlations between infant migration propensities and those of all other ages, over time. It is assumed that a change in a particular infant migration propensity mirrors changes in the migration probabilities of all other age cohorts.
5.1 Predicting 2000 Migration Flows Using 1990 Data: Mexico
Table 7 examines predicted and observed inter-regional migrants and associated MAPE values for the 100%, 90%, and 80% samples and using fitted data. All regressions used 2000 infant migration propensities and regression parameters from the 1990 data to predict 2000 age-specific data on migration probabilities. The MAPE values are slightly higher than those observed in the two “test” runs conducted earlier using Mexican data. The highest errors are still associated with flows out of the Border Region, and the lowest errors with flows into and out of the Central Region -- particularly the flow from the South to the Central Region. Note that the MAPE for the fitted data is higher than that of any of the observed samples. Also note that the flows exhibiting the highest and lowest errors are generally the same flows that earlier exhibited those in the fitted data. (Insert Table 7 here)
5.2 Predicting 1990 Migration Flows Using 1980 Data: Indonesia
Table 8 presents predicted and observed inter-regional migrations and associated MAPE values, for the 100%, 90%, and 80% samples, using fitted data. All regressions used 1990 infant migration propensities and regression parameters from the 1980 data to predict 1990 data on migration probabilities. The MAPE values are slightly higher than to those observed for the 100% sample, and also when outliers were removed. However, the MAPEs are actually better when parameters derived from 20
1980 fitted data and 1990 observed infant migration propensities are used, than when 1990 fitted data were used to predict 1990 migration probabilities. There is no single region that exhibits generally higher error than any other, in contrast to the earlier “test” runs. The lowest errors are associated with flows into Eastern Java and Bali. Note that the MAPE for the fitted data is lower than for any of the observed samples, in direct contrast to the results obtained using the Mexican data. (Insert Table 8 here)
5.3 Predicting 2000 Migration Flows Using 1990 Data: Indonesia
Table 9 contains results from the second predictive exercise using Indonesia data, this time with 2000 infant migration propensities along with regression parameters from 1990, to predict 2000 data on migration probabilities. Recall that the 2000 Indonesian census was problematic due to incomplete and possibly erroneous data. Total inter-regional migration is over-predicted by nearly 1,000,000 when using the observed data from the 100% 1990 sample and 2000 infant migration probabilities to make the predictions. This is actually an encouraging result, given the known existence of many zero values, or missing data from the 2000 census. MAPE values associated with the 100% sample and with samples with removed outliers are very high, again almost always due to significant over-prediction. When fitted data from 1990 are substituted for observed data, the MAPE values drop considerably. When the data are smoothed, zero values are replaced with values interpolated from the model schedule. The inclusion of these data points in the regression model leads to improved correlations between observed and predicted values. The drop in MAPE values indicates that this is indeed happening. Again, because we know that the 2000 census data has considerable problems, these findings are encouraging. (Insert Table 9 here)
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6. Conclusion
This study explored the use of a methodology successfully tested in the United States for estimating age-specific inter-regional migration propensities in countries lacking accurate internal migration data, Mexico and Indonesia. Rogers and Jordan (2004) used observed infant migration propensities and observed migration data from a previous census to predict the entire age-specific migration schedule of a current census by means of simple linear regression. In this study, this method was improved by using confidence intervals to remove outlying data points, and by using model migration schedules to smooth irregular age-profiles. The initial results of the study are promising. The use of confidence intervals to remove outliers significantly improved the ability of the model to predict age-specific migration propensities, particularly in the case of Mexico. Fitting data with model schedules appeared to improve the predictive capacity of the model as well, especially in the case of Indonesia.
Also encouraging was the
methodology’s ability to predict the 2000 migration schedule for Indonesia. These data contain several missing values, and are known to be incomplete, a result of ongoing conflict in many regions of the country. The presence of large errors between predicted and observed values in the direction of overpredictions of internal migration is something that would be expected given the presence of missing data points. That said, the lack of adequate data from this census make it impossible to confirm the assertion that our model is correctly predicting migration probabilities. Nevertheless, the results of this study suggest that further investigations into the use of this approach to indirect estimation in developing countries are warranted. Future research will add a second independent regression variable, such as lifetime migration, as was examined in Rogers and Jordan (2004). Additionally, to account for regional differences in migration patterns, direction-specific regional flows will be split into “families” of schedules that exhibit particular characteristics, such as “retirement peaks” and “adolescent troughs.” 22
In general, our initial results indicate that the infant migration model could be useful in developing countries such as Mexico and Indonesia. However, given the difficulties associated with testing the model (a result of inadequate data), the process of assessing and modifying the model will be decidedly more difficult than was the case in previous application of the model in the more developed world.
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References
Hugo, G. (1997). Changing Patterns of Internal and International Population Mobility in Indonesia. Paper presented at Seminar on Challenges of Indonesian Population Mobility Towards the Globalization. Jakarta: State Ministry of Population. ICBS. (1997). Estimasi Fertilitas, Mortalitas, dan Migrasi: Hasil Survey Penduduk Antar Sensus (SUPAS) 1995 [Estimation of Fertility, Mortality, and Migration: Results of the 1995 Intercensal Population Survey]. SUPAS Series S3. Jakarta: ICBS. Partida, Virgilio (1993). Estimación de los niveles de migración en el censo de México de 1980 (Estimation of migration levels in the 1980 census of Mexico). Centro de Estudios en Población y Salud, Secretaría de Salud. Rogers, A., and Castro, L.J. (1981). Model Migration Schedules. Research Report. Laxenburg, Austria: International Institute for Applied Systems Analysis. Rogers, A. and Jordan, L. (2004). Estimating Migration Flows from Birth-specific Population Stocks of Infants. Geographical Analysis 36(1): 38-53. Rogers, A., J. Raymer and L. Jordan (2003). Inferring Migration Flows From Birthplace-Specific Population Stocks. Population Program, Institute of Behavioral Science, University of Colorado, Boulder. (Unpublished paper) Tirtosudarmo, R. (2000). Population Mobility and Ethnic Conflict: the Aftermath of Economic Crisis in Indonesia. Paper presented at Workshop on the Socioeconomic Situation During the Economic Crisis in Indonesia. Singapore, May 30–June 1, 2000.
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Figure 2. The Four Regions of Mexico
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1
4 2
5 3
Figure 3. The Five Regions of Indonesia
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Migration Probability m(x)
Profile Parameters Level Parameters α 1 rate of descent of pre-labor force curve a 1 area under pre-labor force curve λ 2 rate of ascent of labor force curve a 2 area under labor force curve µ 2 position of labor peak (high peak x h ) a 3 area under post-labor force curve α 2 rate of descent of labor force curve c constant λ 3 rate of ascent of post-labor force curve µ 2 position of post-labor force peak (retirement peak x r )Other / Derived Measures x l the low point α 3 rate of descent of post-labor force curve A the parental shift B the jump (low point to labor peak)
Figure 4. Age-specific Patterns of Migration Probabilities
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Table 1. Regression Statistics for Full Sample, Mexico, Total Population: 1990 and 2000 R² S.E. S.E. R² Age α (1990) α (2000) β (1990) β (2000) (1990) (2000) (1990) (2000) 0.0011 0.0009 0.7296 0.6872 0.81 0.85 0.0020 0.0014 0-4 0.0009 0.0008 0.6820 0.5784 0.71 0.78 0.0025 0.0015 5-9 0.0005 0.0010 1.1616 0.9735 0.48 0.43 0.0069 0.0053 10-14 0.0009 0.0020 1.4365 1.1980 0.51 0.41 0.0080 0.0068 15-19 0.0020 0.0023 1.1782 1.0197 0.68 0.59 0.0046 0.0041 20-24 0.0023 0.0019 0.9555 0.8339 0.70 0.70 0.0035 0.0026 25-29 0.0019 0.0015 0.7921 0.6655 0.72 0.75 0.0028 0.0018 30-34 0.0015 0.0012 0.6553 0.5588 0.68 0.73 0.0026 0.0016 35-39 0.0010 0.0010 0.5728 0.4596 0.67 0.72 0.0023 0.0014 40-44 0.0007 0.0007 0.5102 0.3973 0.66 0.68 0.0021 0.0013 45-49 0.0005 0.0005 0.4773 0.3624 0.65 0.68 0.0020 0.0012 50-54 0.0004 0.0004 0.4602 0.3322 0.69 0.68 0.0018 0.0011 55-59 0.0003 0.0002 0.4587 0.3251 0.67 0.68 0.0019 0.0011 60-64 0.0004 0.0001 0.4457 0.3373 0.68 0.65 0.0017 0.0012 65-69 0.0002 -0.0001 0.4932 0.3649 0.64 0.67 0.0021 0.0012 70-74 0.0010 0.0011 0.8872 0.7675 0.72 0.70 0.0031 0.0024 Totals
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MAPE (1990) 31.42% 40.93% 70.49% 56.64% 29.57% 33.11% 33.62% 37.18% 37.97% 40.80% 38.91% 39.02% 42.95% 45.04% 53.19% 42.05%
MAPE (2000) 19.17% 25.50% 68.78% 66.41% 36.88% 28.08% 26.07% 27.87% 27.44% 31.42% 31.57% 30.56% 33.40% 32.44% 32.35% 34.53%
Table 2. Observed and Predicted Migration Flows and MAPE Table 2A. Mexico 1985-1990 Reg85 Reg90 Predicted Observed B NC 189,633 112,944 B C 116,647 59,736 B S 26,916 13,913 NC B 259,505 334,483 NC C 145,747 145,561 NC S 43,824 22,768 C B 144,882 182,890 C NC 235,416 276,820 C S 215,444 191,080 S B 34,384 40,277 S NC 58,996 68,673 S C 149,106 216,659 B All 333,197 186,593 NC All 449,076 502,812 C All 595,742 650,790 S All 242,486 325,609 All B 438,772 557,650 All NC 484,045 458,437 All C 411,500 421,956 All S 286,184 227,761 All All 1,620,501 1,665,804
MAPE 63.10% 95.12% 102.52% 17.93% 10.98% 92.65% 17.22% 28.82% 11.22% 21.74% 15.06% 28.31% 86.91% 40.52% 19.09% 21.70% 18.96% 35.66% 44.80% 68.80% 42.05%
Table 2B. Mexico 1995-2000 Reg95 Reg00 Predicted Observed B NC 180,699 123,014 B C 130,897 69,873 B S 35,953 20,960 NC B 245,922 308,479 NC C 135,121 134,209 NC S 53,680 28,656 C B 195,112 278,297 C NC 220,677 219,258 C S 216,548 199,607 S B 63,900 90,048 S NC 89,294 89,005 S C 147,934 200,303 B All 347,549 213,847 NC All 434,723 471,344 C All 632,337 697,162 S All 301,127 379,356 All B 504,934 676,824 All NC 490,670 431,277 All C 413,951 404,385 All S 306,182 249,223 All All 1,715,737 1,761,709
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MAPE 43.85% 83.31% 64.66% 15.76% 12.01% 76.88% 19.95% 21.97% 11.04% 23.84% 16.67% 24.44% 63.94% 34.88% 17.65% 21.65% 19.85% 27.49% 39.92% 50.86% 34.53%
Table 3. Regression Statistics for Full Sample, Indonesia Total Population: 1980, 1990 α α β β β R² R² R² S.E. S.E. S.E. α Age (1980) (1990) (2000) (1980) (1990) (2000) (1980) (1990) (2000) (1980) (1990) (2000) 0.0003 0.0008 0.0007 1.4613 1.1027 1.0840 0.67 0.69 0.76 0.0005 0.0004 0.0003 0-4 0.0002 0.0005 0.0005 1.6017 1.1528 0.6777 0.83 0.85 0.66 0.0004 0.0002 0.0003 5-9 0.74 0.79 0.70 0.0010 0.0012 0.0006 10-14 -0.0009 -0.0025 0.0007 3.6120 4.5408 1.7528 0.77 0.82 0.81 0.0014 0.0016 0.0010 15-19 -0.0008 -0.0024 0.0008 5.0838 6.9383 3.7709 0.0002 -0.0001 0.0012 3.5838 4.2464 3.1801 0.87 0.95 0.91 0.0007 0.0005 0.0005 20-24 0.0006 0.0008 0.0010 2.5586 2.5408 2.1607 0.87 0.91 0.84 0.0005 0.0004 0.0005 25-29 0.0005 0.0011 0.0006 1.9267 1.7169 1.2906 0.80 0.78 0.78 0.0005 0.0005 0.0004 30-34 0.0005 0.0011 0.0009 1.5024 1.2129 0.6011 0.75 0.71 0.42 0.0004 0.0004 0.0004 35-39 0.0003 0.0009 0.0004 1.2090 1.0270 0.4736 0.67 0.60 0.58 0.0004 0.0004 0.0002 40-44 0.0007 0.0007 0.0003 1.0993 0.8181 0.4858 0.43 0.59 0.50 0.0006 0.0003 0.0003 45-49 0.0006 0.0007 0.0003 0.9519 0.6904 0.4077 0.50 0.43 0.32 0.0005 0.0004 0.0003 50-54 0.0006 0.0007 0.0003 0.8908 0.6209 0.2156 0.41 0.42 0.28 0.0005 0.0004 0.0002 55-59 0.0006 0.0005 0.0003 0.7771 0.6555 0.1321 0.39 0.46 0.11 0.0005 0.0004 0.0002 60-64 0.0009 0.0005 0.0003 0.7531 0.5794 0.0762 0.31 0.52 0.04 0.0005 0.0003 0.0002 65-69 0.0007 0.0004 0.0003 0.8033 0.6422 0.1450 0.52 0.44 0.10 0.0004 0.0004 0.0002 70-74 0.92 0.95 0.88 0.0003 0.0003 0.0003 Totals 0.0001 -0.0001 0.0006 2.1561 2.3606 1.4512
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MAPE MAPE (1980) (1990) 33.69% 58.47% 25.27% 42.17% 31.69% 54.67% 35.84% 48.86% 27.79% 25.75% 28.12% 33.98% 28.11% 42.65% 28.94% 40.72% 35.39% 51.09% 45.07% 52.13% 59.12% 67.92% 63.96% 85.00% 75.07% 87.69% 90.73% 63.73% 64.26% 124.45% 44.87% 58.62%
MAPE (2000) 67.30% 52.03% 112.23% 80.74% 48.87% 50.40% 45.67% 105.42% 149.81% 177.64% 149.04% 66.42% 89.19% 52.75% 44.42% 94.61%
Table 4A. Observed and Predicted Migration Flows and MAPE, Indonesia 1975-1980 Reg75 Reg80 Predicted Observed MAPE 1 2 178,916 187,645 14.54% 1 3 120,522 78,250 43.84% 1 4 24,532 14,362 152.02% 1 5 30,843 15,768 113.77% 2 1 220,105 181,683 15.17% 2 3 200,418 139,934 45.48% 2 4 35,019 31,771 55.22% 2 5 47,405 37,062 36.71% 3 1 579,909 632,969 17.84% 3 2 491,784 540,278 56.36% 3 4 146,508 151,932 50.55% 3 5 92,381 83,315 74.69% 4 1 6,703 12,626 41.92% 4 2 27,730 31,944 16.25% 4 3 40,165 63,069 47.12% 4 5 20,675 20,601 39.76% 5 1 19,593 26,153 22.54% 5 2 32,719 33,304 11.68% 5 3 23,745 21,928 20.99% 5 4 36,403 45,546 20.95% 1 All 354,813 296,025 81.04% 2 All 502,948 390,450 38.15% 3 All 1,310,583 1,408,494 49.86% 4 All 95,272 128,240 36.27% 5 All 112,460 126,931 19.04% All 1 826,311 853,431 24.37% All 2 731,149 793,171 24.70% All 3 384,850 303,181 39.36% All 4 242,462 243,611 69.69% All 5 191,304 156,746 66.24% All All 2,376,076 2,350,140 44.87%
Table 4B. Observed and Predicted Migration Flows and MAPE, Indonesia 1985-1990 Reg85 Reg90 Predicted Observed MAPE 1 2 224,530 274,418 28.98% 1 3 158,910 183,473 34.08% 1 4 27,173 18,554 163.55% 1 5 31,223 19,824 101.53% 2 1 253,787 198,467 26.72% 2 3 304,448 293,316 15.74% 2 4 42,028 45,365 103.77% 2 5 38,928 39,997 64.64% 3 1 446,449 420,683 16.53% 3 2 840,581 880,315 53.44% 3 4 211,069 240,001 48.66% 3 5 116,622 127,058 66.81% 4 1 23,726 9,998 164.65% 4 2 31,505 49,069 34.01% 4 3 100,683 90,920 20.91% 4 5 44,397 42,848 64.45% 5 1 17,923 42,848 89.27% 5 2 29,170 40,686 44.33% 5 3 50,162 44,961 19.21% 5 4 51,231 55,544 11.11% 1 All 441,837 496,269 82.04% 2 All 639,190 577,145 52.72% 3 All 1,614,721 1,668,057 46.36% 4 All 200,312 192,835 71.01% 5 All 148,486 184,039 40.98% All 1 741,885 671,996 74.29% All 2 1,125,786 1,244,488 40.19% All 3 614,203 612,670 22.49% All 4 331,501 359,464 81.77% All 5 231,170 229,727 74.36% All All 3,044,546 3,118,345 58.62%
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Table 5. R² Results, Mexico and Indonesia: All Periods Mexico Indonesia R² (1990) R² (2000) R² (1980) R² (1990) Sample 100% 0.72 0.70 0.92 0.95 90% 0.77 0.79 0.97 0.95 80% 0.97 0.96 0.97 0.97
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R² (2000) 0.88 0.92 0.96
Table 6. MAPE at 100%,90%,80% Confidence Intervals: Mexico and Indonesia Mexico Indonesia Sample 1990 2000 1980 1990 2000 100% 42.05% 34.53% 44.87% 58.62% 94.61% 90% 32.35% 23.75% 27.19% 27.92% 43.30% 80% 20.25% 15.32% 22.43% 25.27% 36.01%
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Table 7. Observed and Predicted Migration Flows and MAPE for all Samples and Fitted Data, Mexico 1995-2000 MAPE MAPE MAPE Fitted Reg95 Reg00 Predicted Observed 100% 90% 80% Data B NC 208,908 123,014 77.40% 61.64% 25.75% 45.80% B C 150,274 69,873 125.66% n/a* n/a* 104.68% B S 38,493 20,960 99.93% 86.31% 53.67% 131.37% NC B 283,838 308,479 12.91% 7.15% 24.17% 21.40% NC C 153,421 134,209 14.56% 14.97% 20.16% 14.62% NC S 57,563 28,656 114.73% 101.05% 67.62% 115.86% C B 220,489 278,297 22.96% 17.60% 21.86% 8.20% C NC 250,594 219,258 11.09% 41.41% 39.07% 32.66% C S 245,731 199,607 23.80% 23.55% 28.01% 9.03% S B 71,530 90,048 37.20% 31.74% 33.61% 86.92% S NC 101,375 89,005 40.29% 37.41% 46.48% 38.08% S C 170,294 200,303 7.83% 2.13% 2.79% 32.74% B All 397,675 213,847 101.00% 49.32% 26.47% 93.95% NC All 494,822 471,344 47.40% 41.06% 37.32% 50.63% C All 716,814 697,162 19.28% 27.52% 29.65% 16.63% S All 343,199 379,356 28.44% 23.76% 27.63% 52.58% All B 575,857 676,824 24.35% 18.83% 26.55% 38.84% All NC 560,877 431,277 42.93% 46.82% 37.10% 38.85% All C 473,988 404,385 49.35% 8.55% 11.47% 23.68% All S 341,787 249,223 79.49% 70.30% 49.77% 85.42% All All 1,952,509 1,761,709 49.03% 38.63% 33.02% 53.45%
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Table 8. Observed and Predicted Migration Flows and MAPE for all Samples and Fitted Data, Indonesia 1985-1990 MAPE MAPE MAPE Fitted Reg85 Reg90 Predicted Observed 100% 90% 80% Data 1 2 214,134 274,418 23.17% 23.69% 24.14% 15.88% 1 3 152,986 183,473 26.83% 37.19% 34.57% 29.89% 1 4 24,967 18,554 138.30% 88.06% 99.56% 97.48% 1 5 31,271 19,824 80.27% 58.82% 71.79% 48.26% 2 1 239,917 198,467 33.41% 27.16% 25.84% 12.32% 2 3 286,522 293,316 16.40% 14.08% 10.29% 61.87% 2 4 44,165 45,365 116.19% 87.91% 55.28% 46.64% 2 5 40,498 39,997 64.75% 44.98% 57.24% 9.73% 3 1 424,428 420,683 21.29% 23.54% 24.59% 43.04% 3 2 790,399 880,315 85.33% 55.59% 56.57% 99.62% 3 4 205,865 240,001 72.38% 17.92% 17.07% 64.79% 3 5 118,165 127,058 82.64% 37.13% 29.31% 74.97% 4 1 24,068 9,998 186.85% 149.61% 159.60% 26.44% 4 2 31,336 49,069 33.38% 37.59% 38.34% 25.06% 4 3 95,970 90,920 12.93% 16.02% 12.49% 39.29% 4 5 43,381 42,848 90.53% 16.66% 18.15% 72.58% 5 1 18,784 42,848 97.70% 87.71% 107.37% 41.44% 5 2 29,327 40,686 55.46% 54.65% 58.46% 26.38% 5 3 48,825 44,961 23.17% 25.90% 22.83% 63.06% 5 4 49,818 55,544 14.30% 12.77% 12.73% 16.55% 1 All 423,358 496,269 67.14% 51.94% 57.51% 47.87% 2 All 611,103 577,145 57.69% 43.53% 37.16% 32.64% 3 All 1,538,857 1,668,057 65.41% 33.55% 31.88% 70.61% 4 All 194,756 192,835 80.92% 54.97% 57.15% 40.84% 5 All 146,754 184,039 47.66% 45.26% 50.35% 36.86% All 1 707,197 671,996 84.81% 72.01% 79.35% 30.81% All 2 1,065,196 1,244,488 49.33% 42.88% 44.38% 41.73% All 3 584,303 612,670 19.83% 23.30% 20.05% 48.53% All 4 324,815 359,464 85.29% 51.66% 46.16% 56.37% All 5 233,316 229,727 79.55% 39.40% 44.12% 51.38% All All 2,914,828 3,118,345 63.76% 45.85% 46.81% 45.76%
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Table 9. Observed and Predicted Migration Flows and MAPE for all Samples and Fitted Data, Indonesia 1995-2000 MAPE MAPE MAPE Reg85 Reg90 Predicted Observed 100% 90% 80% 1 2 200,427 212,398 24.99% 25.32% 16.81% 1 3 123,166 134,648 30.49% 17.71% 12.91% 1 4 20,323 14,957 402.05% 179.97% 157.27% 1 5 14,174 16,985 227.12% 110.28% 91.81% 2 1 380,337 178,392 178.62% 175.27% 182.57% 2 3 685,859 451,720 153.82% 178.98% 188.84% 2 4 92,540 39,816 524.09% 390.77% 346.68% 2 5 82,741 28,314 244.11% 199.15% 204.61% 3 1 107,648 129,377 99.34% 68.60% 79.39% 3 2 879,208 502,608 224.05% 94.43% 54.72% 3 4 213,206 137,626 149.01% 115.77% 92.80% 3 5 71,347 47,543 302.45% 182.94% 119.55% 4 1 10,559 17,644 186.35% 93.43% 65.97% 4 2 6,824 42,544 98.97% 83.67% 88.02% 4 3 125,844 112,713 32.64% 32.02% 22.17% 4 5 40,841 33,670 52.18% 38.11% 40.02% 5 1 17,838 33,670 610.09% 467.92% 520.07% 5 2 17,431 25,826 48.11% 42.15% 34.68% 5 3 42,718 42,486 43.38% 32.75% 34.61% 5 4 78,656 67,658 66.80% 63.69% 65.88% 1 All 358,090 378,988 171.16% 83.32% 69.70% 2 All 1,241,477 698,242 275.16% 236.04% 230.68% 3 All 1,271,409 817,154 193.71% 115.44% 86.61% 4 All 184,067 206,571 92.54% 61.81% 54.05% 5 All 156,643 169,640 192.10% 151.63% 163.81% All 1 516,381 359,083 268.60% 201.31% 212.00% All 2 1,103,890 783,376 99.03% 61.39% 48.56% All 3 977,587 741,567 65.08% 65.36% 64.63% All 4 404,725 260,057 285.49% 187.55% 165.66% All 5 209,103 126,512 206.46% 132.62% 114.00% All All 3,211,686 2,270,595 184.93% 129.65% 120.97%
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Fitted Data 41.18% 48.73% 162.35% 103.10% 37.76% 64.57% 139.33% 87.92% 68.42% 53.00% 37.80% 57.15% 91.21% 74.81% 20.30% 17.63% 77.05% 48.18% 21.72% 27.44% 88.84% 82.40% 54.09% 50.99% 43.60% 68.61% 54.29% 38.83% 91.73% 66.45% 63.98%
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