Workshop on Population Projections The Census Bureau’s Subnational Projections Toolkit

Overview The Census Bureau’s Subnational Projections Toolkit addresses existing needs in making population projections by providing tools that are: Designed for use in making both cohort-component and non-cohort-component projections Intended for use at multiple administrative levels Flexible User-friendly and documented The Census Bureau’s Subnational Projections Toolkit addresses existing needs for subnational and local area population projections by providing a set of tools that Are designed for use in making both cohort-component and non-cohort-component population projections Suited for use at national and higher administrative subnational levels (e.g., state, province) as well as at lower administrative levels (e.g., county, district, local government area) Work together in either a bottom-up or a top-down approach to projection, and Are user friendly, documented, suited to either production or classroom use. 2

Overview The Census Bureau’s Subnational Projections Toolkit comprises The Census Bureau’s RUP (Rural-Urban Projections) software for making cohort-component projections The Census Bureau’s RUPAGG software The Excel-based RUPEX workbook interface for RUP and RUPAGG A series of Excel workbooks for specialized projection tasks The Census Bureau’s Subnational Projections Toolkit comprises The Census Bureau’s RUP (Rural-Urban Projections) software for making cohort-component projections The Census Bureau’s RUPAGG software for preparing consistent cohort-component projections as the sum of a series of subarea projections or as the difference between a national control projection and a subset of subarea projections A series of Excel workbooks 3

Overview The Excel workbooks are designed for Preparing consistent base year population, and consistent assumptions about fertility, mortality, and migration Projecting population totals by logistic extrapolation Ensuring consistency of cohort-component projections at higher and lower geographic levels The Excel workbooks are designed for Preparing consistent base year population, and consistent assumptions about fertility, mortality, and migration Projecting population totals by logistic extrapolation Ensuring consistency of cohort-component projections at higher and lower geographic levels using proportional adjustment for population, vital events, and international migrants, and an algorithm to ensure zero net internal migration in every year, and for every age-sex group, over the projection horizon. 4

Overview For some countries, data are available for cohort- component projection at relatively low administrative levels. For other countries, vital statistics are incomplete and migration data may be weak or non-existent, and a combination of projection methods may be warranted. For some countries, data are available for cohort-component projection at relatively low administrative levels. For other countries, vital statistics are incomplete and migration data may be weak or non-existent, and a combination of projection methods may be warranted. 5

Overview If preparing subnational projections is defined as a combination of cohort-component projection at national and first administrative levels, but non-cohort-component projection at lower levels, then the progression can be: Preparation of consistent base year population Preparation of consistent assumptions about future levels Subarea cohort-component projection The combination of subarea projections, final projections Non-cohort-component projections Then the Subnational Projections Toolkit provides tools for each of these steps. If the task of preparing subnational projections is defined as a combination of cohort-component projection at national and first administrative levels but non-cohort-component projection at lower levels, the overall process may be viewed as a progression from: Preparation of consistent base year population and consistent assumptions for a first series of projections, followed by Subarea cohort-component projection, followed by The combination of subarea projections , or forced consistency with a control projection, followed by Non-cohort-component projection for lower administrative areas. Then the Subnational Projections Toolkit provides tools for each of these steps. 6

Overview Preparation of consistent base year population (and numbers of vital events), for a first series of projections From data to preliminary subnational area estimates of population by age and sex The Toolkit provides an Excel workbook to help the analyst with the first task – preparing a set of preliminary subnational area estimates of population by age and sex for the base year. The CTBL32 workbook, though designed for contingency table adjustment, can also be used to rake subarea populations to match estimated values for higher administrative levels. CTBL32 7

Overview Preparation of consistent assumptions about future migration and, optionally, consistent assumptions about future fertility and mortality From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels ProjTFR32 Proje032 The Toolkit provides 3 Excel workbooks to help the analyst with the second task – preparing consistent assumptions about future fertility, mortality, and migration. The ProjTFR32 and Proje032 workbooks facilitate preparation of fertility and mortality trends for subareas that are consistent with higher administrative level trends. The MIGSUB workbook supports the preparation of internal and international migration for subareas. CTBL32 MIGSUB 8

Overview Preparation of subarea cohort-component projections DAPPS/ From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels Subarea cohort-component projections ProjTFR32 DAPPS/ RUP Proje032 The Toolkit includes the Census Bureau’s Rural-Urban Projections software for preparing single-age single-year cohort-component projections – the third step in the process. CTBL32 MIGSUB 9

Overview Combination of subarea cohort-component projections by addition, subtraction, or by proportional adjustment to match a control projection From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels Subarea cohort-component projections Combination of subarea projections, or proportional adjustment to match a control projection ProjTFR32 RUP Proje032 The Toolkit includes the Census Bureau’s RUPAGG program and an Excel workbook for ensuring consistency between subarea cohort-component projections by addition, subtraction, or by proportional adjustment to match a control projection. RUPAGG may be used to ensure consistency in projected population, births, deaths, migrants, and associated rates by addition or subtraction. RUPSubAdj performs the same task using proportional adjustment. RUPAGG CTBL32 MIGSUB RUPSubAdj 10

Overview Preparation of non-cohort-component projections for lower-level subareas consistent with higher-level cohort-component projections From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels Subarea cohort-component projections Combination of subarea projections, or proportional adjustment to match a control projection Non-cohort-component projections for lower-level subareas consistent with higher-level cohort-component projections ProjTFR32 RUP Proje032 The Toolkit includes 2 Excel workbooks for the fifth task – preparing non-cohort-component projections for subareas and ensuring consistency between these projections and cohort-component projections for higher administrative levels. SALGST may be used to project subarea population totals using a series of logistic curves, with resultant populations raked to a control projection. CTBL32 may be used, to ensure that subarea populations by age and sex match a national or higher administrative level control population over the course of the projection horizon. RUPAGG CTBL32 MIGSUB SALGST RUPSubAdj CTBL32 11

Overview The Census Bureau’s Subnational Projections Toolkit, including RUP, RUPAGG, the RUPEX interface, Excel workbooks, Method descriptions and the User’s Guide, can be downloaded at no cost from www.census.gov/population/international/software/sptoolkit During the rest of this session I will describe and demonstrate elements of the Toolkit. Your take-away from this overview should be, First, that the Toolkit includes tools designed for use in making bottom-up and top-down cohort-component projections as well as non-cohort-component population projections, and Second, that the Toolkit is available to you at no cost from the Census Bureau’s website 12

Tools for Non-Cohort-Component Projection 5/22/2018 Tools for Non-Cohort-Component Projection

Non-Cohort-Component Projection Methods and Tools 5/22/2018 Non-Cohort-Component Projection Methods and Tools Projection of the proportional distribution of total population by subnational area (SALGST). Iterative proportional fitting or raking age-sex distributions to projected subnational totals and higher-level age-sex distributions (CTBL32)

From the Overview Preparation of non-cohort-component projections for lower-level subareas consistent with higher-level cohort-component projections From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels Subarea cohort-component projections Combination of subarea projections, or proportional adjustment to match a control projection Non-cohort-component projections for lower-level subareas consistent with higher-level cohort-component projections ProjTFR32 RUP Proje032 In the Overview, we described one of the last steps as: Non-cohort-component projection for lower administrative areas. RUPAGG CTBL32 MIGSUB SALGST RUPSubAdj CTBL32 15

Non-Cohort-Component ADM1 Projections by Sex and Age Preparation of “quick and dirty” non-cohort-component projections for ADM1 subareas consistent with the national cohort-component projections National cohort-component projection Non-cohort-component projections for lower-level subareas consistent with higher-level cohort-component projections DAPPS/ RUP However, these procedures could be used for “quick and dirty” short-term projections at higher levels of geography as well. This version is what I will be demonstrating. SALGST CTBL32 16

Non-Cohort-Component Projection Methods: Totals 5/22/2018 Non-Cohort-Component Projection Methods: Totals Projected totals by sex Projected total population by sex and subarea Toolkit SALGST Subarea total population by sex for two dates In this diagram we see that SALGST is used to combine subarea data from two dates with projections by sex for selected years to get projections by sex and subarea. This may be all that is needed for the geographic level being studied.

5/22/2018 SALGST: SETUP Sheet The first step in using the SALGST workbook is to describe the inputs you need. This is done on the SETUP sheet. These include: the dates of the two censuses (or other estimates), the number of subareas, the labels of the subareas (e.g., district, state, province, or region), and the desired projection years specified as the starting date, ending date and interval. Pressing the “Set up workbook” button will format the INPUT sheet based on the data entered.

5/22/2018 SALGST: INPUT Sheet On the SALGST INPUT sheet, we entered the projection for the higher-level in row 7. In section C we enter the names of the subareas and the populations at the two dates. We can also enter the Lower and Upper Asymptotes, either for all subareas, or for each subarea separately. Pressing the “Project” button will project the subarea populations.

SALGST: Population Results 5/22/2018 SALGST: Population Results The program fits a logistic curve to the proportions in each district with the given asymptotes, adjusts the resulting projected proportions to sum to 1.00, and then distributes the projected total population for each projected year among the subareas (shown here on the POP sheet).

Non-Cohort-Component Projection Methods: By Age 5/22/2018 Non-Cohort-Component Projection Methods: By Age Projected total population by age and sex Projected subarea population by age and sex Projected total population by sex and subarea Toolkit CTBL32 Now we can take the results from SALGST (projected total population by sex and subarea) and combine it with the projected total population by age and sex and a preliminary distribution of the subareas by age and sex to get the final age-sex distribution by subarea consistent with the total projection using the workbook CTBL32. Subarea preliminary population by age and sex

5/22/2018 CTBL32: INPUT As noted before, CTBL32 implements iterative proportions fitting (IPF) or raking of the population by age. Here we see the INPUT sheet. On the far left is the desired total male population by age (for 2015 in this example). In columns E, F, and G are the subarea populations by age, usually from the latest census. The other inputs are the alternate column totals shown in row 32. In this example, these can come from the workbook SALGST we just looked at, and represent the desired total population distribution by subarea.

5/22/2018 CTBL32: OUTPUT The OUTPUT sheet displays the age distributions by subarea that are consistent with the age distribution of the higher geographic area (country in this example) and with the distribution of total populations by subarea. CTBL32 does five cycles of row and column “rakes” (adjustments) to get the final results.

Non-Cohort-Component Projection Summary 5/22/2018 Non-Cohort-Component Projection Summary First use SALGST to get projected total populations by subarea and sex. Then use CTBL32 to get the age distribution for each subarea and sex. Note that there can be consistency issues in this approach because the sexes are projected independently, so the sex ratios of young children may imply an implausible sex ratio at birth.

Tools for Making Assumptions for Cohort-Component Projection 5/22/2018 Tools for Making Assumptions for Cohort-Component Projection

From the Overview Preparation of consistent base year population, for a first series of projections Preparation of consistent assumptions about future migration and, optionally, consistent assumptions about future fertility and mortality From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels ProjTFR32 The Toolkit provides an Excel workbook to help the analyst with the first task, preparing a set of preliminary subnational area estimates of population by age and sex. The Toolkit provides 3 Excel workbooks to help the analyst with the second task, preparing consistent assumptions about future fertility, mortality, and migration. Proje032 CTBL32 MIGSUB 26

Preparing for Cohort-Component Projections   Preparing consistent base-year population structures. CTBL32 may also be used to provide consistent subnational base population age-sex structures prior to cohort-component projection. Projecting fertility and mortality. ProjTFR32 and Proje032 -- are designed to help ensure internal consistency of national and subnational projections of fertility (TFR) and mortality (e(0)), respectively. Projecting migration. MIGSUB computes estimates and projections of migration for subnational areas based on tabulated responses to a question about residence one or five years prior to a census. This section is a demonstration of four Toolkit workbooks for preparing base populations, fertility, mortality, and migration for subareas. CTBL32 may also be used to provide consistent subnational base population age-sex structures prior to cohort-component projection. The second and third tools, ProjTFR32 and Proje032, are designed to help ensure internal consistency of national and subnational projections of fertility (TFR) and mortality (e(0)), respectively. These workbooks facilitate calculation of projected TFR and e(0) for subarea populations as inputs to cohort-component projection. A fourth tool, MIGSUB, which will be added to the toolkit soon, estimates area-specific in-migration, out-migration, and net migration for subnational areas based on tabulated responses to a question about residence one or five years prior to a census or from a published table of flows of in-migrants and out-migrants for that period. The pattern of internal migration from the reference census is used, along with user-provided assumptions about trend in migration levels, to project numbers of internal migrants for a user-specified time horizon. The same pattern is used to model international migration into and out of subareas over the projection horizon.

Introduction to ProjTFR32 and ProjE032 The process of preparing assumptions for subnational projections carries with it a number of challenges not faced by the demographer involved in the process of preparing assumptions for national projections. These challenges include the requirement of consistency between projected subnational and national populations but, for cohort-component projections, the desirability of some level of inter-regional consistency. ProjTFR32 and Proje032 allow the analyst to model subarea TFR and e(0)s using the assumed trend for the country as a whole or the trend for a similar region, to avoid implausible assumptions based on historically atypical region-specific trends.

ProjTFR32 This method computes the relative change, RC, in the complement or gap between TFR and the limit TFR (K) for the country as a whole over period t to t+n RC = [K - National TFRt+n] /[K - National TFRt] ProjTFR32 calculates projected subarea TFR as the relative change in national (or model area) gap times initial subarea gap, and the resulting subarea TFR is then taken as the limit (K) minus the product, or Subnational TFRt+n= K - { (K-Subnational TFRt) * RC } The TFR trajectory in relation to the TFR target level for all subnational areas follows that for the national population. For each projected year, the relative change in the complement for each subarea is the same as for the national projection.   This workbook requires an estimated TFR time series for a national or model population and base year estimates of TFR for subarea, or dependent, population. For change in the complement or gap between TFR and the limit TFR (K) for the country as a whole over period t to t+n K − National TFRt+n K − National TFRt ProjTFR32 calculates projected subarea TFR as the relative change in national (or model area) gap times initial subarea gap, and the resulting subarea TFR is then taken as the limit (K) minus the product, or Subnational area TFRt+n= K−{(K−Subnational area TFRt) ∗ (K − National TFRt+n)) (K − National TFRt)

ProjTFR32 To implement this we need the base year and the limit TFR used to compute the complement of the TFR.

ProjTFR32 We then need to enter the national base year TFR value and the corresponding TFR values for the subnational areas so we can compute the base complement values. The names of the subnational areas can also be changed.

ProjTFR32 The final inputs are the projected years (which default to 5 year intervals from the base year but can be changed) and the corresponding national projected TFR values. Note that the method is based only on the TFR values and not the years.

ProjE032 Basically uses the same formulas as ProjTFR32, but separately by sex Again requires a limit, in this case the upper limit of life expectancy by sex

ProjE032 Here we can see the inputs are similar to ProjTFR32, but we need to include male and female limit values. Once the subnational area names are entered for males they will transfer to the section for females.

MIGSUB Projects internal and international migrants by sex and subnational area Internal in- and out-migrants based on census data about residence X years before the census Internal migration projection based on the implied total internal net number of migrants, user-specified future growth rate of the total internal migration rate, and projected total population Total internal migrants are distributed by subarea based on the patterns of estimated in- and out-migrants from the census International net migration by subarea is projected based on input total net international migrants and the pattern of internal in-migrants by subarea MigSub projects internal and international migrants by sex and subnational area. Internal in- and out-migrants are estimated from the population by subarea at the time of a census and at a prior time point (based on a question in the census about residence X years before the census). The internal migration projection is based on the implied total internal net number of migrants and a user-specified future growth rate of the total internal migration rate and the projected total population. The resulting projected total internal migrants are distributed by subarea based on the patterns of estimated in- and out-migrants from the census. International migration by subarea is projected based on input total net international migrants and the pattern of internal in-migrants by subarea. The method does not provide information on the age distribution of migrants. This can be based on models such as the Rogers and Castro (1981) model or on other data sources.

MIGSUB: SETUP Sheet Setup tab allows user to specify number of subareas, recent census dates, time reference of the migration question, and the desired years for the projected migration output.

MIGSUB: Internal Migration Estimation The user enters data based on the census migration data on the INPUT sheet. The migrant numbers shown reflect only the population ages X and over at the time of the census, and cover the X-year period before the census. Internal in-migrants are calculated as the difference between those enumerated in the subarea and non-migrants in the subarea. Internal out-migrants are the difference between those resident in the subarea X years before and non-migrants.

MIGSUB: Total Internal Migration Projection Using estimates of migrants under age X at the time of the census entered on the Internal tab, MIGSUB adjusts total migrants to reflect the fact that some percentage of migrants are under age X at the time of the census and may not be tabulated in census report. If the user decides not to estimate this omitted number of migrants, the adjustment is based on the migration reference period, X, the total number of internal migrants by sex based on the census data, an assumed sex ratio of missing child migrants of 1.0, and estimates of both sexes percent missing based on models of migration rate age patterns and estimated populations by age and sex.

MIGSUB: Output One of the output pages – PROJ-FEMALE. Based on internal migration pattern in total migrants, assumed population growth, and assumed change in migration rates, the workbook calculates projected number of internal migrants by sex for output years specified by the user.

MIGSUB: Output One of the output pages – PROJ-FEMALE. Net international migration, also assumed by the user, is distributed using the pattern of internal in-migration. We also get the total net migration for each area.

Tools for Cohort-Component Projection 5/22/2018 Tools for Cohort-Component Projection

From the Overview Here we are looking at tools for doing cohort-component projections and ensuring that they are consistent at different levels of geography. From data to preliminary subnational area estimates of population by age and sex Consistent assumptions about future levels Subarea cohort-component projections Combination of subarea projections, or proportional adjustment to match a control projection Non-cohort-component projections for lower-level subareas consistent with higher-level cohort-component projections ProjTFR32 DAPPS/ RUP Proje032 Borrowing a slide from the overview, this section will focus on: Production of subarea cohort-component projections The combination of subarea projections , or forced consistency with a control projection RUPAGG CTBL32 MIGSUB SALGST RUPSubAdj CTBL32 42

Cohort-Component Projection Methods and Tools 5/22/2018 Cohort-Component Projection Methods and Tools Cohort-component projections at national or subnational levels (DAPPS/RUP) Aggregation or disaggregation of cohort-component projections (RUPAGG) Adjustment of preliminary subnational cohort-component projections to agree with national cohort-component projection (RupSubAdj)

Cohort-Component Projection Methods (Aggregation) 5/22/2018 Cohort-Component Projection Methods (Aggregation) (DAPPS/ RUP) (DAPPS/ RUP) (DAPPS/ RUP) The simplest approach to ensuring consistency is to use the “bottom-up” approach. This means doing projections at a lower geographical level (Region in this example) and aggregating the results to the next level (national in this example). The RUP program can be used for each Region projection and RUPAGG is then used to sum up the results to the national level.

Cohort-Component Projection Methods (RUPAGG Aggregation) 5/22/2018 Cohort-Component Projection Methods (RUPAGG Aggregation) TITL 2 Aggregation of RUP files for Regions 1, 2, and 3 of the Republic of Demographica BASE 2000 PROJ 2025 N 17 TOT CODE 3 *********|*********|*********| INPF 1 Region1.IO1 Region2.IO1 Region3.IO1 OUTP 1 2025 OMX 2025 END   Here is a sample RUPAGG input file. Its purpose is to point the program to the intermediate files to aggregate (as well as provide some information to label the output and direct what outputs are desired).

Cohort-Component Projection Methods (Disaggregation) 5/22/2018 Cohort-Component Projection Methods (Disaggregation) (DAPPS/ RUP) (DAPPS/ RUP) RUPAGG can also be used to do disaggregations. In this case we subtract projections for Regions 1 and 2 from a national projection to get a projection of Region 3 as a residual. (DAPPS/ RUP)

Cohort-Component Projection Methods (RUPAGG Disaggregation) 5/22/2018 Cohort-Component Projection Methods (RUPAGG Disaggregation) TITL 1 Residual projection of Demographica's Region 3 BASE 2000 PROJ 2025 N 17 TOT CODE 3 *********|*********|*********| INPF 1 Country.IO1 INPF -1 Region1.IO1 Region2.IO1 OUTP 1 2025 OMX 2025 END   Note the -1 for Region1 and Region2 indicating these should be subtracted from the national totals in Country.io1. For the disaggregation, we simply indicate which projections are to be subtracted in the disaggregation process.

Adjustment of Subnational Projections to Total 5/22/2018 Adjustment of Subnational Projections to Total National-level cohort-component projection (DAPPS/RUP) Final subnational cohort-component projections (RUPAGG) Toolkit: RUPSubAdj Preliminary subnational cohort-component projections (DAPPS/RUP) Another way to implement the “top-down” approach is to do preliminary projections of the subareas as well as the total (national). We then adjust the subnational projections to be consistent with the national projection. The RUPSubAdj workbook adjusts the population, deaths, and international and internal migrants by sex and single year of age, and births by single age of mother to agree with the corresponding values for the national projection. Since each year is adjusted, the base year data do not necessarily have to be consistent between the national and subarea values.

RupSubAdj Control Sheet 5/22/2018 RupSubAdj Control Sheet The Control sheet of the RUPSubAdj requires three inputs (assisted by the numbered buttons): The location of where to store the adjusted subnational projections (they will all be stored in the same location) The national projection RUP input file (name and file location) The preliminary subnational RUP input files (names and locations) Pressing button 4 will do the adjustment, create RUPAGG input and IO1 files with the adjusted data, and run RUPAGG to create all the output needed by RUPEX (the RUP/RUPAGG Excel interface) to display the results.

RupSubAdj Population Adjustment Factors 5/22/2018 RupSubAdj Population Adjustment Factors The other sheets in the workbook display the adjustment factors applied to each subarea’s population, deaths, births, and migrants, by sex and single years of age. All of the adjustments (except for migrants) are simply ratios of the independent national projection value to the sum of the preliminary subnational projection values.

RupSubAdj Population and Vital Events Adjustment Factors 5/22/2018 RupSubAdj Population and Vital Events Adjustment Factors The adjustment factor, fV, for variable V (population, deaths, or births) is computed as:  fV y,s,a = NV(y,s,a)/ r V(r,y,s,a) if > 0  and the adjusted value of V (called V’) is then: V’(r,y,s,a) = V(r,y,s,a) * fV(y,s,a) where: NV=national value for variable V r= region or subarea s=sex y=year a=age

RupSubAdj Migration Adjustment Factors 5/22/2018 RupSubAdj Migration Adjustment Factors The adjustment factor, fM, for variable M (internal or international migrants) is computed as:  fM y,s,a = r M(r,y,s,a)−NM(y,s,a) / r P(r,y,s,a)   And the adjusted value of M (called M’) is then: M’(r,y,s,a) = M(r,y,s,a) - fM(y,s,a) * P(r,y,s,a) The adjustment for migrants is different because it needs to deal with positive, negative, and zero values, and the desired values for internal migration are all zeroes (by sex and age). The procedure for migrants essentially assumes that each sex-age-specific migration rate by subarea is off by a constant value. The result is a slight shifting in the same direction of the net number of migrants for a given age-sex group for all subareas. where: P(r,y,s,a) = value of population variable P for subnational area r Other variables are as previously defined

RupSubAdj Migration Adjustment Factors 5/22/2018 RupSubAdj Migration Adjustment Factors The factors shown are essentially the change in the net migration rate for each subarea for the particular age-sex group. We can see here that the values are close to zero (rounding to less that one per thousand) for the first few years. The values increase to about two per thousand for some age groups by 2025.

Cohort-Component Projection Summary 5/22/2018 Cohort-Component Projection Summary Cohort-component projections at national or subnational levels (DAPPS/RUP) Aggregation or disaggregation of cohort-component projections (RUPAGG) allows bottom-up or top-down consistent projections RupSubAdj is an alternative top-down approach that adjusts preliminary subnational cohort-component projections to agree with national cohort-component projection

Review The Census Bureau’s Subnational Projections Toolkit, includes: RUP, RUPAGG, the RUPEX interface, Excel workbooks, Method descriptions and the User’s Guide, can be downloaded at no cost from www.census.gov/population/international/software/sptoolkit Your take-away from this presentation should be, First, that the Toolkit includes tools designed for use in making bottom-up and top-down cohort-component projections as well as non-cohort-component population projections, and Second, that the Toolkit is available to you at no cost from the Census Bureau’s website 55