| UN DESA stock data and associated estimates |
| --- |
| The `stock_data.nc` file contains the various UN stock data estimates. |
| Stock data is provided by the [UN DESA](https://www.un.org/development/desa/pd/content/international-migrant-stock), |
| and give the foreign-born stocks at midyear. We have two revisions of the stock data, one from 2020, one from 2024. |
| We use the 2024 values where available, and fill NaNs with the 2020 value. |
| Some obvious mistakes are manually corrected. We interpolate missing values using neighbourhood correlation, |
| and then scale the estimates at mid-year to give a value at the start of each year. |
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| The data contains the following data variables: |
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| - `2020 Revision`: original data from the 2020 Revision, mid-year estimates |
| - `2025 Revision`: original data from the 2025 Revision, mid-year estimates |
| - `Combined`: Union of the two, with mistakes corrected |
| - `Mask`: Mask for `NaN` values |
| - `Interpolated`: interpolated stock values |
| - `Start of year estimate`: start of year estimates, latest version |
| - `Error`: errors on stock data |
| - `Weight`: weights on the stocks |
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| Details on each are given below: |
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| ## `2020 Revision`/`2025 Revision` |
| These are all the original estimates. |
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| ## `Combined` |
| The union of the 2025 and 2020 estimates, with the following mistakes corrected: |
| ```python |
| # Canada |
| stock_data["Combined"].loc[{"Origin ISO": "SYC", "Destination ISO": "CAN", "Year": [1990, 1995]}] = [2248., 1160.] |
| stock_data["Combined"].loc[{"Origin ISO": "CUW", "Destination ISO": "CAN", "Year": 2010}] = 399 |
| stock_data["Combined"].loc[{"Origin ISO": "BES", "Destination ISO": "CAN", "Year": [2010, 2015, 2020]}] = [40.0, 40.0, 44.0] |
| stock_data["Combined"].loc[{"Origin ISO": "SXM", "Destination ISO": "CAN", "Year": 2010}] = 105.0 |
| |
| # Germany in US |
| stock_data['Combined'].loc[{"Origin ISO": "DEU", "Destination ISO": "USA", "Year": 1995}] = 1335539 |
| # France |
| stock_data["Combined"].loc[{"Origin ISO": "AIA", "Destination ISO": "FRA", "Year": 2005}] = 12 |
| |
| # Vietnamese in Malaysia |
| stock_data["Combined"].loc[{"Origin ISO": "VNM", "Destination ISO": "MYS", "Year": range(1990, 2023, 5)}] = stock_data["2020 Revision"].sel({"Origin ISO": "VNM", "Destination ISO": "MYS", "Year": range(1990, 2023, 5)}).copy() |
| stock_data["Combined"].loc[{"Origin ISO": "VNM", "Destination ISO": "MYS", "Year": 2024}] = 1.09e+5 |
| |
| # Turkmenistan in Greece |
| stock_data["Combined"].loc[{"Origin ISO": "TKM", "Destination ISO": "GRC", "Year": [1990, 1995]}] = [96., 82.] |
| |
| # Bangladeshis in Egypt |
| stock_data["Combined"].loc[{"Origin ISO": "BGD", "Destination ISO": "EGY", "Year": [2010, 2015, 2020, 2024]}] = [557., 1015., 1173., 762.] |
| |
| # Russians in Serbia |
| stock_data["Combined"].loc[{"Origin ISO": "RUS", "Destination ISO": "SRB", "Year": 1995}] = 810 |
| |
| # Russians in Egypt |
| stock_data["Combined"].loc[{"Origin ISO": "RUS", "Destination ISO": "EGY", "Year": 2015}] = 23462 |
| |
| # Ukrainians in Egypt: mask 2015 value |
| stock_data["Combined"].loc[{"Origin ISO": "UKR", "Destination ISO": "EGY", "Year": 2015}] = 2349 |
| |
| # Lebanese in Egypt |
| stock_data["Combined"].loc[{"Origin ISO": "LBN", "Destination ISO": "EGY", "Year": 2015}] = 2045 |
| |
| # North Macedonia in Hungary |
| stock_data["Combined"].loc[{"Origin ISO": "MKD", "Destination ISO": "HUN", "Year": [1990, 1995]}] = [460, 230] |
| |
| # Comoros in South Africa |
| stock_data["Combined"].loc[{"Origin ISO": "COM", "Destination ISO": "ZAF", "Year": 2005}] = 71 |
| |
| # Aruba in France |
| stock_data["Combined"].loc[{"Origin ISO": "ABW", "Destination ISO": "FRA", "Year": 2005}] = 7 |
| ``` |
| We also require the stocks to be at least as large as the UNHCR refugee data. |
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| ## `Mask` |
| We calcualte a mask of missing (NaN) values. The mask excludes these points from the loss function |
| used to train the neural network. |
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| ## `Interpolated` |
| We extrapolate and interpolate missing values to obtain initial values for stocks, where missing. |
| This is necessary because the migrant stocks are a training covariate, and though they are recursively |
| estimated through the neural network, the initial value (at 1990) is needed to start the process. |
| The interpolation is performed using a weighted average growth rate: |
| let $S_{ij}(t)$ be a stock time series with missing data. We then consider the correlation |
| $$C_{jk} = \mathrm{corr}(S_{ij}, S_{ik})$$ and the distance coefficient |
| $$\rho_{jk} = \exp(-d_{jk})$$ and calculate the weighted growth rate using the weight |
| $$w_{jk} = C_{jk} \times \rho_{jk} / \sum_k \rho_{jk}.$$ Then, given a matrix of stock growth values, |
| $$g_{ij}(t) = S_{ij}(t) / S_{ij}(t-1) - 1,$$ the average growth rate is simply |
| $$\bar{g}_{ij}(t) = \dfrac{\sum_k g_{ik} w_{jk}}{\sum_k w_{jk}}.$$ |
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| The diagonal is filled with estimates of the native-born population, given by $$S_{ii} = P_i - \sum_{j \neq i} S_{ji}.$$ |
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| ## `Start of year estimate` |
| Since DESA provides mid-year estimates, we need to scale our estimates to the start of the year. We do this using iterative |
| proportional fitting (IPF). We do so by subtracting half the total births from that year, and then dividing by the half-annual |
| death rate $1-\gamma_{1/2} = \sqrt{1-\gamma}$. |
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| ## `Error` and `Weights` |
| Weights on the stock targets are calculated by scaling successive stock matrices to the midpoints of their marginals, |
| after accounting for demographic change (births and deaths). |
| We can scale two matrices to their midpoints or their endpoints. |
| This gives between 2 and 4 new estimates for each value $S_{ij}(t)$, from which we can calculate a weight. |
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| The weights and errors are based on the start-of-year estimates. |
| Weights are given by the negative exponential of the normalised relative error $$\dfrac{\langle \hat{S}_k - S \rangle_k}{S},$$ |
| where $k$ indexes the different stock matrix estimates we obtain from IPF. |
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| The weight is clipped to $[0.5, 2]$. |
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| ## Stock differences |
| We are actually training the neural network to match stock *differences*, not absolute values. |
| We actually want to learn the stock differences, not the absolute values. |
| As before, we then set the weights on the differences to the negative exponential of the normalised relative error |
| $$\dfrac{\sqrt{\sigma_1^2 + \sigma_2^2}}{\max(\vert \Delta S\vert, 1)}.$$ |
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