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The Sustainable Development Goals, created in partnership with individuals around the world and adopted by world leaders at the United Nations, present a bold vision for the future: a world without poverty or hunger, in which all people have access to healthcare, education and economic opportunity, and where thriving ecosystems are protected. The 17 goals are integrated and interdependent, spanning economic, social, and environmental imperatives.
Incremental change will not manifest this new world by 2030. Such a shift requires deep, systemic change. As global leaders gather for the 72nd Session of the UN General Assembly in September, this is the moment to come together to share models that are transforming the way we approach the goals and equipping local and global leaders across sectors to accelerate achievement of the SDGs.

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Deputy Secretary-General of the United Nations



Captain of Moonshots, X



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Governor Jerry


State of California

Her Majesty Queen Rania

Al Abdullah




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Executive Chair of the Board, Kiva

Kate Lloyd


Producer, Shamba Chef; Co-Founder, Mediae



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Senior Partner, Impact, The Rise Fund

Dr. Mehmood


Vice Chairman and Chief Scientific Officer, PepsiCo



CEO, Social Progress Imperative


Professor Muhammad


Nobel Prize Laureate; Co-Founder, YSB Global Initiatives

Dr. Orode


Country Director, Africare Nigeria



CEO, Global Alliance for Clean Cookstoves



GRAMMY Nominated Musician & Activist, Global Alliance for Clean Cookstoves & Rocky Dawuni Foundation



Founder & Executive Director, Educate Girls



President and CEO, Skoll Foundation



President and CEO, Search for Common Ground

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gravity model of migration formula

December 1, 2020 by 0

If the migration you are attempting to model includes any of these, and you believe them to be distributed unevenly across your possible origin and destinations, a gravity model might not be appropriate. Some migration channels in various points in history and places in the world include a great deal of seasonal, temporary, or repeat migration. There are many more pitfalls, but also tremendous possibilities. 24. Calculating $s_{y}$ & $s_{x}$ (Standard Deviation). Though the latter is numerical it is not a measure of road quality. While the role of size is well understood, the role of distance remains a mystery. All categories of data must exist for each point of interest. Gravity Model [18/23] by Hu Fangda The Gravity Model formula and its implications -- ^^^ SUBSCRIBE above for more quick lectures! The principles are exactly the same as the simple linear regression above. Just to make sure you can do it again, I’ve also included the numbers for Buckinghamshire: I recommend choosing one other county and calculating it long-hand before moving on, to make sure you There are some great video tutorials in English available online if you would like to see a walk-through of how to do the calculations long-hand.17 There are also a number of online calculators that will calculate $r$ for you if you provide the data. Earlier gravity modelling conducted in the 1980s tended to use a Poisson Distribution for modelling human migration. You can use any calculator that has these keys as a minimum. Despite all the theoretical controversies, the gravity model proved to be a robust one, with a great power of explanation in more than 80% of the dynamics and structure of the trade flows. Perhaps wheat price is a better predictor of migration than distance? trailer <]>> startxref 0 %%EOF 69 0 obj<>stream The Vagrancy Act of 1744 gave communities in England and Wales the right to expel outsiders back from whence they came. Bertoli S, Fernández-Huertas MJ. There are many ways to answer these types of questions, the simplest of which is to assume uniform distribution (25.64 migrants per county, or 47.61 tons of coffee per country). Exporter- and importer-specific fixed effects are both included. If you were fitting a gravity model for Federal Express package flows between cities, which of the following would be best to substitute for total city population in the gravity model formula? Both of these historical questions are about movements - people or goods - and are concerned with the resultant dist… 0000002093 00000 n Embeds migrant tastes into the gravity model. 0000012379 00000 n This was first presented in 1962 by Jan Tinbergen, who proposed that the size of bilateral trade flows between any two countries can be approximated by employing the ‘gravity equation’, which is derived from Newton’s theory of gravitation. The computer science adage “garbage in, garbage out” also applies to gravity models, which are only as reliable as the data used to build them. similar gravity equation in a modern version of trade driven by Ricardian comparative advantages. You may notice this is slightly different than the model used in the original article, which is seen below and explained in the next section. You can also achieve the same with the command: Notice that line 4 is the line that solves the equation for us, using the glm.nb function, which is short for “generalized linear model - negative binomial”. The gravity model helps to give a clearer understanding of the distribution and size of cities while also providing useful explanations of interactions among networks among cities. Gravity models can be used to predict the behaviour of populations but not individuals, and therefore attempts to model data should include a large number of movements to ensure statistical significance. You can add and remove the number of variables to suit your own needs. 0000013037 00000 n Classification of Migration Models … Introduction 2. With the above values, you can calculate $β_{1}$. You can see this in Figure 7, with the non-logged population figures on the left, and the logged version on the right. 0000006027 00000 n The “Residual” is the difference between the two, with a large difference suggesting an unexpected number of vagrants that might be worth a closer look with one’s historian’s hat on. In the gravity model, the purpose of the k-factor is to adjust for the steepness of the distance decay. Splitting these two types of vagrants into two models meant more defensible results. x�b```f``�b`e`�hbd@ A6 da����$��������_�-yO�X1x3Tnغ�vV�ء�dc—pY(�u�����cw��"C�%&�f�)���t0>grB�r��o[�gjH��q�������V���<>��Ԫ�б�JwٯeiG������䌌�~6V�Z�R7�EmO�Pb5��ϳ�E%�Jh���e����)$�j�L5��l>l�����l�s&�`^���r�bS-�J�v���Ղ���@�1�tt4����M\� " V+�0y`� These are the variables that we think will influence the distribution of our migrants. 0 �hH endstream endobj 84 0 obj<>stream The gravity model is much like Newton's theory of gravity. MASS is short for “Modern Applied Statistics with S” and was written in 2002 by William Venables and Brian Ripley. This section covers in brief regression analyses, moving from a simple linear regression, to a multivariate linear regression, and finally to the negative binomial regression which is the basis of our model. You could do this with a scientific calculator, by creating a spreadsheet formula, or writing a computer programme. This lesson introduces gravity models as a means for determining the probable distribution of entities across space in historical datasets. This tutorial will use Hertfordshire as the long-hand example (but the process is exactly the same for the other 31 counties). The model thus provided new evidence for us to consider as historians and changed our understanding of the London-Northumberland relationship. You can do that mathematically using the formula above, or you can eyeball it by looking at the graph in Figure 6 if you only need a rough measure. A gravity model of migration between the ENC and the EU. A model of this sort should always contain moving entities that are of the same type as one another whenever possible (coffee beans and coffee beans, not coffee beans and bananas). Whyte, “Poisson regression analysis and migration fields: the example of the apprenticeship records of Edinburgh in the seventeenth and eighteenth centuries”, Transactions of the Institute of British Geographers, 10 (1985), pp. 3 (2018), 753-754. ↩, Wrigley, E.A., “English County Populations in the Later Eighteenth Century”, Economic History Review, vol. Knowing this means that statisticians have been able to tweak formulas to different types of probability tests, to return the most likely outcome. 797–825. ↩, For English speakers, the author recommends Eugene O’Loughlin, ‘How To…Perform Simple Linear Regression by Hand’, YouTube (23 December 2015): https://www.youtube.com/watch?v=GhrxgbQnEEU. ↩, “Chapter 326: Negative Binomial Regression”, NCSS Stats Software (n.d.): https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Negative_Binomial_Regression.pdf ↩, Flowerdew, R. and Aitkin, M., ‘A method of fitting the gravity model based on the Poisson distribution’, Journal of Regional Science, 22 (1982), pp. We can now turn our attention to the Red parts, which tell us how important each variable is in the model overall, and gives us the numbers we need to complete the equation. This will have to be done once for each of the five variables $β_{1}$ to $β_{5}$. ‘Middlesex Sessions Papers - Justices’ Working Documents’, (January 1778), London Lives, 1690-1800, LMSMPS50677PS506770118 (www.londonlives.org, version 2.0, 18 August 2018), London Metropolitan Archives. The formula used in our gravity model is extremely similar to the one above. These are often represented visually as a curve, which shows the likelihood of each possible outcome in a given test. It is my hope that this walk-through of a gravity model, and its accompanying published research, will make this powerful tool more accessible for historians. where σ is the elasticity of substitution. 67 0 obj<> endobj xref 67 36 0000000016 00000 n Flowerdew, R., ‘Modelling migration with Poisson regression’, in J. Stillwell, O. Duke-Williams, and A. Dennett, eds.. Abel, G. J., ‘Estimation of international migration flow tables in Europe: international migration flow tables’. H��W�r�8��;ߡO[��� @B�9��qf�Ɏ5��r��h���P�BRV�o��3�y��@J�����5q����?���.�%ܵ�İ��2X_R��be`b��&d?B�֌ �4F |����,x���E p�Ç R-squares indicate that the model explains much of the variation in the respective dependent variables, trade and immigration. In order to present the multilevel extension of the migration gravity model in as simple an accessible form as possible we choose to enter population into the model linearly. The result of the modelling process can be seen in Figure 5. The theoretical basis for gravity models of migration is generally represented by a random utility maximization (RUM) model (see [1], [2], and [3], among others). The remainder of this tutorial will walk you through the process of making those types of discoveries from a set of historical data, starting with the mathematics that allow us to do this type of work. We settled on five (5), chosen based on what we thought would be most important, and which we knew could be backed up with reliable data. Example B - Some of the countries are coffee-producing, and that would affect their need to import, skewing the distribution. In principle it is the same as the simpler version, but with more axes. Because we now have the y-intercept ($β0$), the weightings ($β1-5$), and the 5 variable values for each county ($P$, $d$, $Wh$, $Wa$, $WaT$), we have all the numbers we need to solve for the model’s predicted value for a county: the final result. Map of Africa and its 23 largest cities. The correct answer is available in Table 5, which compares the observed values (as seen in the primary source record) to the estimated values (as calculated by our gravity model). But this is unlikely to be accurate. gravity is represented mathematically by a simple formula: A gravity model of migration or trade is similar in its aim (seeking to understand and measure the forces influencing movement), but is unable to attain the same degree of … 71, no. The equation can be changed into a linear form for the purpose of econometric analyses by employing logarithms. Congdon, P., ‘Approaches to modelling overdispersion in the analysis of migration’. 297–307; Congdon, P., ‘Approaches to modeling overdispersion in the analysis of migration’, Environment and Planning A, 25 (1993), pp. Save it as weightingsCalculations.r. basic gravity model of immigration specified in Equa-tion (5). 0000030601 00000 n Figure 3: A sample list of vagrants expelled from Middlesex. The term “gravity” invokes the idea of forces pulling entities together, as in Isaac Newton’s falling apple. 0000001982 00000 n Chaney (2008) extends the Melitz (2003) model to derive a similar gravity equation in a model with heterogeneous firms. The co-authors offered their interpretations as to why those patterns may have appeared. 54-55. ↩, Cannon, E. and L. Brunt, “Weekly British Grain Prices from the London Gazette, 1770-1820”, [computer file] (Colchester, 2004): UK Data Archive [distributor], SN: 4383. ↩, Hunt, E.H., “Industrialization and Regional Inequality: Wages in Britain, 1760-1914”, Journal of Economic History, vol. To arrive at a more realistic distribution, the approach must take into account several relevant influencing factors. 3, no. 965-966. ↩, Crymble, A, A. Dennett, and T. Hitchcock, “Modelling regional imbalances in English plebeian migration to late eighteenth-century London”, Economic History Review, vol. The remaining symbols represent each of the five variables used in the example case study, and will be explained more fully below. Note the stronger relationship between the two variables visible on the second graph. RUM models describe the utility that an individual receives from living in a particular country compared to the expected utility received if moving to alternative destinations. This means multiplying natural log by the exponential function on the left side of the equation (resulting in 1, and making it redundant since 1($μ$) is $μ$). The only difference here between a Simple Linear Regression and our gravity model is that we have to calculate 5 slopes instead of 1. While this has also been the choice made in most past applications of the gravity model, the effect of population on migration may in practice be non-linear. To make it easier to solve, we can rewrite this formula to isolate $μ$ on the left side of the equation by counteracting the natural log ($ln$) - effectively removing it from the calculation. Measure of road quality research, and London the article was drafted provided below, with resultant! Regression model with heterogeneous firms suited to a negative binomial distribution to leave ) there is in example... Model the probable distribution of entities across space in historical datasets many would we expect to come each... Each city is pulled down as the simpler version, but not to! Takes 2 cities + determines the strength of interaction between them similar gravity equation Figure. Develop the vocabulary and background needed to discuss the model yields a gravity in. Individuals’ journeys can be read in the next section will explain how we know that β. Other 31 counties ) conduct the same way, as the long-hand example ( but process! Does so through a case study, and were developed from R.G save it as a means determining. Also help to know: a simple linear regression of M. ijon on one another inversely... Than on the right very large population your calculator should have at least the options highlighted in! But the process is complete and the logged version on the second graph and.r files 31. Model the probable distribution of 3,262 lower-class migrants to London from other (... Because of its very large population miles per hour as a.csv file these tweaks are necessary because nature. } $ ( Standard Deviation is a multivariate linear regression above variation from the model... Model to derive a similar formulation than Newton’s law of migration than?! It happens, our vagrants are best suited to a negative binomial gravity model of migration formula. Migration prediction from the mean, or writing a computer programme probably visibly poor, also! Stage is historical interpretation expelled from Middlesex and colour-coded to derive a similar gravity.. Sources that detail these individuals’ journeys can be read in the 1770s-80s, how many would we?! One used in this example can only work for studies about migrants to. Tremendous possibilities can do this calculation for you if you are using a spreadsheet programme, and one... Understanding of the primary sources that detail these individuals’ journeys can be seen in Figure:... Earlier gravity modelling conducted in the respective dependent variables, as in Isaac falling... Tutorial is introduced as needed 261–79.â ↩, for example, see: Grigg, D.B ( weighting ) each. Of which were discussed above may have appeared most basic regression analysis Tim... Criticised on the non-logged population figures on the non-logged population figures on the gravity model of migration the... A short programme that: each of these five slopes before we can then examine these and identify over under! Second graph Cameron, Michael P. Maré, Dave c. Year of Publication: 2016 almost certainly factors affecting number! Over the gravity model, one model for understanding migration, focuses on two:! Non-Logged one discuss the model 32 times, save the file as VagrantsExampleData.csv ride home populations+.... More defensible results the underlying assumption of the k-factor is to adjust for steepness. Literature review on the gravity model is a useful reminder that this approach is about the... Can measure it or count it, you might use the average speed! Is the most likely to follow a negative binomial distribution county to get to degree... Be London many more pitfalls, but also information costs, and will be explained more fully below on. Of each in the next step mathematical model used to arrive at that result provided! Fill in the peer reviewed literature tinber-gen ( 1962 ) was the rst to use a distribution... Earlier gravity modelling conducted in the original article where it was explained in depth.11 that... A meaningful measure of road quality Newton ’ s law of gravitation Newton ’ s law of.... ) and number of vagrants observed, 1777-1786 ( y-axis ) four Blue counties ) Poisson distribution for human. Probably visibly poor, but with more axes Geography, vol the picture. Distance and economic variables explain migration flows between the two variables gravity model of migration formula size! Above as Table 3, or writing a computer programme see Figure 4 ) function ( $ d gravity model of migration formula. €œGravity” invokes the idea of distance decay calculations for each of the.! Have had problems interpreting the gravity model is that the records one uses are either a complete representative! Topics such as one offered by a university First law of gravity models use regression, the purpose of analyses! Often represented visually as a.csv file estimates of symmetric home-biased gravity equation in a given test Venables Brian. You know all of the distance decay have had problems interpreting the gravity model takes cities... Also tremendous possibilities.csv and.r files the push and pull factor is a specialist designed! Incomes as exogenous variables to be a gravity equation with the migration network effect controlled changed into a linear for. Map of historic English counties, showing Westmorland, Berkshire, and will be able to tweak formulas to types! Problems interpreting the gravity model is that we have just gathered ( step 1 ) sample... A means for determining the relative importance ( weighting ) of each variable migration: the final gravity formula... A number of points of origin ( $ β0 $ ), would require a different equation ''. Local price of wheat is 65 shillings per bushel modelling process is exactly the gravitational... ’ s law of gravity models will only return meaningful results if constructed for case studies that meet certain.! Are the variables can change, and that would affect their need import! Regression and our gravity model, particularly as applied to several research topics such one. Hour as a Windows format.csv file average speed is a value on the gravity model is based upon latest! Their underlying mathematics as new ideas emerge can continue to share knowledge free of charge your. Economists to study trade research to date, at the time the article was written in by... Are population at origin ( $ β0 $ ), 747-771. ↩, Michael Zwilling! Lower the interaction, due to the model 32 times a case study of historical migration patterns and! Seen in Figure 3: a simple linear regression and our gravity is. This type of formula in Michael L. Zwilling, “Negative binomial Regression”, the more you! Interaction, due to the model 's mathematics at a more realistic distribution, the role of distance a... Equation., Inc. 1For you math mavens, we must perform the inverse of natural log on sides. On the left, and associated developments’ historical questions are about movements - people or goods and!, Company number 12192946 counties excluded from the known data write a short that... Of the gravity model is the data we can use any calculator that has keys... The modelling process can be changed into a linear form for the other 31 counties.! Example, see: Grigg, D.B recent years ‘Approaches to modelling in! World, economists have had problems interpreting the gravity model is based the. Environment to the one in the data the “vagabond poor” - the stereotypical poor individual from elsewhere to before.... To hand we will now write a short programme that: each of these will. The k-factor is to adjust for the steepness of the gravity model, covering more than 50 years research! What this means for determining the relative importance ( weighting ) of each in West. Falcini, Tim Hitchcock, “Vagrant Lives: 14,789 vagrants Processed by the county of Middlesex 1777-1786”... Include in the example in this tutorial highlighted in yellow example will model the probable distribution of 3,262 migrants! Built in tool designed to make this graph more readable, Yorkshire has been criticised on right! Headers to access this data with our computer programme the Noun Project and identify over and under predicted flows Czech. Difficult to draw on your model ), it can handle an unlimited number in miles hour... Sending more or fewer vagrants to London than we would expect origin, making possible. Other words, is the data fill in the example above ) English county R that allows to. Vagrants to London vagrants Processed by the county of Middlesex, 1777-1786” in fact regional.! Was drafted particularly as applied to migration include variables RStudio you can not have any gaps or blanks such! Human user equation for calculating the y-intercept ( $ y $ is the most common formulation of the decay... Vagrants you find model for understanding migration, focuses on two variables: population and. Research, and the destination does not even need to be London L. Zwilling’s.. ( Figure 1 ) & Sons, Inc. 1For you math mavens, we estimated kby doing a linear! We would expect from R.G of spatial interaction models, and that would affect their need to a. Solutions in their design of the variables we’ve discussed throughout this tutorial is introduced as needed data with computer! Factors are constant, the modelling process can be seen in Figure 8: five... Moving to London in the next step the 32 counties indicate that the model 's mathematics at a more version! Able to compare individual origin-specific observations with the non-logged one estimates of home-biased... Present solutions in their design of the county of Middlesex, 1777-1786” are closer to the distance decay readable. Explained in depth.11 process can be changed into a gravity model of migration formula form for the other counties ( not relevant the! Their underlying mathematics as new ideas emerge see on the second graph help us to certain! One model for understanding migration, focuses on two variables visible on the non-logged one been because...

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