# Mij = β0 + β1ln(Pi) + β2ln(Pj) + β3ln(Dij) + β4ln(Xi) + β5ln(Xj) + εij       (4)

**This approach solves two fundamental problems of estimating gravity models using OLS.** First, the loglinearization of the dependent variable truncates the sample in the absence of migrants for certain specific origin‐destination combinations (which is common in large and sparse gross migration matrices or when dividing the sample by subpopulation groups). Second, under heteroskedasticity, the parameters of loglinearized models estimated by OLS lead to biased estimates of the true elasticities.

**The model specification includes the basic gravity variables: population sizes and distance.** The population sizes in origin and host states are expected to have a positive effect. On the one hand, the more people in the source state, the more people are likely to migrate. On the other hand, the larger the population in the host state, the larger the labor market for immigrants. The distance is considered a fundamental explanatory variable that proxies the migration costs. The longer the distance, the lower the incentive to migrate due to higher migration costs. In this study, the distance between a state pair is calculated as the approximate distance in kilometers between the most populated cities of each state. The data come from the “Catalog of Geographic Metadata" of the National Commission for the Knowledge and Use of Biodiversity (CONABIO),<sup>8</sup> which provides information on the latitude and longitude coordinates of each municipality in Mexico.

**Following the literature on spatial determinants of migration flows, economic variables, labor market variables, and environmental variables are used as explanatory variables for describing different features of the origin and destination (push and pull factors).** The most representative and common economic variable used is the per capita gross domestic product (GDP).<sup>9</sup> In terms of labor market variables, both employment rate and informality rate in the origin and destination are included as regressors. Average wages are also included to capture income perspectives in the respective states. Labor market indicators at the state level were calculated using the National Labor Force Survey (ENOE).

**Environmental variables are those that affect the quality of life.** These variables are included to account for the fact that people may decide to move from one state to another not only due to economic reasons. As a proxy of the quality of life in each state, the Deprivation Index, _Índice de Rezago Social_ ,<sup>_10_</sup> which accounts for deprivations in non-monetary dimensions such as education, health care, and basic services (electricity, sewerage, etc.); the incidence of crimes,<sup>11</sup> following Anjomani (2002); and a variable capturing perceived levels of public sector corruption<sup>12</sup> in the states of origin and destination are added as regressors. Variables indicating preschool educational offer in the origin and destination are also added as they might be important push and pull factors, especially for women with children.

**Additionally, the stock of internal immigrants in the destination state at the time of migration is included as a proxy for the availability of social networks.** This variable is expected to have a positive

> 8http://www.conabio.gob.mx/informacion/metadata/gis/muni_2018gw.xml?_httpcache%20=%20yes&_xsl=/db/metadata/xsl/f <u>gdc_html.xsl&_indent%20=%20no</u>

> 9 GDP data come from INEGI (National Accounts).

> 10 The _Índice de Rezago Social_ is calculated by CONEVAL based on the Population and Housing Census.

> 11 The data on the incidence of crimes come from the National Survey on Victimization and Perception of Public Safety (ENVIPE).

> 12 The data on perceived levels of public sector corruption at the state level comes from the National Survey on Governmental Quality and Impact (ENCIG).

21