## Abstract

Using data gathered by the author in two communities in Southwestern Colombia, this paper tests a model of migration which incorporates relative deprivation as one of many possible reasons to migrate. The study finds that the product of relative deprivation and family income not only has a sensible interpretation; it is a better predictor of migration than its two component variables alone. Results also show that families with the highest propensities to migrate are those with the most to gain in terms of being better able to reduce relative deprivation through successful migration. These families, however, are neither at the bottom nor at the top of the income distribution in their communities. The study also finds that those most likely to migrate to the USA conform most closely to the immigration policies of the USA.

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## Notes

- 1.
Most families living in El Prado owned their home since this was a government-sponsored housing project in 1962 that gave families that qualified a chance to own their own home.

- 2.
Since the best-fitting estimates of the Hickman model revealed that the p-value of the null hypothesis that (rho)

*ρ*= 0 was only 11.88%, I decided to use the Hickman adjusted estimates of the individual’s contribution for those that had migrated anyway and thus be more cautious. The Hickman estimates eliminated some high contributing individuals. For those that did not migrate (1,366 individuals), the actual monthly mean contribution to family income was a penny away from their mean contribution as estimated by the Hickman selection bias model. Those with negative estimated contributions were of course set to zero. - 3.
Assuming the more tractable logit distribution for the error term and denoting as L its cumulative density function leads to the classical definition of the probability of migrating defined as:

$$P\left( {y_1 = {1 \mathord{\left/ {\vphantom {1 {x_1 }}} \right. \kern-\nulldelimiterspace} {x_1 }}} \right) = P\left( {\varepsilon _i \leqslant x_i \beta } \right) = \Lambda \left( {\varepsilon _i = x_i \beta } \right) = \frac{{\exp \left( {\varepsilon _i } \right)}}{{1 + \exp \left( {\varepsilon _i } \right)}} = \frac{{\exp \left( {x_i \beta } \right)}}{{1 + \exp \left( {x_i \beta } \right)}}$$ - 4.
Stark and Taylor (1991, p. 1175, footnote 6 also noted in their work that the costs of migration could represent an obstacle to migration especially for the poorest families in the community. They thus reasoned that relative deprivation may not have a positive effect on the propensity to migrate but only for these families.

- 5.
For the purposes of this study, a migrant was someone that had migrated within the previous 18 months. Migrants within Colombia were only those that migrated to another State (Departamento).

- 6.
A likelihood ratio test was used to test the significance of each coefficient in explaining migration as a whole. The coefficients for “age” and “agesq” were tested together as a set. All tests rejected the null hypothesis of no significance at better than 99.9% probability. The variable “state” did so at better than 98.5% and the variable “rdxfinc” at better than 99%.

- 7.
Given that the factor change in the odds ratio as a result of an d change in the variable x

_{k}is equal to$$\frac{{\Omega \left( {{{x\beta } \mathord{\left/ {\vphantom {{x\beta } {x_{k'} = x_k + \delta }}} \right. \kern-\nulldelimiterspace} {x_{k'} = x_k + \delta }}} \right)}}{{\Omega \left( {x\beta } \right)}} = \frac{{\exp \left( {const} \right)\exp \left( {x_1 \beta _1 } \right) \ldots \exp \left( {x_k \beta _k } \right)\exp \left( {\delta \beta _k } \right) \ldots \exp \left( {x_7 \beta _7 } \right)}}{{\exp \left( {const} \right)\exp \left( {x_1 \beta _1 } \right) \ldots \exp \left( {x_k \beta _k } \right) \ldots \exp \left( {x_7 \beta _7 } \right)}} = \exp \left( {\delta \beta _k } \right)$$. The change in the factor odds as both age and agesq change simultaneously should be calculated as follows:

$$\frac{{\Omega \left[ {{{x\beta } \mathord{\left/ {\vphantom {{x\beta } {\left( {\operatorname{age} + \delta } \right),\left( {\operatorname{agesq} + \delta ^2 + 2*\operatorname{age} *\delta } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\operatorname{age} + \delta } \right),\left( {\operatorname{agesq} + \delta ^2 + 2*\operatorname{age} *\delta } \right)}}} \right]}}{{\Omega \left[ {{{x\beta } \mathord{\left/ {\vphantom {{x\beta } {\left( {\operatorname{age} ,\,\operatorname{agesq} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\operatorname{age} ,\,\operatorname{agesq} } \right)}}} \right]}} = \exp \left( {\delta \beta _{{\text{age}}} } \right)\exp \left[ {\left( {\delta ^2 + 2*\operatorname{age} *\delta } \right)\beta _{{\text{agesq}}} } \right]$$. The resulting factor change in the odds is a function of the person’s age, as it should be.

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## Acknowledgements

The author wishes to acknowledge the cooperation of the economics department at Universidad Javeriana in Cali, Colombia, for their support in the survey phase of this study. The author also wishes to thank Dr. James Hughes and Dr. Alan Levy, both of Slippery Rock University, for their editorial suggestions. The usual caveats remain regarding errors.

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Valencia, J.M. Migration and its Determinants: A Study of Two Communities in Colombia.
*Atl Econ J* **36, **247–260 (2008). https://doi.org/10.1007/s11293-008-9109-y

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### Keywords

- Migration
- Relative deprivation
- Colombian migration
- Latin American studies

### JEL Classification

- J21
- O10
- O50
- O15
- F22
- R23