Migrants Networks:An Estimable Model fo Illegal Mexican Immigration. Aldo Colussi

Transcription

1 Migrants Networks:An Estimable Model fo Illegal Mexican Immigration Aldo Colussi 23

2 This paper analyzes the network effect of the Mexican immigrants in the U.S. The U.S. wage offer probability depends on the number of Mexican immigrants in the U.S. The author calibrates the dynamic model with migration and return migraction. The parameters of the model are calibrated to the time series of the immigration rate from 1965 when there was very small number of immigrants.

3 Model Network Effect An individual with age a receives a job offer from Mexico with probability 1, and from the U.S. with the probability ( ) p(a) = p x(a), Nt 1 US where x(a): years of experience in the U.S. Nt 1 US : Number of total people in the U.S. from the individual s village: Network Effect.

4 Wage Offer The wage offer at location l {U.S., Mexico}: w l it(a) = r l t s l i (a it ) rt l : rental price of skill si l(a it): skill level of individual i at time t. ( ) si l (a it ) = exp α l + α1a l it + α2a l it 2 + ɛ l i ɛ l i : idiosyncratic wage shock.

5 Per Period Utility u(a) = d(a)u us (a) + [1 d(a)] u mx (a) d(a) [1 d(a 1)] C C: border crossing cost. u mx (a) = w mx u us (a) = w us φ (z(a), a) φ(): psychic cost of being in the U.S. z(a): tenure in the U.S. (number of periods continuously in the U.S.)

6 Dynamic Choice of Individuals State Space: Ω t (a) = {r us t, r mx t Value of being in the U.S. V us t, Nt us, x(a), z(a), ρ t, ɛ us (a), ɛ mx (a)} (Ω t (a), a) = wt us (a)φ(a) +δe t [ Max { V us t+1(a + 1), V mx t+1(a + 1) } Ω t (a), d(a) = 1 ] Value of being in Mexico V mx t (Ω t (a), a) = wt mx (a)φ(a) [ +δe t pt+1 (a + 1)Max { Vt+1(a us + 1) C, Vt+1(a mx + 1) } + (1 p t+1 (a + 1)) Vt+1(a mx + 1) Ω t (a), d(a) = 1 ]

7 If the immigrant is in the U.S., it automatically receives an offer from both U.S. and Mexico. If the individual is in Mexico, it only receives the U.S. offer with probability p(a), which is a function of the network effect. Rental Price of Skills U.S. The rental price of skill si us (a it ) is exogenous. logr us t = µ + θlogrt 1 us + ξt us

8 Mexico The rental price of skill from the village in Mexico comes from the Cobb-Douglass production function. Y t = γexp (λρ t ) (St mx ) α ρ t : period t rainfall : Aggregate stock of skill in Mexico S mx t S mx t = 64 a=15 i s mx i (a it ) (1 d i (a it )) rental rate r mx t = αγexp (λρ t ) (St mx ) α 1

9 Equilibrium Rental rate rt mx satisfies labor supply equals labor demand. Labor supply in Mexican village S mx t = 64 a=15 i s mx i (a it ) (1 d i (a it )) where d i (a it ) satisfies individual optimal choice Labor demand in Mexican village r mx t = αγexp (λρ t ) (St mx ) α 1 Assume that the equilibrium rantal rate follows r mx t r Nt us N t = logit ( β 11 r us t = logit ( β 21 r us t + β 12 ρ t + β 13 rt 1 mx + β 14 Nt 1 us ) + β 22 ρ t + β 23 rt 1 mx + β 24 Nt 1 us ) Then, compute the coefficient that approximately satisfy the equilibrium conditions.

10 Data Mexican Migration Project Data 1987-, conducts interviews in a number of villages in Mexico, on demographics, retrospective migration and occupation histories. Sample: male household heads at least 15 years of age at the time of survey. villages: Primarily agricultural with population less than 3, in 195.

11 Calibration Parameters are chosen to match the percentage of migrants, wages, by year, age of individuals in one of the three villages. Earnings function: s us i s mx i Psychic cost: Type 1 Type 2 (a it ) = exp ( a it +.ait 2 + ɛ us ) i ) (a it ) = exp ( a it +.a 2 it + ɛ mx i φ 1 (z(a), a) =.5z(a) +.1a φ 2 (z(a), a) = 2.1z(a) +.1a Standard error of idiosyncratic wage shocks. σ us =.65, σ mx =.5

12 Production function Y t = 2.5exp (.3ρ t ) (S mx t ).9 Border crossing cost U.S. skill rental price C = 1. logr us t = logr us t 1 + ξ us t, σ ξ =.68 Type 1 proportion:.4

13 Model Fit The model fits the percentage of migrants in the U.S. from 1965, by year and by age reasonably well. It also roughly matches the wage offer and the tenure in the U.S. Policy: Eliminate Network Effect Without network effect, the rate of increase in immigration decreases over time, in contrast to the results with network effect, where there is an initial increase in the rate. The steady state with network effect exhibits more volatility. Policy: Increase Border Cost Does not change the steady state ratio of imigrants. Immigrants increase the length of stay in the U.S.

14 Policy: 1 Percent Wage Reduction Reduces the steady state number of immigrants by 4%

15 Figure 1: Rain Fall (Annual Precipitations in mm) Village 1 Village 2 Village 3 Figure 2: Percentage of Migrants in the U.S. by Year Village 1 Village 2 Village 3

16 Figure 3: Percentage of Migrants in the U.S. by Year Village 1 Village 2 Village 3 Figure 4: Estimated Year Dummies Real U.S. Dollars

17 Figure 5: 1988 MX Peso - US Dollar Real Exchange Rate Real Exchange Rate Smoothed Exchange Rate Figure 6: Village 1 - Percentage of Migrants in the U.S. by Year Simulation Data

18 Figure 7: Village 1 - Percentage of Migrants in the U.S. by Age Simulation Data Figure 8: Mean U.S. Accepted Wages by Year Real MX Pesos Simulation Data

19 Figure 9: Village 1 - Mean U.S. Tenure by Year Simulation Data Figure 1: Village 1 - Network Effect.35 Percentage of Migrants in the U.S Year No Network Network

20 Figure 11: Network Effect.35.3 Percentage of Migrants in the U.S Netw ork NoNetw ork Figure 12: Cost of Crossing the Border 1 Year of U.S. Wages since Percentage of Migrants in the U.S Netw ork Netw ork & Cost Increase No Netw ork No Netw ork & Cost Increase

21 Figure 13: Cost of Crossing the Border 1 Year of U.S. wages since Average U.S. Tenure Netw ork Netw ork & Cost Increase No Netw ork No Netw ork & Cost Increase Figure 14: Cost of Crossing the Border 1 Year of U.S. Wages since Percentage of Migrants in the U.S Network Network & Cost Increase No Network No Network & Cost Increase

22 Figure 19: Cost of Crossing the Border 2.5 Years of U.S. Wages since Average U.S. Tenure Netw ork Netw ork & Cost Increase NoNetw ork NoNetw ork & Cost Increase Figure 2: 1% Reduction in U.S. Wages since Percentage of Migrants in the U.S Network Network & Wage Reduction No Network No Network & Wage Reduction