## _wp0819

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---

### Introduction and context
- NELM (The New Economics of Labor Migration) emphasizes remittances' microeconomic incentives for family members left behind.
- Worldwide remittances have grown to become the second source of development finance after foreign direct investment (World Bank, 2005).
- Potential adverse effects of remittances highlighted:
  - loss of productive labor for the home country;
  - disincentives to work, study, and stay in the home country for family members left behind;
  - reduced incentives for authorities to improve business and human rights environments and address systemic economic and social problems.
- Author’s empirical synopsis for Armenia:
  - Remittances reduce incentives to work.
  - Remittances lead to less spending on education.
  - Remittance-receiving families save more.
  - Increased saving does not lead to more borrowing from the banking system.
- Armenia-specific facts preserved:
  - Armenia’s industrial sector generated 55 percent of total output and employed 39 percent of the labor force in 1987 (USSR Statistical Handbook, 1988).
  - Upper secondary and higher education enrollments were 87 and 19 percent of the relevant population groups in 1989.
  - Armenia gained independence in 1991.
  - Emigration involved educated and skilled individuals; brain drain severe (IWPR, 2000).
  - Remittances in Armenia may have reached 20 percent of GDP in recent years (CBA, 2006).
  - Armenia’s average divorce rate: 14.6 percent for 1989–2005 (UNISEF TransMONEE database).
- Paper structure (as stated): Section II theoretical review; Section III two-period overlapping generations model with altruism and strategic behavior; Section IV data and econometric estimates; Section V conclusions.

### Theoretical considerations and motives to remit
- Two broad motive categories:
  - altruistic motive (migrant’s utility contains utility of household member(s));
  - self-interest motive (self-enforcing contracts or “enlightened selfishness” / “tempered altruism”).
- Interaction notes:
  - Altruism and self-interest can operate simultaneously and may be complementary.
  - Altruism may ensure enforcement of implicit contracts; self-interest can be central to self-enforcing arrangements.
- Divergent comparative statics:
  - Altruism implies more remittances to poorer households.
  - Self-interest motives can imply co-movement of the relative’s income and remittances.
- Specific self-interest drivers enumerated:
  - (i) to allocate risks among remitting and receiving parties;
  - (ii) to receive inheritance/bequest;
  - (iii) to smooth consumption;
  - (iv) to relax capital constraints faced by household members;
  - (v) to accumulate wealth in the home country;
  - (vi) to defray migration costs or repay education expenses;
  - (vii) to pay for social status in the home country;
  - (viii) to pay for services provided by household members (e.g., asset care);
  - (ix) to encourage or discourage migration from the home country.
- Remittance Decay Hypothesis (RDH):
  - The longer migrants live away, the less likely they are to remit.
  - Relationship likely non-linear; time away affects probability of return and remittance/saving behavior of relatives.

### Macro and micro evidence summarized
- Macro findings cited:
  - Chami and others (2005): negative effect of remittances on growth and productivity.
  - Acosta and others (2007): remittances can shrink and reallocate resources away from tradable sector via (i) increasing nontradable prices and (ii) reducing labor supply to labor-intensive nontradable sector.
  - Van Dalen and others (2005): remittances can stimulate further migration among family members left behind.
- Micro findings — mixed evidence on investment vs consumption:
  - Studies reporting positive relationships between remittances and investment/education include Taylor (1992), Glytsos (1993), Brown (1994), Adams (1998), Massey and Parrado (1998), Rozelle and others (1999), McCormick and Wahba (2001), Muent and others (2001), Dustmann and Kirchkamp (2002), Kule and others (2002), Taylor and others (2003), Mesnard (2004), Woodruff and Zenteno (2007), Yang (2007), and Zarate-Hoyos (2004).
  - Studies arguing remittances are absorbed into immediate consumption include Lipton (1980); Reichert (1981); Massey et al. (1987); Grindle (1988); Ahlburg (1991); Russell (1992); Brown and Ahlburg (1999).
- Evidence on education:
  - Yang (2007): remittances increase child schooling and educational expenditures.
  - Lopez Cordoba (2004): municipalities receiving more remittances have greater literacy and higher school attendance among 6–14 year olds.
  - Cox Edwards and Ureta (2003): remittances have large, significant effect on school retention in El Salvador.
  - Hanson and Woodruff (2003): Mexican children in migrant households complete significantly more years of schooling.
  - Contrasting evidence: Acosta (2006) finds positive impact on children’s education in El Salvador vanishes and turns negative after addressing selection; McKenzie (2005) finds migration lowers completed years of education in Mexican households.

### Model contribution and main analytical results
- Model features:
  - Two agents: migrant (m) and representative relative (r); two periods; dynamic strategic interaction modeled.
  - Timing: in each period migrant acts as Stackelberg leader choosing transfers; remittance choice followed by consumption and investment.
  - Motivations in non-cooperative model: pure altruism and self-interest to increase bequest.
  - Cooperative outcome modeled as self-enforcing, total surplus–maximizing arrangement (not Nash bargaining).
- Utility and parameters (preserved notation):
  - Additively separable utilities with weights α (migrant), γ (relative), α−1, γ−1; private sub-utilities use log separability with parameters 0<η<1 and 0<ρ<1.
  - Discount factors m β and r β.
- Budget constraints (period 1 expressions preserved):
  - mmff clwRLw 11111 +=−             (1)
  - hrrhhh XclwiXRLw 1111011 ++=++,      (2)
  - Migrant period-2 budget constraint: mmfhf clwiXLw 22212 +=+       (3)
- Non-cooperative Result 1 (selected expressions preserved):
  - Migrant’s first-stage remittance choice:
    - ⎟⎟⎠⎞⎜⎜⎝⎛++ + − ⎟⎟⎠⎞⎜⎜⎝⎛+ − = i Lw iXLwLw R f hh m f m 2 0111 11 1 αβ α αβ α ;
  - Migrant’s second-stage choices (examples):
    - () () f f m w RLw Rl 1 11 11 1 − − = η ,
    - () () 1111 RLwRc fm − = η ,
  - Migrant period-2 consumption and leisure:
    - hfhm iXLwXc 1212 += η ;
    - () () f hf hm w iXLw Xl 2 12 12 1+ − = η.
- Cooperative Result 2 (selected expressions preserved):
  - Cooperative remittance:
    - ()() rm f hhfrm i Lw iXLwLw R βγαβ αγβγαβγα −++ ⎟⎟⎠⎞⎜⎜⎝⎛ +++ − − − +++ − = 12 111 ˆ 2 011 1 ;
  - Cooperative investment h X1ˆ and leisure expressions available in closed form in source.
- Comparative statics (key preserved statements):
  - Similarities across cooperative and non-cooperative:
    1. Remittances decrease in both the wage and the non-wage income of the relative.
    2. Remittances increase in migrant’s wage in period 1 and decrease in migrant’s wage in period 2.
    3. Investment/bequest, relative’s consumption and leisure increase in remittances.
    4. Investment/bequest increases in migrant’s wage in period 1 and decreases in period 2.
    5. Leisure is a normal good: relative’s labor income reduces leisure; non-labor income increases leisure.
    6. For sufficiently high expected migrant wage in period 2 and sufficiently low rates of interest (condition hf XiLw 0 2 2 >), higher interest rates lead to more remittances and more hours supplied by the relative.
  - Differences across models:
    - Relative’s selfishness γ and discount r β do not affect non-cooperative remittance level but positively affect cooperative remittances.
    - Migrant’s selfishness α negatively affects non-cooperative investment but positively affects cooperative investment.
    - Increases in migrant’s discount rate m β have positive effect on non-cooperative leisure but negative effect on cooperative leisure.
  - Dynamics: if family ties (proxied by (1−α) and (1−γ)) fade with time, both models predict remittances decline; non-cooperative unambiguous decline as (1−α) declines.
- Results comparing cooperative vs non-cooperative (preserved conditions):
  - Result 3 (cooperative remittance exceeds non-cooperative iff):
    - ()()() mr ββγααγ − − + ≤ − 11 .
  - Under m β = r β = β simplified conditions include:
    - Result 3’: 1 > + γ α
  - Qualitative depiction: for sensible parameter values, cooperative solution yields higher remittances and investment/bequest and lower leisure than non-cooperative solution.

### Empirical estimation: Armenian data and stylized facts
- Data:
  - 2004 Integrated Living Standards Measurement Survey (ILSMS); nationally representative: over 28,000 individuals from over 6,800 households.
  - Sample sizes reported for first and second stage: 6,816 observations.
- Remittance prevalence and migration:
  - 23 percent of surveyed households report receiving transfers from abroad.
  - 14 percent report having a migrant abroad.
  - Only 37 percent of all remittances are migration-related (i.e., 63 percent comes from out-of-household sources).
  - Only 62 percent of families with migrant members report receiving remittances (potential underreporting).
- Remittance Decay evidence (time-away patterns and regressions):
  - Propensity maximum at 5 years; amount maximum at 7 years.
  - Regressions (households with migrants; other regressors at mean included in constants):
    - Probability = 0.59 + 0.04*(Time away) − 0.004*(Time away)^2
    - Value = 28.9 + 9.57*(Time away) − 0.61*(Time away)^2

### Structural estimation approach and instruments
- 3-stage structural model (following Rozelle et al., 1999) to separate migration (M) and remittance (R) decisions and estimate outcomes:
  - Stage 1 (migration): εγβα+⋅+⋅+=M ZHHM 111  (equation 9)
  - Stage 2 (remittances): σθγβα+⋅+⋅+⋅+=− MZHHR R2222  (equation 10), where − M is fitted migration from equation 9
  - Stage 3 (outcomes): ωθγβα+⋅+⋅+⋅+=−− MRHHOutcome 3333  (equation 11), where − R is fitted remittance from equation 10
- Estimation method: 3-Stage Least Squares (3SLS) to account for correlated errors between equations 9 and 10.
- Instruments for migration:
  - Regional corruption measure (share mentioning corruption and absence of law and order);
  - Historic region-wide migration rates (emigration);
  - Interactions of regional instruments with household percent with post-secondary degrees (Ppostsec).
- Instruments for remittances:
  - Region-wide unemployment rate among men (Unemploy);
  - Ratio of vulnerable population to total regional population (Vulnerable);
  - Interactions with Ppostsec.
- Household-level controls: age and age-squared of household head; average age of working-age members and its square; HHheadmale; Ppostsec; Pelderly; Pkids; Pwomen; HHsize; dwelling condition dummies (Good, Normal, Not good; “Excellent” left out); Urban (non-capital) and Rural dummies (capital Yerevan left out).

### First- and second-stage estimation highlights (selected coefficients from Table 2)
- Migration equation (notable coefficients and significance):
  - Emigration (region-wide past migration): 0.012 [0.002]***
  - Corruption: -0.002 [0.001]**
  - HHheadmale: -0.019 [0.011]*
  - Pkids: -0.203 [0.039]***
  - HHsize: 0.024 [0.003]***
  - Urban (non-capital): 0.067 [0.010]***; Rural: 0.023 [0.012]*
  - Dwelling quality: Good 0.047 [0.018]**, Normal 0.026 [0.015]*, Not good 0.012 [0.016]
- Remittances equations (Remittances Yes/No and Remittances in ‘000 dram):
  - Migration → remittances: 0.611 [0.189]*** (probability); 100.628 [30.313]*** (amount, ‘000 dram)
  - Unemploy: -0.352 [0.136]*** (probability); -62.666 [21.909]*** (amount)
  - Vulnerable: -0.001 [0.001] (probability); -0.454 [0.151]*** (amount)
  - Interaction terms largely not significant (e.g., Unemploy*Ppostsec -0.361 [0.440]; Vulnerable*Ppostsec -0.003 [0.003])
- Interpretations:
  - Migration networks encourage migration.
  - Corruption associated with lower migration probability.
  - Remittance patterns support self-interest motives: higher regional unemployment and larger vulnerable share discourage remittances; larger households less likely to receive remittances and receive smaller amounts; households with greater share of women more likely to receive larger transfers.

### Third-stage outcomes (Table 3: remittance impacts on household outcomes)
- Key third-stage coefficient estimates (Remittances(hat) and Migration(hat)):
  - Remittances(hat):
    - Hours Worked: -7.677 [3.250]** (remittances reduce hours supplied)
    - Education Expenditures: -355.958 [70.834]*** (remittances reduce per-student education spending, in 1,000 drams)
    - Savings: 213.0 [85.889]** (remittances increase household savings, in 1,000 drams)
    - Banking (borrowed from banks dummy): 0.294 [0.552] (not significant)
  - Migration(hat):
    - Hours Worked: 1.329 [1.527] (insignificant)
    - Education Expenditures: 215.365 [37.330]*** (positive and significant)
    - Savings: -95.527 [40.357]** (migration reduces reported savings)
    - Banking: -0.253 [0.259] (not significant)
- Instrument validity tests for equation 10 instruments:
  - Anderson-Rubin OR test, χ2(2): Hours Worked 0.720, p=0.70; Education Expenditures 1.456, p=0.48; Savings 2.104, p=0.35; Banking 2.104, p=0.35 (cannot reject instrument exogeneity).
  - Hansen’s J-test of overidentification, χ2(1): Hours Worked 1.292, p=0.26; Education Expenditures 0.272, p=0.60; Savings 0.317, p=0.57; Banking 34.40, p=0.00 (Banking regression shows instrument correlation concern; interpret Banking results with caution).
- Additional controls (selected patterns):
  - Age: Hours Worked -0.062 [0.024]***; Banking 0.006 [0.003]**.
  - Ppostsec: Hours Worked 1.531 [0.153]***; Education Expenditures 111.729 [7.966]***.
  - HHsize: Hours Worked -0.131 [0.035]***; Savings -9.019 [1.497]***.
- Sample size for reported regressions: 6,816 observations.

### Main empirical conclusions and numeric highlights
- Migration increases probability and amount of remittances:
  - 0.611 [0.189]*** (probability)
  - 100.628 [30.313]*** (‘000 dram amount)
- Remittances’ estimated third-stage impacts:
  - Hours Worked: -7.677 [3.250]** (negative effect on labor supply)
  - Education Expenditures: -355.958 [70.834]*** (negative effect on per-student spending, in 1,000 drams)
  - Savings: 213.0 [85.889]** (positive effect on household savings, in 1,000 drams)
  - Banking borrowing dummy: 0.294 [0.552] (no significant increase)
- Remittance decay pattern:
  - Probability and amount rise initially and then decline after peaks at 5 and 7 years, respectively.
- Instrument diagnostics:
  - Anderson-Rubin tests indicate instruments pass exogeneity for the four third-stage equations reported.
  - Hansen’s J-test indicates potential instrument correlation for Banking (χ2(1)=34.40, p=0.00), so Banking results should be treated with caution.

### Policy implications and suggested extensions
- Policy implications emphasized:
  - Strengthen rule of law, improve human rights and business environment to encourage return migration and convert brain drain into brain gain.
  - Engage non-returning migrants in development processes abroad.
  - Policies influencing households’ rate of time preference (directly or via consumption/wealth) can mitigate remittance-related micro-level drawbacks.
  - Reforms that raise earnings of those remaining at home can reduce remittance-associated disincentives to work.
  - Consider interest-rate and borrowing policy levers; explore using unconsumed remittances as collateral in extended models.
- Suggested empirical and theoretical extensions:
  - Allow borrowing in the model.
  - Include household production functions.
  - Analyze degrees of cooperation between migrants and households.
  - Further investigate reasons behind remittances’ negative effect on education spending and limited effect on banking borrowing.

### Appendix highlights: proofs and variable definitions
- APPENDIX I contains formal proofs of Result 1 and Result 2 with first-order conditions and solved expressions for equilibrium choices (migrant’s and relative’s consumption, leisure, investment, remittances).
- APPENDIX II defines variables and measurement:
  - Hours Worked: per capita market hours aggregated with 4 for part time, 8 for full time, 10 for overtime, 0 otherwise (ILSMS).
  - Education Expenditures: per student, in 1,000 drams (ILSMS).
  - Savings: amount saved during 12 months preceding survey, in 1,000 drams (ILSMS).
  - Banking: dummy =1 if household members had borrowed from banks during the 12 months preceding the survey (ILSMS).
  - Age, Aveagework, HHheadmale, Ppostsec, Pelderly, Pkids, Pwomen, HHsize, Timeaway, dwelling quality dummies, Rural/Urban dummies: all from ILSMS.
  - Corruption: regional share citing corruption/absence of law and order (Yaganyan and Shahnazaryan, 2001, Table 5).
  - Emigration: ratio of population involved in migration in region (Yeganyan and Shahnazaryan, 2004, Table 2.3).
  - Unemployment: region-wide male unemployment (authors’ calculations based on ILSMS).
  - Vulnerable: ratio of vulnerable population in region (Jrbashian, 2001, Table 1).
  - Nonfunctioning: region-wide ratio of non-functioning enterprises (UNDP, 1999, Table 2.5).
- Note: original survey described as “An Overview of External Migration Processes in the Republic of Armenia during 1991-1998” conducted by the National Statistical Service of Armenia with TACIS and Eurostat.

*Italicized source: IMF Working Paper _wp0819 (excerpts provided).*

### References..............................................................................................................

### _wp0819 - References

### Introduction
- The New Economics of Labor Migration (NELM) highlights implications of migration-driven remittances on microeconomic incentives of family members left behind.
- Worldwide remittance flows have grown to become the second source of development finance after foreign direct investment (World Bank, 2005).
- Potential adverse effects of remittances include:
  - loss of productive labor for the home country;
  - disincentives to work, study, and stay in the home country for family members left behind;
  - reduced incentives for authorities to improve business and human rights environments and address systemic economic and social problems.
- Empirical results in the paper suggest remittances:
  - reduce incentives to work;
  - lead to less spending on education;
  - increase household saving, but do not lead to more borrowing from the banking system.
- Context and Armenian-specific facts preserved from the source:
  - Armenia’s industrial sector generated 55 percent of total output and employed 39 percent of the labor force in 1987 (USSR Statistical Handbook, 1988).
  - Upper secondary and higher education enrollments were 87 and 19 percent of the relevant population groups in 1989.
  - Armenia gained independence in 1991.
  - Emigration from Armenia has involved educated and skilled individuals; the brain drain has been severe (IWPR, 2000).
  - Remittances in Armenia may have reached 20 percent of GDP in recent years (CBA, 2006).
  - Armenia’s low divorce rate—with an average of 14.6 percent for 1989–2005—could indicate strong family ties (UNISEF TransMONEE database).
- Paper structure (as stated): Section II reviews theoretical considerations; Section III builds a two-period overlapping generations model with altruism and strategic behavior; Section IV describes data and econometric estimates; Section V concludes.

### Theoretical considerations and motives to remit
- Two broad categories of motives:
  - altruistic motive (migrant’s utility contains utility of household member(s));
  - self-interest motive (self-enforcing contracts or “enlightened selfishness” / “tempered altruism”).
- Interaction of motives:
  - Both altruism and self-interest can operate simultaneously and may be complementary.
  - Altruism may ensure enforcement of implicit contracts; self-interest can be central to self-enforcing arrangements (Stark and Lucas, 1988; Lucas and Stark, 1985).
- Divergent comparative statics:
  - Altruism implies more remittances to poorer households.
  - Self-interest motives can imply co-movement of the relative’s income and remittances.

### Specific self-interest drivers behind remittances (as enumerated)
- (i) to allocate risks among remitting and receiving parties;
- (ii) to receive inheritance/bequest;
- (iii) to smooth consumption;
- (iv) to relax capital constraints faced by household members;
- (v) to accumulate wealth in the home country;
- (vi) to defray migration costs or repay education expenses;
- (vii) to pay for social status in the home country;
- (viii) to pay for services provided by household members (e.g., asset care);
- (ix) to encourage or discourage migration from the home country.

### Empirical determinants of remittances
- Factors influencing likelihood and amount of remittances include characteristics of both remitter and receiving family.
- Findings and hypotheses preserved:
  - More educated migrants may remit less because migration is more often permanent (e.g., Faini, 2003).
  - Closeness of family ties can boost both self-enforcement and altruistic motives and varies across countries.
  - Income levels of receiving families are a major determinant (e.g., Osili, 2007).
  - The link between household income and migration/remittances may be non-linear.
  - A high wage/income differential between host and home countries can weaken self-interest/bequest motives.
- Remittance Decay Hypothesis (RDH):
  - The longer migrants live away, the less likely they are to remit.
  - Relationship likely non-linear due to host-country labor market dynamics and wearing out of family ties.
  - Time away influences probability of return and thereby affects remittance transfer and saving behavior of relatives.

### Impact of remittances (macro and micro evidence summarized)
- Macro findings cited:
  - Chami and others (2005): negative effect of remittances on growth and productivity (reasons include loss of productive workers and adverse effects on those staying behind).
  - Acosta and others (2007): remittances can shrink and reallocate resources away from the tradable sector via (i) increasing nontradable prices and (ii) reducing labor supply to labor-intensive nontradable sector.
  - Van Dalen and others (2005): remittances can stimulate further migration among family members left behind.
- Micro findings on household behavior:
  - Mixed evidence on whether remittances fund productive investment versus immediate consumption.
  - Studies reporting positive relationships between remittances and investment/education include: Taylor (1992), Glytsos (1993), Brown (1994), Adams (1998), Massey and Parrado (1998), Rozelle and others (1999), McCormick and Wahba (2001), Muent and others (2001), Dustmann and Kirchkamp (2002), Kule and others (2002), Taylor and others (2003), Mesnard (2004), Woodruff and Zenteno (2007), Yang (2007), and Zarate-Hoyos (2004).
  - Studies arguing remittances are absorbed into immediate consumption include: Lipton (1980); Reichert (1981); Massey et al. (1987); Grindle (1988); Ahlburg (1991); Russell (1992); Brown and Ahlburg (1999).
- Evidence on education:
  - Yang (2007): remittances increase child schooling and educational expenditures.
  - Lopez Cordoba (2004): Mexican municipalities receiving more remittances have greater literacy and higher school attendance among 6–14 year olds.
  - Cox Edwards and Ureta (2003): remittances have a large and significant effect on school retention in El Salvador; impact larger than other income.
  - Hanson and Woodruff (2003): Mexican children in migrant households complete significantly more years of schooling; results consistent with emigration relaxing household credit constraints.
  - Contrasting evidence: Acosta (2006) finds the positive impact on children’s education in El Salvador vanishes and turns negative after controlling for selection and omitted variable biases; McKenzie (2005) finds migration lowers years of completed education in Mexican households.

### Contribution and empirical findings (as stated for Armenia)
- Contributions:
  - Presents a model explicitly modeling dynamic strategic interactions between migrant and remittance-receiving relative(s), comparing non-cooperative and self-enforcing (total surplus–maximizing) outcomes.
  - Provides empirical evidence from Armenia, a region not previously studied in this context.
- Empirical findings reported in the paper:
  - Remittances reduce incentives to work.
  - Remittances lead to less spending on education.
  - Remittance-receiving families save more.
  - Increased saving does not result in more borrowing from the banking system, contrary to the remittances-as-collateral argument.

_ _wp0819 - References_

### 1.4 years for boys and 1.7 years for girls. The author attributes this result to the following

### _wp0819 - 1.4 years for boys and 1.7 years for girls. The author attributes this result to the following

### Key empirical observation on schooling
- Estimated schooling loss: "1.4 years for boys and 1.7 years for girls."
- The author attributes this schooling loss to:
  - Children ages 16–18 may be forced to migrate to obtain work instead of going to school, or to migrate with their parents, and, as a result, drop out of school.
  - Future returns to schooling for children who are likely to migrate in the future are lower.
  - Lack of parental supervision/presence in families with migrants is likely to lead to poorly supervised students and the need for them to do more household chores than otherwise.

### Effects of remittances on labor supply and participation (literature evidence summarized)
- Amuedo-Dorantes and Pozo (2006a), Mexico (nationally representative income and expenditure survey):
  - Overall male labor supply does not vary with remittances, but composition changes:
    - Remittances reduce formal sector work and self-employment for men in urban areas.
    - Remittances increase informal sector work in both urbanized and rural areas.
  - For women, remittances result in an overall drop in female labor supply, coming mostly from reductions in informal sector and non-paid work in rural areas.
- Yang (2007), Philippines:
  - Increases in remittances cause households to raise hours worked in self-employment and increase likelihood of starting relatively capital-intensive household enterprises.
  - Positive income shocks from remittances lead to decreased child labor supply.
- Acosta (2006):
  - Finds support for the disincentive hypothesis behind remittances for both men and women.

### Theoretical considerations — model setup and motivations
- Distinctive modeling choices:
  - Explicitly model dynamic strategic interaction between migrant (m) and remittance-receiving relative (r).
  - Timing: in each period the migrant behaves as a Stackelberg leader by choosing the level of transfers; remittance choice is followed by consumption and investment decisions.
  - Motivations for remitting in the non-cooperative model:
    - Pure altruism.
    - Self-interest to increase the relative’s bequest to the migrant.
  - Interaction to realize gains from exchange modeled via self-enforcing contracts maximizing total surplus (cooperative solution), rather than Nash bargaining.
- Agents and timing:
  - Two agents: migrant (m) who relocates from home country (h) to foreign country (f), and representative relative (r).
  - Two time periods. In period 1 first stage migrant remits R1 ≥ 0; second stage migrant and relative simultaneously choose leisure and consumption (m chooses m l1 and m c1; r chooses h X1 (investment), r l1, r c1).
  - Only the relative makes investment decisions (h X1) for simplicity; relative has access only to home capital market.
  - Migrant survives to period 2; relative does not. In period 2 migrant chooses m l2 and m c2; relative’s period-2 variables set to zero.
- Budget constraints (period 1 examples preserved exactly as in source):
  - mmff clwRLw 11111 +=−             (1)
  - hrrhhh XclwiXRLw 1111011 ++=++,      (2)
  - Migrant period-2 budget constraint: mmfhf clwiXLw 22212 +=+       (3)
  - Notation: f w1, h w1, L, h X0, i as in source.

### Utility specification and parameter notation
- Interdependent utilities with additive separability:
  - Migrant and relative utilities incorporate weights α (migrant) and γ (relative) and their complements α−1 and γ−1.
  - Private sub-utilities specified with log separability and leisure-consumption functional forms with parameters 0<η<1 and 0<ρ<1, e.g.:
    - ()() m t m t m t m t m lclculn1ln,ηη−+=        (4)
    - ()() r t r t r t r t r lclculn1ln,ρρ−+=      (5)
- Discount factors m β and r β for migrant and relative, respectively.

### Non-cooperative solution — main equilibrium results (Result 1)
- The unique subgame perfect equilibrium is characterized; principal expressions preserved from source:
  - (a) Migrant chooses remittance in first stage of period 1:
    - ⎟⎟⎠⎞⎜⎜⎝⎛++ + − ⎟⎟⎠⎞⎜⎜⎝⎛+ − = i Lw iXLwLw R f hh m f m 2 0111 11 1 αβ α αβ α ;
  - (b) For any given 1 R, migrant’s and relative’s choices in second stage of period 1 given by specific closed-form expressions (examples in source):
    - () () f f m w RLw Rl 1 11 11 1 − − = η ,
    - () () 1111 RLwRc fm − = η ,
    - Relative’s leisure and consumption and investment expressions as given in text (see source for exact expressions).
  - (c) Migrant’s period-2 consumption and leisure for any given h X1 are given by:
    - hfhm iXLwXc 1212 += η and () () f hf hm w iXLw Xl 2 12 12 1+ − = η, respectively.
- Subgame perfect equilibrium path restated with variables denoted by ~ (tilde) for non-cooperative levels in source.

### Cooperative solution — main results (Result 2)
- Under a self-enforcing cooperative arrangement that maximizes total surplus (allowing transfers in either direction), cooperative levels of endogenous variables are derived; principal expressions preserved:
  - Cooperative remittance:
    - ()() rm f hhfrm i Lw iXLwLw R βγαβ αγβγαβγα −++ ⎟⎟⎠⎞⎜⎜⎝⎛ +++ − − − +++ − = 12 111 ˆ 2 011 1 ;
  - Cooperative investment h X1ˆ and leisure expressions given in closed form in source.
- Cooperative levels denoted by ^ (hat) in source.

### Comparative statics — qualitative and specific findings
- Investment-remittance relationships for cooperative and non-cooperative models preserved as in source:
  - () [] []() () rm fhhrm h i LwiXLwR X βγαβγα γαβγαβ −+++− + − − ++ − + = 11 1 ˆ 1 ˆ 2011 1 ,
  - () () r f hhr r h i Lw RiXLw X βγγ γβγ − + − ++ − = 1 ~ 1 ~ 2 101 1 .
- Summary of comparative statics (as reported in Table 1 and text highlights):
  - Similarities across models:
    1. Level of remittances is decreasing in both the wage and the non-wage income of the relative.
    2. Level of remittances is increasing in the migrant’s wage in period 1 and decreasing in the migrant’s wage in period 2.
    3. Level of investment/bequest, the relative’s consumption and leisure are all increasing in the level of remittances.
    4. Investment/bequest is increasing in migrant’s wage in period 1 and decreasing in migrant’s wage in period 2.
    5. Leisure is a normal good: relative’s labor income reduces consumption of leisure; non-labor income increases consumption of leisure.
    6. For sufficiently high expected migrant wage in period 2 and sufficiently low rates of interest (condition hf XiLw 0 2 2 >), higher interest rates lead to more remittances and more hours supplied by the relative.
  - Differences across models:
    - Changes in the relative’s selfishness γ and discount factor r β do not affect non-cooperative remittance level but have positive effect on cooperative remittances.
    - Migrant’s selfishness α has a negative effect on non-cooperative investment but a positive effect on cooperative investment.
    - Increases in migrant’s discount rate m β have a positive effect on non-cooperative leisure but a negative effect on cooperative leisure.
- Dynamics prediction:
  - If family ties (proxied by (1−α) and (1−γ)) fade with time, both models predict a decline in remittances over time.
  - Non-cooperative solution yields unambiguous reduction in remittances as (1−α) declines; cooperative outcome depends on relative magnitudes and time preferences.
- Second-order derivatives insights:
  - Share of remittances used for investment increases as relative’s rate of time preference and weight on her own consumption decrease:
    - 0 ) ~ / ~ ( 11 > ∂ ∂ ∂ ∂ r h R X β and 0 ) ~ / ~ ( 11 < ∂ ∂ ∂ ∂ γ R X h .
  - Sensitivity of remittance to relative income affected by migrant’s subjective discount factor:
    - ∂ ∂ ∂ ∂ m h w R β ) / ~ ( 1 0 > — i.e., the more weight migrant places on present utility (smaller m β), the smaller share of income transferred.

### Comparisons of cooperative vs non-cooperative (Results 3–5 and simplified forms)
- Result 3: Cooperative remittance exceeds non-cooperative if and only if:
  - ()()() mr ββγααγ − − + ≤ − 11 .
- Result 4: Cooperative investment/bequest exceeds non-cooperative if and only if:
  - ()()()()()()()() [] 011212111 ≥ + − − − ++ − + − ++ mrrmrrmm αββγβγαββγαβγαβαβγ .
- Result 5: Cooperative leisure exceeds non-cooperative if and only if:
  - ()()()()()() 01211 ≥ − − − + − − + − − + − + mrrmmrmr βαβββαβγαγβαβγαβγγαγ.
- Under assumption β β β == m r (i.e., m β = r β = β), simplified conditions:
  - Result 3’: 1 > + γ α
  - Result 4’: ()() 01 2 ≥ − − − + α β β γ γ α
  - Result 5’: ()( ) 0)1)(1(21 ≥ − − − + − + + α β α γ γ α α β γ
- Qualitative depiction: for sensible parameter values, cooperative solution yields higher remittances and investment/bequest and lower leisure than non-cooperative solution (Figure 1 in source).

### Empirical estimation — Armenian case (data and stylized facts)
- Data source: 2004 Integrated Living Standards Measurement Survey (National Statistical Service of Armenia).
  - Dataset is nationally representative: over 28,000 individuals from over 6,800 households.
- Remittance pattern peculiarities in Armenia:
  - 23 percent of all surveyed households report receiving transfers from abroad.
  - 14 percent report having a migrant abroad.
  - Only 37 percent of all remittances are migration-related (i.e., 63 percent comes from out-of-household sources).
  - Only 62 percent of families with migrant members report receiving remittances (potential underreporting).
- Time-away and remittances relationship (remittance decay hypothesis):
  - Both propensity to remit and amount remitted decline over time after reaching maxima:
    - Propensity maximum at 5 years; amount maximum at 7 years (as presented in source figure discussion).
  - Regressions used to depict Figure 2 (exact specifications from source):
    - Probability = 0.59 + 0.04*(Time away) − 0.004*(Time away)^2
    - Value = 28.9 + 9.57*(Time away) − 0.61*(Time away)^2
    - Note: these regressions use only households with migrants; estimates of other regressors (not reported) are included in constants at their mean values.
- Measurement concerns noted:
  - Underreporting of remittances and migrants is possible (survey by official agency may bias downward reported remittances; households might underreport migrants to conceal reasons for emigration).
  - Dataset does not distinguish between pure transfer and investment components of remitted amounts.

*Italicized source: IMF Working Paper _wp0819 (excerpts provided).*

### Section III, the observed transfer is the sum of altruistic (with potential strategic motives in

### _wp0819 - Section III, the observed transfer is the sum of altruistic (with potential strategic motives in mind) and return-driven amounts.

### Structural model and estimation approach
- Employed a 3-stage structural model following Rozelle and others (1999) to separate migration (M) and remittance (R) decisions and estimate microeconomic outcomes.
- Equations (preserved notation):
  - Stage 1 (migration): εγβα+⋅+⋅+=M ZHHM 111 (equation 9)
  - Stage 2 (remittances): σθγβα+⋅+⋅+⋅+=− MZHHR R2222 (equation 10), where − M is fitted migration from equation 9
  - Stage 3 (outcomes): ωθγβα+⋅+⋅+⋅+=−− MRHHOutcome 3333 (equation 11), where − R is fitted remittance from equation 10
- Outcomes analyzed: (i) per capita hours worked by household members, (ii) per student expenditures on education, (iii) household savings, and (iv) a dummy indicating whether household members had borrowed from the banking sector during the 12 months preceding the survey.
- Estimation method: 3-Stage Least Squares (3SLS) to jointly estimate the system (preferred due to likely correlated errors between equations 9 and 10).

### Instruments and control variables
- Instruments for migration (M):
  - Regional corruption measure (share of respondents mentioning corruption and absence of law and order as obstacles to rising living standards)
  - Historic region-wide migration rates (emigration)
  - Interactions of regional instruments with household percent with post-secondary degrees (Ppostsec)
- Instruments for remittances (R):
  - Region-wide unemployment rate among men (Unemploy)
  - Ratio of vulnerable population to total regional population (Vulnerable)
  - Interactions with Ppostsec
- Household-level control variables included:
  - Age of household head and age-squared
  - Average age of working-age members and its square
  - Dummy for male household head (HHheadmale)
  - Percent with post-secondary education (Ppostsec)
  - Percent above 64 (Pelderly)
  - Percent under 6 (Pkids)
  - Percent women (Pwomen)
  - Household size (HHsize)
  - Dummies for dwelling condition (“Good”, “Normal”, “Not good”; “Excellent” left out)
  - Dummies for Urban (non-capital) and Rural (capital city left out)
- Additional controls and instruments rationale: interaction with household educational attainment, wealth proxies via housing quality, robustness checks (alternative instrument: region-wide ratio of non-functioning enterprises, noted but not reported).

### First- and second-stage key estimated results (Table 2)
- Migration equation notable coefficients and significance:
  - Emigration (region-wide past migration): 0.012 [0.002]***
  - Corruption: -0.002 [0.001]**
  - HHheadmale: -0.019 [0.011]* (households with male heads less likely to have a migrant)
  - Pkids: -0.203 [0.039]*** (more children → less likely to have a migrant)
  - HHsize: 0.024 [0.003]*** (larger households → more likely to have a migrant)
  - Urban (non-capital): 0.067 [0.010]***; Rural: 0.023 [0.012]* (migration most likely from urban non-capital, then rural, then capital)
  - Dwelling quality inverted-U: Good 0.047 [0.018]**, Normal 0.026 [0.015]*, Not good 0.012 [0.016]
- Remittances equations (two forms reported: Remittances (Yes/No) and Remittances (‘000 dram)):
  - Migration → remittances: 0.611 [0.189]*** (probability); 100.628 [30.313]*** (amount, ‘000 dram)
  - Unemploy: -0.352 [0.136]*** (probability); -62.666 [21.909]*** (amount)
  - Vulnerable: -0.001 [0.001] (probability); -0.454 [0.151]*** (amount)
  - Interaction terms generally not significant (e.g., Unemploy*Ppostsec -0.361 [0.440]; Vulnerable*Ppostsec -0.003 [0.003])
  - Age, household composition, and dwelling quality affect both probability and amounts with an inverted-U pattern for wealth: households with “good” and “normal” housing receive more/larger remittances than “not good” and “excellent” categories.

- Observed interpretations:
  - Migration networks encourage migration.
  - Corruption associated with lower probability of migration (possible affordability or fear of leaving family behind).
  - Remittance patterns support self-interest motives: higher regional unemployment and larger vulnerable share discourage remittances; larger households less likely to receive remittances and receive smaller amounts; households with greater share of women more likely to receive larger transfers.

- Sample sizes:
  - Number of observations (first and second stage): 6,816 (for each reported column).

### Third-stage results and interpretation (Table 3)
- Table 3 reports regressions for Hours Worked, Education Expenditures, Savings, and Banking (borrowed from banks). Key coefficient estimates (Remittances(hat) and Migration(hat)):
  - Remittances(hat):
    - Hours Worked: -7.677 [3.250]** (negative and significant)
    - Education Expenditures: -355.958 [70.834]*** (negative and significant)
    - Savings: 213.0 [85.889]** (positive and significant)
    - Banking: 0.294 [0.552] (not significant)
  - Migration(hat):
    - Hours Worked: 1.329 [1.527] (insignificant, positive)
    - Education Expenditures: 215.365 [37.330]*** (positive and significant)
    - Savings: -95.527 [40.357]** (negative and significant)
    - Banking: -0.253 [0.259] (not significant)
- Tests of instruments (for equation 10 instruments):
  - Anderson-Rubin OR test, χ2(2): Hours Worked 0.720, p=0.70; Education Expenditures 1.456, p=0.48; Savings 2.104, p=0.35; Banking 2.104, p=0.35 (cannot reject exogeneity)
  - Hansen’s J-test of overidentification, χ2(1): Hours Worked 1.292, p=0.26; Education Expenditures 0.272, p=0.60; Savings 0.317, p=0.57; Banking 34.40, p=0.00 (Banking regression shows instrument correlation concern; results for Banking should be treated with caution)
- Additional control variable patterns (selected):
  - Age: Hours Worked coefficient -0.062 [0.024]***; Education Expenditures 1.125 [0.955] (insignificant); Banking 0.006 [0.003]**.
  - Ppostsec: positive and significant for Hours Worked 1.531 [0.153]*** and Education Expenditures 111.729 [7.966]***.
  - HHsize: Hours Worked -0.131 [0.035]*** (larger households supply fewer aggregate hours); Savings -9.019 [1.497]***.
  - Dwelling quality (Good, Normal) associated with higher Education Expenditures and Savings, and higher Banking borrowing propensity in descriptive interpretation.
- Interpretations emphasized in text:
  - Remittances reduce hours worked (disincentive/labor supply effect); migration (absence of a family member) has a positive but insignificant effect on hours worked.
  - Remittances reduce education expenditures; migration increases education expenditures—possible reasons: expectation of future migration, remitter oversight leading to conservative/sustenance-focused spending.
  - Remittances increase savings; migration reduces reported savings (likely due to migration costs).
  - Remittances do not increase borrowing from commercial banks (contrary to remittances-as-collateral hypothesis); for Banking variable, instrument validity is questioned by Hansen’s J-test.

### Main substantive findings and numeric highlights
- Migration increases probability and amount of remittances: 0.611 [0.189]*** (probability), 100.628 [30.313]*** (‘000 dram amount).
- Remittances’ estimated impacts (third stage):
  - Hours Worked: -7.677 [3.250]** (remittances reduce hours supplied)
  - Education Expenditures: -355.958 [70.834]*** (remittances reduce per-student education spending)
  - Savings: 213.0 [85.889]** (remittances increase household savings)
  - Banking borrowing dummy: 0.294 [0.552] (no significant increase in borrowing)
- Instrument validity: Anderson-Rubin tests indicate instruments pass exogeneity for all four third-stage equations; Hansen’s J-test indicates instruments may be correlated with Banking outcome (Hansen’s J χ2(1)=34.40, p=0.00), signaling caution interpreting Banking results.

### Conclusions and policy implications (as presented)
- The overlapping-generations model incorporating altruistic and self-interest motives predicts higher remittances and, under cooperation, higher investment and hours worked; empirical results for Armenia show mixed support:
  - Empirical evidence: remittance-receiving households in Armenia work fewer hours, spend less on education, save more, but do not borrow more from banks.
- Dynamic pattern of remittances:
  - Evidence supporting remittances decay hypothesis: probability of sending and amount transferred rise initially and then decline after peaks at 5 and 7 years, respectively.
  - Implication: with subsiding net migration and rising real wages, remittances may decline over time—possible macroeconomic impact through reduced aggregate demand.
- Policy recommendations and extensions suggested:
  - Strengthen rule of law, improve human rights and the business environment to encourage return migration and convert brain drain into brain gain.
  - Engage non-returning migrants in development processes abroad.
  - Policy measures that influence households’ rate of time preference (directly or via consumption/wealth) can mitigate remittance-related micro-level drawbacks.
  - Reforms that raise earnings of those remaining at home can reduce disincentives to work associated with remittances.
  - Consider interest-rate and borrowing policy levers, and explore using unconsumed remittances as collateral in extended models.
  - Suggested empirical extensions: allow borrowing in the model, include household production functions, and analyze degrees of cooperation between migrants and households; further investigate reasons behind remittances’ negative effect on education spending and limited effect on banking borrowing.

*Source: _wp0819 - Section III, the observed transfer is the sum of altruistic (with potential strategic motives in mind) and return-driven amounts (IMF working paper content provided in the source PDF).*

### APPENDIX I

### APPENDIX I

### Proof of Result 1
- In period 2, the migrant chooses m c 2 and m l 2 to maximize his period-2 utility. The migrant will set
  - []hfm iXLwc 122 +=η
  - ()[]f hf m w iXLw l 2 12 2 1+− = η.
- Substituting for m c 2 and m l 2, the migrant’s period-2 utility function can be written as:
  - ()() [] ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − − − hf f iXLw w 12 1 2 1 1 ln η η η ηη .
- In the second stage of period 1 the migrant and the relative simultaneously and independently make their choices; the migrant chooses m c 1 and m l 1 while the relative chooses r c 1, r l 1 and h X 1. The migrant’s continuation payoff in the beginning of the second stage of period 1 can be written as:
  - ()() () []()() () [] () () [] ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − + −+−++−−+−+−− − − hf f m rhhrhmmf iXLw w lXRiXlLwlRlLw 11 1 1 1 1110111111 1 ln ln1ln)1(ln1ln η η η ηη αβ ρραηηα .
- Hence, the migrant will set
  - ()() f f m w RLw l 1 11 1 1−− = η
  - () 111 RLwc fm − = η.
- The relative’s continuation payoff in the beginning of the second stage of period 1 is given by:
  - ()() () [] ()() () [] () () [] ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − −+ −+−−−+−+−++− − − hf f r mmfrhhrh iXLw w lRlLwlXRiXlLw 12 1 2 1 1111111011 1 ln)1( ln1ln)1(ln1ln η η η ηη βγ ηηγρργ .
- From the relative’s optimization problem we obtain:
  - ()() () ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +++ −+ − = i Lw RiXLw w l f hh hr r 2 101 1 1 1 1 βγγ ργ ;
  - () ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +++ −+ = i Lw RiXLwc f hh r r 2 1011 1βγγ γρ ;
  - ()() () r f hhr h i Lw RiXLw X βγγ γβγ −+ −++− = 1 1 2 101 1 .
- In the first stage of period 1 the migrant chooses remittance 1 R to maximize his continuation payoff:
  - ()() () () ()() () () () () [] ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +++ + − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +++ + − −+ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − − − − − − − LwRiXLwi w i Lw RiXLw w RLw w fhh fr r m f hh hr f f 2101 1 2 1 2 101 1 1 1 11 1 1 1 1 ln 1 ln)1( 1 ln η η η ρ ρ ρ η η η βγ ηηβ αβ βγ ργρ α ηη α .
- Hence, the migrant will set
  - () ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ +++ + − = i Lw iXLwLwLwR f hhf m f 2 01111 1αβ α.
- Substituting this expression into the above formulas for the choice variables of the migrant and the relative yields the stated result. QED.

### Proof of Result 2
- The first-order conditions for problem 8 can be written as:
  - m l 2 :  ()() hfmf iXLwlw 1222 1+− = η
  - h X 1 : ()() ()() hrhhhmfhf rm XlwiXRLwlwiXLw i 1110112212 )1(1 −−++ +− = −+ −+γαρβγαβη
  - m l 1 : ()() 1111 1RLwlw fmf −− = η
  - r l 1 : ()() hhh rh XiXRLwlw 101111 1−++− = ρ
  - 1 R:  ()() mffhrhhh lwRLwXlwiXRLw 1111111011 )1()1( −− +− = −−++ +− ηαγγαρ
- These can be equivalently written as:
  - m l 2 :  ()() hfmf iXLwlw 1222 1+− = η
  - h X 1 : ()() ()() hhhhf rm XiXRLwiXLw i 101112 )1(1 −++ +− = + −+ γαβγαβ
  - m l 1 : ()() 1111 1RLwlw fmf −− = η
  - r l 1 : ()() hhh rh XiXRLwlw 101111 1−++− = ρ
  - 1 R:  ()() 111011 )1()1( RLwXiXRLw fhhh − +− = −++ +− αγγα
- Solving the above equalities yields the stated result. QED.

### APPENDIX II. Definitions of Variables
- Variable Names — Description — Source
- Hours Worked
  - Per capita hours supplied to the market by the working-age members of the household. The following number of hours were assumed and aggregated across the household members: 4 for part time, 8 for full time, 10 for overtime, and 0 otherwise.
  - Integrated Living Standards Measurement Survey (ILSMS)
- Education Expenditures
  - Per student expenditures on education, in 1,000 drams.
  - ILSMS
- Savings
  - Amount saved by the household during the 12 months preceding the survey, in 1,000 drams.
  - ILSMS
- Banking
  - Dummy variable taking value of 1 if household members had borrowed from the banking sector during the 12 months preceding the survey, and 0 otherwise.
  - ILSMS
- Age
  - Age of the household head.
  - ILSMS
- Aveagework
  - Average age of working-age members of the household.
  - ILSMS
- HHheadmale
  - Dummy for male household head.
  - ILSMS
- Ppostsec
  - Percent of household members with post-secondary education.
  - ILSMS
- Pelderly
  - Percent of household members above 64.
  - ILSMS
- Pkids
  - Percent of household members under 6.
  - ILSMS
- Pwomen
  - Percent of women in the household.
  - ILSMS
- HHsize
  - Number of household members.
  - ILSMS
- Timeaway
  - Number of years that a migrant has been away.
  - ILSMS
- Good, Normal, Not good
  - Dummy variables based on household members’ assessment of their housing conditions. The left-out category is “Excellent”.
  - ILSMS
- Rural, urban
  - Dummy variables to distinguish the rural and non-capital urban areas from the capital. The left-out category is capital Yerevan.
  - ILSMS
- Corruption
  - Share of respondents in every region who mentioned corruption and absence of law and order as obstacles for rising living standards.
  - Yaganyan and Shahnazaryan (2001), Table 5.
- Emigration
  - Ratio of population involved in migration as a share of total population in the region.
  - Yeganyan and Shahnazaryan (2004), Table 2.3.
- Unemployment
  - Region-wide unemployment rate among men. Authors’ calculations based on ILSMS.
- Vulnerable
  - Ratio of vulnerable population as a share of total population of the region.
  - Jrbashian (2001), Table 1.
- Nonfunctioning
  - Region-wide ratio of non-functioning enterprises to total number of enterprises.
  - UNDP (1999), Table 2.5.
- Note: The original survey was contained in “An Overview of External Migration Processes in the Republic of Armenia during 1991-1998” and conducted by the National Statistical Service of Armenia jointly with the TACIS Program and Eurostat.

*APPENDIX I and APPENDIX II content as provided in the source PDF.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0819.pdf_