## 1. Summary Statistics for First-Differenced Remittance Data

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---

### Introduction
- Remittance flows sent by migrant workers to Latin America have grown rapidly and for some countries account for a significant share of GDP and rival or dwarf FDI as a source of external financing.
- Paper objective: assess the extent to which economic conditions in the United States influence remittance flows to Latin America.
- Approach: deliberately empirical; subject data to broad and rigorous testing rather than testing a single theoretical model.
- Paper structure (as provided): literature survey; data and measurement issues; econometric procedures and results; concluding remarks.

### Literature review (selected findings cited in the source)
- Vargas-Silva and Huang (2006): using quarterly data 1981–2003, found some evidence of linkages from the U.S.; for the rest of the world only U.S. inflation Granger-caused remittance flows; home country conditions were unimportant in that study.
- Lueth and Ruiz-Arranz (2006): gravity model on 11 receiving countries; per capita growth (host country cycle proxy) coefficient of 0.03 (positive, significant, yet small), which disappears in some specifications.
- Gupta (2005): estimated remittance elasticity to U.S. employment of 0.13 for India; given a standard deviation of total nonfarm payrolls of less than 0.4 percent, this appears economically insignificant.
- El-Sakka and McNabb (1999): for Egypt, source country conditions were important with a lag, elasticity ~0.03.
- Sayan (2004): for Turkey, no statistically significant relationship between remittances and Germany’s business cycle.
- Aydas, Metin-Ozcan, and Neyapti (2005): find a link for Germany-Turkey but methodology regresses remittance growth on host country income levels (interpretation for business cycle less clear-cut).

### Data: definitions and measurement issues
- Definition: remittances broadly as portion of migrant worker earnings sent back; growing use of “personal transfers” definition (United Nations, 2005).
- Measurement issues highlighted:
  - Official data typically include only formal-channel financial transfers; decline in transaction costs may partly reflect diversion of existing flows.
  - Remittances-in-kind typically not counted.
  - Potential mismeasurement: official remittance data might capture other transfers including illegal activity.
- Data used in the paper:
  - Quarterly remittance flow data from 1990 Q1 to 2007 Q2 as reported by national authorities and typically included in the balance of payments.
  - Data were seasonally adjusted (U.S. Census Bureau's X12) and deflated by the U.S. consumer price index.
  - For stationarity, two methods used: first-differencing and Hodrick-Prescott filter cyclical component extraction.
- Note on series: Table 1 presents summary of remittance data (seasonally adjusted first differences of log values in constant US dollars).
- Table footnote: 1/ Seasonally adjusted first differences of log values in constant US dollars.

### Table 1 — Summary Statistics for First-Differenced Remittance Data, 1990 Q1 - 2007 Q2 (seasonally adjusted first differences of log values in constant US dollars)
- South America
  - Argentina: Sample size 52; Mean -0.534; Maximum -34; Minimum 14.085; Standard deviation 4
  - Brazil: Sample size 49; Mean -0.439; Maximum -30; Minimum 14.214; Standard deviation 4
  - Colombia: Sample size 44; Mean 3.729; Maximum -28; Minimum 11.427; Standard deviation 1
  - Ecuador: Sample size 32; Mean 2.118; Maximum -15; Minimum 6.719; Standard deviation
  - Mexico: Sample size 49; Mean 3.214; Maximum -19; Minimum 5.971; Standard deviation
  - Peru: Sample size 68; Mean 4.230; Maximum -25; Minimum 7.248; Standard deviation
  - Uruguay: Sample size 28; Mean 4.873; Maximum -78; Minimum 24.41; Standard deviation
  - Venezuela: Sample size 40; Mean 2.951; Maximum -42; Minimum 17.435; Standard deviation
- Central America
  - Costa Rica: Sample size 19; Mean 3.719; Maximum -20; Minimum 10.118; Standard deviation
  - El Salvador: Sample size 37; Mean 2.114; Maximum -5; Minimum 4.376; Standard deviation
  - Guatemala: Sample size 53; Mean 4.678; Maximum -20; Minimum 15.511; Standard deviation
  - Honduras: Sample size 17; Mean 6.713; Maximum -24; Minimum 3.47; Standard deviation
  - Nicaragua: Sample size 28; Mean 2.614; Maximum -21; Minimum 6.312; Standard deviation
  - Dominican Republic: Sample size 36; Mean 1.914; Maximum -16; Minimum 5.495; Standard deviation
- Source noted in table: National authorities; authors' calculations.
- Note: the table as presented in the source contains formatting and spacing that may separate fields; the numeric values above are preserved exactly as they appear in the source text.

### Estimating linkages — Correlations (first-differenced and HP-filtered)
- Two sets of correlations computed:
  - Cross-country distributions: distribution of correlations between a specified U.S. economic indicator and remittance flows across the sample of 14 countries (Appendix Figures A2 and A3).
  - Within-country distributions: distribution of correlations between a specified country and a range of 19 U.S. economic and financial indicators, contemporaneous and with 1 to 4 quarter lags (Figures A4 and A5).
- Summary of empirical correlation results (Figure 2 summary in source):
  - Simple correlations, averaged across countries and indicators, are close to zero.
  - No single U.S. indicator is strongly correlated across the set of country remittance flows.
  - No single country has remittances that are particularly sensitive, on average, to U.S. economic indicators.
  - Distribution extremes exist (strong positive or strong negative correlations), but extremes are centered around zero; strongly negative correlations are as likely as strongly positive ones.
  - Mexico and El Salvador highlighted: El Salvador exhibits the highest correlations with U.S. economic indicators in the sample.
  - Similar results obtained for housing market and financial indicators.
- Interpretation emphasized in source:
  - The overall randomness and near-zero average correlations make it difficult to attach strong weight to positive extremes; absence of consistent systematic correlation patterns across countries and indicators.

### Appendix highlights — Mexico and maximum correlations
- The indicator with the highest correlation to remittances to Mexico in each period—contemporaneously and for up to 3 lags of the U.S. indicators—are shown.
- In all cases, these maximum correlations are neither large, nor statistically significant.
- The correlations do not exhibit a pattern through time; correlations do not tail off after the peak but rather continue to follow a random process around zero.

### Cointegrating long-run relationships
- Theoretical and empirical reasons suggest no stable long-run relationship between aggregate remittance flows to a country and the level of GDP (or other measure of income or activity) in the host country.
- Key structural factors include: home country income, earning potential and sociodemographic profile of migrants, the stock of migrants, and the average length of stay.
- Sample limitations: maximum sample of just 17 years (and much less in most cases).
- Engle-Granger and Johansen procedures indicate GDP is the most likely candidate for a long-run relationship (see Appendix Tables A2 and A3).
- Cautions:
  - Johansen tests biased toward Type I errors in small samples; bias increases with lag length (Cheung and Lai, 1993).
  - Decision rule used: reject the null if the sample size is greater than 20 and the null is rejected at the 5 percent level by 2 out of 3 tests (Engle Granger, Johansen’s trace and max-eigenvalue).
- Findings:
  - Relatively stable long-run relationships between remittances and U.S. GDP found for three countries: Brazil, El Salvador, and Peru.
    - Estimated long-run elasticity of remittances to U.S. GDP from VECM models ranges from 1.9 (Peru) to 3.6 (El Salvador).
    - A one standard deviation shock to U.S. real GDP amounts to a 0.5 percent change quarter on quarter.
    - These elasticity estimates are sensitive to the lag length of the VECM and often became weaker as more lags are added.
  - Including home country GDP in cointegration:
    - Johansen procedure evidence of cointegration again for Brazil, El Salvador, and Peru (Appendix Table A4).
    - Test results are sensitive to lag length (Appendix Table A5).
    - When home country GDP is included, the positive effect of U.S. GDP on remittances disappears; the cointegrating relationship appears to pick up a common trend between the GDP series, not remittances.
    - The normalized unit coefficients on remittances compare to much higher and statistically significant coefficients on both GDP series; the short-run adjustment coefficient for remittances on the long-run relationship became insignificant.
- Summary: very few countries show evidence of a stable long-run relationship between remittance flows and U.S. GDP (or other economic indicators). Where evidence exists, results may be influenced by small sample bias and are highly sensitive to lag length and specification.
- Notes:
  - All cointegration tests and vector error correction models used the lag length selected by the sequential log likelihood ratio test, as presented in the Appendix.
  - Results for Nicaragua and Uruguay: very sensitive to lag length and did not converge, respectively; results for these two countries are not shown.

### Distributed lag estimation
- Assumes no long-run relationship; remittances affected by contemporaneous and lagged values of exogenous variables.
- Model form (as presented in the source):
  it
  R
  s
  sts
  P
  s
  stsiit
  ezxr+++=
  ∑∑
  =
  −
  =
  −
  00
  γβα
  where r_it is the quarterly percentage change in remittance flows to country i in period t, α_i is a constant, β_s is a sensitivity parameter to be estimated, and x_{t-s} is a stationary measure of the U.S. business cycle in period t – s.
- Control variables z_{t-s} may include home country GDP growth; models estimated both with and without origin country GDP growth.
- Polynomial distributed (Almon) lag approach used to conserve degrees of freedom; models selected by lowest Akaike information criteria.
- Results:
  - No clear evidence of linkages between remittances and U.S. economic indicators (see Appendix Table A6).
  - Very few long-run coefficients significant at the 5 percent level.
  - Joint tests of the hypothesis that all coefficients in each equation were significantly different from zero could not be rejected in most cases.
  - R-squares were typically low.
- Literature notes: remittances tend to increase when conditions in the origin country deteriorate (e.g. Attzs and Samuel, 2007; Yang and Choi, 2007).

### Dynamic factor model
- Purpose: reduce dimensionality and measure an unobservable U.S. business cycle factor using a state-space / dynamic factor approach.
- Model setup (as presented): state-space representation with disturbance covariance assumptions and Gaussian likelihood; observable vector affected by contemporaneous and lagged business cycle factor and one remittance-specific factor.
- Data and variables:
  - Estimated using first-differenced and HP-filtered data for 6 countries with data at least back to 1995; El Salvador and the Dominican Republic start in 1998.
  - Observed U.S. indicators included: housing starts, GDP, construction employment, services employment.
- Main findings:
  - Results indicate weak, or nonexistent, linkages between remittances and the U.S. indicators over the sample period.
  - In most cases, the coefficients for remittance flows (the a’s from equation (10)) are not significant.
  - U.S. indicators show significant sensitivity to a common cycle (with the exception of Housing Starts, which is not shown).
  - Joint restrictions on coefficients (Appendix Table A7) suggest the U.S. cycle has little influence on remittance behavior.
  - Possible exception: remittances to Mexico, which appear to share some similarities with a broad measure of the U.S. economic cycle; recent data for Mexico continue to suggest an emerging linkage.
- Selected estimated factor loadings (coefficients and standard errors in brackets; significance indicated by ***, **, * for 1, 5, 10 percent levels):
  - First-differences model - estimated factor loadings (US cycle)
    - Argentina: 0.08 [0.53]
    - Brazil: -0.24 [0.72]
    - Dominican Republic: 0.42 [0.38]
    - El Salvador: 0.03 [0.54]
    - Guatemala: 0.15 [0.43]
    - Mexico: 0.51 [0.62]
    - U.S. GDP: 0.30** [0.12]
    - U.S. construction: 0.36*** [0.12]
    - U.S. services: 0.22** [0.08]
  - First-differences model - estimated factor loadings (Remittances)
    - Argentina: 0.49 [0.40]
    - Brazil: 0.94 [0.54]
    - Dominican Republic: -0.08 [0.73]
    - El Salvador: -0.27 [0.46]
    - Guatemala: 0.28 [0.36]
    - Mexico: -0.08 [0.27]
  - Hodrick-Prescott cyclical component model - estimated factor loadings (US cycle)
    - Argentina: -0.13 [0.58]
    - Brazil: -0.10 [0.68]
    - Dominican Republic: -0.06 [0.58]
    - El Salvador: 0.09 [0.48]
    - Guatemala: 0.14 [0.34]
    - Mexico: 0.66* [0.35]
    - U.S. GDP: 0.29*** [0.06]
    - U.S. construction: 0.32*** [0.05]
    - U.S. services: 0.24*** [0.06]
  - Hodrick-Prescott cyclical component model - estimated factor loadings (Remittances)
    - Argentina: 0.55** [0.22]
    - Brazil: 0.67** [0.30]
    - Dominican Republic: 0.31 [0.49]
    - El Salvador: -0.33 [0.57]
    - Guatemala: 0.32 [0.42]
    - Mexico: -0.02 [0.33]
- Plausibility checks:
  - Plotted estimated state variables (U.S. cycle and common remittance factor): U.S. cycle traces downturns of early 1990s and 2001–02.
  - Remittance factor exhibits far less persistence and sharp spikes; Figure A8 (with Latin EMBI+ sovereign debt spread) suggests spikes relate to economic or financial crises, consistent with an “insurance” motive.

### Conclusion and policy-relevant implications
- Using a range of methods, no compelling evidence found of linkages between the U.S. business cycle and remittance flows to Latin America over the sample period 1990–2007.
- Potential explanations (as discussed in the source):
  - Migrant smoothing: migrants may send fixed U.S. dollar amounts each month or quarter, making remittances less volatile than income; survey evidence from the UK supports regular fixed remittances (Boon, 2006).
  - Supply-side inflexibility of immigrant labor: immigrants may have lower “reservation” wages and stronger incentives to remain employed, making remittances less sensitive to host-country unemployment and wage fluctuations (evidence cited: Miller and Meo, 2003; Chiswick and Hurst, 2000; Hansen, 2000).
  - Measurement issues: decline in costs of formal remittance transfer may have diverted informal to formal channels, increasing official estimates and damping apparent sensitivity to host-country economic fluctuations. Freund and Spatafora (2005) estimate informal remittances amount to about 35–75 percent of official remittances to developing countries.
- Cautions:
  - Sample size short for many countries and significant uncertainties remain about data reliability.
  - Recent decline in remittances to Mexico may reflect increased border security, greater immigrant insecurity leading to increased saving (IDB, 2007), slowing down in remittance diversion following declines in transfer costs, or may signal the beginning of linkage between U.S. cycle and remittances.
- Overall policy-relevant takeaway: available evidence suggests remittance flows to Latin America remain relatively insensitive to fluctuations in the U.S. economic cycle, underlining their role as a relatively stable source of external financing, in good times and bad.

*Source: _wp07273 - 1. Summary Statistics for First-Differenced Remittance Data (extracted content).*

### 1. Summary Statistics for First-Differenced Remittance Data ..................................................6

### 1. Summary Statistics for First-Differenced Remittance Data

### Introduction
- Remittance flows sent by migrant workers to Latin America have grown rapidly and for some countries account for a significant share of GDP and rival or dwarf FDI as a source of external financing.
- The paper assesses the extent to which economic conditions in the United States influence remittance flows to Latin America.
- Approach: deliberately empirical; subject data to broad and rigorous testing rather than testing a single theoretical model.
- Paper structure (as provided): literature survey; data and measurement issues; econometric procedures and results; concluding remarks.

### Literature review (selected findings cited in the source)
- Vargas-Silva and Huang (2006): using quarterly data 1981–2003, found some evidence of linkages from the U.S.; for the rest of the world only U.S. inflation Granger-caused remittance flows; home country conditions were unimportant in that study.
- Lueth and Ruiz-Arranz (2006): gravity model on 11 receiving countries; per capita growth (host country cycle proxy) coefficient of 0.03 (positive, significant, yet small), which disappears in some specifications.
- Gupta (2005): estimated remittance elasticity to U.S. employment of 0.13 for India; given a standard deviation of total nonfarm payrolls of less than 0.4 percent, this appears economically insignificant.
- El-Sakka and McNabb (1999): for Egypt, source country conditions were important with a lag, elasticity ~0.03.
- Sayan (2004): for Turkey, no statistically significant relationship between remittances and Germany’s business cycle.
- Aydas, Metin-Ozcan, and Neyapti (2005): find a link for Germany-Turkey but methodology regresses remittance growth on host country income levels (interpretation for business cycle less clear-cut).

### Data
- Definition: remittances broadly as portion of migrant worker earnings sent back; growing use of “personal transfers” definition (United Nations, 2005).
- Measurement issues highlighted:
  - Official data typically include only formal-channel financial transfers; decline in transaction costs may partly reflect diversion of existing flows.
  - Remittances-in-kind typically not counted.
  - Potential mismeasurement: official remittance data might capture other transfers including illegal activity.
- Data used in the paper:
  - Quarterly remittance flow data from 1990 Q1 to 2007 Q2 as reported by national authorities and typically included in the balance of payments.
  - Data were seasonally adjusted (U.S. Census Bureau's X12) and deflated by the U.S. consumer price index.
  - For stationarity, two methods used: first-differencing and Hodrick-Prescott filter cyclical component extraction.
- Note on series: Table 1 presents summary of remittance data (seasonally adjusted first differences of log values in constant US dollars).

### Table 1 — Summary Statistics for First-Differenced Remittance Data, 1990 Q1 - 2007 Q2 (seasonally adjusted first differences of log values in constant US dollars)
- South America
  - Argentina: Sample size 52; Mean -0.534; Maximum -34; Minimum 14.085; Standard deviation 4
  - Brazil: Sample size 49; Mean -0.439; Maximum -30; Minimum 14.214; Standard deviation 4
  - Colombia: Sample size 44; Mean 3.729; Maximum -28; Minimum 11.427; Standard deviation 1
  - Ecuador: Sample size 32; Mean 2.118; Maximum -15; Minimum 6.719; Standard deviation
  - Mexico: Sample size 49; Mean 3.214; Maximum -19; Minimum 5.971; Standard deviation
  - Peru: Sample size 68; Mean 4.230; Maximum -25; Minimum 7.248; Standard deviation
  - Uruguay: Sample size 28; Mean 4.873; Maximum -78; Minimum 24.41; Standard deviation
  - Venezuela: Sample size 40; Mean 2.951; Maximum -42; Minimum 17.435; Standard deviation
- Central America
  - Costa Rica: Sample size 19; Mean 3.719; Maximum -20; Minimum 10.118; Standard deviation
  - El Salvador: Sample size 37; Mean 2.114; Maximum -5; Minimum 4.376; Standard deviation
  - Guatemala: Sample size 53; Mean 4.678; Maximum -20; Minimum 15.511; Standard deviation
  - Honduras: Sample size 17; Mean 6.713; Maximum -24; Minimum 3.47; Standard deviation
  - Nicaragua: Sample size 28; Mean 2.614; Maximum -21; Minimum 6.312; Standard deviation
  - Dominican Republic: Sample size 36; Mean 1.914; Maximum -16; Minimum 5.495; Standard deviation
- Source noted in table: National authorities; authors' calculations.
- Table footnote: 1/ Seasonally adjusted first differences of log values in constant US dollars.
- (Note: the table as presented in the source contains formatting and spacing that may separate fields; the numeric values above are preserved exactly as they appear in the source text.)

### Estimating linkages — Correlations
- Two sets of correlations computed using first-differenced data (HP-filtered results are similar):
  - Cross-country distributions: distribution of correlations between a specified U.S. economic indicator and remittance flows across the sample of 14 countries (Appendix Figures A2 and A3).
  - Within-country distributions: distribution of correlations between a specified country and a range of 19 U.S. economic and financial indicators, contemporaneous and with 1 to 4 quarter lags (Figures A4 and A5).
- Summary of empirical correlation results (Figure 2 summary in source):
  - Simple correlations, averaged across countries and indicators, are close to zero.
  - No single U.S. indicator is strongly correlated across the set of country remittance flows.
  - No single country has remittances that are particularly sensitive, on average, to U.S. economic indicators.
  - Distribution extremes exist (strong positive or strong negative correlations), but extremes are centered around zero; strongly negative correlations are as likely as strongly positive ones.
  - Mexico and El Salvador highlighted: El Salvador exhibits the highest correlations with U.S. economic indicators in the sample.
  - Similar results obtained for housing market and financial indicators.
- Interpretation emphasized in source:
  - The overall randomness and near-zero average correlations make it difficult to attach strong weight to positive extremes; absence of consistent systematic correlation patterns across countries and indicators.

### Key empirical implications (from source content)
- Short-term remittance flows do not show a consistent, strong relationship with U.S. business cycle indicators across the sample of Latin American countries.
- Exceptions exist at the country-indicator level (e.g., El Salvador showing higher correlations), but these are not uniform or pervasive.
- Measurement limitations and data definitions (formal channels only; exclusion of in-kind transfers; possible inclusion of other transfers) complicate inference.

*Source: _wp07273 - 1. Summary Statistics for First-Differenced Remittance Data (extracted content).*

### Appendix highlights Mexico. The indicator with the highest correlation to remittances to

### Appendix highlights Mexico. The indicator with the highest correlation to remittances to

### Correlations between remittances and U.S. indicators
- The indicator with the highest correlation to remittances to Mexico in each period—contemporaneously and for up to 3 lags of the U.S. indicators—are shown.
- In all cases, these maximum correlations are neither large, nor statistically significant.
- The correlations do not exhibit a pattern through time; correlations do not tail off after the peak but rather continue to follow a random process around zero.

### Cointegrating long-run relationships
- Theoretical and empirical reasons suggest no stable long-run relationship between aggregate remittance flows to a country and the level of GDP (or other measure of income or activity) in the host country.
- Key factors that can cause structural shocks to any long-run relationship include: home country income, earning potential and sociodemographic profile of migrants, the stock of migrants, and the average length of stay.
- Short sample period limits identification of long-run relationships: maximum sample of just 17 years (and much less in most cases).
- The Engle-Granger and Johansen procedures for bivariate cointegration indicate that GDP is the most likely candidate for a long-run relationship (see Appendix Tables A2 and A3).
- Caution: system cointegration tests such as Johansen are often biased toward Type I errors in small samples; bias increases with lag length (e.g. Cheung and Lai, 1993).
- Decision rule used: reject the null if the sample size is greater than 20 and the null is rejected at the 5 percent level by 2 out of 3 tests (Engle Granger, Johansen’s trace and max-eigenvalue).
- Relatively stable long-run relationships between remittances and U.S. GDP found for three countries: Brazil, El Salvador, and Peru.
  - Estimated long-run elasticity of remittances to U.S. GDP from VECM models ranges from 1.9 (Peru) to 3.6 (El Salvador).
  - A one standard deviation shock to U.S. real GDP amounts to a 0.5 percent change quarter on quarter.
  - These elasticity estimates are sensitive to the lag length of the VECM and often became weaker as more lags are added.
- Including home country GDP in cointegration:
  - Johansen procedure evidence of cointegration again for Brazil, El Salvador, and Peru (Appendix Table A4).
  - Test results are sensitive to lag length (Appendix Table A5).
  - When home country GDP is included, the positive effect of U.S. GDP on remittances disappears; the cointegrating relationship appears to pick up a common trend between the GDP series, not remittances.
  - The normalized unit coefficients on remittances compare to much higher and statistically significant coefficients on both GDP series; the short-run adjustment coefficient for remittances on the long-run relationship became insignificant.
- Summary: very few countries show evidence of a stable long-run relationship between remittance flows and U.S. GDP (or other economic indicators). Where evidence exists, results may be influenced by small sample bias and are highly sensitive to lag length and specification.
- Notes:
  - All cointegration tests and vector error correction models used the lag length selected by the sequential log likelihood ratio test, as presented in the Appendix.
  - Results for Nicaragua and Uruguay: very sensitive to lag length and did not converge, respectively; results for these two countries are not shown.

### Distributed lag estimation
- Assumes no long-run relationship; remittances affected by contemporaneous and lagged values of exogenous variables.
- Model form (as presented in the source):
  it
  R
  s
  sts
  P
  s
  stsiit
  ezxr+++=
  ∑∑
  =
  −
  =
  −
  00
  γβα
  where r_it is the quarterly percentage change in remittance flows to country i in period t, α_i is a constant, β_s is a sensitivity parameter to be estimated, and x_{t-s} is a stationary measure of the U.S. business cycle in period t – s.
- Control variables z_{t-s} may include home country GDP growth; models estimated both with and without origin country GDP growth.
- Polynomial distributed (Almon) lag approach used to conserve degrees of freedom; models selected by lowest Akaike information criteria.
- Results:
  - No clear evidence of linkages between remittances and U.S. economic indicators (see Appendix Table A6).
  - Very few long-run coefficients significant at the 5 percent level.
  - Joint tests of the hypothesis that all coefficients in each equation were significantly different from zero could not be rejected in most cases.
  - R-squares were typically low.
- Literature notes: remittances tend to increase when conditions in the origin country deteriorate (e.g. Attzs and Samuel, 2007; Yang and Choi, 2007).

### Dynamic factor model
- Purpose: reduce dimensionality and measure an unobservable U.S. business cycle factor using a state-space / dynamic factor approach.
- Model setup (as presented):
  ttt
  uξAy+
  ′
  =
  (2)
  11++
  +=
  ttt
  vΘξξ
  (3)
  with disturbance covariance assumptions (4)-(6) and Gaussianity leading to likelihood (7) and MSE matrix P_{t|t-1} in (8).
- Observable vector affected by contemporaneous and lagged business cycle factor and one remittance-specific factor; expanded state equation represented (9).
- For any remittance variable, remittances equation (10) and expanded forms (11), (12) yield parameters of interest: sensitivity to common business cycle innovations a_{i1} and factor persistence θ_1.
- Data and variables:
  - Estimated using first-differenced and HP-filtered data for 6 countries with data at least back to 1995; El Salvador and the Dominican Republic start in 1998.
  - Observed U.S. indicators included: housing starts, GDP, construction employment, services employment.
- Main findings:
  - Results indicate weak, or nonexistent, linkages between remittances and the U.S. indicators over the sample period.
  - In most cases, the coefficients for remittance flows (the a’s from equation (10)) are not significant.
  - U.S. indicators show significant sensitivity to a common cycle (with the exception of Housing Starts, which is not shown).
  - Joint restrictions on coefficients (Appendix Table A7) suggest the U.S. cycle has little influence on remittance behavior.
  - Possible exception: remittances to Mexico, which appear to share some similarities with a broad measure of the U.S. economic cycle; recent data for Mexico continue to suggest an emerging linkage.
- Selected estimated factor loadings (Table 2; coefficients and standard errors in brackets; significance indicated by ***, **, * for 1, 5, 10 percent levels):
  - First-differences model - estimated factor loadings (US cycle)
    - Argentina: 0.08 [0.53]
    - Brazil: -0.24 [0.72]
    - Dominican Republic: 0.42 [0.38]
    - El Salvador: 0.03 [0.54]
    - Guatemala: 0.15 [0.43]
    - Mexico: 0.51 [0.62]
    - U.S. GDP: 0.30** [0.12]
    - U.S. construction: 0.36*** [0.12]
    - U.S. services: 0.22** [0.08]
  - First-differences model - estimated factor loadings (Remittances)
    - Argentina: 0.49 [0.40]
    - Brazil: 0.94 [0.54]
    - Dominican Republic: -0.08 [0.73]
    - El Salvador: -0.27 [0.46]
    - Guatemala: 0.28 [0.36]
    - Mexico: -0.08 [0.27]
  - Hodrick-Prescott cyclical component model - estimated factor loadings (US cycle)
    - Argentina: -0.13 [0.58]
    - Brazil: -0.10 [0.68]
    - Dominican Republic: -0.06 [0.58]
    - El Salvador: 0.09 [0.48]
    - Guatemala: 0.14 [0.34]
    - Mexico: 0.66* [0.35]
    - U.S. GDP: 0.29*** [0.06]
    - U.S. construction: 0.32*** [0.05]
    - U.S. services: 0.24*** [0.06]
  - Hodrick-Prescott cyclical component model - estimated factor loadings (Remittances)
    - Argentina: 0.55** [0.22]
    - Brazil: 0.67** [0.30]
    - Dominican Republic: 0.31 [0.49]
    - El Salvador: -0.33 [0.57]
    - Guatemala: 0.32 [0.42]
    - Mexico: -0.02 [0.33]
- Plausibility checks:
  - Plotted estimated state variables (U.S. cycle and common remittance factor): U.S. cycle traces downturns of early 1990s and 2001–02.
  - Remittance factor exhibits far less persistence and sharp spikes; Figure A8 (with Latin EMBI+ sovereign debt spread) suggests spikes relate to economic or financial crises, consistent with an “insurance” motive.

### Conclusion and policy-relevant implications
- Using a range of methods, no compelling evidence found of linkages between the U.S. business cycle and remittance flows to Latin America over the sample period 1990–2007.
- Potential explanations:
  - Migrant smoothing: migrants may send fixed U.S. dollar amounts each month or quarter, making remittances less volatile than income; survey evidence from the UK supports regular fixed remittances (Boon, 2006).
  - Supply-side inflexibility of immigrant labor: immigrants may have lower “reservation” wages and stronger incentives to remain employed, making remittances less sensitive to host-country unemployment and wage fluctuations (evidence cited: Miller and Meo, 2003; Chiswick and Hurst, 2000; Hansen, 2000).
  - Measurement issues: decline in costs of formal remittance transfer may have diverted informal to formal channels, increasing official estimates and damping apparent sensitivity to host-country economic fluctuations. Freund and Spatafora (2005) estimate informal remittances amount to about 35–75 percent of official remittances to developing countries.
- Cautions:
  - Sample size short for many countries and significant uncertainties remain about data reliability.
  - Recent decline in remittances to Mexico may reflect increased border security, greater immigrant insecurity leading to increased saving (IDB, 2007), slowing down in remittance diversion following declines in transfer costs, or may signal the beginning of linkage between U.S. cycle and remittances.
- Overall policy-relevant takeaway: available evidence suggests remittance flows to Latin America remain relatively insensitive to fluctuations in the U.S. economic cycle, underlining their role as a relatively stable source of external financing, in good times and bad.

*Source: Authors' calculations, Appendix highlights Mexico. The indicator with the highest correlation to remittances to Mexico in each period—contemporaneously and for up to 3 lags of the U.S. indicators—are shown.*

### References

### _wp07273 - References

### Literature Cited: thematic coverage
- Natural disasters and remittances: Attzs, Marlene and Wendell Samuel, 2007. “Natural Disasters and Remittances in Central America and the Caribbean,” Mimeo.
- Determinants and macroeconomic drivers of remittances: Aydas et al. 2005; El-Sakka and McNabb; Freund and Spatafora, 2005; Giuliano and Ruiz-Arranz, 2006; Gupta, 2005; Lueth and Ruiz-Arranz, 2006; Vargas-Silva and Huang, 2006; Rapoport and Docquier, 2005.
- Remittances, costs, and market structure: Boon, 2006; Orozco, 2004 and 2006; Pew and Inter-American Dialogue reports.
- Labor-market and migration dynamics: Chiswick and Hurst, 2000; Miller and Neo, 2003; Hansen, 2000; Lianos, 1997; Lowell and De La Garza, 2000; Stark, 1995.
- Econometric and time-series methods referenced: Cheung and Lai, 1993; Croux, Renault, and Werker, 2004; Stock and Watson, 1988; Johansen and Engle-Granger methodologies applied in appendix tables.
- Data and statistical guidance: United Nations, 2005 (BOPTEG Outcome Paper #9B).

### Appendix: tests, estimations, and key quantitative notes
- Table A1. Levels VAR lag length tests and information criteria
  - Figures indicate the lag length selected by each test and criteria.
  - Entries shown as concatenated digits per country (as reported): Argentina331; Brazil361; Colombia111; Costa Rica666; Dominican Republic331; Ecuador111; El Salvador121; Guatemala311; Honduras444; Mexico141; Nicaragua111; Peru153; Uruguay661; Venezuela311.
  - For the three-variable system (Remittances, U.S. GDP, and domestic GDP) entries: Argentina261; Brazil551; Colombia351; Ecuador161; El Salvador561; Mexico221; Peru366; Venezuela161. (Results reported only for countries with quarterly domestic GDP and sufficient observations.)
- Table A2. Cointegration Tests: Engle-Granger probability values (null: no cointegration)
  - Lag length used in the test was selected by the Schwarz Information Criterion.
  - Figures in bold indicate where the null may be rejected at the 5 percent level.
  - Example probability values as reported (by country and indicator, concatenated in table): Argentina 0.0260.0180.0120.0000.0010.021; Brazil 0.0900.0820.1300.1390.0930.066; Costa Rica 0.5060.0080.0070.0090.1880.006; Dominican Republic 0.1730.0000.0580.0240.0160.000.
- Table A3. Cointegration Tests for Remittances and U.S. GDP (Engle-Granger and Johansen tests)
  - Null hypothesis: no cointegration. Lag length in Engle-Granger selected by Schwarz.
  - Based on sequential small-sample modified log-likelihood ratio tests for Johansen.
  - Decision rule: If sample size > 20, reject null if at least 2 out of 3 cointegration tests can be rejected at the 5 percent level.
  - Example reported rows: Argentina 5 2 3; Brazil 4 9 30; Colombia 4 4 1; El Salvador 3 7 1 (with Engle-Granger p-value 0.000 and Johansen trace and max-eigen p-values 0.01 0.01; rejection = Yes); Peru 6 8 1 (Engle-Granger p-value 0.000; Johansen trace and max-eigen p-values 0.01 0.02; rejection = Yes).
- Table A4. Johansen cointegration tests for remittances and U.S. GDP (multiple lag lengths)
  - Lag lengths reported: 4, 6, 8. Figures in bold indicate rejection at 5 percent.
  - Examples: Argentina trace/max-eigen: 0.36/0.28 (lag 4); Brazil entries include 0.000.00; El Salvador entries include 0.01/0.01 and 0.000.00.
- Table A5. Johansen cointegration tests for remittances, U.S. GDP, and domestic GDP
  - Lag lengths reported: multiple (including 2, 4, 6). Examples: Argentina 2 0.21 0.16 and Engle-Granger p-values 0.02 0.01 0.02 0.01 (reject = No); Brazil trace/max-eigen entries 50.12 0.24 and Engle-Granger p-values 0.000.000.010.01 (reject = Yes); El Salvador entries include 60.01 0.07 and Engle-Granger p-values 0.010.01 0.000.00 (reject = Yes).
  - Decision rule: If sample size > 20, reject null if at least 1 of the cointegration tests can be rejected at the 5 percent level.
- Table A6. Distributed Lag Estimations — Results Summary
  - Two specifications: polynomial distributed lag without origin country control; with origin country control.
  - Results include "Sum of coefficients on U.S. variables", "R-squared", and "F-statistic (p-value)"; significance notation: ** (5 percent), * (10 percent).
  - Examples (selected reported numbers, preserved exactly):
    - U.S. Housing Starts, Colombia: Sum of coefficients 0.7 R-squared 0.32 F-statistic 0.01; with origin country control: Sum -1.2-3.9 **0.510.00.
    - U.S. Gross Domestic Product, Peru: Sum of coefficients 6.6 ** R-squared 0.29 F-statistic 0.07; with origin country control: Sum 7.6 0.10 0.29 0.38.
    - U.S. Gross Domestic Product, Venezuela: Sum 19.6 ** R-squared 0.27 F-statistic 0.01; with origin country control: Sum 21.1 ** -2.6 0.42 0.02.
    - U.S. Construction Employment, Venezuela: Sum 9.0 ** R-squared 0.14 F-statistic 0.15; with origin country control: Sum 9.7 -1.2 *0.24 0.22.
    - U.S. Services Employment, Brazil: Sum -12.2 *0.11 0.14; with origin country control: -11.1 2.9 0.20 0.14.
    - U.S. ISM Manufacturing Index, Ecuador: Sum 1.0 *0.19 0.12; with origin country control: -0.2 0.1 0.44 0.02.
  - Source note: ** (*) implies significance at the 5 (10) percent level.
- Table A7. Wald tests on factor model coefficients (first-differenced and Hodrick-Prescott filtered data)
  - Reported tests, critical values, degrees of freedom, and probabilities:
    - First-differenced data:
      - Test 1 (βi2 = 0 for all i): Null critical value 2.96 probability 0.8187
      - Test 2 (βi2 = βi4 = 0): 4.81 probability 0.9642
      - Test 3 (βi2 = βi3 = βi4 = 0): 33.218 probability 0.0157
      - Test 4 (βi3 = 0): 9.86 probability 0.1338
    - Hodrick-Prescott filtered data:
      - Test 1: 5.46 probability 0.4946
      - Test 2: 14.412 probability 0.2780
      - Test 3: 26.918 probability 0.0811
      - Test 4: 8.76 probability 0.1918
  - Nulls described (i)–(iv) indicating coefficients of zero on various contemporaneous and lagged common cyclical factors and remittance factor.
- Figure A1. Impulse responses of remittances to U.S. GDP
  - Note: Estimated impulse responses to a one standard deviation shock to U.S. GDP—which amounts to a 0.5 percent change quarter on quarter—from vector error correction (VECM) models with lag lengths chosen by the small sample adjusted LR test.
  - Two-variable system (Remittances and U.S. GDP) and three-variable system (Remittances, U.S. GDP, and Domestic GDP) shown for Brazil, El Salvador, and Peru across 1–20 quarters; vertical scales reported in "Percent change" (two-variable) and "Percent change" (three-variable) with ranges explicitly labeled (two-variable: -1.0 to 3.0; three-variable: -4.0 to 6.0).
- Figures A2–A6. Correlations of remittances to U.S. indicators (first-differences)
  - Source: National authorities; Haver analytics; and authors' calculations.
  - Correlations use the first difference of the log for each series. Remittance series seasonally-adjusted using U.S. Census Bureau's X12 filter and deflated using U.S. CPI.
  - Charts display lowest, highest, and mean correlations across indicators and countries at lags tt, t-1, t-2, t-3, t-4.
  - Figure A6 (Mexico): note that the correlation coefficient is significant at the 5 percent level when higher than 0.28; sample charts for Existing Home Sales, Mortgage Rates (inverted), Leisure Services Employment, Housing Starts with lag profiles tt-1 to tt-4 and coefficient ranges reported (e.g., Existing Home Sales axis -0.15 to 0.25; Leisure Services Employment axis -0.30 to 0.20).
- Figure A7. Remittances common factor model: unobserved components
  - Model using first-differences with 2-standard error bounds.
  - Displayed common factors 1 (the U.S. cycle) and 2 (remittances) for period 1990 Q1 - 2007 Q2.
  - Vertical scales for common factor 1: -10 to 8; for common factor 2: -4 to 4.
- Figure A8. Remittances common factor and sovereign bond yield spreads
  - Time series plotted from 1994Q2 through 2007Q2.
  - Left-hand scale: Remittances common factor (range -3 to 3). Right-hand scale: EMBI+ Latin America stripped spread over US Treasuries (percent, right-hand scale) with vertical range 0 to 18.

*Source: _wp07273 - References; appendix tables and figures as reported in the source PDF.*

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