## 1. Developing Countries: Workers’ Remittances

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### Overview and motivations
- International integration in the early 21st century includes increased flows of labor services alongside goods, services, and capital.
- Recorded remittance increases: in some developing countries remittances dwarf official development assistance, foreign direct investment, or other capital flows.
- Empirical magnitudes cited:
  - In 2007, remittance flows to sub-Saharan Africa were equal in magnitude to flows of official development assistance.
  - Remittance flows account for some 17 percent of GDP and 77 percent of exports in El Salvador.
  - Remittance flows are over 20 percent of GDP and nearly 50 percent of exports in Honduras.
  - In these countries, remittance flows are more than five times larger than FDI flows.
- Macroeconomic concern: large remittance inflows could produce “Dutch disease,” i.e., appreciation of the equilibrium real exchange rate undermining international competitiveness, particularly nontraditional exports.

### Analytical framework and theoretical results
- Strategy: simple “workhorse” small open economy model (building on Montiel (1999)) to derive remittance effects on the equilibrium real exchange rate.
- Benchmark theoretical result:
  - A permanent increase in worker remittances leads to an appreciation of the long-run equilibrium real exchange rate comparable to a similar permanent increase in exogenous international transfers.
- Model caveat and ambiguity:
  - The benchmark case is a special one; reasonable modifications can moderate or reverse the expected appreciation.
  - Multiple channels can alter the sign and magnitude of the effect (induced remittances, risk-premium pricing, preferences over tradables vs nontradables, transactions costs, openness, factor intensities).

### Key theoretical channels (from Appendix A)
- Exogenous remittances:
  - Permanent remittance increase shifts external balance (EB) right → equilibrium real appreciation and higher private absorption; magnitude depends on traded-goods share and PPF curvature.
- Induced remittances:
  - rem = μ_0 + μ_1 y ; if remittances decline when domestic income rises (μ_1 < 0), EB slope flattens and autonomous remittance effects on e are weakened.
- Risk-premium channel:
  - If r* = r_W + p(a + rem/r*), a permanent remittance increase can be offset by a deterioration in net international assets so remittance-inclusive national wealth is unchanged; result: no long-run effect on EB and no long-run effect on equilibrium e.
- Preference/composition and transaction-cost channels:
  - If remittances are directly treated as tradable consumption (household utility adjusted), the EB shift is smaller and the internal balance (IB) shifts right → appreciation effect weakened; in a nonmonetary world with remittances fully spent on tradables and zero transactions costs, permanent remittance increases have no effect on long-run e.
  - With nonzero transaction costs, outcomes become indeterminate; depending on which sector bears transaction costs, appreciation or depreciation may result.
- Theoretical conclusion:
  - While appreciation is a plausible outcome in the simple exogenous-remittance case, the net effect is theoretically ambiguous and depends on country-specific channels and parameters.

### Empirical approach
- Data and method:
  - Unbalanced panel annual data 1980-2007.
  - Dependent variable: log of the effective (trade-weighted) real exchange rate (REER).
  - Fundamentals included: workers’ remittances-to-GDP (WREC), official aid-to-GDP, net international assets (NFA), log real per capita GDP, fertility, terms of trade, government consumption-to-GDP, trade and capital account restriction indexes (and black market premium), administered agricultural prices and their maxima, incidence of natural disasters.
  - Estimation: Dynamic least squares (DOLS) with fixed effects, one lead and one lag of changes.
  - Panel unit root results: REER nonstationary in almost all countries; most fundamentals I(1) (exceptions: natural disaster, black market premium, capital account liberalization).
- Identification objective: estimate effects of sustained/permanent remittance changes on equilibrium REER using panel cointegration to identify common stochastic trends.

### Main empirical findings
- Aggregate importance (1980–2010 and recent periods):
  - Remittance inflows averaged about 5¼ percent of GDP for a group of 134 countries with remittance data over 2001–10, versus 4½ percent over 1970-2007.
  - Mean workers' remittances-to-GDP ratio across countries and time: 4.5 (1970 - 2010), 5.3 (2001 - 2010), 4.5 (2010).
  - Maximum workers' remittances-to-GDP ratio across countries and time: 108.7, 49.5, 37.0.
  - Number of countries: 134, 129, 156.
  - Number of observations: 3,471, 1,262, 156.
  - Cross-country standard deviation: 7.0, 6.6, 6.8.
- Relative importance in balance of payments (means across countries and time, 2001-2010):
  - Ratio of Workers' Remittances to Official Transfers: 20.3
  - Ratio of Workers' Remittances to Official Capital Flows: 18.5
  - Ratio of Workers' Remittances to Private Capital Flows: 2.7
  - Ratio of Workers' Remittances to Exports: 0.4
- Recent observation (2010, means across countries):
  - Ratio of Workers' Remittances to Official Transfers: 16.1
  - Ratio of Workers' Remittances to Official Capital Flows: 4.7
  - Ratio of Workers' Remittances to Private Capital Flows: 2.8
  - Ratio of Workers' Remittances to Exports: 0.5
- Core panel estimation results (preserve reported estimates and statistical significance):
  - All countries (Table 4 highlights):
    - Full fundamentals included (column (1)): WREC coefficient = -0.0013 (t-statistic -0.2576) — negative sign, statistically insignificant.
    - Restricted specification including black market premium (column (4)): WREC = 0.0189*** (t-statistic 2.7448). Interpretation in text: a one percentage-point increase in the remittance ratio would result in an equilibrium real appreciation of about two-hundredth of one percent (coefficient 0.019).
    - General observation: sign and significance of WREC depend on sample and fundamentals; positive magnitudes are very small.
  - Low-income countries (Table 5):
    - WREC coefficients vary in sign and significance across specifications; generally weak and often insignificant.
  - Low and lower-middle-income countries (Table 6):
    - WREC coefficients are positive and statistically significant in most specifications: e.g., column (1) WREC = 0.0116** (t-statistic 2.3146); column (4) WREC = 0.0265*** (t-statistic 3.2704).
    - Magnitude: effects remain small (between one and three hundredths of one percent in many specifications).
  - Robustness and heterogeneity:
    - Restricting country samples to be identical across specifications generally leaves small effects; sign flips often attributable to sample changes.
    - Regional differences: Asia shows consistently negative coefficients (often significant); Middle East/Africa tends to show conventional positive and often significant effects.
    - Trade and capital account openness: among low and lower-middle-income countries, relatively closed countries tend to show stronger conventional appreciation effects; more open countries show smaller and less certain effects.
    - Panel IV/interaction regressions: significant interaction only with real GDP per capita (richer countries more likely to display conventional positive relationship); interactions with procyclicality, capital account openness, or openness not consistently significant.
- Empirical summary:
  - Sign and statistical significance of remittance effect on equilibrium REER are not robust across samples and specifications.
  - Where positive and significant, magnitudes are consistently very small (semi-elasticities on the order of 0.01–0.03 in many specifications).
  - Evidence supports heterogeneity: conventional appreciation more likely in poorer, less open economies and in Middle East/North Africa; Asia often shows opposite sign.

### Summary, conclusions, and policy implications
- The conventional presumption that permanent increases in remittances cause equilibrium real appreciation is:
  - Theoretically plausible in the simple exogenous-remittance framework, but
  - Not generally robust once induced remittances, risk-premium pricing, preference/composition effects, transactions costs, and openness are considered.
- Main conclusions:
  - Net effect of remittances on the long-run equilibrium real exchange rate can be small, muted, absent, or even reversed depending on country characteristics and operative channels.
  - Panel cointegration estimates find effects are not robust across countries and fundamentals; when conventional effects are present magnitudes are very small (example reported coefficient 0.019 ≈ 0.02 percent appreciation per one percentage-point rise in remittance ratio).
  - Heterogeneity: closed low- and lower-middle-income countries and Middle East/North Africa more likely to experience conventional appreciation; Asia less likely and sometimes shows depreciation; richer recipient countries more likely to display conventional positive relationship.
- Policy implication:
  - Dutch disease concerns from remittance inflows may be overstated in many cases: remittance inflows need not necessarily generate sizable long-run contractions in traded goods production or reduced long-run growth.
  - Policy assessment should be country-specific, focusing on openness, financial market pricing of remittances, the composition of remittance spending (tradables vs nontradables), and possible induced patterns in remittance behavior.

### Appendix summaries
- Appendix A (The Model) highlights:
  - Two-sector model with traded and nontraded goods, flexible domestic wages/prices, fixed nominal exchange rate; real exchange rate e is relative price of traded goods in terms of nontraded goods.
  - Labor market and production conditions yield aggregate output y(e) with y’ < 0.
  - Household demand features transaction costs c_T(m,c) = τ(m/c), money demand m = h(r*) c with h’ < 0, and Cobb-Douglas-like allocation c_T = θ c, c_N = (1 – θ) e c.
  - Consolidated public sector maintains exchange parity; government lumpsum tax t = i* m.
  - External interest rate r* = r_W + p(a) with p decreasing in net international investment position a.
  - Steady-state external balance condition: 0 = y_T(e) + rem + r* a* - (τ* + θ) c and comparative statics show conventional ∂e/∂rem < 0 in benchmark specification, but extensions alter sign and magnitude.
  - Extensions explicitly model induced remittances rem = μ_0 + μ_1 y, risk-premium dependence r* = r_W + p(a + rem/r*), and direct utility effects where remittances enter household consumption of tradables.
- Appendix B (Country Sample) classifies countries by World Bank income groups and lists sample countries in high/upper-middle, lower-middle, and low-income groups used in empirical work.

*Italic source: IMF Working Paper, _wp10287.*

### 1. Developing Countries: Workers’ Remittances ......................................................................5

### 1. Developing Countries: Workers’ Remittances

### Overview and motivations
- International economic integration in the early 21st century includes increased flows of labor services as well as goods, services, and capital.
- There has been a sharp recorded increase in flows of worker remittances to many developing countries; in some cases remittances dwarf other resource inflows such as development assistance, foreign direct investment, or other capital flows.
- Empirical magnitudes cited:
  - In 2007, remittance flows to sub-Saharan Africa were equal in magnitude to flows of official development assistance.
  - Remittance flows now account for some 17 percent of GDP and 77 percent of exports in El Salvador.
  - Remittance flows are over 20 percent of GDP and nearly 50 percent of exports in Honduras.
  - In these countries, remittance flows are more than five times larger than FDI flows.
- Macroeconomic concern highlighted: large inflows of worker remittances could lead to “Dutch disease,” i.e., an appreciation of the equilibrium real exchange rate that undermines international competitiveness, particularly of nontraditional exports.

### Analytical framework and theoretical results
- Strategy: use a simple “workhorse” model of a small open economy (building on Montiel (1999)) to derive the standard result on remittances and the equilibrium real exchange rate.
- Benchmark theoretical result:
  - A permanent increase in the flow of worker remittances results in an appreciation of the long-run equilibrium real exchange rate comparable to that which would result from a similar permanent increase in the receipt of exogenous international transfers.
- Model caveat and theoretical ambiguity:
  - The benchmark case is described as a rather special one.
  - Reasonable modifications in modeling the factors driving remittances, or in the macroeconomic roles that remittances play, could moderate or even reverse the expected impact on the equilibrium real exchange rate.
  - Thus, the presumption that a permanent increase in workers’ remittances causes an appreciation in the long-run equilibrium real exchange rate is too facile; multiple possible outcomes exist depending on the detailed macroeconomic roles of remittances.

### Empirical approach and findings
- Empirical strategy:
  - Apply panel cointegration techniques.
  - Employ the largest set of countries for which remittance data are available.
  - Control for a large number of fundamental determinants of the equilibrium real exchange rate.
- Main empirical findings:
  - Despite the theoretical ambiguities, empirical evidence is consistent with an appreciation of the equilibrium real exchange rate in response to a sustained inflow of workers’ remittances.
  - The empirical effects are quantitatively very small.
- Policy implication drawn from empirical magnitudes:
  - The presence of substantial remittance inflows need not necessarily pose a challenge to an export-oriented development strategy.

### Paper organization (informative)
- Section I: overview of the scale of the remittance phenomenon.
- Section II: analytical framework, derivation of standard result, and analysis of conditions under which remittance effects could differ.
- Section III: review of previous empirical work and presentation of the paper’s panel estimates.

*Source: _wp10287 - 1. Developing Countries: Workers’ Remittances ......................................................................5*

### Section IV. The final section summarizes and concludes. Appendix A provides a formal

### _wp10287 - Section IV. The final section summarizes and concludes. Appendix A provides a formal

### I. How important are remittance flows?
- Remittance inflows averaged about 5¼ percent of GDP for a group of 134 countries that have remittance data over the past decade (2001–10), compared to 4½ percent over the entire 1970-2007 period.
- Aggregate context and comparisons (developing countries):
  - Mean workers' remittances-to-GDP ratio across countries and time: 4.5 (1970 - 2010), 5.3 (2001 - 2010), 4.5 (2010).
  - Maximum workers' remittances-to-GDP ratio across countries and time: 108.7, 49.5, 37.0.
  - Number of countries: 134, 129, 156.
  - Number of observations: 3,471, 1,262, 156.
  - Cross-country standard deviation: 7.0, 6.6, 6.8.
- Relative importance in balance of payments (recent period, 2001-2010; means across countries and time):
  - Ratio of Workers' Remittances to Official Transfers: 20.3
  - Ratio of Workers' Remittances to Official Capital Flows: 18.5
  - Ratio of Workers' Remittances to Private Capital Flows: 2.7
  - Ratio of Workers' Remittances to Exports: 0.4
- Recent observation: 2010 (means across countries):
  - Ratio of Workers' Remittances to Official Transfers: 16.1
  - Ratio of Workers' Remittances to Official Capital Flows: 4.7
  - Ratio of Workers' Remittances to Private Capital Flows: 2.8
  - Ratio of Workers' Remittances to Exports: 0.5
- Geography and recipients:
  - Remittance receipts are larger in Developing Asia and Latin America than in Africa, Central and Eastern Europe, and the CIS.
  - Top recipient countries by remittances-to-GDP (2010) include small diasporic economies and larger economies such as Nigeria and Bangladesh with remittances in excess of 10 percent of GDP (list shown in Figure 3 of source).

### II. Theory: Effects of remittances on the equilibrium real exchange rate
- Analytical framework:
  - Small open economy, fixed nominal exchange rate, flexible domestic wages and prices.
  - Two-sector dependent economy: traded and nontraded goods; real exchange rate e = relative price of traded goods in terms of nontraded goods.
  - Internal balance (IB locus): higher household consumption c → requires real appreciation to clear nontraded goods market (IB negative slope).
  - External balance (EB locus): current account = trade balance + remittances + interest payments/receipts; EB has positive slope.
  - Equilibrium real exchange rate e* at intersection of IB and EB.
- Case analyses and qualitative implications:
  - B. Exogenous remittances:
    - Permanent increase in remittances shifts EB right → equilibrium real appreciation and higher private absorption (standard result).
    - Magnitude depends on: (a) share of traded goods in domestic absorption (higher share → smaller appreciation), (b) curvature of PPF (weaker diminishing returns → smaller appreciation).
    - Expectation: more open economies, flexible labor markets, traded-sector intensive in factors used by nontraded sector → smaller real exchange rate response.
  - C. Induced remittances (remittances endogenous to domestic income):
    - If remittances decline when domestic income rises, EB slope flattens → autonomous remittance changes have weaker effects on equilibrium e; induced remittances weaken but do not reverse conventional appreciation result.
  - D. Effects via the risk premium:
    - If risk premium depends on international investment position plus capitalized value of permanent remittances, a permanent remittance increase will be offset by a deterioration in the net international investment position so that the remittance-inclusive national wealth is unchanged in steady state.
    - Result: no long-run effect on EB locus and thus no long-run effect on equilibrium e; the conventional appreciation presumption can be eliminated.
  - E. Effects via household utility (preferences over tradables vs nontradables):
    - If remittances are directly spent on traded goods (households treat remittances as altering marginal utility of traded consumption), the EB shift is smaller and IB shifts right → weakens appreciation effect.
    - In a nonmonetary economy with remittances fully spent on tradables and zero transactions costs, permanent remittance increases have no effect on long-run equilibrium e.
    - With nonzero transactions costs, outcomes become indeterminate; depending on whether transaction costs are borne in traded or nontraded goods, appreciation or depreciation may result.
- Theoretical conclusion:
  - While a priori there is a presumption for appreciation, multiple channels (openness, induced remittances, risk-premium pricing, preference/composition effects, transactions-costs) can weaken, eliminate, or reverse that presumption. The net effect is thus empirical.

### III. Empirical evidence overview
- Literature findings (selected studies):
  - Bourdet and Falck (Cape Verde 1980–2000), Hyder and Mahboob (Pakistan 1978–2005), Saadi-Sedik and Petri (Jordan 1964–2005): remittances associated with appreciation (conventional).
  - Izquierdo and Montiel (six Central American countries 1960–2004): mixed results; some countries no effect, others conventional effect but differing magnitudes.
  - Panel studies (Amuedo-Dorantes & Pozo 1978–98; Holzner; Lopez, Molina, & Bussolo; Lartey, Mandelman & Acosta; Acosta, Baerg & Mandelman): generally find conventional appreciation effect, but quantitative magnitudes vary and effects attenuate with financial development or legal origin.
  - Rajan & Subramanian (1990s sample): did not find predicted sectoral consequences.
  - Mongardini & Rayner (29 sub-Saharan African countries): no significant remittance effect on long-run REER; aid associated with long-run depreciation.
- Methodological note:
  - Many panel studies estimate contemporaneous effects on actual REER rather than cointegrating relations; transitory versus permanent effects may differ.
  - Current paper uses panel cointegration to identify common stochastic trends and estimate effects of sustained/permanent remittance changes on equilibrium REER.

### IV. Panel evidence from this study
- Data, fundamentals, and method:
  - Unbalanced panel annual data 1980-2007.
  - Dependent variable: log of the effective (trade-weighted) real exchange rate (REER).
  - Fundamentals include: workers’ remittances-to-GDP (WREC), official aid-to-GDP, net international assets (NFA), real per capita GDP (log), fertility (as dependency proxy), terms of trade, government consumption-to-GDP, trade and capital account restriction indexes (and black market premium), administered agricultural prices, maximum agricultural price intervention, incidence of natural disasters.
  - Estimation: Dynamic least squares (DOLS) with fixed effects, one lead and one lag of changes.
  - Panel unit root tests: REER nonstationary in almost all countries; most fundamentals I(1) (exceptions: natural disaster, black market premium, capital account liberalization).
- Key empirical results (selected, preserving reported estimates):
  - All countries (Table 4 highlights):
    - When full set of fundamentals included (column (1)), WREC coefficient = -0.0013 (t-statistic -0.2576) — sign inconsistent with conventional view and statistically insignificant.
    - Restricted sample/specifications (column (4), black market premium included): WREC = 0.0189*** (t-statistic 2.7448). Interpretation: estimated semi-elasticity; a one percentage-point increase in remittance ratio would result in an equilibrium real appreciation of about two-hundredth of one percent (coefficient 0.019).
    - General observation: remittance coefficient sign and significance depend on country sample and set of fundamentals; magnitudes are very small when positive.
  - Low-income countries (Table 5):
    - WREC coefficients vary in sign and significance across specifications; generally weak and often insignificant.
  - Low and lower-middle-income countries (Table 6):
    - WREC coefficients are positive and statistically significant in most specifications: e.g., column (1) WREC = 0.0116** (t-statistic 2.3146); column (4) WREC = 0.0265*** (t-statistic 3.2704).
    - Magnitude: effects remain small (between one and three hundredths of one percent in many specifications).
  - Robustness and heterogeneity (Table 7 and additional checks):
    - Restricting country samples to be identical across specifications generally leaves small effects; signs sometimes flip attributable to sample changes.
    - Regional differences: Asia shows consistently negative coefficients (often significant); Middle East/Africa tends to show conventional positive and often significant effects.
    - Trade and capital account openness: among low and lower-middle-income countries, relatively closed countries (low trade or capital account openness) tend to show stronger conventional appreciation effect; more open countries show smaller and less certain effects.
    - Panel IV/interaction regressions (Table 8): significant interaction only with real GDP per capita (richer countries more likely to display conventional positive relationship); interactions with procyclicality, capital account openness, or openness not consistently significant.
- Empirical summary:
  - Sign and statistical significance of remittance effect on equilibrium REER are not robust across samples and specifications.
  - When positive and significant, magnitudes are consistently very small (semi-elasticities on the order of 0.01–0.03 in many specifications).
  - Overall, evidence supports heterogeneity: conventional appreciation more likely in poorer, less open economies and in Middle East/North Africa; Asia often shows opposite sign.

### V. Summary and conclusions (policy-relevant findings)
- The conventional presumption—permanent increases in remittance inflows cause equilibrium real appreciation—is:
  - Theoretically plausible in a simple exogenous-remittance framework, but
  - Not generally robust once additional channels are considered (induced remittances, risk-premium pricing, preference effects, transactions costs).
- Main conclusions from theoretical and empirical work:
  - The net effect of remittances on the long-run equilibrium real exchange rate can be small, muted, absent, or even reversed depending on country characteristics and operative channels.
  - Empirical panel cointegration estimates find:
    - Effect is not robust across country samples and fundamental sets.
    - Where a conventional effect is present, its magnitude is very small (example: coefficient 0.019 interpreted as about 0.02 percent appreciation for a one percentage-point rise in remittance ratio).
    - Heterogeneity: closed low- and lower-middle-income countries and Middle East/North Africa more likely to experience conventional appreciation; Asia less likely and sometimes shows depreciation.
    - Richer recipient countries more likely to show the conventional positive relationship.
- Policy implication:
  - Dutch disease concerns from remittance inflows may be overstated in many cases: remittance inflows need not necessarily generate sizable long-run contractions in traded goods production or reduced long-run growth.
  - Policy assessment should be country-specific, focusing on openness, financial market pricing of remittances, the composition of remittance spending (tradables vs nontradables), and possible induced patterns in remittance behavior.

*Italic source: IMF Working Paper, Section IV (Summary and Conclusions) from _wp10287.*

### Appendix A. The Model

### Appendix A. The Model

### A. Supply
- Production:
  - Traded and nontraded goods produced in amounts y_T and y_N using sector-specific factors and homogeneous labor.
  - Sectoral production functions: y_T(L_T) and y_N(L_N).
- Labor market:
  - Profit-maximizing conditions: y_T’(L_T) = w and y_N’(L_N) = we, implying labor demand functions L_T(w) and L_N(we).
  - Labor market equilibrium: L_T(w) + L_N(we) = L  (1)
  - Equilibrium real wage as a function of the real exchange rate:
    - w = w(e), with w’ = -w L_N’/(L_T’ + L_N’) < 0  (2)
- Sectoral outputs:
  - y_T = y_T(L_T(w)) with y_T’ > 0  (3a)
  - y_N = y_N(L_N(we)) with y_N’ < 0  (3b)
- Aggregate real output (measured in traded goods):
  - y(e) = y_T(L_T(w(e))) + y_N(L_N(w(e)e)), with y’ = -y_N/e^2 < 0  (3c)

### B. Demand — Households
- Household assets and portfolio:
  - Net worth a allocated between net foreign bonds f_H and domestic money m:
    - a = f_H + m  (4)
  - Foreign bonds pay interest r*; money reduces transaction costs.
- Transaction costs:
  - Transaction cost function: c_T(m, c) = τ(m/c), with τ’ < 0 and τ’’ > 0  (5)
- Budget constraint and dynamics:
  - Household budget constraint (flow form):
    - ȧ = y_H + rem + r*f_H - tc - τ(c, m)  (6)  [as in text structure]
  - Alternative written form used:
    - ȧ = ȧ = *1_H ayremrf tc τ = + + - - - + (6’)  [text uses (6’) as reformulation]
  - Transversality: lim_{T→∞} exp(-ρT) a(T) = 0  (11)
- Preferences and consumption allocation:
  - Total consumption expenditure c = c_T + c_N/e.
  - Utility: constant-relative-risk-aversion, Cobb-Douglas between traded and nontraded goods:
    - U(c_T, c_N, e) = κ [θ c_T^{(σ-1)/σ} + (1-θ) (e c_N)^{(σ-1)/σ}]^{(1-σ)/(1-σ)} (7)  [text form retained]
  - Constant shares:
    - c_T = θ c
    - c_N = (1 – θ) e c  (8)
  - Indirect utility expressed with κ positive constant (9).
- Household optimization:
  - Objective: maximize ∫_0^∞ exp(-ρ t) U(c_T, c_N, e) dt  (10) subject to (6’) and (11).
  - First-order conditions / Hamiltonian yield:
    - (12a), (12b), (12c) as stated in the text.
  - Money demand:
    - m = h(r*) c, h’ < 0  (13)
  - Euler equation (consumption dynamics):
    - (e^{...}) equation in text (14) — exact form preserved:
      (1/γ) e^{*} rhrr ċ = ... (14)  [Refer to equation (14) as given]

### B. Demand — Consolidated Public Sector
- Central bank:
  - Maintains exchange rate parity by unlimited exchange of domestic and foreign currency at fixed parity.
  - Balance sheet: f_C = m (foreign reserves equal domestic money).
  - Interest on reserves transferred to government.
- Government:
  - Collects lump-sum taxes t; consolidated government and central bank maintain a continuously balanced budget:
    - t = i* f_C = i* m  (15)

### Equilibrium Conditions and Steady State
- External interest rate (supply-of-funds schedule):
  - r* = r_W + p(a)  (16)
  - p is a risk premium, decreasing in net international investment position a.
- Nontraded goods market equilibrium:
  - y_N(e) = c_N = (1 – θ) e c  (17)
  - Solve (17) for short-run equilibrium real exchange rate:
    - e = e(c), with e’ = [1 / (1 – θ)] (y_N’ )^{-1} < 0  (18)  [text states sign]
- Dynamic system for (c, a):
  - Using (3), (13), (15), (16), (17) the budget constraint becomes:
    - ȧ = ȧ = [y_T(w(e)) + rem + r* a - (τ + θ) c]  (19)/(20)  [equations manipulated into form in text]
  - Summarized as:
    - ȧ = f_1(c, a, rem)  (21)
  - The Euler equation gives:
    - ċ = f_2(c, a, rem)  (23)  (system (21) and (23))
  - Stability:
    - The steady state (c*, a*) satisfying ċ = ȧ = 0 is saddlepoint stable (determinant of transition matrix negative).
- Long-run equilibrium conditions:
  - From steady-state Euler condition:
    - r_W + p(a*) = ρ  (24)
    - Hence r* = ρ  (25)
  - Consumption velocity and transaction cost in steady state:
    - h* = h(r*) = h(ρ)  (26)
    - τ* = τ[h(r*)] = τ[h(ρ)]  (27)
- External balance condition (zero-growth noninflationary steady state):
  - 0 = y_T(e) + rem + r* a* - (τ* + θ) c  (28)
  - Interpretation:
    - Current account measured in traded goods must be zero; trade surplus = y_T - (τ + θ) c; adding remittances and interest on a* yields (28).
  - Comparative effect of remittances on equilibrium real exchange rate:
    - ∂e/∂rem = [ (1/ ( (1 - θ) y_N’ ) ) * ( ... ) ] with sign:
      - ∂e/∂rem = [ y_T’ / (y_N’ (θ + τ) + y_T’ ) ] * ... leading to:
      - ∂e/∂rem < 0 as given in equation (29)  (29)

### Extensions
- Induced remittances:
  - Remittances as function of domestic real income:
    - rem = μ_0 + μ_1 y  (30)
  - Budget constraint becomes:
    - ȧ = ȧ = [ y_T(w(e)) + μ_0 + μ_1 y + r* a - τ c - θ c ]  (31)
  - Because y’ < 0 from (3c), the real exchange rate has a stronger impact on external balance when remittances are income-induced.
- Effects operating through the risk premium:
  - Alternative specification:
    - r* = r_W + p(a + rem/r*)  (32)
  - In long-run equilibrium r* = ρ, differentiating yields:
    - ∂a*/∂rem = -1/ρ  (33)
  - External balance then:
    - 0 = y_T(e) + rem + r* a*(rem) - (τ* + θ) c  (34)
  - Differentiation shows changes in rem have no effect on external balance when a* responds via the risk premium as specified.
- Direct effects on household utility (remittances spent on tradables):
  - Modified utility:
    - U(c_T, c_N) = v(e, c) = [ (c_T – rem)^θ (c_N)^{1 – θ} ]^{1 – σ}  (7’)
  - Implied consumption allocations:
    - c_T = θ(c – rem) + rem  (8’)
    - c_N = (1 – θ) e (c – rem)
  - Nontraded goods market:
    - y_N(e) = c_N = (1 – θ) e (c – rem)  (17’)
  - External balance:
    - 0 = y_T(e) + rem + r* a* - τ c - [ θ(c – rem) + rem ]  (28’)
    - Equivalent expression: 0 = y_T(e) + rem + r* a* - τ c - θ(c – rem)

*Source: _wp10287 - Appendix A. The Model*

### Appendix B. Country Sample

### Appendix B. Country Sample

### Classification
- The countries are classified as high, upper middle income, lower middle income, and low income countries based on the World Bank classification.

### High- and upper-middle-income countries in the sample
- New Zealand, Greece, Australia, Norway, Switzerland, United Kingdom, Canada, Germany, Spain, Sweden, Portugal, France, Austria, Denmark, Czech Republic, Belgium, Ireland, Finland, United States, Korea, Japan, Netherlands, Italy, Luxembourg, Saudi Arabia, Singapore, Trinidad and Tobago, United Arab Emirates, Israel, Slovenia, Estonia, Romania, Mexico, Russia, Oman, Slovak Republic, Costa Rica, Uruguay, Brazil, Lithuania, Bulgaria, South Africa, Mauritius, Latvia, Croatia, Malaysia, Libya, Panama, Hungary, Venezuela, Rep. Bol., Gabon, Kazakhstan, Botswana, Turkey, Poland, and Lebanon.

### Low-income countries in the sample
- Bangladesh, Lao People's Democratic Republic, Eritrea, Tajikistan, Mongolia, Tanzania, India, Vietnam, Uganda, Kyrgyz Republic, Sierra Leone, Democratic Republic of Congo, Mozambique, Central African Republic, Guinea, Zambia, Zimbabwe, Niger, Ethiopia, Kenya, Burkina Faso, Benin, Ghana, Nigeria, Mali, Madagascar, Sudan, Côte d'Ivoire, Cambodia, Haiti, Togo, Pakistan, Rwanda, Nepal, Burundi, Islamic Republic of Afghanistan, Malawi, Republic of Yemen, Chad, The Gambia, Mauritania, Senegal, Uzbekistan, and Papua New Guinea.

### Lower-middle income countries in the sample
- Macedonia FYR, Islamic Republic of Iran, Republic of Congo, Bosnia and Herzegovina, El Salvador, Nicaragua, Lesotho, Thailand, Georgia, Cameroon, Angola, Albania, Dominican Republic, Algeria, Belarus, Ukraine, Armenia, Philippines, Moldova, Turkmenistan, Paraguay, Namibia, Tunisia, Morocco, Syrian Arab Republic, Peru, Swaziland, Guatemala, Honduras, Sri Lanka, Indonesia, Egypt, Jamaica, Bolivia, Ecuador, People’s Republic of China, Colombia, and Jordan.

*Source: Appendix B. Country Sample, _wp10287 - Appendix B. Country Sample*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10287.pdf_