## Unintended Consequences of U. S. Monetary Policy Shocks: Dutch Disease and Capital Flow Measures in Emerging Markets and Developing Economies

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### Abstract — core findings
- Sample: 25 EMDEs, 2000-17.
- Empirical: Surges in capital inflows driven by accommodative U.S. monetary policy coincided with currency appreciation and contraction of the tradable sector in many EMDEs.
- Empirical: Use of capital flow measures (CFMs) was a common policy response in several EMDEs to U.S. monetary policy shocks.
- Theoretical: A two-sector small open economy DSGE with a learning-by-doing (LBD) mechanism in the tradable sector rationalizes the empirical findings.
- Welfare: CFMs can be a second-best policy when agents do not internalize the LBD externality arising from costly resource misallocation due to greater capital inflows.
- Implementation challenges: Adequate calibration of CFMs and quantification of the LBD externality are important and difficult.

### Empirics — identification, data, and main impulse-response results
- Identification strategy:
  - Exploits exogeneity of U.S. monetary policy shocks to EMDE innovations using PVAR with block exogeneity and recursive ordering.
  - U.S. monetary policy proxy: Wu and Xia (2016) shadow federal funds rate (end of period).
  - CFM index: Fernández and others (2016) based on IMF AREAER, distinguishes inflow and outflow CFMs.
- Data and variables:
  - Panel of 25 EMDEs (list of economies provided in source) representing around 80 percent of total GDP of EMDEs.
  - Tradable output: share of manufacturing value added in GDP.
  - Exchange rate: CPI-based real effective exchange rate (REER).
  - Variables in PVAR: ∆FFRt, ∆CFMi,t, ∆REERi,t, ∆Yi,t.
- Estimation details:
  - PVAR estimated with 2 lags (Schwartz Criterion).
  - Bootstrap inference with 500 replications following Runkle (1987); one standard deviation confidence intervals using structural errors.
- Key empirical impulse-response findings (five year horizon unless otherwise noted):
  - One year after a one percentage point reduction in the U.S. monetary policy rate:
    - Currencies appreciate significantly.
    - Share of tradable output in total GDP decline by around half a percentage point.
  - U.S. shadow policy rate: cumulative decline of 1.6 percentage points in the five year horizon window following the initial shock.
  - REER appreciation is somewhat temporary (reverts after second year); decline in tradable output is relatively more persistent across the five year horizon.
  - EMDEs tend to increase capital flow restrictions on inflows after U.S. monetary policy shocks; tightening of CFMs can last several years.
  - Dutch disease effects stronger in EMDEs with more flexible exchange rates and during the post global financial crisis period (2009–2017).
  - No evidence of Dutch disease effects in advanced economies (AEs); in expanded sample of eight small open AEs, currency tends to depreciate and manufacturing share increases somewhat by end of IRF horizon.
  - Robustness: results hold using alternative U.S. monetary policy shock measures (e.g., Jarociński and Karadi (2020) FOMC surprises), with noisier IRFs but consistent qualitative patterns.
- Additional empirical notes:
  - PVAR treats CFMs as endogenous; IRFs reflect introduction of new restrictions (interpretable as increasing restrictions on one additional asset category).
  - Limitations: PVAR coefficients are not deep micro-founded parameters; counterfactuals (e.g., setting CFM coefficients to zero) require structural modeling.

### Theoretical model — structure, mechanism, and calibration
- Model structure:
  - Small open economy DSGE with representative household, two sectors (tradable T and non-tradable N), international credit markets, and a tax on interest rate payments (CFM) on external debt.
  - Tradable sector features organizational capital l_t and a learning-by-doing (LBD) mechanism: l_{t+1} = l_t^{ζ} Y_{T,t}^{ψ} with ζ + ψ = 1.
  - Production functions: Y_{T,t} = A_{T,t} l_t^{ξ} k_t^{α} h_{T,t}^{1−α}; Y_{N,t} = A_{N,t} h_{N,t}.
  - Foreign borrowing interest rate: r^d_t = (1 + τ(B_t)) exp(−η_t) r^*, with τ(B_t) = τ_2 (B_t − B̄)^2 and B̄ calibrated to 0.
  - Government: balanced budget; CFM tax revenues rebated lump-sum.
- Parameterization (quarterly frequency; selected values from Table 1):
  - Foreign interest r^* = 0.02.
  - Share of tradables in consumption φ = 0.45.
  - Subjective Discount Factor β = 0.98.
  - Inv. elast. of intertemp. sub. γ = 2.
  - Elast. of sub., consumption ω = 0.22.
  - Elast. of sub., tradables μ = 0.316.
  - Foreign debt adjustment cost κ = 0.0003.
  - Parameter for investment adj. cost φ = 2.2.
  - Capital share α = 0.33.
  - Labor share, tradable sector Φ = 0.67.
  - Learning rate ξ = 0.26.
  - Output elasticity, org. capital ψ = 0.5.
  - Depreciation rate, org. capital ζ = 0.5.
  - Depreciation rate δ = 0.025.
  - Shock processes: σ_T = 0.007, σ_N = 0.0035, σ_η = 0.01; A_{T,t} and A_{N,t} AR(1) with coefficient 0.95; η_t AR(1) with coefficient 0.98.
- Mechanism:
  - Without LBD externality, greater foreign capital availability raises demand and wages, reducing tradable production—an efficient reallocation as imports substitute.
  - With LBD externality in tradables, reduction in tradable output lowers productivity and future production; private agents do not internalize this externality, causing tradable production to fall below the efficient level.
- Numerical solution:
  - Model solved via log-linear approximation around steady state; foreign debt adjustment cost set to a very small positive value to avoid unit root in bond holdings.

### Quantitative simulations and welfare analysis
- Simulation experiment:
  - Two standard deviation reduction in the world interest rate; responses evaluated one year (four quarters) after impact.
  - Simulations run across different levels of the tax on foreign interest rate payments (τ).
- Simulated dynamics one year after a −2σ world interest rate shock:
  - Net foreign borrowing increases.
  - Consumption of both tradables and non-tradables increases.
  - Demand for non-tradables raises wages and the relative price of non-tradables (p_{N,t}).
  - Labor reallocates from tradable to non-tradable sector.
  - Tradable output contracts.
- Role and effects of CFMs (tax τ):
  - CFMs raise cost of foreign capital, discouraging foreign borrowing.
  - By curbing foreign capital availability, CFMs limit the rise in relative price of non-tradables (i.e., appreciation) and attenuate resource reallocation from tradable to non-tradable.
  - Limiting the contraction in tradables can increase long-term total output and household welfare if LBD externality is present and misallocation would otherwise be excessive.
- Welfare results (benchmark vs. CFM regime):
  - Benchmark economy B: τ = 0.
  - Economy C: τ > 0.
  - Welfare is increasing in τ up to τ = 0.045.
  - At τ = 0.045: welfare interpretation provided — "0.25 percent of household consumption should be transferred to a regime with no capital controls in order for households in that regime to have the same expected level of utility as households in a regime with capital controls in place." (i.e., Ψ_lbd = 0.0025).
  - Benefits of CFMs concentrate at relatively low τ values and dissipate quickly as τ increases beyond the optimal range.
  - Some access to international capital markets remains valuable; CFMs trade off reduced foreign-financed consumption for protection of tradable-sector productivity.
- Sensitivity to learning parameter ξ:
  - Reducing ξ from 0.26 to 0.08 lowers the welfare benefit of CFMs but the benefit remains positive.
  - Lower ξ does not materially change model dynamics to global interest rate shocks.
  - LBD mechanism plausibly larger in EMDEs (higher manufacturing share), so actual welfare gains from CFMs could be larger in some EMDEs; presented results may be a lower bound.

### Policy implications, trade-offs, and implementation challenges
- Role for CFMs:
  - CFMs on inflows can be welfare-increasing when a tradable-sector LBD externality exists by preventing excessive currency appreciation and protecting tradable-sector productivity.
  - CFMs act as a second-best policy when the LBD externality cannot be directly internalized.
- Implementation challenges and trade-offs:
  - Benefits of CFMs can be large but concentrated within a narrow range of tax rates; careful calibration of magnitude and duration is critical.
  - The LBD externality is not directly observable and difficult to measure, complicating calibration.
  - CFMs could amplify macroeconomic volatility in the presence of other frictions (e.g., nominal rigidities).
  - CFMs are most suitable for EMDEs with sizeable manufacturing export sectors where LBD accrues most.
  - CFMs should not substitute for necessary macro adjustment to correct underlying imbalances; they can provide policymakers breathing space but are not a replacement for fundamental adjustment.
- Practical caveats:
  - Some capital inflows yield efficiency gains; optimal policy balances preserving efficiency gains from international capital access against preventing costly misallocation due to uninternalized LBD externalities.

### Contribution and avenues for future research
- Contributions:
  - Empirical: Documents Dutch disease effects from global financial shocks across 25 EMDEs and treats CFMs as endogenous within a PVAR framework.
  - Theoretical: Introduces LBD externality in a two-sector DSGE to analyze CFMs as a policy response to global interest rate shocks.
  - Complements CFM literature by focusing on real-sector frictions (costly resource misallocation) alongside pecuniary and aggregate demand externalities.
- Future research directions:
  - Consider interactions of LBD with other externalities and the role of other policies in an integrated framework.

*Authored by Juan F. Yépez; WP/21/209; Strategy, Policy, and Review Department; July 2021.*

### Section 1

### Unintended  Consequences  of U. S. Monetary Policy  Shocks: Dutch Disease and Capital Flow Measures in Emerging Markets and Developing  Economies

### Abstract
- Paper documents that surges in capital inflows driven by accommodative U.S. monetary policy coincided with currency appreciation and contraction of the tradable sector in many emerging markets and developing economies (EMDEs).
- Sample: 25 EMDEs, 2000-17.
- Empirical finding: U.S. monetary policy shocks coincided with episodes of currency appreciation and contraction in tradable output in these economies.
- Empirical finding: Use of capital flow measures (CFMs) has been a common policy response in several EMDEs to U.S. monetary policy shocks.
- Theoretical contribution: A two-sector small open economy DSGE augmented with a learning-by-doing (LBD) mechanism in the tradable sector rationalizes the empirical findings.
- Welfare analysis: Provides rationale for CFMs as a second-best policy when agents do not internalize the LBD externality arising from costly resource misallocation due to greater capital inflows.
- Implementation challenges: Adequate calibration of CFMs and quantification of the LBD externality are important and difficult.

### Introduction and Motivation
- Context: Ultra-accommodative monetary policies in advanced economies, particularly the United States, generated large spillovers to EMDEs via capital flows.
- Figure referenced: Non-Resident Capital Inflows to Selected EMDEs and U.S. Shadow Policy Rate; Wu and Xia (2016) shadow federal funds rate used as proxy for U.S. monetary policy.
- Behavior of EMDEs: Defensive accumulation of reserves and increased resort to CFMs amid uncertainty over sustainability of inflows.
- Prior literature focus: Externalities from capital flows mainly financial (borrowing too much, insufficient insurance, excessive short-term borrowing).
- Alternate channel emphasized: Resource reallocation across industries (Dutch disease) linked to inflows causing real appreciation and contraction of tradable sector.

### Empirical Strategy and Key Findings
- Identification strategy: Effects of U.S. monetary policy shocks on currencies and tradable output of 25 EMDEs, exploiting exogeneity of U.S. monetary policy to EMDE innovations.
- CFMs measurement: Uses Fernández and others (2016) index based on IMF’s AREAER distinguishing inflow and outflow CFMs.
- Estimation framework: Panel vector auto-regression (PVAR) treating CFM index as endogenous; results summarized as impulse responses within a five year horizon.
- Key empirical results:
  - One year after a one percentage point reduction in the U.S. monetary policy rate:
    - Currencies appreciate significantly.
    - Share of tradable output in total GDP decline by around half a percentage point.
  - Currency appreciation is somewhat temporary; decline in tradable output is relatively more persistent.
  - EMDEs tend to increase capital flow restrictions on inflows after U.S. monetary policy shocks; tightening of CFMs can last several years.
  - Robustness: Dutch disease effects stronger in EMDEs with more flexible exchange rates and during the post global financial crisis period.
  - No evidence of Dutch disease effects in advanced economies (AEs), though use of CFMs in AEs was common during accommodative U.S. monetary policy periods.
  - Results robust to alternative measures of U.S. monetary policy shocks.

### Theoretical Model and Quantitative Analysis
- Model summary:
  - Small open economy DSGE with representative household, two sectors (tradable and non-tradable).
  - Households access international credit markets; a tax on interest rate payments (CFM) on external debt is included.
  - International interest rate taken as given; firms have no effect on price of tradable goods.
  - Impulse responses computed for a negative shock to the global interest rate; welfare implications evaluated for various tax rates on foreign debt service.
- Mechanism:
  - Without frictions: Greater foreign capital availability raises demand and wages, reducing tradable production (imports substitute), which is the efficient response.
  - With LBD externality in tradable sector: Reduction in tradable output lowers productivity and future production; if firms do not internalize this externality, tradable production falls below efficient level.
- Quantitative findings:
  - A tax on foreign debt service (CFM) raises cost of foreign capital, discouraging foreign borrowing.
  - Lower foreign capital availability attenuates currency appreciation and resource reallocation from tradable to non-tradable sector by limiting the increase in relative price of non-tradables.
  - Model qualitatively matches observed Dutch disease effects from sudden reduction in U.S. monetary policy rate and shows how CFMs could limit these effects.
  - Under standard calibration parameters, limiting the increase in relative price of non-tradables prevents inefficient reallocation and leads to higher total output in the long-term and increased household welfare.
  - Conclusions robust to different levels of the LBD externality.

### Policy Implications and Trade-offs
- Role for CFMs:
  - CFMs on inflows can be welfare-increasing in presence of tradable-sector LBD externality by preventing excessive currency appreciation and protecting tradable sector productivity.
  - CFMs act as a second-best policy when externality cannot be directly internalized.
- Implementation challenges:
  - Benefits of CFMs can be large but concentrated within a narrow range of tax rates; careful calibration of magnitude and duration is critical.
  - LBD externality is not directly observable and difficult to measure, complicating calibration of CFMs.
- Potential trade-offs:
  - CFMs could amplify macroeconomic volatility in presence of other frictions (e.g., nominal rigidities).
  - Suitability of CFMs highest in EMDEs with sizeable manufacturing export sectors where LBD accrues most.
  - Given evolving monetary policy frameworks and weakly anchored inflation expectations in many EMDEs, policies that avoid sharp currency fluctuations and prevent losses in tradable output may dominate alternatives.

### Contribution to Literature
- Empirical contribution: Extends literature by documenting Dutch disease effects from global financial shocks across a larger set of EMDEs and treating CFMs as endogenous within a PVAR framework.
- Theoretical contribution: Adds to literature on policy responses to Dutch disease by analyzing shocks to global interest rates in an RBC/DSGE model and explicitly examining CFMs as policy response.
- Relation to CFM literature: Complements work on pecuniary and aggregate demand externalities by focusing on real-sector frictions (costly resource misallocation) and CFMs’ role.

### Organization of the Paper
- Section 2: Empirical analysis.
- Section 3: Model and quantitative analysis of CFMs limiting Dutch disease.
- Section 4: Conclusion.

_Authored by Juan F. Yépez; WP/21/209; Strategy, Policy, and Review Department; July 2021._

### Section 2

### EMPIRICS

### Data
- Sample: panel of 25 EMDEs at an annual frequency from 2000 until 2017.
- The selected sample represents around 80 percent of total GDP of EMDEs according to the IMF’s World Economic Outlook data.
- The sample consists of the following economies: Argentina, Brazil, Bulgaria, Chile, China, Colombia, Costa Rica, Egypt, Guatemala, Hungary, India, Indonesia, Kazakhstan, Malaysia, Mexico, Pakistan, Paraguay, Peru, Philippines, Poland, Romania, Russia, South Africa, Turkey, and Ukraine.
- CFM index: measures intensity of capital controls distinguishing between inflows and outflows; developed by Fernandez and others (2016) using information from the IMF’s Annual Report on Exchange Arrangements and Exchange Restrictions (AREAER). Index allows cross-country comparison of inflow CFMs and documents frequent use of CFMs across EMDEs in the last two decades.
- Tradable output variable: share of manufacturing value added in GDP (World Bank WDI and Eurostat). Noted cross-country variation; non-commodity exporting EMDEs have the highest manufacturing share (around 20 percent of GDP).
- Exchange rate variable: CPI-based real effective exchange rate (REER) from the IMF’s Information Notice System.
- U.S. monetary policy proxy: Wu and Xia (2016) shadow federal funds rate (end of period) obtained from Haver Analytics; used to account for zero lower bound periods after the global financial crisis.

### PVAR Framework
- Objective: capture dynamic response of REER, tradable output, and inflows CFMs to U.S. monetary policy shocks using a PVAR for 25 EMDEs with block exogeneity and recursive ordering.
- Variables and notation:
  - ∆FFRt: one-year change in the Wu and Xia (2016) shadow U.S. federal funds rate.
  - ∆CFMi,t: one-year change in CFM index.
  - ∆REERi,t: log one-year change in the REER.
  - ∆Yi,t: log one-year change in the ratio of manufacturing output to total GDP.
- Identification:
  - Assume U.S. monetary policy innovations are exogenous to EMDEs (ε1t is the U.S. monetary policy shock).
  - Recursive ordering and block exogeneity imply ai,2,1, ai,3,1, and ai,4,1 are identified; set ai,2,3 = ai,2,4 = ai,3,4 = 0 (Cholesky decomposition).
- Representation:
  - Structural form and companion matrix representation provided; impulse response for variable k to U.S. monetary policy shock at horizon h is IRFk(1,h) = Λh−1i A−1i,0 (k,1).
- Estimation details:
  - Each equation estimated by OLS with 2 lags following the Schwartz Criterion.
  - Bootstrapping inference follows Runkle (1987) procedure:
    1. Estimate PVAR(p) and generate 500 bootstrap replications of the coefficient matrix Âi.
    2. Compute IRFs 500 times for each generated variable k* to the U.S. monetary policy shock at horizons h = 1,...,H.
    3. Use bootstrap simulations to compute empirical IRF distributions; construct one standard deviation confidence intervals using structural errors without imposing symmetry in confidence bands.
  - Bootstrapping for the panel: generate initial conditions separately for each country (Runkle, 1987) but sample from the entire panel vector of residuals to account for possible cross-country correlations.
- Lag length: p determined (2 lags used).

### Results
- Main experiment: effect of a one percentage point reduction in the U.S. policy rate; results summarized as cumulative impulse responses at a five year horizon.
- U.S. shadow policy rate response:
  - Protracted decline following the initial shock, reaching a cumulative decline of 1.6 percentage points in the five year horizon window.
- REER:
  - Real effective exchange rate appreciated on the year of the U.S. monetary policy shock; appreciation is not statistically significant and reverts after the second year.
- Tradable output (share of manufacturing value added in GDP):
  - U.S. monetary policy shock and ensuing currency appreciation coincided with a contraction in the share of manufacturing production.
  - The contraction of tradable output is relatively long-lasting throughout the IRF 5 year horizon.
  - Result consistent with Rajan and Subramanian (2011) finding that exportable industries grow slower by about half percentage point per year relative to non-exportable industries in aid surge episodes.
- CFMs:
  - Common to observe tightening of CFMs on inflows in the sample following U.S. monetary policy shocks.
  - Given the CFM index construction, the IRF reflects the introduction of new restrictions in the capital account (interpretable as EMDEs increasing restrictions on one additional asset category in the year after the shock).

### Robustness and extensions
- Robustness checks include expanding sample to small open AEs, censoring to post-GFC period, and conditioning on exchange rate regimes; results remain robust.
- Post-GFC interaction (dummy = 1 for 2009–2017):
  - Pre-GFC: expansionary U.S. monetary policy shocks led to weaker currencies, limited effect on tradable output, and many economies reduced number of CFM restrictions following the U.S. shock.
  - Post-GFC: looser U.S. monetary policy resulted in significant currency appreciation with protracted REER effects; large reductions in tradable output confirming Dutch disease; EMDEs typically imposed additional restrictions on the capital account.
- Exchange rate regime interaction (Ilzetzki and others, 2017 classification; dummy "fix" = 1 for peg, "flex" = 0 for non-peg):
  - Dutch disease effects were more common among EMDEs with more flexible exchange rate regimes.
  - In flexible-regime EMDEs, expansionary U.S. monetary policy shocks led to currency appreciation, larger declines in manufacturing share of GDP, and imposition of additional restrictions on capital inflows.
- Comparison with small open advanced economies (AEs):
  - Expanded sample includes eight small open AEs: Canada, Czech Republic, Iceland, Israel, Korea, Norway, Singapore, and Sweden.
  - Results suggest Dutch disease following U.S. monetary policy shocks occurred mainly in EMDEs.
  - For AEs, the currency depreciates following the shock (not statistically significant); weaker currency helped stimulate tradable output (manufacturing share increases somewhat by end of IRF horizon). AEs also used CFMs.
- Alternative U.S. monetary policy shocks (Jarociński and Karadi (2020) high-frequency FOMC surprise measure, aggregated within a year):
  - Expansionary U.S. monetary policy surprises lead to multilateral real appreciation of EMDE currencies on the year after the shock and a protracted contraction in the share of manufacturing in GDP.
  - EMDEs respond by tightening CFMs; IRF is noisier and less precise but consistent with baseline.
- On whether CFMs attenuate Dutch disease:
  - Conceptual channels: direct contemporaneous effect of U.S. shock on REER (ai,3,1); indirect effect via CFMs if U.S. shocks lead to more CFMs contemporaneously (ai,2,1) and CFMs impact REER (ai,3,2); dynamic insulation if lagged CFMs coefficients in REER and output equations are significant.
  - Limitation: PVAR coefficients are not "deep" micro-founded parameters; counterfactual analysis (e.g., setting CFM coefficients to zero) is constrained by Lucas (1976) critique on policy process changes affecting other equations.
  - Conclusion: a structural model with micro-founded parameters is needed to evaluate the appropriateness of CFMs in limiting Dutch disease; such a model is developed in the next section.

*Source: Section 2 (EMPIRICS) of the provided PDF chapter.*

### Section 3

### THETHEORETICALMODEL

### A. Households — preferences, budget, and optimality
- Representative household utility:
  - U = E_0^∞ ∑_{t=0} β^t ( (c_t^ω (1−h_t)^{1−ω})^{1−γ} − 1 ) / (1−γ).
- Consumption aggregator:
  - c_t = [ φ(c_{T,t})^{−μ} + (1−φ)(c_{N,t})^{−μ} ]^{−1/μ}.
- Labor mobility:
  - h_t = h_{T,t} + h_{N,t}; wage identical across sectors.
- Flow budget constraint (in tradable good terms):
  - B_t = (1 + r^d_{t−1}) B_{t−1} − w_t h_t − r^k_t k_t − T_t − Π^f_t + p_{N,t} c_{N,t} + c_{T,t} + i_t + κ/2 (B_t − B̄)^2.
  - κ/2 (B_t − B̄)^2 is foreign debt adjustment cost (Schmitt-Grohé and Uribe, 2003).
- Foreign borrowing interest rate:
  - r^d_t = (1 + τ(B_t)) exp(−η_t) r^*.
  - τ(B_t) = τ_2 (B_t − B̄)^2, with τ parameter representing intensity of the tax and B̄ the steady state foreign debt position.
  - B̄ is calibrated to equal to 0 in steady state, thus tax revenues are on the full stock of foreign debt.
- Capital accumulation:
  - k_{t+1} = (1−δ) k_t + i_t − φ/2 ( (k_{t+1} − k_t) / k_t )^2.
- First-order conditions (representative expressions preserved):
  - (1−φ)/φ (c_{N,t}/c_{T,t})^{−(μ+1)} = p_{N,t}.
  - ω/(1−ω) (1−h_t)/c_t = p_{N,t} w_t.
  - Euler/foreign debt FOC and capital FOC as given (equations (10) and (11)).
- Marginal utility of consumption:
  - λ_t = ω c_t^{ω(1−γ)−1} (1−h_t)^{(1−ω)(1−γ)}.

### B. Firms — production, LBD externality, and factor prices
- Two competitive sectors: tradable and non-tradable.
- Tradable sector production (Cobb-Douglas):
  - Y_{T,t} = A_{T,t} l_t^{ξ} k_t^{α} h_{T,t}^{1−α}.
  - l_t denotes average organizational capital.
- Learning-by-doing (LBD) mechanism (Cooper and Johri (2002) specification):
  - l_{t+1} = l_t^{ζ} Y_{T,t}^{ψ}, with ζ + ψ = 1.
- Micro vs. aggregate returns:
  - Firms take l_t as given → constant returns to scale at firm level.
  - Planner internalizes LBD → increasing returns to scale at aggregate level.
- Non-tradable sector:
  - Y_{N,t} = A_{N,t} h_{N,t}.
- Factor price equalization in equilibrium:
  - w_t = (1−α) Y_{T,t} / h_{T,t} = p_{N,t} Y_{N,t} / h_{N,t}.
  - r^k_t = α Y_{T,t} / k_{T,t}.

### C. Government
- Balanced budget assumed.
- CFM tax revenues rebated lump-sum:
  - T_t = τ(B_t) exp(−η_t) r^* B_t.

### D. Equilibrium
- Market clearing:
  - h_t = h_{T,t} + h_{N,t}.
  - Y_{N,t} = c_{N,t}.
  - Y_{T,t} = c_{T,t} + i_t.
- Competitive equilibrium defined by sequences { c_{N,t}, c_{T,t}, k_{t+1}, h_t, h_{N,t}, h_{T,t}, p_{N,t}, B_t, r^k_t, w_t }_{t=0}^∞ satisfying household optimization, firm profit maximization, and market clearing.

### E. Parameterization (quarterly frequency)
- Shock processes:
  - ln(A_{T,t}) = 0.95 ln(A_{T,t−1}) + ε_{T,t}, ε_{T,t} ∼ N(0, σ_T^2), σ_T = 0.007.
  - ln(A_{N,t}) = 0.95 ln(A_{N,t−1}) + ε_{N,t}, ε_{N,t} ∼ N(0, σ_N^2), σ_N = 0.0035.
  - η_t = 0.98 η_{t−1} + ε_{η,t}, ε_{η,t} ∼ N(0, σ_η^2), σ_η = 0.01.
- Selected parameter values (as reported in Table 1):
  - Foreign interest r^* = 0.02.
  - Share of tradables in consumption φ = 0.45.
  - Subjective Discount Factor β = 0.98.
  - Inv. elast. of intertemp. sub. γ = 2.
  - Elast. of sub., consumption ω = 0.22.
  - Elast. of sub., tradables μ = 0.316.
  - Foreign debt adjustment cost κ = 0.0003.
  - Parameter for investment adj. cost φ = 2.2.
  - Capital share α = 0.33.
  - Labor share, tradable sector Φ = 0.67.
  - Learning rate ξ = 0.26.
  - Output elasticity, org. capital ψ = 0.5.
  - Depreciation rate, org. capital ζ = 0.5.
  - Depreciation rate δ = 0.025.
- Numerical solution:
  - Model solved via log-linear approximation around the steady state.
  - Foreign debt adjustment cost set to smallest possible positive value close to zero to avoid unit root in bond holdings.

### F. Model simulations — response to global interest rate shocks
- Experiment:
  - Two standard deviation reduction in the world interest rate; responses evaluated one year (four quarters) after impact.
  - Simulations run for different levels of the tax on foreign interest rate payments (τ).
- Key simulated dynamics (one year after a −2σ world interest rate shock):
  - Net foreign borrowing increases (Figure 8, panel 1).
  - Consumption of both tradables and non-tradables increases.
  - Demand for non-tradables raises wages and the relative price of non-tradables (p_{N,t}) (Figure 8, panel 2).
  - Labor reallocates from tradable to non-tradable sector (Figure 8, panel 3).
  - Tradable output contracts (Figure 8, panel 4).
- Role of CFMs (tax τ on foreign debt payments):
  - By curbing foreign capital availability, CFMs limit the rise in relative prices (i.e., appreciation) and the contraction in tradable output.
  - Limiting the contraction in tradables may or may not align with the social planner’s optimal reallocation given some efficient reallocation to non-tradables in response to capital inflows.

### G. Welfare Analysis — optimality and gains from CFMs
- Welfare comparison setup:
  - Benchmark economy B: τ = 0 (no CFMs).
  - Economy C: τ > 0 (with CFMs).
  - Conditional welfare functions:
    - V^B_0 = E_0 ∑_{t=0}^∞ β^t U(c^B_t, h^B_t).
    - V^C_0 = E_0 ∑_{t=0}^∞ β^t U(c^C_t, h^C_t).
  - Define Ψ_lbd as fraction of economy C’s consumption required for households in economy B to have same welfare as in C:
    - V^C_0 = E_0 ∑_{t=0}^∞ β^t U((1 + Ψ_lbd) c^B_t, h^B_t).
  - Closed form for Ψ_lbd (given utility specification) provided in equation (21); welfare gain computed through second order approximation.
- Main welfare results:
  - Welfare is increasing in τ up to τ = 0.045.
  - At τ = 0.045, the welfare interpretation: "0.25 percent of household consumption should be transferred to a regime with no capital controls in order for households in that regime to have the same expected level of utility as households in a regime with capital controls in place." (i.e., Ψ_lbd = 0.0025 interpretation).
  - CFMs discourage foreign-financed tradable consumption and limit costly resource reallocation from tradable to non-tradable, increasing welfare when an LBD externality is present.
  - Benefits of CFMs dissipate relatively quickly and accrue mainly at relatively low τ values.
  - Some access to international capital markets yields benefits; there is a trade-off as some reallocation to non-tradables is efficient under capital inflows.
  - Calibrating CFMs (magnitude and duration) is challenging because the LBD externality is unobservable and hard to measure.

### H. Sensitivity Analysis — variation in learning rate ξ
- Robustness check:
  - Reduce ξ from 0.26 to 0.08 (lowest value that preserves α + (1−α) + ξ > 1 to maintain aggregate increasing returns).
- Findings:
  - Welfare benefit of CFMs is smaller under lower ξ but remains positive.
  - Lower ξ does not materially change model dynamics to global interest rate shocks.
  - LBD mechanism plausibly larger in EMDEs (higher manufacturing share), so actual welfare gains from CFMs could be larger in some EMDEs; presented results may be a lower bound.

### IV. CONCLUSION — synthesis of theoretical results
- Empirical motivation: accommodative U.S. monetary policy increased non-resident capital flows to EMDEs, associated with Dutch disease symptoms: real currency appreciation and contraction in tradable output.
- Model conclusion:
  - With an LBD externality in tradables, CFMs on inflows can serve as a second-best policy to limit costly misallocation and move tradable production toward the efficient level.
  - CFMs are most suitable for EMDEs with a sizable manufacturing export sector where LBD accrues most.
  - Policy caveats:
    - Some capital inflows yield efficiency gains; CFMs’ benefits concentrate at relatively low restriction levels.
    - Calibration of CFMs is difficult due to unobservability of LBD externality; both magnitude and duration of CFMs present implementation challenges for policymakers.

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021209-print-pdf.pdf*

### Section 4

### wpiea2021209-print-pdf - Section 4

### Main conclusions
- "The use of CFMs should not be a substitute for necessary macro adjustment to correct underlying imbalances, although CFMs appear as a sensible policy alternative that can provide policymakers some breathing space."
- "This paper puts forward an analytical framework with a novel mechanism to think about the merits of CFMs in the presence of LBD externalities."
- "By doing so, it puts forward a rationale for why CFMs can be a useful part of the toolkit to manage the consequences of capital flows."
- The analysis is built "through a parsimonious model" that highlights the role of CFMs given LBD externalities.

### Policy implications
- CFMs can serve as a sensible policy alternative to manage capital flow consequences and provide policymakers breathing space.
- CFMs are not a replacement for macroeconomic adjustment needed to address fundamental imbalances.

### Directions for future research
- "Future research should consider also the interactions of LBD with other externalities as well as the role of other policies in an integrated fashion."

*wpiea2021209-print-pdf - Section 4*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021209-print-pdf.pdf_