## wpiea2022028-print-pdf

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---

### 2.1 Household — Preferences, aggregation, budget, and first-order conditions
- Preferences and consumption aggregation:
  - Household preferences in economy j:
    - ∞ ∑ t=0 β t u(C j t ,L j t ) = ∞ ∑ t=0 β t { ζ ζ−1 C j ζ−1 ζ t −Γ j θ 1 +θ L j θ+1 θ t } (2.1)
  - Consumption basket C j t is a CES aggregate of regional goods CR j t and global goods CW j t:
    - C j t = ( a 1 ξ j { CR j t } ξ−1 ξ + (1−a j ) 1 ξ { CW j t } ξ−1 ξ ) ξ ξ−1 (2.2)
  - Regional goods CR j t combine goods from each regional trading partner:
    - CR j t = ( b 1 ψ j { CA j t } ψ−1 ψ + (1−b j ) 1 ψ { CB j t } ψ−1 ψ ) ψ ψ−1 (2.3)
  - Relative demand for global and regional goods:
    - CR j t = a j ( PR j t CPI j t ) −ξ C j t
    - CW j t = (1−a j ) ( PW j t CPI j t ) −ξ C j t (2.4)
  - Demand for goods from A and B within regional goods:
    - 1 CA j t CR j t = b j ( PA j t PR j t ) −ψ
    - CB j t CR j t = (1−b j ) ( PB j t PR j t ) −ψ (2.5)

- Household budget constraint and asset holdings:
  - Households hold bonds B j t denominated in international dollars and face the budget constraint:
    - B j t = (1 +r j t−1 )B j t−1 + W j t L j t − CPI j t C j t + Π j t S j t (2.6)
  - Nominal exchange rate S j t: units of j currency per dollar; an increase denotes a domestic depreciation and S W t = 1 by definition.
  - W j t denotes nominal wage. Interest rate (1 +r j t ) is the effective interest rate on international bonds relevant to household j. Π j t represents lump-sum profit pay-outs and taxes.
  - Paper studies dynamics around a steady state with zero net international investment positions; wealth effects from international bond holdings are second order.

- First-order conditions:
  - Labor supply condition:
    - Ω j t W j t = Γ j L j 1 θ t (2.7)
  - Consumption Euler-type condition linking shadow value and consumption:
    - Ω j t CPI j t = C j −1 ζ t (2.8)
  - Intertemporal asset pricing condition:
    - 1 = E t [ β Ω j t+1 Ω j t (1 + i j t ) ] = E t [ β Ω j t+1 Ω j t S j t+1 S j t (1 + r j t ) ]
  - Ω j t denotes the shadow value of domestic currency and i j t is the domestic currency nominal interest rate.

- Role in broader model:
  - Household consumption and labor choices feed into:
    - Domestic value added production (Y j t = L j t) and marginal cost MCY j t = W j t.
  - Consumption aggregator parameters {a j , b j , ξ, ψ} and household intertemporal parameters β, ζ, Γ j , θ determine demand elasticities and substitution between regional and global goods, central to quantifying how exchange rate and monetary shocks transmit through consumption and trade channels.

### 2.4 Market Equilibrium — goods, platforms, interest rates, calibration, and simulated comparisons
- Goods and platform market equilibrium:
  - Goods market equilibrium for economy j:
    - Y_j_t = ∫{h_l,t + ex_l,t} dl = DH_j_t H_j_t + DX_j_t EX_j_t  (equation (2.26))
    - DH_j_t ≡ [∫(ppi_l,t / PPI_j_t)^−φ dl]
    - DX_j_t ≡ [∫(ipi_l,t / IPI_j_t)^−φ dl]  (equation (2.27))
  - For regional economies, platform output equals exports to the global economy:
    - V_d_t = ∫{m_l,t} dl = DW_d_t M_d_t  (equation (2.28))
    - DW_d_t ≡ [∫(xpi_l,t / XPI_d_t)^−φ dl]  (equation (2.29))

- Interest rates and international bond market:
  - External interest rates:
    - 1 + r_d_t = {1 + (i_W_t e^(−η B_j_t))}  (equation (2.30))
    - Risk premium is a decreasing function of wealth B_j_t.
  - Domestic policy (CPI-targeting Taylor Rule with persistence):
    - 1 + i_j_t = ( (1 + i_j_{t−1}) / (1 + i) )^χ_i (CPI_j_t / CPI_j_{t−1})^χ_π^(1−χ_i) (Y_j_t / Y)^χ_Y^(1−χ_i) λ_j_t  (equation (2.31))
    - λ_j_t is an exogenous monetary policy shock.
  - International bond market equilibrium:
    - B_A_t + B_B_t + B_W_t = 0  (equation (2.32))

- Calibration targets and trade-weight assumptions:
  - Size of total exports of regional economies as a share of GDP = 50% (average of China, Indonesia, Korea, Malaysia, Philippines, Thailand, and Vietnam between 2010 and 2018).
  - Foreign value added = 25% of exports (as in 2018 in East Asia & the Pacific).
  - About 55% of foreign value added comes from within the region.
  - About 50% of the trade of the regional economy is with the regional trading partner (Dent (2017)).
  - Preferences: two regional economies identical; global economy treats each regional economy identically.
  - Normalizations:
    - Γ_d normalized so steady state employment in the regional economies L_d = 1.
    - Γ_W set so the world economy is twice as large as either regional economy.
  - No Value Chain (NoVC) trade weight parameterization:
    - e_d = 1; f_A = 1; f_B = 0
    - Exports are 50% of GDP and 50% of exports are to the regional economy.

- Key parameter values preserved exactly:
  - ξ = ψ = ν = γ = 2
  - ζ = 0.5
  - θ = 2
  - φ = 11
  - Subsidy: τ φ φ−1 = 1
  - Price stickiness parameter: κ = .75
  - Subjective discount factor: β = .99
  - Interest rate smoothing parameter: χ_i = .75
  - Policy rule parameters: {χ_π, χ_Y} are set to a standard value of {1.5, 0.5 4 }
  - Risk premium parameter: η = −.0001

- Models compared:
  - Value Chain / No Value Chain across invoicing regimes:
    - Dominant Currency: (1) Benchmark  (2) DCP-NoVC
    - Local Currency: (3) LCP
    - Producer Currency: (4) Textbook

- Domestic monetary policy shock design:
  - Shock: exogenous decrease in policy interest rates in regional economy A (leading to exchange rate depreciation).
  - One-time shock specification:
    - λ_A_t=1 = .9925, calibrated to generate an equilibrium domestic exchange rate depreciation of approximately 2%.

- Simulation findings (impulse response summary, preserved language):
  - Exchange rate and CPI pass-through:
    - Exchange rate depreciation is close to equivalent in Benchmark, Textbook, and DCP-NoVC; slightly larger under LCP.
    - Depreciation raises the price of imported goods and passes through into CPI.
    - CPI pass-through: minimal under LCP; stronger in Textbook and NoVC; strongest in models where import content of consumption is large.
  - Interest rate responses (via CPI-targeting Taylor rule):
    - Decline in interest rates similar in NoVC and Textbook.
    - Slightly sharper decline in Benchmark (due to stronger CPI response).
    - Sharply larger decline under LCP (due to weaker CPI pass-through).
  - Consumption and demand:
    - Persistent cut in interest rates leads to a proportional expansion in consumption.
    - Expansion in consumption: sharpest under LCP; roughly equivalent under NoVC and Textbook; intermediate under Benchmark.
  - Imports and expenditure switching:
    - Under LCP, import volumes increase proportionally with domestic demand.
    - Under Benchmark, Textbook, and DCP-NoVC, domestic depreciation makes imports more expensive and leads to expenditure switching toward domestic goods; imports can contract despite rising domestic consumption.
    - In Benchmark, imports are partially for materials, so imports fall more than in models where imports concentrate on consumption.
  - Gross exports vs. value added exports:
    - Textbook: depreciation immediately improves export competitiveness and increases gross exports.
    - In DCP and Producer Currency cases, local or dominant currency pricing limits pass-through of depreciation into import prices in destination markets → small increases in gross exports.
    - Benchmark DCP: very muted expansion in gross exports; however, value added exports increase sharply due to platforms switching to domestic content when imported material costs rise.
    - Under LCP, no motivation to switch to domestic content; no increase in value added exports.
    - In Textbook and DCP-NoVC, gross exports and value added exports are identical (imported materials are zero).
  - Domestic output and production composition:
    - Domestic output increases in all cases.
    - Strongest output response in Textbook (due to strong export response).
    - Benchmark: no increase in gross exports but substantial increase in value added exports through higher domestic content; output increases almost as much as Textbook and more than DCP-NoVC.
    - Smallest domestic demand increase in LCP (no decline in imports).
  - Current account effects:
    - Measured as B_A_t − B_A_{t−1}.
    - LCP: current account improves through valuation effects (imports priced in local currency cost less in global dollar terms due to depreciation).
    - Other models: decline in import volumes plus increase in value added exports improves current account.
  - Sectoral export responses:
    - Textbook: gross exports to global and regional markets increase as depreciation passes through.
    - Benchmark and DCP-NoVC: platform gross exports to global economy weak due to global currency invoicing; Benchmark especially muted because higher imported material costs reduce competitiveness.
    - Exports to regional partner: mildly crowded out in Benchmark, LCP, and DCP-NoVC; Textbook shows improvement.
    - Imported materials (V_BA_t): priced in global dollars (Benchmark) → lose competitiveness and platform switches to domestic content; priced in local currency (LCP) → imported materials increase with final exports.
    - Value added embedded in exports to global economy (V_HA_t + V_AB_t) increases immediately in Benchmark despite modest change in gross exports.
  - Cross-regional spillovers:
    - When regional imports are priced in global dollars or producer currency, country A’s depreciation reduces the competitiveness of those imports → imports from regional partner B fall.
    - Decline concentrated in imported value chain materials in Benchmark, so cross-regional trade falls more in Benchmark than in Textbook and DCP-NoVC.
    - Under LCP, imports from the regional partner rise (depreciation has little effect on competitiveness).
    - Gross exports of partner B to the global economy are little affected by A’s monetary policy under any specification; percent changes smaller than direct bilateral trade changes.
    - Value added exports of partner decline by a similar amount to its gross export change when affected.
    - Under LCP, spillover to partner B’s production is positive via increasing imports of consumer goods.
    - In other cases, partner B faces negative spillovers; decline in imports from B leads to a small decline in B’s output.

### 3.2 Global Interest Rate Shocks — shock design, propagation, trade and empirical predictions
- Shock setup and macro response:
  - Shock specification: one-time shock to the interest rate rule at period 1 such that λ_W_t=1 = 1.0075.
  - Equilibrium outcome in the Global economy:
    - Interest rates increase by slightly greater than 200 annualized basis points.
    - Dominant global currency appreciates by 2% relative to both regional currencies.
  - New Keynesian mechanism:
    - Persistent rise in the nominal global interest rate due to interest smoothing.
    - Decline in global consumption and output.

- Exchange rate, CPI pass-through, and monetary policy responses:
  - Regional exchange rate response:
    - Regional exchange rates depreciate temporarily by nearly 2% relative to the global dollar (near uncovered interest parity).
    - Depreciation is sharper in the LCP case due to weaker domestic policy rate response.
  - CPI pass-through:
    - Pass-through into consumer prices occurs to the degree consumer goods are priced in global currency.
    - Largest CPI pass-through in the DCP-NoVC case: imported consumer goods priced in dominant currency are the largest share of the consumer market basket (all imports are for consumer and all imports priced in dominant currency).
    - Textbook case: imported regional consumer goods are not priced in global dollars and do not face inflation.
    - Benchmark model: imports are a smaller fraction of consumer goods, so CPI response weaker than DCP-NoVC.
    - LCP case: no pass-through and virtually no CPI response.
  - Monetary tightening and interest rate changes:
    - CPI increases lead to monetary tightening; magnitude reflects CPI rise in each model.
    - Interest rates rise by 100 annualized basis points in the Benchmark and Textbook cases.
    - Interest rates rise more in the DCP-NoVC case.
    - Interest rates rise little in LCP.
    - Consumption declines where interest rates rise; negligible consumption response under LCP.

- Trade flows: imports, exports, and global value chains:
  - Invoicing and import responses:
    - LCP (invoicing in destination currency): imports insulated from depreciation → only a small decline in imports.
    - DCP (all imports invoiced in global dollars): depreciation sharply and immediately reduces gross imports from all locations.
    - Textbook (regional imports priced in exporter’s currency): regional imports face less exposure to the global shock → decline in overall imports smaller than Benchmark.
  - Exports and disruption:
    - LCP: exchange rates have little immediate impact on exports; export declines mainly reflect fall in regional and global consumption.
    - Textbook: depreciation against the global currency mostly insulates exports to the global economy; regional exports not priced in global currency → small decline in exports.
    - DCP-NoVC: substantially larger decline in gross exports than under LCP or Textbook.
    - Benchmark: even larger decline in gross exports, driven by decline in platform exports to the global economy and parallel decline in exports to the regional partner’s platform.
  - Gross exports vs value added exports:
    - Benchmark and DCP-NoVC: declines in value added content of exports are similar (Panel H).
    - Materials imports from regional and global economies are priced in global dollars and become more expensive with appreciation; regional platforms shift to domestic content → value added exports fall by less than gross exports in the Benchmark model.
    - Textbook and DCP-NoVC: no difference between gross and value added exports.
    - LCP: global value chain not disrupted → gross and value added exports responses similar.
  - Output and trade composition:
    - LCP: limited response of domestic consumption and imports, but exports decline → output declines.
    - Benchmark and NoVC (both with DCP): sharp decline in imports implies output falls by less than the decline in domestic consumption and exports.
    - Textbook: very small decline in exports combined with relatively large decline in imports → small increase in output.
  - Current account:
    - All cases show an increase in the current account.
    - Under Benchmark, Textbook, and DCP-NoVC this reflects an increase in trade balance in volume terms; under LCP it reflects valuation effects.
  - Directional effects within the region:
    - Benchmark: appreciation of the international dollar makes imports from the regional partner less competitive and symmetrically reduces exports to the regional partner; decline in regional materials trade for processing into exports to the contracting global economy intensifies regional trade disruption relative to DCP-NoVC.
    - LCP: decline in regional trade is minimal.
    - PCP case (notation in text): sharper decline in regional exports relative to LCP due to larger interest-rate led decline in regional consumption; region-wide depreciation does not disrupt regional trade as much as DCP cases.

- Robustness checks and testable implications:
  - Main testable implication 1:
    - In value added terms, a US monetary contraction leads to value added exports to the US declining by much less than value added exports to the rest of the world in the Benchmark model.
    - This is true in DCP and intensified by the global value chain; not true in LCP.
    - Size of effects depends on parameterization:
      - Substitutability between domestic content and imports: if weak, appreciation effect on regional trade weakens.
      - Demand sensitivity to interest rates: if demand response is large, exports to the global economy may fall more than exports to the regional economy.
  - Robustness parameterizations examined:
    - Low Elasticity case: ξ=ψ=ν=γ= 0.5.
    - Low Demand Response case: Frisch elasticity θ=  0.75 and inter-temporal elasticity of substitution ζ=.2.
    - Findings:
      - With Benchmark demand response and Low substitution, responses of exports to regional partners nearly as large as to the global economy.
      - If demand response is also low, regional exports can fall more than value added exports to the global economy.
    - Interpretation: demand responses can mask the impact of dominant currency pricing; empirical specification controls for GDP of the US and relevant parties to isolate DCP effects.
  - Main testable implication 2:
    - In the Benchmark model, gross exports to the US decline much more sharply than value added exports to the US.
    - Panel P: ratio of gross exports to the US to value added exports to the US declines across Benchmark, Low Elasticity, Low Demand Response, & Low Elasticity and Demand Response cases.
    - Decline is more intense when substitutability is high (easier shift toward domestic content).
  - Conclusion of robustness exercise:
    - Alternate parameterizations affect magnitudes, but the two main testable implications remain qualitatively robust.
    - Empirical focus is on direction of effects rather than precise magnitudes.

- Empirical analysis: data, measurement, and estimation (method and sample specifics preserved):
  - Objective: provide suggestive evidence on model predictions about elasticity of different trade flow measures to US interest rates.
  - Data and decomposition:
    - Use granular decomposition of exports from Wang et al. (2013) and Wang et al. (2017b) to split total bilateral exports into gross and value added components and identify ultimate destination of final consumption.
    - Measures at country-sector-destination level: VAF, VAB, IVAF, IVAB (definitions preserved as in source).
  - Testable empirical prediction:
    - Define ratio R_x = x_non-USdestination / x_US for x ∈ {VAF, VAB, IVAF, IVAB}.
    - Model predicts r_x should fall in response to US interest rate increases (US-targeted value added shares decline less than non-US shares).
  - Estimation specification and identification:
    - r_{x,i,j,t+h}(s) = α_{i,j}^h(s) + η^h r_{i,j,x,t-1}(s) + β^h_i us,t + δ^h X_{ij,t} + ε_{i,j,t+h}(s)
    - us,t proxied by the shadow rate in Lombardi and Zhu (2018); first-stage regression orthogonalizes the interest rate with respect to contemporaneous and lagged US GDP and inflation.
    - Controls X_{ij,t}: contemporaneous and lagged bilateral exchange rate, real GDP of importer, exporter and the US, total imports by importer, unit labor cost in exporter, inflation in importer, quadratic time trend, and dummy for financial crisis years 2008 and 2009.
    - Impulse responses computed using local projections (Jordà (2005)).
  - Sample and aggregation:
    - Main data source: World Input Output Database (WIOD).
    - Available sample: 1995-2011 (annual).
    - Coverage: 35 sectors in 40 countries.
    - Total bilateral export observations at sector level per year: 54,600 (=40*39*35).
    - Exclusions: observations where exporting and importing country are in Europe are excluded.
  - Estimation choices:
    - Regressions estimated at bilateral country-sector-destination level.
    - GMM estimator (Arellano and Bond (1991)) with forward orthogonal deviation transformation used; results similar with linear fixed effects estimator.
  - Empirical findings summary:
    - Figure 4.1: the ratio r_x declines persistently in response to a US monetary contraction, consistent with model prediction that trade serving final demand outside the US contracts by more than trade eventually serving final demand in the US.
    - Forward and backward export measures react similarly.
    - Figure 4.1 notes: each term represents the response (in % change) of the corresponding ratio in equation 4.1 to a 1% increase in the US interest using a dynamic panel fixed effects model with country-sector-importer fixed effects.

### 4.2 Sectoral decomposition and robustness — sector-specific empirical findings and interpretation
- Key empirical findings: sectoral responses of bilateral value added exports:
  - Dynamics of primary sectors (commodities) are "somewhat different on impact" from secondary and tertiary sectors, although "the ratio still declines sharply beyond two years" similar to secondary and tertiary sectors.
  - Reason: estimation can only control for one sector being primary; other sectors in the value chain may be involved so the invoicing channel can still be present even if originating in the primary sector.
  - Online Appendix B: patterns in figures 4.1 and 4.2 hold when restricting to indirect value added exports (involvement of third countries).
  - Estimation for Figure 4.2: responses (in % change) to a 1% increase in the US interest using a dynamic panel fixed effects model with country-sector-importer fixed effects.

- Gross versus value added exports to the US:
  - Model predicts a differential response of gross and value added exports to the US (Figure 3.2 Panels K, N and P).
  - Empirical approach: estimate response of ratio of gross to value added exports from non-US country-sectors to the US using framework similar to equation 4.2.
  - Despite smaller sample and high comovement, pooled OLS estimates in Figure 4.3 provide "indicative evidence" that both forward and backward based ratios of gross to value added exports to the US decline in line with model predictions.
  - Figure 4.3 estimation notes: percentage deviations from steady state; shaded 95% confidence interval; linear and quadratic trend; importing country restricted to the US; pooled OLS with clustered standard errors at country-sector-destination level.
  - Online Appendix B (Figure B.3): patterns hold when using only indirect value added exports in the denominator.

- Indirect value added exports (Online Appendix B) — definitions and empirical results:
  - Definitions preserved exactly: VAF, VAB, IVAF, IVAB (as summarized in source).
  - Empirical results for indirect flows:
    - Figures B.1–B.3 show IVAF and IVAB decline following a 1% increase in the US interest rate when estimated with a dynamic panel fixed effects model with country-sector-importer fixed effects.
    - Figure B.3 estimation notes mirror Figure 4.3: percentage deviations from steady state; shaded 95% confidence interval; linear and quadratic trend; importing country restricted to the US; pooled OLS with clustered standard errors.

- Interpretation and policy-relevant implications:
  - Framework exploits differences in responses of bilateral sector-level value added and gross trade flows by destination; differential responses align with models featuring global value chains and dollar invoicing.
  - Model and normative implications:
    - DCP and GVC imply appreciation of the global currency disrupts use of imported materials and shifts regional production toward domestic content for exports to the global economy.
    - DCP and GVC "combine to bring the dynamics of output and inflation more in line with the textbook model," but the gap is not fully closed, especially in trade responses to external monetary shocks.
    - Textbook model policy implications "need not carry over more broadly"; full normative analysis is beyond scope and recommended for future research.
  - Empirical takeaway:
    - Components of trade that are GVC-oriented and directed toward US consumers are "less affected" by US interest rate changes than gross exports or value added exports to other partners.
    - Countries exporting to the US increase domestic content of their exports in response to US interest rate changes "in a manner consistent with the model."
  - Broader relevance:
    - Results generalize to other shocks that move the exchange rate, informing policymakers on how exogenous shocks and policy actions affect trade flows in a world with dollar invoicing and rising prevalence of global value chains.
  - Suggested further work:
    - Investigate relationship between gross and value added exports in response to different shocks (including domestic shocks) using higher frequency data and tighter identification schemes.

*Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022028-print-pdf.pdf*

### 2.1  Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    7

### 2.1  Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    7

### Preferences and consumption aggregation
- Household preferences in economy j:
  - ∞
    ∑
    t=0
    β
    t
    u(C
    j
    t
    ,L
    j
    t
    ) =
    ∞
    ∑
    t=0
    β
    t
    {
    ζ
    ζ−1
    C
    j
    ζ−1
    ζ
    t
    −Γ
    j
    θ
    1 +θ
    L
    j
    θ+1
    θ
    t
    }
    (2.1)
- Consumption basket C
  j
  t is a CES aggregate of regional goods CR
  j
  t and global goods CW
  j
  t:
  - C
    j
    t
    =
    (
    a
    1
    ξ
    j
    {
    CR
    j
    t
    }
    ξ−1
    ξ
    + (1−a
    j
    )
    1
    ξ
    {
    CW
    j
    t
    }
    ξ−1
    ξ
    )
    ξ
    ξ−1
    (2.2)
- Regional goods CR
  j
  t combine goods from each regional trading partner:
  - CR
    j
    t
    =
    (
    b
    1
    ψ
    j
    {
    CA
    j
    t
    }
    ψ−1
    ψ
    + (1−b
    j
    )
    1
    ψ
    {
    CB
    j
    t
    }
    ψ−1
    ψ
    )
    ψ
    ψ−1
    (2.3)
- Relative demand for global and regional goods:
  - CR
    j
    t
    = a
    j
    (
    PR
    j
    t
    CPI
    j
    t
    )
    −ξ
    C
    j
    t
  - CW
    j
    t
    = (1−a
    j
    )
    (
    PW
    j
    t
    CPI
    j
    t
    )
    −ξ
    C
    j
    t
    (2.4)
- Demand for goods from A and B within regional goods:
  - 1
    CA
    j
    t
    CR
    j
    t
    = b
    j
    (
    PA
    j
    t
    PR
    j
    t
    )
    −ψ
  - CB
    j
    t
    CR
    j
    t
    = (1−b
    j
    )
    (
    PB
    j
    t
    PR
    j
    t
    )
    −ψ
    (2.5)

### Household budget constraint and asset holdings
- Households hold bonds B
  j
  t denominated in international dollars and face the budget constraint:
  - B
    j
    t
    = (1 +r
    j
    t−1
    )B
    j
    t−1
    + W
    j
    t
    L
    j
    t
    − CPI
    j
    t
    C
    j
    t
    + Π
    j
    t
    S
    j
    t
    (2.6)
- Nominal exchange rate S
  j
  t is defined as units of j currency per dollar; an increase denotes a domestic depreciation and S
  W
  t = 1 by definition.
- W
  j
  t denotes nominal wage. Interest rate (1 +r
  j
  t
  ) is the effective interest rate on international bonds relevant to household j. Π
  j
  t represents lump-sum profit pay-outs and taxes.
- The paper studies dynamics around a steady state with zero net international investment positions; wealth effects from international bond holdings are second order in this case.

### First-order conditions
- Labor supply condition:
  - Ω
    j
    t
    W
    j
    t
    = Γ
    j
    L
    j
    1
    θ
    t
    (2.7)
- Consumption Euler-type condition linking shadow value and consumption:
  - Ω
    j
    t
    CPI
    j
    t
    = C
    j
    −1
    ζ
    t
    (2.8)
- Intertemporal asset pricing condition:
  - 1 = E
    t
    [ β
    Ω
    j
    t+1
    Ω
    j
    t
    (1 + i
    j
    t
    ) ] = E
    t
    [ β
    Ω
    j
    t+1
    Ω
    j
    t
    S
    j
    t+1
    S
    j
    t
    (1 + r
    j
    t
    ) ]
- Ω
  j
  t denotes the shadow value of domestic currency and i
  j
  t is the domestic currency nominal interest rate.

### Role in the broader model (contextual points from the chapter)
- Household consumption and labor choices feed into:
  - Domestic value added production (Y
    j
    t = L
    j
    t) and marginal cost MCY
    j
    t = W
    j
    t.
- Consumption aggregator parameters {a
  j
  , b
  j
  , ξ, ψ} and household intertemporal parameters β, ζ, Γ
  j
  , θ determine demand elasticities and substitution between regional and global goods, which are central to quantifying how exchange rate and monetary shocks transmit through consumption and trade channels in the overall model.

*Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022028-print-pdf.pdf*

### 2.4  Market Equilibrium

### 2.4  Market Equilibrium

### Goods and platform market equilibrium
- Goods market equilibrium for economy j:
  - Y_j_t = ∫{h_l,t + ex_l,t} dl = DH_j_t H_j_t + DX_j_t EX_j_t  (equation (2.26))
  - DH_j_t ≡ [∫(ppi_l,t / PPI_j_t)^−φ dl]  
  - DX_j_t ≡ [∫(ipi_l,t / IPI_j_t)^−φ dl]  (equation (2.27))
- For regional economies, platform output equals exports to the global economy:
  - V_d_t = ∫{m_l,t} dl = DW_d_t M_d_t  (equation (2.28))
  - DW_d_t ≡ [∫(xpi_l,t / XPI_d_t)^−φ dl]  (equation (2.29))

### Interest rates and international bond market
- External interest rates:
  - 1 + r_d_t = {1 + (i_W_t e^(−η B_j_t))}  (equation (2.30))
  - Risk premium is a decreasing function of wealth B_j_t.
- Domestic policy (CPI-targeting Taylor Rule with persistence):
  - 1 + i_j_t
    = ( (1 + i_j_{t−1}) / (1 + i) )^χ_i
      (CPI_j_t / CPI_j_{t−1})^χ_π^(1−χ_i)
      (Y_j_t / Y)^χ_Y^(1−χ_i)
      λ_j_t  (equation (2.31))
  - λ_j_t is an exogenous monetary policy shock.
- International bond market equilibrium:
  - B_A_t + B_B_t + B_W_t = 0  (equation (2.32))

### Calibration targets and trade-weight assumptions
- Calibration matches East Asian region trade weights and GVC significance:
  - Size of total exports of regional economies as a share of GDP = 50% (average of China, Indonesia, Korea, Malaysia, Philippines, Thailand, and Vietnam between 2010 and 2018).
  - Foreign value added = 25% of exports (as in 2018 in East Asia & the Pacific).
  - About 55% of foreign value added comes from within the region.
  - About 50% of the trade of the regional economy is with the regional trading partner (Dent (2017)).
  - Preferences: two regional economies identical; global economy treats each regional economy identically.
- Normalizations:
  - Γ_d normalized so steady state employment in the regional economies L_d = 1.
  - Γ_W set so the world economy is twice as large as either regional economy.
- No Value Chain (NoVC) trade weight parameterization:
  - e_d = 1; f_A = 1; f_B = 0
  - Exports are 50% of GDP and 50% of exports are to the regional economy.

### Key parameter values preserved exactly
- ξ = ψ = ν = γ = 2
- ζ = 0.5
- θ = 2
- φ = 11
- Subsidy: τ φ φ−1 = 1  (as specified)
- Price stickiness parameter: κ = .75
- Subjective discount factor: β = .99
- Interest rate smoothing parameter: χ_i = .75
- Policy rule parameters: {χ_π, χ_Y} are set to a standard value of {1.5, 0.5 4 }
- Risk premium parameter: η = −.0001

### Models compared (as in Table 1)
- Value Chain / No Value Chain across invoicing regimes:
  - Dominant Currency: (1) Benchmark  (2) DCP-NoVC
  - Local Currency: (3) LCP
  - Producer Currency: (4) Textbook

### Domestic monetary policy shock design
- Shock: exogenous decrease in policy interest rates in regional economy A (leading to exchange rate depreciation).
- One-time shock specification:
  - λ_A_t=1 = .9925, calibrated to generate an equilibrium domestic exchange rate depreciation of approximately 2%.

### Simulation findings (impulse response summary)
- Exchange rate and CPI pass-through:
  - Exchange rate depreciation is close to equivalent in Benchmark, Textbook, and DCP-NoVC; slightly larger under LCP.
  - Depreciation raises the price of imported goods and passes through into CPI.
  - CPI pass-through: minimal under LCP; stronger in Textbook and NoVC; strongest in models where import content of consumption is large.
- Interest rate responses (via CPI-targeting Taylor rule):
  - Decline in interest rates similar in NoVC and Textbook.
  - Slightly sharper decline in Benchmark (due to stronger CPI response).
  - Sharply larger decline under LCP (due to weaker CPI pass-through).
- Consumption and demand:
  - Persistent cut in interest rates leads to a proportional expansion in consumption.
  - Expansion in consumption: sharpest under LCP; roughly equivalent under NoVC and Textbook; intermediate under Benchmark.
- Imports and expenditure switching:
  - Under LCP, import volumes increase proportionally with domestic demand.
  - Under Benchmark, Textbook, and DCP-NoVC, domestic depreciation makes imports more expensive and leads to expenditure switching toward domestic goods; imports can contract despite rising domestic consumption.
  - In Benchmark, imports are partially for materials, so imports fall more than in models where imports concentrate on consumption.
- Gross exports vs. value added exports:
  - Textbook: depreciation immediately improves export competitiveness and increases gross exports.
  - In DCP and Producer Currency cases, local or dominant currency pricing limits pass-through of depreciation into import prices in destination markets → small increases in gross exports.
  - Benchmark DCP: very muted expansion in gross exports; however, value added exports increase sharply due to platforms switching to domestic content when imported material costs rise.
  - Under LCP, no motivation to switch to domestic content; no increase in value added exports.
  - In Textbook and DCP-NoVC, gross exports and value added exports are identical (imported materials are zero).
- Domestic output and production composition:
  - Domestic output increases in all cases.
  - Strongest output response in Textbook (due to strong export response).
  - Benchmark: no increase in gross exports but substantial increase in value added exports through higher domestic content; output increases almost as much as Textbook and more than DCP-NoVC.
  - Smallest domestic demand increase in LCP (no decline in imports).
- Current account effects:
  - Measured as B_A_t − B_A_{t−1}.
  - LCP: current account improves through valuation effects (imports priced in local currency cost less in global dollar terms due to depreciation).
  - Other models: decline in import volumes plus increase in value added exports improves current account.
- Sectoral export responses (panels J–N summary):
  - Textbook: gross exports to global and regional markets increase as depreciation passes through.
  - Benchmark and DCP-NoVC: platform gross exports to global economy weak due to global currency invoicing; Benchmark especially muted because higher imported material costs reduce competitiveness.
  - Exports to regional partner: mildly crowded out in Benchmark, LCP, and DCP-NoVC; Textbook shows improvement.
  - Imported materials (V_BA_t): priced in global dollars (Benchmark) → lose competitiveness and platform switches to domestic content; priced in local currency (LCP) → imported materials increase with final exports.
  - Value added embedded in exports to global economy (V_HA_t + V_AB_t) increases immediately in Benchmark despite modest change in gross exports.
- Cross-regional spillovers (panels O–R summary):
  - When regional imports are priced in global dollars or producer currency, country A’s depreciation reduces the competitiveness of those imports → imports from regional partner B fall.
  - Decline concentrated in imported value chain materials in Benchmark, so cross-regional trade falls more in Benchmark than in Textbook and DCP-NoVC.
  - Under LCP, imports from the regional partner rise (depreciation has little effect on competitiveness).
  - Gross exports of partner B to the global economy are little affected by A’s monetary policy under any specification; percent changes smaller than direct bilateral trade changes.
  - Value added exports of partner decline by a similar amount to its gross export change when affected.
  - Under LCP, spillover to partner B’s production is positive via increasing imports of consumer goods.
  - In other cases, partner B faces negative spillovers; decline in imports from B leads to a small decline in B’s output.

*Source: wpiea2022028-print-pdf - 2.4  Market Equilibrium*

### 3.2  Global Interest Rate Shocks

### 3.2 Global Interest Rate Shocks

### Shock setup and macro response
- Shock specification: one-time shock to the interest rate rule at period 1 such that λ_W_t=1 = 1.0075.
- Equilibrium outcome in the Global economy:
  - Interest rates increase by slightly greater than 200 annualized basis points.
  - Dominant global currency appreciates by 2% relative to both regional currencies.
- New Keynesian mechanism:
  - Persistent rise in the nominal global interest rate due to interest smoothing.
  - Decline in global consumption and output.

### Exchange rate, CPI pass-through, and monetary policy responses
- Regional exchange rate response:
  - Regional exchange rates depreciate temporarily by nearly 2% relative to the global dollar (near uncovered interest parity).
  - Depreciation is sharper in the LCP case due to weaker domestic policy rate response.
- CPI pass-through:
  - Pass-through into consumer prices occurs to the degree consumer goods are priced in global currency.
  - Largest CPI pass-through in the DCP-NoVC case: imported consumer goods priced in dominant currency are the largest share of the consumer market basket (all imports are for consumer and all imports priced in dominant currency).
  - Textbook case: imported regional consumer goods are not priced in global dollars and do not face inflation.
  - Benchmark model: imports are a smaller fraction of consumer goods, so CPI response weaker than DCP-NoVC.
  - LCP case: no pass-through and virtually no CPI response.
- Monetary tightening and interest rate changes:
  - CPI increases lead to monetary tightening; magnitude reflects CPI rise in each model.
  - Interest rates rise by 100 annualized basis points in the Benchmark and Textbook cases.
  - Interest rates rise more in the DCP-NoVC case.
  - Interest rates rise little in LCP.
  - Consumption declines where interest rates rise; negligible consumption response under LCP.

### Trade flows: imports, exports, and global value chains
- Invoicing and import responses:
  - LCP (invoicing in destination currency): imports insulated from depreciation → only a small decline in imports.
  - DCP (all imports invoiced in global dollars): depreciation sharply and immediately reduces gross imports from all locations.
  - Textbook (regional imports priced in exporter’s currency): regional imports face less exposure to the global shock → decline in overall imports smaller than Benchmark.
- Exports and disruption:
  - LCP: exchange rates have little immediate impact on exports; export declines mainly reflect fall in regional and global consumption.
  - Textbook: depreciation against the global currency mostly insulates exports to the global economy; regional exports not priced in global currency → small decline in exports.
  - DCP-NoVC: substantially larger decline in gross exports than under LCP or Textbook.
  - Benchmark: even larger decline in gross exports, driven by decline in platform exports to the global economy and parallel decline in exports to the regional partner’s platform.
- Gross exports vs value added exports:
  - Benchmark and DCP-NoVC: declines in value added content of exports are similar (Panel H).
  - Materials imports from regional and global economies are priced in global dollars and become more expensive with appreciation; regional platforms shift to domestic content → value added exports fall by less than gross exports in the Benchmark model.
  - Textbook and DCP-NoVC: no difference between gross and value added exports.
  - LCP: global value chain not disrupted → gross and value added exports responses similar.
- Output and trade composition:
  - LCP: limited response of domestic consumption and imports, but exports decline → output declines.
  - Benchmark and NoVC (both with DCP): sharp decline in imports implies output falls by less than the decline in domestic consumption and exports.
  - Textbook: very small decline in exports combined with relatively large decline in imports → small increase in output.
- Current account:
  - All cases show an increase in the current account.
  - Under Benchmark, Textbook, and DCP-NoVC this reflects an increase in trade balance in volume terms; under LCP it reflects valuation effects.
- Directional effects within the region:
  - Benchmark: appreciation of the international dollar makes imports from the regional partner less competitive and symmetrically reduces exports to the regional partner; decline in regional materials trade for processing into exports to the contracting global economy intensifies regional trade disruption relative to DCP-NoVC.
  - LCP: decline in regional trade is minimal.
  - PCP case (notation in text): sharper decline in regional exports relative to LCP due to larger interest-rate led decline in regional consumption; region-wide depreciation does not disrupt regional trade as much as DCP cases.

### Key comparative outcomes (global vs regional destinations)
- All models: decline in gross exports to the global economy primarily driven by declining global aggregate demand.
- Textbook: depreciation against the global currency mostly insulates exports from this decline.
- DCP-NoVC and LCP: sharper declines in exports to the global economy because exports to the global economy are priced in global currency.
- Benchmark: value chain intensifies decline in gross exports to the global economy because:
  - Export platform relies on imported materials which rise in price with global currency appreciation.
  - Platform exports to the global economy are reduced to the extent higher materials prices pass-through into platform export prices.
- Materials imports:
  - Panel L: materials imports decline sharply under the Benchmark in response to global appreciation.
  - Disruption of imported materials trade much smaller under LCP due to destination currency invoicing.

### Robustness checks and testable implications
- Main testable implication 1:
  - In value added terms, a US monetary contraction leads to value added exports to the US declining by much less than value added exports to the rest of the world in the Benchmark model.
  - This is true in DCP and intensified by the global value chain; not true in LCP.
  - Size of effects depends on parameterization:
    - Substitutability between domestic content and imports: if weak, appreciation effect on regional trade weakens.
    - Demand sensitivity to interest rates: if demand response is large, exports to the global economy may fall more than exports to the regional economy.
- Robustness parameterizations examined:
  - Low Elasticity case: ξ=ψ=ν=γ= 0.5.
  - Low Demand Response case: Frisch elasticity θ=  0.75 and inter-temporal elasticity of substitution ζ=.2.
  - Findings:
    - With Benchmark demand response and Low substitution, responses of exports to regional partners nearly as large as to the global economy.
    - If demand response is also low, regional exports can fall more than value added exports to the global economy.
  - Interpretation: demand responses can mask the impact of dominant currency pricing; empirical specification controls for GDP of the US and relevant parties to isolate DCP effects.
- Main testable implication 2:
  - In the Benchmark model, gross exports to the US decline much more sharply than value added exports to the US.
  - Panel P: ratio of gross exports to the US to value added exports to the US declines across Benchmark, Low Elasticity, Low Demand Response, & Low Elasticity and Demand Response cases.
  - Decline is more intense when substitutability is high (easier shift toward domestic content).
  - Global demand response affects numerator and denominator similarly and is less important for this ratio.
- Conclusion of robustness exercise:
  - Alternate parameterizations affect magnitudes, but the two main testable implications remain qualitatively robust.
  - Empirical focus is on direction of effects rather than precise magnitudes.

### Empirical analysis: data, measurement, and estimation
- Objective: provide suggestive evidence on model predictions about elasticity of different trade flow measures to US interest rates.
- Data and decomposition:
  - Use granular decomposition of exports from Wang et al. (2013) and Wang et al. (2017b) to split total bilateral exports into gross and value added components and identify ultimate destination of final consumption.
  - Measures at country-sector-destination level:
    - VAF: Value added exports (forward) eventually consumed as final demand in a destination country (includes indirect exports via other sectors in the same country).
    - VAB: Value added exports (backward) eventually consumed as final demand in a destination country (includes indirect exports of other sectors in the same country via this sector).
    - IVAF and IVAB: Indirect value added exports (forward and backward) intermediated via third countries.
  - Example interpretation: if commodity sector in country A provides x units of inputs to electronics processing sector in A, which exports y (> x) units to country B, then commodity sector VAF = x and electronics processing VAB = y.
- Heterogeneity:
  - Large heterogeneity across countries and sectors in forward/backward value added exports and GVC participation.
  - Examples: mining sectors have larger forward exports across countries; electronics processing sectors in China have higher backward exports.
- Testable empirical prediction:
  - Define ratio R_x = x_non-USdestination / x_US for x ∈ {VAF, VAB, IVAF, IVAB}.
  - Model predicts r_x should fall in response to US interest rate increases (US-targeted value added shares decline less than non-US shares).
- Estimation specification:
  - r_{x,i,j,t+h}(s) = α_{i,j}^h(s) + η^h r_{i,j,x,t-1}(s) + β^h_i us,t + δ^h X_{ij,t} + ε_{i,j,t+h}(s)
  - r_{x,i,j,t+h}(s) is log of the ratio in equation 4.1 for source country i, sector s, destination j.
  - us,t proxied by the shadow rate in Lombardi and Zhu (2018); first-stage regression orthogonalizes the interest rate with respect to contemporaneous and lagged US GDP and inflation.
  - Controls X_{ij,t}: contemporaneous and lagged bilateral exchange rate, real GDP of importer, exporter and the US, total imports by importer, unit labor cost in exporter, inflation in importer, quadratic time trend, and dummy for financial crisis years 2008 and 2009.
  - Impulse responses computed using local projections (Jordà (2005)).
- Sample and aggregation:
  - Main data source: World Input Output Database (WIOD).
  - Available sample: 1995-2011 (annual).
  - Coverage: 35 sectors in 40 countries.
  - Total bilateral export observations at sector level per year: 54,600 (=40*39*35).
  - Exclusions: observations where exporting and importing country are in Europe are excluded (dollar invoicing likely limited and data availability on covariates reduced).
- Estimation choices:
  - Regressions estimated at bilateral country-sector-destination level to exploit granularity, increase sample size (important given 15-year time dimension), reduce endogeneity concerns, and better measure value added trade flows.
  - GMM estimator (Arellano and Bond (1991)) with forward orthogonal deviation transformation used to address endogeneity from lagged dependent variable; results similar with linear fixed effects estimator.
- Empirical findings (summary):
  - Figure 4.1: the ratio r_x declines persistently in response to a US monetary contraction, consistent with model prediction that trade serving final demand outside the US contracts by more than trade eventually serving final demand in the US.
  - Forward and backward export measures react similarly, consistent with significant positive correlation between forward and backward GVC participation.
  - Figure 4.1 notes: each term represents the response (in % change) of the corresponding ratio in equation 4.1 to a 1% increase in the US interest using a dynamic panel fixed effects model with country-sector-importer fixed effects.

*Italic: Source: wpiea2022028-print-pdf - 3.2 Global Interest Rate Shocks*

### 4.2 by splitting the sample into three broad categories by export sector-primary, secondary

### 4.2 by splitting the sample into three broad categories by export sector-primary, secondary and tertiary

### Key empirical findings: sectoral responses of bilateral value added exports
- The dynamics of primary sectors, which are dominated by commodities, are "somewhat different on impact" from secondary and tertiary sectors, although "the ratio still declines sharply beyond two years" similar to secondary and tertiary sectors.
- One reason offered: the estimation can only control for the fact that one of the sectors in a particular bilateral value added trade flow is primary, but other sectors (including manufacturing and services) may be involved in the value chain over time before it reaches the final consumer; in that case "the invoicing channel would still be present in the value chain even if it originates in the primary sector."
- Online Appendix B shows the patterns in figures 4.1 and 4.2 also hold when restricting attention to only indirect value added exports, i.e. "the subset of bilateral value added exports that entail explicit involvement of third countries."
- Estimation details for Figure 4.2:
  - Each term represents the response (in % change) of the corresponding ratio as in equation 4.1 to a 1% increase in the US interest using a dynamic panel fixed effects model with country-sector-importer fixed effects.

### Gross versus value added exports to the US
- The model predicts a differential response of gross and value added exports to the US (referenced: Figure 3.2, Panels K, N and P).
- Empirical approach: estimate the response of the ratio of gross to value added exports from non-US country-sectors to the US using a framework similar to equation 4.2.
- Despite a smaller sample and high comovement between gross and value added series making patterns harder to disentangle with saturated fixed effects, pooled OLS estimates in Figure 4.3 provide "indicative evidence" that both forward and backward based ratios of gross to value added exports to the US decline in line with the model's predictions.
- Figure 4.3 estimation notes:
  - Percentage deviations from steady state shown.
  - The shaded error band is the 95% confidence interval for the pooled sample.
  - Linear and quadratic trend included in the regression.
  - Importing country restricted to the US.
  - Pooled OLS estimates with standard errors clustered at country-sector-destination level.
- Online Appendix B (Figure B.3) shows these patterns "continue to hold even when we use only indirect value added exports in the denominator, i.e the value added exports that are explicitly routed via third countries."

### Indirect value added exports (Online Appendix B)
- Definitions summarized in the source:
  - VAF: Value added exports (forward) of the country-sector that are eventually consumed as final demand in a particular destination country. "Forward" includes indirect exports of this sector via other sectors in the same country.
  - VAB: Value added exports (backward) of the country-sector that are eventually consumed as final demand in a particular destination country. "Backward" includes indirect exports of other sectors in the same country via this sector.
  - IVAF: Indirect value added exports (forward) — subset of VAF capturing value added by the source country-sector consumed as final demand in the destination but not exported directly (involves at least one more country different from source and ultimate destination).
  - IVAB: Indirect value added exports (backward) — subset of VAB capturing value added by the source country-sector consumed as final demand in the destination but not exported directly, involving at least three countries.
- Example from the Appendix illustrating IVAF/IVAB: if commodity sector in country A provides x units of inputs to electronics sector in country A, which exports y (> x) units to country B, then VAF of the commodity sector = x; if country B uses y, adds z, and exports to country C, then for commodity sector in A, IVAF to country C = x, and IVAB for the electronics sector in A to country C = y.
- Empirical results for indirect flows:
  - Figures B.1–B.3 show that the response patterns for indirect value added exports and the ratio of gross to indirect value added exports to the US mirror the main results: both IVAF and IVAB decline following a 1% increase in the US interest rate when estimated with a dynamic panel fixed effects model with country-sector-importer fixed effects.
  - Figure B.3 estimation notes mirror Figure 4.3: percentage deviations from steady state; shaded 95% confidence interval; linear and quadratic trend; importing country restricted to the US; pooled OLS with clustered standard errors at country-sector-destination level.

### Interpretation and policy-relevant implications (summary from section 4 and Conclusion)
- The paper provides a framework exploiting differences in responses of bilateral sector-level value added and gross trade flows by destination, and demonstrates that their differential responses are "in line with models that feature a prominent role for both global value chains as well as dollar invoicing."
- Model and normative implications (from Conclusion):
  - A world with a dominant currency pricing (DCP) and global value chains (GVC) implies that an appreciation of the global currency disrupts the use of imported materials and shifts the regional economy toward producing domestic content for exports to the global economy.
  - DCP and GVC "combine to bring the dynamics of output and inflation more in line with the textbook model," suggesting textbook policy implications (e.g., Benigno and Benigno (2003)) "may not be as far out of line even in a world with GVCs and DCP combined," but "the gap between the two models is not entirely closed, as evidenced most clearly in the response of trade to an external monetary shock."
  - Policy implications from the textbook model therefore "need not carry over more broadly"; a full-fledged normative policy analysis is beyond the paper's scope and is suggested as a fruitful avenue for future research.
- Empirical takeaway: components of international trade flows that are global value chain oriented and directed toward US consumers are "less affected" by US interest rate changes than gross exports or value added exports to other trading partners; countries exporting to the US increase the domestic content of their exports in response to changes in the US interest rate "in a manner consistent with the model."
- Broader relevance: results for monetary shocks generalize to other shocks that move the exchange rate, informing policymakers on how exogenous shocks and policy actions are likely to affect trade flows in a world with dollar invoicing and rising prevalence of global value chains.
- Suggested further work: investigate the relationship between gross and value added exports in response to different types of shocks (including domestic shocks) using higher frequency data and tighter identification schemes.

*Italic: Dollar Invoicing, Global Value Chains, and the Business Cycle Dynamics of International Trade — Working Paper No. WP/2022/028*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022028-print-pdf.pdf_