## Section 3–4: Data, empirical methodology, model, and results (wpiea2024013-print-pdf — Sections 3–4 excerpt)

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---

### Model structure and identification strategy
- Canonical DSGE model of a large open economy with nominal frictions via rigid producer currency pricing; two countries, two goods, and two nominal noncontingent bonds.
- Purpose: derive general equilibrium sign restrictions for identification of tariff shocks and trade policy uncertainty shocks.
- Model features and simplifications:
  - Limits additional functional and parametric assumptions to a necessary minimum.
  - Omits features (home bias, local currency pricing) that change quantitative but not qualitative implications.
  - Solved with third-order perturbation methods many times to derive a range of impulse responses for alternative parameter values.
- Government policy and shocks:
  - Domestic tariff follows AR(1) with stochastic volatility:
    - τ1 t = (1 − ρ) τ1 + ρ τ1 t−1 + ω t−1 ε t
    - ω t = (1 − ρ) ω + ρ ω t−1 + μ ν t
    - ε t and ν t are iid standard normal innovations.
  - τ1 t referred to as tariff shocks; ω t as uncertainty shocks.
  - Foreign retaliation: τ2 t = (1 − ρ) τ2 + ρ τ2 t−1 + ζ ω t−1 ε t, with ζ ∈ [0,1].
  - Tariff proceeds redistributed lump-sum to domestic households.
  - Central banks keep nominal money supply constant.
  - Equilibrium: symmetric, markets clear (goods, labor, money), both bonds zero net supply.

### Households and firms (model details)
- Households:
  - Global population normalized to 1; domestic households indexed z ∈ [0,n], foreign z ∈ (n,1].
  - Representative domestic household maximizes expected utility with discount factor β ∈ (0,1); utility arguments include real consumption C1t(z), demand shock d1t, nominal money M1t, consumption price index P1t, labor supply L1,S t(z).
  - Budget constraint (as written in source):
    - P1t C1t(z) + M1t(z) + T1t + B1,1 t(z) + S1,2 t B2,1 t(z)
      = M1t−1(z) + R1 t−1 B1,1 t−1(z) + S1,2 t R2 t−1 B2,1 t−1(z) [1 − ψ/2 B2,1 t−1] + W1t L1,S t(z) + Π1t.
  - S1,2 t is nominal exchange rate (price of foreign currency in home currency); increase implies depreciation.
  - ψ > 0 governs adjustment cost of foreign bond holdings.
- Firms:
  - Two-stage production: upstream imperfectly competitive intermediate goods; downstream perfectly competitive final good producer with CES aggregator.
  - Final good production (home):
    - YS,1 t = [∫0^n y1,1 t(z)^{(θ−1)/θ} dz + ∫_n^1 y2,1 t(z)^{(θ−1)/θ} dz]^{θ/(θ−1)}, with θ > 1.
    - Final good producer faces import tariff τ1t at the border; law of one price need not hold.
    - Demand for intermediate goods and price index specified in model (see source).
  - Intermediate firms set prices subject to quadratic Rotemberg (1982) price adjustment cost:
    - AC1 t(z) = (φ/2) [(p1 t(z) / p1 t−1(z) − 1)^2] p1 t y1 t.
  - Intermediate production linear in labor: yS,1 t(z) = a1 t L D,1 t(z).

### Calibration, priors, and solution method
- Frequency: quarters. Country 1 interpreted as the US.
- Calibrated parameter values (verbatim):
  - β = 1/1.01
  - θ = 6
  - κ = (θ − 1) / θ
  - ε = 3
  - χ = (1 − β) [(θ − 1) / (κ θ)]^{ε − 1} / 2
  - ψ = 0.0025
  - τ1 = τ2 = 0
  - Assume zero inflation in steady state.
- Additional parameter choices and distributions (mean and s.d. where applicable):
  - S.d. tariff rate shocks ω: 1 → 0.01
  - S.d. tariff volatility shocks μ: 1 → 0.01
  - Risk aversion σ: Inverse gamma, mean 1, s.d. 0.5 (presented as "Inverse gamma 1 0.25")
  - Inverse Frisch elasticity η: Inverse gamma, mean 1, s.d. 0.5 (table: "Inverse gamma 1 0.25")
  - Country size n: Beta, mean 0.5, s.d. 0.25
  - Persistence tariff shocks ρ: Beta, mean 0.95, s.d. 0.025
  - Price adjustment cost φ: Normal, mean 60, s.d. 15
  - Retaliation ζ: Beta, mean 0.6, s.d. 0.25
- Calibrated/steady-state implications:
  - Quarterly interest rate of 1% in steady state.
  - Interest rate elasticity of money demand of −0.33.
  - Consumption elasticity of 0.33.
  - Markup over marginal cost of 20%.
- Simulation and solution details:
  - Draw 10,000 parameter combinations from distributions.
  - For each draw compute impulse responses to tariff level shock and to a trade policy uncertainty shock.
  - Trade policy uncertainty shock computed with third-order approximation with pruning; simulate model for 1000 periods without shocks to obtain stochastic steady state (ergodic mean), discard first 1000 periods as burn-in, then feed in a trade policy uncertainty shock that doubles the standard deviation of tariff level shocks.
  - Third-order approximation and pruning follow Fernández-Villaverde et al. (2015) and Basu and Bundick (2017).

### Theoretical impulse-response results (key dynamics)
- Responses to a 1 percentage point (pp) tariff level shock (home country), over 12 quarters:
  - Tariff rate increases persistently for more than three years.
  - Domestic price of imported goods and consumer price level increase.
  - Producer prices remain initially unchanged due to price adjustment costs.
  - Nominal exchange rate appreciates; terms of trade improve.
  - Households substitute away from foreign goods toward domestic goods.
  - Exports fall; imports fall more than exports → trade balance tends to rise.
  - Labor and private consumption fall; output tends to decline.
- Responses to a trade policy uncertainty shock (doubling standard deviation of innovations to tariff level shocks):
  - Imports fall persistently.
  - Domestic firms raise producer prices and markups.
  - Consumer prices increase.
  - Domestic households increase precautionary saving relative to foreign households → demand for external assets rises.
  - Domestic demand falls more than foreign demand → nominal exchange rate tends to depreciate, exports increase, trade balance improves.
  - Depreciation further raises consumer prices.
  - Output: tends to rise initially and then to fall.
  - Key difference vs. Caldara et al. (2020): short positive output effect here (they assume full retaliation, eliminating differential demand and saving effects and yielding negative output response throughout).

### Empirical strategy and data (Bayesian SVAR)
- Estimated reduced-form Bayesian VAR:
  - yt = ν + Σ_{i=1}^p A_i y_{t−i} + u_t, with p = 4 (quarterly data).
  - Structural representation: B0 y_t = θ + Σ_{i=1}^p B_i y_{t−i} + ε_t, with u_t = B0^{−1} ε_t and Σ = B0^{−1} B0^{−1}′.
- Endogenous variables yt (quarterly, log levels), sample 1960Q1 to 2019Q4 (Covid-19 excluded):
  - real GDP
  - real exports
  - real imports
  - consumer price index (CPI)
  - nominal effective exchange rate
  - real customs duties
  - trade policy uncertainty for the United States
- Data treatment:
  - All series in log levels.
  - Nominal variables deflated by the consumer price index.
  - Tariff rate τ calculated from customs duties CD and imports M as τ = CD / M.
  - Customs duties, GDP, imports, and exports are in real terms.
  - A decrease in the nominal exchange rate denotes a US-Dollar appreciation (note on measurement).

### Structural identification approach and narrative sign restrictions
- Identification methods:
  - Traditional sign restrictions (Faust, 1998; Uhlig, 2005) placed on impact matrix B0^{-1}.
  - Narrative sign restrictions (Antolín-Díaz and Rubio-Ramírez, 2018) to refine admissible solutions.
- Impact sign restrictions (as used in the SVAR; signs shown for tariff shocks among others):
  - Customs duties: + for Tariff shock.
  - Imports: – for Tariff shock.
  - Exports: – for Tariff shock.
  - Consumer prices: + for Tariff shock.
  - Nominal exchange rate: – for Tariff shock (a decrease denotes a US-Dollar appreciation).
  - GDP: no sign restriction for Tariff shock.
  - * denotes no restriction for some entries.
- Rationale for tariff shock sign restrictions:
  - Real customs duties increase.
  - Real imports decrease.
  - Real exports decrease.
  - Consumer prices increase.
  - Nominal exchange rate appreciates.
  - No sign restriction on output due to theoretical ambiguity.
- Identification of TPU shocks:
  - Positive TPU shock raises the TPU index.
  - TPU shock assumed to lower customs duties on impact (imports decrease persistently per model predictions).
  - TPU shock assumed to increase consumer prices persistently.
  - Other responses left unrestricted.
- Narrative restrictions (selected episodes tied to shock signs to shrink admissible B0^{-1}):
  - 1971Q3 (Nixon shock): Tariff + ; TPU + ; Customs duties largest contributor.
  - 1975Q1 (Ford shock): Tariff + ; TPU + ; Customs duties largest contributor.
  - 2018Q1 (Trump steel and aluminum tariffs): Tariff + ; Customs duties largest contributor; TPU + noted for Trump episodes.
  - 2008Q4–2009Q1 (Great Recession): Tariff – ; Imports smallest — tariff least important driver of imports.
  - 2016Q4–2017Q1: TPU + ; TPU largest — Trump election and inauguration.
  - 2019Q2–2019Q3: TPU + ; Trump shock.

### Bayesian estimation and inference with sign restrictions
- Bayesian setup:
  - Priors: Minnesota prior with shrinkage (tightness λ = 0.2, decay α = 2); sum-of-coefficients; dummy-initial-observation prior.
  - Prior variance for reduced form coefficients: var((A_i)_{jj}) = λ^2 ψ_j i^α, with ψ_j set to OLS residual variance.
  - Variance for priors on exogenous variables set to 1,000.
- Inference:
  - Identification via sign restrictions yields sets of admissible parameter intervals for elements of B0^{-1}.
  - Obtained 1000 admissible draws.
  - Reported point-wise median and percentiles of impulse responses; 68% highest posterior density credible sets reported.

### Estimated shock series (summary)
- Estimated median shock series:
  - Largest tariff-shock spikes occur in 1971, 1975, and 2018/19.
  - Two large negative tariff shocks in 1972Q1 and 1976Q1 following quick withdrawal of Nixon and Ford tariff surcharges.
  - Third largest positive spike in 2018 (tariffs mainly on China).
- Cumulative tariff level series:
  - Sequence of tariff reduction shocks in the mid-1970s (US average tariffs on dutiable imports decreased from 14% in 1967 to about 6% by 1975).
  - Protectionist shocks in early 1980s and 1987.
  - Easing shocks after 1993; final major rise in 2018/19 related to President Trump’s tariffs.
- Trade policy uncertainty (TPU) series behavior:
  - TPU spikes in 1971, 1975, and 1993; marked rise from 2016 onward.
  - TPU shocks typically occur a few quarters before the largest tariff-level spikes (uncertainty rises before tariff changes).
  - Historical decompositions indicate tariff-level shocks drive customs duties; uncertainty shocks drive TPU series.

### Key empirical impulse-response results — Tariff level shocks
- A positive tariff level shock of one standard deviation raises customs duties by about 5% on impact.
- Immediate and short-run trade and output responses to a unit tariff level shock:
  - Imports drop on impact by 1% and further to −1.5% in the second quarter after the shock; after eight years they are still below the level where they would have been without the shock.
  - Exports show a similar response and recover marginally quicker than imports.
  - GDP falls immediately by 0.2%, and then to 0.3% below trend (the bands cover zero).
  - The nominal effective exchange rate tends to appreciate by up to 0.8%.
  - The consumer price level rises by 0.3%.
  - The trade policy uncertainty index increases following tariff changes.
- Persistence and general equilibrium elasticities:
  - Import elasticity (response of imports divided by response of customs duties):
    - upon impact: −0.2
    - after two years: −0.4
    - after six years: −0.8
    - after eight years: −0.9 (estimation uncertainty is high)
  - Export elasticity:
    - starts at −0.2
    - falls to −0.5 after eight years
  - GDP elasticity:
    - −0.05 when the shock hits
    - −0.2 after eight years
- Responses of other macro variables:
  - Domestic consumption declines persistently but the effect is small and only different from zero for a few quarters.
  - Investment drops strongly by 1% and remains persistently below trend for more than eight years.
  - Employment drops marginally on impact, then tends to overshoot (positive medium-run employment response not distinguishable from zero).
  - Wages decline by 0.3%.
  - Trade balance increases by 0.5 percentage points of GDP after one quarter; credible sets exclude zero after two years and the positive effect remains for another six years.
  - Import prices decline for many years; pass-through scaled by customs duties response is 0.1 upon impact and 0.5 in the medium run.
  - Terms of trade improve by up to 0.5% in the first year before falling back.

### Key empirical impulse-response results — Trade policy uncertainty shocks
- Immediate and short-run responses to a unit TPU shock:
  - The uncertainty index increases by more than 15% on impact.
  - Imports fall by about 1% and remain below trend for the full horizon though the effect is not distinguishable from zero after the first quarters.
  - Customs duties fall upon impact and then overshoot.
  - The nominal exchange rate tends to depreciate.
  - Exports increase (response imprecisely measured).
  - Output reaction is first negative and then positive but insignificant.
  - Consumer prices increase strongly and persistently by up to 0.5%; credible sets exclude zero over the full horizon of eight years.
- Additional variables under TPU shocks:
  - Consumption does not respond materially.
  - Investment, employment, and wages fall; employment and wages declines are distinguishable from zero.
  - Trade balance improves quickly and persistently; credible sets exclude zero.
  - Terms of trade tend to worsen.

### Forecast error variance and macroeconomic relevance
- Tariff level shocks (average importance over sample, 32-quarter horizon):
  - Explain half of the impact variability in customs duties.
  - Contribute 10-18% to variability in exports and imports.
  - Explanatory power for nominal exchange rate and consumer prices is lower at the 1-2 year horizon but increases to 10-15% in the 8th year.
  - Contribution to unexpected GDP volatility is close to 10% for most quarters.
- Trade policy uncertainty shocks:
  - Relevance for variability in exports, imports, and output is about half that of tariff shocks.
  - Explain a bit less than 5% of forecast errors at short horizons and a little more than 5% at longer horizons.
  - Account for more than half of the impact variation in the uncertainty index.

### Historical decomposition and episode analysis
- Long-run historical contributions:
  - Until the mid-1980s, tariff shocks contributed little to GDP and the trade balance, with exceptions in 1971 and 1974.
  - Since the mid-1980s, tariff shocks are an important driver of output and trade:
    - Trade tensions with Japan lowered GDP and raised the trade balance until the mid-1990s.
    - Trade liberalization (NAFTA in 1993, WTO in 1995, China WTO accession in 2001) generated a long boom.
    - The shift to lower tariffs raised the output gap by up to 3 log points for nearly 20 years.
  - Tariff shocks account for about one fourth of the deficit during the last 10 years.
- The 2018–2019 trade disputes (2018Q1–2019Q4):
  - Contributions of restrictive tariff shocks are negative from 2018Q2 onward.
  - Cumulative output costs of upward shift in US import tariffs:
    - reduced GDP by 1.1% in 2018
    - reduced GDP by 2.9% in 2019
  - Trade policy uncertainty shocks in 2018/19 raised output by 2% over both years.
  - Net effect: the trade disputes in 2018/19 entailed an output cost of 2% of GDP to the US.

### Sectoral and regional effects (method and findings)
- Methodology:
  - Local-projection regressions: yi,t+h = αi,h + (βi,h)′ xi,j,t−1 + φi,h Shockj,t + ξi,t+h for h = 0,...,H.
  - Shockj,t = ˆεj,t is estimated tariff level or TPU shock; xi,j,t−1 includes one lag of the outcome variable.
  - Estimated for each posterior draw of the shock series and computed 68% point-wise credible sets; focus on peak/trough responses.
- Sectoral responses to a unit positive tariff level shock:
  - Imports: All but two sectors reduce imports significantly; mineral fuels, industrial supplies, and crude material respond most negatively, with import reductions of 5-15%.
  - Exports: Firms reduce exports across the board, by between 2-10%.
  - Investment: 13 out of 19 sectors cut back on capital formation; effects often different from zero.
  - Employment: Declines in majority of sectors but increases in others; estimation uncertainty is high.
  - Summary: Tariffs reduce US international trade and investment in most sectors; employment effects are mixed.
- Sectoral responses to a unit positive TPU shock:
  - Imports: Imports drop in 6 sectors and increase in 10 sectors; many peak responses indistinguishable from zero.
  - Exports: Increase in all but one sector; increases largely different from zero.
  - Investment: Mostly negative; firms reduce investment when TPU increases.
  - Employment: Falls in 10 out of 11 sectors; decline distinguishable from zero in 4 sectors.
  - Summary: TPU produces diverse sectoral outcomes; reduces sectoral investment but generally raises exports.
- Comparison:
  - Tariff level shocks are more detrimental to sectoral activity than uncertainty shocks.
  - Tariffs: broad reductions in trade and investment across sectors.
  - Uncertainty: reduces investment but raises exports and partially imports.

### Spatial distribution: state-level employment effects
- Employment effect of a unit positive tariff level shock (peak/trough):
  - Most states: no discernible to slightly negative employment reaction (map legend: -0.97, -0.47, 0.02, 0.52, 1.01 % change).
  - States with clear job losses: Alaska, Luisiana, Nevada, Oklahoma, West Virginia, Wyoming.
  - States with some job gains: Arizona, Florida, Georgia.
- Employment effect of a unit positive TPU shock:
  - Map predominantly red at coasts and Rust Belt; middle-west and Alaska yellow to green.
  - Possible explanation: differential exposure to exchange rate depreciation and commodity production.
- Overall spatial finding:
  - Results question idea that protectionism systematically creates more domestic jobs or allows redistributing them across the country.

### Scenario: output effects of a return to free trade (summary)
- Scenario: customs duties and TPU gradually decrease back to pre-2016 levels over 2020Q1-2022Q4, driven only by trade policy level and uncertainty shocks; paths return linearly within three years.
- GDP and cumulative output effects:
  - After three years, median GDP difference between free-trade scenario and unconditional forecast: 3.3%.
  - Cumulative output differences over three years: 4.4% (first year: 0.3%; second year: 1.4%; third year: 2.7%).
  - Comparing free-trade scenario to alternative where tariffs remain at 2019 levels for three years yields cumulative output gain of 5.3%.
  - Paper-wide summary estimate: reversing 2018/19 protectionism → cumulative output gain of 4% over three years.
- Note: numbers likely conservative because unconditional forecast already implies some tariff and uncertainty reductions absent in actual data.

### Sensitivity, robustness, and additional results
- Sensitivity analyses reported across multiple alternative specifications: replacing output with consumption, investment, employment; using real effective exchange rate instead of nominal; producer prices instead of consumer prices; including trade in services; alternative samples and lag lengths; adding TFP and monetary policy shocks.
- Additional diagnostics and figures: impulse responses for all draws, historical decompositions for customs duties, TPU, employment, investment, and scenario comparisons.
- Online Appendix contains Figures A.1–A.36 and Tables with data descriptions and robustness checks.

*Source: wpiea2024013-print-pdf (Sections 3–4 excerpt).*

### Section 3 describes the data and the empirical methodology.  Section 4 presents the results.  Section

### Section 3–4: Data, empirical methodology, model, and results (wpiea2024013-print-pdf — Sections 3–4 excerpt)

### Model structure and identification strategy
- Canonical DSGE model of a large open economy with nominal frictions via rigid producer currency pricing; two countries, two goods, and two nominal noncontingent bonds.
- Purpose: derive general equilibrium sign restrictions for identification of tariff shocks and trade policy uncertainty shocks.
- Model features and simplifications:
  - Limits additional functional and parametric assumptions to a necessary minimum.
  - Omits features (home bias, local currency pricing) that change quantitative but not qualitative implications.
  - Solved with third-order perturbation methods many times to derive a range of impulse responses for alternative parameter values.

### Households
- Two countries with constant number of households and firms; global population normalized to 1.
- Domestic households indexed z ∈ [0,n]; foreign households z ∈ (n,1]. n measures fraction of domestic economy in world economy.
- Representative domestic household maximizes expected utility:
  - Discount factor β ∈ (0,1).
  - Utility arguments include real consumption C1t(z), demand shock d1t, nominal money M1t, consumption price index P1t, labor supply L1,S t(z).
  - First-order conditions obtained from maximization subject to the budget constraint and ruling out Ponzi schemes.
- Budget constraint components (as written in source):
  - P1t C1t(z) + M1t(z) + T1t + B1,1 t(z) + S1,2 t B2,1 t(z)
    = M1t−1(z) + R1 t−1 B1,1 t−1(z) + S1,2 t R2 t−1 B2,1 t−1(z) [1 − ψ/2 B2,1 t−1] + W1t L1,S t(z) + Π1t.
  - S1,2 t is nominal exchange rate (price of foreign currency in home currency); increase implies depreciation of domestic currency.
  - ψ > 0 governs adjustment cost of foreign bond holdings.

### Firms
- Two-stage production: upstream imperfectly competitive producers of differentiated intermediate goods; downstream perfectly competitive final good producers using CES aggregator.
- Final good production (home):
  - YS,1 t = [∫0^n y1,1 t(z)^{(θ−1)/θ} dz + ∫_n^1 y2,1 t(z)^{(θ−1)/θ} dz]^{θ/(θ−1)}, with θ > 1.
  - Final good producer faces import tariff τ1t at the border; law of one price need not hold.
  - Demand for intermediate goods:
    - y1,1 t(z) = [p1 t(z) / P1 t]^{−θ} YS,1 t
    - y2,1 t(z) = [S1,2 t (1 + τ1t) p2 t(z) / P1 t]^{−θ} YS,1 t
  - Price index of final good:
    - P1 t = [∫_0^n p1 t(z)^{1−θ} dz + ∫_n^1 [S1,2 t (1 + τ1t) p2 t(z)]^{1−θ} dz]^{1/(1−θ)}
- Intermediate firms:
  - Production linear in labor: yS,1 t(z) = a1 t L D,1 t(z) (a1 t is technology shock).
  - Aggregate demand for firm z: yD,1 t(z) = n y1,1 t(z) + (1−n) y1,2 t(z).
  - Firms set p1 t(z) to maximize profits with quadratic Rotemberg (1982) price adjustment cost:
    - AC1 t(z) = (φ/2) [(p1 t(z) / p1 t−1(z) − 1)^2] p1 t y1 t.

### Government policy, shocks, and equilibrium
- Trade policy specified exogenously; domestic tariff follows AR(1) with stochastic volatility:
  - τ1 t = (1 − ρ) τ1 + ρ τ1 t−1 + ω t−1 ε t
  - ω t = (1 − ρ) ω + ρ ω t−1 + μ ν t
  - ε t and ν t are iid standard normal innovations to the level and variance of tariffs, respectively.
  - τ1 t are referred to as tariff shocks; ω t as uncertainty shocks.
- Tariff proceeds redistributed lump-sum to domestic households.
- Foreign retaliation allowed ad-hoc:
  - τ2 t = (1 − ρ) τ2 + ρ τ2 t−1 + ζ ω t−1 ε t, with ζ ∈ [0,1]; ζ = 0 no retaliation, ζ = 1 full retaliation.
- Central banks keep nominal money supply constant.
- Equilibrium: symmetric, markets clear (goods, labor, money), both bonds zero net supply.

### Calibration, priors, and solution method
- Frequency: quarters. Country 1 interpreted as the US.
- Calibrated parameter values (as given verbatim in source text):
  - β = 1/1.01
  - θ = 6
  - κ = (θ − 1) / θ
  - ε = 3
  - χ = (1 − β) [(θ − 1) / (κ θ)]^{ε − 1} / 2  (notation preserved as in source)
  - ψ = 0.0025
  - τ1 = τ2 = 0
  - Assume zero inflation in steady state.
- Additional parameter choices and distributions (mean and standard deviation where applicable):
  - S.d. tariff rate shocks ω: 1 → 0.01 (as listed in table header style)
  - S.d. tariff volatility shocks μ: 1 → 0.01
  - Risk aversion σ: Inverse gamma, mean 1, s.d. 0.5 (presented as "Inverse gamma 1 0.25" in table)
  - Inverse Frisch elasticity η: Inverse gamma, mean 1, s.d. 0.5 (table: "Inverse gamma 1 0.25")
  - Country size n: Beta, mean 0.5, s.d. 0.25
  - Persistence tariff shocks ρ: Beta, mean 0.95, s.d. 0.025
  - Price adjustment cost φ: Normal, mean 60, s.d. 15
  - Retaliation ζ: Beta, mean 0.6, s.d. 0.25
- Calibrated/steady-state implications:
  - Quarterly interest rate of 1% in steady state.
  - Interest rate elasticity of money demand of −0.33.
  - Consumption elasticity of 0.33.
  - Markup over marginal cost of 20%.
- Simulation and solution details:
  - Draw 10,000 parameter combinations from distributions.
  - For each draw compute impulse responses to tariff level shock and to a trade policy uncertainty shock.
  - Trade policy uncertainty shock computed with third-order approximation with pruning; simulate model for 1000 periods without shocks to obtain stochastic steady state (ergodic mean), discard first 1000 periods as burn-in, then feed in a trade policy uncertainty shock that doubles the standard deviation of tariff level shocks.
  - Third-order approximation and pruning follow Fernández-Villaverde et al. (2015) and Basu and Bundick (2017).

### Theoretical impulse-response results (summary of key dynamics)
- Responses to a 1 percentage point (pp) tariff level shock (home country), over 12 quarters:
  - Tariff rate increases persistently for more than three years.
  - Domestic price of imported goods and consumer price level increase.
  - Producer prices remain initially unchanged due to price adjustment costs.
  - Nominal exchange rate appreciates; terms of trade improve.
  - Households substitute away from foreign goods toward domestic goods.
  - Exports fall (exchange rate appreciation and foreign demand decline).
  - Imports fall more than exports → trade balance tends to rise.
  - Labor and private consumption fall (domestic households are wealthier due to terms of trade effect and substitute toward leisure).
  - Output tends to decline.
  - Visualization notes: figure shows point-wise median with shaded 68% credible set.
- Responses to a trade policy uncertainty shock (doubling standard deviation of innovations to tariff level shocks):
  - Imports fall persistently.
  - Domestic firms raise producer prices and markups (upward pricing incentive).
  - Consumer prices increase (producer price pass-through).
  - Domestic households increase precautionary saving relative to foreign households → demand for external assets rises.
  - Domestic demand falls more than foreign demand → nominal exchange rate tends to depreciate, exports increase, trade balance improves.
  - Depreciation further raises consumer prices.
  - Output: tends to rise initially and then to fall.
  - Key difference vs. Caldara et al. (2020): short positive output effect here (they assume full retaliation, eliminating differential demand and saving effects and yielding negative output response throughout).
- Additional theoretical responses to home demand and home supply shocks are provided in Online Appendix A (Figures A.1 and A.2) and used for identification in empirical section.

### Empirical strategy and data (Bayesian SVAR)
- Estimated model: reduced form Bayesian VAR:
  - yt = ν + Σ_{i=1}^p A_i y_{t−i} + u_t, with p = 4 (quarterly data).
  - u_t mean-zero i.i.d. reduced form errors with covariance Σ.
  - Structural representation: B0 y_t = θ + Σ_{i=1}^p B_i y_{t−i} + ε_t, with u_t = B0^{−1} ε_t and Σ = B0^{−1} B0^{−1}′.
- Endogenous variables yt (quarterly, log levels), sample 1960Q1 to 2019Q4 (Covid-19 excluded):
  - real GDP
  - real exports
  - real imports
  - consumer price index (CPI)
  - nominal effective exchange rate
  - real customs duties
  - trade policy uncertainty for the United States
- Data treatment:
  - All series in log levels.
  - Nominal variables deflated by the consumer price index.
  - Table A.1 (not reproduced here) provides sources, data, and variable construction details.
- Identification rationale:
  - Variable selection guided by theoretical model sign patterns to disentangle tariff shocks and trade policy uncertainty shocks from demand and supply shocks.
  - Customs duties included as measure of tariff proceeds (should increase after positive tariff level shock).
  - Trade policy uncertainty: news-based measure of Caldara et al. (2020) (news occurrences of US newspaper articles with terms related to trade policy and uncertainty).
  - Consumer prices included to help identify supply vs demand shocks.
  - Variable ordering in yt not relevant (no reliance on recursive identification).

### US customs duties and trade policy uncertainty (data patterns)
- Evolution of US customs duties relative to GDP (visual description in source):
  - Duties fluctuate between 0.15 and 0.40 percent of GDP.
  - Series increased until end of 1980s, decreased and then low/constant from early 2000s onward.
  - Spikes observed in 1971 and 1975 and at onset of US-China trade war in 2018.
- Trade policy uncertainty index (Caldara et al., 2020, news-based measure):
  - Major spikes in 1971, 1975, and 1993.
  - Marked rise from 2016 onward (spikes in this period are relatively large compared to earlier spikes).
- Vertical grey areas in the referenced figure mark NBER recession dates (figure not reproduced here).

*Source: wpiea2024013-print-pdf (Sections 3–4 excerpt).*

### 3.2    Identification

### 3.2 Identification

### Structural identification approach
- Applied identification methods:
  - Traditional sign restrictions following Faust (1998) and Uhlig (2005) placed on the impact matrix B0^{-1}.
  - Narrative sign restrictions following Antolín-Díaz and Rubio-Ramírez (2018) to refine the set of admissible solutions.
- Table of impact sign restrictions (as used in the SVAR):
  - Customs duties: + for Tariff shock; – for Supply shock; * denotes no restriction for some shocks.
  - Trade policy uncertainty (TPU): ∗+∗ for TPU shock (TPU increases on a positive TPU shock).
  - Imports: – – ∗ + (Tariff shock decreases imports on impact).
  - Exports: – ∗ + ∗ (Tariff shock decreases exports on impact).
  - Consumer prices: + + – + (Tariff shock raises consumer prices on impact).
  - Nominal exchange rate: – ∗ – + (Tariff shock appreciates the nominal exchange rate on impact; a decrease denotes a US-Dollar appreciation).
  - GDP: ∗  ∗ ++ (no sign restriction on GDP response to tariff shock).
- Notes on variable measurement:
  - Customs duties, GDP, imports, and exports are in real terms.
  - A decrease in the nominal exchange rate denotes a US-Dollar appreciation.
  - * denotes no restriction.

### Rationale for tariff shock sign restrictions
- Imposed theoretical signs for a positive tariff shock:
  - Real customs duties increase (higher tariff rate → higher tariff proceeds).
  - Real imports decrease (higher final price incl. tariffs → households switch expenditure to domestic goods).
  - Real exports decrease (higher import costs of inputs → firms switch to domestic production).
  - Consumer prices increase (import-cost passthrough).
  - Nominal exchange rate appreciates (expenditure switching toward domestic goods → reduced demand for foreign currency).
- No sign restriction on output (GDP) because theoretical impact is ambiguous and GDP is an outcome variable of main policy interest; the data are allowed to determine the sign.
- Terms of trade response is not used in the SVAR because it is typically the mirror image of the nominal exchange rate; excluded to keep the empirical model tractable.

### Identification of Trade Policy Uncertainty (TPU) shocks
- Imposed on TPU shock:
  - Positive TPU shock raises the trade policy uncertainty index.
  - TPU shock assumed to lower customs duties on impact (imports decrease persistently per model predictions).
  - TPU shock assumed to increase consumer prices persistently.
  - Other responses (e.g., exports, exchange rate, trade balance) left unrestricted due to parameter sensitivity or because they are key outcome variables.
- To distinguish TPU shocks from domestic drivers, the model also identifies domestic demand and supply shocks using theoretical signs from the DSGE model (Figures A.1 and A.2), robust to parameter uncertainty.

### Use of narrative sign restrictions
- Narrative restrictions derived from customs duties series, TPU index (Figure 3), and historical account of US trade policy (Irwin, 2017).
- Selected unanticipated major tariff changes where announcement and implementation fall within the same quarter (to avoid anticipation effects).
- Narrative episodes used to restrict shock signs include:
  - 1971Q3 (Nixon shock): Tariff +, TPU +, customs duties largest contributor.
  - 1975Q1 (Ford shock): Tariff +, TPU +, customs duties largest contributor.
  - 2018Q1 (Trump steel and aluminum tariffs): Tariff +, customs duties largest contributor; TPU + noted for Trump shock episodes.
  - 2008Q4–2009Q1 (Great Recession): Tariff identified as the least important driver of imports (tariff contribution smallest) given governments refrained from increasing tariffs.
  - 2016Q4–2017Q1 (Trump election and inauguration): TPU +, TPU largest contributor.
  - 2019Q2–2019Q3: TPU +, Trump shock.
- Rationale: these narrative restrictions shrink the set of admissible B0^{-1} solutions and sharpen inference by tying certain quarters to specific exogenous shocks.

### Specific narrative sign restriction table entries (periods and contributions)
- 1971Q3: Tariff + ; Customs duties largest — Nixon shock.
- 1975Q1: Tariff + ; Customs duties largest — Ford shock.
- 2008Q4–2009Q1: Tariff – ; Imports smallest — Great Recession (tariff least important driver of imports).
- 2018Q1: Tariff + ; Customs duties largest — Steel and aluminum tariffs.
- 1971Q3: TPU + ; TPU largest — Nixon shock.
- 1975Q1: TPU + ; TPU largest — Ford shock.
- 2016Q4–2017Q1: TPU + ; TPU largest — Trump election and inauguration.
- 2018Q1 and 2019Q2–2019Q3: TPU + ; Trump shock.

---

### 3.3 Estimation

### Bayesian estimation setup
- Estimation and inference are Bayesian following Antolín-Díaz and Rubio-Ramírez (2018).
- Priors used:
  - Minnesota prior with standard shrinkage parameters (Giannone et al., 2015).
  - Sum-of-coefficients prior (Doan et al., 1984).
  - Dummy-initial-observation prior (Sims, 1993).
- Prior variance specification for reduced form coefficients:
  - var((A_i)_{jj}) = λ^2 ψ_j i^α, where i denotes the lag and j the variable.
  - Tightness λ = 0.2.
  - Decay α = 2.
  - Scales ψ_j set to the OLS residual variance of an autoregressive model for each variable j.
- Variance for priors on the exogenous variables set to 1,000.

### Inference with sign restrictions
- Identification via sign restrictions yields sets of admissible parameter intervals for elements of B0^{-1}.
- Obtained 1000 admissible draws.
- Inference uses these admissible draws to indicate uncertainty around pointwise median estimates.
- Reported statistics: point-wise median and percentiles of impulse responses (common practice in the literature).

---

### 4 The macroeconomic effects of US trade policy

### 4.1 Estimated tariff shocks and trade policy uncertainty shocks
- Estimated median shock series observations:
  - Largest tariff-shock spikes occur in 1971, 1975, and 2018/19.
  - Two large negative tariff shocks detected in 1972Q1 and 1976Q1 following quick withdrawal of Nixon and Ford tariff surcharges.
  - Third largest positive spike in 2018 corresponding to tariffs mainly on China.
- Cumulative tariff level shock series:
  - Sequence of tariff reduction shocks in the mid-1970s (Kennedy Round concluded in 1967; US average tariffs on dutiable imports decreased from 14% in 1967 to about 6% by 1975).
  - Protectionist shocks in the early 1980s (e.g., tariffs on Japanese trucks in August 1980 and motorcycles in 1983; quotas in steel and textiles).
  - Increase in 1987 when the US imposed tariffs on computers, televisions, and power tools from Japan.
  - Easing shocks starting after 1993 (NAFTA approval and GATT Uruguay Round → WTO), continued tariff reductions into the late 1990s and early 2000s.
  - Final major rise in cumulative series related to President Trump’s tariffs on steel and aluminum and on imports from China in 2018/19.
- Notable historical policy facts cited:
  - Kennedy Round (concluded in 1967) contributed to tariff reductions.
  - The 25% ‘chicken tax’ on trucks imposed by President Johnson in 1964 is noted as still active.
  - From 1980 to 1984 the share of imports covered by trade restrictions increased from 12% to 21%.
  - From 2002 to 2007 the US concluded several free trade agreements; the Doha round failed and was put to rest in 2015.
  - During the Great Recession in 2008/09 no major increase in tariffs except duties on car and truck tires from China.

### Trade policy uncertainty shock series behavior
- TPU shocks partially mirror tariff-level developments, but largest TPU shocks typically occur a few quarters before the largest tariff-level spikes (uncertainty rises before actual tariff changes).
  - Example: TPU rises more than a year before the cumulative tariff level picks up in the 2018–20 US-China trade dispute.
- Historical decompositions (Figure A.5) indicate:
  - Tariff-level shocks are much more important for dynamics of customs duties than uncertainty shocks.
  - Uncertainty shocks are more relevant for time-variation in the TPU index than level shocks.
  - This suggests successful disentanglement of the two dimensions of US trade policy by the model.

---

### 4.2 Dynamic effects and trade elasticities (selected findings)
- Impulse response estimation details:
  - Responses shown over a horizon of 32 quarters.
  - Point-wise median estimates reported with 68% highest posterior density credible sets; full-draw responses in Figure A.3.
  - Responses to domestic demand and supply shocks shown in Figure A.4.
- Key quantitative result for a tariff level shock:
  - A positive tariff level shock of one standard deviation raises customs duties by about 5% on impact.
- Additional model variant result (partial reporting in source):
  - Replacing customs duties with the import-weighted average tariff rate (customs duties relative to imports) shows that the tariff level shock raises the tariff rate by 6% on impact (sentence in source continues beyond provided excerpt).

*Source: wpiea2024013-print-pdf - 3.2 Identification (excerpt).*

### 0.21 percentage points increase for the average tariff rate of 3.56% over the sample horizon (Figure A.27).  Both this

### wpiea2024013-print-pdf - 0.21 percentage points increase for the average tariff rate of 3.56% over the sample horizon (Figure A.27).  Both this

### Effects of a tariff level shock
- Immediate and short-run trade and output responses
  - Imports drop on impact by 1% and further to –1.5% in the second quarter after the shock; after eight years they are still below the level where they would have been without the shock.
  - Exports show a similar response and recover marginally quicker than imports.
  - GDP falls immediately by 0.2%, and then to 0.3% below trend (the bands cover zero).
  - The nominal effective exchange rate tends to appreciate by up to 0.8%.
  - The consumer price level rises by 0.3%.
  - The trade policy uncertainty index increases following tariff changes.
- Persistence and general equilibrium elasticities
  - Import elasticity (response of imports divided by response of customs duties):
    - upon impact: –0.2
    - after two years: –0.4
    - after six years: –0.8
    - after eight years: –0.9 (estimation uncertainty is high)
  - Export elasticity:
    - starts at –0.2
    - falls to –0.5 after eight years
  - GDP elasticity:
    - –0.05 when the shock hits
    - –0.2 after eight years
- Responses of other macro variables
  - Domestic consumption declines persistently but the effect is small and only different from zero for a few quarters.
  - Investment drops strongly by 1% and remains persistently below trend for more than eight years.
  - Employment drops marginally on impact, then tends to overshoot (positive medium-run employment response not distinguishable from zero).
  - Wages decline by 0.3%.
  - Trade balance increases by 0.5 percentage points of GDP after one quarter; credible sets exclude zero after two years and the positive effect remains for another six years.
  - Import prices decline for many years; pass-through scaled by customs duties response is 0.1 upon impact and 0.5 in the medium run.
  - Terms of trade improve by up to 0.5% in the first year before falling back.

### Effects of a trade policy uncertainty shock
- Immediate and short-run responses
  - The uncertainty index increases by more than 15% on impact.
  - Imports fall by about 1% and remain below trend for the full horizon though the effect is not distinguishable from zero after the first quarters.
  - Customs duties fall upon impact and then overshoot.
  - The nominal exchange rate tends to depreciate.
  - Exports increase (response imprecisely measured).
  - Output reaction is first negative and then positive but insignificant.
  - Consumer prices increase strongly and persistently by up to 0.5%; credible sets exclude zero over the full horizon of eight years.
- Additional variables under uncertainty shocks
  - Consumption does not respond materially.
  - Investment, employment, and wages fall; employment and wages declines are distinguishable from zero.
  - Trade balance improves quickly and persistently; credible sets exclude zero.
  - Terms of trade tend to worsen.

### Forecast error variance and macroeconomic relevance
- Tariff level shocks (average importance over sample, 32-quarter horizon)
  - Explain half of the impact variability in customs duties.
  - Contribute 10-18% to variability in exports and imports.
  - Explanatory power for nominal exchange rate and consumer prices is lower at the 1-2 year horizon but increases to 10-15% in the 8th year.
  - Contribution to unexpected GDP volatility is close to 10% for most quarters.
- Trade policy uncertainty shocks
  - Relevance for variability in exports, imports, and output is about half that of tariff shocks.
  - Explain a bit less than 5% of forecast errors at short horizons and a little more than 5% at longer horizons.
  - Account for more than half of the impact variation in the uncertainty index (implying that recursive identification strategies assuming exogeneity of uncertainty may be biased).

### Historical decomposition and episode analysis
- Long-run historical contributions
  - Until the mid-1980s, tariff shocks contributed little to GDP and the trade balance, with exceptions in 1971 and 1974.
  - Since the mid-1980s, tariff shocks are an important driver of output and trade:
    - The trade tensions with Japan lowered GDP and raised the trade balance until the mid-1990s.
    - The trade liberalization of NAFTA in 1993, creation of the WTO in 1995, and China’s WTO accession in 2001 generated a long boom.
    - The shift to lower tariffs raised the output gap by up to 3 log points for nearly 20 years.
  - Tariff shocks account for about one fourth of the deficit during the last 10 years.
- The 2018–2019 trade disputes (historical decomposition for 2018Q1–2019Q4)
  - The contributions of restrictive tariff shocks are negative from 2018Q2 onward.
  - The cumulative output costs of the upward shift in US import tariffs:
    - reduced GDP by 1.1% in 2018
    - reduced GDP by 2.9% in 2019
  - Trade policy uncertainty shocks in 2018/19 raised output by 2% over both years.
  - Net effect: the trade disputes in 2018/19 entailed an output cost of 2% of GDP to the US.

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024013-print-pdf.pdf*

### 4.4    Sectoral and regional effects

### 4.4    Sectoral and regional effects

### Methodology
- Projected disaggregated sectoral and regional responses using local-projection regressions:
  - yi,t+h = αi,h + (βi,h)′ xi,j,t−1 + φi,h Shockj,t + ξi,t+h for h = 0,...,H.
  - Shockj,t = ˆεj,t is the tariff level or trade policy uncertainty shock.
  - xi,j,t−1 includes one lag of the outcome variable i.
- Estimated (6) for each posterior draw of the shock series ˆεj,t and computed 68% point-wise credible sets of impulse responses.
- Focus on peak/trough (absolute maximum) responses; full responses in Online Appendix C.2.

### Sectoral responses to a unit positive tariff level shock
- Imports:
  - All but two sectors reduce imports significantly.
  - Mineral fuels, industrial supplies, and crude material respond most negatively, with import reductions of 5-15%.
- Exports:
  - Firms reduce exports across the board, by between 2-10%.
  - One sector (foods, feeds, and beverages) shows higher exports, but the credible set includes zero.
- Investment:
  - 13 out of 19 sectors cut back on capital formation; effects often different from zero with high probability.
  - A few sectors increase investment, suggesting some redistribution of activity across sectors.
- Employment:
  - Employment declines in the majority of sectors but increases in others.
  - Estimation uncertainty is high; sectoral employment tends to first fall and then overshoot (mirrors aggregate pattern).
- Summary finding:
  - Tariffs reduce US international trade and investment in most sectors; employment effects are mixed.

### Sectoral responses to a unit positive trade policy uncertainty shock
- Imports:
  - Imports drop in 6 sectors and increase in 10 sectors.
  - Many peak responses are indistinguishable from zero.
- Exports:
  - Exports increase in all but one sector; increases are largely different from zero with high probability.
  - Pattern mirrors positive aggregate export response associated with currency depreciation.
- Investment:
  - Investment responses are mostly negative; firms in most sectors reduce investment when trade policy uncertainty increases.
- Employment:
  - Employment falls in 10 out of 11 sectors; the drop is distinguishable from zero in 4 sectors.
- Summary finding:
  - Trade policy uncertainty produces diverse sectoral outcomes; it reduces sectoral investment but generally raises exports.

### Comparison: tariff level shocks vs. trade policy uncertainty shocks
- Tariff level shocks are more detrimental to US sectoral economic activity than uncertainty shocks.
  - Tariffs: broad reductions in international trade and investment across most sectors.
  - Uncertainty: reduces sectoral investment but raises exports and partially imports.
- Aggregate interpretation:
  - Level shocks weigh more heavily on trade and investment; uncertainty shocks have mixed trade effects and more uniformly negative investment effects.

### Spatial distribution: state-level employment effects
- Employment effect of a unit positive tariff level shock (peak/trough):
  - Most states are yellow to orange: no discernible to slightly negative employment reaction.
  - States with clear job losses: Alaska, Luisiana, Nevada, Oklahoma, West Virginia, Wyoming.
  - States with some job gains: Arizona, Florida, Georgia.
  - Figure legend range: -0.97, -0.47, 0.02, 0.52, 1.01 % change.
- Employment effect of a unit positive trade policy uncertainty shock:
  - Spatial pattern clearer than tariff shocks: map predominantly red at the coasts and in the Rust Belt; middle-west and Alaska are yellow to green.
  - Possible explanation: differential exposure to exchange rate depreciation — commodity-producing states respond more to US-Dollar fluctuations; differentiated goods industries more negatively affected when imports fall.
- Overall spatial finding:
  - Results question the idea that protectionism systematically creates more domestic jobs or allows redistributing them across the country.

### Scenario: output effects of a return to free trade (summary of 4.5)
- Constructed a structural scenario in which customs duties and trade policy uncertainty gradually decrease back to pre-2016 levels over 2020Q1-2022Q4, driven only by trade policy level and uncertainty shocks.
- Scenario design:
  - Scenario paths return linearly to initial levels within three years (solid red lines in Figures).
  - Compared scenario to unconditional forecasts (blue) and to an alternative scenario where tariffs remain at 2019 levels for three years.
- GDP and cumulative output effects:
  - After three years, the difference in median GDP between the free-trade scenario and the unconditional forecast is 3.3%.
  - Cumulative output differences of the free-trade scenario versus the unconditional forecast are 4.4%:
    - In the first year: 0.3%
    - In the second year: 1.4%
    - In the third year: 2.7%
  - Comparing free-trade scenario to an alternative scenario with tariffs held at 2019 levels for three years yields a cumulative output gain of 5.3%.
- Interpretation:
  - These numbers are probably conservative because the unconditional forecast already implies some reduction in customs duties and uncertainty that has not materialized in actual data.
  - Reversing 2018/19 protectionism is estimated to generate a cumulative output gain of 4% over three years (conclusion summary).

### Key quantitative findings and comparisons
- Sectoral import reductions to a unit tariff shock: 5-15% for most affected sectors.
- Sectoral export reductions to a unit tariff shock: between 2-10% across sectors.
- Number of sectors cutting investment under tariff shock: 13 out of 19.
- Under uncertainty shocks:
  - Imports drop in 6 sectors and increase in 10 sectors.
  - Employment falls in 10 out of 11 sectors; statistically distinguishable declines in 4 sectors.
- State employment effect range displayed: -0.97 to 1.01 percent change (figure legend).
- Return-to-free-trade scenario impacts on GDP:
  - Median GDP difference after three years: 3.3%.
  - Cumulative output difference over three years: 4.4% (0.3%, 1.4%, 2.7% by year).
  - Cumulative gain vs. tariffs-held-at-2019 scenario: 5.3%.
  - Paper-wide summary estimate: reversing 2018/19 protectionism → cumulative output gain of 4% over three years.

*Source: IMF working paper section 4.4 (Sectoral and regional effects) and related passages in sections 4.5 and 6.*

### References

### wpiea2024013-print-pdf - References

### References (bibliography)
- Comprehensive list of cited works spanning empirical, theoretical, and methodological studies on trade policy, tariffs, uncertainty, SVARs, DSGE models, and related topics.
- Key authors and works cited include:
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  - Alessandria, G. A., Khan, S. Y., and Khederlarian, A. (2019). Taking stock of trade policy uncertainty: Evidence from china’s pre-wto accession. Technical report, National Bureau of Economic Research.
  - Alessandria, G. A., Khan, S. Y., Khederlarian, A., Ruhl, K. J., and Steinberg, J. B. (2021). Trade-Policy Dynamics: Evidence from 60 Years of U.S.-China Trade. NBER Working Papers 29122.
  - Amiti, M., Redding, S. J., and Weinstein, D. E. (2019). The impact of the 2018 tariffs on prices and welfare. Journal of Economic Perspectives, 33(4):187–210.
  - Antolín-Díaz, J., Petrella, I., and Rubio-Ramírez, J. F. (2021). Structural scenario analysis with SVARs. Journal of Monetary Economics, 117(C):798–815.
  - Autor, D. H., Dorn, D., and Hanson, G. H. (2013, 2016). The china syndrome; The china shock.
  - Baker, S. R., Bloom, N., and Davis, S. J. (2016). Measuring economic policy uncertainty. The Quarterly Journal of Economics, 131(4):1593–1636.
  - Baumeister, C. and Hamilton, J. D. (2015, 2020). Sign restrictions, structural vector autoregressions, and useful prior information; Drawing conclusions from structural vector autoregressions identified on the basis of sign restrictions.
  - Bloom, N. (2009). The impact of uncertainty shocks. econometrica, 77(3):623–685.
  - Caldara, D., Iacoviello, M., Molligo, P., Prestipino, A., and Raffo, A. (2020). The economic effects of trade policy uncertainty. Journal of Monetary Economics, 109:38–59.
  - Cavallo, A., Gopinath, G., Neiman, B., and Tang, J. (2021). Tariff pass-through at the border and at the store: Evidence from us trade policy. American Economic Review: Insights, 3(1):19–34.
  - De Walque, G., Smets, F., and Wouters, R. (2006). Firm-specific production factors in a dsge model with taylor price setting. International Journal of Central Banking, 2(3).
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  - Feenstra, R. (1989). Symmetric pass-through of tariffs and exchange rates under imperfect competition: An empirical test. Journal of International Economics, 27(1-2):25–45.
  - Handley, K. and Limão, N. (2017, 2022). Policy uncertainty, trade, and welfare; Trade policy uncertainty. American Economic Review, 107(9):2731–83; Annual Review of Economics, 14:363–395.
  - Irwin, D. (2013, 2017). The nixon shock after forty years: the import surcharge revisited; Clashing over Commerce: A History of US Trade Policy. University of Chicago Press, 1 edition.
  - Kilian, L., Plante, M., and Richter, A. W. (2022). Macroeconomic responses to uncertainty shocks: the perils of recursive orderings.
  - Krugman, P. (1982). The macroeconomics of protection with a floating exchange rate. Carnegie-Rochester Conference Series on Public Policy, 16(1):141–182.
  - Mundell, R. (1961). Flexible exchange rates and employment policy. The Canadian Journal of Economics and Political Science, 27(4):509–517.
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  - Pierce, J. R. and Schott, P. K. (2016). The surprisingly swift decline of us manufacturing employment. American Economic Review, 106(7):1632–1662.
  - Sims, C. A. (1993). A nine-variable probabilistic macroeconomic forecasting model, in business cycles, indicators and forecasting. NBER Studies in Business Cycles.
  - Uhlig, H. (2005). What are the effects of monetary policy on output? Journal of Monetary Economics, 52(2):381–419.
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- References include working papers, journal articles, books, technical reports, and online sources; several entries note web-based sources (e.g., Iacoviello’s webpage, Bruegel webpage, Wu’s webpage, Fernald’s webpage).

### Online Appendix metadata
- Title: Online Appendix to ‘The consequences of import tariffs and trade policy uncertainty for the US economy’
- Authors and affiliations:
  - Lukas Boer, International Monetary Fund, Research Department, Washington DC, USA. Email: lboer@imf.org
  - Malte Rieth, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany; and DIW Berlin, Germany. Email: mrieth@diw.de.
- Date: January 10, 2024

### Theoretical model impulse responses
- Figures:
  - Figure A.1: Impulse responses to a demand shock. Notes: responses to a shock of 1% to the demand shifter d1t of the home country; solid line = point-wise median; shaded area = 68% credible set.
  - Figure A.2: Impulse responses to a technology shock. Notes: responses to a shock of 1% to the technology shifter ra1t of the home country; solid line = point-wise median; shaded area = 68% credible set.

### Data (sources, transformations, series definitions)
- Data sources and treatments:
  - GDP and customs duties: downloaded from the U.S. Bureau of Economic Analysis; both series are seasonally adjusted.
  - Imports and exports of goods: OECD main economic indicators database; seasonally adjusted.
  - Prices: series adjusted for inflation with total consumer price index for all goods from the OECD database.
  - Real effective exchange rate: taken from Darvas (2021); defined as QUS,t = SUS,t · PUS,t / PW,t; QUS,t based on OECD consumer price indices for the US PUS,t and for the world PW,t as average over 51 trading partners; nominal exchange rate SUS,t is a weighted average over the 51 trading partners’ currencies; an increase represents a real appreciation of the US Dollar; monthly values averaged to obtain quarterly values.
  - Tariff rate τ calculated from customs duties CD and imports M as τ = CD / M.
- Table A.1: Data Description, Sources and Coverage — selected entries (variables, source, sample):
  - GDP — Gross Domestic Product (s.a.) — FRED — 1960q1 - 2019q4
  - CPI — Total CPI - all goods — OECD — 1960q1 - 2019q4
  - Goods Imports — Imports in goods (value) — OECD — 1960q1 - 2019q4
  - Goods Exports — Exports in goods (value) — OECD — 1960q1 - 2019q4
  - B235RC1Q027SBEA — Customs Duties (s.a.) — FRED — 1960q1 - 2019q4
  - Nominal Effective Exchange Rate — Zsolt Darvas (2021), against 51 trading partners, quarterly average — Bruegel webpage — 1960q1 - 2019q4
  - Trade Policy Uncertainty — Caldara et al. (2020) — Iacoviello’s webpage — 1960q1 - 2019q4
  - Additional variables (selected): Gross Domestic Investment (W170RC1Q027SBEA), All Employees Total Nonfarm (PAYEMS), Personal Consumption Expenditures (PCE), Trade Balance (Net Exports as (Goods Exports - Goods Imports)/GDP) — all with sample coverage 1960q1 - 2019q4 unless otherwise noted.
  - USTOTPRCFT Terms of Trade — datastream — 1969q2 - 2019q4
  - Shadow Federal Funds Rate — Wu and Xia (2016) — Wu’s webpage — 1990q1 - 2019q4
  - Utilization-adjusted quarterly-TFP — Fernald (2014) — Fernald’s webpage — 1960q1 - 2019q4
  - Tariff Rate — Customs Duties/Goods Imports — 1960q1 - 2019q4
  - Sectoral and state-level series: coverage generally 1960q1 - 2019q4; sectoral imports/exports by end-use from 1978q1 or 1986q1 depending on series; sectoral investment from Haver Analytics.

### Additional SVAR results (figures and diagnostics)
- C.1 Additional results for main model:
  - Figure A.3: Impulse responses to tariff level shock and trade policy uncertainty shock for all draws. Notes: shows responses for each of the 1000 draws with point-wise median impulse responses (solid red), 68% highest posterior density credible sets (dotted red), and modal model using an absolute loss function (dashed green).
  - Figure A.4: Impulse responses to all four types of shocks (tariff level shock, trade policy uncertainty shock, domestic demand shock, domestic supply shock) — point-wise medians and 68% HPD credible sets reported across endogenous variables including Consumer prices, Nom. eff. ex. rate, GDP, Exports, Imports, Customs duties, Trade policy unc.
  - Figure A.5: Historical decomposition of customs duties and trade policy uncertainty — thick black lines = actual detrended data; thin blue lines = counterfactuals driven by respective shock only. Panels show:
    - Tariff level shock contribution to customs duties (1962–2017 timeline labels)
    - Trade policy uncertainty shock contribution to customs duties (1962–2017)
    - Tariff level shock contribution to TPU series (1962–2017)
    - Trade policy uncertainty shock contribution to TPU series (1962–2017)
  - Figure A.6: Historical decomposition of employment and investment — contributions from tariff level shock and trade policy uncertainty shock (1962–2017).
  - Figure A.7: Historical decomposition of output 2016Q1-2019Q4 — tariff level shock and trade policy uncertainty shock contributions by quarter (Q1 2016–Q4 2019).
  - Figures A.8–A.10: Scenario analyses comparing ‘Tariff phase out’ and ‘Protectionism’ scenarios; medians and 40% point-wise credible sets; scenarios driven by series of tariff level and uncertainty shock.
  - Figure A.10: Shock series in the trade policy scenarios of continued protectionism vs. phasing out of tariffs — horizons in quarters plotted for Tariff level shocks, Trade policy uncertainty shocks, Demand shocks, Supply shocks; scenario labels: Protectionism vs. Tariff Phase Out.

### Additional results of sectoral analysis (C.2)
- Sectoral local projection results (each with 1000 draws, point-wise median, 68% HPD sets):
  - Figure A.11: Responses of sectoral imports to a tariff level shock.
  - Figure A.12: Responses of sectoral exports to a tariff level shock.
  - Figure A.13: Responses of sectoral investment to a tariff level shock.
  - Figure A.14: Responses of sectoral employment to a tariff level shock.
  - Figure A.15: Responses of sectoral imports to a trade policy uncertainty shock.
  - Figure A.16: Responses of sectoral exports to a trade policy uncertainty shock.
  - Figure A.17: Responses of sectoral investment to a trade policy uncertainty shock.
  - Figure A.18: Responses of sectoral employment to a trade policy uncertainty shock.
  - Figure A.19: Responses of state employment to a tariff level shock.
  - Figure A.20: Responses of state employment to a trade policy uncertainty shock.

### Sensitivity analysis (C.3)
- Panels and figures testing robustness under multiple alternative specifications; all report point-wise median estimates and 68% highest posterior density credible sets:
  - Figure A.21: Impulse responses replacing output with total private consumption — horizon 32 quarters; effects of positive one standard deviation shocks to import tariffs and to trade policy uncertainty.
  - Figure A.22: Impulse responses replacing output with investment — horizon 32 quarters.
  - Figure A.23: Impulse responses replacing output with non-farm payrolls (employment) — horizon 32 quarters.
  - Figure A.24: Responses when using the real effective exchange rate instead of the nominal (an increase is a depreciation).
  - Figure A.25: Responses when using producer prices instead of consumer prices.
  - Figure A.26: Responses when including trade in services in imports and exports.
  - Figure A.27: Responses when replacing customs duties by the tariff proceeds to import ratio (tariff rate); tariff rate axis labeled in pp.
  - Figure A.28: Responses when adding the ratio of net exports to GDP (trade balance).
  - Figure A.29: Responses when adding terms of trade.
  - Figure A.30: Responses when adding total factor productivity (TFP).
  - Figure A.31: Structural impulse responses including a domestic monetary policy shock in addition to tariff, uncertainty, demand, and supply shocks.
  - Figure A.32: Impulse responses for sample starting in 1973Q2.
  - Figure A.33: Impulse responses for sample ending in 2016Q4.
  - Figure A.34: Impulse responses using eight lags of endogenous variables.
  - Figure A.35: Impulse responses including a linear trend.
  - Figure A.36: Impulse responses with sign restriction on output (restricting impact output response to a level shock to be negative).

*The Macroeconomic Consequences of Import Tariffs and Trade Policy Uncertainty — Working Paper No. WP/2024/013 — Online Appendix and References (wpiea2024013-print-pdf - References).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024013-print-pdf.pdf_