## _wp13110 - introduction of entry-sunk costs. Hence, liberalization is treated assuming a government's

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---

### Overview
- The paper introduces entry-sunk costs and treats liberalization as a government's policy decision aimed at reducing those costs.
- The model is estimated using Bayesian techniques for Tunisia and the Euro Area.
- Services trade barriers are quantified as the difference between entry-sunk costs in Tunisia versus the Euro Area.

### Methodology and model features
- Modeling approach:
  - Two-sector small open economy DSGE with entry-sunk costs and input-output links between services and goods.
  - Features wage rigidities (Calvo-type), costly adjustment of foreign bonds, and a managed nominal effective exchange rate (Tunisia) vs. standard Taylor rule (Euro Area).
  - Second-order approximations used for welfare analysis; first-order used for likelihood estimation.
- Estimation:
  - Bayesian (Metropolis-Hastings) with Kalman-filter likelihood.
  - Observables (sample 2000Q1–2010Q4): real per capita GDP, real per capita domestic service production, CPI inflation, services price inflation, real per capita imports, effective real exchange rate. All series transformed to growth rates.
- Calibration highlights:
  - β = 0.985.
  - δ = 0.025.
  - θ{s,g} calibrated to 10 percent.
  - Input-output shares (Tunisia): ξs = 0.12; ξg = 0.59.

### Key estimated structural parameters (posterior means)
- Tunisia (with trade barriers):
  - χ = 2.884.
  - φ = 0.002.
  - αs = 0.159.
  - αg = 0.240.
  - n = 0.338.
  - φ (elasticity between goods and services) = 1.563.
  - m = 0.641.
  - ν = 2.084.
  - Φs = 0.352.
  - Φg = 0.205.
  - dw = 0.589.
  - ρA,s = 0.804; ρA,g = 0.891.
  - σA,s = 0.009; σA,g = 0.011.
- Euro Area (benchmark):
  - Φs = 0.100.
  - Φg = 0.094.

### Stylized facts for Tunisia (as reported)
- Service sector share: 59 percent of GDP.
- Commercial services (excluding public services) = 47 percent of GDP.
- Capital formation from services: exceeds 57 percent in 2009; commercial services = 47 percent.
- Noted sector shares: transport and communication 32 percent; small commercial services activities 37 percent.
- Labor productivity gap with the European Union: exceeds 50 percent in services; below 30 percent in industry.
- Services export annual growth rate: about 2.5 percent (vs. Middle Eastern and North African average 12 percent).
- Partial liberalization example: telecommunication liberalization multiplied penetration rate by 15 and decreased prices.

### Identification and evidence on entry-sunk costs
- Estimated entry-sunk costs substantially higher in Tunisia than in the Euro Area:
  - Services entry-sunk cost: Tunisia Φs = 0.352 vs. Euro Area Φs = 0.100.
  - Goods entry-sunk cost: Tunisia Φg = 0.205 vs. Euro Area Φg = 0.094.
- Identification challenge:
  - Φs and θs have similar effects on steady-state service price and quantity; macro data alone weakly identifies θs.
  - Focus placed on Φs with sensitivity checks on θs.
- Posterior odds:
  - Model with Φ{s,g} > 0 preferred; marginal data density difference implies posterior odds ratio = 73.995 favoring substantial entry-sunk costs.

### Welfare and real-variable impacts of eliminating service trade barriers (counterfactual: reduce Tunisia Φs to Euro Area level Φs = 0.100)
- Welfare:
  - Compensating consumption variation: households willing to give up 3.57 percent of consumption under the alternative (Euro Area level of Φs) to be as well off as under historical regime.
- Unconditional mean percentage changes (switching Φs from Tunisia value to 0.100):
  - Aggregate output: +2.58 percent.
  - Services production: +1.08 percent.
  - Goods production: +3.66 percent.
  - Exports of services: +10.03 percent.
  - Exports of goods: +4.94 percent.
  - Investment: +4.39 percent.
  - Service real price: −1.01 percent.
- Decomposition:
  - First-order effects capture permanent level changes; second-order effects reflect volatility impacts.
  - Net benefit primarily from permanent increases in long-run production; some negative second-order effects arise from increased volatility in some variables.
- Full liberalization (reduce both Φs and Φg to Euro Area levels):
  - Welfare gain increases compared with services-only liberalization.
  - Goods liberalization contributes about 24 percent of total gains.
  - Goods-only component corresponds to 1.11 percent permanent increase in consumption under full liberalization scenario.

### Transitional dynamics (impulse-response to an unexpected permanent decline in Φs to Euro Area level)
- On impact and near-term:
  - Relative price of services declines and reaches new steady state after about 5 periods.
  - Service sector production initially drops by about 1 percent (deviation from new steady state) then rises toward the new steady state.
  - Real wages increase on impact due to wage stickiness; higher real wage relative to the real price of services (wt / pst) leads to a short-run decline in labor and service production, which reverses after the first period.
  - Aggregate output and goods output do not incur short-term costs during transition; both move toward higher new steady states.

### Sensitivity analysis (selected scenarios and outcomes; percent gains)
- Scenarios and selected results (Welfare; Production; Services production; Goods production):
  - Baseline estimated parameters: Welfare = 3.57; Production = 2.58; Services production = 1.08; Goods production = 3.66.
  - High degree of openness (m = 0.4): Welfare = 3.42; Production = 2.63; Services production = 1.37; Goods production = 3.61.
  - High cost of intermediation (φ = 0.1): Welfare = 3.95; Production = 2.95; Services production = 1.56; Goods production = 4.09.
  - Same share of capital (αs = αg): Welfare = 3.97; Production = 3.04; Services production = 1.77; Goods production = 3.87.
  - Without wage stickiness (dw = 0): Welfare = 3.56; Production = 2.59; Services production = 1.09; Goods production = 3.66.
  - Symmetric input-output matrix (ξg = ξs = 0.12): Welfare = 1.12; Production = 0.57; Services production = 0.30; Goods production = 0.77.
  - High probability of failure (θ = 0.15): Welfare = 5.22; Production = 3.78; Services production = 1.61; Goods production = 5.25.
- Key sensitivity insights:
  - Results robust in qualitative sign to variations in openness, foreign borrowing cost, wage rigidity, and exchange rate regime.
  - Welfare gains highly sensitive to θs: increasing θs from 0.10 to 0.15 raises welfare gain from 3.57 to 5.22 and aggregate growth gain from 2.58 to 3.78.
  - A symmetric input-output structure (lower ξg relative to baseline) dramatically reduces welfare and output gains.

### Business-cycle fit, variance decomposition, and impulse responses (selected quantitative diagnostics)
- Second-order moments (Data vs Model; selected):
  - std(∆log(Ys,t)) / std(∆log(Yt)): Data 1.29 Model 1.11 [0.90,1.34].
  - std(πs,t) / std(πt): Data 1.59 Model 1.63 [1.35,2.11].
  - std(st) / std(∆log(Yt)): Data 3.75 Model 6.02 [1.29,19.01].
  - corr(∆log(Yt), ∆log(Ys,t)): Data 0.84 Model 0.87 [0.80,0.94].
- Variance decomposition (average asymptotic contributions; selected point estimates with [90% CI]):
  - Yt: εs 3.32 [0.25,12.30]; εg 23.79 [7.12,51.37]; εA 27.00 [2.55,71.21]; εyf 22.78 [4.89,45.51]; εRf 10.33 [0.25,33.05].
  - Ys,t: εs 20.90 [2.66,45.49]; εg 15.63 [1.25,44.51]; εA 30.63 [3.07,79.18].
  - Yg,t: εg 24.59 [9.88,46.37]; εyf 34.66 [15.77,53.87].
  - Ym t: εRf 33.68 [2.55,79.97]; επf 14.38 [0.02,74.68].
  - st: εs 40.70 [6.78,71.24]; εg 19.82 [2.48,61.63]; εRf 9.19 [0.06,36.38].
- Impulse-response qualitative findings (selected):
  - Service-sector technology shock: services output rises, prices fall; final goods production declines; consumption and investment experience delayed decline (expenditure switching).
  - Good-sector technology shock: goods output rises, services output rises; good-sector prices fall; monetary policy reacts expansionarily; real depreciation on impact.
  - Expansionary monetary shock: initial higher demand and prices with nominal depreciation; wage rigidity causes slight inflation increase and real exchange rate overshoot; medium-term production declines moderately.
  - Foreign demand shock: raises goods and services production, consumption, investment; real imports increase; real exchange rate declines (real appreciation).

### Main quantitative conclusions
- Large estimated entry-sunk costs in Tunisia:
  - Φs = 0.352 implies a 35.2 percent loss in production associated with entrants in services (posterior mean).
- Eliminating the share of these costs related to trade barriers (matching Euro Area Φs = 0.100) yields:
  - Welfare gain (equivalent consumption variation) = 3.57 percent.
  - Aggregate output increase = 2.58 percent (goods: 3.66 percent; services: 1.08 percent).
  - Exports of services respond strongly: +10.03 percent.
- Transitional dynamics:
  - Limited short-run aggregate costs; temporary service production dip of about 1 percent at impact.
- Sensitivity:
  - Higher business failure probability amplifies gains; symmetric input-output matrix markedly lowers gains.

*Source: Appendix II and appendices of the provided IMF working paper content unit.*

### introduction of entry-sunk costs. Hence, liberalization is treated assuming a government's

### _wp13110 - introduction of entry-sunk costs. Hence, liberalization is treated assuming a government's

### Overview
- The paper introduces entry-sunk costs and treats liberalization as a government's policy decision aimed at reducing those costs.
- The model is estimated using Bayesian techniques for Tunisia and the Euro Area.
- Services trade barriers are quantified as the difference between entry-sunk costs in Tunisia versus the Euro Area.

### Key findings
- The paper finds significant welfare benefits following services liberalization.
- There are aggregate and sectoral growth gains for the Tunisian economy following services liberalization.
- Surprisingly, the goods sector is the one that benefits the most from services liberalization in the short- and long-term horizons.

### Methodology and scope
- Modeling approach: introduction of entry-sunk costs; liberalization modeled as a reduction in those costs.
- Estimation technique: Bayesian estimation for Tunisia and the Euro Area.
- Quantitative objective: precise evaluation of services trade barriers measured as the difference in entry-sunk costs across Tunisia and the Euro Area.

### Classification, keywords, and authors
- JEL Classification Numbers: E1, F1, F4
- Keywords: Liberalization, trade in services and goods, general equilibrium, Bayesian estimation, welfare analysis, Tunisia, Euro Area.
- Authors E-Mail Addresses: n.jouini@afdb.org and nrebei@imf.org

### Acknowledgements and publication note
- The authors wish to thank Hafedh Bouakez, Ray Brooks, Dalia Hakura, and Daniel Mirza for helpful comments.
- This Working Paper should not be reported as representing the views of the IMF.
- The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy.
- Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate.

### Document structure (table of contents excerpts)
- I. Introduction
- II. Tunisian Service sector: Context and some Stylized Facts
- III. The Model
  - A. Model description
  - B. The steady state and identification
- IV. Estimation
  - A. Estimation methodology and data
  - B. Calibration and prior distributions
  - C. Estimation results
- V. The impact of free trade on welfare and some real variables
  - A. Methodology
  - B. Results
  - C. Transitional dynamics
  - D. Sensitivity analysis
- VI. Conclusion
- References
- Appendix I: The model
  - Households
  - Firms
  - The government
  - Closing the model

*Source: _wp13110 - introduction of entry-sunk costs. Hence, liberalization is treated assuming a government's*

### Appendix II: Quantitative results of the estimated model    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    38

### Appendix II: Quantitative results of the estimated model

### Model and data overview
- Model: two-sector small open economy DSGE with entry-sunk costs and input-output links between services and goods; features wage rigidities, costly adjustment of foreign bonds, and managed nominal effective exchange rate.
- Observables used for estimation (sample 2000Q1–2010Q4): real per capita GDP, real per capita domestic service production, CPI inflation, services price inflation, real per capita imports, effective real exchange rate. All series transformed to growth rates.
- Estimation method: Bayesian (Metropolis-Hastings) with Kalman-filter likelihood; second-order approximations used for welfare analysis; first-order approximation used in likelihood estimation.

### Key calibrated and estimated structural parameters (posterior means and notable calibrations)
- Calibration highlights:
  - Subjective discount factor, β = 0.985.
  - Depreciation rate, δ = 0.025.
  - Probability of business failure, θ{s,g} calibrated to 10 percent.
  - Input-output shares (Tunisia): ξs = 0.12 (goods input in services); ξg = 0.59 (services input in goods).
- Selected posterior means (Tunisia, with trade barriers):
  - χ (capital adjustment cost) = 2.884.
  - φ (foreign bonds adjustment cost) = 0.002.
  - αs (share of capital in services production) = 0.159.
  - αg (share of capital in goods production) = 0.240.
  - n (share of services in local product) = 0.338.
  - φ (elasticity between goods and services) = 1.563.
  - m (share of imports) = 0.641.
  - ν (elasticity between imports and local products) = 2.084.
  - Φs (services entry-sunk costs, Tunisia) = 0.352.
  - Φg (goods entry-sunk costs, Tunisia) = 0.205.
  - Calvo wage stickiness, dw = 0.589 (implies average frequency of wage negotiations of two to three quarters).
  - Autocorrelations of technology shocks: ρA,s = 0.804; ρA,g = 0.891.
  - Std. dev. of services technology shocks, σA,s = 0.009; goods technology shocks, σA,g = 0.011.
- Euro Area posterior means (for benchmarking):
  - Φs (services entry-sunk costs, Euro Area) = 0.100.
  - Φg (goods entry-sunk costs, Euro Area) = 0.094.

### Stylized facts for Tunisia (from source text)
- Service sector share: 59 percent of GDP; commercial services (excluding public services) = 47 percent of GDP.
- Capital formation from services: exceeds 57 percent in 2009; commercial services = 47 percent (noted sectors: transport and communication 32 percent; small commercial services activities 37 percent).
- Labor productivity gap with the European Union: exceeds 50 percent in services; below 30 percent in industry.
- Services export annual growth rate: about 2.5 percent (vs. Middle Eastern and North African average 12 percent).
- Partial liberalization example: telecommunication liberalization multiplied penetration rate by 15 and decreased prices.

### Evidence on entry-sunk costs and identification
- Entry-sunk costs estimated substantially higher in Tunisia than in the Euro Area:
  - Services entry-sunk cost: Tunisia Φs = 0.352 vs. Euro Area Φs = 0.100.
  - Goods entry-sunk cost: Tunisia Φg = 0.205 vs. Euro Area Φg = 0.094.
- Identification challenge: Φs and θs (probability of business failure) have similar effects on steady-state service price and quantity; macro data alone weakly identifies θs, so focus placed on Φs with sensitivity checks on θs.
- Posterior odds: model with Φ{s,g} > 0 preferred; marginal data density difference implies posterior odds ratio = 73.995 favoring the existence of substantial entry-sunk costs.

### Welfare and real-variable impacts of eliminating service trade barriers (counterfactual: reduce Tunisia Φs to Euro Area level Φs = 0.100)
- Welfare (compensating consumption variation): households willing to give up 3.57 percent of consumption under the alternative (Euro Area level of Φs) to be as well off as under historical regime.
- Key average changes (switching Φs from estimated Tunisia value to 0.100; numbers are unconditional mean percentage changes):
  - Aggregate output: +2.58 percent.
  - Services production: +1.08 percent.
  - Goods production: +3.66 percent.
  - Exports of services: +10.03 percent.
  - Exports of goods: +4.94 percent.
  - Investment: +4.39 percent.
  - Service real price: −1.01 percent.
- Decomposition:
  - First-order effects capture permanent level changes; second-order effects reflect volatility impacts.
  - Net benefit primarily from permanent increases in long-run production; some negative second-order effects arise from increased volatility in some variables.
- Full liberalization scenario (reduce both Φs and Φg to Euro Area levels):
  - Welfare gain increases: combined effect yields a higher welfare improvement; goods liberalization contributes about 24 percent of total gains (goods-only component corresponds to 1.11 percent permanent increase in consumption under full liberalization scenario).

### Transitional dynamics (impulse-response to an unexpected permanent decline in Φs to Euro Area level)
- On impact and near-term dynamics:
  - Relative price of services declines and reaches new steady state after about 5 periods.
  - Service sector production initially drops by about 1 percent (deviation from new steady state) then rises toward the new steady state.
  - Real wages increase on impact due to wage stickiness; higher real wage relative to the real price of services (wt / pst) leads to a short-run decline in labor and service production, which reverses after the first period.
  - Aggregate output and goods output do not incur short-term costs during transition; both move toward higher new steady states.

### Sensitivity analysis (selected scenarios and outcomes; percentage gains in welfare and key variables)
- Scenarios considered:
  - Higher degree of openness (m = 0.4).
  - Higher foreign bonds adjustment cost (φ = 0.1).
  - Same share of capital in services as goods (αs = αg).
  - Perfect wage flexibility (dw = 0).
  - Symmetric input-output matrix (ξg = ξs = 0.12).
  - Higher probability of business failure (θ = 0.15).
- Selected results from Table 3 (welfare and production gains, percent):
  - Baseline estimated parameters: Welfare = 3.57; Production = 2.58; Services production = 1.08; Goods production = 3.66.
  - High degree of openness (m = 0.4): Welfare = 3.42; Production = 2.63; Services production = 1.37; Goods production = 3.61.
  - High cost of intermediation (φ = 0.1): Welfare = 3.95; Production = 2.95; Services production = 1.56; Goods production = 4.09.
  - Same share of capital (αs = αg): Welfare = 3.97; Production = 3.04; Services production = 1.77; Goods production = 3.87.
  - Without wage stickiness (dw = 0): Welfare = 3.56; Production = 2.59; Services production = 1.09; Goods production = 3.66.
  - Symmetric input-output matrix (ξg = ξs = 0.12): Welfare = 1.12; Production = 0.57; Services production = 0.30; Goods production = 0.77.
  - High probability of failure (θ = 0.15): Welfare = 5.22; Production = 3.78; Services production = 1.61; Goods production = 5.25.
- Key sensitivity insights:
  - Results robust to variations in openness, foreign borrowing cost, wage rigidity, and exchange rate regime in terms of qualitative sign and magnitude.
  - Welfare gains are highly sensitive to the probability of business failure, θs: increasing θs from 0.10 to 0.15 raises welfare gain from 3.57 percent to 5.22 percent and aggregate growth gain from 2.58 percent to 3.78 percent.
  - A symmetric input-output structure (lower ξg relative to baseline) dramatically reduces welfare and output gains from services liberalization.

### Main quantitative conclusions
- Estimated entry-sunk costs are large in Tunisia: φs (services) = 0.352 implies a 35.2 percent loss in production associated with entrants in services (posterior mean).
- Eliminating the share of these costs related to trade barriers (matching Euro Area Φs = 0.100) yields:
  - Welfare gain (equivalent consumption variation) = 3.57 percent.
  - Aggregate output increase = 2.58 percent (mainly driven by goods sector growth of 3.66 percent; services: 1.08 percent).
  - Notable sectoral effects: exports of services respond strongly (+10.03 percent).
- Transitional dynamics show limited short-run aggregate costs; temporary service production dip of about 1 percent at impact.
- Sensitivity: higher business failure probability amplifies gains from liberalization; a symmetric input-output matrix (lower dependence of goods on services) markedly lowers gains.

*Source: Appendix II of the provided IMF working paper content unit.*

### REFERENCES

### _wp13110 - REFERENCES

### APPENDIX I: THE MODEL — Households: preferences, constraints, and optimization
- Preferences (i-th household):
  - Expected utility: E0 ∑t=0∞ βt U(Ct(i), Mt(i)/Pt, Nt(i)).
  - Period utility: U(·) = log(Ct(i)) + γ log(Mt(i)/Pt) − μ Nt(i)1+η/(1+η), with β∈(0,1), γ>0, μ>0, η≥0.
- Budget constraint (real and nominal variables retained):
  - Pt Ct(i) + Pt[I t(i) + CACt(i) + BACt(i)] + Mt(i) + Bd t(i)/Rt + et Bf t(i)/Rf t
    = Wt(i) Nt(i) + Qt Kt(i) + Mt−1(i) + Bd t−1(i) + et Bf t−1(i) + Tt(i) + Dt(i).
  - CACt(i) = χ/2 (It(i)/Kt(i) − δ)2 Kt(i).
  - BACt(i) = φ/2 (Bf t(i) − Bf ss Pf t)2 /(et Pf t) (foreign bonds adjustment cost).
- Capital accumulation:
  - Kt+1(i) = (1−δ) Kt(i) + It(i), with δ∈(0,1).
- Labor aggregation and demand:
  - Nt = [∫0 1 Nt(i) (σ−1)/σ di] σ/(σ−1), σ>1.
  - Nt(i) = (Wt(i)/Wt)−σ Nt.
  - Aggregate wage index: Wt = [∫0 1 Wt(i)1−σ di]1/(1−σ).
- Wage rigidity:
  - Calvo-type: with probability (1−dw) household reoptimizes nominal wage ̃Wt(i); with probability dw wage fixed at previous period.
  - Real wage contract ̃wt(i) equation (real terms) given by equation (15) in text.
- Exogenous foreign stochastic processes:
  - log(Rf t) = (1−ρRf) log(Rf) + ρRf log(Rf t−1) + εRf,t, with ρRf∈(0,1), εRf,t ∼ N(0, σRf).
  - log(πf t) = (1−ρπf) log(πf) + ρπf log(πf t−1) + επf,t, with ρπf∈(0,1), επf,t ∼ N(0, σπf).
- First-order conditions (select):
  - λt(i) = 1/Ct(i). (10)
  - γ mt(i) = λt(i) (1 − 1/Rt). (11)
  - λt(i) Rt = β Et λt+1(i) 1/πt+1. (12)
  - s t Et π∗t+1 κt R∗t [1 + φ(bf t − bf ss)] = Et s t+1 Rt πt+1. (13)
  - Intertemporal condition involving investment and adjustment costs: equation (14).
  - Real wage contract: ̃w t(i) = (σ/(σ−1)) [Et ∑q=0∞ (β dw)q Nt+q(i)η+1] / [Et ∑q=0∞ (β dw)q Nt+q(i) λt+q(i) ∏q l=1 1/πt+l]. (15)
- No-Ponzi-game restrictions on domestic and foreign bonds as specified.

### APPENDIX I: The Model — Firms, production structure, and markets
- Final producers:
  - Final product yi,t (i = s,g) normalized to one per firm; fixed entry cost Φi∈(0,1).
  - Input-demand decision: xi,t = 1 if Pix,t ≤ Pi t; 0 otherwise. (16)
  - Real profit Di,t = pit − pix,t if Pix,t ≤ Pi t; 0 otherwise. (17)
  - Free-entry condition: Vi,t = Φi; firm value recursive equation (18).
  - Number of firms evolution: Ωi,t+1 = (1 − θi,t) Ωi,t + gi,t. (19)
- Intermediate producers:
  - Production function:
    - Xi,t = Ai,t (Y i j,t) ξi [Ki,t αi (At Ni,t)1−αi]1−ξi. (20)
    - Ai,t: sectoral transitory TFP; At: symmetric labor-augmenting permanent technology.
  - Technology processes:
    - log(Ai,t) = ρAi log(Ai,t−1) + εAi,t. (21)
    - log(At) = log(A) + log(At−1) + εA,t. (22)
  - First-order conditions (real):
    - wt / pix,t = (1 − ξi)(1 − αi) Xi,t / Ni,t. (23)
    - qt / pix,t = (1 − ξi) αi Xi,t / Ki,t. (24)
    - pjt / pix,t = ξi Xi,t / Y i j,t. (25)
- Demand and aggregation:
  - Yi,t = Yd i,t + Yf i,t + Y j i,t. (26)
  - Foreign demand: Yf i,t = (st pi t)−μf ωi Yf t. (27)
  - Foreign revenue process: log(Yf t) = (1 − ρYf) log(Yf) + ρYf log(Yf t−1) + εYf,t. (28)
- Imported goods and services:
  - Importer profit: Dm t = (Pm t − et Pf t) Ym t. (29)
  - Real marginal cost expressed via real exchange rate: st ≡ et Pf t / Pt.
  - First-order condition: Pm t / Pt = st. (30)
- Final product aggregators:
  - Domestic final product Yd t CES aggregation of Ys,d,t and Yg,d,t. (31)
  - Demand shares:
    - Yd s,t = n (ps t / pd t)−φ Yd t. (32)
    - Yd g,t = (1 − n) (pg t / pd t)−φ Yd t. (33)
  - Aggregate domestic/imported CES:
    - Zt = [ m1/ν (Yd t) (ν−1)/ν + (1−m)1/ν (Ym t) (ν−1)/ν ]ν/(ν−1). (34)
    - Yd t = m (pd t)−ν Zt. (35)
    - Ym t = (1 − m) (pm t)−ν Zt. (36)
  - CPI (Pt) defined from Pd t and Pm t as in text.

### APPENDIX I: The government and monetary policy rules
- Government budget constraint:
  - Tt + Bd t−1 = Mt − Mt−1 + Bd t Rt. (37)
- Monetary policy (Tunisia):
  - Short-term nominal money growth ζt = Mt / Mt−1 set partly to stabilize nominal exchange rate:
    - log(ζt) = ρζ log(ζt−1) − ρe log(et / et−1) + εζ,t, with ρζ∈(0,1), ρe≥0, εζ,t ∼ N(0, σζ). (38)
- Euro Area policy (ECB):
  - Standard Taylor-type rule in log-deviations:
    - R̂t = ρR R̂t−1 + (1 − ρR) [ρπ π̂t + ρy ŷt] + εζ,t. (38′)
  - Output gap defined as ŷt ≡ log(yt) − log(y), where yt ≡ Yt / At.
- Transformation for trending technology:
  - Non-stationary variables divided by At to solve model around steady state.

### APPENDIX I: Closing the model — aggregates and accounts
- Aggregate resource constraint:
  - Zt = Ct + It + CACt + BACt. (39)
- Gross domestic product:
  - Yt = Ys,t + Yg,t. (40)
- Current account equation:
  - st bf t Rf t = st bf t−1 / π∗t+1 + ps t Yf s,t + pg t Yf g,t − pm t Ym t. (41)
  - bf t ≡ Bf t / Pf t (real stock of foreign bonds).
- Aggregation of hours and capital:
  - Ns,t + Ng,t = Nt. (42)
  - Ks,t + Kg,t = Kt. (43)

### APPENDIX II: QUANTITATIVE RESULTS — Business cycle statistics (selected)
- Table 4: Second order moments (Data vs Model; 90 percent confidence intervals in brackets)
  - std(∆log(Ys,t)) / std(∆log(Yt)): Data 1.29 Model 1.11 [0.90,1.34]
  - std(πs,t) / std(πt): Data 1.59 Model 1.63 [1.35,2.11]
  - std(st) / std(∆log(Yt)): Data 3.75 Model 6.02 [1.29,19.01]
  - corr(∆log(Yt), ∆log(Ys,t)): Data 0.84 Model 0.87 [0.80,0.94]
  - corr(∆log(Yt), πt): Data 0.03 Model 0.17 [−0.01,0.35]
  - corr(∆log(Yt), πs,t): Data 0.39 Model 0.34 [0.17,0.47]
  - corr(∆log(Yt), st): Data 0.19 Model 0.01 [−0.04,0.05]
  - corr(πt, πs,t): Data 0.19 Model 0.87 [0.76,0.94]
  - corr(πt, st): Data −0.36 Model −0.08 [−0.18,−0.02]
  - corr(πs,t, st): Data −0.03 Model −0.09 [−0.17,−0.02]
- Key interpretation:
  - Model matches many sectoral dynamics and correlations well.
  - Model overpredicts relative volatility of the real exchange rate vs output: model ratio 6.02 vs data 3.75 despite strong monetary reaction to nominal exchange rate.
  - Adding price stickiness across sectors could reduce real exchange rate volatility but would complicate analysis for trade liberalization.

### Variance decomposition — average asymptotic contributions (Table 5, with 90 percent CIs)
- Shocks considered: εs (service sector technology), εg (good sector technology), εA (symmetric technology), εζ (money growth), εyf (foreign demand), επf (foreign inflation), εRf (foreign interest rate).
- Selected variable decompositions (point estimates with [90% CI]):
  - Yt: εs 3.32 [0.25,12.30]; εg 23.79 [7.12,51.37]; εA 27.00 [2.55,71.21]; εζ 0.23 [0.01,1.10]; εyf 22.78 [4.89,45.51]; επf 6.97 [0.03,31.07]; εRf 10.33 [0.25,33.05].
  - Ys,t: εs 20.90 [2.66,45.49]; εg 15.63 [1.25,44.51]; εA 30.63 [3.07,79.18]; εζ 0.81 [0.02,3.54]; εyf 7.82 [0.84,25.73]; επf 9.23 [0.06,28.72]; εRf 8.65 [0.26,30.32].
  - Yg,t: εs 4.33 [0.11,21.06]; εg 24.59 [9.88,46.37]; εA 18.72 [1.61,52.55]; εζ 0.02 [0.00,0.12]; εyf 34.66 [15.77,53.87]; επf 3.96 [0.01,24.81]; εRf 8.73 [0.16,28.61].
  - Ym t: εs 10.44 [1.84,38.70]; εg 5.94 [0.61,30.80]; εA 10.64 [0.23,40.49]; εζ 0.05 [0.00,0.29]; εyf 15.81 [1.38,42.06]; επf 14.38 [0.02,74.68]; εRf 33.68 [2.55,79.97].
  - Ct: εs 9.47 [0.47,28.42]; εg 24.28 [9.28,48.49]; εA 21.01 [1.24,60.78]; εζ 0.08 [0.00,0.36]; εyf 16.99 [4.78,32.41]; επf 7.70 [0.03,42.60]; εRf 14.28 [0.58,42.56].
  - It: εs 19.96 [5.27,38.36]; εg 12.90 [3.46,28.96]; εA 5.37 [0.43,18.50]; εζ 0.14 [0.00,0.77]; εyf 36.03 [14.04,60.07]; επf 7.17 [0.08,39.10]; εRf 13.99 [1.13,38.08].
  - πt: εs 11.61 [2.40,25.47]; εg 29.70 [9.28,49.30]; εA 3.54 [0.17,19.44]; εζ 16.71 [0.48,42.23]; εyf 11.53 [2.71,24.29]; επf 19.70 [0.34,41.53]; εRf 3.34 [0.61,9.79].
  - st (real exchange rate): εs 40.70 [6.78,71.24]; εg 19.82 [2.48,61.63]; εA 6.16 [0.08,32.88]; εζ 0.35 [0.01,2.13]; εyf 13.30 [1.68,35.42]; επf 3.30 [0.02,28.58]; εRf 9.19 [0.06,36.38].
- Key interpretation:
  - Rest of the world shocks explain more than one third of output fluctuations in Tunisia in the model.
  - Foreign demand shocks are main drivers of fluctuations in aggregate quantities and prices, except services.
  - Service sector fluctuations are largely explained by sector-specific technology and symmetric technology shocks (suggesting lower integration of services with rest of world, consistent with estimated trade barriers).
  - Foreign shocks contribute substantially to real exchange rate fluctuations—almost half—while domestic shocks dominated by service sector technology.

### APPENDIX II: Impulse-response functions — main qualitative findings
- General observation:
  - Goods and services respond differently to both idiosyncratic and aggregate shocks, illustrating sectoral heterogeneity.
- Service sector technology shock (positive 1 percent):
  - Output rises, prices and inflation fall.
  - Output increase is delayed due to time-to-build.
  - Final goods production declines as resources shift to services.
  - Imports decline as consumers substitute toward locally produced goods/services; nominal exchange rate appreciates but combined effects yield a real depreciation.
  - Consumption and investment experience a delayed decline, consistent with an expenditure switching effect.
- Good sector technology shock (positive 1 percent):
  - Increased goods production raises aggregate demand and services output.
  - Good-sector prices fall on impact, overall inflation drops, local currency appreciates nominally.
  - Monetary policy reacts expansionarily, feeding further demand and causing a real depreciation on impact.
  - Expenditure switching effect observed.
- Monetary shock (expansionary increase in nominal money supply):
  - Unlike some studies, expansionary monetary shock here leads initially to higher demand, higher prices, and nominal depreciation.
  - Wage rigidity implies slight inflation increase and real exchange rate overshoot; real depreciation discourages consumption and investment.
  - First-round demand increase is strong short-term; second-round effects produce a stronger medium-term negative impact on production—aggregate, services, goods, and imports moderately decline following shock.
  - Services production less negative due to additional demand from goods sector propagation.
- Foreign demand shock (positive):
  - Major driver of consumption cyclicality.
  - Sectoral producers increase goods and services; revenue finances higher consumption and investment.
  - Real imports increase.
  - Real exchange rate declines (real appreciation of local currency).

*Source: _wp13110 - REFERENCES (appendices and quantitative results as provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13110.pdf_