## _wp08113 - 1. The budget constraint for the representative household in country 1 now becomes

## Source details

**Canonical URL:** [_wp08113 - 1. The budget constraint for the representative household in country 1 now becomes](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08113.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08113.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08113.pdf.json)

---

### I. Introduction and research question
- Focus: spillover effects of labor market and welfare policy reforms (taxation, regulation, benefits) in Germany (country 1) on the rest of the Euro area (country 2).
- Research gap: limited understanding of cross-border effects of changes in distortionary taxation or welfare benefits; most existing studies use VARs and focus on public consumption rather than taxation/benefits.
- Approach: two-country dynamic general equilibrium model calibrated for Germany (country 1) and the rest of the Euro area (country 2) with unionized labor markets, indivisible labor (extensive-margin employment), monopolistic competition in intermediate goods, and initially perfect international financial markets.
- Key departures: unionized labor market; producers set prices via mark-ups; later extensions introduce price stickiness and a common monetary policy.

### II. Model structure — main blocks and mechanisms
- Geography and agents:
  - Two countries: country 1 (Germany) and country 2 (rest of Euro area), populations of measure s and 1-s.
  - Households: infinitely lived, symmetric within country; indivisible labor (employment probability n = fraction working); labor income taxed at average rate τ; unemployed receive flat unemployment benefits UB; lump-sum transfers TR; government runs balanced budget.
- Firms and production:
  - I-firms: continuum of monopolistically competitive firms producing tradable intermediate goods; use labor and capital; Cobb-Douglas production.
  - F-firms: bundle domestic and foreign intermediates into composite non-traded final good using CES aggregation with home bias parameters ω1, ω2.
- Labor market institutions:
  - Firm-specific trade unions bargain wages via Nash bargaining; firm retains right-to-manage employment after wage set.
  - Unions are risk neutral; relative bargaining power parameter p.
  - Bargained wage characterized by a mark-up relationship with comparative statics:
    - Higher average tax rate τ → higher bargained wage.
    - Higher marginal tax rate t (holding average constant) → lower equilibrium pre-tax wage.
    - Higher union bargaining power p → higher wages.
    - Higher unemployment (lower n) → lower wage.
    - Lower η (greater producer market power) → higher wage.
    - Higher capital share θ → higher wage.
- Equilibrium objects of interest: terms of trade (ToT = PIm/PEx = q1t b / q1t a), real exchange rate (RXR = q1t a / q2t a), net exports/GDP ratio (nx1t).

### III. Solution method and calibration
- Solution:
  - Linearization around balanced-trade steady state; 35 expectational difference equations solved by Blanchard and Kahn (1980) with Anderson and Moore (1985) numeric algorithm.
- Key calibration choices (quarterly frequency) — benchmark model parameters:
  - Discount factor β = .99 (Germany .99, EU11 .99)
  - Depreciation rate δ = .025
  - Capital share θ = .45
  - Intertemporal elasticity of substitution μ = 2.5
  - Intratemporal elasticity across domestic varieties η = 5.8
  - Intratemporal elasticity across traded goods σ = 1.5
  - Capital adjustment cost φ = 10
  - Population share s / 1-s = .275 / .725
  - Employment rate: Germany .65, EU11 .63
  - Import share (): Germany .13, EU11 .07
  - Average tax rate: Germany .33, EU11 .22
  - Marginal tax rate t: Germany .54, EU11 .36
  - Gross replacement rate grr: Germany .29, EU11 .36
  - Union bargaining power p: Germany .59, EU11 .49
- Model-implied bargaining power: p = .59 for Germany, p = .49 for rest of Euro area.

### IV. Policy simulations — baseline experiment and channels
- Baseline experiment:
  - A 3 percent decline in the average tax rate in country 1, financed by adjustment in lump-sum transfers; phase-in period = 5 years; simulation under perfect foresight.
- Core domestic transmission channels:
  - Lower average tax → unions request lower real wage → labor demand ↑ → employment ↑.
  - For given capital, higher employment raises return to capital → investment ↑ → capital accumulation → labor productivity ↑ → output ↑.
  - Wealth effect from tax cut raises consumption.
  - Expansion of home production leads to terms of trade (ToT) deterioration and real exchange rate depreciation (country 1 goods relatively cheaper).
  - Net effect on trade balance depends on σ; with calibrated σ = 1.5, trade balance improves.
- Cross-border transmission channels:
  - Trade channel: country 1 ToT deterioration favors country 2 investment and productivity, enabling unions to bargain higher wages and employment in country 2.
  - Financial channel (with complete markets): risk-sharing transmits home gains to foreign households via asset payouts, boosting foreign consumption more than foreign output.

### V. Role of labor unions versus competitive labor markets
- Comparison under a 3 percent average tax cut:
  - Employment responses (impact / long run):
    - Competitive: +1.2 percent on impact, +5.6 percent in long run.
    - Unionized: +0.7 percent on impact, +2.5 percent in long run.
  - Domestic quantities react qualitatively similarly but quantitatively much more under competitive markets (domestic quantities react more than twice as much in long run).
- Mechanisms:
  - Competitive: tax cut → labor supply ↑ via consumption-leisure substitution → pre-tax wage ↓ → labor demand ↑ → large employment increase.
  - Unionized: collective bargaining captures rents; unions demand lower wages but not as low as competitive outcome; result is smaller employment and quantity responses.
- Spillover differences:
  - Competitive case: larger home output expansion → larger ToT deterioration → substitution reduces foreign output and employment (negative spillover on country 2 output and employment), though foreign consumption increases via wealth effects.
  - Unionized case: smaller home ToT deterioration → foreign output and employment expand (positive spillover).
- Conclusion: labor market structure critically affects domestic propagation and international spillovers; degree of unionization can qualitatively reverse foreign responses.

### VI. Openness, closure, and financial market completeness
- Openness parameter: home bias ω in final consumption and investment. Closed economy scenario: ω1 = ω2 = 1 and no risk sharing.
- Findings on openness:
  - Domestic response in country 1 largely unaffected by openness for most variables (consumption excepted): output, employment, investment react almost the same in closed and open cases.
  - Consumption response larger in open economy because of risk sharing and ToT wealth effects.
  - In country 2, closed economy eliminates consumption rise (no risk sharing, no ToT appreciation), and other variables show little reaction.
  - Overall: trade openness is not the dominant determinant of fiscal shock transmission; labor market competitiveness matters more.
- Financial markets — incomplete markets extension (bond with holding cost):
  - Bond holding cost specification: Γ_{B,t} = exp[γ_{B,1} (B_{1t}/Y_{a,t} − 1)]
  - Representative-household budget identity (notation preserved):
    - C_{1t} + I_{1t} + q^{a}_{1t} Q_{t} (1−Γ_{B,t}) B_{1,t+1} = n_{1t} w_{1t} (1−τ_{1t}) + r_{1t} K_{1t} + TR_{1t} + Π_{1t} + (1−n_{1t}) UB_{1t} + q^{a}_{1t} B_{1t}
  - Global bond market clearing: s B_{1t} + (1−s) B_{2t} = 0
- Incomplete versus complete markets — key effects under the 3 percent average tax cut:
  - Qualitative results from complete markets largely hold under incomplete markets.
  - Absent perfect insurance:
    - Consumption is less positively correlated across countries.
    - Agents in country 2 still consume more due to a positive wealth effect.
    - Agents in country 1 consume more of their output than under perfect risk sharing.
    - Higher consumption in country 1 increases demand for good a (home bias), so ToT depreciate less than under complete markets.
    - Less ToT depreciation ⇒ higher real return to capital ⇒ higher investment demand in country 1.
    - Trade balance and net foreign asset position initially deteriorate as agents in country 1 borrow to finance high consumption and repay gradually with higher output.
  - Reference: "This is a well known result by Cole and Obstfeld (1991)."

### VII. Nominal rigidities, Calvo pricing, and common monetary policy
- Price rigidity setup:
  - Calvo price-setting with partial inflation indexation in intermediate goods sector.
  - Firms reoptimize prices with probability (1−ξ_p); non-reoptimizing firms index partially to last period’s inflation with indexation factor γ_p, with 1−ξ_p γ_p < 1.
  - Producer inflation follows a backward- and forward-looking New-Keynesian Phillips curve reacting to current producer real marginal costs.
- Monetary union:
  - A single central bank sets a common nominal interest rate via Taylor rule:
    - R̂_t = r_i R̂_{t-1} + (1−r_i) (g_p p̂_t^u + g_y ŷ_t^u)
  - Union-wide inflation and output growth are population-weighted averages of country-specific CPI inflation and output growth.
- Simulation results with sticky prices and monetary union (same tax reform):
  - Domestic response in country 1 is dampened; short-run spillover effects abroad (country 2) are magnified relative to flexible price case.
  - Mechanisms:
    - Country 1: lower wage demand → lower real marginal costs → gradual price adjustment → decline in inflation → central bank cuts nominal rate. Initially, lower inflation raises the real interest rate in country 1 because the nominal cut is insufficient to offset disinflationary pressure, producing a contractionary force that damps demand and the expansion of output and employment in country 1.
    - Country 2: consumption price inflation reacts less (home bias) while the lower nominal rate fully feeds through to a lower real interest rate, creating an expansionary force that stimulates output and demand in country 2; short-term spillovers can overshoot long-run levels.
  - Role of unions:
    - Nominal rigidities reinforce union-induced real wage rigidity in country 1 → further short-run dampening of the response to tax reform.
    - For country 2, nominal rigidities magnify positive short-run spillovers compared to the competitive case.
    - Quantitative comparison: in the first period, the relative increase in output and employment in country 2 is now one quarter of the increase in country 1, as opposed to one hundredth in the flexible price model.
  - Long run: prices adjust completely and the flexible price allocation is achieved.

### VIII. Other labor market reform scenarios — long-run quantitative effects (Table 2 summary)
- Three additional reforms (long-run percentage deviations from pre-reform steady state under benchmark model):
  - Scenario descriptions:
    1) Δt = -2%: 2 percent reduction in marginal tax rate, with compensating decrease in lump-sum tax allowance so average tax unchanged.
    2) ΔB = -7.42%: reduction in flat unemployment benefits (average income loss for a benefit-dependent household set at 7.42 percent).
    3) Δp = -10%: reduction in union bargaining power in Germany from .59 to .49 (i.e., Δp = -10%).
- Table 2 — Long Term Effects of Policy Reforms (Percentage Deviation from Pre-reform Steady State — benchmark model)
  - Columns: Baseline: Δτ = -3% | 1) Δt = -2% | 2) ΔB = -7.42% | 3) Δp = -10%
  - Domestic:
    - Output: 2.18 | -1.19 | 1.56 | 4.37
    - Consumption: 1.07 | -0.58 | 0.77 | 2.14
    - Employment: 2.54 | -1.39 | 1.82 | 5.11
    - Investment: 1.73 | -0.95 | 1.24 | 3.47
    - Real wage: -0.81 | 0.44 | -0.58 | -1.63
  - Foreign:
    - Output: 0.24 | -0.13 | 0.17 | 0.47
    - Consumption: 0.66 | -0.36 | 0.47 | 1.32
    - Employment: 0.10 | -0.05 | 0.07 | 0.19
    - Investment: 0.41 | -0.22 | 0.29 | 0.81
    - Real wage: 0.31 | -0.17 | 0.22 | 0.62
  - ToT (terms of trade): 1.64 | -0.90 | 1.18 | 3.30
  - Trade balance (net export/GDP in 1): 0.45 | -0.25 | 0.32 | 0.90
- Interpretation:
  - Scenario 1 (lower marginal tax, average constant): induces more aggressive union bargaining → higher wages → negative responses in both countries (domestic output and employment fall).
  - Scenario 2 (lower unemployment benefits): reduces unions’ outside option → raises employment and output domestically; similar propagation/spillover channels as baseline.
  - Scenario 3 (reducing union bargaining power to EU11 level): largest positive domestic effects — long-run employment +5.11 percent, output +4.37 percent; EU-wide gains also notable.
- Relative magnitudes of spillovers:
  - Foreign per capita output change ≈ one tenth of home output change in long run across reforms.
  - Foreign consumption change ≈ 60 percent of home consumption change.
  - Foreign investment long-run change ≈ one quarter of home investment change.
  - Foreign employment change ≈ 4 percent of the change in Germany.

### IX. Appendix: sensitivity to intratemporal elasticity of substitution σ
- Role of σ (intratemporal elasticity of substitution for traded goods) on spillovers:
  - High σ scenario (example: σ = 2.5):
    - Stronger relative demand response to price changes ⇒ lower ToT depreciation for country 1 after a tax cut.
    - For sufficiently high σ such as σ=2.5, the spillover on output in country 2 is persistently negative because substitution effect dominates wealth effect.
    - Consequences: persistently negative investment response in country 2; consumption increases more in country 2 (and less in country 1) under perfect risk sharing.
    - Long run: benchmark qualitative results remain unchanged.
  - Low σ scenario:
    - Benchmark results regarding aggregate quantities are reinforced.
    - Lower σ ⇒ higher ToT appreciation of country 2 ⇒ higher positive spillovers in output, investment, and employment.
    - Lower σ implies lower consumption spillover through perfect risk sharing.
- Interaction with unionization:
  - Unionization produces effects similar to a low σ with respect to quantity reactions: domestic dampening and positive spillovers via more rigid wages and lower ToT depreciation.
  - This similarity is a potential misspecification risk when estimating models that assume competitive labor markets if union bargaining is present.

### X. Main conclusions and policy implications
- Core findings:
  - Reforms in labor taxation, welfare benefits, and collective bargaining yield strong positive effects on the domestic economy.
  - Positive, albeit limited, effects on foreign output/employment when no nominal rigidities are considered.
  - Sizable positive spillovers on foreign consumption and investment.
  - Compared with competitive labor markets: domestic effects of reforms are dampened by unions; foreign spillovers are strengthened by unions via union-induced real wage rigidity and absence of wealth effect on individual labor supply.
  - Presence of nominal rigidities and a common monetary policy further dampens home effects and magnifies short-run spillovers abroad.
- Policy recommendation implied:
  - Coordinated and simultaneous labor market and social policy reforms across members of a monetary union can internalize positive externalities and raise overall efficiency; reforms are expected to have gradual expansionary national effects and significant positive spillovers on other union members, especially in the first quarters following reform.

*Source: _wp08113 - 1. The budget constraint for the representative household in country 1 now becomes.*

### References..............................................................................................................

### _wp08113 - References

### I. Introduction — motivation and research question
- Focus: spillover effects of labor market and welfare policy reforms (taxation, regulation, benefits) in Germany on the rest of the Euro area.
- Research gap: limited understanding of cross-border effects of changes in distortionary taxation or welfare benefits (most existing studies use VARs and focus on public consumption; less on taxation/benefits).
- Approach: a two-country dynamic general equilibrium model calibrated for Germany (country 1) and the rest of the Euro area (country 2) incorporating unionized labor markets, indivisible (fixed-hours) labor (extensive margin employment adjustment), monopolistic competition in intermediate goods, and initially perfect international financial markets.
- Key modeling departures: unionized labor market; producers set prices via mark-ups; later extensions introduce price stickiness and a common monetary policy.

### II. Model structure — main blocks and mechanisms
- World: country 1 (Germany) and country 2 (rest of Euro area), populations of measure s and 1-s.
- Production structure:
  - I-firms: continuum of monopolistically competitive firms producing tradable intermediate goods; use labor and capital; Cobb-Douglas production.
  - F-firms: bundle domestic and foreign intermediates into a composite non-traded final good using CES aggregation with home bias parameters ω1, ω2.
- Households:
  - Infinitely lived, symmetric within country; indivisible labor (employment probability n = fraction working).
  - Complete international asset markets initially (state-contingent Arrow-Debreu securities) providing full risk sharing.
  - Labor income taxed at average rate τ; unemployed receive flat unemployment benefits UB; lump-sum transfers TR; government runs balanced budget.
- Labor market:
  - Firm-specific trade unions bargain wages via Nash bargaining; firm retains right-to-manage employment after wage set.
  - Unions are risk neutral; relative bargaining power parameter p (union weight).
  - Derived bargained wage is a mark-up relationship (equation (4)), with comparative statics:
    - Higher average tax rate τ → higher bargained wage (tax incidence shifted to firms).
    - Higher marginal tax rate t (holding average constant) → lower equilibrium pre-tax wage (progressivity moderates wages).
    - Higher union bargaining power p → higher wages.
    - Higher unemployment (lower n) → lower wage (weaker outside option).
    - Lower η (greater producer market power) → higher wage.
    - Higher capital share θ → higher wage.
- Equilibrium objects of interest: terms of trade (ToT = PIm/PEx = q1t b / q1t a), real exchange rate (RXR = q1t a / q2t a), net exports/GDP ratio (nx1t).

### III. Solution method and calibration
- Linearization around balanced-trade steady state; 35 expectational difference equations solved by Blanchard and Kahn (1980) with Anderson and Moore (1985) numeric algorithm.
- Key calibration choices (quarterly frequency) — Table 1 reproduced (benchmark model):
  - Discount factor β = .99 (Germany .99, EU11 .99)
  - Depreciation rate δ = .025
  - Capital share θ = .45
  - Intertemporal elasticity of substitution μ = 2.5
  - Intratemporal elasticity across domestic varieties η = 5.8
  - Intratemporal elasticity across traded goods σ = 1.5
  - Capital adjustment cost φ = 10
  - Population share s / 1-s = .275 / .725
  - Employment rate: Germany .65, EU11 .63
  - Import share (): Germany .13, EU11 .07
  - Average tax rate: Germany .33, EU11 .22
  - Marginal tax rate t: Germany .54, EU11 .36
  - Gross replacement rate grr: Germany .29, EU11 .36
  - Union bargaining power p: Germany .59, EU11 .49
- Model-implied bargaining power: p = .59 for Germany, p = .49 for rest of Euro area (consistent with proxy estimates cited).

### IV. Policy simulations — experiments and dynamic channels
- Baseline experiment: 3 percent decline in the average tax rate in country 1, financed by adjustment in lump-sum transfers; phase-in period = 5 years; simulation under perfect foresight. (Figures referenced: dynamic responses over time.)
- Core domestic transmission channels:
  - Lower average tax → unions request lower real wage → labor demand ↑ → employment ↑.
  - For given capital, higher employment raises return to capital → investment ↑ → capital accumulation → labor productivity ↑ → output ↑.
  - Wealth effect from tax cut raises consumption.
  - Expansion of home production leads to terms of trade (ToT) deterioration and real exchange rate depreciation (country 1 goods relatively cheaper).
  - Net effect on trade balance depends on elasticity of substitution between traded goods; with calibrated σ = 1.5, trade balance improves (consistent with Germany’s post-reform experience).
- Cross-border transmission channels:
  - Trade channel: country 1 ToT deterioration favors country 2 investment and productivity (for given inputs), enabling unions to bargain higher wages and employment in country 2.
  - Financial channel (with complete markets): risk-sharing transmits home gains to foreign households via asset payouts, boosting foreign consumption more than foreign output.

### V. Role of labor unions vs competitive labor markets
- Competitive labor market (indivisible labor with highly elastic supply) vs unionized setting:
  - Under a 3 percent average tax cut:
    - Employment responses (impact / long run):
      - Competitive: +1.2 percent on impact, +5.6 percent in long run.
      - Unionized: +0.7 percent on impact, +2.5 percent in long run.
    - Domestic quantities (output, consumption, investment) react qualitatively similarly but quantitatively much more under competitive markets (domestic quantities react more than twice as much in long run).
  - Mechanism:
    - Competitive: tax cut → labor supply ↑ via consumption-leisure substitution → pre-tax wage ↓ → labor demand ↑ → large employment increase.
    - Unionized: collective bargaining captures rents; lower taxes lead unions to demand lower wages but not as low as competitive outcome; expectation of higher employment pressures wages up along contract curve; result is smaller employment and quantity responses.
  - Spillover differences:
    - Competitive case: larger home output expansion → larger ToT deterioration → substitution reduces foreign output and employment (negative spillover on country 2 output and employment), though foreign consumption still increases via wealth effects.
    - Unionized case: smaller home ToT deterioration → foreign output and employment expand (positive spillover).
  - Conclusion: labor market structure critically affects both domestic propagation and international spillovers; degree of unionization can qualitatively reverse foreign responses.

### VI. Openness and closure experiments
- Openness parameter: home bias ω in final consumption and investment.
- Closed economy scenario: ω1 = ω2 = 1 and no risk sharing.
- Findings:
  - Domestic response in country 1 largely unaffected by openness for most variables (consumption excepted): output, employment, investment react almost the same in closed and open cases.
  - Consumption response larger in open economy because of risk sharing and terms-of-trade wealth effects.
  - In country 2, closed economy eliminates consumption rise (no risk sharing, no ToT appreciation), and other variables show little reaction.
  - Overall: contrary to common belief, trade openness is not the dominant determinant of fiscal shock transmission; labor market competitiveness matters more.

### VII. Other labor market reform scenarios — long-run quantitative effects
- Three additional reforms (Table 2 reports long-run percentage deviations from pre-reform steady state under benchmark model):
  - Scenario descriptions:
    1) Δt = -2%: 2 percent reduction in marginal tax rate, with compensating decrease in lump-sum tax allowance so average tax unchanged.
    2) ΔB = -7.42%: reduction in flat unemployment benefits (average income loss for a benefit-dependent household set at 7.42 percent).
    3) Δp = -10%: reduction in union bargaining power in Germany from .59 to .49 (i.e., Δp = -10% expressed in table).
- Table 2 (Long Term Effects of Policy Reforms, Percentage Deviation from Pre-reform Steady State — benchmark model)
  - Columns: Baseline: Δτ = -3% | 1) Δt = -2% | 2) ΔB = -7.42% | 3) Δp = -10%
  - Domestic:
    - Output: 2.18 | -1.19 | 1.56 | 4.37
    - Consumption: 1.07 | -0.58 | 0.77 | 2.14
    - Employment: 2.54 | -1.39 | 1.82 | 5.11
    - Investment: 1.73 | -0.95 | 1.24 | 3.47
    - Real wage: -0.81 | 0.44 | -0.58 | -1.63
  - Foreign:
    - Output: 0.24 | -0.13 | 0.17 | 0.47
    - Consumption: 0.66 | -0.36 | 0.47 | 1.32
    - Employment: 0.10 | -0.05 | 0.07 | 0.19
    - Investment: 0.41 | -0.22 | 0.29 | 0.81
    - Real wage: 0.31 | -0.17 | 0.22 | 0.62
  - ToT (terms of trade): 1.64 | -0.90 | 1.18 | 3.30
  - Trade balance (net export/GDP in 1): 0.45 | -0.25 | 0.32 | 0.90
- Interpretation of scenarios:
  - Scenario 1 (lower marginal tax, average constant): induces more aggressive union bargaining → higher wages → negative responses in both countries (domestic output and employment fall).
  - Scenario 2 (lower unemployment benefits): reduces unions’ outside option → raises employment and output domestically; similar propagation/spillover channels as baseline.
  - Scenario 3 (lower union bargaining power to EU11 level): largest positive effects domestically — long-run employment +5.11 percent, output +4.37 percent; EU-wide gains also notable (~1.5 percent employment/output for whole Euro area).
- Relative magnitudes of spillovers:
  - Foreign per capita output change ≈ one tenth of home output change in long run across reforms.
  - Foreign consumption change ≈ 60 percent of home consumption change (i.e., nearly 6x spillover in consumption relative to output).
  - Foreign investment long-run change ≈ one quarter of home investment change.
  - Foreign employment change ≈ 4 percent of the change in Germany (i.e., small).

### VIII. Financial markets — imperfect markets extension (preview)
- Relaxation: replace complete state-contingent claims with a single non-contingent bond; include bond holding costs to ensure stationarity.
- Preview observation: assuming imperfect financial markets "hardly changes the results" qualitatively because terms-of-trade-driven asymmetric wealth effects still operate as an insurance-like mechanism (details continue beyond provided content).

*Source: _wp08113 - References.*

### 1. The budget constraint for the representative household in country 1 now becomes:

### _wp08113 - 1. The budget constraint for the representative household in country 1 now becomes:

### Budget constraint and bond-holding cost
- Representative-household budget constraint (country 1) includes bond purchases B_{t+1} at price Q_t (in terms of good a) and a bond holding cost that depends positively on the ratio of bond holding to national GDP:
  - Bond holding cost specification (as given): Γ_{B,t} = exp[γ_{B,1} (B_{1t}/Y_{a,t} − 1)]
- Full budget identity displayed in the source (notation preserved):
  - C_{1t} + I_{1t} + q^{a}_{1t} Q_{t} (1−Γ_{B,t}) B_{1,t+1} = n_{1t} w_{1t} (1−τ_{1t}) + r_{1t} K_{1t} + TR_{1t} + Π_{1t} + (1−n_{1t}) UB_{1t} + q^{a}_{1t} B_{1t}
  - Global bond market clearing condition holds: s B_{1t} + (1−s) B_{2t} = 0

### Incomplete versus complete financial markets — quantitative and qualitative effects
- Simulation exercise: comparison of the same tax reform—an average tax cut of 3%—under complete and incomplete financial markets.
- Key quantitative/qualitative findings:
  - Qualitative results from the complete markets model largely hold under incomplete markets.
  - Absent perfect insurance:
    - Consumption is less positively correlated across countries.
    - Agents in country 2 still consume more than before the reform due to a positive wealth effect.
    - Agents in country 1 consume more of their output than under perfect risk sharing.
    - Higher consumption in country 1 increases demand for good a (home bias), so the terms of trade depreciate less than under complete markets.
    - Less depreciation of terms of trade ⇒ higher real return to capital ⇒ higher investment demand in country 1.
  - Trade balance and net foreign asset position initially deteriorate as agents in country 1 borrow to finance high consumption and repay gradually with higher output.
- Reference result: "This is a well known result by Cole and Obstfeld (1991)."

### Nominal rigidities, Calvo pricing, and common monetary policy
- Nominal rigidities introduced: Calvo price-setting with partial inflation indexation in the intermediate goods sector.
  - Firms reoptimize prices with probability (1−ξ_p); non-reoptimizing firms index partially to last period’s inflation with indexation factor γ_p, with 1−ξ_p γ_p < 1.
  - In log-linearized form, producer inflation in country 1 follows a backward- and forward-looking New-Keynesian Phillips curve reacting to current producer real marginal costs (equation structure preserved in source).
- Two-country monetary union:
  - A single central bank sets a common nominal interest rate following a Taylor rule:
    - R̂_t = r_i R̂_{t-1} + (1−r_i) (g_p p̂_t^u + g_y ŷ_t^u)
  - Union-wide inflation and output growth are population-weighted averages of country-specific CPI inflation and output growth.
- Simulation results with sticky prices and monetary union (same policy reform as before):
  - Domestic response in country 1 is dampened; short-run spillover effects abroad (country 2) are magnified relative to the flexible price case.
  - Mechanism:
    - Country 1: lower wage demand → lower real marginal costs → gradual price adjustment → decline in inflation → central bank cuts nominal rate. Initially, lower inflation raises the real interest rate in country 1 because the nominal cut is insufficient to offset disinflationary pressure, producing a contractionary force that damps demand and the expansion of output and employment in country 1.
    - Country 2: consumption price inflation reacts less (home bias) while the lower nominal rate fully feeds through to a lower real interest rate, creating an expansionary force that stimulates output and demand in country 2; short-term spillovers can overshoot long-run levels.
  - Role of labor unions:
    - Nominal rigidities reinforce union-induced real wage rigidity in country 1 → further short-run dampening of the response to tax reform (relative to competitive labor markets).
    - For country 2, nominal rigidities magnify positive short-run spillovers compared to the competitive case.
    - Quantitative comparison: in the first period, the relative increase in output and employment in country 2 is now one quarter of the increase in country 1, as opposed to one hundredth in the flexible price model.
  - Long run: prices adjust completely and the flexible price allocation is achieved.

### Main conclusions and policy implications
- Paper focus: macroeconomic responses to labor market reforms (similar to recent German reforms) using a dynamic open-economy model with explicit wage bargaining and unions.
- Core findings:
  - Reforms in labor taxation, welfare benefits, and collective bargaining yield:
    - Strong positive effects on the domestic economy.
    - Positive, albeit limited, effects on foreign output/employment when no nominal rigidities are considered.
    - Sizable positive spillovers on foreign consumption and investment.
  - Compared with competitive labor markets:
    - Domestic effects of reforms are dampened by unions.
    - Foreign spillovers are strengthened by unions via union-induced real wage rigidity and absence of wealth effect on individual labor supply.
  - Presence of nominal rigidities and a common monetary policy further strengthens the dampening at home and magnification abroad in the short run.
- Policy recommendation implied by the analysis:
  - Coordinated and simultaneous labor market and social policy reforms across members of a monetary union can internalize positive externalities and raise overall efficiency; reforms are expected to have gradual expansionary national effects and significant positive spillovers on other union members, especially in the first quarters following reform.

### Appendix: sensitivity to intratemporal elasticity of substitution σ
- The intratemporal elasticity of substitution σ for traded goods affects spillovers on country 2 along the adjustment path.
- Main comparative scenarios:
  - High σ scenario (example in source: σ = 2.5):
    - Stronger relative demand response to relative price changes ⇒ lower terms of trade depreciation for country 1 after a tax cut.
    - For sufficiently high σ such as σ=2.5, the spillover on output in country 2 is persistently negative because the negative substitution effect dominates the positive wealth effect.
    - Consequences: persistently negative investment response in country 2 due to lower output → lower savings and lower return to capital.
    - Other variables in country 2 still respond positively but with lower magnitude; consumption increases more in country 2 (and less in country 1) due to perfect risk sharing.
    - Long run: benchmark qualitative results remain unchanged.
  - Low σ scenario:
    - Benchmark results regarding aggregate quantities are reinforced.
    - Lower σ ⇒ higher terms of trade appreciation of country 2 ⇒ higher positive spillovers in output, investment, and employment.
    - Lower σ also implies lower consumption spillover through perfect risk sharing.
- Interaction with unionization:
  - Unionization produces effects similar to a low σ with respect to quantity reactions: domestic dampening and positive spillovers via more rigid wages and lower terms of trade depreciation.
  - This similarity represents a potential source of misspecification risk when estimating models that assume competitive labor markets if union bargaining is actually present.

*Source: IMF working paper content unit _wp08113 - 1. The budget constraint for the representative household in country 1 now becomes:*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08113.pdf_