## 3.1 Households ## Source details **Canonical URL:** [3.1 Households](https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019123.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2019/wpiea2019123.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2019/wpiea2019123.pdf.json) --- ### Utility and preferences - Representative household in country i (i = H or F) is a large extended family with continuum of members on the unit interval; family members perfectly insure each other against consumption fluctuations due to employment status. - Household maximization problems: - Home: E0 ∑_{t=0}^{∞} β^{t} [ log C_{t} + ̺_{Ht} A_{Ht} / P_{t} ] - Foreign: E0 ∑_{t=0}^{∞} β^{t} [ log C^{*}_{t} + ̺_{Ft} A_{Ft} / P^{*}_{t} ] - Features preserved exactly: - Utility is log in consumption. - Bonds enter utility to capture a preference for the safe asset (Krishnamurty and Vissing-Jorgensen, 2012). - ̺_{it} captures a shock to liquidity demand in country i; this shock can be interpreted as a structural risk premium/liquidity demand shock transmitting like a financial shock. ### Composite consumption indexes and home bias - Home composite consumption index: - C_{t} = (C_{Ht})^{1−γ} (C_{Ft})^{γ} (1−γ)^{1−γ} (γ)^{γ} - Foreign composite consumption index: - C^{*}_{t} = (C^{*}_{Ft})^{1−γ} (C^{*}_{Ht})^{γ} (1−γ)^{1−γ} (γ)^{γ} - Consumption of good produced in country j by country i: - C_{i j t} follows CES aggregator with elasticity of substitution ǫ > 1. - γ ∈ [0,1] is the weight on imported goods; γ < 1/2 reflects home bias. - Demand functions (for i = H,F (∗), z ∈ [0,1]): - C_{iH,z,t} = (P_{H,z,t} / P_{Ht})^{−ǫ} C_{iHt} - C_{iF,z,t} = (P_{F,z,t} / P_{Ft})^{−ǫ} C_{iFt} - Domestic price indexes: - P_{Ht} = (∫_{0}^{1} (P_{H,z,t})^{1−ǫ} dz)^{1/(1−ǫ)} - P_{Ft} = (∫_{0}^{1} (P_{F,z,t})^{1−ǫ} dz)^{1/(1−ǫ)} - CPI indexes and domestic price levels may differ across countries even under the law of one price because consumption baskets differ: - P_{t} = (P_{Ht})^{1−γ} (P_{Ft})^{γ} - P^{*}_{t} = (P^{*}_{Ht})^{γ} (P^{*}_{Ft})^{1−γ} ### Budget constraint, intermediation cost, and net foreign asset notation - Conditional on optimal allocation of expenditures: - Total Home consumption expenditures: P_{Ht} C_{Ht} + P_{Ft} C_{Ft} = P_{t} C_{t} - Period budget constraint (Home): - C_{t} + A_{Ht} / P_{t} + ψ_{B} ̄C_{t}^{2} (A_{Ht} / P_{t} − ̄a)^{2} = (1−τ^{w}_{Ht}) W_{Ht} / P_{t} L_{Ht} + (1−L_{Ht}) b_{Ht} + R_{t−1} A_{Ht−1} / P_{t} + D_{Ht} - Definitions and assumptions preserved exactly: - R_{t} is gross nominal interest rate of the nominal bond. - Unemployed benefits grow with intangible capital: b_{Ht} = b_{H} N^{C}_{Ht}. - τ^{w}_{Ht} is the tax wedge on labor income. - Intermediation cost: ψ_{B} ̄C_{t}^{2} (A_{Ht} / P_{t} − ̄a)^{2} with ̄a equilibrium net foreign assets as percentage of consumption and ̄C_{t} average consumption rate; cost paid to intermediaries and rebated lump-sum to households. - Notation: - a_{Ht} = A_{Ht} / P_{t} - ς_{Ht} = ̺_{Ht} λ_{Ht} where λ_{Ht} is Lagrange multiplier on budget constraint. ### First-order conditions and Euler equation - Euler equation (Home) preserved exactly: - 1 + ψ_{B} ( a_{Ht} / ̄C_{t} − ̄a ) = E_{t} β_{t,t+1} R_{t} / π_{t+1} + ς_{Ht} - Where β_{t,t+1} = β C_{Ht} / C_{Ht+1} and π_{t+1} = P_{t+1} / P_{t} - Interpretation preserved exactly: - Liquidity demand shock ς_{Ht} acts like an increase in risk: for given R_{t}, higher ς_{Ht} induces precautionary saving, reducing current consumption and lowering β_{t,t+1}. - Decline in the discount factor raises required return on capital, creating a spread with the riskless rate and reducing investment in physical capital and R&D. - Shock generates positive co-movements between investment and consumption typical of downturns. ### Key numeric and parameter references (preserved exactly) - Elasticity of substitution between retail goods: ǫ > 1 - γ ∈ [0,1]; γ < 1/2 indicates home bias - Intermediation cost form: ψ_{B} ̄C_{t}^{2} (A_{Ht} / P_{t} − ̄a)^{2} - Euler equation parameters and variables preserved exactly as above (β_{t,t+1}, R_{t}, π_{t+1}, ς_{Ht}) *Source: wpiea2019123 - 3.1 Households (PDF chapter/section).* ### 3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 ### wpiea2019123 - 3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 ### Chapter and section structure (exact section titles and page references) - 3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 - 3.2 Some definitions and identities . . . . . . . . . . . . . . . . . . . . . .. . 13 - 3.3 The product market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 - 3.3.1 Retail sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 - 3.3.2 Wholesale sector . . . . . . . . . . . . . . . . . . . . . . . . . . 14 - 3.3.3 Intangible good sector . . . . . . . . . . . . . . . . . . . . . . . 16 - 3.3.4 Innovation sector . . . . . . . . . . . . . . . . . . . . . . . . . . 16 - 3.4 The labor market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 - 3.4.1 Search and matching frictions . . . . . . . . . . . . . . . . . . . 17 - 3.4.2 Wage determination . . . . . . . . . . . . . . . . . . . . . . . . 18 - 3.5 Aggregate relationships . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19 - 3.6 Long run equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 ### Subsequent chapters and topics (exact headings and page references) - 4 Calibration21 - 5 Model properties23 - 5.1 Model fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 - 5.2 Model dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 - 6 Effects of market regulation in a currency union26 - 6.1 Regulation and steady state growth . . . . . . . . . . . . . . . . .. . 27 - 6.2 Regulation and business cycle dynamics . . . . . . . . . . . . . .. . 29 - 6.3 Regulation and risk premium shocks . . . . . . . . . . . . . . . .. . 30 *Source: wpiea2019123 - 3.1 Households (PDF chapter/section), canonical URL https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019123.pdf* ### 6.4 An application to the financial and sovereign debt crisis. . . . . . . . . 30 ### 6.4 An application to the financial and sovereign debt crisis. . . . . . . . . 30 ### Introduction: objectives and modelling approach - Objective: study the potential role of different product (PMR) and labor market (LMR) regulations in explaining growth and business cycle dynamics in the euro area. - Model: a two-country currency union DSGE model with endogenous growth and product and labor market frictions; TFP growth is endogenous and depends on the state and institutions of the economy. - Key modelling elements: - Labor market: search and matching frictions and Nash bargaining over sticky wages, capturing employment protection legislation, unemployment benefits, and the labor tax wedge. - Product market: imperfect competition in retail goods sector; product market regulation proxied by retail firm price mark-ups. - Endogenous growth: R&D-driven TFP following Romer (1990) and Kung and Schmidt (2015). - Shocks allowed: monetary policy shocks, technology shocks, and risk premium shocks. - Rationale: endogenous TFP links temporary shocks (e.g., risk premium spikes) to potential permanent reductions in the level of output and productivity, lifting the conventional dichotomy between growth and cycle. ### Empirical motivation and stylized facts (euro area evidence) - Data sources and construction: - AMECO database for TFP growth. - OECD database for R&D investment, employment protection legislation, product market regulation, and unemployment benefit generosity. - Long-run decline in GDP growth and TFP: - GDP growth declined from more than 5 percent in the 1960s to less than 1 percent in the last decade. - TFP growth declined from close to 4 percent in the early 60s to a meager 0.1 in the last decade. - Core empirical facts documented: - Fact 1: TFP was the main driver of growth decline and growth divergence among member countries. - Fact 2: Countries that invested more in business R&D have experienced higher TFP growth. - Example: since 1999, TFP (GDP) growth in Italy and Greece has been more than 0.5 (1) percent lower than the euro area simple average; both entered the euro area with the lowest level of business R&D in 1999. - Fact 3: Countries with more regulated labor and product markets have lower levels of investment in business R&D and lower average TFP growth. - Composite regulation index: sum of standardized product market regulation index, employment protection legislation index, and unemployment benefit generosity in deviation from the European average. - Fact 4: Countries with higher TFP growth experienced lower average inflation rates (holds for sub-periods 2000-2008 and 2008-2016 and for the whole sample). - Fact 5: Following a euro area wide risk premium shock, the TFP recovery is faster in less regulated economies. - Empirical approach: derive quarterly TFP series compatible with AMECO annual series; use euro area non-financial corporation bond spread over sovereigns as a proxy for a shock to firms’ investment incentives. - Local projection estimation (Jorda 2005) for panel of 11 euro area members, 1999q1–2016q4: - Estimation equation: y_{i,t+k} − y_{i,t} = α^k_i + β^k Z_t + γ^h X_{i,t} + ε^k_{i,t} for k = 1,...,16. - One standard deviation risk premium shock ≈ increase of about 35 basis points on impact. - Result: after the shock, TFP falls on impact, reaches about 0.5 percent below initial value four quarters after the shock, partial recovery over next four quarters, and only appears to fully recover after four years. - Smooth-transition local projections: allow β^k to differ across low/high regulation regimes via logistic transition F(R_{t−1}); evidence that initial TFP response may be stronger in less regulated markets, but more regulated markets recover more slowly or remain permanently below the prior trend. - Cross-country observations: - With the onset of the financial crisis (spike in risk premiums), euro area TFP slowed significantly and has not yet recovered. - Output and TFP appear permanently lower in Spain and especially Italy, while Germany and France return toward old trend paths. - Less regulated countries on average: higher R&D investment rates, stronger TFP and output growth, and lower inflation rates. - Heterogeneous recovery and divergence patterns are consistent with the model’s mechanisms linking shocks, institutions, and endogenous TFP. ### Mechanisms and implications from the model - Channels through which regulation affects outcomes: - Short-run: labor and product market institutions shape adjustment to shocks (e.g., size of TFP collapse and speed of recovery). - Long-run: PMR and LMR affect R&D incentives and accumulation of intangible capital, altering long-run TFP growth and output levels. - Divergence and spillovers: - Without strong technology spillovers, asymmetric reforms in one country raise domestic R&D, TFP growth, and lower inflation for the reformer, while the non-reforming member experiences lower long-term output growth and higher inflation—yielding long-run real income divergence within the union. - With strong positive technology spillovers, reform in one country benefits the foreign country as well, increasing TFP, consumption and output growth in both and reducing income divergence. - Policy coordination: - Asymmetric reforms can be beneficial for the union overall, but lead to long-run real income divergence; coordinated reforms are useful to avoid divergence. - Comparison with exogenous-growth DSGE: - Endogenous growth introduces three main differences: 1. R&D investment and intangible capital amplify responses to demand shocks and better match observed moments. 2. Temporary shocks can have sizable permanent effects on TFP, output and relative prices. 3. There is no guarantee of income convergence when technology diffusion is incomplete and growth depends on R&D investment; past shocks and policy responses affect long-run dynamics. ### Model scope, calibration and empirical fit - Model features: - Two countries (Home and Foreign) of equal size (normalized to 1). - Identical, infinitely lived households; full insurance against idiosyncratic risk within each country. - One traded asset: one-period nominal bond in the common currency. - Technology spillovers treated as exogenous. - Calibration and validation: - A deliberately simple calibration replicates behavior of TFP, output and real exchange rates in Italy and Germany around the Great Recession. - Model matches empirical facts on regulation, R&D investment, TFP growth and inflation for the euro area, suggesting that adverse shocks combined with unfavorable institutions and limited technological spillovers help explain poor outcomes in some Southern European countries. ### Key statistics and numeric values preserved from source - Euro introduction timeframe referenced: "almost 20 years ago". - GDP growth fall: "from more than 5 percent in the 1960s to less than 1 percent in the last decade." - TFP growth fall: "from close to 4 percent in the early 60s, to a meager 0.1 in the last decade." - Empirical sample and frequency: panel of 11 euro area members (euro area-12 excluding Luxembourg) for the period from 1999q1 to 2016q4. - Local projection horizon: k = 1,...,16 (quarters). - Risk premium shock magnitude: "one standard deviation ... corresponds to an increase of the risk premium by about 35 basis points on impact." - TFP response to shock: reaches "about 0.5 percent below its initial value" four quarters after the shock; only appears to fully recover after four years. - Sub-periods cited for inflation-TFP correlation: "2000-2008 and 2008-2016". - Reference to estimation methods and model variants: Jorda (2005) local projections; smooth transition/local projection with logistic function F(R_{t−1}). *Source: IMF Working Paper content unit “6.4 An application to the financial and sovereign debt crisis. . . . . . . . . 30” (from provided PDF excerpt).* ### 3.1 Households ### 3.1 Households ### Utility and preferences - Representative household in country i (i = H or F) is a large extended family with continuum of members on the unit interval; family members perfectly insure each other against consumption fluctuations due to employment status. - Household maximization problems: - Home: E0 ∑_{t=0}^{∞} β^{t} [ log C_{t} + ̺_{Ht} A_{Ht} / P_{t} ] - Foreign: E0 ∑_{t=0}^{∞} β^{t} [ log C^{*}_{t} + ̺_{Ft} A_{Ft} / P^{*}_{t} ] - Features: - Utility is log in consumption. - Bonds enter utility to capture a preference for the safe asset (Krishnamurty and Vissing-Jorgensen, 2012). - ̺_{it} captures a shock to liquidity demand in country i; this shock can be interpreted as a structural risk premium/liquidity demand shock transmitting like a financial shock. ### Composite consumption indexes and home bias - Home composite consumption index: - C_{t} = (C_{Ht})^{1−γ} (C_{Ft})^{γ} (1−γ)^{1−γ} (γ)^{γ} - Foreign composite consumption index: - C^{*}_{t} = (C^{*}_{Ft})^{1−γ} (C^{*}_{Ht})^{γ} (1−γ)^{1−γ} (γ)^{γ} - Consumption of good produced in country j by country i: - C_{i j t} follows CES aggregator with elasticity of substitution ǫ > 1. - γ ∈ [0,1] is the weight on imported goods; γ < 1/2 reflects home bias. - Demand functions (for i = H,F (∗), z ∈ [0,1]): - C_{iH,z,t} = (P_{H,z,t} / P_{Ht})^{−ǫ} C_{iHt} - C_{iF,z,t} = (P_{F,z,t} / P_{Ft})^{−ǫ} C_{iFt} - Domestic price indexes: - P_{Ht} = (∫_{0}^{1} (P_{H,z,t})^{1−ǫ} dz)^{1/(1−ǫ)} - P_{Ft} = (∫_{0}^{1} (P_{F,z,t})^{1−ǫ} dz)^{1/(1−ǫ)} - CPI indexes and domestic price levels may differ across countries even under the law of one price because consumption baskets differ: - P_{t} = (P_{Ht})^{1−γ} (P_{Ft})^{γ} - P^{*}_{t} = (P^{*}_{Ht})^{γ} (P^{*}_{Ft})^{1−γ} ### Budget constraint, intermediation cost, and net foreign asset notation - Conditional on optimal allocation of expenditures: - Total Home consumption expenditures: P_{Ht} C_{Ht} + P_{Ft} C_{Ft} = P_{t} C_{t} - Period budget constraint (Home): - C_{t} + A_{Ht} / P_{t} + ψ_{B} ̄C_{t}^{2} (A_{Ht} / P_{t} − ̄a)^{2} = (1−τ^{w}_{Ht}) W_{Ht} / P_{t} L_{Ht} + (1−L_{Ht}) b_{Ht} + R_{t−1} A_{Ht−1} / P_{t} + D_{Ht} - Definitions and assumptions: - R_{t} is gross nominal interest rate of the nominal bond. - Unemployed benefits grow with intangible capital: b_{Ht} = b_{H} N^{C}_{Ht}. - τ^{w}_{Ht} is the tax wedge on labor income. - Intermediation cost: ψ_{B} ̄C_{t}^{2} (A_{Ht} / P_{t} − ̄a)^{2} with ̄a equilibrium net foreign assets as percentage of consumption and ̄C_{t} average consumption rate; cost paid to intermediaries and rebated lump-sum to households. - Notation: - a_{Ht} = A_{Ht} / P_{t} - ς_{Ht} = ̺_{Ht} λ_{Ht} where λ_{Ht} is Lagrange multiplier on budget constraint. ### First-order conditions and Euler equation - Euler equation (Home): - 1 + ψ_{B} ( a_{Ht} / ̄C_{t} − ̄a ) = E_{t} β_{t,t+1} R_{t} / π_{t+1} + ς_{Ht} - Where β_{t,t+1} = β C_{Ht} / C_{Ht+1} and π_{t+1} = P_{t+1} / P_{t} - Interpretation: - Liquidity demand shock ς_{Ht} acts like an increase in risk: for given R_{t}, higher ς_{Ht} induces precautionary saving, reducing current consumption and lowering β_{t,t+1}. - Decline in the discount factor raises required return on capital, creating a spread with the riskless rate and reducing investment in physical capital and R&D. - Shock generates positive co-movements between investment and consumption typical of downturns. ### Key numeric and parameter references (as specified) - Elasticity of substitution between retail goods: ǫ > 1 - γ ∈ [0,1]; γ < 1/2 indicates home bias - Intermediation cost form: ψ_{B} ̄C_{t}^{2} (A_{Ht} / P_{t} − ̄a)^{2} - Euler equation parameters and variables preserved exactly as above (β_{t,t+1}, R_{t}, π_{t+1}, ς_{Ht}) *Source: wpiea2019123 - 3.1 Households* ### 3.6 Long run equilibrium ### 3.6 Long run equilibrium ### Long-run equilibrium: structure and implications - Balanced growth requires the parametric restriction: - 1−v v ξ 1−ξ = 1−α - Home production can be written as: - YHt = ΞHt ((ZHt LHt)1−α (KHt)α) N1−v v ξ1−ξ Ht - with ΞHt = [vξ / μHt]ξ1−ξ and μHt = 1/φHt - Under the restriction above, aggregate production is homogeneous of degree one in KHt and NHt and can be re-written: - YHt = TFPHt (LHt)1−α (KHt)α (equation 17) - TFPHt = ΞHt (ZHt NHt)1−α (equation 18) - Key determinants of observed TFP: - increases with exogenous forcing ZHt - increases with endogenous intangible capital NHt - inversely related to the retail sector mark-up μHt - Intangible capital accumulation: - ∆NH,t+1 ≡ NH,t+1 / NH,t = (1−δN) + θH,t SH,t / NH,t (equation 19) - Analogous relations for Foreign: - YFt = TFPFt (LFt)1−α (KFt)α - ∆NF,t+1 = (1−δN) + θF,t SF,t / NF,t - TFPFt = ΞFt (ZFt NFt)1−α with ΞFt = {ξv / μF t}ξ1−ξ - Consumption growth along the balanced growth path is proportional to growth of intangible stocks embodied in consumption baskets: - NC Ht = (NHt)1−γ (NFt)γ ; NC Ft = (NFt)1−γ (NHt)γ - Differences in trend growth produce different steady state inflation rates; the faster-growing country has lower inflation: - πH = πU (∆NF / ∆NH)0.5 ; πF = πU (∆NF / ∆NH)−0.5 - Secular trends in real exchange rate and terms of trade: - ∆Q = π∗ / π = ∆NC H / ∆NC F - ∆T = πF / πH = ∆NH / ∆NF - Summary implication: - Member countries with higher R&D investment enjoy higher average TFP growth, higher GDP growth, lower average inflation rates, and a secular real exchange rate depreciation. - This long run equilibrium is consistent with facts 1 to 4 documented in section 2. ### Calibration (baseline) - Model frequency and solution: - Quarterly frequency; solved by second-order perturbation using Dynare ver. 4.5.1 - Preferences: - β = 0.99 - Elasticity of substitution of retail goods ǫ = 11 - Home bias parameter γ = 0.25 - Labor markets: - Steady state unemployment rate itour i = 8percent - Job finding rate f i = 0.45 (monthly job finding rate of 0.18) - Job separation rate s i = 0.071 - Quarterly job filling rate q i = 0.9 - Elasticity of job matches with respect to vacancies = 0.5 - Workers’ bargaining power η i = 0.5 - Aggregate hiring costs = 0.44percent of steady state output - ̄m i = 0.636; bi = 0.024 (benefit replacement ratio of 0.523) - Wage and price adjustment costs: - Degree of price rigidities φp = 45 (Calvo parameter 0.63, mean price duration ~3 quarters) - Degree of wage rigidity φw = 16 - Production: - α = 0.33 - Quarterly capital depreciation rate δK = 0.02 (annual capital depreciation rate of 8percent) - Material share ξ = 0.5 - Inverse mark-up parameter in intangible good sector v = 0.6 - Investment adjustment cost ΘI = 0.282 - R&D sector: - Patent obsolescence rate δN = 0.0375 - Elasticity of new patents to R&D κ = 0.83 - Scale parameter χ chosen to match average annual growth rate gu = 1.6 - Technology spillovers σR = 0 (baseline) - Monetary policy: - Central bank reacts to union-wide inflation with elasticity ωπ = 1.5 - Interest rate persistence ωr = 0.85 - Response coefficient on output growth ω∆y = 0.25 - Standard deviation of monetary policy shock = 0.1percent - Trend inflation πU = 2(annualized) - Tax rates and costs: - τpHt = τpFt = 0.2 - τwHt = τwFt = 0.4 - Intermediation costs ψB = 0.001 - Shock processes: - Home and Foreign technology shocks are uncorrelated; persistence ρZi = 0.95; volatility σzi = 0.49percent - Liquidity demand shocks calibrated to ρ̺ i = 0.8 and σ̺ i = 0.1percent - Cross-correlation between Home and Foreign risk premium shocks set to match average cross-country GDP correlation = 0.65 → σ̺H,̺F = 0.35 - Benchmark NK model: - NK model is version with constant R&D investment intensity (exogenous trend growth); calibration identical to baseline growth model ### Model properties: fit and dynamics - Model fit (high-frequency cycles < 32 quarters, HP(1600) filtered): - Model matches relative volatility of TFP, employment, unemployment, and comes close on price inflation - Model underpredicts relative volatility of real wages - Model matches cross-correlation of most variables with output but underpredicts persistence of most series - Medium and long term components (band-pass filtered): - Medium term: periods between 32 and 100 quarters - Long term: periods between 32 and 200 quarters - Model matches medium and long term volatility of output, TFP, employment, and unemployment reasonably well - Model fails to match high medium and long term volatility of wage and price inflation observed in data, partly because model holds annual inflation objective fixed at 2 percent while data include high-inflation episodes in the 70s and 80s - Role of endogenous R&D: - Switching on endogenous growth increases volatility of output: - Business cycle frequency: from 0.84 to 1.16 - Medium term frequency: from 1.06 to 1.51 - Long term frequency: from 2.37 to 3.60 - Introduction of innovation sector reduces wage and price inflation volatility by more than 10 percent - Dynamics to an asymmetric Home risk premium shock (shock = increase of risk premium by 50 basis points, i.e. 2 percent if annualized): - Mechanism: - Higher demand for liquid assets → households increase savings and reduce consumption - Required return on capital increases → fall in home investment and home R&D - Due to nominal rigidities, investment and consumption drops lead to fall in domestic output - Transmission to Foreign via direct spillovers, terms of trade movements, and monetary policy - Direct spillovers reduce foreign consumption and investment when shocks partially spill over - Home goods price reductions and worse terms of trade exert deflationary pressure abroad as consumers shift to cheaper home goods - Central bank lowers interest rate, stimulating foreign economy, but first two effects dominate → foreign inflation and employment fall - Outcomes: - Positive, persistent inflation, employment, and R&D differentials between Home and Foreign - Endogenous productivity and R&D amplify negative effects of asymmetric risk premium shocks: - Employment and inflation differentials increase by almost 50 percent on impact relative to NK model - Pro-cyclicality of R&D: profitability falls → R&D falls → intangible capital stock declines → TFP and output growth decline → amplification of initial contraction - Divergence effects: - In NK model with exogenous growth, TFP drop is temporary and unwinds after ~3 years - With endogenous growth, TFP drop is larger on impact and persistent; output collapse is 1.5percent larger and negative shock permanently shifts down the home economy’s trend - Temporary shocks can have permanent effects on relative output and real exchange rates in endogenous growth model - Implication: No reason to expect real income convergence among member countries; histories of shocks and policy responses matter for long-run dynamics - The model reproduces strong GDP contraction and trend GDP shift experienced by many European countries after the Great Recession and euro area debt crisis ### Effects of market regulation in a currency union (policy experiments) - Policy questions addressed: - Effects of deregulation on long-term growth prospects of currency union members - Impact of deregulation on volatility of member economies - Impact of regulation on adjustment to large shocks - Extent to which shocks and market regulation explain divergence before and after the financial and sovereign debt crisis - Product market deregulation experiment: - Reduce retail sector tax rate from τpit = 0.2 to τpit = 0.185 - This translates into a reduction of net retail sector mark-up of 7percent, from 0.375 to 0.35 - Labor market experiments: - First: permanent reduction of unemployment benefits by 20percent → lowers equilibrium benefits over wage ratio from 0.523 to 0.431 - Second: reduction of tax wedge τwit from 40 to 30percent - Third: change labor market rigidity by increasing match efficiency ̄m i and separation rates such that steady state job-finding rate = 0.7 and unemployment rate = 5percent - Implies separation rate increases from s i = 0.07 to 0.12 - This captures, in reduced form, effects of lower hiring and firing costs - Implementation note: - Exercises fix deep parameters from baseline calibration and allow endogenous variables to adjust to policy parameter changes *Source: wpiea2019123 - 3.6 Long run equilibrium (PDF chapter/section).* ### 6.1 Regulation and steady state growth ### 6.1 Regulation and steady state growth ### Effects of deregulation on trend growth and union equilibrium - Two cases considered: symmetric reforms (deregulation in both countries) and asymmetric reforms (deregulation only in the Home economy). - Synchronized labor or product market reforms are strongly beneficial for member countries and for the union as a whole: all four reforms improve long run growth and lower the unemployment rate. - Mechanisms by reform type: - Product market reform reducing retailer mark-up (τp i in the table): - reduces monopolistic distortions and the relative price of retail goods; - improves efficiency of the retail sector and increases demand for wholesale and intermediate goods; - higher profit opportunities stimulate investment in R&D, increasing the growth rate of new patents (equation 19) and leading to higher TFP and output growth (equations 17 and 18). - Reduction in the tax wedge (τw Ht) or in unemployment benefits (bH): - lowers equilibrium wage via two effects: reduces after-tax wage workers accept and increases effective bargaining power ωt (equation 15), with the first effect dominating so equilibrium wage falls (reference to equation 16); - lower wage raises labor demand and wholesale goods production, increasing demand for patented goods and R&D investment, raising intangible capital accumulation, TFP and output growth. - More flexible labor market (LMR i): - improves matching efficiency, lowers unemployment, reduces unit labor costs, raises production and R&D profitability. - Model patterns consistent with empirical facts: higher market regulation associated with lower R&D spending and lower TFP growth (Facts 2 and 3, Figure 3). ### Asymmetric reforms and international spillovers - When only Home reforms, Home experiences qualitatively similar but larger improvements in unemployment, production and growth because Home competitiveness improves at Foreign firms’ expense, tilting relative demand toward home goods (absent in symmetric case). - Impact on Foreign depends crucially on international technology spillover parameter σR: - σR = 0 (no technology spillovers): lower international demand reduces foreign production and R&D, lowering steady state productivity and output growth; unemployment weakly affected and consumption growth almost constant because of improved terms of trade and much larger Home production growth. - σR < 0 (negative spillovers): asymmetric reforms can be beggar-thy-neighbor. Starting from σR < −0.05, Home reforms reduce Foreign output and consumption growth; Home technological headway reduces Foreign return to R&D and patent growth, further lowering Foreign TFP and output; Foreign terms of trade improvement no longer offsets lower production and consumption declines. - σR > 0 (positive spillovers): asymmetric reforms benefit non-reforming country because higher Home R&D intensity raises productivity of Foreign R&D; direct productivity effects outweigh competition effects; long run inflation, output and consumption growth differentials strongly decreasing in σR. - Policy implication: in absence of coordination, real income divergence among union members with different market regulation can still be reduced through policies fostering integration and enabling technology spillovers. --- ### 6.2 Regulation and business cycle dynamics ### Short-run quantitative effects (business cycle frequency) - Table 4 reports simulated standard deviations of hp-filtered macro time series for different product and labor market constellations; focus on volatilities of inflation and employment (inflation volatility is annualized). - Product market deregulation: - reduces employment volatility; - slightly increases inflation volatility; - slope of Phillips curve proportional to (ǫ−1)(1−τp Ht)ψ̄π 2 H is decreasing in τp Ht, so lower regulation increases elasticity of inflation to marginal costs (φ̂ Ht) and increases the volatility trade-off (ratio between inflation volatility and employment volatility). - A higher trade-off implies a lower employment cost from stabilizing inflation; reform could be dynamically efficient. - Reductions in tax wedge or unemployment benefits: - increase inflation volatility and reduce employment volatility; - increase flexibility of real wages and allow firms to absorb shocks via wage channel, smoothing hiring and employment responses. - Reductions in hiring and firing costs (more flexible labor market): - increase employment volatility and reduce inflation responsiveness; - volatility trade-off is strongly reduced; in flexible labor markets large average job finding and separation rates make changes in employment produce small variations in labor market tightness (θ̂ Ht expression), flattening Phillips curve and making reform dynamically inefficient. - Synthesis: - Product market deregulation, lower labor tax wedges and lower unemployment benefits are steady-state and “dynamically” beneficial. - Lower employment protection regulation is steady-state beneficial (increases long run growth prospects) but flattens the Phillips curve and makes macro stabilization more costly. --- ### 6.3 Regulation and risk premium shocks ### TFP responses to large financial shocks under different regulations - Figure 9 (referenced) reports Home TFP responses to large risk premium shocks in baseline and in economies with low product market or low labor market rigidities. - Following an increase in the risk premium: - recovery of TFP is much faster in economies with flexible labor and product markets. - Following a risk premium reduction: - more flexible economies benefit more and faster from lower rates than sclerotic economies. - Explanation: combination of institutional effects on short-run dynamics (smaller TFP collapse in low LMR countries) and long-run dynamics (higher trend growth in low regulation countries). - Model consistent with empirical Fact 5: after a union-wide risk premium shock the TFP recovery is faster in less regulated economies. --- ### 6.4 Application to the financial and sovereign debt crisis (Germany vs Italy) ### Calibration and shock design - Observations motivating exercise: - 2008 spike in credit spreads symmetric across countries; 2011 spreads diverged with Italy diverging from Germany. - Excluding 2008 and 2011, average growth rate of Germany slightly higher than Italy, consistent with lower PMR in Germany. - Two-country differences assumed: 1. Degree of PMR: calibrated τp i to match average quarterly GDP per capita growth 1999q1-2015q4 excluding shock years (2008 and 2011): - gDE = 1.0034 - gIT = 1.0008 - implied policy parameters: τp DE = 0.1943 and τp IT = 0.2057 - corresponding gross mark-ups: μDE = 1.365 and μIT = 1.385 2. Credit spread shocks modeled to match patterns observed 2008-2011: - increase in annualized yield by 280 basis points in 2008 and 360 basis points in 2011; - cross-correlation of shocks in 2008: σ̺ IT,̺ DE = 0.9; - cross-correlation in 2011: σ̺ IT,̺ DE = 0.30 (below baseline calibration). ### Model fit and results - Figure 10 (referenced) compares data 2006-2016 for Germany and Italy to simulated series for credit risk spread, TFP and output growth, and real exchange rate (TFP, output and real exchange rate normalized to 1 in 2008). - Findings: - Model replicates qualitatively the behavior of TFP, production and real exchange rate dynamics for Germany and Italy from 2006 to 2016. - Combination of mark-up differences and shocks leads simulated Italian TFP and output to remain effectively unchanged from 2006 to 2016 while German output is about 10 percent higher after ten years. - Divergence after symmetric 2008 shock limited in data and model; divergence following asymmetric 2011 shock large, about 10 percent by 2016 in both data and simulation. - Endogenous bilateral real exchange rate in model closely traces observed pattern up to 2012; after 2012 model fails to capture real exchange rate dynamics accurately, likely due to absence of other shocks and of a financial sector in the model. - Interpretation: to explain diverging performance of currency union members, explicit consideration of shocks and institutions is necessary. --- ### Conclusions and policy implications - Model structure and main implications: - Two-country currency union DSGE model with endogenous growth where labor and product market regulation affect R&D investment and intangible capital accumulation, determining long run TFP and output growth. - Model reproduces empirical observations that more regulated countries have lower business R&D, lower average TFP growth and higher average inflation rates. - Key findings enabled by endogenous growth channel: 1. Endogenous growth amplifies business cycle fluctuations and output/inflation differentials from asymmetric shocks or asymmetric regulation. 2. Large shocks can have permanent effects on output path; history of shocks matters for long-run trend. 3. When reforms are asymmetric, long-term effects depend on technology spillovers: - absent spillovers, asymmetric reforms mainly benefit reformer and can harm non-reformers, calling for coordination; - with meaningful positive spillovers, asymmetric reforms can be beneficial for all members. - Policy message: in a currency union with endogenous productivity and diverse market structures, there is no guarantee of real income convergence without coordination or policies that foster integration and technology spillovers. - Suggested future research: explore union-wide policies that can address divergence stemming from shocks and regulatory differences and differences relative to standard New Keynesian models with exogenous growth. *Source: IMF Working Paper section 6.1–6.4 (wpiea2019123).* ### References ### wpiea2019123 - References ### References list - Comprehensive bibliography of works cited in the study, including journal articles, working papers, IMF publications, and manuscripts. (Full citation list preserved in source.) ### Annex 1: Derivation of quarterly TFP series - Purpose - No single source for quarterly series of TFP growth in the euro area is available; the annex describes the method used to derive a quarterly TFP series for the sample of euro area members. - Methodology (Levy and Chen (1994) approach) - Quarterly investment denoted I_{j,i} for quarter j in year i. - Net real capital stock recursive identity: - K_{j,i} = (1−δ_i) K_{j−1,i} + I_{j,i} - Iterated to end-of-year form: - K_{4,i} = (1−δ_i)^4 K_{4,i−1} + sum_{k=1}^4 (1−δ_i)^{4−k} I_{k,i} - The depreciation rate δ_i is obtained by solving the non-linear equation for δ_i using Newton’s iteration formula. - Implementation notes and empirical properties - The deprecation rate in a given year is assumed to be constant. - The discount factor (annual depreciation) for the 11 euro area countries in the sample is very stable over time, showing only some variation for Greece, Belgium and Ireland. - Values are clustered around 1.5% for most countries and remain within the interval of 1-2% across countries. - Convergence in the sample was achieved at least after 3 iterations. - Post-processing to obtain quarterly TFP - After estimating δ_i, the recursive capital accumulation equation is used to derive the quarterly capital stock. - Quarterly TFP series derived using quarterly real GDP, employment, and wage share data under the Cobb-Douglas production function assumption. - The quarterly series of TFP is derived in a way that is compatible with the annual series provided by the European Commission’s AMECO database. - Caveats and potential extensions (as stated in source) - The method could be modified to exclude residential investment to better capture the channel from productivity enhancing investment to TFP. - Using total hours worked instead of employment would be preferable, but is left for future extensions. ### Key tables — selected quantitative results (preserved values) - Table 1: Business cycle component of macroeconomic moments (HP-filtered) - Nominal wages: Data σ(x)/σ(y) = 1.71; Model Baseline = 1.73; NK Model = 1.91 - ρ(x,y): Data = 0.50; Model Baseline = 0.88; NK Model = 0.80 - ρ(x_t,x_{t−1}): Data = 0.16; Model Baseline = 0.17; NK Model = 0.25 - Prices: Data σ(x)/σ(y) = 1.07; Model Baseline = 0.89; NK Model = 1.03 - ρ(x,y): Data = 0.31; Model Baseline = 0.94; NK Model = 0.89 - ρ(x_t,x_{t−1}): Data = 0.22; Model Baseline = 0.35; NK Model = 0.46 - Real wages: Data σ(x)/σ(y) = 0.84; Model Baseline = 0.32; NK Model = 0.38 - ρ(x,y): Data = 0.67; Model Baseline = 0.87; NK Model = 0.95 - ρ(x_t,x_{t−1}): Data = 0.92; Model Baseline = 0.72; NK Model = 0.75 - Unemployment: Data σ(x)/σ(y) = 5.46; Model Baseline = 5.97; NK Model = 6.40 - ρ(x,y): Data = -0.85; Model Baseline = -0.97; NK Model = -0.97 - ρ(x_t,x_{t−1}): Data = 0.91; Model Baseline = 0.62; NK Model = 0.69 - Employment: Data σ(x)/σ(y) = 0.43; Model Baseline = 0.52; NK Model = 0.56 - ρ(x,y): Data = 0.80; Model Baseline = 0.97; NK Model = 0.97 - ρ(x_t,x_{t−1}): Data = 0.95; Model Baseline = 0.62; NK Model = 0.70 - Investment: Data σ(x)/σ(y) = 2.36; Model Baseline = 2.31; NK Model = 3.77 - ρ(x,y): Data = 0.91; Model Baseline = 0.84; NK Model = 0.92 - ρ(x_t,x_{t−1}): Data = 0.89; Model Baseline = 0.80; NK Model = 0.81 - TFP: Data σ(x)/σ(y) = 0.74; Model Baseline = 0.68; NK Model = 0.67 - ρ(x,y): Data = 0.93; Model Baseline = 0.99; NK Model = 0.98 - ρ(x_t,x_{t−1}): Data = 0.83; Model Baseline = 0.37; NK Model = 0.53 - Output: normalized to 1.00 across Data, Model Baseline, NK Model - σ(y): Data = 1.16; Model = 1.16; NK Model = 0.84 - Table 2: Medium and low frequency component of macroeconomic moments - Medium term component (frequency 32-100) - Nominal wages σ(x)/σ(y): euro area Data = 7.43; Baseline Model = 3.85; NK Model = 4.22 - ρ(x,y): euro area Data = 0.27; Baseline = 0.60; NK = 0.64 - Prices σ(x)/σ(y): euro area Data = 6.02; Baseline = 2.63; NK Model = 3.24 - ρ(x,y): euro area Data = -0.41; Baseline = 0.41; NK = 0.37 - TFP σ(x)/σ(y): euro area Data = 0.51; Baseline = 0.70; NK Model = 0.67 - ρ(x,y): euro area Data = 0.80; Baseline = 0.99; NK = 0.95 - Output normalized to 1.00 across columns; σ(y): euro area Data = 1.53; Baseline = 1.51; NK = 1.06 - Long term component (frequency 32-200) - Nominal wages σ(x)/σ(y): euro area Data = 9.15; Baseline = 3.17; NK Model = 3.62 - ρ(x,y): euro area Data = -0.65; Baseline = 0.60; NK = 0.65 - Prices σ(x)/σ(y): euro area Data = 10.29; Baseline = 2.07; NK Model = 2.70 - ρ(x,y): euro area Data = -0.85; Baseline = 0.41; NK = 0.37 - TFP σ(x)/σ(y): euro area Data = 0.55; Baseline = 0.72; NK Model = 0.69 - ρ(x,y): euro area Data = 0.90; Baseline = 0.99; NK = 0.96 - Output normalized to 1.00 across columns; σ(y): euro area Data = 3.05; Baseline = 3.60; NK = 2.37 - Table 3: Steady state growth rate for different levels of regulation (selected preserved entries) - Baseline calibration: ∆y_U = 1.60; ∆c_U = 1.60; u_U = 8.00; π_U = 2.00 - Symmetric Reforms (examples): for τ_p^i τ_w^i b^i LMR^i columns: ∆y_U = 2.34 2.02 2.12 1.93; ∆c_U = 2.34 2.02 2.12 1.93; u_U = 6.62 4.24 3.30 5.00; π_U = 2.00 2.00 2.00 2.00 - Asymmetric Reforms (Home and Foreign examples): Home ∆y_H = 2.68 2.19 2.34 2.06; Home π_H = 1.28 1.62 1.53 1.71; Foreign ∆y_F = 1.25 1.43 1.39 1.47; Foreign π_F = 2.72 2.38 2.48 2.29 - Rel. prices: ∆ToT baseline = 0.00; Asymmetric case ∆ToT = 1.44 0.76 0.95 0.58; ∆RER asymmetric = 0.72 0.38 0.48 0.30 - Table 4: Second moments for different levels of regulation (HP-filtered) - Union-level examples: - σ(π_U): Data = 1.25; Calibration = 1.03; Symmetric reforms entries = 1.06 1.07 1.08 0.95; Asymmetric reforms entries = 1.05 1.05 1.06 0.99 - σ(L_U): Data = 0.50; Calibration = 0.60; Symmetric reforms entries = 0.57 0.46 0.43 0.90; Asymmetric reforms entries = 0.59 0.53 0.51 0.75 - σ(π_U)/σ(L_U): Data = 2.49; Calibration = 1.72; Symmetric reforms entries = 1.86 2.33 2.51 1.06; Asymmetric = 1.78 1.98 2.08 1.32 - Home and Foreign panels and differentials preserved in table (see source for full matrix of values). ### Figures and empirical dynamics (high-level preserved findings and numeric references) - Figure 1: Credit spreads, TFP and GDP dynamics in the euro area - Time series plots for 2000–2015 of Credit Spreads EA, TFP EA, GDP EA, and country breakdowns (DE, FR, IT, SP). - Figure 2: Euro area: TFP contribution to growth since 1965 - Figure 3: Long run relationships between regulation, TFP and growth - Scatter and fitted plots showing relationships between Average TFP growth (1999–2015, 2015–1999, etc.), Business R&D (1999 percent of GDP), Composite regulation index (PMR−EPL−BEN), and GDP growth deviations. - Figure 4: Short and medium term dynamics of TFP - Impulse response to one percent common euro area NFC–sovereign rate spread (Gilchrist and Mojon 2017), using local projection methods for a panel of 11 euro area members from 1999Q1−2016Q4. - Separate IRFs reported for High regulation and Low regulation groups (Regulation measured by composite (PMR−EPL−BEN)). - Figures 5–7: Responses to Home risk premium shock (+50 b.p.) and spillovers - Dynamic responses over 12–15 quarters for Home and Foreign inflation, employment, R&D, output, TFP, relative output, and RER under different model variants (Growth Model, Benchmark NK, Balanced Growth Path). - Figures 8–10: Asymmetric reforms, institutions, and heterogeneous risk premium shocks - Figure 8 illustrates how steady state growth rates of output and consumption and the real exchange rate change with different values of the technology spillover parameter σ_R. - Figure 9 reports TFP_H responses to positive and negative risk premium shocks under Baseline, Low PMR, and Low LMR scenarios. - Figure 10 compares data and model for heterogeneous risk premium shocks and real income around 2008/11 for selected countries (DE, IT). _Italic: Source — wpiea2019123 - References (PDF) _ --- _Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019123.pdf_