## 2.1 Demographic structure

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---

### Overview and context
- Two simultaneous long-term trends: climate change (rising temperatures, more frequent/severe natural disasters) and demographic change (slowdown in workers’ population growth and substantial increase in longevity).
- Global population projections used as context: 8 billion in 2022, 9.7 billion in 2050, and 10.4 billion in 2100.
- Aging concentrated in advanced economies; many developing economies, particularly in Sub-Saharan Africa, not projected to face aging until later this century.
- Research question: What are the macroeconomic implications of climate change in an aging world?
- Approach: a New Keynesian DSGE model with heterogeneous age structure (workers and retirees), calibrated to United Nations “more developed regions” demographic estimates and projections.

### Key model features related to demographics
- Two household types: workers and retirees; workers supply labor, retirees do not.
- Worker survival/retirement and population dynamics:
  - Workers face probability ωt to remain workers and probability 1−ωt to retire.
  - Workforce grows at rate nw t with labor force evolution: Nw t+1 = (1 + nw t) Nw t.
  - Retirees stay alive with probability γt; death probability (1−γt).
  - Retiree population evolution: Nr t+1 = (1−ωt) Nw t + γt Nr t.
  - Old-age dependency ratio ψt = Nr t / Nw t evolves according to: ψt+1 = (1 + nr t)= 1−ωt ψt + γt.
- Demographic shocks and trends enter via time-varying ωt, γt, and nw t.

### Preferences, life-cycle and saving behavior
- Epstein and Zin (1989) preferences: separate risk aversion and intertemporal elasticity of substitution and early resolution of risk.
- Workers face income risk and retirement risk; model captures precautionary saving for retirement.
- Wealth and consumption differences:
  - Workers: labor income, save for retirement.
  - Retirees: consume from savings and receive benefits ej t.
- Marginal propensity to consume:
  - Retirees’ marginal propensity to consume (&tπt in source notation) is higher than workers’ (&>1 implies Ω>1).
  - Worker marginal propensity to consume πt given by equation (7) (structural form preserved).

### Decision problems (representative agents)
- Representative retiree:
  - Objective: V rj t = [ (crj t)ρ + β γt [V rj t+1]ρ ]1/ρ.
  - Budget constraint: crj t + a rj t = 1 + r t−1 γt−1 a rj t−1 + ej t.
  - Euler equation (retirees): crj t+1 = β(1 + r t) crj t.
- Representative worker:
  - Objective: V wj t = [ [(cwj t)v1 (1−lwj t)v2]ρ + β [ωt V wj t+1 + (1−ωt) V rj t+1]ρ ]1/ρ.
  - Budget constraint: cwj t + a wj t = (1 + r t−1) a wj t−1 + wt lwj t + fj t − τj t.
  - Consumption-Euler equation (reflecting retirement transition):
    - ωt cwj t+1 + (1−ωt)(&t+1)σ/(1−σ) c rj t+1 = [ β(1 + r t) Ωt+1 (wt/wt+1) v2/ρ ]σ cwj t, with Ωt+1 = ωt + (1−ωt) &1/(1−σ) t+1.
  - First-order condition for leisure: 1−lwj t = v2/v1 cwj t / wt.
  - Effective discounting: workers discount future income at (1 + r t) Ωt+1 > (1 + r t).

### Aggregation and policy relevance
- PAYG pensions ej t financed by lump-sum taxes τt on workers; overlapping generations implies fiscal policy non-neutrality.
- Private non-human wealth at = pk t kt + bt.
- Demographic structure affects aggregate saving, investment, equilibrium real interest rate, inflation dynamics, and fiscal sustainability through retirement flows and life expectancy.

---

### 3. Calibration and Demographic trends

### Demographic calibration and inputs
- United Nations projections for "more developed regions" used as deterministic inputs to calibrate nw t and γt.
- Projections (Figure 1 observations):
  - Working-age (15-64) population growth rate: 0.5% in 2000; turned negative in 2010 and remains negative; expected to remain negative until the end of the century.
  - Life expectancy: around 75 years in 2000; expected to be about 90 years in 2100.

### Calibrated parameter values (from Table 1)
- Intertemporal elasticity of substitution σ = 1/3
- Discount factor β = 0.99
- Cobb-Douglas share of labor α = 2/3
- Depreciation rate of capital δ = 0.05
- Growth rate of technological progress x = 0.01
- Elasticity of demand θ = 10
- Preference parameter: consumption v1 = 0.64
- Preference parameter: leisure v2 = 0.358
- Debt-to-output-ratio b* = 0.7
- Government spending share g/y = 0.18
- Replacement rate μ = e_j/w = 0.47
- Direct adjustment parameter in debt rule γ1 = 0.04
- Smoothing parameter in debt rule γ2 = 0.3
- Inertial parameter in the Taylor-rule ρ_i = 0.7
- Inflation coefficient in the Taylor-rule γ_π = 1.5
- Calvo survival probability of contracts ζ = 0.2
- Elasticity of investment function η = 0.25

Notes on calibration choices:
- Steady-state growth rate of technological progress set to 1% (x = 0.01).
- Debt-to-GDP ratio calibrated at 70% (b* = 0.7).
- Government spending share g/y = 0.18.
- Annual depreciation rate δ = 0.05.
- Replacement rate 0.47 implies share of total retirement benefits in output e/y of 0.11.
- Fiscal feedback rule: γ1 = 0.04 and γ2 = 0.3.
- Monetary policy rule: ρ_i = 0.7 and γ_π = 1.5.
- ζ = 0.2 implies average duration of prices of 1.25 years.

### Implied steady-state/endogenous variables (from Table 4)
- Real interest rate r = 0.039
- Share of consumption in output c/y = 0.60
- Share of investment in output i_k/y = 0.22
- Share of taxes in output τ/y = 0.31
- Share of total benefits in output e/y = 0.11
- Capital-output ratio k/y = 3.50
- Distribution of wealth λ = 0.23
- Participation rate of workers l_w = l_w/N_w = 0.70
- Consumption share of workers c_w/y = 0.47
- Consumption share of retirees ψ c_r/y = c/y − c_w/y = 0.13
- Propensity to consume out of wealth (workers) π = 0.05
- Propensity to consume out of wealth (retirees) &π = 0.09
- Relative discount term Ω = 1.05

Key implied observations:
- Steady-state real interest rate is 3.9% (r = 0.039).
- Share of taxes in output is 0.31.
- Marginal propensity to consume out of wealth: retirees 0.09 vs workers 0.05.
- Consumption share of output is 60%; investment share is 22%.

### Macroeconomic effects of demographic changes (flexible vs sticky prices)
- Simulation setup:
  - Demographic projections deterministic until 2100; reported simulation horizon is 40 years (until 2060).
  - Two price-setting assumptions compared: flexible prices (interest rate = equilibrium r*_t, output = natural y*_t) and sticky prices.
- Main dynamic responses:
  - Demographic changes produce small but persistent effects.
  - Aggregate consumption share rises; intertemporal substitution toward future consumption occurs; workers consume less; retirees consume more.
  - Higher consumption leads to lower investment and lower capital stock; rental rate of capital is higher.
  - Equilibrium interest rate r*_t declines slightly and persistently, peaking in decline around period 15 with maximum decline around 0.1%.
  - Natural output y*_t shows a slight but persistent increase.
  - Falling population growth lowers labor supply; real wages initially increase, then fall mirroring reduced investment.
  - Debt-to-GDP does not change significantly in baseline.
- Sticky prices vs flexible prices:
  - Sticky prices: inflation is higher and real interest rate is lower than in flexible case.
  - Fall in real interest rate under sticky prices is almost twice that under flexible prices.
  - With sticky prices: workers' consumption share is lower, total consumption is lower, investment share is higher, capital stock is higher, rental rate of capital is lower, and output increases by about 1%.
  - Policy implication: to stabilize inflation, central banks must respond more aggressively to inflation under sticky prices.

### Contribution of life expectancy vs working-age population growth
- Life expectancy changes largely drive consumption and real interest rate dynamics.
- Anticipation of higher life expectancy leads workers to increase savings, reducing workers' consumption and increasing retirees' consumption share.
- Increased savings lower real interest rates and reduce investment share; muted capital stock increase raises rental rate of capital.
- Fall in workers' population growth lowers labor supply; increased life expectancy induces workers to work more, increasing labor supply and lowering real wages.

### Macroeconomic effects of disaster shocks
- Disaster shock setup:
  - Persistent shock with ρ_d = 0.99.
  - Size calibrated so the model yields about a 1% fall in output at the end of the 40-year simulation.
- Responses to a persistent disaster shock:
  - Capital stock: fall around 1% initially; persistent fall culminating in maximum decline around 10% of steady-state toward end of simulation period.
  - Output: persistent fall around 1% throughout simulation.
  - Consumption: workers' consumption falls around 1% on impact; retirees' consumption does not change significantly; aggregate consumption falls around 1%.
  - Investment: investment share is about 1% higher as share of output shifts toward investment.
  - Factor prices: rental rate of capital is higher; real wages fall more.
  - Labor supply: workers increase labor supply persistently.
  - Inflation: increases persistently after the disaster shock; inflation around 1% higher at end of simulation.
  - Real interest rate: higher real interest rate resulting from higher inflation and the Taylor-rule nominal response (γ_π > 1); destruction of capital also requires higher savings and investment, pushing real rates up.
  - Fiscal implications: debt-to-GDP ratio persistently increases; fiscal rule in Equation (22) is insufficient to stabilize debt-to-GDP. Increasing γ1 to 1.4 stabilizes debt-to-GDP but at the cost of lower output (unreported experiment).

### Isolating demographic contribution in disaster responses
- Comparison: model with demographic changes vs model with demographic variables fixed at steady-state.
- Key differences:
  - Consumption falls more when demographic changes are not accounted for.
  - With demographic changes, retirees' consumption increases and mitigates the consumption decline from the disaster; workers' consumption falls but retirees' increase offsets much of the decline.
  - Smaller fall in consumption implies smaller fall in output and higher inflation relative to the model without demographic changes.
  - Real interest rate: with demographic changes, higher workers' savings lead to lower real interest rates.
- Conclusion: demographic changes are major determinants of key macroeconomic variables (e.g., equilibrium interest rate) and must be accounted for when considering persistent shocks like climate change.

### Macroeconomic effects of uncertainty about disaster magnitude
- Uncertainty shock specification:
  - d_t = ρ_d d_{t-1} + σ_{d,t} &d,t (24)
  - σ_{d,t} = (1 − ρ_{σd}) σ_d + ρ_{σd} σ_{d,t-1} + σ_{σd} &σ_{d,t} (25)
  - &σ_{d,t} is i.i.d. standard normal; ρ_{σd} measures persistence of volatility.
- Effects:
  - Uncertainty amplifies contractionary effects: larger fall in capital stock and output relative to no-uncertainty case.
  - Output falls due to precautionary increases in household savings (demand channel) and lower capital stock reducing production capacity (supply channel).
  - Inflation rises despite lower output: price stickiness leads firms to increase price markups as precaution, generating an inflationary effect that outweighs demand-driven deflationary pressure.
  - Larger uncertainty magnitudes exacerbate these effects.
  - Policy implication: cost of climate change can rapidly increase with growing uncertainty.

### Comparison with developing countries
- Demographic shocks for developing countries are larger (aging process kicks in during simulation); other parameters same as baseline.
- Responses:
  - Aging increases consumption and crowds out investment, reducing the investment share.
  - Because demographic shocks are larger in developing countries, consumption increases more and the crowding-out effect on investment is larger than in developed countries.
  - Overall dynamics mirror developed-country results but with amplified magnitudes on consumption and investment effects.

---

### 5. Climate Change as a Negative Productivity Shock

### Shock specification and calibration
- Production: y_t = z_t (l_t)^α (k_{t−1})^{1−α}.
- TFP process: z_t = ρ_z z_{t−1} − σ_{zt}, with ρ_z = 0.99.
- Shock size chosen to generate a 1% fall in output.

### Simulated responses and key mechanisms
- Aggregate responses to the persistent negative TFP shock producing a 1% output decline:
  - Output: fall on impact, with recovery toward the end of the simulation period.
  - Investment: lower, leading to a fall in the capital stock.
  - Consumption: does not change much.
  - Labour supply of workers: increases.
  - Real wage: lower.
  - Real rental rate, real interest rate, and inflation: effects appear small.
  - Debt-output ratio and Tobin’s q: modest dynamics shown in simulations.
- Mechanism for higher labour supply and lower real wages:
  - Lower productivity reduces marginal product of labour → lower real wages.
  - Persistent TFP decreases and lower wages reduce private wealth → lower consumption.
  - Negative wealth effect induces workers to supply more labor to offset lower consumption.

### Comparison with disaster (capital-destruction) shock
- Both shocks produce similar fall in output, but dynamics differ:
  - Productivity shock is less damaging than disaster shock because increased labour supply and lower real wages partly offset productivity loss.
  - Disaster shocks reduce capital directly, raise cost of capital, raise inflation permanently (cost-push), and have stronger effects on workers’ consumption and capital accumulation.
  - Uncertainty from disaster shocks increases firms’ mark-ups (with sticky prices), amplifying output contraction and inflation dynamics via higher precautionary savings and lower consumption.

### Implications for public finances and policy-relevant aggregates
- Climate change (through disasters and productivity channels) tends to raise the deficit and the debt-to-GDP ratio, requiring fiscal tightening to realign debt with targets.
- Uncertainty-induced higher mark-ups (sticky prices) increase inflationary pressures and contribute to output contraction.
- Long-run consequences: persistent reductions in output and increases in inflation; indirect adverse effects via increased uncertainty.

### Policy recommendations and priorities
- Contain the impact of climate change through mitigation and adaptation:
  - Global mitigation policies remain critical to limit temperature rises and macroeconomic costs.
  - Adaptation policies needed to enhance resilience to near-term locked-in greenhouse gas effects.
- Monetary policy:
  - Central banks need greater attention to climate change, especially given uncertainty-induced mark-ups and cost-push inflation from natural disasters.
  - Monitor distributional effects and implications for equilibrium interest rates and potential output.
- Fiscal policy:
  - Rising debt-to-GDP ratios require tightening fiscal policy via higher taxes or lower expenditure to respect debt rules.
- Social protection:
  - Reconsider long-term design of social safety nets, since assumed labor-supply adjustments by workers may not always be feasible and retirees could face inadequate savings.

*Source: wpiea2022258-print-pdf (section 2.1, 3, and 5) — https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022258-print-pdf.pdf*

### 2.1  Demographic structure . . . . . . . . . . . . . . . . . . . . . . . . . .   8

### 2.1  Demographic structure

### Overview and context
- Two simultaneous long-term trends: climate change (rising temperatures, more frequent/severe natural disasters) and demographic change (slowdown in workers’ population growth and substantial increase in longevity).
- Global population projections cited: 8 billion in 2022, 9.7 billion in 2050, and 10.4 billion in 2100.
- Aging concentrated in advanced economies; many developing economies, particularly in Sub-Saharan Africa, not projected to face aging until later this century (UN population projections, 2022).
- Research question: What are the macroeconomic implications of climate change in an aging world?
- Approach: a New Keynesian DSGE model with heterogeneous age structure (workers and retirees), calibrated to United Nations “more developed regions” demographic estimates and projections.

### Key model features related to demographics
- Two household types: workers and retirees; workers supply labor, retirees do not.
- Workers face a time-varying probability ωt to remain workers and probability 1−ωt to retire; workforce grows at rate nw t.
  - Labor force evolution: Nw t+1 = (1 + nw t) Nw t (equation preserved).
- Retirees stay alive with probability γt; death probability (1−γt).
  - Retiree population evolution: Nr t+1 = (1−ωt) Nw t + γt Nr t.
- Old-age dependency ratio ψt = Nr t / Nw t evolves according to:
  - ψt+1 = (1 + nr t)= 1−ωt ψt + γt (equation verbatim from source).
- Demographic shocks and trends enter the model through time-varying ωt, γt, and nw t.

### Preferences, life-cycle and saving behavior
- Households have Epstein and Zin (1989) preferences; key implication: separation of risk aversion and intertemporal elasticity of substitution and an early resolution of risk/uncertainty.
- Workers face income risk and retirement risk; Epstein-Zin preferences help model precautionary saving for retirement.
- Workers and retirees differ in level and composition of wealth:
  - Workers: labor income, save for retirement.
  - Retirees: consume from savings and receive benefits ej t.
- Marginal propensity to consume:
  - Retirees’ marginal propensity to consume (&tπt in source notation) is higher than workers’ (&>1 implies Ω>1).
  - Worker marginal propensity to consume πt is given by equation (7) in source (preserved structural form).

### Decision problems (structure and implications)
- Representative retiree:
  - Objective: V rj t = [ (crj t)ρ + β γt [V rj t+1]ρ ]1/ρ.
  - Budget constraint: crj t + a rj t = 1 + r t−1 γt−1 a rj t−1 + ej t.
  - Euler equation (retirees): crj t+1 = β(1 + r t) crj t (same form as standard New Keynesian).
  - Retiree consumption function and marginal propensity relationships preserved as in source (equation (5)).
- Representative worker:
  - Objective: V wj t = [ [(cwj t)v1 (1−lwj t)v2]ρ + β [ωt V wj t+1 + (1−ωt) V rj t+1]ρ ]1/ρ.
  - Budget constraint: cwj t + a wj t = (1 + r t−1) a wj t−1 + wt lwj t + fj t − τj t.
  - Consumption-Euler equation for workers (reflecting retirement transition):
    - ωt cwj t+1 + (1−ωt)(&t+1)σ/(1−σ) c rj t+1 = [ β(1 + r t) Ωt+1 (wt/wt+1) v2/ρ ]σ cwj t, with Ωt+1 = ωt + (1−ωt) &1/(1−σ) t+1 (equation (6) preserved).
  - First-order condition for leisure: 1−lwj t = v2/v1 cwj t / wt (equation (8) preserved).
- Effective discounting: workers discount future income streams at an effective rate (1 + r t) Ωt+1 > (1 + r t), reflecting finite expected life.

### Aggregation and policy relevance
- Overlapping generations structure implies fiscal policy is non-neutral; pension PAYG benefits ej t financed by lump-sum taxes τt on workers (pension budget nested in government budget).
- Private non-human wealth defined as at = pk t kt + bt (equation (20) preserved).
- Demographic structure affects aggregate saving, investment, equilibrium real interest rate, inflation dynamics, and fiscal sustainability through retirement flows and life expectancy.

*Source: wpiea2022258-print-pdf (section 2.1 and related model description) — https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022258-print-pdf.pdf*

### 3. Calibration and Demographic trends

### 3. Calibration and Demographic trends

### Demographic calibration and inputs
- Population projections: United Nations projections for "more developed regions" are used as time-varying deterministic inputs to calibrate paths for n_w_t and γ_t.
- Projections (Figure 1 observations):
  - Working-age (15-64) population growth rate: 0.5% in 2000; turned negative in 2010 and remains negative; expected to remain negative until the end of the century.
  - Life expectancy: around 75 years in 2000; expected to be about 90 years in 2100.
- Projections source: UN population projections for "more developed regions" (available at http://esa.un.org/unpp as noted in source).

### Calibrated parameter values (set parameters from Table 1)
- Intertemporal elasticity of substitution σ = 1/3
- Discount factor β = 0.99
- Cobb-Douglas share of labor α = 2/3
- Depreciation rate of capital δ = 0.05
- Growth rate of technological progress x = 0.01
- Elasticity of demand θ = 10
- Preference parameter: consumption v1 = 0.64
- Preference parameter: leisure v2 = 0.358
- Debt-to-output-ratio b* = 0.7
- Government spending share g/y = 0.18
- Replacement rate μ = e_j/w = 0.47
- Direct adjustment parameter in debt rule γ1 = 0.04
- Smoothing parameter in debt rule γ2 = 0.3
- Inertial parameter in the Taylor-rule ρ_i = 0.7
- Inflation coefficient in the Taylor-rule γ_π = 1.5
- Calvo survival probability of contracts ζ = 0.2
- Elasticity of investment function η = 0.25

Notes on calibration choices:
- Intertemporal elasticity of substitution is set to 1/3; discount factor 0.99; labor share 2/3.
- Steady-state growth rate of technological progress set to 1% (x = 0.01).
- Debt-to-GDP ratio calibrated at 70% (b* = 0.7).
- Government spending share set at 18% (g/y = 0.18).
- Annual depreciation rate assumed 5% (δ = 0.05).
- Replacement rate 0.47 implies share of total retirement benefits in output (e/y) of 0.11.
- Fiscal feedback rule: γ1 = 0.04 and γ2 = 0.3 (following Mitchell et al. (2000)).
- Monetary policy rule: ρ_i = 0.7 and γ_π = 1.5.
- ζ = 0.2 implies average duration of prices of 1.25 years.

### Implied steady-state/endogenous variables (from Table 4)
- Real interest rate r = 0.039
- Share of consumption in output c/y = 0.60
- Share of investment in output i_k/y = 0.22
- Share of taxes in output τ/y = 0.31
- Share of total benefits in output e/y = 0.11
- Capital-output ratio k/y = 3.50
- Distribution of wealth λ = 0.23
- Participation rate of workers l_w = l_w/N_w = 0.70
- Consumption share of workers c_w/y = 0.47
- Consumption share of retirees ψ c_r/y = c/y − c_w/y = 0.13
- Propensity to consume out of wealth (workers) π = 0.05
- Propensity to consume out of wealth (retirees) &π = 0.09
- Relative discount term Ω = 1.05

Key implied observations:
- Steady-state real interest rate is 3.9% (r = 0.039).
- Share of taxes in output is 0.31.
- Marginal propensity to consume out of wealth: retirees 0.09 vs workers 0.05.
- Consumption share of output is 60%; investment share is 22%.

### Macroeconomic effects of demographic changes (flexible vs sticky prices)
- Simulation setup:
  - Demographic projections used deterministically until 2100; reported simulation horizon is 40 years (until 2060).
  - Two price-setting assumptions compared: flexible prices (interest rate = equilibrium r*_t, output = natural y*_t) and sticky prices.
- Main dynamic responses (Figure 2 and discussion):
  - Demographic changes (declining working-age growth and increasing life expectancy) produce small but persistent effects.
  - Composition and level of consumption: aggregate consumption share rises; intertemporal substitution toward future consumption occurs; workers consume less; retirees consume more.
  - Higher consumption leads to lower investment and lower capital stock; rental rate of capital is higher.
  - Equilibrium interest rate r*_t declines slightly and persistently, peaking in decline around period 15 with maximum decline around 0.1%.
  - Natural output y*_t shows a slight but persistent increase.
  - Labor market: falling population growth lowers labor supply; real wages initially increase, then fall mirroring reduced investment.
  - Debt-to-GDP does not change significantly in baseline.
- Sticky prices vs flexible prices:
  - Sticky prices: inflation is higher and real interest rate is lower than in flexible case.
  - Fall in real interest rate under sticky prices is almost twice that under flexible prices.
  - With sticky prices, workers' consumption share is lower, total consumption is lower, investment share is higher, capital stock is higher, rental rate of capital is lower, and output increases by about 1%.
  - Policy implication: to stabilize inflation, central banks must respond more aggressively to inflation under sticky prices.

### Contribution of life expectancy vs working-age population growth
- Figure 3 isolating effects:
  - Changes in life expectancy largely drive consumption and real interest rate dynamics.
  - Anticipation of higher life expectancy leads workers to increase savings, reducing workers' consumption and increasing retirees' consumption share.
  - Increased savings lower real interest rates and reduce investment share; muted capital stock increase raises rental rate of capital.
  - Fall in workers' population growth lowers labor supply; increased life expectancy induces workers to work more, increasing labor supply and lowering real wages.

### Macroeconomic effects of disaster shocks
- Disaster shock setup:
  - Persistent shock with ρ_d = 0.99.
  - Size calibrated so the model yields about a 1% fall in output at the end of the 40-year simulation.
- Responses to a persistent disaster shock (Figure 4):
  - Impact: fall in capital stock around 1% initially; persistent fall culminating in maximum decline around 10% of steady-state toward end of simulation period.
  - Output: persistent fall around 1% throughout simulation.
  - Consumption: significant reduction in workers' consumption (around 1% fall on impact); retirees' consumption does not change significantly; aggregate consumption falls around 1%.
  - Investment: investment share is about 1% higher as share of output shifts toward investment.
  - Factor prices: rental rate of capital is higher; real wages fall more, reducing marginal costs.
  - Labor supply: workers increase labor supply persistently; real wages are lower.
  - Inflation: increases persistently after the disaster shock; inflation around 1% higher at end of simulation.
  - Real interest rate: higher real interest rate resulting from higher inflation and the Taylor-rule nominal response (γ_π > 1); destruction of capital also requires higher savings and investment, pushing real rates up.
  - Fiscal implications: debt-to-GDP ratio persistently increases; fiscal rule in Equation (22) is insufficient to stabilize debt-to-GDP. In unreported experiments, increasing γ1 to 1.4 stabilizes debt-to-GDP but at the cost of lower output.

### Isolating contribution of demographic changes in disaster responses
- Comparison experiment (Figure 5): model with demographic changes vs model with demographic variables fixed at steady-state.
- Key differences:
  - Consumption falls more when demographic changes are not accounted for.
  - With demographic changes, retirees' consumption increases and mitigates the consumption decline from the disaster; workers' consumption falls but retirees' increase offsets much of the decline.
  - Smaller fall in consumption implies smaller fall in output and higher inflation relative to the model without demographic changes.
  - Real interest rate: with demographic changes, higher workers' savings lead to lower real interest rates.
- Conclusion: demographic changes are major determinants of key macroeconomic variables (e.g., equilibrium interest rate) and must be accounted for when considering persistent shocks like climate change.

### Macroeconomic effects of uncertainty about disaster magnitude
- Uncertainty shock specification:
  - Disaster shock d_t = ρ_d d_{t-1} + σ_{d,t} &d,t (24)
  - σ_{d,t} = (1 − ρ_{σd}) σ_d + ρ_{σd} σ_{d,t-1} + σ_{σd} &σ_{d,t} (25)
  - &σ_{d,t} is i.i.d. standard normal; ρ_{σd} measures persistence of volatility.
- Effects of uncertainty (Figure 6):
  - Uncertainty amplifies contractionary effects of disaster shocks: larger fall in capital stock and output relative to no-uncertainty case.
  - Output falls for two reasons: precautionary increases in household savings (demand channel) and lower capital stock reducing production capacity (supply channel).
  - Inflation rises despite lower output:
    - Price stickiness leads firms to increase price markups as precaution against uncertainty while prices are fixed, generating an inflationary effect that outweighs demand-driven deflationary pressure.
  - Larger uncertainty magnitudes exacerbate these effects: greater falls in capital and output and larger increases in inflation.
  - Policy implication: cost of climate change can rapidly increase with growing uncertainty.

### Comparison with developing countries
- Setup: demographic shocks for developing countries are larger (as aging process kicks in during simulation); other parameters same as baseline.
- Responses (Figure 7):
  - Aging increases consumption and crowds out investment, reducing the investment share.
  - Because demographic shocks are larger in developing countries, consumption increases more and the crowding-out effect on investment is larger than in developed countries.
  - Overall dynamics mirror developed-country results but with amplified magnitudes on consumption and investment effects.

*Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022258-print-pdf.pdf*

### 5. Climate Change as a Negative Productivity Shock

### 5. Climate Change as a Negative Productivity Shock

### Shock specification and calibration
- Production: y_t = z_t (l_t)^α (k_{t−1})^{1−α}.
- TFP process: z_t = ρ_z z_{t−1} − σ_{zt}, with ρ_z = 0.99.
- Shock size chosen to generate a 1% fall in output.

### Simulated responses and key mechanisms
- Aggregate responses (Figure 8) to the persistent negative TFP shock that produces a 1% output decline:
  - Output: fall on impact, with recovery toward the end of the simulation period.
  - Investment: lower, leading to a fall in the capital stock.
  - Consumption: does not change much.
  - Labour supply of workers: increases.
  - Real wage: lower.
  - Real rental rate, real interest rate, and inflation: effects appear to be small.
  - Debt-output ratio and Tobin’s q: shown in simulated responses (Figure 8) with modest dynamics.
- Mechanism explaining higher labour supply and lower real wages:
  - Lower productivity reduces the marginal product of labour → lower real wages.
  - Persistent TFP decreases and lower wages reduce private wealth → lower consumption.
  - Negative wealth effect induces workers to supply more labor to offset lower consumption.

### Comparison with disaster (capital-destruction) shock
- Both shocks produce a similar fall in output, but aggregate dynamics differ:
  - The productivity shock is less damaging than the disaster shock because increased labour supply and lower real wages partly offset the productivity loss.
  - Disaster shocks reduce capital directly, raise cost of capital, raise inflation permanently (cost-push), and have stronger effects on workers’ consumption and capital accumulation.
  - Uncertainty from disaster shocks increases firms’ mark-ups (with sticky prices), amplifying output contraction and inflation dynamics via higher precautionary savings and lower consumption.

### Implications for public finances and policy-relevant aggregates
- Climate change (through disasters and productivity channels) tends to raise the deficit and the debt-to-GDP ratio, requiring fiscal tightening to realign debt with targets.
- Uncertainty-induced higher mark-ups (sticky prices) increase inflationary pressures and contribution to output contraction.
- Long-run consequences: persistent reductions in output and increases in inflation; indirect adverse effects via increased uncertainty.

### Policy recommendations and priorities
- Contain the impact of climate change through mitigation and adaptation:
  - Global mitigation policies remain critical to limit temperature rises and macroeconomic costs.
  - Adaptation policies are needed to enhance resilience to near-term locked-in greenhouse gas effects.
- Monetary policy:
  - Central banks need greater attention to climate change, especially given uncertainty-induced mark-ups and cost-push inflation from natural disasters.
  - Monitor distributional effects and the implications for equilibrium interest rates and potential output.
- Fiscal policy:
  - Rising debt-to-GDP ratios require tightening fiscal policy via higher taxes or lower expenditure to respect debt rules.
- Social protection:
  - Reconsider long-term design of social safety nets, since assumed labor-supply adjustments by workers may not always be feasible and retirees could face inadequate savings.

*Source: wpiea2022258-print-pdf - 5. Climate Change as a Negative Productivity Shock*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022258-print-pdf.pdf_