Automated summary
A macroeconomics reference skill that guides model choice, CES production function setup, parameter calibration, and welfare variation calculations.
Strengths
- Model selection table (two-period, OLG, infinite horizon, DSGE) mapped to appropriate use cases
- Explicit CES formulas including Cobb-Douglas and Leontief limits, plus factor share derivations
- Calibration checklist with typical targets and data sources such as national accounts and labor surveys
- Clear definitions of compensating variation, equivalent variation, and consumption-equivalent welfare
Limitations
- No code or worked numeric examples: it supplies formulas and checklists, not a runnable implementation
- Parameter targets are generic ranges that must be re-verified for a specific country and time period
- Focused on deterministic analysis and steady states; DSGE Bayesian estimation is not covered in depth
Use it to structure a macro model, justify a calibration choice, or interpret comparative statics and welfare results.
Avoid it for purely applied econometrics work or for numerical solution code, which the skill does not provide.
Security analysis
SafeThe skill is a purely declarative reference document on macroeconomic modeling: notation tables, CES production formulas, calibration checklists, and welfare definitions. Although Bash, Write, and Edit are declared as allowed tools, the content never instructs any command execution, file manipulation, network access, or handling of credentials; there are no obfuscated payloads or attempts to alter agent behavior.
No concerns found
How this analysis is madeExamples
I'm building a two-sector growth model with CES production. Help me set up the calibration: which moments should I target for the capital share and depreciation, and how do I check the parameters are identified?Compute the compensating variation of a tax reform in my two-period model and compare it with the consumption-equivalent welfare change.I want to study the effects of pension reform on savings. Should I use an OLG model or an infinite-horizon model, and what are the trade-offs?name: econ-macro-modeling description: Macroeconomic modeling, calibration, and comparative statics. Use when working with DSGE models, growth models, general equilibrium, CES production, welfare analysis, or policy counterfactuals. allowed-tools:
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Macroeconomic Modeling
Model Selection Guide
| Model Type | Use When | Key Features | |------------|----------|--------------| | Two-period | Policy comparison, welfare | Simple, closed-form solutions | | OLG | Demographics, pensions, debt | Generational heterogeneity | | Infinite horizon | Long-run growth, BGP | Transversality conditions | | DSGE | Business cycles, monetary policy | Stochastic shocks, estimation |
Production Functions
CES (Constant Elasticity of Substitution)
$$Y = A \left[ \beta K^\rho + (1-\beta) L^\rho \right]^{1/\rho}$$
- Elasticity of substitution: $\sigma = \frac{1}{1-\rho}$
- $\rho \to 0$: Cobb-Douglas ($Y = A K^\beta L^{1-\beta}$)
- $\rho \to -\infty$: Leontief (fixed proportions)
- $\rho = 1$: Perfect substitutes
Factor Shares (CES)
$$s_L = (1-\beta) \left( \frac{AL}{Y} \right)^{1-\rho}$$ $$s_K = 1 - s_L$$
Equilibrium Concepts
- Competitive equilibrium: Price-taking, markets clear
- Walrasian: Auctioneer, no money
- Monetary equilibrium: Cash-in-advance or MIU
- Nash equilibrium: Strategic interaction (games)
Calibration Checklist
- Targets: Identify moments to match (labor share, K/Y ratio, growth rate)
- Parameters: List all parameters, note which are calibrated vs estimated
- Data sources: National accounts, labor surveys, I-O tables
- Identification: Ensure parameters are identified from chosen moments
- Robustness: Test sensitivity to alternative calibrations
Common Calibration Targets
| Parameter | Typical Target | Data Source | |-----------|----------------|-------------| | $\beta$ (discount) | 0.96-0.99 annual | Risk-free rate | | $\alpha$ (capital share) | 0.33-0.40 | National accounts | | $\delta$ (depreciation) | 0.05-0.10 | Investment data | | $\sigma$ (IES) | 0.5-2.0 | Consumption Euler |
Welfare Analysis
Compensating Variation (CV)
Income needed to achieve reference utility at new prices: $$V(p_1, y + CV) = V(p_0, y)$$
Equivalent Variation (EV)
Income change equivalent to policy at original prices: $$V(p_0, y - EV) = V(p_1, y)$$
Consumption-Equivalent Welfare
$$\lambda: \quad U((1+\lambda)c_0) = U(c_1)$$
Standard Notation
| Symbol | Meaning | |--------|---------| | $Y, C, I, G$ | Output, consumption, investment, govt spending | | $K, L, H$ | Capital, labor, human capital | | $w, r, R$ | Wage, rental rate, gross interest rate | | $s_L, s_K$ | Labor share, capital share | | $\beta, \delta$ | Discount factor, depreciation | | $\rho, \sigma$ | CES parameter, elasticity of substitution | | $A, z$ | TFP, productivity shock |
Common Mistakes to Avoid
- Not checking Inada conditions: Ensure interior solutions exist
- Ignoring transitional dynamics: BGP may not be reached
- Over-parameterization: More parameters than identifying moments
- Units mismatch: Annual vs quarterly rates, levels vs logs
- Forgetting budget constraints: Walras' law check
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