Appendix B. Review and self-study questions
These questions consolidate the core conceptual, mathematical and empirical ideas and provide a framework for independent study.
Models and microfoundations
1. Distinguish a quantitative equilibrium model from a purely accounting identity.
2. Explain endogenous versus exogenous variables in the basic RBC framework.
3. Why can an exogenous saving rule be unsuitable for a policy counterfactual?
4. Derive the simple Keynesian fiscal spending multiplier for fixed lump-sum taxes and explain the effect of proportional income taxation.
5. Discuss how leisure–consumption indifference curves relate to the marginal rate of substitution.
Empirical measurement
1. Distinguish trend growth, business cycles and seasonal movements.
2. Write the objective function of the Hodrick–Prescott filter and interpret its smoothing penalty.
3. State the five Kaldor balanced-growth facts and distinguish them from RBC cyclical facts.
4. Explain why output and investment should be measured in comparable real, seasonally adjusted units.
5. Interpret a relative standard deviation greater than one and a contemporaneous correlation near one.
Firm and shocks
1. Derive marginal products from Cobb–Douglas production and identify factor shares.
2. Explain why using kₜ instead of kₜ₋₁ changes the timing of the firm’s problem.
3. Compute the impulse path of an AR(1) process after a one-time innovation.
4. Explain why the Solow residual may reflect more than pure technological progress.
Household and equilibrium
1. Set up the representative household lifetime objective and period resource constraint.
2. Derive and interpret the Euler equation under log utility.
3. Derive the labor–leisure first-order condition for u(c,l)=ln(c)+ϕl.
4. Explain why consumption smoothing generates investment following a positive productivity disturbance.
5. Construct the five-equation RBC equilibrium system.
Steady state, calibration and solution
1. Find the steady-state return to capital in terms of β and δ.
2. Explain how the capital share and investment/output ratio are used in calibration.
3. Derive the log-linearized Cobb–Douglas production condition.
4. Why does the linearized resource constraint contain steady-state level weights?
5. Explain the role of stability and predetermined variables in the method of undetermined coefficients.
6. Interpret the P, Q, R and S matrices in a recursive toolkit solution.
Impulse responses and validation
1. Use the policy coefficients to calculate impact responses to a 1% productivity shock.
2. Describe how a shock affects investment and later capital through time.
3. Contrast a shock to current productivity with a deviation in installed capital.
4. Construct a simulation-based comparison using volatility and cross-correlation moments.
5. Identify two empirical features that the baseline RBC calibration fits imperfectly.