Appendix L — Self-Assessment Questions and Quizzes

This appendix provides self-assessment questions organized by chapter and topic. Questions range from conceptual checks (testing understanding of definitions) to analytical exercises (applying models) to critical thinking questions (evaluating assumptions). Answers to conceptual and analytical questions appear after each set; critical thinking questions are open-ended.

Part I: Foundations (Chapters 1–6)¶

Chapter 1: What Is Macroeconomics?¶

1.1 Conceptual. Which of the following is a positive statement and which is normative? (a) “A 10% increase in the minimum wage reduces teenage employment by 1–3%.” (b) “The minimum wage should be raised because it reduces poverty.” (c) “Countries with more independent central banks have lower average inflation.” (d) “Inflation is a greater threat to welfare than unemployment.”

Answers: (a) Positive — testable empirical claim. (b) Normative — value judgment. (c) Positive — empirical claim. (d) Normative — involves a welfare weighting between two outcomes.

1.2 Analytical. Define potential output $\bar{Y}_t$ and explain how it differs from actual output $Y_t$ in the short run and long run.

Answer. Potential output is the level of real GDP consistent with full price and wage flexibility — the economy’s productive capacity at given technology, capital, and labor. In the short run (with nominal rigidities), $Y_t$ can deviate from $\bar{Y}_t$: negative demand shocks cause $Y_t < \bar{Y}_t$ (negative output gap); positive demand shocks cause $Y_t > \bar{Y}_t$ (positive output gap). In the long run, prices and wages adjust, returning $Y_t \to \bar{Y}_t$. The output gap $\hat{x}_t = Y_t - \bar{Y}_t$ is the key variable linking short-run fluctuations to inflation dynamics.

1.3 Critical thinking. The Lucas critique implies that estimated policy multipliers are unreliable. Does this mean econometric evidence is useless for policy? What conditions would make estimated multipliers more credible?

(Open-ended — no single answer. Consider: structural vs. reduced-form estimation; stability of the policy rule; role of natural experiments; conditions under which the Lucas critique matters more or less.)

Chapter 3: GDP, Inflation, and Unemployment¶

3.1 Conceptual. Explain three reasons why the CPI overstates the true increase in the cost of living. For each, explain whether the GDP deflator is subject to the same bias.

Answer. (1) Substitution bias: CPI uses fixed base-period weights; households substitute toward cheaper goods. GDP deflator (chain-weighted) partially corrects this. (2) Outlet bias: consumers shift to cheaper retailers; CPI does not fully capture this. GDP deflator is not subject to this since it covers all output, not household-specific shopping behavior. (3) Quality/new goods bias: price increases partly reflect quality improvements; new goods enter the basket with a lag. GDP deflator is subject to the same bias for the goods it covers.

3.2 Analytical. If the unemployment rate falls from 6% to 5% and the Okun coefficient is $\psi = 2$, by how much does the output gap change? If the EAPC coefficient $\alpha = 0.3$, by how much does inflation change?

Answer. Okun’s Law: $\Delta\hat{x} = -\psi\Delta u = -2\times(-1) = +2$ pp. The output gap rises by 2 percentage points. EAPC: $\Delta\pi = -\alpha\Delta u = -0.3\times(-1) = +0.3$ pp above $\pi^e$. Inflation rises by 0.3 percentage points above expected inflation.

3.3 Analytical. The natural rate of unemployment in a particular economy satisfies $u^* = \delta/(\delta + f(\theta^*))$ with $\delta = 0.03$ (monthly) and $f(\theta^*) = 0.12$ (monthly job-finding rate). Compute $u^*$. If $\delta$ rises to 0.04 (more frequent layoffs), what happens to $u^*$?

Answer. $u^* = 0.03/(0.03+0.12) = 0.03/0.15 = 20\%$. This seems high, but monthly flows generate a large natural rate. With $\delta = 0.04$: $u^* = 0.04/0.16 = 25\%$. The natural rate rises with job destruction because the higher the rate at which workers enter unemployment, the larger the stock required to match outflows with inflows.

Chapter 5: Economic Growth¶

5.1 Conceptual. State and explain Kaldor’s six stylized facts. Which does the Solow model match, and which does the AK model match?

Answer. (See Section 5.1 of main text.) The Solow model matches facts 1–5 (constant growth rates, capital-output ratio, factor shares, interest rate on the balanced growth path) but predicts zero cross-country growth rate differences in the long run — inconsistent with fact 6. The AK model generates different permanent growth rates across countries based on saving rates (matching fact 6) but may not reproduce constant factor shares depending on specification.

5.2 Analytical. In the Solow model with $\alpha = 1/3$, $n=0.01$, $g=0.02$, $\delta=0.05$: (a) What saving rate gives the Golden Rule capital stock? (b) If the actual saving rate is 0.20, is the economy above or below the Golden Rule? Should the saving rate be increased or decreased to maximize steady-state consumption?

Answer. (a) Golden Rule: $f'(\tilde{k}^{GR}) = n+g+\delta = 0.08$. With $f(\tilde{k}) = \tilde{k}^{1/3}$: $f'(\tilde{k}) = (1/3)\tilde{k}^{-2/3} = 0.08 \implies \tilde{k}^{GR} = (1/(3\times 0.08))^{3/2} = (4.17)^{1.5} = 8.52$. The Golden Rule saving rate: $s^{GR} = 0.08 \times \tilde{k}^{GR}/(\tilde{k}^{GR})^{1/3} = 0.08 \times 8.52^{2/3} = 0.08 \times 4.17 = 0.333$. (b) Actual $s = 0.20 < s^{GR} = 0.333$: the economy is below the Golden Rule. To maximize steady-state consumption, the saving rate should be increased.

5.3 Critical thinking. The AK model predicts that saving rate differences permanently affect growth rates. Why does this prediction appear to be violated in the data (the Jones, 1995, critique)? What does semi-endogenous growth theory predict instead?

(Open-ended. Key points: scale effects in the basic AK model predict larger countries grow faster, violated in data; Jones proposes diminishing returns in knowledge production, yielding growth rates independent of R&D intensity in the long run but level effects from policy.)

Part II: Core Theories (Chapters 7–10)¶

Quiz 2.1 (Multiple choice).

1. Which of the following shifts the IS curve to the right?
   (a) An increase in the real interest rate. (b) A decrease in government spending. (c) An increase in consumer confidence (autonomous consumption). (d) A reduction in the money supply.

2. Under the Mundell–Fleming trilemma with a fixed exchange rate and perfect capital mobility, which policy is effective?
   (a) Monetary policy, because the interest rate can be set independently. (b) Fiscal policy, because the BP curve prevents crowding out. (c) Both fiscal and monetary policy. (d) Neither, because the exchange rate is fixed.

3. The New Keynesian Phillips Curve implies that disinflation is:
   (a) Always costly, requiring a recession. (b) Costless if credibly announced, under pure NKPC. (c) More costly with more frequent price adjustment. (d) More costly with lower $\beta$.

Answers: 1. (c). 2. (b). 3. (b).

Quiz 2.2 (Short answer).

(a) What is the Keynesian multiplier and why is it greater than one?
(b) Explain the difference between the Keynesian cross multiplier and the IS–LM fiscal multiplier. What causes the IS–LM multiplier to be smaller?
(c) What is the sacrifice ratio? Give two reasons why it may be lower with a credible central bank commitment.

Answers. (a) $\kappa_G = 1/(1-b) > 1$: each dollar of government spending generates income for households, who spend fraction $b$, generating more income, in an infinite series summing to $1/(1-b)$. (b) IS–LM multiplier: $h/(h+b_r k) < 1/(1-b)$. The difference is crowding out: fiscal expansion raises income, raises money demand, raises interest rates, reduces private investment. (c) Sacrifice ratio is cumulative output loss per pp of disinflation. It is lower with credible commitment because: (i) forward-looking price-setters immediately lower their prices when they expect future output gaps, so the NKPC requires less actual slack; (ii) wage setters incorporate the expected disinflation into wage demands, reducing the wage inflation that drives price inflation.

Part III: Microfoundations (Chapters 11–16)¶

11.1 Conceptual. State Hall’s (1978) random walk hypothesis for consumption. What does it predict about the response of consumption to (a) an anticipated tax refund, (b) an unanticipated bonus?

Answer. Hall’s hypothesis: under rational expectations and quadratic utility, $c_{t+1} = c_t + \epsilon_{t+1}$, where $\epsilon_{t+1}$ is unpredictable from $\mathcal{F}_t$. (a) An anticipated tax refund should not affect consumption when it arrives — it was already incorporated into permanent income when announced, so consumption adjusted at the announcement date, not the payment date. (b) An unanticipated bonus represents a shock to permanent income and should cause an immediate increase in the level of consumption equal to $r/(1+r)$ times the windfall (the annuity value).

12.1 Analytical. In the real options framework, if the annual volatility of project cash flows $\sigma$ doubles from 0.2 to 0.4 and all other parameters remain constant ($r = 0.1$, $\mu = 0.05$), what happens to the investment trigger $\Pi^*$? Does this make investment more or less likely?

Answer. The parameter $\beta = \frac{1}{2} - \frac{\mu}{\sigma^2} + \sqrt{(\frac{\mu}{\sigma^2}-\frac{1}{2})^2 + \frac{2r}{\sigma^2}}$.

With $\sigma = 0.2$: $\beta = 0.5 - 1.25 + \sqrt{(0.75)^2 + 5} = 0.5 - 1.25 + \sqrt{5.5625} = 0.5 - 1.25 + 2.358 = 1.608$. $\Pi^*/c^K = 1.608/0.608 = 2.65$.

With $\sigma = 0.4$: $\beta = 0.5 - 0.3125 + \sqrt{(0.1875)^2 + 1.25} = 0.5 - 0.3125 + \sqrt{1.285} = 0.5 - 0.3125 + 1.134 = 1.321$. $\Pi^*/c^K = 1.321/0.321 = 4.12$.

The trigger rises from 2.65 to 4.12 times the user cost of capital. Higher volatility raises the option value of waiting, making investment less likely for any given level of $\Pi_t$.

16.1 Critical thinking. The Barro–Gordon model predicts a positive inflationary bias under discretionary monetary policy. But many central banks in advanced economies achieved and maintained low inflation during 1990–2020 without constitutional precommitment. How can this be reconciled with the model?

(Open-ended. Consider: reputation effects and Rogoff’s repeated-game extension; institutional changes (central bank independence, inflation targeting frameworks) that effectively precommit policy; structural changes in the economy (lower Phillips curve slope $\kappa$, lower inflationary bias when $y^*$ is close to $\bar{y}$); the role of credibility built through costly disinflation in the 1980s.)

Parts IV–IX: Cross-Cutting Questions¶

General 1. A government is considering whether to respond to a large negative demand shock with fiscal expansion or to wait for automatic self-correction. What factors should determine this choice according to macroeconomic theory? List at least five.

Key considerations: (1) Speed of automatic adjustment (degree of nominal rigidity); (2) multiplier size (depends on monetary policy regime, ELB); (3) hysteresis risk — if the shock could permanently raise the natural rate, quick action is more valuable; (4) existing debt levels (fiscal space, sustainability concerns); (5) confidence effects (expansionary austerity vs. Keynesian multiplier debate); (6) supply vs. demand nature of shock (fiscal expansion is appropriate for demand shocks but may be counterproductive for supply shocks).

General 2. Explain how quantitative easing (QE) works and why it might be less effective than conventional interest rate cuts.

Answer. QE operates by purchasing long-duration assets (Treasuries, MBS), reducing term premia and driving down long-term interest rates. Channels: portfolio balance (investors rebalance into riskier assets), signaling (QE signals extended low short rates), and market functioning (reduces illiquidity premia). Potential limitations: (1) if the ELB has lowered term premia to very low levels, further compression may have little effect on investment and borrowing; (2) the pass-through from long rates to credit conditions may be attenuated if bank net interest margins are compressed; (3) QE raises asset prices primarily, benefiting wealthy households with limited MPC, reducing the consumption boost per dollar of asset purchase.

General 3 (essay). “Macroeconomic models increasingly require heterogeneous agents. The representative-agent assumption is not just unrealistic but actively misleading for policy analysis.” Evaluate this claim.

(Open-ended essay. Arguments for: HANK models show monetary transmission operates primarily through income effects on constrained households, not through intertemporal substitution as RANK predicts; distributional effects of policy depend entirely on agent heterogeneity; multipliers depend on the fraction of liquidity-constrained households. Arguments against: RANK provides useful benchmarks and tractability; many aggregate predictions are similar with and without heterogeneity for small shocks; HANK models are data-intensive and their parameters uncertain. Balanced conclusion expected.)

Answers to remaining exercises are provided in Appendix G. Instructors may obtain additional assessment materials from the publisher.