Appendix A — Key Terms and Reserved Concepts

This appendix collects the technical terms and notation used consistently throughout the book. Entries are organized thematically rather than alphabetically; a full alphabetical glossary appears in Appendix E. The purpose here is to establish, in one place, the precise meanings of terms that are used across multiple chapters and that sometimes carry different meanings in different parts of the literature.

A.1 Reserved Notation¶

The following symbols carry fixed meanings throughout the book unless explicitly stated otherwise in a given chapter.

Aggregate Quantities¶

Prices and Rates¶

Government and Monetary Variables¶

Household Parameters¶

Growth and Production Parameters¶

Monetary Policy Parameters (Taylor Rule)¶

A.2 Reserved Concepts: Precise Definitions¶

The following concepts appear throughout the book and carry precise technical meanings that differ from their colloquial usage. Where the book uses a term in a technical sense, it is this sense that applies.

Aggregate demand. The total quantity of domestically produced goods and services that all sectors of the economy (households, firms, government, and the foreign sector) wish to purchase at a given price level, with all other exogenous variables held fixed. The aggregate demand curve traces how this quantity changes as the price level changes, for fixed money supply, fiscal stance, and expectations.

Aggregate supply (short-run). The quantity of output that producers are willing and able to supply at a given price level in the short run, when at least one input price (typically the nominal wage) is predetermined. The short-run aggregate supply curve is upward sloping because higher prices erode predetermined nominal wages, making production more profitable and inducing higher employment.

Aggregate supply (long-run). The level of output consistent with flexible-price, market-clearing equilibrium — potential output $\bar{Y}_t$. The long-run aggregate supply curve is vertical because, with fully flexible prices, the price level has no real effect on output.

Animal spirits. Keynes’s term for the autonomous waves of optimism and pessimism that drive investment decisions in the face of genuine (non-probabilistic) uncertainty about the future. In modern formalization, animal spirits are often modeled as self-fulfilling expectational shocks that shift the economy between multiple equilibria.

Automatic stabilizer. A fiscal mechanism that reduces the magnitude of output fluctuations in response to shocks without requiring any discretionary policy action. Progressive income taxes and unemployment insurance are the two most important automatic stabilizers: in a recession, both reduce the leakage of income from the circular flow and sustain household spending.

Balanced growth path. A trajectory of the economy along which output per effective worker $\tilde{y}_t$, capital per effective worker $\tilde{k}_t$, and consumption per effective worker $\tilde{c}_t$ are all constant. On a balanced growth path, output per actual worker $y_t$ grows at the rate of technological progress $g$, consistent with Kaldor’s stylized facts.

Business cycle. The irregular, recurrent fluctuation of aggregate economic activity — measured primarily by real GDP — around its long-run trend. Business cycles are asymmetric (recessions tend to be sharper than expansions), have variable duration (typically 2–10 years from peak to peak), and are associated with co-movement of output, employment, investment, and trade.

Calvo pricing. A model of nominal price rigidity in which, each period, a randomly selected fraction $1-\theta$ of firms are able to reset their price optimally while the remaining fraction $\theta$ keep their price unchanged. The parameter $\theta \in [0,1]$ is the probability that a given price spell continues for at least one more period, and the average duration of a price spell is $1/(1-\theta)$ periods.

Conditional convergence. The empirical prediction of the Solow growth model that countries converge to their own steady-state income levels at an approximately exponential rate. Poor countries grow faster than rich countries conditional on having the same steady-state characteristics (saving rate, population growth, human capital). Unconditional convergence — poor countries simply growing faster — is not predicted by the model and is not supported in broad cross-country data.

Crowding out. The reduction in private investment (or consumption) caused by a fiscal expansion. When government spending increases, higher income raises money demand, raising interest rates, which depress private investment. The degree of crowding out determines how much of the gross fiscal multiplier is offset, reducing the net effect on output.

Current account. The component of the balance of payments that records transactions in goods and services (trade balance), factor income (wages and investment income across borders), and transfer payments. The current account surplus equals national saving minus national investment: $CA = S - I + (T - G)$.

Dynamic efficiency. An economy is dynamically efficient if the net return on capital exceeds the economy’s growth rate: $r > n + g$. In a dynamically efficient economy, the capital stock is not excessive — reducing investment would reduce consumption at every future date rather than increasing it. Empirical evidence suggests that advanced economies are dynamically efficient.

Effective lower bound (ELB). The lower bound on the nominal interest rate set by the return on physical currency (approximately zero, adjusted for storage costs). Below the ELB, agents prefer to hold cash rather than lend, making interest rate cuts ineffective. Empirically, the ELB is estimated at approximately $-0.5\%$ to $-1\%$ for major central banks.

Endogenous growth. Growth in which the long-run rate of per-capita income growth is determined within the model — by savings decisions, research investment, or human capital accumulation — rather than by an exogenous technology parameter. In endogenous growth models, policy can permanently raise the growth rate, not merely the level of income.

Exogenous growth. Growth in which the long-run rate of per-capita income growth is determined by variables taken as parameters outside the model, typically the rate of technological progress $g$. In exogenous growth models, policy can change the level of income on the balanced growth path but not its long-run growth rate.

External finance premium. The spread between the cost of external finance (borrowing from banks or capital markets) and the risk-free rate, reflecting agency costs and informational asymmetries between borrowers and lenders. The external finance premium is a decreasing function of borrower net worth: when net worth is low, the premium rises, constraining investment and amplifying downturns (financial accelerator).

Financial accelerator. The mechanism by which financial market conditions amplify macroeconomic fluctuations. A negative shock reduces asset prices and firm net worth, raising the external finance premium, which reduces investment, which further reduces asset prices and net worth — a self-reinforcing cycle that amplifies the initial shock.

Fiscal multiplier. The change in equilibrium output per unit change in government spending or taxes: $\mu_G = \partial Y^* / \partial G$, $\mu_T = \partial Y^* / \partial T$. The size of the fiscal multiplier depends on the monetary policy regime, the degree of openness, the state of the business cycle, and the behavior of expectations.

Forward guidance. A monetary policy tool by which the central bank communicates its intended future path of interest rates to the public, influencing long-term interest rates and inflation expectations without immediately changing the current policy rate. Forward guidance is particularly important when the policy rate is at the effective lower bound.

Frisch elasticity. The elasticity of labor supply with respect to a temporary wage change, holding the marginal utility of wealth constant. It is the relevant elasticity for analyzing business cycle fluctuations. Macroeconomic models typically require a Frisch elasticity of 2 or more to match employment volatility; microeconomic estimates are much lower (0.1–0.5).

Golden rule. The saving rate, or equivalently the capital stock, that maximizes steady-state consumption per effective worker. At the Golden Rule, the marginal product of capital equals the effective depreciation rate: $f'(\tilde{k}^{GR}) = n + g + \delta$, or equivalently $r^{GR} = n + g$.

Hysteresis. The property by which temporary shocks have permanent effects on equilibrium outcomes — most importantly, by which cyclical unemployment raises the structural (natural) rate of unemployment. Hysteresis in unemployment arises through the atrophying of skills during unemployment spells, the erosion of search intensity, and labor force exit by discouraged workers.

Inada conditions. The regularity conditions on a production function that ensure interior solutions in growth models: $\lim_{K\to 0} F_K(K, L) = \infty$ and $\lim_{K\to\infty} F_K(K, L) = 0$. These conditions ensure the economy does not want to hold zero or infinite capital in equilibrium.

Inflationary bias. The tendency for a central bank operating under discretion to choose positive inflation even when inflation is not desirable, because it has an incentive to exploit the short-run Phillips curve to raise output above the natural rate. In the Barro–Gordon model, the equilibrium inflation rate under discretion is $\pi^D = b\lambda(y^* - \bar{y}) > 0$.

IS curve. The locus of interest rate and output combinations consistent with goods-market equilibrium: $Y = C(Y-T) + I(r) + G$. The IS curve is downward sloping because a higher real interest rate reduces investment, which reduces income through the multiplier. Fiscal expansions shift IS to the right.

Kaldor stylized facts. Six empirical regularities of long-run growth identified by Kaldor (1961): roughly constant growth rates of output per worker and capital per worker; roughly constant real interest rates; roughly constant capital-to-output ratios; roughly constant factor income shares; and large cross-country differences in growth rates.

Labor market tightness. The ratio of vacancies to unemployed workers, $\theta = V/U$. High tightness indicates that workers find jobs quickly and firms fill vacancies slowly; low tightness indicates the opposite. Labor market tightness is the key state variable in search-and-matching models of unemployment.

Liquidity trap. The situation in which the nominal interest rate is at its lower bound and money demand is perfectly elastic with respect to the interest rate. In a liquidity trap, increases in the money supply are entirely absorbed by money demand without affecting interest rates or output. Conventional monetary policy is ineffective.

LM curve. The locus of interest rate and output combinations consistent with money-market equilibrium: $M/P = L(Y, i)$. The LM curve is upward sloping because higher income raises money demand, requiring a higher interest rate to restore money-market equilibrium at a fixed real money supply. Open market purchases shift LM to the right.

Lucas critique. The observation (Lucas, 1976) that estimated reduced-form econometric relationships embed the policy regime in place during the estimation period and will shift when the regime changes, because rational agents adjust their behavior to the new regime. Valid policy analysis requires structural models with parameters describing preferences and technology that are invariant to policy changes.

Marginal propensity to consume (MPC). The fraction of each additional dollar of disposable income that households choose to spend on consumption: $b = \partial C / \partial (Y-T)$. The MPC satisfies $b \in (0,1)$ in the Keynesian model. The size of the fiscal multiplier depends directly on the MPC through $\kappa = 1/(1-b)$.

NAIRU. Non-Accelerating Inflation Rate of Unemployment. The unemployment rate consistent with stable, non-accelerating inflation. Equivalent to the natural rate of unemployment $u^*$ in the context of the expectations-augmented Phillips curve.

Natural rate of interest. The real interest rate consistent with output at its potential level and stable inflation — the Wicksellian neutral rate $r^n$. When the actual real rate exceeds the natural rate, monetary policy is contractionary; when it falls below, policy is expansionary.

Natural rate of output. The level of real GDP that would prevail if all prices and wages were fully flexible — the productive capacity of the economy at a given state of technology, capital, and labor. Also called potential output $\bar{Y}_t$.

Natural rate of unemployment. The unemployment rate consistent with stable, non-accelerating inflation, comprising frictional and structural unemployment but not cyclical unemployment. Also called the NAIRU or $u^*$.

Nominal rigidity. Any friction that prevents nominal prices or wages from adjusting immediately in response to changes in demand or the money supply. Nominal rigidities are the key feature that gives monetary policy real short-run effects; without them, money would be neutral at all horizons.

Output gap. The difference between actual output and potential output, $\hat{x}_t = Y_t - \bar{Y}_t$, usually expressed as a percentage of potential output. A positive output gap (boom) is associated with rising inflation; a negative output gap (recession) is associated with falling inflation or deflationary pressure.

Permanent income. Friedman’s concept: the constant annuity equivalent of the household’s expected lifetime income stream, reflecting not current income but long-run average earning capacity. Households base consumption on permanent income, saving transitory income and dissaving when current income falls temporarily below permanent income.

Phillips curve. The empirical and theoretical relationship between inflation and unemployment (or equivalently, between inflation and the output gap). The original (1958) Phillips curve showed a stable negative relationship between wage inflation and unemployment. The expectations-augmented Phillips curve adds inflation expectations, showing that the trade-off is only between unexpected inflation and unemployment deviations from the natural rate. The New Keynesian Phillips Curve derives this relationship from Calvo pricing and shows inflation depends on the discounted sum of future expected output gaps.

Policy ineffectiveness proposition. The Sargent–Wallace (1975) proposition that, under rational expectations and flexible prices, systematic monetary policy cannot affect real output. Only the unforecastable innovation in the money supply — the part that genuinely surprises agents — can move real variables.

Potential output. See natural rate of output.

Precautionary saving. The additional saving undertaken by risk-averse households facing uncertain future income, beyond what they would save in a world of certainty. Precautionary saving arises when the utility function satisfies $u''' > 0$ (prudence) and increases with income uncertainty.

Purchasing power parity (PPP). The exchange rate at which a reference basket of goods costs the same in two countries, after converting at that rate. PPP-adjusted GDP comparisons remove price-level differences across countries, allowing meaningful comparison of real living standards.

Quantity theory of money. The proposition that the price level is proportional to the money supply, with the proportionality factor determined by velocity and real output: $MV = PY$. Under stable velocity and supply-determined real output, money growth equals inflation: $\hat{m} = \pi$.

Rational expectations. The assumption that agents’ forecasts equal the mathematical conditional expectation of the variable given all available information: $\mathbb{E}_t[x_{t+1}] = \mathbb{E}[x_{t+1} | \mathcal{F}_t]$. Rational expectations eliminates systematic forecast errors; agents may be surprised but are not persistently wrong in the same direction.

Sacrifice ratio. The cumulative output loss (as a percentage of annual GDP) required to permanently reduce inflation by one percentage point. Empirical estimates for the United States cluster around 1.4–2.8. The sacrifice ratio is lower when disinflation is fast (preserving credibility) and when the central bank has a strong inflation-fighting reputation.

Seigniorage. Revenue earned by the government from money creation: $S = (\dot{M}/M)\cdot(M/P)$. In steady state, seigniorage equals the inflation tax: $\pi\cdot(M/P)$.

Stochastic discount factor (SDF). The pricing kernel $M_{t+1} = \beta u'(c_{t+1})/u'(c_t)$ that prices all assets via $p_t = \mathbb{E}_t[M_{t+1}(p_{t+1}+d_{t+1})]$. The SDF equals the representative agent’s intertemporal marginal rate of substitution. Assets that pay poorly in bad states (when $M_{t+1}$ is high) must offer a positive risk premium.

Taylor rule. The monetary policy rule proposed by Taylor (1993): $i_t = r^n + \pi^* + \phi_\pi(\pi_t - \pi^*) + \phi_y\hat{x}_t$. The Taylor principle requires $\phi_\pi > 1$ so that the real interest rate rises when inflation rises, stabilizing the economy. Violation of the Taylor principle leads to sunspot-driven instability.

Time inconsistency. The property of a policy plan whereby the plan that appears optimal at date $t$ is no longer optimal to implement at a later date $s > t$, once expectations formed at $t$ are embedded in contracts and behavior. Time inconsistency in monetary policy leads to inflationary bias under discretion, motivating institutional solutions such as central bank independence and inflation targeting.

Tobin’s q. The ratio of the market value of installed capital to its replacement cost. When $q > 1$, firms should invest (installed capital is worth more than it costs); when $q < 1$, firms should allow capital to depreciate. Under constant returns to scale in production and adjustment costs, marginal $q$ equals observable average $q = V/(p^I K)$.

User cost of capital. The implicit rental price of using one unit of capital for one period: $c^K = r + \delta$, the sum of the opportunity cost of funds and physical depreciation. With taxes: $c^K = [(1-k^{ITC})(1-\tau_c D^{PV})/(1-\tau_c)](r+\delta)$.

Walras’ Law. The accounting identity that the sum of the values of excess demands across all markets equals zero: $\sum_i p_i z_i = 0$ for all price vectors. It follows from the budget constraints of all agents summing to zero and does not imply that individual markets clear.

A.3 Notational Conventions¶

Hats and tildes. $\hat{x}_t$ denotes either the log-deviation of $x_t$ from its steady-state value, or the output gap $Y_t - \bar{Y}_t$ (context-dependent, but always specified). $\tilde{x}_t$ denotes $x_t$ expressed per unit of effective labor $A_t L_t$.

Dots. $\dot{x}_t \equiv \mathrm{d}x_t/\mathrm{d}t$ denotes the time derivative in continuous-time models. In discrete-time models, $\Delta x_t = x_t - x_{t-1}$.

Growth rates. $\hat{x}_t \equiv \mathrm{d}\ln x_t/\mathrm{d}t = \dot{x}_t/x_t$ in continuous time; $\hat{x}_t = (x_t - x_{t-1})/x_{t-1}$ in discrete time.

Expectations. $\mathbb{E}_t[\cdot]$ denotes the mathematical expectation conditional on information available at date $t$. When expectations are rational, this equals $\mathbb{E}[\cdot | \mathcal{F}_t]$.

Stars. $x^*$ denotes a steady-state or equilibrium value, except where $\pi^*$ denotes the inflation target and $u^*$ denotes the natural rate of unemployment.

Subscripts. $x_t$ denotes the value of variable $x$ at date $t$. $x_i$ (Roman subscript) denotes the value for agent or sector $i$. $F_K$ denotes the partial derivative of production function $F$ with respect to $K$.

See also Appendix E (Glossary) for alphabetical reference and Appendix D (Statistical Tools) for econometric notation.