Macroeconomics

2026-09-26

The economy as a whole: how output, prices and employment are measured, what drives long-run growth, how money and banks work, why economies boom and slump, and what fiscal and monetary policy can and cannot do. Individual markets, costs and market failure are in microeconomics. Live data for every series here is on FRED (opens in a new tab).

Measuring output

Gross domestic product (GDP): the market value of all final goods and services produced within a country in a period. Three approaches give the same total (up to a statistical discrepancy):

Approach	Sums	Formula
expenditure	spending on final output	$Y = C + I + G + NX$
income	incomes earned producing it	compensation of employees + gross operating surplus + mixed income + taxes on production less subsidies
production	value added by every producer	output minus intermediate consumption

Component	Includes	Excludes
$C$ consumption	household goods and services	purchases of existing homes
$I$ investment	business equipment and structures, new housing, change in inventories	buying shares or bonds (financial, not real, investment)
$G$ government purchases	public wages, equipment, infrastructure	transfers (pensions, benefits): no output is bought
$NX = X - M$ net exports	exports minus imports

Also excluded from GDP: intermediate goods (double counting), second-hand sales, unpaid household work, most illegal activity, leisure and environmental damage. GDP measures production, not welfare.

Measure	Definition
nominal GDP	valued at current prices
real GDP	valued at base-year (chained) prices: tracks quantities
GDP deflator	$\dfrac{\text{nominal GDP}}{\text{real GDP}} \times 100$
GNI / GNP	GDP + income earned abroad by residents − income earned here by non-residents
GDP per capita	GDP / population: the usual living-standards proxy
PPP-adjusted GDP	converted at purchasing-power-parity rates rather than market exchange rates, for cross-country comparison
potential output $Y^*$	output with resources at normal utilization, without accelerating inflation
output gap	$\dfrac{Y - Y^}{Y^}$ : positive in a boom, negative in a slump

Growth rates: $g = \dfrac{Y_t - Y_{t-1}}{Y_{t-1}}$ . Quarterly rates are often annualised: $(1 + g_q)^4 - 1$ (the US convention; the UK and euro area headline quarter-on-quarter rates unannualised).

Inflation and prices

Inflation: the rate of increase in the general price level, $\pi_t = \dfrac{P_t - P_{t-1}}{P_{t-1}}$ .

Index	What	Note
CPI	fixed basket bought by urban consumers	headline US inflation (BLS); overstates cost-of-living changes (substitution, new goods, quality bias)
core CPI	CPI excluding food and energy	less noisy signal of trend
PCE price index	all personal consumption, weights update as spending shifts	the Federal Reserve's target measure (BEA)
HICP	harmonized index across the EU	the ECB's target measure
GDP deflator	all domestically produced goods	includes investment and government; excludes imports
PPI	prices received by producers	often leads consumer prices

Relation	Formula
real value	$\text{real} = \dfrac{\text{nominal}}{P} \times 100$ (with $P$ an index, base 100)
Fisher equation	$(1 + i) = (1 + r)(1 + \pi^e)$ , so $i \approx r + \pi^e$
ex post real rate	$r = i - \pi$ (actual inflation)
quantity equation	$MV = PY$ , so $\%\Delta M + \%\Delta V \approx \%\Delta P + \%\Delta Y$
quantity theory	with $V$ stable and $Y$ set by real factors, money growth drives inflation in the long run

Cost of inflation	Mechanism
shoe-leather	effort spent holding less cash
menu costs	resetting prices
relative-price distortion	prices change at different times, misallocating resources
tax distortions	taxes on nominal capital gains and interest rise with inflation
redistribution	unexpected inflation shifts wealth from lenders to borrowers and hurts fixed-income earners
uncertainty	harder long-term planning and contracting

Deflation is not the cure: falling prices raise the real burden of debt (debt deflation, Fisher 1933), push real rates up when nominal rates cannot go below zero, and reward postponing purchases. Hyperinflation (conventionally above 50% a month, Cagan 1956) is almost always the result of printing money to finance government deficits.

Unemployment and the labor market

Measure	Definition
labor force	employed + unemployed (actively looking in the last four weeks, available to work)
unemployment rate	$u = \dfrac{U}{E + U}$
participation rate	$\dfrac{E + U}{\text{working-age population}}$
employment-to-population ratio	$\dfrac{E}{\text{working-age population}}$
discouraged workers	want work but stopped searching: not counted as unemployed
U-3 / U-6	US official rate / broad rate adding marginally attached and involuntary part-time workers

Type	Cause	Policy
frictional	time to match workers and jobs	better information, job boards
structural	skills or location mismatch; wages above market-clearing (unions, minimum wages, efficiency wages)	retraining, mobility
cyclical	too little aggregate demand in a downturn	fiscal and monetary stimulus
seasonal	predictable yearly patterns	none; data are seasonally adjusted

The natural rate $u^*$ = frictional + structural: unemployment when output is at potential. The NAIRU (non-accelerating inflation rate of unemployment) is its operational twin.

Okun's law (an empirical rule, not a law): each percentage point of unemployment above the natural rate goes with output roughly 2% below potential (Okun's original 1962 estimate was about 3%).

\frac{Y - Y^*}{Y^*} \approx -2\,(u - u^*)

Long-run growth

Over decades, growth in output per person dominates everything else: at 2% a year living standards double in about 35 years.

\text{doubling time} \approx \frac{70}{g\ (\text{in } \%)} \qquad \text{(rule of 70)}

Production function (Cobb–Douglas, capital share $\alpha \approx \tfrac13$ ):

Y = A\,K^{\alpha} L^{1-\alpha} \qquad\Rightarrow\qquad g_Y = g_A + \alpha\,g_K + (1 - \alpha)\,g_L

Growth accounting splits output growth into capital, labor and the residual $g_A$ , total factor productivity (TFP): technology, organization, institutions.

Solow model (per worker $k = K/L$ , $y = f(k)$ , saving rate $s$ , depreciation $\delta$ , population growth $n$ ):

Result	Formula / statement
capital accumulation	$\Delta k = s f(k) - (\delta + n)k$
steady state	$s f(k^) = (\delta + n)k^$
higher saving	raises the level of $k^$ and $y^$ , not the long-run growth rate
golden rule	consumption per worker is maximized where $f'(k) = \delta + n$
sustained growth	only from technological progress ( $g_A > 0$ )
conditional convergence	poorer countries with similar fundamentals grow faster toward their own steady state

Endogenous growth models (Romer 1990) make technology the product of deliberate R&D with non-rival ideas, so policy (education, research, competition, property rights) can change the growth rate. Institutions (secure property rights, rule of law, constraints on elites) are the deepest determinant in most empirical work (Acemoglu, Johnson and Robinson).

Saving, investment and finance

National saving is income not spent on consumption or government purchases:

S = Y - C - G = \underbrace{(Y - T - C)}_{\text{private}} + \underbrace{(T - G)}_{\text{public}}

Identity	Meaning
closed economy: $S = I$	saving finances investment
open economy: $S - I = NX$	a country saving more than it invests lends abroad and runs a trade surplus
twin deficits	a larger budget deficit ( $T - G$ falls) lowers $S$ ; with $I$ unchanged, $NX$ must fall

Loanable funds: saving supplies and investment demands funds; the real interest rate clears the market. A larger government deficit shifts supply left, raising $r$ and crowding out private investment (strongest when the economy is at full employment, weakest in a slump with idle saving).

Asset	Relation
bond price vs yield	move opposite: $P = \sum \dfrac{C}{(1 + y)^t} + \dfrac{F}{(1 + y)^T}$
term structure	long rates ≈ average expected short rates + term premium; an inverted yield curve has preceded most US recessions
stock price	present value of expected future dividends

Money and banking

Function of money	Meaning
medium of exchange	accepted in payment; avoids the double coincidence of wants
unit of account	prices quoted in it
store of value	holds purchasing power over time (imperfectly under inflation)

Aggregate	Contents
monetary base (M0)	currency + bank reserves at the central bank
M1	currency + demand and other liquid deposits
M2	M1 + small time deposits + retail money-market funds

How money is created. The textbook money multiplier ( $1/rr$ for reserve ratio $rr$ ) says banks lend out reserves. In practice commercial banks create deposits when they lend, limited by profitable demand for loans, capital requirements and regulation, not by reserves (McLeay, Radia and Thomas 2014). The US reserve requirement has been zero since March 2020, and the Federal Reserve runs an ample-reserves system.

Central-bank tool	How it works
policy rate	Fed: target range for the federal funds rate; ECB: deposit facility rate; BoE: Bank Rate
interest on reserve balances (IORB)	the main lever in an ample-reserves system: banks won't lend overnight below it
overnight reverse repo (ON RRP)	floor for rates paid to non-banks (money-market funds)
open-market operations	buying or selling government securities
discount window / standing repo	lender of last resort to solvent banks (Bagehot: lend freely, against good collateral, at a penalty rate)
quantitative easing (QE) / tightening (QT)	large-scale asset purchases or run-off to move long-term rates
forward guidance	signaling the future path of rates

Central bank	Inflation target
Federal Reserve (US)	2% PCE inflation over the longer run; dual mandate with maximum employment
European Central Bank	2% HICP, symmetric, over the medium term
Bank of England	2% CPI, set by the government

Aggregate demand and supply

AD–AS: a demand shock moves the economy from E₀ to a short-run boom at E₁

Curve	Slope	Why	Shifts with
AD	down	higher prices cut real wealth, raise interest rates and make exports dearer	$C$ , $I$ , $G$ , $T$ , $NX$ , money supply, confidence, foreign demand
SRAS	up	sticky wages and prices: higher prices raise profit margins in the short run	wages, input prices (oil), productivity, expected inflation, supply shocks
LRAS	vertical at $Y^*$	in the long run prices and wages adjust fully; output set by $K$ , $L$ , $A$	capital, labor force, technology, institutions

Shock	Short run	Long run (no policy response)
AD ↓ (confidence falls)	output ↓, prices ↓ (or disinflation), unemployment ↑: recession	wages fall, SRAS shifts right, back to $Y^*$ at a lower price level (slowly)
AD ↑ (stimulus, boom)	output ↑ above $Y^*$ , prices ↑	wages rise, SRAS shifts left, back to $Y^*$ at a higher price level
SRAS ↓ (oil shock)	stagflation: output ↓ and prices ↑	policy dilemma: stimulating output worsens inflation
LRAS ↑ (productivity)	output ↑, prices ↓	higher potential output

IS–LM (short run, fixed prices): the IS curve is combinations of $Y$ and $r$ where goods-market spending equals output; the LM curve (or, in modern versions, a monetary-policy rule setting $r$ ) closes the model. Fiscal expansion shifts IS right; monetary expansion shifts LM right or lowers the policy rate.

Fiscal policy

Tool	Effect on AD
government purchases $G$	direct: $\Delta Y = \text{multiplier} \times \Delta G$
taxes $T$	indirect via disposable income: smaller effect than $G$ per unit
transfers	like tax cuts; larger effect when paid to people who spend it
automatic stabilizers	progressive taxes and unemployment benefits cushion cycles with no new law

Simple Keynesian multipliers (fixed prices and interest rates, marginal propensity to consume MPC):

Multiplier	Formula	MPC = 0.8
spending	$\dfrac{1}{1 - MPC}$	5
lump-sum tax	$\dfrac{-MPC}{1 - MPC}$	−4
balanced budget ( $\Delta G = \Delta T$ )	$1$	1
with income tax $t$ and imports $m$	$\dfrac{1}{1 - MPC(1 - t) + m}$	smaller

The textbook numbers are far too large. Leakages to taxes, imports and saving, crowding out through interest rates and monetary offset shrink them: empirical estimates for US government purchases mostly fall around 0.6 to 1, possibly higher when interest rates are stuck at zero (Ramey 2019).

Concept	Formula / meaning
budget deficit	$G + \text{transfers} + \text{interest} - T$
primary balance	the budget balance excluding interest payments
cyclically adjusted balance	the balance if output were at potential
debt dynamics	$\Delta b \approx (r - g)\,b - s$ : debt-to-GDP $b$ rises if the interest rate $r$ exceeds growth $g$ and the primary surplus $s$ is too small
Ricardian equivalence	if households foresee future taxes, debt-financed tax cuts are saved, not spent (a benchmark; rarely holds fully)

Policy lags: inside lags (recognizing and legislating) are long for fiscal policy; outside lags (effect on the economy) are long for monetary policy.

Monetary policy

Transmission from the policy rate to the economy: short-term market rates → loan and mortgage rates, bond yields and asset prices (wealth effect) → exchange rate (net exports) → credit supply → expectations. The effect on inflation takes roughly one to two years.

Taylor rule (Taylor 1993), a description of how the Fed set rates and a benchmark for judging policy:

i = r^* + \pi + 0.5\,(\pi - \pi^*) + 0.5\,\frac{Y - Y^*}{Y^*} \times 100

with $r^*$ the neutral real rate (Taylor used 2%) and $\pi^*$ the inflation target (2%). Inflation above target raises the nominal rate more than one-for-one (the Taylor principle), so the real rate rises.

Problem	Meaning	Response
zero (effective) lower bound	nominal rates can't go much below zero because cash pays 0%	QE, forward guidance, negative rates (ECB, BoJ, SNB), fiscal policy
liquidity trap	more money is hoarded, not spent	fiscal policy matters more
time inconsistency	a promise of low inflation is tempting to break later	central-bank independence, inflation targets, rules
unanchored expectations	expected inflation feeds into wages and prices	credibility, acting early
financial stability	low rates can feed asset bubbles and leverage	macroprudential tools (capital buffers, loan-to-value limits)

Phillips curve and expectations

The original Phillips curve (Phillips 1958, wage data for the UK) showed lower unemployment with higher wage inflation. Friedman (1968) and Phelps (1967) argued the trade-off is only temporary; the expectations-augmented Phillips curve:

\pi = \pi^e - \beta\,(u - u^*) + \varepsilon

Implication	Meaning
short run	lower unemployment only by surprising people with inflation above expectations
long run	vertical at $u^*$ : no permanent trade-off
supply shocks $\varepsilon$	shift the curve up: higher inflation at every unemployment rate (1970s stagflation)
sacrifice ratio	output lost (% of a year's GDP) per percentage point of lasting disinflation
anchored expectations	a credible target keeps $\pi^e$ near 2%, flattening the curve and making shocks transitory

Expectation schemes: adaptive ( $\pi^e_t = \pi_{t-1}$ ) versus rational (using all available information, including the policy regime). Under rational expectations only unexpected policy moves real variables (Lucas critique: estimated relationships change when policy changes).

Business cycles

Business cycle: expansions and recessions around potential output (schematic)

Phase	Output	Unemployment	Inflation
expansion	rising	falling	typically rising late in the expansion
peak	at its highest, above trend	at its lowest	often at its highest
recession / contraction	falling	rising	falling (with a lag)
trough	at its lowest	at or near its highest	low

"Two consecutive quarters of falling real GDP" is a rule of thumb. In the US, the NBER's Business Cycle Dating Committee dates recessions as "a significant decline in economic activity that is spread across the economy and lasts more than a few months", judged on employment, income, spending and production.

Indicator	Type	Examples
leading	turns before the economy	yield-curve slope, building permits, new orders, initial jobless claims, stock prices, consumer expectations
coincident	moves with it	payroll employment, industrial production, real income, retail sales
lagging	turns after	unemployment duration, inflation, loan rates
Sahm rule	real-time recession signal	3-month average unemployment rate 0.5 percentage points or more above its low of the previous 12 months

Theory	Driver of cycles
Keynesian / New Keynesian	demand shocks with sticky prices and wages
real business cycle	technology (supply) shocks with flexible prices
monetarist	unstable money growth
financial accelerator / Minsky	credit booms and busts amplify shocks via balance sheets

The open economy

Account (BPM6)	Records
current account (CA)	trade in goods and services + primary income + secondary income (transfers)
capital account (KA)	capital transfers, non-produced non-financial assets (small)
financial account (FA)	net acquisition of foreign assets minus net incurrence of liabilities
identity	$CA + KA = FA$ (plus net errors and omissions): a current-account deficit is financed by net borrowing from abroad

Exchange-rate concept	Formula / meaning
nominal rate $e$	price of foreign currency in home currency (conventions vary: check which way round)
real exchange rate	$\varepsilon = \dfrac{e\,P^*}{P}$ : price of foreign goods in terms of home goods
purchasing power parity	in the long run $e \approx P / P^*$ ; relative PPP: depreciation ≈ inflation differential
uncovered interest parity	$i \approx i^* + \text{expected depreciation of the home currency}$
Marshall–Lerner	a depreciation improves the trade balance if export and import demand elasticities sum above 1 (after a J-curve lag)

The impossible trinity (Mundell–Fleming): a country can have at most two of fixed exchange rate, free capital movement and independent monetary policy.

Choice	Gives up	Example
float + open capital + own policy	fixed rate	US, UK, euro area as a whole
peg + open capital	own monetary policy	Hong Kong dollar board, Denmark
peg + own policy	free capital flows	China (managed, with capital controls)

Worked examples

GDP by expenditure

$C = 14{,}000$ , $I = 3{,}500$ , $G = 4{,}000$ , exports $2{,}500$ , imports $3{,}000$ (billions):

Y = 14{,}000 + 3{,}500 + 4{,}000 + (2{,}500 - 3{,}000) = 21{,}000

If real GDP is $19{,}800$ , the deflator is $21{,}000 / 19{,}800 \times 100 = 106.1$ .

Unemployment and participation

Employed 160 million, unemployed 8 million, working-age population 270 million:

u = \frac{8}{168} = 4.8\%, \qquad \text{participation} = \frac{168}{270} = 62.2\%

If 2 million unemployed give up searching: $u = 6/166 = 3.6\%$ while nobody found a job. Participation falls to $166/270 = 61.5\%$ .

Real interest rate

A loan at 7% when inflation turns out to be 4%: $r \approx 3\%$ (exactly $1.07/1.04 - 1 = 2.9\%$ ). Had inflation been expected at 2% but come in at 4%, the lender lost about 2 points of expected real return to the borrower.

Multiplier

MPC 0.75, government spends an extra 100:

\Delta Y = \frac{1}{1 - 0.75} \times 100 = 400

A 100 lump-sum tax cut instead: $\dfrac{0.75}{0.25} \times 100 = 300$ . Both together (balanced budget): 100.

Taylor rule

Inflation 3%, target 2%, output 1% below potential, $r^* = 2\%$ :

i = 2 + 3 + 0.5(3 - 2) + 0.5(-1) = 5\%

Solow steady state

$y = k^{0.5}$ , $s = 0.2$ , $\delta = 0.05$ , $n = 0$ :

0.2\sqrt{k^*} = 0.05\,k^* \Rightarrow \sqrt{k^*} = 4 \Rightarrow k^* = 16,\ y^* = 4,\ c^* = 0.8 \times 4 = 3.2

Golden rule: $f'(k) = 0.5k^{-0.5} = 0.05$ gives $k = 100$ , $y = 10$ , needing $s = \delta k / y = 0.5$ , and $c = 5$ : a higher saving rate here raises long-run consumption.

Doubling time

Real GDP per person growing at 1.5% a year doubles in about $70 / 1.5 \approx 47$ years; at 3.5%, in 20.

References

OpenStax: Principles of Macroeconomics 3e (opens in a new tab): free introductory textbook
CORE Econ: The Economy 2.0 (opens in a new tab): free, modern, data-driven introduction
FRED, Federal Reserve Bank of St. Louis (opens in a new tab): data for GDP, inflation, unemployment, rates and more
BEA: NIPA Handbook (opens in a new tab): how US GDP is measured
BLS: How the Government Measures Unemployment (opens in a new tab): labor-force definitions
Federal Reserve: Monetary policy (opens in a new tab): goals, tools and the policy framework
Bank of England: Money creation in the modern economy (2014) (opens in a new tab): McLeay, Radia and Thomas on how banks create money
NBER: Business Cycle Dating (opens in a new tab): US recession dates and definition
IMF: Balance of Payments Manual, 6th ed. (BPM6) (opens in a new tab): balance-of-payments accounting
Taylor (1993), Discretion versus policy rules in practice (opens in a new tab), Carnegie-Rochester Conference Series on Public Policy 39: the Taylor rule
Solow (1956), A Contribution to the Theory of Economic Growth (opens in a new tab), Quarterly Journal of Economics 70(1): the Solow model
Ramey (2019), Ten Years After the Financial Crisis (opens in a new tab), Journal of Economic Perspectives 33(2): fiscal multiplier evidence
N. Gregory Mankiw, Macroeconomics (Worth): intermediate text for growth, AD–AS and policy
Microeconomics: the companion sheet