Beveridge Curve

Origins — Lord Beveridge and the postwar labour problem

William Beveridge, architect of the British welfare state, did not invent the curve that bears his name. The diagram first appeared in scattered postwar studies of vacancies and unemployment — Bowen and Berry (1963) in the US, Dow and Dicks-Mireaux (1958) in the UK — but acquired Beveridge's name because of his 1944 white paper Full Employment in a Free Society, which made the vacancy–unemployment relationship a centrepiece of labour-market analysis. Today every Federal Reserve research department, every IMF country desk, and every search-and-matching macro paper reproduces the Beveridge plot.

The diagram is austere. On the horizontal axis is the unemployment rate u = U/L, the fraction of the labour force without a job and actively looking. On the vertical axis is the vacancy rate v = V/L, the fraction of the labour force represented by unfilled posted positions. Each month, the economy lands on one point in (u, v) space. Connecting those points over time produces a locus that slopes downward and is convex to the origin — the Beveridge curve.

Why the curve slopes downward

The intuition is matching. Take the standard Cobb-Douglas matching function used in Diamond-Mortensen-Pissarides search models:

M_t = μ · U_t^α · V_t^(1−α)

where M is the flow of new hires per period, μ is the matching-efficiency parameter, and α ≈ 0.5 is the matching elasticity with respect to unemployment. In steady state, the inflow into unemployment (separations) must equal the outflow (matches):

s · (1 − u) = μ · u^α · v^(1−α)

Solve for v as an implicit function of u: v decreases as u increases for fixed s and μ. As unemployment rises, fewer vacancies are needed to clear the same flow because there are more unemployed workers per vacancy and matching speeds up. The locus is the Beveridge curve. It slopes negatively and is convex because of the Cobb-Douglas structure.

The curve is "structural" only in the sense that it depends on the parameters s, μ, and α. Changes in those parameters shift the curve. Changes in aggregate demand move the economy along it.

Cyclical loops — clockwise around the business cycle

Watch the actual data, not the steady-state diagram, and the curve gets richer. Entering a recession, employers stop posting new vacancies before lay-offs ramp up, so the economy moves leftward and slightly downward — vacancies fall while unemployment is still low. As the downturn deepens, layoffs accumulate and unemployment climbs while vacancies stay depressed — the economy traverses the bottom-right of the curve. Recovery is the mirror image: firms post vacancies before unemployment falls (top-right), and only later does unemployment work its way back down to the pre-recession level (back to the upper-left). The loops are clockwise.

The 2008-2014 US Beveridge loop was unusually large and prompted serious concerns about a permanent outward shift. By 2014 the curve had largely returned to the pre-2008 locus, and the broad lesson was reinforced: outward movements during recoveries often reflect slow churn through the matching technology, not permanent damage. The COVID experience, with its rapid and enormous shift, has tested that interpretation again.

When the curve shifts — diagnosing matching breakdown

The most informative use of the Beveridge curve is in identifying parallel shifts. If for a given vacancy rate the unemployment rate is now higher than it used to be, the curve has shifted outward — and that means matching efficiency μ has fallen. Three structural channels typically generate such shifts.

• Skills mismatch. Posted vacancies require skills the unemployed don't have. Classic example: manufacturing layoffs producing displaced workers whose machine-shop skills don't match expanded software-sector vacancies. Sahin et al. (2014) estimate that 1-3 percentage points of US unemployment in 2009 was due to mismatch, much of it sectoral.
• Geographic mismatch. Vacancies are in places the unemployed aren't, and migration costs prevent the workers from following. The post-2008 collapse in US interstate mobility — caused partly by underwater mortgages locking workers into depressed regions — has been argued to contribute to mismatch (Mian and Sufi, 2014).
• Reservation-wage shifts. Unemployed workers won't accept offered wages, often because unemployment insurance is generous or because preferences have shifted. The pandemic-era expansion of UI benefits and pandemic-era reassessment of work-life balance have both been invoked.

The post-COVID shift and the inflation debate

The 2020-2024 Beveridge experience was extraordinary. By mid-2022 the US unemployment rate was 3.5 percent — historically associated with vacancy rates around 4.5 percent — yet the vacancy rate was running near 7 percent. The curve had shifted outward by roughly 30 percent. Similar shifts occurred in the UK, euro area, and Canada.

The shift triggered a famous policy debate. Blanchard, Domash, and Summers (2022) used the shift to argue that the natural rate of unemployment had risen — perhaps to 5 percent — and that bringing inflation back to target would require unemployment to climb materially above that level, implying a recession. Their inference was Beveridge-based: an outward shift in the curve means u* is higher, so the labour market in 2022 was tighter than the headline unemployment number suggested.

Bernanke and Blanchard (2024), in a much-discussed Brookings paper, refined the view. They concluded that most of the early COVID shift reflected temporary frictions — quit rates that snapped back, sectoral reallocation that resolved — and that the residual permanent component was much smaller, around 0.5 percentage points. By late 2023 and into 2024, US data has partially confirmed: the vacancy rate fell from 7 percent toward 5 percent without unemployment rising materially, an inward shift of the curve consistent with the matching-efficiency story rebounding.

A worked numerical example

Suppose the matching function is M = 0.7 · U^0.5 · V^0.5, the separation rate is s = 0.03 per month, and the labour force is normalised to 1. In steady state, s·(1−u) = M, so:

0.03·(1 − u) = 0.7 · sqrt(u·v)
sqrt(u·v) = 0.0429·(1 − u)
u·v = 0.00184·(1 − u)²
v = 0.00184·(1 − u)² / u

At u = 0.04 (4 percent unemployment), v = 0.00184·(0.96)²/0.04 ≈ 0.0424 — a 4.2 percent vacancy rate.

At u = 0.06 (6 percent unemployment), v = 0.00184·(0.94)²/0.06 ≈ 0.0271 — a 2.7 percent vacancy rate.

The downward slope is clear: a 2-percentage-point rise in unemployment is associated with a 1.5-percentage-point fall in vacancies. The convexity comes from the (1−u)²/u shape.

Now suppose matching efficiency falls by 25 percent: μ goes from 0.7 to 0.525. Reworking the algebra, at u = 0.04 the vacancy rate must now be roughly 30 percent higher — about 5.5 percent — to clear the same flow of separations. The curve has shifted outward.

Comparison — what the shape tells you

Pattern	What's happening	Cause	Policy implication
Movement along the curve	Cyclical fluctuations	Aggregate demand shock	Standard counter-cyclical monetary/fiscal
Clockwise loop	Normal recession dynamics	Vacancies adjust before unemployment	Patience — loop closes on its own
Outward shift	Matching efficiency μ falls	Skills, geographic, or reservation-wage mismatch	Training, mobility subsidies, UI reform
Inward shift	Matching improves	Better job search tech, online matching, lower frictions	Welcome news — u* may have fallen
Steep curve	Vacancy-heavy slack	Strong labour demand	Watch for wage pressure
Flat curve	Unemployment-heavy slack	Weak demand	Stimulus needed

The matching function in detail

The Cobb-Douglas matching function M = μ · U^α · V^(1−α) is empirically robust but not mechanically derived — it's a reduced-form representation of a complex search process. The parameter α governs how matches respond to relative scarcity of workers versus jobs. Petrongolo and Pissarides (2001), in a comprehensive survey, find α typically estimated between 0.4 and 0.6, with 0.5 as the modal value used in calibrated DSGE models. The efficiency parameter μ captures everything else: how good the job-search technology is, how well workers and jobs are matched in characteristics, how much friction the institutional environment imposes.

In the full Diamond-Mortensen-Pissarides model, the Beveridge curve is one of two equilibrium relations. The other is the job-creation curve, derived from the firm's free-entry condition. Their intersection determines the equilibrium (u, v) pair. Shocks to productivity, separations, or matching efficiency move both curves; the Beveridge curve framework isolates the matching-efficiency channel.

Practical uses for forecasters and central banks

• Slack measurement. Combine the Beveridge curve with a job-creation curve to estimate u* — the natural rate of unemployment — in real time. The Kansas City Fed and the IMF have published Beveridge-based u* estimates since the early 2010s.
• Inflation forecasting. If the Beveridge curve has shifted outward, the inflationary pressure from a given unemployment rate is higher than the pre-shift relationship would suggest. Domash-Summers (2022) used this logic to argue for aggressive Fed tightening.
• Recession diagnosis. The trajectory in (u, v) space distinguishes recession types. A 2001-style demand-driven recession moves along the curve. A 2020-style supply shock or shift-driven recession can pop the economy off the curve.
• Cross-country comparison. Different countries' Beveridge curves have different positions and slopes, reflecting labour-market institutions. The euro-area periphery sits further from the origin than the US — more unemployment per vacancy — reflecting higher structural frictions.
• Industry-level analysis. JOLTS publishes vacancy data by industry. Sector-specific Beveridge curves can identify which industries have especially poor matching, useful for targeted training programs.

Limits and common pitfalls

• Vacancy measurement. Vacancy data is the weak link. JOLTS only began in late 2000. Pre-JOLTS, the Conference Board Help-Wanted Index served as a proxy but broke when job ads moved online. Cross-country comparisons are hampered by definitional differences.
• "Outward shift" can be transitory. The post-2008 outward movement looked permanent for a while but partially reversed by 2014. The post-COVID shift also appears to be reversing. Permanent shift claims should be made cautiously.
• The curve is not the natural rate. The Beveridge curve tells you about matching frictions, not about the inflation-compatible unemployment rate directly. You need to combine it with a wage-Phillips relationship to extract u*.
• Loops and shifts are easy to confuse. A clockwise loop during a recession can look exactly like an outward shift in the early stages. Only the full path through the cycle tells you which it was.
• Endogeneity. Policy itself affects the curve. UI extensions can shift it outward in the short run; training programs can shift it inward over time. Causal inference is difficult.
• Heterogeneity. Aggregate Beveridge curves average over workers and jobs that differ markedly. A small fraction of mismatched workers can drag the aggregate curve outward.