The "plucking" model of the unemployment rate floor: cross-country estimates and empirics

BIS Working Papers  |  No 1159  | 
10 January 2024



We use unemployment rate (u-rate) data from 19 economies to analyse the uneven ups and downs in the economy – an idea from Friedman's "plucking theory". Larger upturns follow deeper downturns, but deeper downturns do not necessarily follow larger upturns. Bad shocks lift, or "pluck", the u-rate up from a floor, and then it rebounds. We estimate what that floor is in 19 economies and ask what this means for policy.


We add two things to the literature. The first is estimation. Using a mathematical approach adapted from recent literature, we show that as new data become available, estimates remain the same. These estimates are useful for policy in real time. Using US data, we also compare these estimates with those implied by a symmetric view of the economy. The second is policy. We analyse whether the link between inflation and the u-rate changes when the latter hits the floor. We then check whether shocks (including policy) feed into the rest of the economy differently when the u-rate is at the floor. This analysis matters for setting policies at central banks.


First, the u-rate floor can be easily estimated in real time as and when new data come in. Second, when the u-rate hits the floor, lower unemployment corresponds to even more inflation than at other times. That said, the trade-off is initially small. Third, how some shocks (like interest rate, price and output) affect the rest of the economy depends on whether the u-rate is at the floor, but others (exchange rate and debt) do not.


The unemployment rates (u-rates) of 19 economies (10 advanced and 9 emerging) demonstrate properties consistent with the plucking model. That the amplitude of expansions and subsequent contractions are unrelated, but that the deeper the contraction, the greater the subsequent expansion. The plucking model, which suggests that the u-rate hovers at or above a theoretical floor, has implications for the unemployment-inflation trade-off as well as shock propagation mechanisms, including the effects of policy shocks. This paper does three things. First, building on existing empirics, it demonstrates a straightforward way to estimate the u-rate floor based on identified peaks in the business cycle and interpolation methods. Second, it analyses the empirical relationship between the u-rate and core inflation, and the effect of a binding u-rate floor on this. Third, it analyses the threshold effects of the u-rate gap on the propagation of macroeconomic shocks, with special attention given to interest rates, using a threshold panel local projections model. The paper finds that: (i) the u-rate hovers at or above the floor and converges towards the floor after each downturn; (ii) the relationship between core inflation and the u-rate weakens when the u-rate is further from the floor; and (iii) the propagation of interest rate, price and output shocks display threshold effects, while exchange rate and debt shocks do not.

JEL classification: E24, E31, E32, E52

Keywords: plucking model, unemployment rate, nonlinear Phillips curve, threshold effects