Another way to measure matching efficiency is to estimate a relationship between the aggregate job-finding rate and the labour market conditions.^[10] The estimated model is ln(M_t/U_t)= a + b*ln(V_t-1/U_t-1) + ε_t where M is the number of matches, U is the number of unemployed persons and V is the number of vacancies. The model thus shows how the aggregate job-finding rate (the number of matches in relation to the number of unemployed persons) is explained by the labour market conditions (the number of vacancies in relation to the number of unemployed persons in the previous period). The model is estimated with quarterly data for the period 1997–2014, after which a forecast is made of the job-finding rate for 2015–2024, in which job opportunities are assumed to follow the historical relationship with the labour market conditions. The model assumes that the matching function is constant over time, so that all variation in the job-finding rate is driven by fluctuations in vacancies and unemployment, and that matching is random. The aggregate job-finding rate is defined here as the proportion of unemployed persons who move from unemployment to employment in one quarter. The labour market conditions are defined as the number of vacancies in relation to the number of unemployed persons in the previous quarter.

Figure 6 shows an estimate of the historical correlation between the job-finding rate and the labour market conditions (red line) from 1997 to 2014 and thereafter a model forecast of what the job-finding rate would have looked like if it had followed this historical correlation (red dashed line).^[11] After 2014, refugee arrivals were very high for some years, leading to an unusually high inflow into the labour market of groups with a low job-finding rate. This by definition entails poorer matching efficiency. If the latter time period is included in the estimation, the model estimate gives much lower expected job-finding rates. We have chosen to estimate the historical correlation for the period 1997–2014, as part of the purpose of the analysis is to see whether matching efficiency has returned to the historical correlation that applied before the major refugee crisis in 2015. The figure shows that the expected job-finding rate varies with the economic situation. Unemployed persons are much more likely to find employment in booms than in recessions. The figure also shows that the actual job-finding rate (blue line) was significantly lower than the model forecast between the third quarter of 2016 and the first quarter of 2020. Since then, the actual job-finding rate has been volatile but broadly in line with what is suggested by the historical correlation with labour market conditions. The matching function thus shows that matching efficiency was low for a long period but that it has recovered in recent years.

Figure 6. Matching function 1997–2024 Job-finding rate, per cent