Ambitious minimum wages of 60% or more of the national mean wage are currently being debated in many countries. This column discusses the trade-off policymakers face when setting minimum wages. A quantitative spatial general equilibrium model predicts that the welfare-maximising minimum wage is higher than the employment-maximising minimum wage. Beyond 50% of the mean wage, increases in the minimum wage reduce employment at an increasing rate. Therefore, the optimal minimum wage depends on the social welfare function.
The European Commission advocates an adequate minimum wage of 60% of the median wage. A recent report published by HM Treasury recommends a similar level. Germany’s Minister of Labour and Social Affairs has committed to a minimum wage of €12 per hour, about 70% of the national median wage and a nearly a 25% increase over the current level. The Raise the Wage Act would increase the US federal minimum wage to $15 per hour by 2025. Will such ambitious minimum wage increases improve the living conditions of low-wage workers as advocated by proponents or lead to massive job loss as feared by opponents?
A large literature provides ex-post evaluations of past minimum wage increases. It is fair to say that the empirical results are mixed (see Manning 2021 and Neumark and Shirley 2021 for recent reviews). Also, while this literature seeks to identify causal effects of minimum wages on employment with an increasing degree of sophistication, minimum wages affect many other economic outcomes. It is therefore difficult to conclude on whether higher minimum wages would be desirable based on the extant literature (Neumark 2017). Thus, we take a different approach to answering this question in a recent paper (Ahlfeldt et al. 2022).
We develop a quantitative spatial model with heterogeneous firms and a monopsonistic labour market to study minimum wage effects in spatial general equilibrium. This model is uniquely equipped to derive optimal minimum wage schedules. For one thing, it accounts for qualitatively and quantitatively heterogeneous employment responses in regions of distinct productivity. This allows us to predict both regionally differentiated and aggregate employment effects. At the same time, our model accounts for a broad range of minimum-wage effects that have recently been documented in the literature, including effects on labour force participation, tradable goods prices, housing rents, commuting costs, and worker-firm matching. This allows us to derive a worker welfare measure that incorporates all those general equilibrium channels along with the effects on wages and employment probabilities.
We quantify the model for more than 4,400 German municipalities using almost 30 million employment biographies per year, 20 million property transactions, and fine-grained bilateral trade data. Since average wages vary significantly between countries and over time, we use a relative minimum wage measure that is straightforward to generate within our model: The ratio of the minimum wage over the mean wage. Since the OECD reports this measure along with the Kaitz Index (ratio of minimum wage over median wage) for various countries, it is easy to put our results in international perspective.
To speak to the question of what minimum wage might be optimal, we use the calibrated model to simulate the effects of a range of minimum wage levels. We summarise the results at the national level in Figure 1. The simulated regional effects on several outcomes such as real wages, employment, welfare, and labour force can be conveniently explored in interactive maps here.
Figure 1 Minimum wage effects on employment, equity, and welfare
Notes: Results are model-based counterfactuals. Employment is the total number of workers in employment. Equity is measured as 1-G where G is the Gini coefficient of real wage inequality across all workers in employment. Welfare is the expected utility. It captures individuals who are active on and absent from the labour market and accounts for minimum wage effects on employment probabilities, wages, tradable goods prices, housing rents, commuting costs, and worker-establishment matching qualities. In the short run, workers are immobile across residence locations whereas workers re-optimise their residential location choice in the long run.
In a nutshell, our simulations reveal that ambitious federal minimum wages may achieve a reduction in wage inequality without having a detrimental effect on welfare – compared to the counterfactual of no minimum wage. However, they will likely cause significant job loss. While employment effects remain small up until about 50% of the national mean wage, they build up at an increasing rate at higher levels. Given that the current German federal minimum wage has remained close to 48% of the national mean wage ever since its introduction in 2015, our model simulations are in line with reduced-form evidence pointing to small employment effects (Ahlfeldt et al. 2018, Dustman et al. 2021). Based on the simulated employment effects, however, we must caution against extrapolating from encouraging reduced-form evidence on employment effects of moderate minimum wages to the likely effects of more ambitious levels.
We recommend that ambitious minimum wages are implemented in small steps, under careful evaluation of short-run employment effects so that potential tipping points can be detected in time.
More generally, our results illustrate how the desirability of any minimum wage will depend on the considered relative level and the social welfare function. In setting minimum wages, policy makers trade employment, equity, and welfare effects and, depending on priorities, different minimum wage levels will be optimal. As an example, maximising employment requires setting a relatively low level – in the case of Germany, about 38% of the national mean wage (42% of the national median wage or €7.60 per hour in absolute terms). This should generate a small positive employment effect, but also negligible equity and welfare effects. Maximising welfare requires a more ambitious minimum wage of 58% of the national mean wage (64% of the national median wage or close to €12 per hour in absolute terms), which will also lead to a greater reduction in nominal wage inequality. Any increase in the minimum wage level within these bounds will trade positive equity and welfare effects against negative employment effects. Of course, even higher minimum wage levels can be advocated on the grounds of an equity objective. In fact, our simulations suggest that the minimum wage could be set as high as 70% of the national mean wage (77% of the national median wage or €14 per hour) before the welfare effect would turn negative. However, recommending such a high minimum wage level would imply that one strictly cared about the expected real wage – the product of the real wage earned conditional on being in employment and the employment probability – without any aversion to higher unemployment rates.
While these trade-offs may appear frustrating from a policy perspective, our analysis also reveals some more encouraging news. Rather than going down the route of ever higher federal minimum wages, policymakers have the alternative of implementing regional minimum wages. We find that regional minimum wages – if set for spatial units no larger than counties—are targeted policy instruments that mitigate the trade-off of negative employment effects and positive welfare effects. To illustrate the potential, the employment-maximising minimum wage, at 50% of the municipality mean wage, could increase welfare by 4% – as much as the welfare-maximising federal minimum wage and generate a sizable positive employment effect of 1.1%.
Ahlfeldt, G, D Roth and T Seidel (2018), “Spatial implications of minimum wages”, VoxEU.org, 04 September.
Ahlfeldt, G M, D Roth and T Seidel (2022), “Optimal minimum wage”, CEPR Discussion Paper 16913.
Dustman, D, A Lindner, U Schӧnberg, M Umkehrer and P vom Berge (2021), “Reallocation effects of the minimum wage”, VoxEU.org, 07 October.
Manning, A (2021), “The Elusive Employment Effect of the Minimum Wage”, Journal of Economic Perspectives 35(1): 3–26.
Neumark, D and P Shirley (2021), “Myth or Measurement: What Does the New Minimum Wage Research Say about Minimum Wages and Job Loss in the United States?”, NBER Working Paper No. 28388.
Neumark, D (2017), “Promising ideas for future research on the employment effects of minimum wages”, VoxEU.org, 09 October.