Minimum wages in an automating economy

• Published date: 01 February 2022
• Author: Marcel Steffen Eckardt
• Date: 01 February 2022
• DOI: http://doi.org/10.1111/jpet.12528

J Public Econ Theory. 2022;24:58–91.58

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wileyonlinelibrary.com/journal/jpet

Received: 10 November 2020

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Revised: 9 April 2021

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Accepted: 16 May 2021

DOI: 10.1111/jpet.12528

ORIGINAL ARTICLE

Minimum wages in an automating economy

Marcel Steffen Eckardt

Department of Law and Economics,

Technical University of Darmstadt,

Darmstadt, Germany

Correspondence

Marcel Steffen Eckardt, Department of

Law and Economics, Technical

University of Darmstadt,

Hochschulstraße 1, D‐64289 Darmstadt,

Germany.

Email: eckardt@vwl.tu-darmstadt.de

Abstract

We explore the suitability of the minimum wage as a

policy instrument for reducing emerging income in-

equality created by new technologies. For this, we

implement a binding minimum wage in a task‐based

framework, in which tasks are conducted by machines,

low‐skill, and high‐skill workers. In this framework, an

increasing minimum wage reduces the inequality be-

tween the low‐skill wage and the other factor prices,

whereas the share of income of low‐skill workers in the

national income is nonincreasing. Then, we analyze

the impact of an automating economy along the ex-

tensive and intensive margins. In a setting with a

minimum wage, it can be shown that automation at

the extensive margin and the creation of new, labor‐

intensive tasks do not increase the aggregate output in

general, as the displacement of low‐skill workers

counteracts the positive effects of cost‐savings. Finally,

we highlight a potential trade‐off between less in-

equality of the factor prices and greater inequality of

the income distribution when a minimum wage is in-

troduced into an automating economy.

KEYWORDS

automation, displacement effects, employment, inequality,

labor demand, minimum wage, tasks, wages

JEL CLASSIFICATION

E25, J20, J31, J38

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

© 2021 The Authors. Journal of Public Economic Theory published by Wiley Periodicals LLC

1|INTRODUCTION

In the last decades, new technologies, such as artificial intelligence and robots and other forms

of automation, have been rapidly developing. These new technologies will likely have a sig-

nificant impact on the economy. In particular, the labor market will change fundamentally in

the future (e.g., Brynjolfsson & McAfee, 2014; Ford, 2015). Frey and Osborne (2017) explore the

susceptibility of jobs in relation to automation and estimate that approximately 47% of current

jobs in the United States (US) could be automated within one or two decades. Empirical studies

show that automation has a substantial impact on routine tasks, leads to a polarized labor force,

and increases inequality in the economy (e.g., Acemoglu & Restrepo, 2020a; Autor, 2015;

Autor & Dorn, 2013; Autor et al., 2003,2015; Goos & Manning, 2007; Graetz & Michaels, 2018).

Moreover, Goos et al. (2019) emphasize that the adjustment costs from automation on un-

employed job seekers are unequally distributed between low‐skill and high‐skill workers. To

reduce the emerging inequality various policy instruments, such as taxing robots, a basic

universal income, or a minimum wage, are discussed (e.g., Acemoglu et al., 2020; Costinot &

Werning, 2018; Freeman, 2015; Furman, 2019; Guerreiro et al., 2017; McAfee & Brynjolfsson,

2016; Thuemmel, 2018).

Little is known, however, about the effects of the minimum wage in conjunction with

automation. In one of the few existing studies, Lordan and Neumark (2018) empirically show

that higher minimum wages reduce employment in automatable jobs. Moreover, they em-

phasize that there are groups of workers, such as older and less‐skilled workers, that are

frequently ignored in the empirical literature on the effects of minimum wages. However, it

appears that scarcely any theoretical work exists on the effects of a minimum wage in a task‐

based framework, in which tasks are increasingly conducted by machines replacing low‐skill

workers. One exception is the work by Aaronson and Phelan (2019), who develop a theoretical

framework based on tasks to test for the labor market consequences of minimum wages.

The aim of this paper is to explore the effects of a binding minimum wage on aggregate

output, employment, factor prices, and various measures of the income distribution in an

automating economy.

To analyze the labor market effects of a minimum wage in conjunction with automation, we

build on the work of Acemoglu and Restrepo (2018a,2018b,2018d) and that of Acemoglu and

Autor (2011), both of which are interconnected, and are based on Zeira (1998) and Acemoglu

and Zilibotti (2001). A task‐based framework takes up the notion of labor markets that can be

empirically characterized by the task content of jobs (e.g., Goos et al., 2019). Theoretically, a

task‐based framework allows us to model automation along intensive and extensive margins

(Acemoglu & Restrepo, 2018c), also with respect to the effects that may arise in the interplay

with the introduction of a minimum wage. In our task‐based framework, tasks in a unit interval

are conducted by machines, low‐skill, and high‐skill workers. The range of tasks that machines

and low‐skill workers can produce is bounded by exogenous thresholds. The assumption of

comparative advantage for each production factor on a subset of the tasks leads to a simple

allocation of the factors. Hence, our task interval is divided into three intervals with increasing

complexity, where machines produce the tasks in the first interval, low‐skill workers produce

the tasks in the middle interval, and high‐skill workers produce the tasks in the last interval. By

assuming a fixed and inelastic supply of machines, low‐skill, and high‐skill workers, we im-

plement a minimum wage that is higher than the equilibrium low‐skill wage and determine the

new equilibrium.

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Under an automating economy, we understand the impact of technological progress on

changing exogenously the thresholds of tasks, the productivity of production factors, and the

task interval. More precisely, we consider the consequences of increasing automation, whereby

we distinguish between automation at the extensive and intensive margins. Automation at the

extensive margin increases the measure of tasks that machines are able to produce whereas

automation at the intensive margin (which we call the “deepening of automation”) means that

the productivity of machines on the tasks increases (e.g., by replacing older machines with

newer ones). Analogously to the increasing automation, technological progress can enable low‐

skill and high‐skill workers to raise their productivity in their tasks and their range of tasks.

Furthermore, technological progress can lead to the creation of new, more complex tasks that

are labor‐intensive, as assumed above.

First, we analyze the effects of an increase in the minimum wage and show that the low‐

skill employment, and thus the aggregate output, decrease. Moreover, a higher minimum wage

reduces the inequality between the low‐skill and the high‐skill wage, as well as the rental rate

of machines. In other words, machines and high‐skill workers become relatively cheaper than

low‐skill workers: this can lead to a displacement of low‐skill workers wherein the share of

their income in the national income decreases. Furthermore, the expected low‐skill wage

decreases. Here, we consider the expected low‐skill wage as a group‐specific welfare measure of

low‐skill workers, as the income of the low‐skill workers who retain their job increases,

whereas the income of those who become unemployed falls to zero.

Subsequently, we explore the effects of an automating economy in the presence of a

minimum wage. We start by increasing automation at the extensive margin. Machines displace

low‐skill workers if they are relatively cheaper in performing the new tasks. On the one hand,

this increases the aggregate output that has a positive impact on the labor demand. On the

other hand, the displacement of low‐skill workers from the tasks, which are automated, re-

duces the demand for low‐skill workers and, consequently, the low‐skill employment that has a

negative impact on the aggregate output. We observe two counteracting effects of the dis-

placement of low‐skill workers on the aggregate output and on low‐skill employment. The

magnitude of these effects decides whether the impacts on the aggregate output and low‐skill

employment are positive or negative. In particular, it is possible that the impact on the ag-

gregate output is positive and the impact on low‐skill employment is negative. Therefore, in

contrast to Acemoglu and Restrepo (2018a,2018b,2018d), the impact on aggregate output and

low‐skill employment is ambiguous whenever there is a displacement of low‐skill workers in

the economy with a binding minimum wage.

We show that automation at the intensive margin raises the aggregate output, the rental

rate, and the high‐skill wage. Consequently, as the low‐skill wage is fixed by the minimum

wage, the inequality between the low‐skill wage and the other factor prices increases. Fur-

thermore, low‐skill workers can displace high‐skill workers in some cases and this can be

greater than the displacement of machines. This is contrary to the model without a minimum

wage (e.g., Acemoglu & Restrepo, 2018a). Moreover, the sign of the effect of the deepening of

automation on the employment is ambiguous. Analogously, we can consider an increase in the

productivity of low‐skill or high‐skill workers. If the productivity of high‐skill workers in-

creases, the mechanisms are similar and lead to the same results. If the productivity of low‐skill

workers increases, their employment increases and the share of income of low‐skill workers in

the national income is nondecreasing, as low‐skill workers can displace machines and high‐

skill workers in some cases.

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