Peter Skott;Adam Aboobaker;

• 1:Aalborg University Business School
• 2: Aalborg University
• 3:Global Development Institute
• 4: University of Manchester

Abstract：

Like the functional distribution of income, wage inequality is subject to fairly regular cyclical fluctuations. In this paper, we(i) analyze sources of these fluctuations,(ii) present models of endogenous cycles that include heterogeneous labor and wage inequality,(iii) show that these models generate patterns of both wage inequality and the functional income distribution that are in line with the evidence, and(iv) caution against any extrapolation of cyclical patterns to long-term trends and beliefs in expansionary aggregate demand policy as the key instrument to promote greater economic equality.

Key Words： wage inequality;Goodwin cycles;functional distribution;aggregate demand policy

Abstract:

Keywords:

Foundation:

Authors: Peter Skott;Adam Aboobaker;

References：

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• (1)Large public sectors or the presence of other significant non-capitalist sectors can also introduce noise into the patterns predicted by models of a pure capitalist economy.The evidence on Goodwin patterns is discussed in greater detail in Zipperer and Skott (2011) and Barrales-Ruiz et al.(2021).
• (2)Burdett and Mortensen consider an extension of the model that retains the assumption of identical workers but introduces two types of firms,one type having a higher labor productivity than the other.This extended model still generates anon-degenerate wage distribution.There will be wage dispersion among both low and high productivity firms,with all high productivity firms offering wages above the range offered by low productivity firms.Like the extended model,in a recent paper examining trends in wage inequality in the US,Autor et al.(2024) assume the co-existence of low- and high-productivity firms.
• (3)Autor et al.(2024) employ this theoretical framework in their interpretation of the recent of US wage inequality.Tightening labor markets in an economy with labor market frictions,they argue,led to an increase in the elasticity of labor supply,inducing firms to raise wages,especially in low wage firms.Hirsch et al.(2018) also interpret their findings of the cyclicality of wage patterns in German administrative data using a monopsony model.
• (4)As a simple example,suppose there 10 types of jobs (numbered 1 to 10) and that the pre-compression wages of group i are distributed uniformly over the interval (i-1,i).Following the within-group compression,all workers in group i receive a wage of (i-0.5).The aggregate 90/10 ratio increases from 9 to 19 as a result of the within-group compression.Other inequality measures will decrease in this example.But modify the assumptions and consider a positive shock to the demand for goods produced by workers in the top decile.Firms' monopsony power declines in this segment but the compression is confined to this segment.For simplicity,suppose that after the shock all workers in the top decile receive a wage of 10.Any reasonable measure will show a widening of inequality despite a reduction in monopsony power.
• (5)The variations in the ratio of employed workers do not in general mirror those in the ratios of unemployed workers:the ratio of employed workers with a college degree to employed workers with high school degrees is negatively correlated with the aggregate employment rate,but the ratio of those unemployed with a college degree to those unemployed with high school degrees was also negatively correlated with the aggregate employment rate in recent decades (Mueller,2017).Mathematically,if x and y both lie in the unit interval,the growth rates of (x/y) and (1-x)/(1-y) are given by ■,respectively.Thus,both growth rates can be negative if x>y and ■
• (6)The Leontief coefficients can be interpreted as describing the choice of technique along the steady growth path.Whatever substitutability may exist in the long run,the labor inputs are complementary in the short run,and cyclical fluctuations around a steady growth path leave the choice of technique largely unaffected.
• (7)The presence of significant mismatch is consistent with assignment or matching models (e.g.Sattinger,2006;Albrecht and Vroman,2002;Dolado,et al.,2009) as well as with efficiency wage models that distinguish between the skill requirements of the job and the skills of the worker (Skott,2006;Slonimczyk and Skott,2012).
• (8)Federal Reserve Bank of New York,The Labor Market for Recent College Graduates;https://nyfed.org/collegelabor
• (9)Equation (9) implies that if the aggregate employment rate is at (or above) 80 percent and β=0.5,the condition will be satisfied as long as the employment rate of college workers in tech jobs is at (or above) 65 percent.
• (10)The perceived fairness of the wage determines workers' effort in some efficiency wage models (e.g.Akerlof and Yellen,1990).Social norms—including fairness norms—typically exhibit path dependency;they are reinforced when outcomes conform to the norm but become undermined and lose power if outcomes violate the norms.This path dependency can map into path dependent employment rates and wage patterns (Skott 2005,2023a chapter 6).
• (11)The general price level over the contract period will not be known when nominal wages are set,and the real wages wT and wM should more accurately be referred to as the expected real wage.Since we are interested in the relative wage,wM/wT,this distinction between real and expected real wages will be irrelevant if the same expected price level is used in the determination of the real wages.
• (12)With output as exogenously given,standard assumptions treat the real wage as an increasing function of the employment rate and the level of unemployment benefits.Thus,with two distinct labor markets and induced mismatch,we would expect to have ■ and ■ Using equation (*) to substitute for wM in equation (10),the efficiency wage argument generates the same reduced form for the relative wage.Taking the level of unemployment benefits as exogenously given,this variable has been omitted from equation (11).
• (13)The effect of an increase in tech employment may also appear to be ambiguous.From an economic perspective,however,it would seem highly unlikely for an increase in tech employment to have a larger effect on manual wages than on tech wages.
• (14)Indivisibilities in plant size and the use of excess capacity as a deterrent to new entry may accentuate the desire for excess capital capacity.
• (15)In a contemporary version of the two-class approach,Foley et al.(2019) assume that capitalists optimize intertemporally with an infinite horizon,while workers engage in life cycle saving,leaving no bequests.Their specification implies that aggregate consumption is determined by aggregate wage income,aggregate wealth and the share of wealth owned by capitalists.
• (16)Nominal wages are sticky,and sticky prices may be a reasonable approximation in some activities (mainly within the service sector).Other activities,however,exhibit great price flexibility and sticky output,and the general presumption among both post- and new-Keynesians of all prices as being highly sticky is empirically questionable (Skott,2023a,chapter 10).The extended model in section 3.3 includes wage and price Phillips curves and cyclical variations of real wages.A constant real wage would be consistent with constant markups on normal unit labor cost (as argued by Lavoie,2014 and others).
• (17)The system also has a trivial solution with l=e=0.For the non-trivial solution to be economically meaningful,we must have 0
• (18)The desired utilization rate is likely to depend on structural features that may vary over time.For present purposes,we ignore these complications and take ld as constant.
• (19)The Jacobian matrix is given by ■ The determinant (-λKleh3) is unambiguously positive and,evaluated at the stationary solution,the trace is equal to lλK(h1-1)+lh2+eh3 .
• (20)Skott and Zipperer estimate the effects of profitability and employment on output growth.The results have implications for the specification of employment growth because of the relation between labor productivity and the profit share (equation (17)) and between employment and output growth.
• (21)Steady growth solutions of T/K=M/K=0.5,LHM/N=0.7 in combination with equations (3)～(4) and (7)～(8) imply that in steady growth N/K=17/28,(LCT+LCM)/N=0.575(28/17)≈0.95 LCT/N=14/17 and e=(M+T)/(2N)=0.5(0.7+0.575*(28/17))≈0.825.
• (22)The introduction of nonlinearities to prevent upward divergence is straightforward and easy to justify.As pointed out by Hicks (1950),it is the floor under the downturn that presents a problem.
• (23)The robustness is further improved by recognizing that policy rules can and do change.Deep depressions or explosive inflation provoke the development of new instruments and policies.Central banks reacted to the financial crisis and a binding zero lower bound by adding quantitative and qualitative easing to their toolbox,while discretionary fiscal expansion was rediscovered with the stimulus package in 2009 and used more aggressively during the COVID pandemic.
• (24)See Ryoo and Skott (2017) and Franke (2018) for analyses of stabilization policy in models with Harrodian instability.
• (25)Wage heterogeneity is typically abstracted from in heterodox macro models.Tavani and Vasudevan (2014),Carvalho and Rezai (2016),and Palley (2017) are among the exceptions;unlike in the present paper,these contributions analyze the effects of exogenously given wage heterogeneity on long-run growth in models without Harrodian instability and endogenous cycles.
• (26)In an open economy nominal wage gains may raise real wages via its effects on the real exchange rate.The resulting decline in international competitiveness and a deteriorating balance of payments are likely to make these gains unsustainable.
• (27)These issues are discussed in greater detail by Auerbach and Skott (2021),Aboobaker and Skott (2025) and Skott (2025) .