Minimum Wages in the UK Searching for Non-linearities David Zentler-Munro UCL April 2018
Motivation Introduction ➓ Minimum wages are an increasingly popular policy Motivation Methodology/ response to low wage growth for low paid workers. Literature Model Figure: Minimum wages on the rise Environment - Workers Environment - Firms Calibration Results Conclusion 2/30
Motivation Introduction ➓ Political logic behind minimum wage (MW) increases Motivation Methodology/ Literature in UK seems to be: “introduction of MW doesn’t seem Model to have hit unemployment, so let’s put it up some Environment - Workers more” Environment - Firms Calibration ➓ This is risky: is it a linear relationship or are there Results nonlinearities to be wary of? Conclusion ➓ To answer this, we need a model to forecast impacts. ➓ The model presented here can, eventually, help to address this and a wide range of questions: 1. Are there significant nonlinearities in minimum wage impacts? 2. How does minimum wage compare to other redistributive policies? 3. What are likely long term impacts on e.g. productivity, capital use, income and wealth inequality? 3/30
Preview of Results Introduction Motivation ➓ We develop a model that combines search frictions Methodology/ Literature with a production function featuring several margins of Model substitution between factor inputs. Environment - Workers Environment - Firms ➓ Nonlinear unemployment reaction in model from: Calibration 1. Exogenous nonlinearities : Results ➓ Non-uniform distribution of skills. Conclusion 2. Endogenous nonlinearities : ➓ Vacancy creation with Cobb-Douglas matching function ➓ Imperfect substitution between capital and labour and between labour types ➓ When calibrated to the UK economy, we find: 1. quantitatively, imperfect substitution between inputs is most important endogenous source of nonlinearities 2. nonlinearity in unemployment lies within range of minimum wages planned in UK over next two years. 4/30
Outline Introduction Motivation Methodology/ Literature Model 1 Introduction Environment - Workers Environment - Firms Calibration 2 Model Results Conclusion 3 Calibration 4 Results 5 Conclusion 5/30
Methodology: Key Ingredients Introduction Motivation Methodology/ Literature Model Environment - Workers 1. Frictional Labour Markets . Search frictions can help Environment - Firms explain findings of small impacts of UK minimum Calibration wage on employment and firm exit. Results Conclusion 2. Capital. How does the minimum wage affect firms’ choice of capital vs. labour? 3. Heterogeneous Agents. Will minimum wage hikes cause companies to substitute towards higher skill workers? 6/30
Methodology: Ingredients Missing... Introduction Motivation Methodology/ Literature 1. Hours Worked . Labour is entirely discrete, but model Model could be extended to include hours worked, as chosen Environment - Workers by firms and workers. Environment - Firms Calibration 2. Participation Margin . We do not consider positive Results impact of minimum wage on labour market Conclusion participation. Again useful extension. 3. Firm Heterogeneity . All firms use same technology in this model. But could there be a useful role for minimum wage in eliminating low productivity firms? 4. Business Cycles . Should minimum wage increase in recession to provide stimulus to high MPC workers, or decrease to support labour demand? 7/30
Related Literature Introduction 1. Structural literature on optimum minimum wage Motivation Methodology/ ➓ Search with wage posting - van den Berg and Ridder Literature Model (1998): no unemployment effects until minimum wage Environment - equals productivity level then match is destroyed Workers Environment - Firms ➓ Search with wage bargaining - Flinn (2006): if vacancy Calibration creation is present then smooth unemployment Results response until minimum wage equals productivity Conclusion level then match is destroyed ➓ Contribution : Introduction of decreasing returns to labour in search frameworks, removes cliff-edge effects. 2. Empirical literature on UK minimum wage Small employment effects, decrease in firm profits and limited price effects e.g. Leonard et al (2014), Draca and Machin (2011). ➓ Contribution : Developing a model consistent with these findings, but also capable of examining future risks. 8/30
The Model: Environment Introduction Motivation Methodology/ Workers . Literature Model ➓ Workers differ in observable skill level, which is given Environment - Workers (not chosen). Environment - Firms Calibration ➓ Two broad skill types - unskilled and skilled ( u and s ). Results ➓ Within broad skill types workers, workers differ by Conclusion unobservable productivitiy level. ➓ Unobservable productivity, indexed by i , of a skilled (unskilled) worker is denoted x s , i ( x u , i ), for i = 1.. M ➓ Productivity is distributed exogenously according to the pdf l s ( x s , i ) ( l u ( x u , i ) ) ➓ Both workers and firms have a common discount factor, β and are risk neutral 9/30
The Model: Environment Introduction Motivation Methodology/ Firms Literature Model ➓ We wish to allow for both capital to labour substitution Environment - Workers in production and substitution between skill types. Environment - Firms Calibration ➓ Not easy in pure search/match framework. Results ➓ Proposed solution is to have two sectors of production: Conclusion 1. Intermediate sector with search frictions . Intermediate firms hire labour and sell it onto a final good producer - think of hiring agencies. ➓ One segmented intermediate sector for each skill and productivity level of workers. 2. Final good sector that combines labour hired in intermediate sector and capital, with no frictions. Capital-skill complementarity as per Krusell et al (2000) - “KORV” production function. 10/30
The Model: Environment Introduction Motivation Figure: Model Economy Overview Methodology/ Literature Model Environment - Workers Environment - Firms Calibration Results Conclusion 11/30
The Model: Environment Introduction Motivation Final Good Firms Methodology/ Literature Model ➓ Competitive firms which produce using technology Environment - shown below.Inputs used: Workers Environment - Firms ➓ K eq is amount of capital equipment, K st is amount of Calibration capital structures Results ➓ U is effective amount of goods purchased from the low Conclusion skill intermediate sectors, S is total effective labour from high skill intermediate sectors st [ µ U σ + ( 1 ✁ µ )( λ K ρ σ 1 ✁ α ρ ] Y = AK α eq + ( 1 ✁ λ ) S ρ ) (1) σ � M Ψ u � M Ψ s � Ψ u ✁ 1 � Ψ s ✁ 1 Ψ u ✁ 1 Ψ s ✁ 1 ➳ ➳ U = ( x i , u h i , u ) , S = ( x i , s h i , s ) Ψ u Ψ s i = 1 i = 1 (2) 12/30
The Model: Environment Introduction Intermediate Firms Motivation Methodology/ Notation: j will be a vector valued index containing both the Literature broad skill index ( u , s ) and productivity index (1.. M ) of a worker. Model Environment - Workers ➓ One intermediate sector for each worker type j . Environment - Firms Calibration ➓ One intermediate firm for every worker (so density of Results intermediate firms = density of workers) Conclusion ➓ Number of matches given by matching function M ( S j , V j ) . S j = number of effective type m job searchers. V j = vacancies. ➓ θ j ✑ V j / S j denotes labour market tightness ➓ Contact rate for type j firms is q ( θ j ) ✑ M ( S j , V j ) / V j , and ( θ j q ( θ j ) , χθ j q ( θ j ) ) are the contact rates for unemployed and employed workers respectively. ➓ Vacancies determined by free entry : i.e. firms issue a vacancy until expected profit equals vacancy cost. 13/30
The Model: Environment Introduction Motivation Intermediate Firms: Wage Setting Methodology/ Literature Model ➓ Assume that firms and unemployed workers engage in Environment - Nash bargaining - the minimum wage acts as a Workers Environment - Firms constraint to the Nash maximisation. Calibration Results ➓ When workers gets poached, incumbent and rival Conclusion bid-up the wage until the value of employing a poached worker equals the value of carrying a vacancy i.e. zero (Postel-Vinay and Robin (2002)) ➓ Therefore poached workers will get paid their marginal product in final good production. ➓ Minimum Wage reduces expected profit from employing not-poached worker, and decreases vacancy creation 14/30
The Model: Behaviour Introduction Workers Motivation Methodology/ A worker of a given type j exist in one of three states: Literature ➓ unemployed, receiving flow income b ,with lifetime Model Environment - value function denoted V ue Workers j Environment - Firms Calibration ➓ employed but not poached, receiving the higher of Nash bargained wage w b Results j and the minimum wage m w , Conclusion with value function V np ; j ➓ employed and poached, receiving wage w p j , with value function V p j = b + β [ θ j q ( θ j ) V np V ue + ( 1 ✁ θ j q ( θ j )) V u j ] (3) j j V np = max ( w b j , m w )+ j + ( 1 ✁ δ j )[ χθ j q ( θ j ) V p j + ( 1 ✁ χθ j q ( θ j )) V np δ j V ue � � ] (4) β j j V p j = w p + ( 1 ✁ δ j ) V p j + β [ δ j V ue j ] (5) j 15/30
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