Abstract
Over the past decade, federal, state and local governments have restricted the types and uses of information in hiring and promotion decisions. Examples include the banning of credit reports and criminal records. This paper presents a simple microeconomic model of a competitive labor market and studies the economic effects of information bans. The key trade off is between allocative efficiency and helping a labor type with an undesirable characteristic. We compare information bans to direct subsidies. Moreover, we discuss the case where the ban creates negative feedback on the perceptions of firms considering workers of the bad type.
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Notes
See Avery and Hernandez (2018).
See Privacy rights Clearing House (2018).
See HR Drive (2018).
Cortes et al. (2016) does look at the overall vacancy rate, but in addition they examine the effects on subprime district dwellers.
We will not consider taste based discrimination.
The direct subsidy approach was implemented durintg the Obama administration under The Work Opportunity Tax Credit for business hiring ex-felons. See the United States Department of Labor (2018).
We treat \(g_{ij}\) as deterministic in the eyes of the firm. If \(g_{ij}\) enters the production function multiplicatively, \(f(L_{ij},g_{ij})\equiv g_{ij}\hat{f}(L_{ij}),\) then we can think of the firm as facing a distribution of \(g_{ij}.\) Then \(E(g_{ij})\) would replace \(g_{ij}\) in all of our analysis. The multiplicative form is adopted later for simplification in the analysis of ex ante employment.
We have that \(\partial L_{ij}^{d}/\partial w_{ij}=1/pf_{LL}<0,\)\(\partial L_{ij}^{d}/\partial g_{ij}=-f_{Lg}/f_{LL}>0,\) and \(\partial L_{ij}^{d}/\partial p=-f_{L}/pf_{LL}>0.\)
We have \(\partial L_{ij}/\partial w_{ij}=-1/u^{\prime \prime }>0.\)
With regard to A.3(ii), Minor et al. (2017) provide empirical evidence on the relationship between actual job performance and criminal record possession. Their data shows that sales employees with records are more likely to leave due to misconduct, but that for customer service employees this is not true. Whether or not productivities are actually affected by a record, firms assume liability for harm done by those with records in the workplace. This alone can significantly reduce a worker’s marginal valuation, if that worker has a record. Friedman (2015) provides statistics on criminal records for different groups in the U.S. which support assumption A.4(ii).
We have that \(\partial L_{i}/\partial g_{i1}=[\frac{h_{i1}}{h_{i}(a_{i})} f_{Lg}(L_{i},g_{i1})]/(-1)[\frac{h_{i1}}{h_{i}(a_{i})}f_{LL}(L_{i},g_{i1})+ \frac{h_{i2}}{h_{i}(a_{i})}f_{LL}(L_{i},g_{i2})]>0,\)\(\partial L_{i}/\partial g_{i2}=[\frac{h_{i12}}{h_{i}(a_{i})} f_{Lg}(L_{i},g_{i2})]/(-1)[\frac{h_{i1}}{h_{i}(a_{i})}f_{LL}(L_{i},g_{i1})+ \frac{h_{i2}}{h_{i}(a_{i})}f_{LL}(L_{i},g_{i2})]>0,\)\(\partial L_{i}/\partial p=[E_{g}[f_{L}(L_{i},g)|a_{i}]/(-p)[\frac{h_{i1}}{h_{i}(a_{i}) }f_{LL}(L_{i},g_{i1})+\frac{h_{i2}}{h_{i}(a_{i})}f_{LL}(L_{i},g_{i2})]>0,\) and \(\partial L_{i}/\partial w=-1/(-p)[\frac{h_{i1}}{h_{i}(a_{i})} f_{LL}(L_{i},g_{i1})+\frac{h_{i2}}{h_{i}(a_{i})}f_{LL}(L_{i},g_{i2})]<0,\)
Employment is measured in terms of people hours.
Agan and Starr (2018) among others document decreases in minority employment post ban.
All of the results below hold for the case where \( f(L_{ij},g_{ij})=m(g_{ij})f(L_{ij}),\)where m is an increasing function.
In the case of criminal records, there is a high social cost associated with under employment of those with records. Indeed, Bucknor and Barber (2016) estimate that under employment of former criminals results in a loss of GDP of $78 to $87 billion on an annual basis.
While a tax credit for hiring ex-felons is not a direct per unit subsidy, it is in the spirit of directly subsidizing firms hiring those with records. The Work Opportunity Tax Credit for business hiring ex-felons is currently available. See the United States Department of Labor (2018).
All of the results below hold for the case where \( f(L_{ij},g_{ij})=m(g_{ij})f(L_{ij}),\)where m is an increasing function.
See Sabia et al. (2018) for documentation of increased crime for some groups under ban the box laws.
The dynamic macro model of Corbae and Glover (2017) predicts more credit unworthyness as a result of a credit ban. See Cortes et al. (2018) for empirical documentation of increased credit unworthyness under credit bans.
We have that \(\partial L_{ij}^{b}/\partial r=-1/(\alpha _{ij}^{2}u^{\prime \prime })>0\) and \(\partial L_{ij}^{b}/\partial \alpha _{ij}=(u^{\prime }-\alpha _{ij}u^{\prime \prime }L_{ij}^{b})/(\alpha _{ij}^{2}u^{\prime \prime })<0.\)
References
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I thank my colleagues Odilon Camara, Tom Chang, Ayse Imrohoroglu, Emily Nix, Rodney Ramcharan, Joao Ramos, Sandra Rozo, and Yanhui Wu. Two anonymous referees and the editor contributed through their insightful comments. I thank the Marshall School of Business for generous research support.
Appendices
Appendix
Proof of Lemma 1
First we show existence of solutions to (2) and (3). For (2) form the difference \(pf_{L}(L_{ij},g_{ij})-u^{\prime }(T-L_{ij})\) and note that under A.1 and A.2 this difference is decreasing and differentiable in \(L_{ij}.\) Moreover, \(\underset{L_{ij}\rightarrow 0}{ \lim }[pf_{L}(L_{ij},g_{ij})-u^{\prime }(T-L_{ij})]=\infty \) while \(\underset{L_{ij}\rightarrow T}{\lim }[pf_{L}(L_{ij},g_{ij})-u^{\prime }(T-L_{ij})]=-\infty .\) Thus, there is an \(L_{ij}\in (0,T)\) solving (2). Likewise, \(\underset{L_{i}\rightarrow 0}{\lim } [pE[f_{L}(L_{i},g)|a_{i}]-u^{\prime }(T-L_{i})]=\infty \) while \(\underset{ L_{i}\rightarrow T}{\lim }[pE[f_{L}(L_{i},g)|a_{i}]-u^{\prime }(T-L_{i})]=-\infty .\) Thus, there is an \(L_{i}\in (0,T)\) solving (3).
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(i)
For notational economy, let \(\Omega _{i}(L)\equiv E[f_{L}(L,g)|a_{i}]\) and \(\Omega _{ij}(L)\equiv f_{L}(L,g_{ij}).\) Each \(L_{i}\) is defined by \( \Omega _{i}(L)=u^{\prime }(T-L)/p\) and each \(L_{ij}\) is defined by \(\Omega _{ij}(L)=u^{\prime }(T-L)/p.\) Under A.1 and A.2, each \(\Omega _{i}(L)\) and \( \Omega _{ij}(L)\) is strictly decreasing in L, and \(u^{\prime }(T-L)/p\) is strictly increasing in L. Furthermore, for each L, \(\Omega _{i1}(L)<\Omega _{i2}(L)\), \(\Omega _{i}(L)\in (\Omega _{i1}(L),\Omega _{i2}(L))\), with \(\Omega _{11}(L)=\Omega _{21}(L)\) and \(\Omega _{12}(L)=\Omega _{22}(L)\). Because the function \(u^{\prime }/p\) is strictly increasing and these properties hold, we have \(\Omega _{i}(L_{i})\in (\Omega _{i1}(L_{i1}),\Omega _{i2}(L_{i2}))\). By A.4(ii), \(\Omega _{11}(L)=\Omega _{21}(L)\) and \(\Omega _{12}(L)=\Omega _{22}(L),\) for all L, and the increasingness of \(u^{\prime }/p,\) we have \(\Omega _{2}(L)>\Omega _{1}(L),\) for all L, and \(\Omega _{2}(L_{2})>\Omega _{1}(L_{1})\) as was to be shown.
-
(ii)
The wages are determined by (2) and (3). The left side of each of these conditions represents a decreasing demand for labor and the right side is an increasing supply of labor, as a function of labor. The demand for labor in the full information solution is greater, equal to, or less than that of the banning solution as
$$\begin{aligned} f_{L}(L_{ij},g_{ij})\gtreqqless E[f_{L}(L_{i},g)|a_{i}]. \end{aligned}$$Because \(u^{\prime }/p\) (normalized supply of labor) is increasing in labor and the demand is decreasing, the results of Lemma 1 (i) imply that
$$\begin{aligned} w_{i2}>w_{i}>w_{i1}\text { and }L_{i2}>L_{i}>L_{i1}\text {, }w_{2}>w_{1}\text { , and }L_{2}>L_{1}. \end{aligned}$$ -
(iii)
We note that in an equilibrium of the banning or full information problem with an optimal \(L^{*}\), equilibrium utility is increasing in the worker’s wage. That is,
$$\begin{aligned} \frac{du(T-L^{*})}{dw}=(-u^{\prime }+w)\frac{\partial L^{*}}{ \partial w}+L^{*}=L^{*}>0. \end{aligned}$$To determine changes in utility between the full information and banning solution for each type, we need only examine the movement in the equilibrium wage across solutions. Given (ii), the results hold.
\(\square \)
Proof of Proposition 2:
Note that \(\partial \phi /\partial L=\frac{1}{p}(\frac{-u^{\prime \prime }f^{\prime }-f^{\prime \prime }u^{\prime }}{(f^{\prime })^{2}})>0,\) so that \(\phi \) is strictly increasing in L. Consider the case where \(\partial ^{2}\phi /\partial L^{2}>0\) and \(\phi \) is increasing and strictly convex. The three equilibria under consideration are \(L_{i2}\) defined by \(g_{i2}=\phi (L_{i2}),\)\(L_{i}\) defined by \(E(g|a_{i})=\phi (L_{i}),\) and \(L_{i1}\) defined by \(g_{i1}=\phi (L_{i1}).\) If \(\phi \) is increasing and strictly convex, then the point \( (E(L|a_{i}),E(g|a_{i}))\) lies to the left of the point \((L_{i},\phi (L_{i}))=(L_{i},E(g|a_{i})).\) Thus, \(L_{i}>E(L|a_{i}).\) The cases where \( \phi \) is strictly concave or linear are shown analogously. \(\square \)
Extension of the basic model to the case of monopsony.
Let us adopt all of the assumptions on the \(g_{ij}\) as depicted in Sect. 3.1, although those of 3.2 could also be used. The consumer solves the utility maximization problem as before, so that \(w_{ij}=u^{\prime }(T-L_{ij})\equiv w(L_{ij}).\) The consumer is assumed to take the wage as given from the monopsonist. The latter supply is faced by the monopsonist. It is upward sloping as expected, \(w^{\prime }(L_{ij})=-u^{\prime \prime }(T-L_{ij})>0.\) The full information solution has the firm solving \( pf_{L}(L_{ij},g_{ij})=MC_{L}(L_{ij}),\) where
We assume that \(MC_{L}^{\prime }(L_{ij})=2w^{\prime }(L_{ij})+w^{\prime \prime }(L_{ij})L_{ij}=-2u^{\prime \prime }(T-L_{ij})+u^{\prime \prime \prime }(L_{ij})L_{ij}>0\) and note that, as usual, for all L, \( MC_{L}(L)>w(L).\) The equilibrium wage is then given by \(w(L_{ij}).\) The banning solution has the firm solving \( pE[f_{L}(L_{i},g)|a_{i}]=MC_{L}(L_{i}) \) for \(L_{i},\) and the wage is \( w(L_{i}).\)
Because both \(MC_{L}\) and \(w(L)\ \)are increasing in L with \(MC_{L}>\)w(L), for all L, we have that all of the results of Lemma 2 hold for this model. Thus, all of the results of Proposition 1 also hold when comparing the full information monopsony with the information banned monopsony, except for the results regarding whether a firm hiring a good or bad agent will be hurt or harmed. We turn to these next.
If the firm observes \(a_{i}\) and hires an agent with the good characteristic, then profit with a ban is \( \int _{0}^{L_{i}}pf_{L}(L,g_{i2})dL-w_{i}L_{i},\) whereas profit with full information is \(\int _{0}^{L_{i2}}pf_{L}(L,g_{i2})dL-w_{i2}L_{i2,}\) where \( w_{i2}>w_{i}\) and \(L_{i2}>L_{i}.\) The difference between full information and the ban is \( \int _{L_{i}}^{L_{i2}}pf_{L}(L,g_{i2})dL-(w_{i2}L_{i2}-w_{i}L_{i}).\) The first term is positive and the second is negative, so that we are comparing the extra revenue generated by full information’s higher labor use with the extra cost of that labor use, as in the competitive case. The illustration of this case is analogous to that of Fig. 2, except that \(MC_{L}(L)\) and \( pf_{L}(L,g_{i2})\) determine the amount of labor and \(w(L)\ \)determines the wage. We will not re-illustrate here.
If the firm observes \(a_{i}\) and hires an agent with the bad characteristic, then profit under the ban is \(\int _{0}^{L_{i}}pf_{L}(L,g_{i1})dL-w_{i}L_{i}.\) Profit under full information is \( \int _{0}^{L_{i1}}pf_{L}(L,g_{i1})dL-w_{i1}L_{i1},\) where \(w_{i}>w_{i1}\) and \( L_{i}>L_{i1}.\) We will show that the firm is hurt by the ban relative to full information, as in the competitive case. We will break this situation down into two cases. Define \(L^{o}\) as \(w_{i}=pf_{L}(L^{o},g_{i1}).\)
Case 1 is where \(MC_{L}(L_{i1})\leqq w_{i}\) such that \(L_{i1}\geqq L^{o}.\) For this case, profit under full information minus that under the ban can be written as
The first term of this expression is positive, and the second minus the third is positive, because \(w_{i}=w(L_{i})>pf_{L}(L_{i1},g_{i1})\,\) and the latter is decreasing in L. Thus, the sum of the three terms is positive as stated. The first positive term is illustrated in Fig. 4 as the area of the rectangle enclosed by the vertices \([w_{i1}w_{i}BA]\) and the second minus the third is the area of the trapezoid enclosed by the vertices [EBCD].
Case 2 is where \(MC_{L}(L_{i1})>w_{i}.\) Define the competitive wage and labor amount as \(w_{i1}^{c}=w(L_{i1}^{c})=pf_{L}(L_{i1}^{c},g_{i1}).\) We have that \(L_{i1}<L^{o}\leqq L_{i1}^{c}<L_{i}\) and \(w_{i}\geqq w_{i1}^{c}>w_{i1}.\) We can write the difference between full information profit and profit under banning as
The first and the last terms of this expression are positive and the middle term is negative. The second term, \(-[ \int _{L_{i1}}^{L^{o}}pf_{L}(L,g_{i1})dL-w_{i}(L^{o}-L_{i1})],\) is negative because \(pf_{L}(L_{i1},g_{i1})\,=MC_{L}(L_{i1})>w_{i}=pf_{L}(L^{o},g_{i1})\) and the value of marginal product is decreasing in L. The last term is positive because \(w_{i}=pf_{L}(L^{o},g_{i1})\) and the value of marginal product is decreasing in L. Figure 5 illustrates the three terms of (a.1). The first term is the area of the rectangle enclosed by the vertices \( [w_{i1}w_{i}BA],\) the second is minus one times the area of the triangle enclosed by the vertices [BCD], and the third is the area of the triangle enclosed by the vertices [DEF]. An upper bound on the absolute value of the middle term \([\int _{L_{i1}}^{L^{o}}pf_{L}(L,g_{i1})dL-w_{i}(L^{o}-L_{i1})]>0\) is \([\int _{L_{i1}}^{L_{i1}^{c}}pf_{L}(L,g_{i1})dL-w_{i1}^{c}(L_{i1}^{c}-L_{i1})].\) Thus, a lower bound on (a.1) is
We will show that (a.2) is positive so that the result holds. We know that monopsony profit is at least as large as competitive profit, \( \int _{0}^{L_{i1}}pf_{L}(L,g_{i1})dL-w_{i1}L_{i1}\geqq \int _{0}^{L_{i1}^{c}}pf_{L}(L,g_{i1})dL-w_{i1}^{c}L_{i1}^{c}.\) Rewriting,
However (a.2) can be stated as
From (a.3), the first two terms are nonnegative and the last term is positive, so that (a.2) is strictly positive and the result holds.
Finally, let us consider expected employment for monopsony and full information, \(E(L|a_{i}),\) and monopsony with the ban, \(L_{i}\). As in Propositions 2 and 4, we assume that A.1–A.4 or A.1, A.2, A.4(i), and A.5 hold, and let the production function take on the multiplicative form \( f(L_{ij},g_{ij})=g_{ij}f(L_{ij})\). Let \(\psi (L)\) be defined as the marginal value ratio \(MC_{L}(L)/pf^{\prime }(L),\) where, under \(MC_{L}^{\prime }>0,\) we have \(\psi ^{\prime }(L)>0.\) Using the proof of Proposition 2, we can substitute \(\psi \) for \(\phi \) and state \(L_{i}\gtreqqless E(L|a_{i})\) if \( \frac{\partial ^{2}\psi }{\partial L^{2}}\gtreqqless 0\). \(\square \)
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Marino, A.M. Banning information in hiring decisions. J Regul Econ 58, 33–58 (2020). https://doi.org/10.1007/s11149-020-09410-3
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DOI: https://doi.org/10.1007/s11149-020-09410-3