Unintended Displacement Effects of Youth Training Programs in a Directed Search Model

Abstract

The rise in the productivity of inexperienced young workers suggests a positive partial equilibrium effect of youth training programs on employment. However, in a general equilibrium context, displacement effects that impact other groups of workers could also arise. We build a directed search model to study the unintended displacement effects of youth training programs. We calibrate the model to match data from the US labor market. The model is then used to simulate a policy experiment that resembles a training program that raises the productivity of a targeted group of low-skilled and inexperienced agents. Our counterfactual analysis shows that the policy indeed triggers displacement effects. Consequently, these unintended displacement effects must be taken into account in the evaluation of youth training programs.

Appendix A

In this appendix, we discuss the system of equations that solve the symmetric competitive equilibrium of the model.

A.1 Queue lengths

In equilibrium, adult highly skilled workers have no incentives to apply to low-tech firms because those firms offer them the same expected wage to both low- and highly skilled workers since they produce the same output. Therefore, we have that $q_{s,l}^{*}= 0$ in equilibrium.¹³ Then, by using this condition, we can solve the following maximization problems:

$$ \begin{array}{@{}rcl@{}} \max {\Pi}_{h} = (1-e^{-q_{s,h}})\{\theta_{1}Z-w_{s,h}\}+e^{-q_{s,h}}(1-e^{-q_{u,h}})\{Z-w_{u,h}\} \\+ e^{-q_{s,h}-q_{u,h}}(1-e^{-q_{y,h}}) \{\theta_{2}Z-w_{y,h}\} \end{array} $$

(13)

such that:

$$ \begin{array}{@{}rcl@{}} w_{s,h}&=& \frac{\overline{w}_{s}q_{s,h}}{1-e^{-q_{s,h}}} \end{array} $$

(14)

$$ \begin{array}{@{}rcl@{}} w_{u,h}&=& \frac{\overline{w}_{u} q_{u,h}}{e^{-q_{s,h}} (1-e^{-q_{u,h}})} \end{array} $$

(15)

$$ \begin{array}{@{}rcl@{}} w_{y,h}&=& \frac{ \overline{w}_{y} q_{y,h}}{e^{-q_{s,h}-q_{u,h}} (1-e^{-q_{y,h}})} \end{array} $$

(16)

$$ \begin{array}{@{}rcl@{}} \max {\Pi}_{l} = (1-e^{-q_{u,l}})\{Z-w_{u,l}\} + e^{-q_{u,l}}(1-e^{-q_{y,l}}) \{\theta_{2}Z-w_{y,l}\} \end{array} $$

(17)

such that:

$$ \begin{array}{@{}rcl@{}} w_{u,l} &=& \frac{\overline{w}_{u} {q_{u,l}}}{(1-e^{-q_{u,l}})} \end{array} $$

(18)

$$ \begin{array}{@{}rcl@{}} w_{y,l} &=& \frac{\overline{w}_{y}q_{y,l}}{e^{-q_{u,l}}(1-e^{-q_{y,l}})} \end{array} $$

(19)

We first solve for the application queue as a function of y, 𝜃₁, 𝜃₂, $\overline {w}_{s}$, $\overline {w}_{u}$ and $\overline {w}_{j}$.

$$ \begin{array}{@{}rcl@{}} q_{s,h} &=& Ln \left( \frac{Z(\theta_{1}-1)}{\overline{w}_{s}-\overline{w}_{u}} \right) \end{array} $$

(20)

$$ \begin{array}{@{}rcl@{}} q_{u,h} &=& Ln \left( \frac{1-\theta_{2}}{\theta_{1}-1} \frac{\overline{w}_{s}-\overline{w}_{u}}{\overline{w}_{u}-\overline{w}_{y}} \right) \end{array} $$

(21)

$$ \begin{array}{@{}rcl@{}} q_{y,h} &=& Ln \left( \frac{\theta_{2}}{1-\theta_{2}} \frac{\overline{w}_{u}-\overline{w}_{y}}{\overline{w}_{y}} \right) \end{array} $$

(22)

$$ \begin{array}{@{}rcl@{}} q_{s,l} &=& 0 \end{array} $$

(23)

$$ \begin{array}{@{}rcl@{}} q_{u,l} &=& Ln \left( \frac{Z(1-\theta_{2})}{\overline{w}_{u}-\overline{w}_{y}} \right) \end{array} $$

(24)

$$ \begin{array}{@{}rcl@{}} q_{y,l} &=& Ln \left( \frac{\theta_{2}}{1-\theta_{2}} \frac{\overline{w}_{u}-\overline{w}_{y}}{\overline{w}_{y}} \right) \end{array} $$

(25)

Note that q_{s, h} + q_{u, h} = q_{u, l} and q_{y, h} = q_{y, l}. We can solve the equilibrium queues as functions of the exogenous variables π_s, π_u, π_y, π_h and of the endogenous variable n:

$$ \begin{array}{@{}rcl@{}} q_{s,h} &=& \frac{n \pi_{s}}{\pi_{h}} \end{array} $$

(26)

$$ \begin{array}{@{}rcl@{}} q_{u,h} &=& (\pi_{u}+\pi_{s})n-\frac{\pi_{s} n}{\pi_{h}} \end{array} $$

(27)

$$ \begin{array}{@{}rcl@{}} q_{y,h} &=& \pi_{y} n \end{array} $$

(28)

$$ \begin{array}{@{}rcl@{}} q_{s,l} &=& 0 \end{array} $$

(29)

$$ \begin{array}{@{}rcl@{}} q_{u,l} &=& (\pi_{u}+\pi_{s})n \end{array} $$

(30)

$$ \begin{array}{@{}rcl@{}} q_{y,l} &=& \pi_{y} n \end{array} $$

(31)

Finally, it is feasible to calculate the reservation wages, $\overline {w}_{s}$, $\overline {w}_{u}$ and $\overline {w}_{y}$, as functions of the exogenous π_s, π_u, π_y, π_h, and of the endogenous variable n, by appropriately combining (20)–(31).

$$ \begin{array}{@{}rcl@{}} \overline{w}_{s} &=& Z (\theta_{1}-1) e^{-\frac{\pi_{s}n}{\pi_{h}}}+Z(1-\theta_{2}) e^{-(\pi_{u}+\pi_{s})n}+\theta_{2}Ze^{-n} \end{array} $$

(32)

$$ \begin{array}{@{}rcl@{}} \overline{w}_{u} &=& Z(1-\theta_{2}) e^{-(\pi_{u}+\pi_{s})n}+\theta_{2}Ze^{-n} \end{array} $$

(33)

$$ \begin{array}{@{}rcl@{}} \overline{w}_{y} &=& Z\theta_{2}e^{-n} \end{array} $$

(34)

A.2 Free entry condition

By replacing Eqs. (26)–(34), into the profit function described by (06) for j ∈{h, l}, and imposing the free entry condition, we have

$$ \begin{array}{@{}rcl@{}} \frac{K_{l}}{Z} = 1-(1+(1-\theta_{2})(\pi_{u}+\pi_{s})n-\theta_{2})e^{-(\pi_{u}+\pi_{s})n} \\ -(\theta_{2}(\pi_{u}+\pi_{s})n+\theta_{2}+\theta_{2}\pi_{y}n)e^{-n}, \end{array} $$

(35)

for the case of low-tech firms. Following an analogous procedure for high-tech firms, we get

$$ \begin{array}{@{}rcl@{}} \frac{K_{h}}{Z} = (\theta_{1}-\theta_{1}e^{-\frac{\pi_{s}n}{\pi_{h}}}-(\theta_{1}-1)e^{-\frac{\pi_{s}n}{\pi_{h}}}\frac{\pi_{s}n}{\pi_{h}}+e^{-\frac{\pi_{s}n}{\pi_{h}}} ) \\ -((1+(1-\theta_{2})(\pi_{u}+\pi_{s})n-\theta_{2})e^{-(\pi_{u}+\pi_{s})n} +(\theta_{2}(\pi_{u}+\pi_{s})n+\theta_{2}+\theta_{2}Zn)e^{-n}). \\ \end{array} $$

(36)

Moreover, the previous equation can be rewritten as follows

$$ \frac{K_{h}-K_{l}}{(\theta_{1}-1)Z} = 1-e^{\frac{-\pi_{s}n}{\pi_{h}}}-e^{-\frac{\pi_{s}n}{\pi_{h}}}\frac{\pi_{s}n}{\pi_{h}}. $$

(37)

In this model, given the exogenous parameters, the equilibrium value n^∗ is obtained by solving (37). Once the equilibrium value for n^∗ has been computed, the expected wages $\overline {w}_{s}^{*}$, $\overline {w}_{u}^{*}$ and $\overline {w}_{y}^{*}$, and the application queues are determined by substituting that value of n^∗ back into the system (26)–(34).