Licensing Simulation | Tomas Larroucau

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Physicians’ Occupational Licensing Simulation

Explore the Quantity-Quality trade-off in occupational licensing. Adjust the threshold and parameters to see how they affect labor supply, average quality, and the optimal outcome.

Parameters

Mass ($m$): 1000

Matching probability ($p$): Matching prob ($p$): 1.0

Threshold ($\underline{s}$): 50

Returns to Quantity ($\alpha_L$): Quantity return ($\alpha_L$): 1.5

Returns to Quality ($\alpha_\theta$): Quality return ($\alpha_\theta$): 0.3

Signal-to-Noise Ratio (SNR): SNR: 0.8

Mean Score ($\mu_s$): 50

Std Dev Score ($\sigma_s$): 15

$$ \begin{aligned} L &= m \cdot p \cdot (1 - F(\underline{s})) \\ \bar{\theta} &= \mu + \text{SNR} \cdot (\mathbb{E}[s | s \ge \underline{s}] - \mu) \end{aligned} $$

$$ \text{Raise } \underline{s} \iff R(\underline{s}) > \frac{\alpha_L}{\alpha_{\theta}} $$

Key Equations

Production Function:

$$ \begin{aligned} Y &= \exp(\alpha_{\theta}\bar{\theta}) \cdot L^{\alpha_L} \\ \implies \ln(Y) &= \alpha_L \ln(L) + \alpha_{\theta} \bar{\theta} \end{aligned} $$

Elasticity of Labor w.r.t. Threshold:

$$\eta^L_{\underline{s}} \equiv \frac{d\ln(L)}{d\underline{s}} = \frac{-m\,h(\underline{s})}{L}\cdot p(\underline{s})$$

Semi-elasticity of Quality w.r.t. Threshold:

$$\tilde{\eta}^{\bar{\theta}}_{\underline{s}} = -\eta^L_{\underline{s}} \cdot \text{SNR} \cdot \left(\mathbb{E}[s | s > \underline{s}] - \underline{s} \right)$$

Marginal Rate of Transformation:

$$R(\underline{s}) \equiv -\frac{d\bar{\theta}/d\underline{s}}{d\ln(L)/d\underline{s}} = \text{SNR} \cdot \left(\mathbb{E}[s | s > \underline{s}] - \underline{s} \right)$$