Effectiveness of policy against illegal disposal of waste

Abstract

Our objective is to analyze the effectiveness, against the illegal disposal of waste, of a licensing system that has been introduced in a waste management policy. We theoretically find enforcement leverage in the licensing system, and then examine the theoretical result empirically. The results suggest that extending liability to disposers, which forms the basis of the enforcement leverage, deters illegal disposal more effectively than increasing penalties for illegal disposal. We also obtain evidence of transboundary movement of illegal disposal, and find how the court determines penalties for illegal disposal.

Appendix: Derivation of (2): The waste management cost of a marginal WMF that is indifferent as to compliance or noncompliance (\( \widehat{\theta } \))

Let us consider a competitive economy which allows the existence of improper treatment of waste by WMFs in the equilibrium. Then, in the equilibrium, disposers must be indifferent as to the choice of consigning waste to licensed WMFs or to unlicensed WMFs. If we represent by and the waste price per ton offered by a licensed and an unlicensed WMF, respectively, the following equation must be satisfied in the equilibrium.

$$ p_{1} = p_{0} + \mu f^{\prime} $$

(A1)

Consequently, the waste management fee charged by an unlicensed WMF (p ₀) is lower than that offered by a licensed WMF (p ₁).

WMFs have two options: proper waste treatment, or illegal dumping. Intuitively, WMFs that are licensed and have a relatively lower value of θ will comply with the required standard for waste treatment. On the other hand, WMFs with a higher value of will violate the standard. Note that all WMFs want to be licensed because the fee for waste treatment is higher for a licensed WMF [see (A1)]. Therefore, in the stationary state, there are three types of WMFs: licensed WMFs that will comply with the standard (let us call them compliant licensed WMFs), licensed WMFs that will violate the standard or illegally dump the waste but will still keep their licenses (noncompliant licensed WMFs), and WMFs whose licenses are suspended (unlicensed WMFs). Note that unlicensed WMFs have no incentive to comply with the standard, because any operations of an unlicensed WMF are themselves illegal.

To obtain the steady-state equilibrium, we have to compare the current-value profits from proper waste treatment and illegal dumping with each other. Before calculating them, we need to look at the following list of notations.

$\pi_{1}^{p}$ :

The current value of the total amount of profit that a compliant licensed WMF can earn from the current period to an indefinite future period. The superscript p and the subscript 1 represent proper waste treatment and the licensed WMF, respectively.

$\pi_{0}^{i}$ :

The current value of the total amount of profit that an unlicensed WMF can earn from the current period to an indefinite future period. The superscript i and the subscript 0 represent illegal dumping and the unlicensed WMF, respectively.

$\pi_{1}^{i}$ :

The current value of the total amount of profit that a noncompliant licensed WMF can earn from the current period to an indefinite future period.

β:

The discount factor.

First we derive the current value of profit for proper waste treatment ($\pi_{1}^{p}$). A compliant licensed WMF earns every period. Then the following equation must be satisfied:

$$ \pi_{1}^{p} = p_{1} - \theta + \beta \pi_{1}^{p} . $$

(A2)

We can easily calculate $\pi_{1}^{p}$ as follows:

$$ \pi_{1}^{p} = \frac{{p_{1} - \theta }}{1 - \beta }. $$

(A3)

Next, the current value of profit for illegal dumping can be derived as follows. The profit of an unlicensed WMF, $\pi_{0}^{i}$, must satisfy the following equation:

$$ \pi_{0}^{i} = p_{0} - \mu f + \beta \{ \mu \pi_{0}^{i} + (1 - \mu )\pi_{1}^{i} \} . $$

(A4)

Note that the expected fine imposed for illegal dumping is denoted by μf. In addition, if an unlicensed WMF is not caught operating without a license during the current period, the suspended license is returned to the WMF at the beginning of the next period and the firm becomes a noncompliant licensed WMF in that same period (the probability is). Otherwise, the license of the WMF continues to be suspended during the next period. Therefore, the expected profit earned by an unlicensed WMF from the next period to an indefinite future period can be written as the bracket in the second term of (A4).

Similarly, $\pi_{1}^{i}$ for (the current value of profit of a noncompliant licensed WMF), we can obtain the following equation:

$$ \pi_{1}^{i} = p_{1} - \mu f + \beta \{ (1 - \mu )\pi_{1}^{i} + \mu \pi_{0}^{i} \} . $$

(A5)

Note that a noncompliant licensed WMF has to pay a fine (f) and loses its license in the next period if illegal dumping is detected (the probability is μ), but otherwise it can keep its license in the next period, as shown in the bracket of equation (A5).

By (A4) and (A5) we can calculate $\pi_{0}^{i}$ and $\pi_{1}^{i}$

$$ \pi_{1}^{i} = \frac{{(1 - \beta \mu )(p_{1} - \mu f) + \beta \mu (p_{0} - \mu f)}}{1 - \beta }. $$

(A6)

$$ \pi_{0}^{i} = \frac{1}{1 - \beta \mu }[p_{0} - \mu f + \beta (1 - \mu )\pi_{1}^{i} ]. $$

(A7)

Improper WMFs include both noncompliant licensed WMFs and unlicensed WMFs. Denote by and $1 - \alpha$ the relative proportion of unlicensed WMFs and noncompliant licensed WMFs among all WMFs illegally dumping waste, respectively. In the steady state, must stay at a unique value. Note that unlicensed WMFs can apply for and obtain a license in the next period if they are not caught operating without a license during the current period. In the steady-state equilibrium, then, the proportion of unlicensed WMFs that will acquire licenses in the next period ($(1 - \mu )\alpha$) must be equal to the proportion of the noncompliant licensed WMFs that lose their licenses in the same period ($\mu (1 - \alpha )$). We can, therefore, obtain the steady-state value of α.

$$ \alpha = \mu $$

(A8)

The expected profit of a WMF that illegally dumps waste represented by $E(\pi^{i} )$ in the steady state can be calculated as:

$$ E(\pi^{i} ) = \alpha \pi_{0}^{i} + (1 - \alpha )\pi_{1}^{i} . $$

(A9)

As stated above, whether WMFs choose proper or illegal dumping depends on the level of θ In other words, only licensed WMFs with a lower value of comply with the standard for proper recycling. We can now derive the critical value of θ that is represented by $\widehat{\theta }$. Since the marginal licensed WMF with must be indifferent as to compliance or noncompliance, the following equation must hold:

$$ \pi_{1}^{p} = E(\pi^{i} ) $$

(A10)

By substituting (A6), (A7), and (A8) into (A9) and solving (A10), we can derive the critical value of θ (or $\widehat{\theta }$). The result is represented by (2) in Sect. 3.2.