**4. Methodology**

### *4.1. Theoretical Framework*

This section examines the mechanisms of how regulations a ffect a firm's performance and the related hypotheses. It is obvious that environmental policies increase firms' production costs directly. But this impact is asymmetric to economic units and depends on the di fferences in their production functions and the demand that they face. This means that besides divisions between regulation-targeting groups and others, systematic di fferences between the entities also lead to changes in relative costs. The Pollution Haven Hypothesis is also based on the asymmetric e ffects of environmental regulations between countries [24]. Figure 2 illustrates the asymmetric e ffects of environmental policies on a firm (or industry). Here *c*1 and *c*2 indicate each sector's compliance costs brought on by environmental regulations. Since the polluting industries have a higher cost burden of environmental regulations as compared to the less-polluting industries, they have higher compliance costs (*<sup>c</sup>*2 > *c*1).

**Figure 2.** The e ffects of environmental regulations in industries di fferentiated by the level of pollution.

Although the contemporaneous e ffects of regulations on firms will be negative for their competitiveness (point 2 in Figure 2), firms take optimal decisions to react to stricter environmental regulations. In this process, firms have the incentive to invest and develop new cost-e fficient techniques which can reduce emissions at lower costs and subsequently o ff-set the direct negative e ffects of the policies (PH holds). Then increased pressure of the regulations in the past can have a positive impact on economic growth.

In research, the directions that indirect e ffects take in productivity, investments, and jobs have been controversial. However, if firms recover enough then their output will increase based on their improved productivity. In particular, strengthening regulations in the case of the green sector can lead to an increase in demand for environment-related goods and services over time by stimulating the need for green outputs in all the sectors. This is represented in Figure 2 by point 3 . This upward demand shift (from *d*2 to *d*- 2) should lead to an increase in output and employment.

If the industries can off-set their compliance costs (if PH holds), the regulation-induced losses in output and employment will dissolve. The green sector, in particular, could recover its losses faster than the non-green sector even in the polluting industries. It has an opportunity to expand its market under environmental regulations as compared to its non-green counterparts. Figure 2 explains this phenomenon with a demand shift excluding the price effect.

### *4.2. Empirical Model*

This study categorizes the establishments into the environmental sector (green and non-green) and carbon dioxide emitting (polluting and non-polluting) industries for examining the effects of strengthened environmental regulations on employment and labor productivity. It allows estimation of the industrial sector's heterogeneity in response to tightened regulations in the Korean manufacturing industry. It estimates difference-in-differences regressions with three different specifications to shed light on the effects of tightened environmental regulations on the performance of the establishments.

The dependent variables (ln*Yijrt*) are the logarithms of employment and labor productivity. Employment and labor productivity are often used for measuring a firm's performance. For calculating labor productivity, we use both output and value–added variables. The subscripts *i*, *j*, *r*, and *t* denote establishment, industry, region, and year of observations respectively. The main estimated equation is specified as:

$$\ln Y\_{ijrt} = \alpha + \beta \left| \text{Post} \chi \times \text{Poll}\_j \times \text{Greer}\_{i \in S} \right| + X\gamma + \mu\_j + \theta\_I + \lambda\_l + \varepsilon\_{ijrt} \tag{1}$$

The purpose of the reduced form estimation is identifying the effects of environmental regulations in the context of LCGG using the DDD (difference-in-differences-in-differences) term. The variable Postt is an indicator of whether the year is after 2010 since the LCGG Act was enacted in January 2010. The Act on Low-Carbon Green Growth includes the following provisions: Reduction in the consumption of fossil fuels; reduction of GHG emissions by 27–30 percent by 2020 relative to the 'business as usual' of 2005; and increasing energy independence by using new and renewable energy sources. Poll*j* represents the polluting industry dummy variable and Green*i*∈*<sup>S</sup>* is another dummy variable which has a value of one if the establishment is included in the green sector or zero otherwise. So, the estimated coefficient of β captures the asymmetric effects of environmental regulations between industries.

This study used three specifications. First, we did the DD (difference-in-differences) regression using interaction Post*t* × Poll*j* to confirm the effects of regulations on polluting industries; this has also been done by previous studies. Then, we compared the green and non-green sectors using Post*t* × Green*i*∈*S*. And lastly, we applied Equation (1) to identify the regulations' effects on the dependent variables through an interaction among these three variables. The first and second terms of the DD term are all included and DD specifications are also saturated.

*X* is a vector of other control variables such as HHI*jt*, age*it*, ln *kit*, and ln wage*it*. HHI*jt* is a concentration index measuring the degree of competition within the five-digit industries and age*it* is control for the size of a plant. lnkit is the logarithm of capital intensity calculated by capital stock of labor and it is included in the labor productivity equation. We also use ln wage*it* which is the logarithm of average wages of employees when estimating the employment equation. μ*j*, θ*<sup>r</sup>*, and λ*t* are industry, region, and time fixed effects. These fixed effects capture the unobservable industry, region, and time-specific characteristics. *ijrt* is robust standard errors.
