## 5. Graphical Analysis

This section will provide a graphical analysis of the data, which will also serve as a foundation for the difference-in-differences strategy outlined in section 6. Figure 1a and 1b show the development of the two outcomes under consideration, the average PM10 concentrations and the number of days recording average concentrations above 50µg /m³, over time. The developments are shown separately for cities treated with an air quality plan, a basic LEZ and an advanced LEZ. The figure also shows that both the average concentrations and the number of days in exceedance of the 24h limit move largely parallel for the three groups and exhibit a constant, quite similar downward trend over time. Moreover , there seem to exist some underlying differences between the three groups, causing different levels of PM10 pollution, a fact that could already be concluded from the summary statistics in table 3. However , figure 1a and b show also that these differences stay largely constant over time.

**Figure 1:** Average PM10 concentrations and number of days above 50µg/m³ by treatment status, 2004–2010 [Figure not shown]

While figure 1 shows the general development of PM10 concentrations over time, it is necessary to standardize treatment times to be able to analyze the behavior of concentrations before and after the policy implementation, since LEZs were introduced at different points in time. Because the seasonal and yearly variation observed above could conceal possible changes in concentrations after treatment, such variation also has to be removed from the data to make an analysis possible. This is done in figures 2–5.

Figures 2 and 3 show residual plots for the cities treated with a basic LEZ respectively the control cities when regressed on monthly and yearly dummies to remove the seasonal variation. The residuals were added to the estimated average concentration over the whole period to put them in relation to the scale of the outcome variable. Treatment times in figure 2 were standardized so that the month in which treatment occurred is represented by zero. The green respectively yellow lines represent the mean values of the residuals before and after treatment. From figure 2a, there seems to be a small decrease in average concentrations by less than 0.5µg/m³ following the treatment. Figure 2b shows a reduction of approximately 0.4 days with concentrations above 50µg/m³ per month. However , these changes have to be evaluated in comparison with the control group. To make this possible, hypothetical treatment times were generated for the cities that only had an AQP in place11. The results are shown in figure 3. It seems like the control group experienced a small increase both in average concentrations (figure 3a) and in the number of days in violation with the 24h limit (figure 3b) following the hypothetical treatment. However , this increase was shown to not be statistically significant when it was tested via a dummy for the hypothetical treatment in a simple fixed effects regression. Therefore , the graphical examination suggests the presence of at least a small treatment effect as a result of introducing a basic LEZ.

**Figure 2:** Development of PM10 concentrations and the number of days above the 24 hour limit before and after treatment with basic LEZ, treatment group [Figure not shown]

**Figure 3:** Development of PM10 concentrations and the number of days above the 24 hour limit before and after treatment with basic LEZ, control group [Figure not shown]

Figures 4 and 5 show the same developments for cities treated with an advanced LEZ, using cities with a basic LEZ as a control group. For the cities treated with only with a basic LEZ, hypothetical treatment times were generated similarly as for the control group in figure 3. Comparing figures 4 and 5 can thus give an idea about the effects of introducing an advanced LEZ in comparison to having only a basic LEZ in place. From the figures, it looks like the introduction of an advanced LEZ results in a considerable treatment effect for both outcomes in the treated cities, while a small increase can be observed in the control group after a potential treatment. However , it have to / have got tohas to be kept in mind that[/annotax] figures 2–5 can only serve as a first evaluation of a possible treatment effect of establishing LEZs. Especially since the control group in the regression analysis will also include treated stations before an LEZ is implemented in the respective city, the size of the treatment effect will differ between the graphical analysis and the regression results.

Yet , the figures strengthen some important assumptions with regard to the evaluation strategy. Figure 1 already showed that the underlying trend is similar between the groups for both outcome variables, which is an important assumption for the validity of the difference-in-differences approach. From figures 3 and 5 it can be concluded that no events reducing PM10 concentrations in the control group occur at the same time as the establishment of LEZs, which would cause a problem in identifying the actual effect of the treatment under consideration. A third important feature that can be observed from figures 2–5 is the absence of different underlying trends in the groups before policy implementation. This gives reason to believe that treatment assignment does not depend on recent developments in the outcomes, such as for example the implementation of an LEZ as a response to rising pollution levels over the last few months. It also strengthens the assumption that there exists no time-varying unobserved heterogeneity between the groups, which influences both treatment assignment and outcomes. Moreover , no anticipation effects that lead to sudden dips in the concentrations before LEZ implementation seem to present. Such an anticipation effect would lead to an overestimation in of the treatment effect in an empirical approach. Thus , figures 1–5 support the suitability of the chosen control group and the evaluation strategy that is presented in the next section.

**Figure 4:** Development of PM10 concentrations and number of days above the 24 hour limit before and after treatment with advanced LEZ, treatment group [Figure not shown]

**Figure 5:** Development of PM10 concentrations and number of days above the 24 hour limit before and after treatment with advanced LEZ, control group [Figure not shown]

## 6. Empirical Strategy

Building on the graphical analysis, this section will outline the baseline empirical model used to estimate the average effects of introducing a basic or advanced low emission zone on PM10 pollution. The main challenge arises from the presence of underlying variables that influence both treatment assignment and outcome. If such observed or unobserved variables are present, as both table 3 and figures 1-3 suggest, treatment assignment is no longer exogeneous and the estimated effects are likely to be biased. However , the availability of panel data makes it possible to control for unobserved heterogeneity between groups by the use of fixed effects.

Hence , using OLS, the following basic specification to identify the average effect of LEZs on particle concentrations at station *i* at time *t* will be estimated:

(1)

*yit* denotes the outcome variable and will be specified in two different ways to represent the two political targets that were set by the EU for PM10. The first specification will use monthly averages of PM10 concentrations as a dependent variable to capture effects of the policy on compliance towards the yearly average limit value of 40µg/m³. To estimate the effects on the second limit value, which requires that a concentration of more than 50µg/m³ should not be exceeded on more than 35 days a year, a new variable was constructed from the data that records the violation of this limit value for each observation per month. Possible treatment effects on monthly limit violations can then easily be converted into yearly effects.

Time fixed effects are introduced on a yearly and monthly level by *λyear* and *λmonth*. Such time fixed effects are used to control for seasonality or time related shocks on a country-wide level, for example a recession in a specific year.

Individual fixed effects are introduced by *λstation* and control for constant unobserved heterogeneity between the observations. Thus , it is assured that no time-constant unobserved variables that could influence both treatment assignment and outcome are omitted from the analysis.

The variables *AQPit*, *LEZ1it*, and *LEZ2it* indicate the coming into effect of policies. *AQPit* takes the value 1 if an air quality plan is in place at observation *i* at time *t* and zero otherwise. Thus, *α1* should capture the effect of an air quality plan on PM10 concentrations12. The introduction of a basic LEZ is represented by the indicator variable *LEZ1it*, equaling 1 if an observation is treated with a basic LEZ at time *t* and zero otherwise. Thus , a potential additional treatment effect of a basic LEZ compared to only having an AQP in place is represented by *α2*. If the stricter standards of an advanced LEZ are introduced , this is represented by the variable *LEZ2it* taking the value 1. Hence, *α3 *estimates the additional effects of an advanced LEZ in comparison to having an AQP and a basic LEZ in place.

Control variables relevant to both treatment assignment and the outcome variables that vary over time at the individual level can be introduced by the vector *xit*. Such variables could for example be meteorological data or data on economic developments. Due to a lack of suitable control data (see section 4), the main analysis will include only a variable controlling for changes in the population of a city. In the sensitivity analysis, additional economic control variables are included into *xit*.

Another aspect that has to be taken into account is the spatially imbalanced distribution of LEZs within Germany (see the data section). As LEZs are concentrated within some of the federal states, events influencing PM concentrations that could otherwise be considered random, such as meteorological conditions or transboundary air pollution, could be correlated with both the treatment status and the outcome. For example, if they occur more often in states with treated observations than in others after the treatment has come into effect, the estimated treatment effect could be biased. Another source of such bias could be regional-specific economic developments. For instance, it is / areis possible that[/annotax] the economic decline of 2009 had a larger effect in states with a higher share of manufacturing industries, which could in turn influence PM concentrations (see for example Chay and Greenstone (2003) for an example from the US). To control for such regional-specific events, dummies representing the federal states interacted with monthly dummies will be used.

After controlling for unobserved heterogeneity between the stations, seasonal and region-specific effects, a remaining threat to a valid estimation of the treatment effect could be the presence of different underlying trends between the treatment and the control group. In the case of LEZs, such underlying trends could for example be caused by changes in emissions due to technical developments, changes in the mobility behavior of people (for example an increased or decreased use of cars), or changes in traffic volume due to economic shocks. However , when referring to figure 1, it can be stated that the PM concentrations move largely parallel over the whole observation period for the three treatment groups and therefore it can be concluded that different trends do not threaten the evaluation strategy. Yet , there could be time-varying factors influencing both treatment assignment and outcomes, causing non-random treatment assignment and an omitted variable bias (see for example Besley and Case (2000)). However , referring to figures 2 and 3, the development of PM concentrations before treatment implementation shows no sign of time-varying unobservable factors that influence the PM10 concentrations directly, while the use of fixed effects controls for all time-constant unobservable factors.

While the estimation strategy outlined above enables the identification of average treatment effects, it can easily be extended to test for heterogeneous treatment effects . Testing for such heterogeneity can be important with regard to policy recommendations: probably an LEZ works under specific conditions which are disguised when establishing average treatment effects; or it might even work in opposite directions for different groups within the treated observations and therefore be “averaged out” in the main analysis. The estimation strategy for heterogeneous treatment effects will be explained further in the results section.

Remaining threats to the evaluation of the treatment effect arise especially from spillover effects of the policy that affect the outcomes of the control group (see section 3). This will be checked for by estimating a model where controls located close to an LEZ are systematically excluded from the sample. If the estimated treatment effects vary significantly as a result, spillover effects could be present. It can also be tested for spillover effects directly by defining an indicator for control observations located closely to a low emission zone that becomes active simultaneously with the LEZ implementation. Such a “secondary treatment” can be used to identify spillover effects and thereby help to understand the mechanisms of how an LEZ works in a better way.

## Footnotes

11 The same method was used for example by Lechner (1999). The hypothetical treatment times were generated as random draws from the actual treatment times and in proportion to the frequency of the actual treatment times, as for example described in Buis (2007) .

12 Though all cities introduce an air quality plan at some point in time and thus no real control group exists, the different implementation times allow for the use of observations before their AQP comes into force as control units. Thus , the effect captured by the coefficient α1 can still be interpreted as causal.