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A change point analysis of the impact of "environmental federalism" on aggregate air quality in the United States: 1940-98.


A major purpose of this article is to examine three important national air pollution series (nitrogen oxides [NOX], sulfur dioxides [SO2] and volatile organic compounds VOCs) for change points in their trends and in so doing determine to what extent President Ronald Reagan's "Environmental Federalism" (Economic Report of the President 1982, p. 44) had any effect on the trends of these series. Did his devolution of environmental policy from federal control to state and local control positively or negatively affect the trends in these series? Did the Reagan devolution provide the impetus for the beneficial trends in these series that we currently observe? Might the aggregate series we examine tell us anything about the current controversy concerning whether increased state and local competition in environmental decision making might give rise to a "race to the bottom" or "race to the top" with respect to the stringency of environmental standards? (See for example, Cumberland 1981; Glazer 1999; List and Gerking 2000.) First, to give proper context to these questions, we must take a brief look at the history of environmental policy making in the United States.

Before 1955 there was very little environmental policy making. Two major exceptions were the Federal Refuse Act of 1899 and the Federal Food, Drug, and Cosmetic Act of 1938. The first act prevented navigational obstruction of waterways, and the second act set limits on the amount of pesticide residuals allowed in farm products. However, beginning in 1955, federal activism concerning the environment increased resulting in the enactment of several federal environmental laws. The Air Pollution Act of 1955 facilitated cross-state air quality management. The Clean Air Act of 1963 provided permanent federal support for research on air pollution. The Motor Vehicle Air Pollution Control Act of 1965 was aimed at decreasing the level of air pollution from vehicles, and the Air Quality Act of 1967 provided national auto emissions standards. Moreover, the Clean Air Act of 1970 established the Environmental Protection Agency (EPA) for the purpose of setting and enforcing national environmental quality standards. In the following year the EPA established the uniform National Ambient Air Quality Standards (NAAQS). The Clean Air Act was amended in 1977 primarily to set new goals for achieving the NAAQS.

In contrast to the previous 1955-80 era of federal control of air quality standards, much of the environmental decision-making power was devolved from the federal level to the state and local levels under the presidential administrations of Ronald Reagan (1981-89) and George Herbert Walker Bush (1989-93). This policy regime shift has been referred to as the shift to environmental federalism (Economic Report of the President 1982, p. 44).

With respect to environmental federalism, Figures 1 and 2 display governmental expenditures for air pollution abatement and control obtained from Vogan (1996). Unfortunately, the Bureau of Economic Analysis of the Commerce Department discontinued their Pollution Abatement and Control survey with the Vogan article and more recent abatement and control data are unavailable to extend the series in Figures 1 and 2 beyond 1994.


In Figure 1 we have plotted total governmental expenditures for air pollution abatement and control in 1992 chain-weighted dollars. Obviously, from 1972 90, total real governmental expenditures oscillated at or below 1 trillion 1992 dollars and there was no discernible trend in total governmental commitment to environmental policy. However, beginning in 1991, real expenditures on abatement and control doubled to approximately 2 trillion 1992 dollars. With respect to the federal to state and local devolution, Figure 2 displays the proportion of state and local expenditures to total governmental expenditures, both in current and real (1992) dollars. From 1972 to 1981 state and local expenditures, as a proportion, were generally steady and never exceeded 40% of the total. In fact, in one view, the Reagan devolution of environmental expenditures to the state and local governments did not truly begin until 1987, when a discernible trend in the proportion of state and local expenditures becomes evident. As of 1994, the last year of data we have available, the proportion had increased to 59.17%.

Alternatively, in Figure 2, one might consider the trough of 1976 and the increase of 1977, the first year of the Carter administration, as the beginning of a federal to state and local devolution, though not publicly announced as policy. Even so, in 1976-80, total real expenditures on air pollution abatement and control eventually declined after a beginning increase. Our interpretation here is that real devolution did not begin until 1987 during the Reagan administration when the proportion of state and local expenditures as a proportion of total expenditures began a discernable upward trend and total real governmental expenditures began a steady increase. (1) Thus, in our analysis here, if breaks in trend in the NOX, VOC, and SO2 series occur before 1987, they must be attributed to something other than the Reagan devolution and his so-called environmental federalism.

The plan of the rest of this article is as follows: In the next section we discuss the data and empirical methodologies that we use to investigate possible change points in the NOX, VOC, and SO2 series. In section III we describe our change point analysis results in detail. Finally, in section IV, we summarize the results and discuss whether prior federal legislation or the Reagan devolution provided the impetus to the beneficial trends in air pollutant emissions that we see today. In addition, using the previous break point analysis results, along with the expenditure statistics of Figures 1 and 2, we consider the competing "race to the bottom" (for example, Cumberland 1981) and "race to the top" (for example, Glazer 1999) hypotheses in the environmental economics literature regarding Reagan's environmental federalism and in light of the data that we have examined here.



The data we analyze are annual time-series observations on three principal air pollutants in the United States from 1940 to 1998, SO2, NOX, and VOCs. See the EPA publication National Air Pollutant Emission Trends, 1900-1998, Table 3-13, titled "Total National Emissions by Pollutant and Year," pp. 3-19 to 3-20. The EPA also reports data on the following emission series: carbon dioxide (CO), lead (Pb), particulate matter less than 10 microns (PM10), particulate matter under 2.5 microns (PM2.5), and ammonia (NH3). Although these latter five series are important pollution series, they are not analyzed here because of the following reasons. The CO data is made up of several linearly interpolated values that prohibit break point analysis. The Pb series is only available from 1970 forward. Unfortunately, with this series the number of observations in the first regime is so small that conducting meaningful endogenous data-based analysis of change points is not feasible. The series PM10 is quite peculiar in that in 1985 there appears to have been a change in the definition and/or measurement of the series. Annual observations on the emission series PM2.5 and NH3 are, unfortunately, only available from 1990 onward, thus preventing us from investigating any devolution hypothesis of interest.

We intentionally choose "total" emissions for the NOX, SO2, and VOC series rather than per capita emissions because we feel that the effects of pollution emissions on the population are not ameliorated by population growth. That is, if pollution emissions remain the same while the size of the population grows, the impacts of pollution, in terms of contracted diseases, shortened life span, and so on, is not reduced by growing the population. Therefore, it is total emissions rather than per capita emissions on which we will focus our attention.

Much on the issue of the effect of Reagan's decentralization move in environmental policy can be gleaned from the simple time-series plots of the NOX, VOC, and SO2 series depicted in Figure 3. From this graph we can see that there appears to be at least one change point in each series but at different dates during the early to mid-1970s. Positive trends in the VOC and SO2 series appear to break into subsequent negative trends after each series' change point, whereas the subsequent trend in the NOX series appears to be flat. Of course, when using casual inspection, what might appear to be a change point for one investigator might not appear to be a change point for another investigator. The statistical techniques of Bai (1997a, 1997b) that we subsequently use will help us identify potential change points using objective statistical criteria. Moreover, the techniques of Bai allow us to compute confidence intervals of the breaks which visual inspection would not provide. We discuss the econometric methodology of the Bai's endogenous change point analysis in the next section.


Empirical Methodology

The asymptotic theory for change point analysis in multiple regression was developed by Bai (1997a). In that publication he assumes that only one change point occurs. In a later work, Bai (1997b) allows multiple change points. In the following we focus on the single change point case. Somewhat later we will comment on our subsequent multiple change point analysis. Bai's model is more general than the previous change point models in the literature. It allows for lagged dependent variables and trending regressors. Furthermore, the disturbances of the regression can be heterogeneous and dependent over time.

The model that Bai considers is of the following form:

(1) [y.sub.t] = [w.sup.'.sub.t][alpha] + [z.sup.'.sub.t][[delta].sub.1] + [[epsilon].sub.t],

t = 1, 2, ..., [k.sub.0]

[y.sub.t] = [w.sup.'.sub.t][alpha] + [z.sup.'.sub.t][[delta].sub.2] + [[epsilon].sub.t],

t = [k.sub.0] + 1, ..., T.

It is assumed that the change point [k.sub.0] is unknown and, without loss of generality, that the change in the regression model may be partial in the sense that the coefficients on the explanatory variables wt need not change over time, but at the breakpoint [k.sub.0], the coefficients on the [z.sub.t] explanatory variables change from [[delta].sub.1] to [[delta].sub.2].

The least squares method applied to the above piecewise linear regression model is used to estimate the change point [k.sub.0] and, conditional on the estimate of [k.sub.0], is used to estimate the coefficients [alpha], [[delta].sub.1], and [[delta].sub.2]. Let [S.sub.T](k) denote the sum of squared residuals for model (1) with the change point chosen to be k. The least squares change point estimate, k, is defined as the value of k that minimizes [S.sub.T](k). That is,


where the fraction [pi] must be chosen so that at least there are sufficient degrees of freedom to allow the estimation of separate regression models for each regime.

Consider the Wald statistic for testing [H.sub.0]: [[delta].sub.1] = [[delta].sub.2] in model (1) and thus that there is no structural change and no change point. This test statistic is of the form

(3) [W.sub.T](k) = (S - [S.sub.T](k))/[[sigma].sup.2](k)

where S represents the restricted residual sum of squares obtained by applying least squares to the restricted version of model (1) with [[delta].sub.1] = [[delta].sub.2] and [S.sub.T](k) is the unrestricted residual sum of squares obtained by estimating model (1) with change point k. The variance estimate is [[sigma].sup.2](k) = [S.sub.T](k)/(T - q), where q is the number of regression parameters in the unrestricted model (1).

It follows with some algebra that another expression for k is


That is, the least squares point estimate of k is that value of k that maximizes the Wald test statistic over all possible change points k.

Of course, following Andrews (1993, 2003), the critical values for the sup-Wald test statistic


of the null hypothesis [H.sub.0]: [[delta].sub.1] = [[delta].sub.2], assuming the change point [k.sub.0] is unknown, are much larger than the critical values for the conventional Wald test statistic where it is assumed that the change point is known. (2) Andrews (1993) recommends that the fraction [pi] be set at 0.15 to ensure reasonable power of the test. (3)

The approach of Bai (1997a) is to choose the change point k if the sup-Wald test statistic is statistically significant given the adjusted chi-square statistics reported in Andrews (1993, 2003). Otherwise, there is assumed to be no change point and no structural change in the regression model. In the case of a significant change point Bai (1997b) suggests examining, separately, the two regimes defined by the change point. If either or both of these regimes produce a significant change point, then additional, separate, subregime change point analyses (conditional on the previously determined change points) are conducted until no further subregimes produce a significant change point. (4) Of course, if one significant change point is detected and the resulting two regimes produce no additional significant change points, the change point analysis stops.

In his paper Bai (1997a) specifies assumptions concerning the asymptotic behavior of the regressors ([w.sub.t], [z.sub.t]) and the errors et that provide the consistency of the change point estimator k (plim(k) = [k.sub.0]), the rate of convergence of the estimator k ([square root of T]), and the limiting normal distribution of k that provides the foundation for constructing a confidence interval for the unknown change point [k.sub.0].

To proceed with the construction of confidence intervals for [k.sub.0], one must commit to an assumed stochastic nature of the regressors wt and [z.sub.t] and the disturbance [[epsilon].sub.t]. In the following discussion we will assume that [w.sub.t] is not present in the model and, instead of a partial change model, we are assuming that all of the regression parameters change at the change point. Bai considers four major cases: (1) ([z.sub.t], [[epsilon].sub.t]) is a second-order stationary process for the whole sample, (2) ([z.sub.t], [[epsilon].sub.t]) is second-order stationary within each regime, (3) the regressors [z.sub.t] are trend stationary and et is stationary for the entire sample, and (4) the regressors [z.sub.t] are trend stationary and et is stationary for each regime. The computation of the confidence interval for [k.sub.0] is, of course, case-specific.

The confidence interval is given by

[k - [[c.sub.2]L] - 1, k+ [[c.sub.1]/L] + 1]

where k is the point estimate of the timing for the structural change and [c.sub.1], [c.sub.2], and L are dependent on the assumed stochastic nature of ([z.sub.t], [[epsilon].sub.t]), that is, case (1), (2), (3), or (4). In our analysis we have modeled serial correlation in the errors of the regression models when necessary and adjusted the confidence intervals for the change points accordingly. (5)

In the following empirical analysis we used a Gauss program kindly provided by Bruce Hansen to conduct analyses of cases (1) and (2) (see Hansen 1997, 2001). We wrote our own SAS program to investigate the deterministic trend cases (3) and (4).


Now we turn to the analysis of the NOX, SO2, and VOC emission series to determine which of the four Bai cases is appropriate for each series. Looking at the raw data in Figure 3, it seems appropriate to consider the initial part of the data 1940-68 as free of change points. (We call the period 1940-68 "conservative regime 1.") Therefore, we use this initial period to test each series for difference stationarity (DS) or trend stationarity (TS) by means of the augmented Dickey-Fuller test (1979) and to determine whether a tog transformation of the data is necessary or not. Then given a determination of the stochastic nature of the data (DS versus TS) and the need of log transformation or not, we tentatively assume that each series' initial stationary form continues into the second regime after the change point, if such a change point occurs. Then graphical and autocorrelation inspections of the stationary form of each series is used to choose one of the above four possible Bai cases in constructing the confidence intervals for the change points in the series.


In Table 1 we report the results of augmented Dickey-Fuller tests applied to each of the series NOX, SO2, and VOC both in level and log-level form. The Dickey-Fuller test equation contains an intercept and trend in each case because, in the conservatively chosen regime 1, each series exhibits trend. The lag length of the augmented Dickey-Fuller test equations is determined by minimizing the Schwarz-Bayesian Information Criterion (SBC). These results were generated in EVIEWS, version 4.1. As is evident from Table 1, the unit-root tests of the level and log forms of both the NOX and SO2 series indicate that they are DS, whereas the unit-root tests for level and log VOC indicate TS, at least at the 10% (more exactly the 7%) level.

Now we turn to the decision on the proper transformation of the NOX and SO2 series before differencing and the proper transformation to apply to the VOC series before modeling it with deterministic trend. In the case of the NOX and SO2 series we can apply the %logtest procedure in SAS to determine which transformation provides the largest likelihood value, the smallest root mean square error of fit, and smallest Akaike information criteria (ALC) and SBC goodness-of-fit values (see SAS/ETS User Guide 2003, p. 954). From Table 2 we can see that the appropriate stationary transformations of the NOX and SO2 series, given the initial data 1940-68, are, respectively, NO[X.sup.*] = NO[X.sub.t] - NO[X.sub.t-1], the first difference in NOX, and S02" = log(SO[2.sub.t]) - log(SO[2.sub.t-1]), the annual percentage change (in decimal form) in SO2. For the NOX series the log likelihood value is larger and the AIC and SBC goodness-of-fit measures are smaller for the "none" transformation than for the log transformation. The root mean square error criterion using the log transformation is smaller than the "none" transformation but, using a "majority" rule, the "none" transformation is preferred for the NOX series. With respect to the SO2 series, the log likelihood value and the AIC and SBC measures argue for the log transformation whereas the root mean square error favors the "none" transformation. Again, using the majority rule, we choose the log transformation for the SO2 series.

Because the %logtest is only appropriate for DS data, we apply another test for determining whether the VOC series is a log or level deterministic trend. (6) In the initial period, we run a least squares regression of VOC on an intercept and a time index (t) and record the coefficient of determination ([R.sup.2]). Then we run a least squares regression of log(VOC) on an intercept and a time index (t) and compute the fitted values

Log(VOC) = [[gamma].sub.0] + [[gamma].sub.1]t.

Next we compute the transformed fitted values of VOC by computing

VOC = exp(Log(VOC) + 0.5 [(SER).sup.2]),

where SER is the standard error of the log(VOC) deterministic trend regression. Computing the sample correlation between VOC and VOC and then squaring it produces a coefficient of determination, say, [R.sup.2.sub.log]. Then, if [R.sup.2] > [R.sup.2.sub.log], we use the untransformed VOC in a deterministic trend. Otherwise, we use the log transformation of VOC in a deterministic trend. As reported in Table 2, we see that the log deterministic trend for VOC is appropriate.

The stationary forms of each of the series NOX, SO2, and VOC are plotted in Figures 4, 5, and 6. In Figure 4 we see the differenced NOX data appears to have two levels determined by a change point in the early 1970s. Because the variation and temporal correlation in the series appears to be roughly the same across the two regimes, we adopt Bai's case (1) assumption in constructing the confidence interval for the change point, should the regime change be statistically significant according to the sup-Wald test.


In Figure 5 we can see two levels for the percentage change in SO2 data with a possible change point in the early 1970s as well. However, in the first part of the data we note that the variance changes in the first regime in about 1950. Rather than adjusting the data in the first regime to attain homoskedasticity, we choose to restrict the analysis of regime 1 data beginning with 1950. Given the data beginning with 1950 and again looking at Figure 5, it looks like the variation and temporal correlation in the series are roughly the same across the two regimes. Thus, using the SO2 data beginning in 1950, we will adopt Bai's case (1) assumption in constructing the confidence interval for the change point, should the regime change be statistically significant according to the sup-Wald test.

In the plot of the log-transformed VOC depicted in Figure 6, there is a possible change point in the early 1970s. Looking at Figure 6, it looks like the variation and intertemporal correlation of the data around two imaginary log trends before 1970 and after 1970 are roughly the same. Thus, we will adopt Bai's case (3) assumption in constructing the confidence interval for a change point, should the regime change be statistically significant according to the sup-Wald test.

We report our formal Bai change point estimation and confidence interval results for the NOX, SO2, and VOC series in Table 3. Note that from the analysis presented in Tables 1 and 2, the preferred functional forms for the change point analysis of the NOX, SO2, and VOC are, respectively, DNOX, DLSO2, and LVOC. However, for comparison purposes, we present the results for the other possible functional forms in Table 3 as well. Using the preferred functional forms, the estimated change points for the NOX, SO2, and VOC series are, respectively, 1978, 1973, and 1969, all occurring before the first year of the Reagan presidency (1981) and the date of effective devolution, 1987. With respect to the confidence intervals of the change points in these three series, only the confidence interval for the change point in the NOX series encompasses what we believe is the real beginning year of the Reagan devolution, namely, 1987, and then only in the extreme end of the interval. In contrast, the confidence intervals for the change points in the SO2 and VOC series definitely do not include the proposed devolution date of 1987.

As discussed, we must consider the possibility of additional change points in each series. As reported in Table 3, the construction of sup-Wald tests in the separate regimes in each series produce insignificant results. Thus, we conclude that, in each of the series NOX, SO2, and VOC, there is only one change point. (7)


What do we conclude from the change point analysis? First, the change point estimates for the NOX, SO2, and VOC series indicate that the downward trend in these emissions began before President Reagan took office in 1981 and certainly before 1987 when we propose that the real Reagan devolution began. Evidently, the federal legislation before 1981 and 1987 played a significant role in providing the impetus in bringing about the beneficial change in trend for these series. Although it is impossible to attribute the occurrence of the change points of these series to any one federal legislative act, one might surmise, given the proximity of the change points, that the Air Quality Act of 1967, the Clean Air Act of 1970, and the 1977 amendments to the Clean Air Act played important roles in changing the trends of the SO2 and VOC series from positive to negative and at least arresting the positive trend of the NOX series.

Given the results we previously obtained, it would be interesting to entertain the competing "race to the bottom" and "race to the top" hypotheses in the environmental economics literature as it relates to the Reagan devolution that began in earnest in 1987. The former hypothesis (for example, Cumberland 1981) states that the devolution of federal control of environmental regulation of air pollution to state and local control will, because of state and local competition, lead state and local jurisdictions, in the pursuit of higher employment, greater wage income, and a larger tax base, to lower environmental standards to attract new companies who desire to evade strict pollution controls. In contrast, the latter hypothesis (for example, Glazer 1999) claims that state and local jurisdictions would have a tendency to impose excessively stringent regulations to induce firms causing pollution to leave the jurisdiction, thereby exporting pollution out of their jurisdictions. What do our current data say about these competing hypotheses?

With respect to the effect of Reagan's environmental federalism on the trends in the NOX, SO2, or VOC series, in none of them did there occur any additional change points after the initial change point occurred. From Figure 2 we previously noted that the real Reagan devolution probably began in 1987 when the proportion of state and local participation began to increase dramatically. At the same time, in Figure 1, the level of real total governmental expenditures for air pollution abatement and control began to increase and significantly so in the last four years for which we have data, 1991-94. Possibly the downward trends in SO2 and VOC and the flat trend in NOX, were sustained because of the increased real expenditures that occurred in 1987 following the change points identified in these three series and despite the Reagan devolution that began in the same year. We might ask whether these beneficial trends could have been made more beneficial (negative) had not the participation of the state and local governments increased beginning in 1987. To the contrary, we might ask whether, in the absence of the Reagan devolution, if the continuation of the beneficial trends we currently see would have not been sustained given a continuation of the previous level of federal control. Maybe the current beneficial trends would have been worsened without the Reagan devolution.

What we are missing is a counterfactual that would allow us to clearly determine the effect of the Reagan devolution on the recent trends of our emissions series. One useful counterfactual, of course, would have been for real total expenditures to remain the same while state and local government participation increased. Had this case prevailed while the trend in the emission series incurred no additional change points, one might have concluded that the Reagan devolution, and hence redistribution of control, had no significant impact as postulated in the theoretical model of Fredriksson and Gaston (2000). Unfortunately this counterfactual did not occur, and we are left with the fact that we are unable, given the aggregate data we examine, to determine either detrimental, beneficial, or neutral effects on trend of the Reagan devolution. One conclusion we can draw from our analysis, however, is that the beneficial change points of the NOX, SO2, and VOC series occurred because of federal legislation and not the Reagan devolution.

To be definitive on the issue of the effect of Reagan's environmental federalism on the trend in our air pollutant emissions, one would need to proceed beyond the current aggregate data to state level data. Unfortunately, previous analyses of state level data (including most recently, List and Gerking 2000; Millimet 2003; and Millimet and List 2003) have not applied change point analysis to the panel data analyzed. One recent econometric paper that addresses the issue of detecting change points in panel data is de Wachter and Tzavalis (2004). This would be a beneficial area for additional research on the effect of Reagan's environmental federalism on environmental policy making.


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(1.) From 1981-82, a substantial amount of devolution from the federal level to the state and local level occurred through administrative channels. According to the Executive Office's Council on Environmental Quality (1983, p. 75): "By the end of 1982 state governments had been delegated enforcement responsibilities for over 95% of applicable New Source Performance Standards, up from 64% at the beginning of the year. In addition, of the 60 State and Local agencies eligible to grant and enforce new source (air) permits, 48 had been delegated full or partial authorities by the end of 1982, up from 26 at the end of 1981." After assuming office, Reagan cut the size of the Councel on Environmental Quality from 60 (under President Carter) to 6. Moreover, excluding the Superfund, between 1981 and 1983, Reagan reduced employment at the EPA by 22.6% (Davies 1984, p. 147). Evidently, according to the percentage of state and local participation in environmental expenditures displayed in Figure 2, significant devolution occurred with a delay and began in approximately 1987, as argued in the text.

(2.) Some adjustment of the critical values of the sup-Wald test must be made to accommodate the increased possibility that over many choices of k there are likely to be more rejections of the null hypothesis in repeated samples than if k is fixed.

(3.) Andrews argues that the use of [pi] values smaller than 0.15 increases the power of the test al the extreme ends of the sample, but at the same time, greatly reduces the power over the rest of the sample. On the other hand, a choice of [pi] greater than 0.15 will tend to limit one's ability to detect change points even in the moderately early or late stages in the data.

(4.) Bai (1997b) calls this procedure "sequential change point estimation." In the case of multiple change points he shows that the sequential change point estimation approach results in consistent estimation of the multiple change points.

(5.) See sction II.D in Bai (1997a) for more detail on the calculation of [c.sub.t], [c.sub.2], and L both with and without serial correlation in the regression errors.

(6.) For a discussion of this procedure see, for example, Wooldridge (2003), p. 209.

(7.) In work not reported here, we examined the sensitivity of the estimated change points to the choice of the characterization of trend, be it stochastic or deterministic. When modeling the NOX series as a deterministic trend, we found significant change points in 1957, 1969, 1979, and 1987. When modeling LSO2 as a deterministic trend, we found significant change points in 1954 and 1965. With respect to modeling DLVOC as a level shift we found a significant change point in 1970. Therefore, as one can see, the choice of the characterization of the trend for a series is important in determining the results of a change point analysis of the series. Using deterministic trends to characterize change points in stochastically trending data leads to the identification of many more change points. In contrast, in our case, the characterization of the change points of a deterministically trending series by means of level shifts in differenced data does not seem to significantly increase the number of change points found or their locations. We prefer our change point analysis as presented in Table 3 because of two reasons. First, the numerous change points identified in the NOX and LSO2 series using deterministic trends do not correspond to the dates of commonly cited environmental legislation. Second, we have some confidence in our characterization of trend vis-a-vis the results of unit root tests conducted on several subsamples of the data. For example, in the NOX data we used a prechange point period of 1940-57 and found a unit root (stochastic trend). In the LSO2 series we examine the subsamples 1955-65 and 1966-98 and found a unit root in each subsample. We could not conduct a unit root test on the first subsample of 1950-54 for LSO2 because of the lack of data. Given the single change point of 1970 obtained by modeling DLVOC as a level shift in differenced series, we let the prechange point analyses of the VOC and LVOC series prior to 1969 reported in Tables 1 and 2 speak for themselves.


AIC: Akaike Information Criteria

DS: Difference Stationarity

EPA: Environmental Protection Agency

NAAQS: National Ambient Air Quality Standards

NOX: Nitrous Oxides

PM: Particulate Matter

SBC: Schwarz-Bayesian Information Criterion

SO2: Sulfur Dioxides

TS: Trend Stationarity

VOC: Volatile Organic Compound


* This paper was presented at the Exploring Frontiers in Applied Economics Conference, a symposium in honor of Professor Stanley R. Johnson held at Iowa State University on October 25, 2003. Several participants provided some very useful comments. We very much appreciate that Professor Bruce Hansen of the University of Wisconsin provided his Gauss Change Point program to us. We extensively used it in our analysis. We also appreciate comments and suggestions provided by Professors Nathan Balke, Per Fredriksson, Dann Millimet, and the anonymous referees for this journal. All errors that remain in this paper are the sole responsibility of the authors.

Fomby: Professor, Department of Economics, 301M Umphrey Lee Building, Southern Methodist University, Dallas, TX 75275. Phone 1-214-768-2559, Fax 1-214-768-1821, E-mail

Lin: Finance Department, Consumer Markets Division, Countrywide Home Loans, Piano, TX 75024. Phone 1-972-781-3509, Fax 1-972-608-1127, E-mail

Augmented Dickey-Fuller Unit Root Test Results

 ADF Test
Series Transformation Regime I Statistic p-Value *

NOX Level 1940-68 0.484545 0.9985
 Log 1940-68 -0.784412 0.9526
 Differenced level 1940-68 -5.485057 0.0001
 Differenced log 1940-68 -6.971551 0
S02 Level 1940-68 -0.809063 0.9492
 Log 1940-68 -1.159640 0.8942
 Differenced level 1940-68 -2.654322 0.0102
 Differenced log 1940-68 -2.809209 0.0069
VOC Level 1940-68 -3.360682 0.0773
 Log 1940-68 -3.409021 0.0704

* MacKinnon (1996) one-sided p-values.


Log Versus Level Transformation Tests Results

 Conservative Log
Series Regime I Transformation Likelihood RMSE

NOX 1940-68 NONE -397.001 1.2103E+11
 1940-68 LOG -398.845 1.1433E+11
SO2 1940-68 NONE -437.019 2.12E+12
 1940-68 LOG -436.819 2.25E+12
VOC 1940-68 NONE 0.9406
 1940-68 LOG 0.9452

Series Regime I AIC SBC

NOX 1940-68 796.001 797.334
 1940-68 799.690 801.023
SO2 1940-68 882.038 887.367
 1940-68 881.637 886.966
VOC 1940-68


Structural Change at Unknown Timing: Estimation and Testing Results

 Break to Model Structure
Series * Model Period Estimate ** Sup-Wald

DNOX# Level shift 1941-98 1978# 9.209740
DNOX# Level shift 1941-78 1961 3.702004
DNOX# Level shift 1979-98 1986 3.264213
DLNOX Level shift 1941-98 1973# 14.082979
DLNOX Level shift 1941-73 1947 1.501649
DLNOX Level shift 1974-98 1978 1.046245
DLS02# Level shift 1950-98 1973# 8.916204
DLS02# Level shift 1950-73 1961 2.152421
DLS02# Level shift 1974-98 1983 1.777319
DS02 Level shift 1950-98 1982 3.544681
LVOC# Time trend 1940-98 1969# 306.274787
LVOC# Time trend 1940-69 1945 4.984311
LVOC# Time trend 1970-98 1993 3.168597
VOC Time trend 1940-98 1969# 329.202497
VOC Time trend 1940-69 1962 5.662975
VOC Time trend 1970-98 1976 2.697577

 Break to Model Structure

Series * p-Value 90% CI Estimate ***

DNOX# 0.037957 (1969, 1988)
DNOX# 0.422159 NA
DNOX# 0.501065 NA
DLNOX 0.003864 (1968, 1982)
DLNOX 0.907551 NA
DLNOX 0.994329 NA
DLS02# 0.043433 (1963, 1982)
DLS02# 0.748010 NA
DLS02# 0.841033 NA
DS02 0.449265 NA
LVOC# 0.000000 (1967, 1971)
LVOC# 0.248967 NA
LVOC# 0.519752 NA
VOC 0.000000 (1967, 1971)
VOC 0.186164 NA
VOC 0.619284 NA

Notes: * DNOX denotes first difference of nitrogen oxides; DLNOX
denotes first difference of the logarithm of nitrogen oxides; DLSO2
denotes first difference of the logarithm of sulfur dioxide; DSO2
denotes first difference of sulfur dioxide; LVOC denotes logarithm of
volatile organic compounds; VOC denotes volatile organic compounds.
DNOX, DLNOX, DLSO2, and DSO2 are analyzed using Bai's case (1) with
white noise errors. LVOC and VOC are analyzed using Bai's case (3) with
AR(2) errors. Boldface is the preferred log versus nonlogarithmic
transformation. ** Boldface indicates that the break is significant.
*** CI = confidence interval.

Note: Figures in bold indicated with #.
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Title Annotation:air pollution control
Author:Fomby, Thomas B.; Lin, Limin
Publication:Economic Inquiry
Geographic Code:1USA
Date:Jan 1, 2006
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