thousand acres of land or is of sufficient size as to make practicable .... income reliance on extraction and primary ...... Montana Proceedings RMRS-P-1 5-VOL-2.
Economies in Transition and Public Land-Use Policy: Discrete Duration Models of Eastern Wilderness Designation Randall S. Rosenberger, Mark Sperow, and Donald B. K. English ABSTRACT Land-use policies nia v affect the structure of local ecoiiOiflic.v (is the' respond to infernal and external factors. We app/v a discrete duration model to estimate the ci f'ct of designated wilderness on the rate and timing 0/ counties economic transition in the Appalachian Region from 1969 to 2000. Transitions are measured as the tear in which non-labor sources of income and services sector employment dominate the aggregate of resource extraction and manufacturing sectors as sources. Marginal effects and elasticities show designated wilderness had no practical effect on rates and timing of transition. (J EL Q24, RI I)
I. INTRODUCTION Federal land-use policies such as the Multiple-Use Sustained-Yield Act and the National Forest Management Act explicitly and implicitly use community economic stability as an important motive for their enactment (Rasker 1994). These policies typically target a reduction in the variability of raw materials supply from federal lands, thereby stabilizing local economies that are dependent upon them. The national park The authors arc, respectively, assistant professor, Department of Forest Resources, Oregon State University, assistant professor, Division of Resource Management, West Virginia University, and Visitor Use Monitoring Program Manager, U.S.D.A. Forest Service, Washington, D.C. This project was supported by funds from the US Department of Agriculture, Forest Service, Southern Research Station, Cooperative Agreement // SRS 01-CA-11330144-397. Mike Strager and Jackie Strager, Natural Resources Analysis Center, West Virginia University, developed the ArcView utility for calculating patial measures of land designations. Any errors are the sole responsibility of the authors.
Land Economics. May 2008 . 84 (2): 267-281 ISSN 0023-7639; E-ISSN 1543-8325 © 2008 by the Board of Regents of the University of Wisconsin System
system and federal land use policies such as the Wilderness Act and the Eastern Wilderness Act,' however, target the protection of pristine areas that have high levels of ecological services and amenity values, but possibly with the loss of raw materials extraction. This paper introduces a method for evaluating the effect of land preservation on local economies, or to address the question "Does preserving large quantities of federal land in pristine condition help or hinder local economies?" The method could be extended to evaluate other land-use policies. The tradeoffs imposed by wilderness designation are a non-trivial issue— the National Wilderness Preservation System in the United States contains 662 designated wilderness areas encompassing nearly 106 million acres (Cordell et al. 2005). Excluding Alaska, the contiguous United States has 614 designated areas covering about 48 million acres, with 128 of these areas and nearly 3 million acres located in the eastern United States (Cordell et al. 2005). The United States' economy, in The Wilderness Act of 1964 defined wilderness as "an area of undeveloped land retaining its primeval character and influence, without permanent improvements or human habitation, which is protected and managed so as to preserve its natural conditions and which (I) generally appears to have been affected primarily by the forces of nature, with the impact of man's work substantially unnoticeable: (2) has outstanding opportunities for solitude or a primitive and unconfined type of recreation; (3) has at least five thousand acres of land or is of sufficient size as to make practicable its preservation and use in an unimpaired condition: and (4) may also contain ecological, geological, or other features of scientific, educational, scenic, or historic value." (Public Law 88-571; 78 Stat. 890) In 1974, the US Congress passed the Eastern Wilderness Act. This act clarified provision (I) of the Wilderness Act by allowing land that has recovered from prior use to be included in the National Wilderness Preservation System.
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general, has been moving away from a dependence on resource extraction and primary manufacturing to a services-based economy. Consequently, employment and income in the United States are no longer dominated by resource extraction and primary manufacturing—the "old economy"—having shifted to services, information technology, and non-labor sources of income—the "new economy." The services sector began to dominate the U.S. economy in 1976; however, resource extraction and primary manufacturing in rural areas dominated the rural landscape until 1982, when rural economies shifted to services and information technology, on average (Rosenberger and English 2005). This shift or transition was fueled, in part, by three forces (Rasker 1994): a decoupling of the industrial economy from the primary products economy (i.e., raw materials); a decoupling of employment from production; and a globally efficient flow of capital. The effect of federally designated wilderness on the structure and function of local economies is currently subject to debate. Power (1996) discussed the arguments regarding the role of wilderness on the well-being of local economies. While these arguments are being investigated in the scientific community, there is no general agreement about the positive or negative effects of wilderness area designation on local communities. The negative argument contends that wilderness designation suppresses economic growth and development by restricting certain uses of these lands (Davis and Davis 1987; Patric and Harbin 1998). The positive argument contends that economies with designated wilderness near them have a comparative advantage for economic growth over other economies that are not near wilderness (Rosenberger and English 2005). These advantages include their ability to keep pace with national trends toward an economy based on services provision and information technology, and to provide residents with higher quality of life. Wilderness supplies amenities such as clean air, clean water, and untrammeled open space that attract people and services-
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sector jobs, retirees, and vacation homeowners, thus fueling economic growth. The downside to this type of growth is the potential replacement of high-wage extraction and manufacturing jobs with lowwage, seasonal services jobs, and the displacement of low-income residents with new residents who will benefit most from changes in land use patterns. Earlier analyses of aggregate-level data for the eastern and western regions of the United States demonstrated (1) significant and positive associations between wilderness and economic indicators of growth in population, jobs, income, and services sectors for rural areas; and (2) a lack of negative associations between wilderness and economic indicators of growth for resource extraction-dependent sectors (Rosenberger and English 2005). Growth equilibrium models that measure the linkages between population and employment migration patterns and the distribution of natural amenities on the landscape found designated wilderness areas had neither a consistent positive effect on population and employment growth nor a negative effect on resource-based employment in rural counties of the western and eastern United States (Duffy-Deno 1998; Rosenberger and English 2005). Acting on evidence from association tests in the western United States, Lorah (2000) hypothesized that high levels of natural or environmental amenities, such as wilderness, may act as catalysts in transforming rural economies away from resource-extractive industries to relatively diversified economies that attract tourists, small businesses, and retirees. In his analysis, Lorah (2000) estimated correlation coefficients between the date of transition away from resourceextraction dominated industries and the percentage of a county's land base in either wilderness or in wilderness, national parks, national monuments, and wilderness study areas for all western counties with populations less than 2,500 for the years 1969 to 1996. Counties were classified as either "old economy" if the ratio of non-labor income from dividends, interest, and real estate (DIRE) to total income from resource
84(2) Rosenberger, Sperow, and English: Discrete Duration Models of Eastern Wilderness 269 extraction (agriculture, forestry, and mining) sectors was less than one; counties with ratios greater than one were classified as 'new economy." The year in which the ratio became greater than one served as the transition year. The negative and significant correlation coefficient he found indicated that increasing quantities of wilderness were associated with earlier transitioning of rural economies. If the study area was further restricted to rural counties not adjacent to metropolitan counties, the same association became stronger. And when additional types of amenity lands were included (e.g., national parks, national monuments, and wilderness study areas), the associations were about the same as with wilderness alone. Lorah (2000) concluded that western rural counties with nearby environmental amenities as supplied by wilderness areas help shape local economies through their comparative advantage to attract tourists, immigrants, and employers as compared to counties dependent upon the extraction of raw materials. However, correlation coefficients identify associations in the data, but do not imply causality. If we are to argue that wilderness designation is a catalyst in the transition of local economies from employment and income reliance on extraction and primary manufacturing to services-sector jobs and non-labor income, then we need to apply a framework that has the potential to measure causality. This paper introduces a discrete duration model for identifying and measuring the effect of wilderness designation on the movement of county economies toward the new economy. Duration models enable us to measure the marginal effect federal wilderness designations may have had on the speed with which county economies have or have not shifted from dependence on resource extraction and primary manufacturing (the old economy) to economies based on amenities, services, and non-labor income (the new economy). II. DISCRETE DURATION MODELS Models based on longitudinal data, known as duration models, event history
models, survival models, and failure-time or reliability models, have been developed and applied by a variety of disciplines (BoxSteffenmeier and Jones 2004; Kiefer 1988; Tuma 1994). These models have been used to identify and measure temporal patterns and causes of change and have been applied by economists to investigate the length of unemployment spells (Meyer 1990), durations of strikes (Kerman 1985; Gunderson and Melino 1990), and job search and migration patterns (Detang-Dessendre and Molho 1999). Other applications include the timing of policy adoption (Kerr and Newell 2003; McCammon 1998; Berry and Berry 1990), political changes (Gasiorowski 1995) and length of peace spells (Beck, Katz, and Tucker 1998; Box-Steffensmeier and Zorn 2001). More recently, duration models have been extended to analyze factors associated with land-use changes (Waldorf 2003; Hite, Sohngen, and Templeton 2003; Irwin and Bockstael 2002; Vance and Geoghegan 2002; Coomes, Grimard, and Burt 2000). The longitudinal data for this analysis consists of historical county-level economic data for all counties in the Appalachian Region (1 = 410 counties; z = 32 years from 1969-2000). This study measures the rate of transition for counties from predominantly resource-extractive industries to non-extractive industries using two transition indicators. The first transition indicator focuses on sources of income, similar to Lorah's (2000) analysis because the primary source of income is an indicator of economic dependency. Economies dependent upon a primary sector such as resource extraction or manufacturing are likely to have these sectors providing the majority of their income. However,'as economies diversify other sources of income such as nonlabor sources increase (Lorah 2000). An income indicator that identifies the primary source of income is estimated as the ratio of non-labor income (DIRE plus government transfer payments for retirement benefits) to income from the mining, manufacturing and agriculture, forestry and fisheries sectors. Two states are defined based on the
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income indicator: (1) a county is dependent on extraction/manufacturing if the income ratio is less than one; and (2) a county is dependent on non-labor income if the income ratio is greater than one. Based on these data, the income indicator captures about 50% of total personal income in the region—non-labor's share of total personal income increased from 20% in 1969 to 33% in 2000, while extraction/manufacturing's share decreased from 31% in 1969 to 15% in 2000. The second transition indicator focuses on changes in sources of employment by assessing the predominant jobs of county residents. The ratios of service-sector jobs to extraction/manufacturing (agriculture, forestry, and fisheries services plus mining plus manufacturing) jobs are calculated for each county in each year. Two additional states are defined based on the employment indicator: (3) a county is dependent on production/manufacturing if the employment ratio is less than one; and (4) a county is dependent on services if the employment ratio is greater than one. The employment indicator captures about 50% of total employment in the region–servicesector's share of total employment increased from 16% in 1969 to 28% in 2000 while extraction/manufacturing's share decreased from 32% in 1969 to 18% in 2000. Our interest is on the transition from Income State (1) to Income State (2), and Employment State (3) to Employment State (4). In discrete duration models, the dependent variable is coded as a binary variable where 0 = county i in time t has survived national trends to the new economy and I = county i has transitioned to the new economy in time t, where t = 1969,. . .,2000. The estimated value of the dependent variable is the hazard rate or transition rate. The hazard rate (h11) is the probability that county i will transition to the new economy in time t conditional on the fact that it has not transitioned—the risk of transitioning. The survival rate (1 - h,) is the risk of not transitioning (or surviving) in time t.
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Discrete duration models are generally estimated using logistic regression given that hazard rates range between 0 and 1. Logistic models take the log-transform of the hazard rates (hi,) for county I in time t: log(/z,/(1 -
[1]
The log-transformation is the log odds ratio of the probability of county I transitioning in time t (i.e., h1, or the hazard rate) to the probability of county I not transitioning in time t (i.e., I - or the survival rate). A commonly used function for this model is the logit function: log ( I hit - hi) =
/ + /3Xi 1,
[2]
+ I2'2it + + [3kA'kü,
where X1 , X2..... Xk are explanatory variables such as population, total income, location factors (proximity to airports and metropolitan areas), and the quantity of federally designated wilderness for county I in time t. The parameters, #0,. flk, are estimated by the model and represent the marginal effect of the explanatory variables on the hazard rate, h,. The predicted probability of a county transitioning in time t (h,,) is recoverable by et'X h it = I + e'
[3]
The logistic distribution, however, assumes the response surface is symmetric about h, = 0.5. In essence, the logit model approximates a parametric exponential model, which implies the underlying hazard rate is flat or constant over time. The assumption of a constant hazard rate with respect to time may not fit the distribution of empirical data. The complementary loglog model is considered to address this constraint imposed by the logistic model. The distribution of the complementary loglog model most closely resembles a Weibull distribution that is asymmetric, slowly departing from h1, = 0 and quickly approaching h, = 1. When there are relatively
Pr 84(2) Rosenberger,
Sperow, and English: Discrete Duration Models of Eastern Wilderness 271
few transitions in the data (i.e., "l's"), logit and complementary log-log model estimates can differ substantially (Box-Steffensmeier and Jones 2004). Non-convexities in the temporal pattern of the data, such as agglomeration effects and accumulations of designated wilderness acreage over time, also may give rise to asymmetric distributions. The complementary log-log or extreme value model may be written as log[ - log( ) Ii)] fib +
= fi 1 X i ,, + /3,X2 1 , + . . + 13 A XA
[4]
Estimated parameters from this model are interpreted in a similar fashion as the logit model. The predicted probability of a county transitioning in time t is recoverable from the complementary log-log model by h11 = I - exp[—exp(/3'X)].
[5]
Two additional issues must be considered when estimating discrete duration models-- temporal-dependency and right-censoring (Box-Steffensmeier and Jones 2004). Each county adds an observation for each year in the dataset. Dependence among repeated observations for each county is likely--the risk of transitioning for a county in any given year is not independent of its status in previous years. However, there are simple methods of accounting for temporal-dependence in discrete time duration data, which makes discrete duration models desirable. These methods include: (1) specifying temporal dummy variables; or (2) specifying some functional form (linear, natural logarithm, polynomial) of the duration length for each observation (Box- Steffen smeier and Jones 2004; Beck, Katz, and Tucker 1998). While the dummy variable approach is simple, if the number of years covered in a dataset is large, then the number of temporal dummy variables is large. We use a parsimonious specification using duration length instead of temporal dummy variables, which is supported by likelihood ratio tests.
The issue of right-censoring makes many standard regression estimators inappropriate for duration models (Allison 1984; BoxSteffensmeier and Jones 1997, 2004). Each county will fall into one of three categories–Al) transition occurred before the study period (all annual observations are equal to 1); (2) a county transitions sometime during the study period; or (3) a county survives transitioning throughout the study period (all annual observations are equal to 0). Counties in (1) are leftcensored—they contain very little information for measuring hazard rates and are dropped from the dataset. Counties in (2) start in one state and transition to the other state during the study period (i.e., a series of zeros followed by a series of ones, the switching point signifying the year of transition). Counties in (3) are right-censored—we do not know when (or if) they will transition to the new state in the future, although the estimated model can provide a prediction. III. STUDY AREA AND DATA
The study area for this analysis is the Appalachian Region of the eastern United States. The Appalachian Region of the eastern United States is an official designation by the Appalachian Regional Commission and consists of 410 counties in all or part of 13 states covering 200,000 square miles ranging from southern New York to northern Mississippi. About 42% of the estimated 23 million people residing in this area are considered rural. Over 90% of Appalachian Region's counties are considered nonmetropolitan. The history of the region is one of economic dependence on natural resource extraction and manufacturing (Billings and Tickamyer 1993). A lack of incentives, information, and motivations to protect natural areas resulted in the exhaustion of timber from forested areas of the Appalachian Region and other parts of the eastern United States. The historic prevalence of a resource extraction based economy and non-resident land ownership patterns have
Ii
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Land Economics TABLE I
VARIABLE DEFINITIONS FOR WILDERNESS DURATION MODELS
Variable
Definition
YRINC 0,1: Unearned income > extraction income DUR_INC Number of years before income transition YREMP 0,1: Services jobs > extraction jobs DUR_EMP Number of years before jobs transition D(POP)_ Lagged annual density of total county population D(EMP)_ 1 Lagged annual density of total county employment PCPSINC Lagged annual per capita personal income (2000 dollars) D(QWA 15), Density of total wilderness acres in time i DUMWAI5 0,1: County has wilderness acres ADJURB 0,1: County is adjacent to an urban county CITY 0,1: County has city with population > 25,000 AIRPORT 0,1: County has a commercial airport RURAL 0,1: County is rural
had devastating economic and social effects on Appalachian communities that persist to this day (Lewis 1998). This legacy led to federal purchases of large tracts of recovering forests for the purposes of protecting watersheds, timber management, recreation opportunities, stabilizing local economies, and preserving natural resources and amenities. Federal wilderness designation was overlaid on parts of these federally managed lands. Data used in this analysis are derived from a variety of sources. Variable names and descriptions are listed in Table 1. The dependent variables (ratios of income sources and employment sectors) are calculated from annual observations collected by the U.S. Department of Commerce, Economics and Statistics Administration, Bureau of Economic Analysis, Regional Econo,nic hiformation System (REIS) CD, 1969-2000 data. Explanatory variables such as total population, total employment, per capita personal income (in constant dollars-2000) are also derived from the REIS CD. Dummy variables were derived from the U.S. Department of Agriculture, Economic Research Service's databases
May 2008
(ERS 2004) that identify the presence of a city with more than 100,000 in total population (Urban Influence Codes), adjacency to an urban county, and rural-urbanmetropolitan classifications (Rural/Urban Continuum Codes). The presence of an airport is identified through Environmental Systems Research Institute, Inc., ESRJ Data and Maps CD 2: United States, 1999. Wilderness quantity is calculated using Geographic Information Systems (GIS) and Conservation Biology Institute. CBI/ W WE Protected Areas Database, Second Edition, November 2001, data CD as the proportion of total area within a 15-mile radius from a county's centroid that is federally designated wilderness. This procedure follows Lorah and Southwick's (2003) application to the western United States where 50-mile buffers were used. Selection of a 15-mile radius for the eastern U.S. is comparable to the 50-mile radius for the western United States when the average county size in each region is considered. Specifying that the analysis consider areas a specific distance from the county center enables us to account for wilderness lands that are just outside the boundary of each county but may be directly influencing county economies. The choice of larger radii (e.g., 35-miles or 50-miles) significantly reduced the variation in wilderness quantity across counties. IV. EMPIRICAL DURATION MODELS The binary coded dependent variable identifies whether or not extraction/manufacturing supported personal income and employment dominate non-labor sources of income and service-sector employment relative to extraction/manufacturing in a given year. If the ratios of non-labor income or services-sector employment to extraction/ manufacturing income or employment, respectively, are greater than one, signifying the county has transitioned to the new economy the dependent variable is coded "1" in a given year. Otherwise, the county is yet to transition (the ratio is less than one), so the dependent variable is coded "0" for
84(2) Rosenberger, Sperow, and English: Discrete Duration Models
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Eastern Wilderness 273
TABLE 2 TRANSITION RATES IN TIlE APPALACHIAN REGION, 1969-2000 (N = 410) Employment Indicator Income Indicator
Duration Number of % of All Hazard Survivor Number of % of All Hazard Survivor Rate't in Years Counties Counties Ratec Rated Counties Counties - -Ratec 137 9
13 4 10 '7 22 3 9 24 27 21 16 6 8 8 6 7 6 2 2 6 3 7 5 5 6 IS
33.41 2.20 3.17 0.98 2.44 4.15 5.37
0.24 0.49 0.73 2.20 5.85 6,59 5.12 3.90 1.46 1.95 1.95 0.24 1.46 1.71 1.46 0.49 0.49 1.46 0.73 1.71 1.22 1.22 0.24 0.24 1.46 3.66
33 0.03 0.05 0.02 0.04 0.08 0.11 0.01 0.01 0.02 0.044 0.15 0.20 0.19 0.17 0.07 0.10 0.11 0.01 0.09 0.12 0.11 0.04 0.04 0.14 0.08 0.21 0.18 0.22 0.04 0.05 0.40
0.96 0.92 0.90 0.86 0.80 0.71 0.70 0.70 0.68 0.65 0.55 0.44 0.36 0.30 0.28 0.25 0.22 0.22 0.20 0.18 0.16 0.15 0.14 0.12 0.11 0.09 0.07 0.06 0.06 0.05 0.03
5 5 2 4 0 2 4 5
4 11 12 5
14 17 8 8 4 16 8 14 7 3 10 13 9 14 9 7 153
8.05 0.24 1.22 0.24 1.22 0.49 0.98 0.49 0.00 0.49 0.98 1.22 0.98 2.68 2.93 1.22 3.41 4.15 1.95 1.95 0.98 3.90 1.95 3.41 1.71 0.73 2.44 3.17 2.20 3.41 2.20 1.71 37.32
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.03 0.04 0.02 0.05 0.06 0.03 0.03 0.02 0.06 0.03 0.06 0.03 0.01 0.05 0.07 0.05 0.08 0.06 0.04
0.99 0.98 0.98 0.97 0.96 0.95 0.95 0.95 0.94 0.93 0.92 0.91 0.88 0.84 0.83 0.79 0.74 0.72 0.70 0.69 0.64 0.62 0.58 0.56 0.56 0.53 0.49 0.47 0.43 0.41 0.39
Income transition indicator = non-labor income > extraction income. Employment transition indicator = services jobs > extraction + manufacturing jobs. Hazard rate = number transitioned in year i/number at risk in year I. d Survivor rate = cumulative proportion surviving to t (I - hazard rate, - )proportion surviving,.
that year. Duration periods range from zero years (left-censored-the county transitioned to the new economy prior to the analysis period) to 32 years (right-censored-the county has survived transitioning to the new economy). Table 2 provides the number of counties in each duration period-along with their empirical hazard rates and survivor rates for both transition ratios. Over 33% of the counties are left-censored for the income indicator-non-labor sources of income exceeded extraction/manufacturing sources
prior to 1969. By 1976, over half of the counties had transitioned to an economy where non-labor income dominated extraction/manufacturing income. Less than 4% of the counties survived transition in the income indicator by 2000. The employment indicator has a much different pattern than the income indicator. Only about 8% of all counties had trànsitioned to services-sector employment dominating extraction/manufacturing employment prior to 1969. The number of counties transitioning did not significantly increase until around 1982 and
1'
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J_aiiI Lcoiiuniu .s
did not reach a majority of the counties until 1995. Over 37% of counties survived transition by 2000—these counties are right-censored for the employment indica01.
\letropolitan counties, on average, had tiansitioned from natural resource extraction and manufacturing as significant sources of personal income and employment earlier than nonmetropolitan (urban ind rural) counties, as noted previously. Therefore, in order to control for the effect of metropolitan counties in the data, four duration models are estimated. Two models are based on all eligible (not left-censored) counties—Model A for the income transition indicator and Model C for the employment transition indicator. Two additional models are based on eligible (not leftcensored), nonmetropolitan (urban and rural) counties—Model B for the income transition indicator and Model D for the employment transition indicator. The dataset began with 13,120 observations-410 counties by 32 years. The dataset was subsequently reduced to account for simultaneity issues between the dependent variables and some of the independent variables, left-censored counties, and information redundancies. Discrete duration models suffer from an identification or simultaneity problem which occurs when dealing with temporal data and causal relationships between observations in any given year. If population is measured in the same year as the transition indicator, the question is whether the population change occurred before or after the transition. A simple solution is to lag all continuous variables, such as population, employment, and per capital personal income. Therefore, the year 1969 data are dropped from the datasets to account for the lagged explanatory variables. The designation of wilderness also may be simultaneously determined with income and employment. It is possible that changes in the local economy (e.g., higher local incomes, changes in employment, or retiree migration) may influence the designation of wilderness. Wilderness designation, in this
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event, could be endogenous to the process requiring a system of equations modeling approach. We tested for simultaneity and endogeneity using the Hausman specification tests (Greene 2003), but found wilderness designation to not be jointly determined with income or employment. Therefore, no adjustments to model specifications were warranted. This does not imply that social forces do not influence the wilderness designation process. In our case study, the temporal pattern of wilderness designation in the east occurred in the mid1970s and mid-1980s, which may be too discrete for isolating dependencies among the data. There is no method for recovering information from left-censored counties-- they transitioned in the indicators prior to the study period. Therefore, 4,384 observations (137 counties by 32 years) are dropped from the income indicator models and 1,056 observations (33 counties by 32 years) are dropped from the employment indicator models. We also did not allow multiple transitions for a county, but instead note the first year for which a county permanently transitioned in each indicator. For some counties, transitioning took several years during which non-labor income and extraction/manufacturing income and services sector employment and extraction/ manufacturing employment were nearly equal. Once the year in which a permanent transition for a county was identified, subsequent years of data for that county were redundant. Therefore, the dataset was further reduced by dropping all county observations beyond the year of transition. Thus, only right-censored counties contained information for the entire study period. Table 3 shows the distribution of county types across the full dataset for Models A, B, C, and D as derived from year 2000 data. More counties had transitioned to nonlabor income than had transitioned to services employment. Fewer counties of all types (metropolitan, urban, and rural) were eligible for consideration with the income transition data due to left-censoring. The
Pr 84(2) Rosenberger, Sperow, and English: Discrete Duration Models of Eastern Wilderness
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TABLE 3 SUMMARY CHARACTERISTICS BY MODEL TYPE, APPALACHIAN REGION, 2000 Income Indicator Variable (Number of Counties) Number of Counties Metropolitan Urban Rural Urban Adjacency City Airport
Jobs Indicator
All Counties' Model A 5 Model Bc Model C Model D 410 140 186 84 122 104 ISO
273 171 377 245 102 0 132 0 132 132 166 166 39 39 79 79 88 49 116 62 68 68 92 92 124 73 140 84
All counties in Appalachian Region. Model A excludes all left-censored counties for income indicator. Model B excludes all left-censored counties for income indicator and metropolitan counties. Model C excludes all left-censored counties for emplo y ment indicator. Model D excludes all left-censored counties for employment indicator and metropolitan counties.
patterns of urban adjacency, city, and airport between Models A and B and Models C and D are similar. Table 4 shows the distribution and quantity of wilderness acres across Models A, B, C, and D. The data indicate that nearly 25% of those counties identified to have federally-designated wilderness within 15 miles of their centroid were metropolitan counties as of 2000.
V. RESULTS Likelihood ratio tests suggest that the logit model fits the data better than the complementary log-log model—there was a significant number of transitions and no evidence of non-convexities arising from the agglomeration of designated wilderness. Therefore, the estimated discrete duration models reported in Tables 5 and 6 are based on the logit estimator (equation [2]). Standard errors of the covariate estimates are corrected for latent heteroskedasticity using White's heteroskedastic consistent covariance method. Temporal dependency is most effectively accounted for using durationyears based on likelihood ratio tests of model specification (other variants of duration-years specification tested include linear and quadratic forms). The logit models measure the effect of covariates on the logodds ratio of a county transitioning over the study period. Since our "hazard" is the
transition from one economic state to another, a positively signed covariate increases (decreases) the risk of transition (survival), while a negatively signed covariate decreases (increases) the risk of transition (survival). The estimated income indicator models were similar in sign and significance of covariates explaining differences in hazard rates across counties whether metropolitan counties were included in the model (Model A) or not (Model B) (Table 5). These models performed very well with a 93% correct prediction success rate. Recall that for the income indicator, a significant proportion of counties were left-censored—they transitioned prior to the study period. It is not surprising to find significant duration dependence among the data—the longer a county stays in the prior state, the lower the probability that it will transition to the new state in the future (DUR_INC) (Beck, Katz, and Tucker 1998). In fact, surviving counties' transition hazard rates are declining over time (DUR_INC), potentially signaling economic stability in these old economy counties. Counties with higher lagged population densities (D(POP)1) and an AIRPORT significantly lowered the hazard rate of transitioning to the new state. RURAL counties and counties with higher lagged per capita personal income (PCPSINC 1 ) were at higher risk of transitioning to the new state. Designated
1k
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TABLE 4 SUMMARY STATISTICS FOR WILDLRNFSS ACRES WITHIN 15-MILL RADIUS OF COUNTY CENTROIDU. APPALACHIAN RIc;toN Model Number of Counties A5 Cd D
(7)t Mean Acres Std. Error Mm. Acres Max. Acres
45(16) 33(19) 69(18) 54(22)
12.151 12,342 12.830 13,514 11.327 11,100 11.694 11.870
312 312 136 136
47.510 47,510 47,510 47.510
452,389 acres in a circle with a 15-mile radius.
Model A excludes all left-censored counties for income indicator. it 273. Model It excludes all left-censored counties for income indicator and metropolitan counties, it = 171. Model C excludes all left-censored counties for employment indicator. it = Model I) excludes all left-censored counties for cmplo y tvient indicator and metropolitan counties. it - 245, Percentage of counties considered in the model that have wilderness area.
wilderness did not have a significant effect on hazard rates for sources of' personal income either as quantity in time t (D(QWAI5),) or its presence, as indicated with a dummy variable (DUMWAI5). The estimated employment indicator models were similar whether all counties (Model C) or nonmetropolitan counties only (Model D) were included (Table 6). These models performed extremely well with a 98% correct predictions success rate. These data were structured differently than the income indicator data (Table 2). Few of the counties were left-censored, with over a third of the counties surviving the general trends of national economic change in employment (right-censored). However, as expected, duration dependence is significant and negative (DLJR_EMP, Table 6)--the longer the duration of remaining in the initial economic state, the lower the probability of transitioning to the new economic state, again signaling stability in these surviving economies.' For employment source transitions, it seems agglomeration effects are most important for transitioning economies—counties with a CITY had significantly higher transition rates. However, for nonmetropolitan counties, being adjacent to an urban county (ADJURB) resulted in lower transition rates. Interestingly, designated wilderness affects employment transitions in two opposing ways. First, counties with some designated wilderness had lower hazard rates than counties without designated wilderness (DUMWAI5),
which implies wilderness counties were transitioning to the new economy later than other counties. But, as the density of designated wilderness (D(QWAI5),) increased in a county, it transitioned to the new economy sooner, which suggests the quantity of wilderness is a statistically significant factor in the growth and development of some counties in terms of employment sources. Marginal effects were estimated for the models, calculated at the means for continuous variables or with vs. without the attribute for dummy, variables. Marginal effects measure the change in hazard rates for a one-unit change (or with vs. without in the case of dummy variables) in the independent variable. For example, for each additional year added to a county's duration in the initial economic state, the probability of transitioning in the next year falls on average by about 0.006% for the income indicator (DUR_INC, Table 5) and by about 0.002% for the employment indicator (DUR_EMP, Table 6). Elasticity measures are reported in Tables 5 and 6. Elasticities provide standardized measures of effect they are the percent change in the hazard rate for a 1% change in the independent variable (dummy variables are with vs. without the attribute). Income hazard rates are most responsive (elastic) to lagged per capita . personal income (PCPSINC j) and ':duration (DURJNC), illustrating strong degrees of temporal and duration dependence in the
84(2) Rosenberger, Speroiv, and English: Discrete Duration Models
of
Eastern Wilderness 277
TABLE 5 INCOME TRANsItIoN DURATION
Loon MODELS, APPALACHIAN REGION. 1969-2000 (EQUATION [2])
MODEL A - All Counties' Variable
Coefficient (Std. Error)
Marginal Coefficient Effect'1 Llasticity (Std. Error)' 0.1635* - 4,3537* (0.5101) -0.3140 _2.7087* (1.3651) --0.0618* 0.0019 0.0185 -0.1666 (0.1726) 0.0038 -0.0191 0.0522 (0.2179) ._0(yJ90* -0.1284 _0.3291* (0.1889) 0.0363* 0.1447 0.6453* (0.2278)
