Socio-Econ. Plan. Sci. Vol. 17, No. 2, pp, 71-77, 1983 0038-0121/83/020071--07503.00/0 Printed in Great Britain. Pergamon Press Ltd.

SORTING URBAN DEVELOPMENT STRATEGIES IN A FEDERAL SYSTEM

AN INFORMATION THEORETIC APPROACH

CHARLES F. ADAMS, JR. and JAMES E. STORBECK Ohio State University, School of Public Administration, 1775 College Road, Columbus, OH 43210, U.S.A.

(Received 22 June 1982)

Abstract--Changes in population for the nation's largest central cities are decomposed into their regional shift and city-suburban disparity components. These decompositions, performed within an information theoretic context, provide a basis for distinguishing urban development policy roles among the federal, state, and local governmental sectors.

INTRODUCTION

Among the nation's largest central cities, population declined by an average of over 6% from 1970 to 1980. To some observers, this decline points up a failure of urban development policies undertaken during the seventies. Substantial increases in federal aid through such pro- grams as revenue sharing, community development, and CETA notwithstanding, declines in population indicate a continued deterioration in the vitality of central cities.

The problem with such generalizations is that they fail to distinguish among a variety of forces acting upon central city population change. Moreover, the policy insights derived are less than robust. In this regard, the current study analyses population changes for forty-nine large central cities and attempts to distinguish between two main forces acting on individual cities; regional shifts and city-suburban hardship disparities. Preliminary results indicate that both factors contribute importantly to the shift in population shares among central cities. With regard to policy implications, two distinct urban development strategies are suggested by the results; a federal program to reckon with the consequences of regional shifts and a state-level program to deal with the consequences of city-suburban disparities.

The primary focus of this paper is on the more tech- nical aspects of analyzing central city population change. The analysis employs an information theoretic frame- work to examine the components of urban population changes from 1970 to 1980. Specifically, an expected information measure, based on the distribution of urban populations within forty-nine central cities for the above years, is decomposed by region and by city-suburban hardship group. The question here is whether such city- suburban disparities, similar to the more commonly cited regional differentiations, can be structurally related to temporal shifts in population. The paper concludes with a discussion of the need for further work to refine these preliminary estimates, as well as a further consideration of the policy-relevant implications from this research which appear to be in the offing.

FRAMEWORK FOR ANALYZING CENTRAL CITY POPULATION CHANGE

While the share of population residing in central cities has generally declined, there is considerable variation in the actual population changes experienced by individual cities. In this regard, regional population shifts can be

expected to work to the advantage of cities in the South and West and to the disadvantage of cities in the North- eastern and North Central regions of the country. Changes in technology, labor costs, energy costs and availability, transportation systems, as well as various sociological phenomena have all contributed to these regional shifts.

Another factor relating to variations in population changes among central cities concerns socio-economic disparities between cities and their adjoining suburbs. In their analysis of central city hardship, Nathan and Adams [1] assessed the socio-economic characteristics of central cities relative to their suburbs as of 1970. Six variables, encompassing measures of housing conditions, income, education, and age of population, were used in the analysis. From these variables, an index of central city-to-suburban hardship was constructed, which was subsequently analyzed according to the particular set of circumstances accounting for the placement of each central city in the hardship index; badly off city adjoining well off suburbs, moderately well off city adjoining very well off suburbs, etc.

While the primary thrust of this earlier study was to gain a better understanding of urban hardship conditions as they then existed, the analysis also revealed a situa- tion in some cities suggesting the likelihood of further deterioration in an already unfavorable set of socio- economic conditions. Specifically, those cities which compared very unfavorably to their suburbs were seen as likely candidates to experience comparatively greater decline vis-a-vis other central cities over time. This notion of a dynamic underlying central city hardship was predicated on the view that, to a large extent, cities compete with their adjoining suburban jurisdictions, and cities operating at a comparative disadvantage were likely to experience relatively greater deterioration in socio-economic conditions over time as suburban areas captured an increasing share of new and existing popu- lations within the SMSA.

The idea of a dynamic underlying central city hard- ship was similarly explored in a subsequent article by Bradbury et al.[2]. As in the Nathan-Adams study, these authors focused on the relationship between cities and suburbs and described several processes associated with that relationship which are "seif-aggravating", giv- ing rise to reactions which contribute to the further deterioration of cities relative to their suburbs.

71

72 C. F. ADAMS, Jr. and J. E. STORBECK

Based on these earlier studies, cities which compare less favorably to their adjoining suburbs can be expected to experience a comparatively greater population decline over the 1970s. Just such a pattern emerges when cities are grouped according to city-suburban disparity. In Table 1, forty-nine of the central cities included in the Nathan-Adams study are grouped according to city- suburban disparity as of 1970. The city-suburban dis- parity index is shown in column 1 for each city. Column 2 presents information based on a comparison (using the same six socio-economic variables) of cities relative to each other. Cities coded 1 are in the top quintile, indicating a high degree of socio-economic hardship in comparison to other central cities. Similarly, column 3 shows the quintile ranking of suburban areas in comparison to one another.

The twelve cities in Group I are those that scored badly in relation to their suburbs, with a score of 200 or more on the city-suburban disparity index. Included in this group are places such as Newark and Cleveland in which very badly off cities adjoin well off suburbs, along with cities such as Chicago and New York which are moderately well off by comparison with other cities, but which adjoin very well off suburban areas.

The twenty-five cities in Groups II-A and II-B each

score in the intermediate range of the city-suburban hardship index. For the cities in Group II-A, such as Birmingham and Youngstown, this is due to badly off central cities adjoining similarly distressed areas. For Group II-B, moderately to very well off cities, such as Kansas City and Columbus, adjoin similarly well off suburbs.

Moving to Group III cities and suburbs again register increasing degrees of disparity, only now the disparity results from cities scoring as well as or better than their suburbs in relation to the six soeio-economic variables. Included here are areas such as Dallas where well off cities adjoin moderately well off suburbs, and places like Greensboro where very well off cities adjoining com- paratively distressed suburban areas.

In terms of the population changes recorded for the 1970- 80 period, a clear pattern can be observed indicat- ing a positive correlation between city-suburban dis- parity and population loss. For Group I, in which cities compare most unfavorably with their adjoining suburbs, a median population loss of 13.8% is recorded for the decade. By contrast, for Group III, in which cities com- pare favorably to their adjoining suburbs, a median population gain of 1.5% is recorded.

Table 1. Population changes from 1970 to 1980 for central cities grouped according to city-suburb disparity

City-Suburb Intercity. Intersuburb Percent Change Disparity a Disparity b Disparity c in City Popu-

lation 197~-~

Group I

Newark 422 l S -13.8 Cleveland 331 l 5 -26.6 Baltimore 256 l 4 -13.1 Hartford 317 2 5 -13.7 Atlanta 226 2 5 -14.7 Philadelphia 205 2 4 -13.8 Detroit 210 l 3 -20.5 Chicago 245 3 5 - I0.7 Rochester 215 3 5 -18.1 Dayton 211 3 5 -16.2 New York 211 3 5 - I0.4 Richmond 209 3 4 -12.1

Median - T . 8

Group I I -A

Birmingham 131 l l -5.5 New Orleans 168 I l -6.0 Youngstown 180 l 2 -18.1 Cincinnati 148 2 l -15.O Grand Rapids l l 9 2 l -8.0 Jersey City 129 2 l -14.1 Providence 12l 2 l -12.5 Tampa I07 2 l -2.2 Louisville 165 2 2 -17.5 Sacramento 135 2 2 +7.2 Springfield, Mass. 152 2 2 -7.1

Median

Group I I -B

Akron 152 3 3 -13.g Pittsburg 146 3 3 -18.4 Boston 198 3 4 -12.2 Fort Worth 149 3 4 -2.7 Milwaukee Ig5 3 4 -11.6 Los Angeles 105 4 3 +5.5 Toledo l l6 4 3 -7.4 Kansas City, Mo. 152 4 4 -11.9 Oklahoma City 128 4 4 +9.1 San Jose 181 4 5 +38.4 Minneapolis 131 5 4 -14.B San Francisco I05 5 4 -5.1 Columbus, Ohio 173 5 5 +4.6 Denver 143 5 5 -4.5

Median

Sorting urban development strategies in a federal system

Table l( Contd). City-Suburb Intercity Intersuburb Disparity a Disparity b Disparity c

Percent Change in City Popu- lation 1970-80

Group I l l

Portland, Oregon lO0 4 3 -3.8 Dallas 97 5 3 +6.8 Ft. Lauderdale 64 5 3 +9.8 Seattle 67 5 3 -7.0 Allentown lO0 5 4 -5.5 Greensboro, NC 43 5 l +7.5 Phoenix 85 4 l +32.3 Salt Lake City 80 4 l -7.3 Omaha 98 5 2 - I0.2 San Diego 77 5 2 +25.5 Houston g3 4 2 +27.6 Norfolk 82 3 l -13.3

Median

73

a. This index was derived from a comparison of c i t ies to their adjoining suburbs (defined as rest-of-SMSA) using the following six variables measured as of 1970:

] . Unemployment (percent of civilian labor force unemployed) 2. Dependency (persons less than 18 or over 64 as a percent of total

population) 3. Education (percent of persons twenty-five of age or older with

less than a twelfth-grade education) 4. Income level (per capita income) 5. Crowded housing (percent of occupied housing units ith more than

one person per room) 6. Poverty (percent of families below 125 percent of low-income

level) The index was constructed so that a c i ty which was identical to its adjoining suburbs would score lO0; a c i t y comparing favorably to its suburbs would score under lO0; and a c i t y which compares unfavorably would score over lO0 on the hardship index.

b. Rankings reported here are on the basis of the quintile in which each c i t y fe l l in the intercity hardship index, which was constructed on the basis of the same six measures described in note a, with an adjustment for cost of living differences across cities. Cities coded l are in the top quintle, evidencing the highest degree of social and economic hardship.

c. Rankings reported here are based on a procedure similar to that described in note b for cities.

For a further discussion of these indexes and relevant data sources, see Richard P. Nathan and Charles Adams, "Understanding Central City Hardship," Pol i t ical Science quarterly, Spring, 1976.

The population changes recorded for Groups II-A and II-B provide further evidence of an important connection between city-suburban disparity and population change. Both of these groups are characterized by a lack of significant disparity between city and suburb, and cor- respondingly, the median population loss of 8.0% for the group of badly off cities in Group II-A is very close to the 6.3% loss recorded for the moderately to very well off cities in Group II-B. The implication is that city- surburban disparity, more than the socio-economic characteristics of the city per se, has an important bear- ing on population change.

In order to more fully explore this implication, as well as the relationship of such disparities to the regional structure of population shifts, the analysis now views these changes within the expected information frame.

INFORMATION THEORETIC FRAMEWORK

The purpose of this analysis is to assess the nature of changes in the urban population structures of the U.S. over time. More specifically, this research seeks to dis- aggregate these changes in such a way as to identify interacting forces which produce significant rearrange- ments of metropolitan populations. While the decline in population numbers from one year to another within all

central cities is of primary concern in this work, the relationship of this change to regional and local situa- tions is also important. Consequently, what is needed in this analysis is a methodology which addresses the prob- lem in its aggregate and disaggregate states. Information theory, in its examination of statistical distributions, provides just such a methodology. Furthermore, the measure known as expected information lends itself to studies of multi-year distributions and can be decom- posed into simple additive forms.

The measurement of information is based on the notion that the information received from an event is proportional to the improbability of the occurrence of the event. Thus, if there are n events El . . . . . E, with asso- ciated probabilities p~ . . . . . p,, then the mean value of the information obtained from these events has been defined as

n

H = ~ p~ log llp~ (1) i=!

where ~ p~ = 1. This information measure is known as i f f i l

the Shannon entropy and has been discussed extensively in Theft [3]. Inevitably, this multi-year analysis must be

74 C. F. ADAMS, Jr. and J. E. STORBECK

concerned with more than one distribution. Con- sequently, we adopt an expected information measure, expressed in terms of prior (P3 and posterior (q3 dis- tributions, which gives the amount of information gained by comparing the state of ignorance encoded in the prior distribution with the additional knowledge obtained from the posterior distribution. Thus, the mean value of expected information in this case is defined as

n

t(q :p) = ~ ~, log ~dp, i = l

where X pi = 1 and ~ q, = 1. This measure is known as i = 1 i = 1

the Kullback entropy and has been compared to the Shannon measure in a number of studies [4--6].

Theil[3] has shown that the expected information, as articulated here in eqn (2), can be decomposed in a systematic fashion when one is concerned with the grouping of events. That is, if one combines the above events Et . . . . . EN into a smaller number of sets of events, $1 . . . . . SR in such a way that each El falls under exactly one S,, then the associated set of probabilities are defined as

e,=Xp,, Or=X ,. ieS r ieSr

The measure of information gain at the set level, then, can be defined mathematically as

R

~o(q : p) = ~.. O• log Or/P~ r = l

where the prior and posterior distributions are defined exclusively for sets of events. For the amount of in- formation produced by such a grouping to be equal to the total information gain of eqn (2), however, an additional element must be identified as

qi[ Qr L(q : p) = ~ q'~Qr log pi/Pr"

ieSr

This measure represents the amount of information gain within each set. Thus, adding the between set infor- mation of eqn (4) to the above within set information (which is weighted by the set probability), one can obtain the total information gain of

o//Qr I ( q : p) : ~ Q• log O,[ Pr + ~ Q• ~ q~ Or log pil Pr"

r = I • = 1 i eS r

(6)

Equation (6), though expressed in a decomposed fashion, is equivalent to eqn (2).

Some form of the above information measures has been used in a variety of spatial analytic studies [6-8]. In fact, these measures have been employed in a number of studies focusing on the distribution of urban populations within the spatial context[4, 5]. The belief among these researchers has been that a single overall measure such as entropy, which captures the changing distribution tendencies within an urban population, can be extremely valuable.

This study, in adopting the information theoretic per-

spective, concurs with that belief, but recognizes the sensitivity of such measures to the consequences of alternative partitiorfings of the urban field. Indeed, this research attempts to fully exploit this sensitivity in order to identify the diverse forces which produce the chang- ing urban structure.

For the assessment of central city population changes in the U.S. from 1970 to 1980, this analysis employs the concept of information gain articulated in eqns (2) and (6). In order to identify population changes associated

(2) with the regional and city-suburban disparity com- ponents mentioned above, the total information gain [represented by eqn 2] from one year to another for the urban system under study is decomposed into its con- stituent between and within set parts [represented by eqn 6]. This decomposition is first performed on a regional basis, and then on a disparity group basis. The significance of the between and within set information components for each decomposition is subsequently determined by comparing these measures to their re- spective maxima.

The analysis begins by letting the prior probabilities denote the distribution of central city population among the forty-nine urban centers for 1970, where p~ equals the 1970 population of city i divided by the total 1970 population. Similarly, let the posterior probabilities denote the distribution of central city populations for

(3) these same forty-nine centers for 1980, where q~ equals the 1980 population of city i divided by the total 1980 population.

By substituting these values of the prior and posterior probabilities into eqn (2), we are determining the amount of information gain for the entire urban system. In a

(4) broad sense, we are "testing the hypothesis" that the distribution of 1980 central city populations is directly proportional to the distribution of 1970 central city populations. When such a situation obtains, the value of the resulting information gain statistic is exactly zero. As this value deviates from zero, we are identifying the extent to which these two distributions are deviating from direct proportionality. Within the context of this analysis, we are identifying the extent to which the

(5) forty-nine city urban system is changing as a whole. In order to examine the regional nature of these

changes, we must first combine the prior and posterior probabilities into their respective set probabilities. In this case, the sets are defined on a regional basis. That is, the above population proportions are grouped into sets denoted as Northeast, North Central, South and West. By substituting the values of city and regional prior and posterior probabilities int eqn (6), we are determining the amount of information gain for the system, decomposed into between-region and within-region components. Consequently, as the two population distributions devi- ate from direct proportionality, we are able to identify how much is due to within-region shifts. As a result of this analysis, we can determine the significance of "regional forces" acting upon the forty-nine city system.

In order to examine the extent to which city-suburban disparities might be related to population changes, we then perform a second decomposition. Similar to that above, we combine the city probabilities into set prob- abilities. In this case, sets are defined on the basis of disparity groupings. Substituting city and disparity-group prior and posterior probabilities into eqn (6), we obtain the information gain within the system, decomposed into be- tween-disparity group and within-disparity group corn-

Sorting urban development strategies in a federal system 75

ponents. The figures indicate how much of the in- formation gain arises as a result of shifts between dis- parity groups and how muh arises as a result of shifts within these groups. From this decomposition, we determine the significance of "disparity group forces" acting upon the urban system under study.

ANALYSIS OF RESULTS

The first task in analyzing the results of this in- vestigation is to determine the total entropy (or in- formation gain) in this urban system. As stated pre- viously, such a determination is made by substituting the prior and posterior probabilities associated with 1970 and 1980 populations, respectively, into eqn (2). In fact, when these substitutions were made, the resulting value of information gain was computed as 0.0089. Though this total entropy value is different from zero (indicating some deviation from direct proportionality between the two distributions), the statistic is closer to this minimum than to its possible maximum of 17.43. Thus, one finds a relatively small amount of information arising from the posterior distribution's revision of prior probabilities.

While this result appears to be less than impressive in a statistical sense, it does conform to our knowledge of the structure of the urban system. Given the substantial population base of central cities, one would expect changes in the mix of urban populations to be in- cremental at most. Furthermore, an information gain value which approaches the maximum would indicate an urban system experiencing substantial shifts in popu- lation structures. Such a situation is counter-intuitive when the entire system under consideration produced only a 6% decline in population over a ten-year period. Of greater interest, therefore, is the question of where within the system this information gain arose.

In order to test the commonly cited notion that regional population shifts account for much of the change within the urban structure, 1970 and 1980 prob- abilities were grouped on the basis of regions. As a result of the application of eqn (6), a regional decomposition of the entropy statistic was produced, with the associated figures displayed in the upper portion of Table 2. One should note that, of the total entropy value of 0.0089, nearly one-half (0.0041) of this information gain amount was associated with the between (regional) grouping component while over one-half (0.0048) of the total amount was associated with the within grouping statistic. Examining these absolute measures, however, can be misleading for purposes of comparison. Thus, we divide each of these terms by their respective maxima to obtain a relative measure of information gain[6]. Performing this operation, we find that between group information

emerges as the significant component of information gain in this time period. Indeed, a comparison of the relative between group figure (0.0024) with that of the within group (0.0003) suggests that the gain in information (i.e. deviation from direct proportionality in terms of popu- lation structures) was substantially greater at the inter- regional level than at the intra-regional level.

Similarly, the notion that city-suburban disparities play a significant role in determining part of population changes within the urban system is tested by resorting to eqn (6); results are displayed in the lower portion of Table 2. In this case, however, probabilities are com- bined on the basis of city-suburban disparity groupings. As in the regional system, the disparity decomposition produced a nearly even split of the total entropy value, with absolute measures of 0.0040 (between disparity groups) and 0.0048 (within disparity groups). Comparing these values to their respective maxima yields results analagous to those above. That is, the larger between group relative measure (0.0021), compared to the within group relative measure (0.0003), suggests that a city- suburan disparity grouping can account for a significant part of the information gain and, consequently, for much of the deviation from directly proportional population structures.

These two decompositions, then, suggest that both regional and city-suburban disparity factors are struc- turally related to shifts in population. Given the mag- nitude of these measures, however, the interpretation of the relationship between these factors is somewhat am- bignous. In fact, the correspondences between decom- positions might suggest that cities are distributed among these two grouping schemes in a highly similar fashion. That is, we might suspect that disparity groups have a marked "regional" character and, likewise, that regional groupings have a "disparity" character.

To test this proposition, we examine the effects of disparity grouping within selected regions. All regions were not analyzed in this manner, since this limited data set failed to give adequate representation of all disparity groups within each region. Table 3, then, displays the results of an entropy decomposition within the South and North Central regions. Upon examination of these values, one can see that a significant amount of in- formation gain is obtained between disparity groups in the South region. Indeed, when the relative between group value (0.0047) is compared to that of the within group value (0.0003), the role of such disparities is com- pelling. Less impressive, though still significant, is the information gain associated with city-suburban disparity in the North Central region. In this case, the within group value (0.0002) is greater than the corresponding between

Table 2. Absolute and relative information measures for regional and disparity groupings Between Groups Within Groups*

Broupinqs Absolute Relative AbsoIvte Relative

Regional .004] .0024 .0048 .0003

City-Suburban .0040 .0021 .0048 .0003

*These "wtthln groups" measures have been weighted by each group's posterior probabi l i ty Qr- Thus, they represent average wlthtn group information measures.

76 C. F. ADAMS, Jr. and J. E. STORBECK

Table 3. Absolute and relative information measures for disparitygroups within selected regions Between Eroups Withln 6roups*

Reqtons Absolute Relattve Absolute Relattve

South .0065 .0047 .0045 .0003

North Central .0003 .0001 .0022 .0002

*These "within group" measures have been weighted by each group's posterior probability, Qr. Thus, they represent average within group information measures.

group value (0.0001). An inspection of the central cities within this region, however, shows that the distribu- tion of group membership is skewed to the upper end of the disparity scale. Given this lack of representation of all groups, therefore, one might expect the resulting decrease in the amount of information gain between groups.

In a similar fashion, Table 4 displays the results of a regional decomposition within disparity group II. As stated previously, the limited data set did not yield adequate representation of all regions within each dis- parity group. Consequently, groups I and III could not be analyzed in this manner. This partial analysis, however, indicates that regional groupings have an effect upon the information gain within this particular disparity group. That is, inspection of the results displayed in Table 4 reveals a substantially greater relative between-region value (0.0014) as compared to the corresponding within- region measure (0.0003). We can conclude, therefore, that a significant amount of the information gain within disparity group II can be attributed to population shifts of a regional nature. Consequently, this analysis suggests that both regional and city-suburban disparity factors are structurally relevant in describing central city population changes.

SUMMARY AND CONCLUSIONS

Because of data limitations, the results reported above must be viewed as indicative of a potentially fruitful approach to analyzing population changes within large cities. Information on more cities is required in order to evaluate the robustness of these results as well as to perform further tests of the independent effects of region and city-suburban disparity for various subgroups of cities. Moreover, a "two-level" decomposition frame- work would be helpful in analyzing these data. With such a methodology, one might decompose information relat- ing to population change on a regional basis, and further partition the within-region information according to city- suburban disparity groupings.

The additional insights to be gained from further refinements to the database and methodology notwith-

standing, the results at this point appear to substantiate the notion that city-suburban disparity has an important bearing on population change among large cities. Attempts to analyze developments within particular places should, therefore, take this factor into account along with information bearing on regional aspects of population change. With regard to implications for urban development policies, two strategies are suggested by this analysis. Regional population shifts related to factors such as energy availability and costs are largely a consequence of national circumstances and call for some form of national policy if such population shifts are deemed contrary to the general welfare of the country. Such policies might be aimed at mitigating the economic and fiscal consequences of such shifts through a revenue sharing type grant, providing general purpose fiscal assistance to cities. Alternatively, federal policy might be aimed at directly affecting such shifts through the use of planning or development grant programs.

The effects of city-suburban disparity on central city population change call for state-level policy initiatives. To a large extent, these disparities are tied to long standing, state-controlled geo-political boundaries. So long as these structural arrangements persist, central cities affected by adverse disparities are likely to con- tinue to lose ground to adjoining suburbs and there may be little that the city alone can do to counter this trend. Specific state actions to mitigate the effects of city- suburban disparity include authorization of commuter taxes, equalization of fiscal capacities through state aid to local governments, state takeover of some functions (such as welfare), expanded roles for county government in service provision, and direct actions to promote con- solidation and annexation.

As a complement to such state initiatives, direct federal involvement to mitigate the effects of hardship disparities on central city decline may be necessary. The results of this analysis suggest a framework for better targeting such assistance, including, for example, the current urban enterprise zone concepts.

Finally, it should be noted that the policy implications from the current analysis do not preclude direct and

Table 4. Absolute and relative information measures for regions within disparity group II Between Regions Within Reglon*

Dtsoart tv Grouo Absolute Relative Absolute Relatlve

6roup II .0032 .0014 .0038 .0003

*These "wi th in region" measures have been weighted by each group's posterior probabl]Ity, Qr. Thus, they represent average within group information measures.

Sorting urban development strategies in a federal system 77

imaginative actions by the cities themselves. However, it should be recognized that the population changes experienced by individual cities result from multiple forces and call for action at each level of government.

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