Exploring Endogenous Dynamics - Wayne State University

Urban Studies, Vol. 44, No. 1, 167– 185, January 2007

Are Neighbourhoods Self-stabilising? Exploring Endogenous Dynamics George Galster, Jackie Cutsinger and Up Lim [Paper first received, July 2005; in final form, February 2006]

Summary. This study investigates how neighbourhoods respond when they are upset by transient, exogenous shock(s). Do they quickly revert to their original, stable state, gradually return to this stable state, permanently settle into another stable state, diverge progressively from any steady state, or evince no discernable pattern of response? A self-regulating adjustment process promoting stability appears the norm, based on econometric investigations of multiple, annually measured indicators from census tracts in five US cities. Stability quickly re-established at the original state characterises most of the indicators analysed: rates of tax delinquency, low-weight births, teenage births and home sales volumes. Violent and property crime rates also evince endogenous stability at the original state, but take considerably longer than the other indicators to return to it when the exogenous shock is sizeable. Moreover, this crime adjustment process is considerably slower in neighbourhoods with higher poverty rates.

Introduction Understanding the dynamics of neighbourhood change is not only relevant to scholars, planners and policy-makers, but also to residents and property owners since neighbourhoods have important impacts on many aspects of quality of life. Neighbourhoods constitute the contexts for moulding the value of real estate assets, loci for consuming local amenities and public services, and environments in which we interact with others and are socialised to the rules and intricacies of our particular social situations (Hunter, 1979; Hallman, 1984; Galster, 2001, 2003). Neighbourhoods can be determinants of behaviour (Olson, 1982; Leventhal and Brooks-Gunn, 2000), sources of personal identity (Useem et al.,

1960), as well as agents of social control (Schwirian, 1983). The social, economic and ecological milieu within a neighbourhood can have significant effects on its residents’ lifeoutcomes, both directly and indirectly through the stereotypical impressions outsiders form about residents of certain neighbourhoods (Galster and Killen, 1995; Ellen and Turner, 1997; Gephart, 1997). Despite their importance, the dynamic processes of how neighbourhood conditions change are poorly understood empirically. Indeed, as the review by Sampson et al. (2002) states There is a clear need for rigorous longitudinal studies of neighbourhood temporal

George Galster is in the Department of Geography and Urban Planning, Wayne State University, 3198 Faculty/Administration Building, Detroit, MI 48202, USA. Fax: 313 577 1274. E-mail: [email protected]. Jackie Cutsinger is in the Centre for Urban Studies, Wayne State University, 3040 Faculty/Administration Building, Detroit, MI 48202, USA. Fax: 313 577 1274. E-mail: [email protected]. Up Lim is in the Department of Urban and Regional Planning, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, Seoul 120 – 74, Korea. E-mail: [email protected]. The authors wish to thank the staff of the Metropolitan Housing and Communities Centre of the Urban Institute, who generously shared the Cleveland and Oakland databases that were employed in this study. Lauren Krivo, Mickey Lauria, anonymous referees and neighbourhood workshop participants at the ACSP –AESOP conference in Leuven, Belgium, provided helpful suggestions on an earlier draft. Ron Malega provided assistance in preparing the Cleveland database for analysis. 0042-0980 Print=1360-063X Online=07=010167 –19 # 2007 The Editors of Urban Studies DOI: 10.1080=00420980601023851

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dynamics . . . We have scant information on how neighbourhood processes evolve over time (Sampson et al., 2002, p. 472). Our study responds to this need. Evolving Research on Neighbourhood Change The earliest scholarly research on neighbourhood change consisted of descriptions, cartographic representations and typologies, soon to be accompanied by causal theories. This body of work attempted to explain the mechanisms through which neighbourhood change was manifested and the larger ecological context governing why it occurred in these distinct ways. The two predominant early theories of neighbourhood change were the invasion– succession model advanced by the Chicago School of Sociology (Park, 1952; Duncan and Duncan, 1957; Taeuber and Taeuber, 1965) and the life-cycle model (Hoover and Vernon, 1959). Other early theories of neighbourhood change include the demographic/ecological model, the sociocultural/organisational model, the stage model, the political economy model and the social movements model (Downs, 1981; Bradbury et al., 1982; Schwirian, 1983). Subsequently, more-or-less comprehensive theories of neighbourhood change have been forwarded by Maclennan (1982), Taub et al. (1984), Grigsby et al. (1987), Rothenberg et al. (1991), Temkin and Rohe (1996), Lauria (1998) and Galster (2003). Beginning in the 1970s, investigators of neighbourhood change began using regression analysis as the basis for empirically testing theories and building predictive models. These predictive modelling efforts specify how exogenous variables putatively affect neighbourhood outcome indicators and estimate parameters using linear multiple regression. Several variants of these models have been estimated, each addressing changes of a specific neighbourhood indicator, such as population density (Guest, 1972, 1973; Fogarty, 1977), income or social class (Guest, 1974; Vandell, 1981; Coulson and Bond, 1990; Galster and Mincy, 1993; Galster et al., 1997; Carter et al., 1998), home-ownership

rates (Baxter and Lauria, 2000), female headship rates (Krivo et al., 1998) and racial composition changes (Guest and Weed, 1976; Schwab and Marsh, 1980; Galster, 1990a, 1990b; Ottensmann et al., 1990; Denton and Massey, 1991; Lee and Wood, 1991; Ottensmann and Gleeson, 1992; Lauria and Baxter, 1999; Baxter and Lauria, 2000; Crowder, 2000; Ellen, 2000). More recently, Quercia and Galster have argued that predictive regression models of neighbourhood change should attempt to identify threshold effects to determine how exogenous variables are associated with changing neighbourhood outcomes. They define a threshold effect as a dynamic process in which the magnitude of the response changes significantly as the triggering stimulus exceeds some critical value (Quercia and Galster, 2000, p. 146). They argue that threshold effects should be adopted as a working hypothesis, based on received theory and limited empirical evidence. Quercia and Galster advocate that researchers utilising non-linear regression techniques should identify neighbourhood threshold effects associated with changes in exogenous variables, such as using categorical dummy, spline or quadratic variables.1 Galster et al. (2000) empirically demonstrate the existence of threshold effects in their study of neighbourhood quality-of-life indicators. They employed non-linear regression analysis to ascertain whether any of five exogenous variables measured in 1980 (percentages of: residents who moved in since 1975, non-professional and nonmanagerial workers, occupied dwelling units with no car available, vacant housing units and renter-occupied housing) evinced threshold-like relationships with 1980–90 changes in four alternative neighbourhood quality-of-life indicators (percentages of: persons below the poverty level, households with children headed by a woman, persons aged 16 –19 who dropped out of high school and persons over age 16 not employed). They found for all metro-area census tracts in the nation that their occupational status

ARE NEIGHBOURHOODS SELF-STABILISING

and rental rates exhibited threshold-like relationships with subsequent decadal changes in several neighbourhood quality-of-life indicators. However, their findings only hint at dynamic processes because they only relate cross-sectional variation at one point to subsequent changes spanning an entire decade and do not examine intradecade changes within neighbourhoods. The Understudied Element: Endogenous Neighbourhood Dynamics In previous empirical investigations of neighbourhood change, researchers typically have focused upon changes in outcome indicators that are associated with cross-sectional variations in a range of exogenous variables. However, there has been comparatively little analysis of how outcome indicators change endogenously after being upset from a stable condition by (perhaps transient) changes in one or more exogenous variables. Put differently, once upset from equilibrium, do neighbourhoods have internal processes that ‘drive themselves’ in one direction or another? The seminal exception is Schelling (1971, 1972) and his theory of neighbourhood racial tipping. Schelling looks at the inclinations of White residents to move out of a neighbourhood as the percentage of Black residents increases, initially as a result of some force external to the neighbourhood. He argues that once a threshold percentage value, or ‘tipping point’, of Black residents is exceeded, the percentage they represent in the neighbourhood will inexorably increase until eventually only Black residents are present. In other words, the model suggests that increases in the outcome indicator, percentage of Black residents, past its threshold point will continually lead to further increases in the indicator itself. Schelling essentially can be thought of as examining the endogenous stability of neighbourhoods in response to an exogenously induced change in Black residency. His central claim is that the Black residency rate of a neighbourhood remains stable so long as exogenous shocks keep it below its tipping point. However, once this critical

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value is surpassed, the rate of Black residency becomes unstable, increasing inevitably without the need of further exogenous assistance, until the neighbourhood is fully occupied by Black households.2 More recently, Schelling’s intuitions have formed the foundation for a new generation of ‘complexity models’ of neighbourhood segregation by race or class, which also owe intellectual debts to the natural sciences (see, for example, Young, 1998; Zhang, 2001). These models specify behavioural rules for stylised individual behavioural agents that specify the nature of social interactions among them. From these individual-level rules follow higher-levels of spatial organisation, derived either mathematically (for example, Brueckner et al., 1999; Blume and Durlauf, 2001) or through computer simulations using cellular automata (for example, Zhang, 2001; Meen and Meen, 2003). For our purposes, two key features of these models appertain (Meen and Andrew, 2002). First, the greater the relative importance individual agents attach to the actions of others, the more likely is the possibility of multiple equilibrium states for the given neighbourhood outcome indicator. Secondly, the models may, depending on the assumptions of individuals’ parameters, exhibit non-linear responses and tipping in response to a random, exogenous shock that upsets the existing spatial organisation.3

Our Approach to Neighbourhood Dynamics Like Schelling and the proponents of emerging complexity models, we are interested in the endogenous dynamics of neighbourhood outcome indicators, but seek to examine other dynamics besides simple stability and instability. In our current investigation, we search for four distinct sorts of potential dynamic properties, which we define at the outset —Stability: A neighbourhood outcome indicator is stable if, upon being upset by some transient external force, the indicator tends to return towards its original state.

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—Multistate stability: A neighbourhood outcome indicator is multistate stable if, upon being upset sufficiently by some transient external force, the indicator tends to gravitate towards a different, yet stable, state. —Instability: A neighbourhood outcome indicator is unstable if, upon being upset by some transient external force, the indicator tends to diverge progressively from its original state. —Threshold instability: A neighbourhood outcome indicator evinces threshold instability if it exhibits stability over some range of values, but becomes unstable past a certain threshold point.4

Although, like some aforementioned researchers, our investigation involves testing for threshold points, it should be noted that we take a fundamentally different perspective. Previous studies typically looked at changes in outcome indicators caused by different, exogenous variables that had surpassed their threshold points (see Galster et al., 2000; and the review in Quercia and Galster, 2000). In these cases, it was the exogenous variables’ threshold points that were of interest. By contrast, we are interested in whether or not our neighbourhood outcome indicators exhibit endogenous threshold points—i.e. what we defined above as threshold instability. Our work is distinguished from prior work in another critical way. Ours is the first study to investigate year-to-year changes in neighbourhood indicators. This permits much more precise estimates of dynamic processes than prior works that, because they were based on census data, could only examine decadal changes. Data for these explorations come from a variety of sources in five large US cities that, although offering somewhat different sets of indicators, provide an opportunity for robustness tests. Our investigations reported in this paper should be viewed as exploratory, not

hypotheses-testing. They have as their main goal probing the following research question Which of the aforementioned year-to-year dynamic processes characterise changes in the following neighbourhood indicators: property crime rate, violent crime rate, rate of low-birth-weight babies born, rate of births to teenage mothers, median value of homes, property tax delinquency rate and home sales rates? This article will continue with four additional sections. The next section will introduce a model of endogenous neighbourhood dynamics and mathematically specify the four processes noted above. Following that will be a detailed description of the data and methods we used to investigate endogenous neighbourhood dynamics. Next, we will discuss the results of our statistical analysis, portraying findings in both tabular and graphic fashion so that the dynamic processes we discovered can be appreciated fully. We find that, although not all of the indicators evince the same speed or pattern of adjustment, the bulk of the results suggest a stable, endogenous neighbourhood adjustment process. Neighbourhoods with poverty rates in excess of 20 per cent do not, in general, adjust as quickly, especially to crime rate shocks. Finally, we offer caveats to our conclusions and make suggestions for future research.

The Nature of Neighbourhood Stability and Instability The endogenous dynamic properties of a neighbourhood can be most simply described mathematically in terms of the linear difference equation Xt ¼ aXt1 þ b

(1)

where, X represents a neighbourhood indicator of interest; t is a marker for a unit of time; t 2 1 is the previous (or lagged) unit of time; and a and b are time-invariant parameters.5 Without recourse to knowledge


about Xt21, Xt can be expressed as (Sydsaeter and Hammond, 1995, p. 732) Xt ¼ at ½X0 b=(1 a) þ b(1 a) when a = 1 (2)

and Xt ¼ X0 þ tb when a ¼ 1

In both cases, X0 is the value of the indicator at the beginning of the period under analysis. For some time S . 0, should XS ¼ b/ (1 2 a) then via substitution into (2) XSþ1 ¼ aSþ1 ½b=(1 a) b(1 a) þ b(1 a) ¼ b=(1 a)

(3)

Similarly, XSþ2 ¼ b=(1 a), and so on for every time thereafter. Thus, because X will remain at value b=(1 a) indefinitely once it is reached X ¼ b(1 a)

(4)

can be called a stable state for neighbourhood indicator (when a = 1). Equation (4) permits us to express (2) as

Xt X ¼ a(Xt1 X ) ¼ at (X0 X )

beginning-of-period deviation of X0 from its stable state will lead to an oscillating, but steadily damped, convergence over time towards X (for details and a graphic explanation, see Sydsaeter and Hammond, 1995, pp. 734–735. By contrast, neighbourhood indicator X will be unstable if jaj . 1, because then at ! 1 as t ! 1, so (2) implies that Xt diverges farther and farther from X as t ! 1. If a . 1, a beginning-of-period deviation of X0 from its stable state will lead to a steady, monotonic divergence over time away from X , with rate of divergence depending on the value of a. If a , 1, a beginning-of-period deviation of X0 from its stable state will lead to an oscillating, ever-increasing divergence over time away from X . Threshold instability is a dynamic property that essentially combines elements of both stability and instability discussed above, with the former associated with values of the indicator below the threshold point l, and the latter associated with values above the threshold. Mathematically, threshold instability can be portrayed as Xt X ¼ at (X0 X )

(5)

Notice that (5) expresses the value of neighbourhood indicator X at any time as a function of its deviation from its stable state value and indicates that this deviation will change at the constant proportional rate a 2 1 each period t. This expression highlights the determining factor for basic stability or instability of X: the value of a. Neighbourhood indicator X will be stable if jaj , 1, because then at ! 0 as t ! 1, so (2) implies that Xt ! X ¼ b=(1 a) as t ! 1. If 0 , a , 1, a beginning-of-period deviation of X0 from its stationary state (due, say, to some exogenous shock) will lead to a steady, monotonic convergence over time towards X , with rate of convergence depending on the value of a. If 1 , a , 0, a

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(6)

where, jaj , 1 as Xt l and jaj . 1 as Xt . l. Finally, multistate stability represents a circumstance where, from the perspective of the original stable state X the initial disequilibrating upset to X0 is unstable, but from the perspective of a different stable state X it is stable. If the indicator’s new value is between the two stable states (X , X0 , X ), it moves progressively over time farther from X but closer to X . If the indicator’s new value is greater than the higher-valued stable state (X , X00 ) it moves progressively over time closer to X . Without loss of generality, assume for illustration X , X0 , X , X00 . Then multistate (in this case, dual-state) stability, with all positive deviations from X producing a new stable equilibrium at X , can be

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expressed

Xt X ¼ at (X0 X ) where, a . 1 as X0 X

(7)

and

Xt X ¼ at (X00 X ) where, a , 1 as X00 . X The empirical implication of this mathematical exercise is straightforward. If equation (1) can be estimated by simple regression techniques, the resulting coefficient for the lagged indicator of interest (a) specifies whether that aspect of neighbourhood is stable or unstable, according to whether jaj , 1 or jaj . 1, respectively. More sophisticated regression specifications that allow the value of a to vary across various ranges of X can be used to estimate equations (6) and (7) and thereby test for threshold instability and multistate stability.6 To this exercise, we now turn. Data and Methods Data and Neighbourhood Indicators Analysed The data on neighbourhood outcome indicators come from a variety of sources of five large cities—Cleveland, Denver, Detroit, Oakland and Seattle. Although they vary across cities, the data consist of annual observations (each spanning at least seven consecutive years during the 1988–2003 period) for census tracts and typically include information on crime rates, vital statistics and various housing market conditions.7 Data sources are presented in Table A1 and details of indicators for each city are presented in Table A2 (see appendix). We selected seven variables as intrinsically interesting indicators of neighbourhood quality of life upon which we would conduct our analyses. They include: property crime rate, violent crime rate, rate of low-birth-weight babies born, rate of births to teenage mothers, median value of single-family housing sales, property tax delinquency rate and single-family home sales rates.8 Descriptive statistics of these indicators are presented in Table A2. We would

have wished to analyse other indicators as well, particularly racial/ethnic composition and poverty rates, but such were unavailable for neighbourhoods on an annual basis. The property crime and violent crime variables are both measured as rates relative to the resident population. For both variables, the rate is computed as the annual number of property or violent crimes respectively, that were reported to police within a census tract, standardised by thousands of population at the beginning of the decade. Beyond their intrinsic interest, crime rates are useful correlates of several neighbourhood elements, including residential satisfaction (Rossi, 1972; Campbell and Converse, 1976; Galster, 1987) and housing reinvestment potential (Taub et al., 1984). The low-weight birth rate indicator is defined as the number of low-birth-weight babies born per 100 live births for mothers residing within a census tract. Low birth weight is often used as an indicator of the quality of pre-natal care the mother received during her pregnancy (Leventhal and Brooks-Gunn, 2000). Low-income mothers typically have higher incidences of delivering low-birth-weight babies than mothers in higher-income-groups. The births to teenage mothers variable is computed as the rate at which women aged 15 –19 gave birth, per 1000 females aged 15 –19 residing within each census tract. We consider this variable to be an important quality-of-life indicator because neighbourhoods with high rates of births to teenage mothers generally also experience high levels of welfare dependency and secondary school dropout.9 The property tax delinquency variable reports the percentage of home-owners that have not paid their property taxes in the past year within a census tract. The percentage of home-owners who are tax delinquent is a key indicator of neighbourhood quality because those who decide not to pay their taxes are likely also to neglect the exterior appearance of their property. Moreover, unpaid property taxes may be an indication that the owner has or is considering abandonment of the


property, which we cannot measure directly, unfortunately. The median housing sale value variable is reported in thousands of current dollars. The median value of homes sold gives arguably the most general indication of neighbourhood quality of life because it capitalises the market’s evaluation of a wide range of conditions, such as racial and class composition, dwelling structural qualities, accessibility, environmental conditions and public service/tax packages (Grieson and White, 1989; Palmquist, 1992). The home sales rate variable is defined as the number of single-family home sale transactions that occurred in a census tract, per 100 single-family homes in each census tract. The rate at which homes sell within a census tract can be a good indicator of the health of the housing market in that neighbourhood. Too few transactions can indicate extremely weak demand conditions; too many can signal rapid household turnover and ‘panic selling’, perhaps triggered by racial or class transitions. Empirical Model and Estimation Procedures As the model of endogenous neighbourhood dynamics explained, the key indicator of stability or instability is the coefficient of the lagged indicator variable. Our data enabled us to create a panel of lagged values for the outcome indicators because they included annual values for each indicator over an extended period. Our basic specification thus consisted of an equation as (1) above, with the addition of a random error term whose statistical properties we discuss next. Since our data consisted of a panel spanning across time and across census tracts, standard regression techniques were not appropriate for estimating parameters of our model. Instead, we employed a time-series/cross-sectional regression analysis on each indicator.10 We tested four different error structures: oneway fixed effects, two-way fixed effects, one-way random effects and two-way random effects. Since Hausman (1978) tests for the fixed and random effects regressions

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were highly significant (p , 0.0001), the fixed effects model was more appropriate. For each indicator, we ended up including a fixed effect for each tract and, for most indicators, a city-wide set of year dummy variables as well. In order to ensure that our results were not skewed by extremely large or small values, we ran models both for the full sample and then removing all values over five standard deviations from the mean for each outcome indicator. Our linear models like (1) will reveal general instability in the outcome indicator if the absolute value of the estimated coefficient of the lagged value of the variable is greater than one, and an endogenous stabilisation process if it is less than one but different from zero. Thus, we not only test whether the lagged variable’s coefficient is significantly different from zero, but also whether it is significantly less than one. However, the linear model cannot test whether values of the coefficient vary over differing ranges of lagged values of the outcome indicator. Our testing for such non-linearities involved a two-step process. First, we estimated quadratic models for each variable by including a term (Xt1 )2 in equation (1). If the relationship between the current and lagged squared values of the outcome indicator did not produce statistically significant results, we concluded that the linear relationship was sufficiently accurate to draw implications for stability. If, on the contrary, the squared value of the lagged indicator proved statistically significant, we proceeded to our second step. Because the stability properties of a quadratic are not so simply related to slope as in the linear case above, we employed a simulation that iterated through values of Xt1 until the value associated with threshold instability was identified. If that value fell within the range of variation observed in our sample, we denoted that as an example of threshold instability. Summary of the Empirical Model Our analysis can be portrayed in the following summary fashion. We examine a series of

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annual snapshots of census tracts for each of the five cities over a period of seven years or longer that undoubtedly vary in the severity, timing and type of external influences to which they have been subjected. Although we cannot identify any details regarding these influences, we ask whether, amid all the ‘noise’, any consistent, endogenous patterns of annual neighbourhood change emerge. Put differently, we seek the degree to which a neighbourhood indicator’s value in one year is affected by its value in the prior year. If the answers were ‘none’ or ‘one-for-one’, the coefficient of the lagged value would be zero or one respectively; in neither case would any dynamic endogenous adjustments be revealed. But if the answers were ‘significantly different from zero and less than one’ or ‘significantly greater than one’, some sort of endogenous adjustment process (stability and instability respectively) would be revealed. Results The main finding of this investigation is that, for most of the neighbourhood indicators that we tested, the coefficient of the lagged indicator variable proved significantly different from zero but significantly less than one. This means that most indicators demonstrated an adjustment process that converges quickly to a stable state. We did not discover instability or threshold instability in any of our neighbourhood indicators. Evidence of Stable, Endogenous Neighbourhood Adjustment Processes The bulk of the results suggest a stable, endogenous neighbourhood adjustment process, although the details vary across indicators. From the results of our linear regressions (see Table 1), we determined that most of the neighbourhood indicators demonstrated stability because the coefficients of the lagged value had a value different from zero and less than one. The results in Table 1 also indicate that most of the sample cities have statistically

significant, positive coefficients for the linear and quadratic terms, implying that the relationship between the indicator and its lagged value is non-linear. In addition, although the property crime rate in Detroit does not show a statistically significant, positive coefficient for the linear model, the coefficients of the lagged and lagged squared terms for the quadratic model are highly significant. Because the stability properties of a quadratic term are not so simply related to a slope coefficient as in the linear model, we conducted the value iteration simulation described above to locate a value at which threshold instability might occur. From the threshold point simulation testing based on quadratic regression results, we concluded that all the indicators with a statistically significant quadratic term were stable across the entire sample range. None of these neighbourhood indicators exhibited threshold points within their respective sample ranges, implying stability. The results of our quadratic regression analyses can most easily be presented graphically. The graphic figures for each neighbourhood indicator were created by calculating the stable state for each individual indicator—X as in (4), above. Note that we used the intercept b from the regression in computing X ; in fact, each neighbourhood with a statistically significant fixed effect w would have its own, distinct value for X based on (w þ b). We then chose hypothetical values (within our sample range) to represent a number of unspecified, exogenous transient upsets (both positive and negative) in each indicator during the initial period and graphed their intertemporal adjustment responses, utilising the values produced by our quadratic regressions (Table 1). Two representative endogenous adjustment process graphs are shown for violent crime rates (Figure 1) and low-weight birth rates (Figure 2) in Cleveland. Both figures illustrate how the neighbourhood indicator (vertical axis), if upset from its original, steady-state value by an amount shown in year 1, will change over time (horizontal axis), as estimated by the quadratic coefficients. Both figures

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Table 1. Linear and quadratic coefficients for neighbourhood indicators (lagged values of indicator appear on right-hand side of equation; standard errors shown in parentheses) Linear model Neighbourhood indicator Violent crime rate Cleveland (1990–2001) Denver (1990–2003) Detroit (1996–2003) Seattle (1996–2003) Property crime rate Cleveland (1990–2001) Detroit (1996–2003) Seattle (1996–2003) Low-weight birth rate Cleveland (1990–2000) Denver (1990–2002) Oakland (1988–97) Teenage birth rate Cleveland (1990–2000) Denver (1990–2002) Oakland (1988–97) Home sales rate Cleveland (1993–99) Oakland (1988–99) Median home sale value Cleveland (1993–99) Oakland (1988–99) Tax delinquency rate Cleveland (1993–99) a

Quadratic model

Constant

Coefficient

Constant

Coefficient

Coefficientˆ

4.042d (2.000) 0.135 (2.042) 25.957b (3.319) 0.407 (0.912)

0.551a (0.017) 0.157a (0.030) 0.130a (0.023) 0.176a (0.037)

5.449b (1.976) 20.281 (1.981) 26.955b (3.377) 0.518 (0.910)

0.377b (0.027) 0.567b (0.061) 0.092b (0.033) 0.060 (0.061)

0.00108b (0.00013) 20.00315b (0.00042) 0.00017 (0.00011) 0.00169d (0.00070)

17.263b (6.468) 75.132b (9.466) 26.055b (5.021)

0.586a (0.012) 20.004 (0.020) 0.209a (0.033)

33.451b (6.262) 65.764b (9.696) 26.692b (5.148)

0.204b (0.029) 0.112b (0.035) 0.178b (0.063)

0.00019b (0.00001) 20.00007b (0.00002) 0.00006 (0.00010)

16.149b (2.300) 8.613b (0.898) 7.609b (1.639)

20.043e (0.024) 20.049 (0.039) 20.120a (0.036)

16.961b (2.334) 9.738b (1.140) 8.485b (1.692)

20.147d (0.058) 20.270f (0.144) 20.287b (0.095)

0.00322d (0.00163) 0.01062 (0.00664) 0.00763d (0.00378)

112.820b (19.273) 173.748b (63.258) 82.203b (12.161)

20.047c (0.023) 0.112a (0.040) 20.015 (0.035)

100.477b (19.388) 151.875d (65.181) 76.334b (12.917)

0.113b (0.043) 0.232d (0.096) 0.088 (0.085)

20.00039b (0.00009) 20.00003 (0.00002) 20.00041 (0.00030)

3.580b (1.220) 5.029b (0.388)

0.185a (0.026) 0.065e (0.036)

5.273b (1.160) 5.155b (0.425)

20.165d (0.034) 20.002 (0.099)

0.88700d (0.07600) 0.00764 (0.01050)

42.570b (7.580) 140.536b (11.662)

20.057 (0.032) 0.146a (0.035)

41.688b (7.591) 171.883b (12.222)

20.030 (0.078) 20.292b (0.071)

20.00001 (0.00003) 1.173E-6b (1.678E-7)

11.440b (0.990)

0.391a (0.025)

13.580b (1.080)

0.155d (0.055)

0.00600d (0.00140)

Denotes p , 0.01 (two-tailed test of H0: coefficient ¼ 0 and one-tailed test of H0: coefficient 1). p , 0.01 (two-tailed test of H0: coefficient ¼ 0). c p , 0.05 (two-tailed test of H0: coefficient ¼ 0 and one-tailed test of H0: coefficient 1). d p , 0.05 (two-tailed test of H0: coefficient ¼ 0). e p , 0.10 (two-tailed test of H0: coefficient ¼ 0 and one-tailed test of H0: coefficient 1). f p , 0.10 (two-tailed test of H0: coefficient ¼ 0). ˆCoefficient of lagged indicator squared. b

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Figure 1. Adjustment process estimated by quadratic: violent crime rate in Cleveland.

convey that both neighbourhood indicators adjust in a steady, monotonic fashion towards their respective stable states, even when the hypothetical exogenous shock was quite large in magnitude.

The fundamental difference that one notices between Figures 1 and 2 is the implied speed of adjustment back to their respective stable states. The violent crime rate reverts back to its stable state at a much slower pace than

Figure 2. Adjustment process estimated by quadratic: low-weight birth rate in Cleveland.


does the low-weight birth rate because the size of the coefficient of the lagged indicator is much larger in the former case. For instance, when both indicators are upset by an arbitrary value of three (3) standard deviations respectively, the low-weight birth rate will adjust to within half of a standard deviation of its stable state in a year, whereas the violent crime rate will take four years to adjust to within half of a standard deviation of its stable state. Adjustment speeds for each of the neighbourhood outcome indicators that produced a significant coefficient of the lagged indicator are summarised in Table 2. Figure 3 illustrates the endogenous adjustment process for median home sale value in Oakland. Contrary to Figures 1 and 2 where neighbourhood indicators adjust in a steady, monotonic fashion towards their respective stable states, Figure 3 shows an oscillating, but steadily damped, convergence over time towards a stable state for the indicator. Mathematically, this is the result of the lagged indicator coefficient being between zero and negative one. Table 2. Speed of adjustment back to equilibrium (estimated from linear models) Neighbourhood indicator Violent crime rate Cleveland (1990–2001) Detroit (1996–2003) Property crime rate Cleveland (1990–2001) Seattle (1996–2003) Low-weight birth rate Oakland (1988–97) Teenage birth rate Cleveland (1990–2000) Denver (1990–2002) Home sales rate Cleveland (1993–99) Median sale value Oakland (1988–99) Tax delinquency rate Cleveland (1993–99)

Years 4 1 4 2 1 1 1 1 1 2

Notes: Indicators were initially upset by 3 standard deviations; speed is period for adjustment to reach 1/2 of a standard deviation from equilibrium; only those with statistically significant stability are shown.

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Evidence of Stability with No Endogenous Adjustment Process No lagged values, either linear or squared, proved statistically significant for the median sales value of homes in Cleveland, controlling for census tract fixed effects and city-wide trends. This suggests that the prior year’s value is not predictive of the current year’s, and thus there is no endogenous adjustment process whatsoever. By implication, however, this result implies great stability. After being perturbed by a transient shock, the market apparently quickly reverts to the capitalisation of the underlying, stable-state amenities reflected in the neighbourhood’s housing stock and environs, as measured by the constant term in the regression plus the tract’s fixed effect coefficient.11 No Evidence of Threshold Instability By conducting a simulation that used the quadratic model coefficients for each indicator and iterated through differing initial values of neighbourhood indicators, we estimated a threshold point—i.e. the value associated with threshold instability. However, since in each case the threshold value did not fall within the range of variation observed in our sample, we did not accept that as an instance of threshold instability. We thus find no evidence that neighbourhood indicators exhibit stability over some range of values but become unstable past a certain threshold point within the range of observed values. A Robustness Test Related to Neighbourhood Poverty Composition To explore the degree to which the aforementioned results were general across various sorts of neighbourhood, we conducted supplemental tests on all indicators for census tracts distinguished by whether their 1990 poverty rates were above or below 20 per cent. (In our sample of cities, this demarcation simultaneously distinguishes heavily Blackand Hispanic-occupied tracts, for the most part.) We estimated linear regressions as

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Figure 3. Adjustment process estimated by quadratic: median home sale value in Oakland.

suggested by Long and Miethe (1988) that include a dummy variable denoting tracts with poverty rates above 20 per cent and an interaction between this dummy and the lagged indicator. A statistically significant coefficient of this latter term indicates that the adjustment processes for the two groups of tracts are not equal. We found that, in almost half of the indicator/city combinations tested, the neighbourhoods with the higher poverty rates adjusted significantly more slowly; in only one case (teenage birth rate in Denver) was the opposite true. This differential in speed of adjustment was most prevalent in the property and violent crime indicators in all cities except Detroit. We can only speculate about the potential reasons for these results, pending further research. One possibility may be that nonpoor residents in poor neighbourhoods perhaps are more likely to respond to a spike in crime by moving out of the area instead of staying, producing thereby a net loss of neighbourhood population that tautologically inflates the population-adjusted rate of crime over time. A closely related reason is that poorer neighbourhoods may tend to have

less collective efficacy (Sampson and Groves, 1989; Sampson et al., 1997), such that crime upsurges are less likely to generate suitably intensified anti-crime responses among neighbours. Another factor might be the lack of responsiveness of police forces to crime increases in poorer neighbourhoods compared with less-poor ones. The dynamic interrelationships between neighbourhood crime and local forces of deterrence have been recently explored theoretically and empirically by Lim and Galster (2005).

Discussion Revisiting Conventional Wisdom about Neighbourhood Dynamics If our results prove to be general, what would they imply about the process of neighbourhood change? One implication is that the sorts of explosive dynamics that historically have been witnessed in the case of racial transition may simply be exceptional. Many other aspects of neighbourhood change do not appear to be characterised by such instability ensuing at a relatively low threshold. The norm we clearly observed for a variety of


indicators in a variety of cities indicates neighbourhood resilience, quickly returning to stable state if upset by a transient shock, instead of progressively moving away from that original state. One should not misinterpret the foregoing as suggesting that neighbourhoods have so much inertia that they cannot be altered significantly from their stable state. On the contrary, our investigation tried to ascertain, amid the ‘noise’ of unobserved shocks— some transitory and some longer-term— whether there were any consistent dynamic patterns across city neighbourhoods during the 1990s. The observation that, on most indicators, neighbourhoods tend to gravitate towards their stable state merely reinforces the widely accepted theoretical formulation that it is the long-term flows of households, property owners and financial resources into and out of a neighbourhood that fundamentally shape what occurs there (Grigsby et al., 1987; Galster, 1987, 2001, 2003). Elsewhere this has been referred to as the homeostatic nature of the forces that forge city structures (Skaburskis and Teitz, 2003). Endogenous stability by no means implies, however, that these long-term flows cannot be altered through persistent changes in economic, social and environmental conditions at the regional or local level, or more intentional, neighbourhood-based interventions by private or public entities. Stability does not mean stasis. Indeed, the growing body of predictive statistical models cited above clearly implies that a persistent change in a wide variety of exogenous forces can lead to significant changes in neighbourhood trajectories. What this implies for community development strategy is that short-term, policy-induced ‘quick fixes’ hold little prospect to alter longer-term outcomes for neighbourhoods; sustained effort is required. The Underpinnings of Neighbourhood Dynamics The aforementioned notion of long-term flows guiding neighbourhood trajectories sheds light on another possible implication of this

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study. Does stability suggest that there are a series of behavioural ‘self-correcting mechanisms’ at play? Put differently, when an exogenous shock pushes an indicator far from its steady state, are there countervailing social, economic or political reactions that endogenously spring forth and drive the indicator back towards steady state? Consider some more pointed examples. When property tax delinquencies rise in a neighbourhood, do city tax collection efforts in the area intensify? When property crime rises, do neighbours organise to demand better police protection and institute block watches so that crime retreats? When home values rise, do owners react in ways that pull values back down the next year, perhaps by putting too many homes on to the market?12 Possibly, but we think such conclusions premature at the current state of knowledge. Another explanation for stability may simply be the powerful momentum of the aforementioned flows underpinning virtually all that we have measured here about neighbourhoods, upon which are superimposed unspecified shocks. Were this to prove valid upon replication, it would challenge some of the tenets of the complexity modelling approaches noted above, especially the claim that strong interactions or locational preferences among individual neighbours produce multiple equilibria among which the neighbourhood can easily tip when upset by external forces. Conclusions, Caveats and Implications for Future Research In the spirit of Schelling’s pioneering work on neighbourhood racial tipping points, we have explored theoretically and empirically the endogenous dynamics of a variety of nonracial neighbourhood indicators. Our goal was to ascertain, amid the welter of immeasurable influences bombarding neighbourhoods, the degree to which their pasts predicted their futures and whether these futures implied stability or instability. Our work is distinguished from prior efforts in four main ways. First, we have provided a mathematical model of four potential forms of endogenous

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neighbourhood dynamics. Secondly, we have analysed empirically for the first time systematic patterns in year-to-year changes in neighbourhoods. Thirdly, we have employed econometric specifications that permitted the identification of non-linearities that might signal threshold instability points. Fourthly, we have probed the robustness of our conclusions by investigating multiple indicators measured over different periods in multiple cities. This exploratory study has focused on the following questions. As measured by a battery of indicators, how do neighbourhoods respond when they are upset by some transient, exogenous shock(s)? Do they quickly revert to their original, stable state, gradually return to this stable state, permanently settle into another stable state, diverge progressively from any steady state, or evince no discernable pattern of response? Are there any threshold points that differentiate stable and unstable dynamic paths? Based on our investigations, we answer as follows. A self-regulating adjustment process promoting stability across a wide range of neighbourhood types is the norm. Stability that is quickly re-established at the original state characterises most of the indicators analysed: rates of tax delinquency, low-weight births, teenage births and home sales volumes. Violent and property crime rates also evince endogenous stability at the original state, but take considerably longer than the other indicators to return to it when the exogenous shock is sizeable. Moreover, this crime adjustment process is considerably slower in neighbourhoods with higher poverty rates. We would point out that the generality of these conclusions—intertemporally, nationally and internationally—should be tested further before definitive conclusions are drawn. The period during which our analysis was undertaken did, it should be noted, encompass both years of economic contraction (early 1990s) and expansion. Moreover, our sample of cities, although admittedly chosen on the basis of data availability, nevertheless represents a wide cross-section of

American city growth trajectories. Denver and Seattle are increasingly populous and prosperous areas; Detroit and Cleveland are depopulating, disadvantaged areas; and Oakland holds an intermediate position (Frey, 2005). As for international generality, we suspect that in urban regimes with more social welfare-oriented/less market-oriented public policy than the US we would see both less variability in magnitude of shocks impinging on neighbourhoods and more speed of public-sector reaction to compensate for any shocks that do impinge. This logic would suggest that neighbourhoods in such regimes would be even more stable than what we have observed in the US, but explicit replication is clearly needed. Of course, there are several additional caveats circumscribing our explorations. First, our findings relate to a limited number of neighbourhood indicators, some of which were available in only a few cities. Secondly, more complicated dynamic processes can be explored with models employing two-period lags, but such was deemed inappropriate for the relatively short time-series available here. Thirdly, endogenous dynamic processes for any single indicator may be contingent not only on neighbourhood context, but on interactions with concurrent changes in other indicators. Suggestions for future research proceed readily from the above. First, our basic empirical investigation should be replicated in other neighbourhoods in a variety of nations, during different and longer periods, using a wider range of indicators, each of which takes on a wider range of values to enhance confidence in our conclusions. In particular, it would be useful to explore the Schelling racial tipping hypothesis by investigating year-to-year changes in racial composition of neighbourhoods, were such data to become available. We also urge dynamic analyses of neighbourhood housing maintenance and rehabilitation behaviour when data permit such. There is some theory and evidence suggesting that home reinvestment may evince threshold instability: neighbourhood-wide reinvestment rates must exceed a


critical mass before the most sceptical investors will join the bandwagon, thereupon pulling the entire neighbourhood up to a higher stable state of maintenance (Taub et al., 1984; Galster, 1987). Secondly, to test further the sensitivity of our findings, future studies might well categorise neighbourhoods into different strata from those explored here, such as owneroccupied residences, teenage residents and employees with managerial or professional occupations. Prior work implies that these characteristics distinguish neighbourhoods by different housing sub-market stability properties (Rothenberg et al., 1991) and vulnerability to a variety of negative social processes (Sampson and Groves, 1989; Crane, 1991; Sampson et al., 1997; Galster et al., 2000). Finally, further empirical and theoretical study is needed as to the behavioural reasons why neighbourhoods seem so stable on a variety of measures. Deeper understanding here is crucial if we are concerned about more efficient and equitable neighbourhood outcomes.

6.

7.

8. 9.

10. 11. 12.

Notes 1.

2.

3.

4. 5.

Carter et al. (1998) employ a quadratic specification of beginning-of-decade census tract poverty rate to predict subsequent decadal change in poverty rates. For a variety of empirical explorations stimulated by the tipping point hypothesis, see Guest and Weed (1976), Schwab and Marsh (1980), Taub et al. (1984), Ottensmann et al. (1990), Galster (1990a, 1990b), Lee and Wood (1991) and Ottensmann and Gleeson (1992). Some econometric efforts have attempted to quantify the importance of neighbourhood social interactions through estimation of discrete-choice models of household mobility (Blume and Durlauf, 2001; Zhang, 2001; Meen and Andrew, 2002). Unfortunately, implications of results for neighbourhood stability or instability are typically not explored. Threshold instability is entirely analogous to Schelling’s notion of a tipping point. Equation (1) is a special case of a more general equation where b is permitted to vary over time. Note that here we model the dynamics of the higher-level spatial entity,

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the neighbourhood, without particular concern over the individual behaviours that might be producing it. For mathematical models of aggregate neighbourhood outcomes that begin at the individual behavioural level, see for example, Brueckner et al. (1999), Blume and Durlauf (2001) and Zhang (2001). Now that all concepts have been introduced, Schelling’s model (1971, 1972) can be reinterpreted as one involving threshold instability (tipping point) of a White-occupied neighbourhood leading to a different (all Black occupants) equilibrium. For the City of Denver, 77 neighbourhoods based on 146 census tracts were analysed because of lack of data availability at the level of census tracts. For reliable estimation of neighbourhood indicators, census tracts with a population of less than 100 were excluded. We had no data on dropouts and the massive welfare reforms post-1996 resulted in welfare receipt rates being an inconsistent indicator of poverty during the decade of our study. Specifically, the TSCSREG procedure in SAS was used. The value of the constant was a statistically significant 42.57 (measured in $1000s). Galster (1987) found that home-owners who expect property values to inflate tend to ‘free ride’, investing somewhat less in their home than otherwise.

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Appendix Table A1. Data sources City

Neighbourhood indicator

Source

Cleveland

Violent crime rate Property crime rate Low-weight birth rate Teenage birth rate Home sales rate Median sale value Tax delinquency rate

Center on Urban Poverty and Social Change, Case Western Reserve University, Cleveland, OH; generated using Cleveland Area Network for Data and Organizing (CANDO) (http://povertycenter.cwru.edu/cando.htm) Collated at the Urban Institute, Center for Metropolitan Housing and Communities

Denver

Violent crime rate Low-weight birth rate Teenage birth rate

Piton Foundation (http://www.piton.org)

Detroit

Violent crime rate Property crime rate

City of Detroit Police Department

Oakland

Low-weight birth rate Teenage birth rate Home sales rate Median home sale value

Collated at the Urban Institute, Center for Metropolitan Housing and Communities

Seattle

Violent crime rate Property crime rate

City of Seattle Police Department

Table A2. Descriptive statistics of neighbourhood indicators N

Mean

Standard deviation

Minimum

Maximum

Violent crime rate (per 1000 population) Cleveland (1990–2001) Denver (1990–2003) Detroit (1996–2003) Seattle (1996–2003)

2343 966 2107 833

17.75 10.16 35.91 7.86

17.29 13.11 34.16 10.59

0.00 0.60 0.00 0.00

268.71 182.30 490.38 94.77

Property crime rate (per 1000 population) Cleveland (1990–2001) Detroit (1996–2003) Seattle (1996–2003)

2343 2107 833

76.26 99.79 85.56

97.74 130.54 82.96

9.75 0.00 12.66

1712.09 1774.44 607.23

Low-weight birth rate (per 100 live births) Cleveland (1990–2000) Denver (1990–2002) Oakland (1988–97)

2130 715 900

11.76 9.33 9.40

7.96 3.31 5.39

0.00 2.10 0.00

60.00 25.50 33.33

Teenage birth rate (per 1000 females aged 15 –19) Cleveland (1990–2000) Denver (1990–2002)

2130 676

109.67 176.52

74.09 240.79

0.00 11.60

930.00 5000.00

Neighbourhood indicator

(Table continued)

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Table A2. Continued Neighbourhood indicator

N

Mean

Standard deviation

Minimum

Maximum

Oakland (1988–97)

909

79.93

60.76

0.00

340.91

Home sales rate (per 100 single family homes) Cleveland (1993–99) Oakland (1988–99)

1460 946

5.33 3.81

7.81 1.71

0.00 0.00

150.00 10.94

Median home sale value (single family homes, thousands of current dollars) Cleveland (1993–99) Oakland (1988–99)

1340 1023

49.90 148.37

38.60 92.58

0.70 0.00

650.00 551.00

Tax delinquency rate (per 100 dwellings) Cleveland (1993–99)

1568

13.20

7.49

0.00

50.00

Notes: N ¼ number of census tracts in city with more than 100 population in 1990 (for Cleveland and Oakland) or 2000 (for Detroit and Seattle) number of years for which data were gathered. Neighbourhoods with missing values were removed.