On the Dynamics of Growth and Poverty in Cities

Transcription

1 Growth and Poverty in Cities On the Dynaics of Growth and Poverty in Cities Marcellus Andrews Wellesley College This article presents a odel of the city as a growing, sall, open econoy in which the uneven distribution of technical knowledge and skills priarily acquired through foral education across population subgroups interacts with the growth of business facilities (factories and associated production facilities) to drive the dynaics of population and eployent. 1 The urban econoy is odelled as a syste in which long-ter capital flows are strongly influenced by relative after-tax rates of return on capital between the local econoy and the outside world. Further, the division of the urban population into a skilled iddle class and a largely uneployable underclass is the consequence of two forces: educational failure and iddle class flight fro the city. The educational underclass is a result of a eritocratic educational syste that divides each student cohort into a skilled iddle class and an underclass bereft of the skills required for legitiate eployent. The presence of an educational underclass creates a nuber of probles for both iddle class residents and city authorities that ay induce a portion of the iddle class to leave the city, thereby worsening the probles associated with poverty. Poverty concentrated in the city increases the costs associated with public services, driving up taxes, reducing city services, and generally worsening the business cliate. This, in turn, reduces the long-ter, after-tax rate of profit fro capital accuulation in the city. The central thee of this article holds that the logic of eritocracy creates class divisions in the urban labor arket which ay underine the very conditions that ake rapid econoic growth possible. Merit, especially in recent years, is essential to securing highwage eployent. Marshall and Tucker (1992), in an iportant study of the changing skill requireents of work in the Aerican econoy, show how odern telecounications, anufacturing, and high value added services in finance, design, inforation processing, and analysis require workers to have significantly greater nueracy, literacy, and technical skills as a prerequisite for training and eployent than was the case 30 years ago. In particular Marshall and Tucker noted that two opposing tendencies have eerged in the afterath of technological change that have profound consequences for the nature of labor deand and the structure of eployent in odern econoies. First, advanced technology is creating a whole new set of eployent possibilities that deand high levels of skill and initiative on the part of workers, leading to high wages and satisfaction (Marshall and Tucker, 1992, p. 36). Indeed any studies suggest that a growing nuber of jobs will require high levels of intellectual ability and initiative, with a steady escalation of skill requireents over tie (Marshall and Tucker, 1992, p. 36). Second, technological advances in counications, precision engineering, and the application of coputers in a wide range of production technology has greatly increased the deand Cityscape 53

2 Andrews for highly educated labor at the expense of jobs for workers with odest acadeic achieveents. As a result of these changes, educational credentials are now essential for obtaining high-paying work, whereas the lack of credentials is increasingly a barrier to these jobs and ay even block the possibility of eployent altogether. In an urban setting, such developents ean that knowledge capital plays a dual role in creating and driving econoic growth at the local level. On the one hand, econoists like Roer (1986) and Lucas (1988) have developed foral analyses of the interaction between capital accuulation and huan capital in generating high rates of growth in per capita output. In particular Lucas presentation has pointed out the role of huan capital whether in the for of ebodied technical skills iparted through foral education or the increase in technical knowledge associated with the creation and growth of a highly educated scientific segent of the labor force in generating rapid and sustained econoic growth. However, there is little reason to assue that knowledge capital is spread evenly over a population. Nor is there a legitiate reason to assue away a basic and frightening aspect of odern urban education: Schools in large cities are failing to provide any of their students with the literacy and nueracy skills necessary to obtain work in a skills-driven econoy. Indeed, in an econoy in which educational achieveent is an increasingly iportant qualification for high-wage eployent, education becoes a de facto class sifter that divides each generation of students in a counity into a class of workers and an underclass. This division of society has caste-like qualities, since ost recent works on education clearly show that the priary deterinant of the educational achieveents of children is the socioeconoic status and educational achieveents of their parents. 2 Thus success in acquiring knowledge capital is concentrated aong those groups that have already succeeded in school while those who have not fared well in school are likely to pass their lack of success on to their children. In an urban setting, the winners and losers in the copetition for credentials live close enough together to have an ipact on each other. The underclass constantly sees the high living standards of the iddle class but is unable to acquire the huan capital that akes this standard of living possible. In turn the anger, frustration, and envy that drive uch of youth crie aong the urban poor reduce the quality of city life for iddle class residents, increasing the likelihood that a portion of the iddle class will leave the city in favor of safer, less poverty-ridden surroundings. The underclass is soeties a labor force for the illegal sector of the urban arket syste, usually, but not solely, represented by the arket in illegal goods sold both inside and outside the regional econoy, such as narcotics, and goods and services sold within the regional econoy only, such as prostitution. Further, class conflict between the educated working class and the underclass is expressed in part by the persistent proble of robbery, burglary, and other property cries, as well as by the gradual coarsening of social relations as differences in living standards and life prospects fuel frustration and violence aong the underclass. 3 The antagonistic relationship between the urban iddle class and underclass has consequences for the long-range coposition of the city s population, affecting the long-ter growth and developent of cities by shaping the size and scope of public-sector activity as the city governent tries to balance the needs to control crie, alleviate poverty, and provide education against the need to attract and retain both capital and iddle class residents. The dynaics resulting fro the logic of eritocracy and iddle class/underclass conflict in a sall, open econoy are studied in detail below. 54 Cityscape

3 Growth and Poverty in Cities The Actors and Their Behavior The Underclass Mebers of the underclass have two sources of incoe: transfer payents and crie. The representative eber of the underclass is assued to axiize the utility of consuption (c u ) and iniize the disutility associated with criinal activity, which is assued to be proportional to the fraction of each period devoted to participating in illegal activity (φ, 0 < φ < 1). Further, ebers of the underclass are strongly affected by the living standards of the iddle class. Increases in the standard of living for iddle class citizens have a deonstration effect on ebers of the underclass, encouraging poor people to consue ore. Underclass participation in criinal activity can be thought of as a labor-leisure choice issue. On the assuption that the poor do not save, the utility of consuption (c u ), leisure and criinal behavior (φ) is represented by the function V u : (1) V u = wlnc u + λln (1 - φ), where λ (λ > 0) is the strength of the utility of leisure. This forulation of underclass preferences assues that increases in the level of iddle class incoe (w) raise the arginal utility of consuption for ebers of the underclass. The budget constraint faced by a eber of the underclass is expressed as (2) c u = [Ω + εφ]w, where w is the level of real incoe per iddle class worker, Ω the ratio of poverty relief per eber of the underclass to real iddle class per worker incoe, and εφ the fraction of incoe per iddle class worker that is transferred to the underclass through theft. Each eber of the underclass is assued to axiize the expected utility of consuption and leisure with respect to a budget constraint (2). The probability of arrest and iprisonent when a person coits a crie is κ. Hence the expected utility associated with a φ degree of participation in criinal activity is (3) (1 - κ) wlnc u + λln (1 - φ), assuing that c u = 0 in the event of arrest and iprisonent. 4 Optial labor-leisure choice on the part of the underclass results in a crie-participation function of the for φ = φ(w, κ), where φ w < 0 and φ κ > 0 if the gain fro criinal activity exceeds poverty relief. 5 Given the fraction of tie each representative eber of the underclass spends in illegal activity (φ), the total nuber of persons participating in crie is φu, where U is the size of the underclass. Assuing that each person engaged in crie earns εy, the total transfer of incoe fro the iddle class to the underclass is φεyu. Further, the loss of incoe per worker is expressed as φεy(1 - )/, where = U/T = (T - M)/T is the iddle class ratio (M is the size of the iddle class, and T the size of the total population). The Middle Class A iddle class worker will stay in the city if the benefits of doing so outweigh the costs. For siplicity it is assued that the pleasure or utility of living in the city is deterined first by the net incoe a iddle class citizen can expect to earn there over his or her See note 5 for equation (4). Cityscape 55

4 Andrews lifetie and second by the pleasures of living and working in a ore densely populated, racially diverse, and socially and culturally liberal setting than could be found in surrounding suburban areas. However, iddle class workers are also victis of robbery, burglary, and other property cries that characterize the underside of the class and caste diversity of cities. The probability of being victiized by crie is assued to be a function of the extent of criinal activity relative to the size of the iddle class. Hence the probability of a iddle class worker being a victi of crie is represented by (5) φ(1 - ). Given the loss suffered by a iddle class victi of crie (εw), the expected loss fro crie for a iddle class worker is expressed as (1 - ) (6) εwφ, and the expected incoe of a iddle class worker as (1 - ) (7) w[x - εφ ], where x is the eployent rate. The lifetie earnings associated with living in the city is siply the present discounted value of expected iddle class after-tax incoe over the tie horizon (T*), given the incoe tax rate (θ) and the discount rate (α), and is denoted by V C. 6 As stated above the typical iddle class citizen stays in the city as long as the perceived benefits of doing so outweigh the costs of oving to the suburbs. Suburbs are assued to offer sure eployent and freedo fro crie. Hence, assuing that the wage earned in the suburbs is the sae as that in the city, the benefit associated with oving to the suburbs is siply the present discounted value of after-tax incoe associated with suburban living. 7 However, two kinds of costs are associated with a ove fro the city to the suburbs. Aside fro the usual financial costs of oving, a ove to the suburbs can entail psychological and cultural costs. Given the realities of racial, ethnic, and cultural conflict and segregation in the United States, as well as the lower quality of artistic and intellectual life in the suburbs, a ove to the suburbs ay well involve significant psychological distress and cultural alienation for any ebers of arginal cultural, lifestyle, and racial groups, leading to a loss of γ in utility (easured in onetary ters for analytical convenience) that partly offsets the pleasures of suburban life. In addition persons who ove fro the city to the suburbs will suffer losses associated with leaving high-density areas that offer a nuber of unique services and opportunities. This aversion to suburban living ay be nonexistent for soe (γ < 0) but quite strong for others. The aversion to suburban living is assued to be distributed over the population of new workers according to the density function f(γ), which satisfies the usual properties of a probability density function. It is further assued that the distribution of the aversion to suburban living does not change uch over tie. 8 Hence a fraction of new workers, F(Γ), will leave the city if the incoe associated with suburban living (V S ) exceeds the incoe See notes 6 and 7 for equations (8), (9), and (10). 56 Cityscape

5 Growth and Poverty in Cities fro living in the city (V C ) plus the preiu (expressed in oney ters) associated with the nonpecuniary benefits of living in the city (Γ), where (11) F(Γ) = Γ 0 f(γ)dγ. and Γ = Γ(w,, θ, θ S ) = V S (w, θ S ) - V C (w,, x, θ). In light of the foregoing analysis, the fraction of each new cohort of workers that chooses to leave the city is F(, x, θ, w). It is a siple atter of algebra to show that the exit rate of new iddle class workers (F) rises if falls or if θ or w rises, that is, where F < 0, F θ > 0, F w > 0. 9 Schools, Poverty, and Population Dynaics Success or failure in school is the critical eleent that deterines the ultiate class position of an adult in this odel of an urban econoy. While the nature of the local race/ caste syste, faily wealth, and other caste factors are obvious forces that shape the fortunes of individuals and groups in a city, educational success is assued to be the ost iportant single deterinant of a child s life prospects. 10 Graduation fro the foral school course with a certificate that deonstrates a person s astery of essential technical subjects and testifies to his or her ability to coplete a course of study allows a student to enter the labor force. Conversely, failure either to graduate fro school (drop out) or to attain sufficient copetence in core subjects greatly reduces a person s likelihood of eployent. 11 Research into educational effectiveness suggests that class size, facilities, and teacher qualifications play only a sall role in accounting for educational success. However, it also shows that the educational and class status of parents, as well as early intervention progras for econoically disadvantaged students (for exaple, Head Start in the United States), have significant effects on educational achieveent. 12 In particular the work of John Ogbu and his associates has clearly shown that attitudes towards education and educational attainent are greatly influenced by a group s caste status in a social syste. Ogbu s cross-cultural research on the role of caste status in educational attainent in the United States, India, Japan, and Israel has deonstrated that lower caste groups defined as groups that have been involuntarily incorporated into a doinant society, systeatically relegated to occupations of the lowest status, and subjected to continual defaation and derogation in public culture perfor poorly on educational tests copared with ore highly favored groups (Ogbu, 1986). Further, Ogbu s research has shown that class and caste status, rather than race, is the ajor correlate of lower educational attainent on the part of disfavored groups. Copetent graduates enter the labor force which, in this context, is synonyous with the iddle class while incopetent graduates are largely cut off fro the possibility of eployent. The interaction between educational success and labor force growth is a critical deterinant of the evolution of poverty in the city. Given the nuber of students at a point in tie (gt), a fraction (ξ, 0 < ξ < 1) of students fro poor counities fail to coplete the curriculu at the required level of copetence. Hence the nuber of students that coplete the educational course at the required degree of copetence is gm + (1 - )(1 - ξ)gt, which is also the increase in the size of the labor force (M). However, iddle class flight leads to the eigration of a fraction (F(x, )) of the labor force, thereby reducing the size of the labor force. These considerations iply that the net increase in the labor force is (12) M = gm + (1 - ξ) (1 - ) gt - F(x, )M. Cityscape 57

6 Andrews The description of the evolution of poverty in the city is copleted by an equation representing population growth. The rate of population growth is siply the difference between the rate of population increases due to natural growth and iigration (gt) and the rate of population decline that results fro iddle class flight (-F(x, )M). Given the size of the current population (T), the rate of population growth is expressed as (13) g T = g - F(Γ). Cobining equations (12) and (13) yields an expression for the change in the iddle class ratio of (14) = (1 - ) [ (1 - ξ)g - F(x, ) ]. The Governent Budget Constraint Incoe tax revenue is expressed as θk/σ, on the assuption of a unifor incoe tax rate. Governent spending finances education, public safety, and poverty relief. Public safety operations consist of the police, prisons, and the court syste. The ratio of the police to the total population is denoted by π. Given the wages of public-sector eployees (ω), total spending on police is represented by πωt. The reaining eleents of public spending are poverty relief and education. Poverty relief is assued to be the siple product of poverty relief per person (Ω) and the nuber of poor people in the city ((1 - )T). In addition education spending (τωgt) is liited to teachers salaries in this analysis. Thus the governent budget constraint can be written as (15) θ σ Κ = [Ω (1 - ) + ω (τg + π) ]T. The per capita for of the governent budget constraint is expressed as (15a) θβx = Ω (1 - ) + ω (τg + π). Eployent Dynaics The urban capital stock grows when the rate of profit in the city (ρ) exceeds the rate of profit elsewhere (ρ*). Given a production function of the for (16) Y = in [ σ Κ, βl], where β is the level of output and L the level of eployent, the rate of profit would then be ρ = (1 - βw ) σ 1. The rate of growth of the capital stock is represented by (17) K K = G [ (1 - θ) ρ - ρ* ] - δ, G > 0, where δ > 0 is the depreciation rate and G a positive constant. Given the growth rate of the labor force (equation (12)), the evolution of the eployent rate is represented by (18).... x x = K L - K L, = (G [ (1 - θ) ρ - ρ*] + F (x, ) - (1 - ξ) (1 - ) g ). 58 Cityscape

7 Growth and Poverty in Cities Dynaics The growth of cities caught in the conflict between the poor and the iddle class can be studied through the use of a siple phase diagra. A phase diagra is a device used by econoists, engineers, and others to study the way a syste develops over tie without actually having to solve coplex dynaic systes. In this case a phase diagra approach to studying urban dynaics is especially helpful since, like ost econoic analyses, the interaction of iddle class dynaics and eployent growth is represented by very general relationships rather than by precise atheatical forulas. Phase diagras are helpful for illustrating the role of feedback and dynaic coupling in causing an econoy to ove over tie. Feedback is a siple and powerful phenoenon that ay be failiar to those who have experienced the annoying noise of an open icrophone at a concert or speech. In that situation the icrophone aplifies its own speaker output, producing an ever-growing resonance that results in the screeching sound called feedback. The open icrophone proble is an exaple of positive feedback: a process that grows on itself. 13 Dynaic coupling is a bit trickier to explain, even though it is a relatively siple process that constantly akes itself felt in econoic life. In the siplest sense, dynaic coupling is the interaction between processes that change over tie. Malthus theory of population growth is a glooy, but unfortunately apropos, exaple of dynaic coupling between the rate of population growth and the growth of the eans of subsistence in a siple industrial econoy. Malthus theory of population growth aintained that the population grows at an exponential rate as long as there is an adequate supply of food, while the supply of food only grows at an arithetic rate. Hence population growth would periodically outstrip the growth of food, leading to ass starvation, crie, and violence as checks on population growth. In Malthus analysis food and population are dynaically coupled together to produce a cycle in population growth rates: a rise in per capita food availability increases the rate of population growth (an exaple of positive dynaic coupling or, ore siply, positive coupling). However, higher levels of population reduce the availability of food, thereby leading to a gradual and painful decline in population growth (an exaple of negative coupling). The cyclical Malthusian dynaic is driven by a cobination of positive feedback on population growth and offsetting positive and negative coupling between food and population growth. The evolution of the urban econoy can be represented by the oveent of the iddle class ratio () and the eployent rate (x) over tie. The dynaic syste governing the evolution of the urban syste is expressed as equations (14) and (15a), given the governent budget constraint (18). 14 Figure 1 shows a phase diagra that illustrates the evolution of the econoy over tie. Line represents those cobinations of the iddle class ratio and the eployent rate that keep the iddle class ratio stable, that is, that keep it constant over tie. Siilarly line xx represents those cobinations of and x that keep the eployent rate stable. Line is positively sloped, because the iddle class rate is a negative feedback process while positively coupled to eployent rate. This eans that a rise in the level of the iddle class ratio leads to a saller rate of change in the iddle class ratio (in uch the sae way that a negative real rate of interest eans that a larger stock of wealth loses ore purchasing power with the passage of tie), while a rise in the eployent rate leads to a copensating influx of iddle class residents into the city, leaving the level of the iddle class ratio unchanged. 15 In addition line xx is negatively sloped on the assuption that x is a negative feedback process while negatively coupled to the iddle class ratio. The negative feedback link Cityscape 59

8 Andrews between the oveent of x and its level eans that a rise in the eployent rate reduces the rate of increases in that rate. In turn the negative coupling of the eployent rate to the iddle class ratio depends on the size of the educational failure rate ξ. A bit of calculus and algebra can show that there exists a level of the educational failure rate ξ = ξ C, the critical failure rate, that just balances the positive effects of a large iddle class ratio on the growth of the iddle class (by slowing iddle class flight) with the negative effects of a rise in on the growth of the iddle class as a result of school graduation. 16 When ξ > ξ C, a rise in leads to saller growth in the iddle class as a result of school copletion relative to iddle class flight, which causes the growth rate of the iddle class to rise and paradoxically, the eployent rate to fall. The econoic eaning of line xx is clear: Line xx is the cobination of points in (x, ) space where the growth rate of labor deand is just equal to the growth rate of labor supply. If a rise in the iddle class ratio raises the growth rate of labor supply (which is the sae as the growth rate of the iddle class), then the only way that balance can be restored between labor deand growth and labor supply growth is with a falling eployent rate (labor deand growth is independent of both and x in this odel). The intersection between and xx is the long-ter equilibriu configuration of the econoy. If xx slopes downward, the equilibriu point shown in phase space is said to be a stable node, eaning that the urban econoy will tend to ove toward this point in the presence of shocks to the econoy. However, if xx is steeper than, then the equilibriu point in phase space is said to be a saddlepoint, eaning that shocks to the econoy can lead to cuulative departures away fro equilibriu. The otion of the econoy in the afterath of a shock is shown by the sall arrows in each part of the phase space. An exaple of the use of phase diagras helps show why this technique is so powerful. A rise in the tax rate (θ) raises the iddle class exit rate (F(x, )), thereby lowering the change in the iddle class rate over tie. In Figure 1 this phenoenon is represented by a leftward shift in line xx, eaning that the region of phase space associated with a decline in x becoes larger. In addition the foregoing analysis shows that a rise in θ reduces the rate of capital accuulation and eployent growth as well as the rate of labor force growth (which is the sae as the rate of growth of the iddle class). This fact eans that a rise in θ has an abiguous effect on the evolution of the eployent rate. If the decline in the rate of capital accuulation is greater than the decline in the growth of the labor force, the eployent rate falls, as shown in Figure 1 by a downward shift in line. These kinds of shifts will lead to a reduction in the long-ter iddle class ratio in a stable regie, as is evident by the lower intersection of xx and along the vertical axis. However, the siultaneous drop in x and over tie eans that the long-ter value of the eployent rate is uncertain. In the case of a saddlepoint, two kinds of cuulative oveents are possible. First, a shock to the econoy that causes both the eployent rate and the iddle class ratio to exceed the equilibriu value can lead to a virtuous circle, in which increases in the eployent rate can lead to increases in the iddle class ratio, which in turn can further boost eployent rates, and so on. Second, an econoic shock that pushes x and below the equilibriu point can lead to the threat of a vicious circle, in which falling eployent rates encourage a decline in the iddle class ratio and lead to further eployent declines. This distinction between dynaic regies is crucial for the understanding of urban growth. On the one hand, a stable growth regie (as shown in Figure 1) is one in which city officials can use public safety and educational policies to affect arginal shifts in the presence of the iddle class in the city. By contrast a saddlepoint regie (as shown in 60 Cityscape

9 Growth and Poverty in Cities Figure 2) is rather ore abitious (if risky), precisely because it is a situation in which, given the right kind of econoic shock, the way a city grows prootes a cuulative expansion in both jobs and iddle class prosperity. The foregoing dynaic analysis highlights the role of educational failure, capital flows, and iddle class tastes in shaping the process of urban growth and developent in a society where conflict between the iddle class and the poor is a central social and econoic force. In particular this analysis shows that when the sensitivity of capital flows to profit differentials (G) is sall and the failure rate is above its critical value (ε C ), poverty and high uneployent can persist indefinitely. It is noted above that, in the language of dynaics, a stable equilibriu is a situation in which changes in iportant paraeters can alter the long-ter position of a syste but do not fundaentally change the way the syste develops over tie. Hence, if G is low and ε > ε C, then governent policy regarding education and taxes can cause inor changes in the long-ter values of the iddle class ratio () and the eployent rate (x). There is no question that iproveents in the lives of a city s residents, no atter how sall, are valuable, especially since sall changes are frequently the only sort that can realistically be pursued. Yet this dynaic analysis is a bit depressing, because it points to the possibility of ore draatic change in the echaniss that generate persistent poverty and uneployent in cities. As noted earlier the critical value of the failure rate, ξ c = 1 + g 2 [Gθ ρ + F + F θ θ ] < 1, plays an iportant role in the analysis of growth in cities suffering fro the conflict between a technologically arginal underclass and an eployable iddle class, called the odern social conflict by sociologist Ralf Dahrendorf (1988). The critical value of the failure rate (ε C ) depends on The sensitivity of capital flows to profit differentials (G). The sensitivity of iddle class flight to change in the iddle class ratio ( F ). The sensitivity of iddle class flight to changes in the tax rate ( F θ ). 17 An increase in G, F, or F θ lowers the critical value of the failure rate. A saller critical value of the failure rate would be bad news for a dynaically stable city, in that it would foreclose the possibility of using public policy to create a virtuous circle. However, a reduction in any or all of these paraeters would raise the critical value of the failure rate, thereby altering the process of urban growth by converting the equilibriu values of the iddle class ratio and the eployent rate fro a stable node to a saddlepoint. If a city can push ε below ε C, then it can create the conditions for a virtuous circle, whereby higher values of the eployent rate lead to reciprocal increases in the iddle class ratio which, in turn, further boost eployent rates. Analysis of the deterinants of the critical value of the failure rate (ε C ) shows that this sort of cuulative expansion in eployent and iddle class prosperity can only be brought about by either (1) changing iddle class attitudes about taxes ( F θ ) and the poor ( F ) or (2) raising the sensitivity of capital flows to profit rate differentials (G). Unfortunately none of these paraeters is under the control of city authorities. Middle class attitudes, as represented by F and F θ, largely deterine the extent to which a city can turn persistent poverty and uneployent into a virtuous circle of growing eployent and ore widespread prosperity. Given the actual failure rate, growing Cityscape 61

10 Andrews iddle class fear of poor people (increases in F ) or increasing iddle class opposition to taxes (increases in F θ ) will lower the critical value of the failure rate, thereby increasing the gap between ξ and ξ C and aking any attept to change the way a city grows that uch harder. Given iddle class attitudes and the dynaics of capital flows, public policy ay be able to influence the long-ter iddle class ratio and long-ter uneployent in two ways: Increase spending on public safety as a way to ste iddle class flight. Increase education spending (by increasing the teacher/student ratio and other resources in schools) as a way of cobatting the caste-creating aspects of urban schooling. Of course the requireent that city budgets be continuously balanced iplies that any attepts to iprove eployent and reduce poverty will require lower tax rates or reduced public services to finance greater spending for police and teachers. Figure 3 shows the effect of a shift in resources fro schools to police in a dynaically stable city where tax rates are unchanged. A policy that substitutes ore police for teachers ay well increase the presence of the iddle class in the city if the link between the educational failure rate and the teacher/student ratio is weak. 18 In a dynaically stable city, the way the city grows is not greatly affected by increased police spending; instead a rise in police spending at the expense of schools increases the long-ter presence of the iddle class (Figure 3). However, if the teacher/student ratio has a significant effect on the educational failure rate, then a policy of reducing educational resources to boost police spending eschews the possibility of creating a virtuous circle of cuulative expansion in favor of increental efforts at crie control. Political considerations ay force the authorities to favor crie control over education, despite the possibility of altering the dynaics of city growth. A ore likely barrier to a policy aied at radically reducing educational failure and longter poverty is the need to secure inially acceptable degrees of public safety in the face of revenue and balanced-budget constraints. It ay not be possible to reduce educational failure to the point at which a virtuous circle of growth and developent eerges without incurring hideous expenses, including ajor cuts in public safety spending. Worse, increases in tax rates siply increase iddle class flight and reduce capital inflow, leading to a reduction in the long-ter iddle class presence. If increases in taxes are not possible and iniu levels of public safety are required, there ay be little prospect of radical and expensive refor in the education of poor children, leaving a city in the ironic position of opting for ore police even if it is possible to create a virtuous circle. Conclusion This article has explored a seeingly exotic question: Can a city use education policy, in the for of ajor increases in resources devoted to schooling, to change the way it grows? In particular can a city reduce the caste-creating aspect of knowledge capital by reforing education, thereby converting a situation of persistent poverty into a virtuous circle of growth and developent? The results of this discussion are, not surprisingly, rather ixed. On the one hand, educational failure plays a critical role in shaping the way a city grows, at least at the level of econoic theory. High degrees of educational failure lead to persistent, stable poverty and uneployent in a city. On the other hand, a stable urban regie (in the dynaic sense) can be iproved through a variety of eans, including changes in cultural, political, and social conditions that ay reduce educational failure 62 Cityscape

11 Growth and Poverty in Cities without dipping into the public purse. Still, without reducing the educational failure rate below the critical level, a city is not likely to greatly increase the presence of the iddle class through policy initiatives. A second ajor point in this article is the effect of iddle class attitudes on the critical value of the educational failure rate. As noted earlier iddle class aversion to the poor a priary deterinant of the sensitivity of iddle class flight to the presence of iddle class residence () and iddle class aversion to taxation deterine the critical failure rate. If the iddle class can be convinced to stay in the city even in the presence of the poor or despite higher taxes (taxes dedicated to education refor and public safety), then changes in iddle class attitudes can theselves change the way a city grows, converting a dynaically stable urban econoy into a virtuous circle. This result is iportant because it suggests that the future of the city, and particularly its ability to change the way it grows, ay ultiately depend on the willingness of the iddle class to reain in the city despite the difficulties of caste division and crie that are the underside of the role of knowledge capital in econoic life. In turn a national governent policy that encourages the exodus of iddle class citizens fro the city ay ake significant urban refor and reconstruction ipossible. Indeed this article points to a theoretical link between knowledge capital and urban poverty that should shape urban policy. The caste-creating aspect of knowledge capital in odern econoic life is a classic exaple of a negative externality, in the sense that the creation of an uneployable underclass is an unintended consequence of technological change in a society with unequally distributed access to learning. The urban syste adjusts to this negative externality through a class conflict between the iddle class and the underclass which, in this article, resolves itself through iddle class flight fro the city. This adjustent process underines the capacity of the city to iprove its long-ter econoic position, because driving the iddle class out of the city condens any cities to persistent poverty. This finding suggests that the increasing iportance of knowledge capital in econoic growth contributes to the proble of urban poverty. The Federal Governent ust recognize the role of knowledge capital in unwittingly exacerbating the urban crisis. In particular any urban policy that intends to ake cities into virtuous circles ust recognize the folly of forcing local governents to deal with the negative aspects of knowledge capital with diinishing econoic resources. Further, a acroeconoic growth strategy that ephasizes huan capital ust carefully address the inequality, poverty, violence, and crie that result fro educational failure. The central arguent of this article has been that knowledge capital, though a ajor factor in ultiplying the productive capacities of huans, divides a population in profound ways. Those who by virtue of social class, accident, or historical circustance are unable to coplete the school course in a anner deeed satisfactory are not siply without adequate technical and intellectual skills. In the context of a odern econoy, the underclass is largely bereft of the language and routines of technology and science, aking its ebers inept in dealing with the daily rigors of politics, coerce, and culture in this country. In a very real sense, the underclass becoes estranged fro and hostile to yet is largely dependent on a iddle class it envies but cannot join. In turn the envy and anger of the estranged underclass drives the iddle class out of the city, thereby deepening the intellectual isolation of the poor. At that point cities becoe reservations for the poor which the iddle class, through its control of local and State governent, ust anage in order to preserve its own safety and well-being. The prospect that knowledge capital creates a for of intellectual apartheid, where the educated class separates itself fro the undereducated and anages public affairs to Cityscape 63

12 Andrews aintain or deepen its physical distance fro the poor, is deeply disturbing to econoists. However, the ost disturbing aspect of the ipact of knowledge capital on the growth of cities is that it threatens to create a peranent, irrevocable breach between a dependent class of uneployables and a resentful, frightened iddle class. This article has explored the consequences of this conflict for the long-ter dynaics of cities in an open econoy, in the hope that a coherent, tractable odel of this subsyste can serve as the basis for serious attepts to refor urban systes. The picture I have painted is stark and no doubt overdrawn, largely because it is being presented in the for of a dynaic syste. Still, even if it were softened a bit, the fundaental challenge that knowledge capital poses to the possibilities of social peace in liberal deocratic cities would reain. 64 Cityscape

13 Growth and Poverty in Cities Author Marcellus Andrews is an associate professor of econoics at Wellesley College, with research interests in acroeconoics, growth theory, poverty, and racial conflict in arket systes. Notes 1. Econoists frequently use the ters huan capital or knowledge capital to designate technical knowledge and skills. 2. As reported in a suary of research on educational achieveent in Jaynes and Willias, 1989, p Currie (1993), in particular, suarizes four decades worth of work by sociologists and psychologists which clearly shows that persistent intergenerational poverty leads to a disidentification with ainstrea social nors by the young poor, fueling the creation of an alternative subculture that establishes status nors different fro and frequently overtly hostile to conventional roles, rules, and behavior. 4. This assuption akes no difference to the results as long as the level of consuption in prison is far lower than that which ight be available outside prison walls. However, it does reduce the aount of tedious algebra that ust be gotten through. 5. Maxiizing (3), subject to (2), yields (4) φ = where (1 - κ) wε - aω. ε[a + (1 - κ) w], φ - aw (ε + Ω). = κ (ε[a + (1 - κ) w]) 2 < 0, φ w a[ε - (1 - κ)ω] = =? (ε[a + (1 - κ) w]) 2 A rise in the level of iddle class incoe (w) will raise φ only if ε - (1 - κ) Ω > The lifetie earnings associated with living in the city is calculated as (8) V C = or (9) V C = T ( w [ x(1 - θ) - εφ 1 - ]) O w α [ ] e -α t dt, (1 - θ) x - εφ 1 - (1 - e -α T ) on the assuption of shortsightedness over real wages (w), eployent rates (x), and the fraction of the population in the iddle class (). Cityscape 65

14 Andrews 7. Because suburban and city wages are identical and suburbs are assued to be free of crie, the present discounted value of incoe associated with suburban living is calculated as (10) V S = where (θ S < θ) is the suburban tax rate. T O w(1 - θ s ) e -α t dt = (1 - θ s ) w α (1 - e -ατ ) 8. This iplies that the fraction of new workers who have a particular distaste for city life those who ay require, for exaple, incoe in the city to exceed incoe in the suburbs by 50 percent in order to see the city as an attractive place to live is about the sae fro year to year. 9. Since and V C = [ ] w α (1 - θ ) x - ε φ 1 - (1 - e -α T* ), V S = (1 - θ s ) w α (1 - e -α T* ), then Γ = - V C / < 0, Γ θ = - V C / θ > 0, Γ x = - V/ x < Kaus (1992) has provided a popular account of the role of credentials in deterining econoic success. Kaus analysis, though quite caustic in its attack on traditional liberal approaches to inequality, notes that the increasing role of technical skills and credentials in odern labor arkets eans that eritocracy is increasingly consistent with a ore or less peranent class syste driven by educational inequality. Marshall and Tucker (1992) provide detailed epirical evidence of the role of skills deficiencies in accounting for the persistent low incoes and poor living conditions of poor and inority (ainly black and Latino) workers. 11. Marshall and Tucker (1992, pp ) note that the United States has few progras for recovering and retraining high school dropouts. The general equivalency diploa (GED) progra certifies that the holder of the certificate is trained to a seventh-grade level of literacy and nuerical ability. Given the increasing levels of technical and nuerical skills required in a growing nuber of occupations and positions, the GED is an increasingly inadequate preparation for secure, high-wage eployent. See Marshall and Tucker, (1992), pp See Kareit (1986). This work shows that the educational achieveent of parents, the level of educational success in the larger counity, the class coposition of the larger counity, and other positive externalities associated with the intellectual and econoic characteristics of a child s environent play a pivotal role in that child s long-ter developent. This finding suggests that an iportant deterinant of educational success is the presence of a iddle class population in urban schools. However, ost studies also show that educational attainent is an exceedingly coplex process involving any extra-econoic factors that have no particular relationship to identifiable econoic factors. 13. Econoic exaples abound: Interest generates a process of positive feedback in wealth accuulation; when real interest rates are positive, the purchasing power of wealth over tie grows as long as a saver refrains fro spending interest incoe. 66 Cityscape

15 Growth and Poverty in Cities Siilarly, a negative real interest rate generates negative feedback. For exaple, the purchasing power of wealth steadily declines with the passage of tie, leaving the patient but isguided saver with ever-saller consuption capabilities. 14. The appendix presents a coplete local stability analysis as well as a brief discussion of the role of ξ as a bifurcating paraeter. 15. The negative feedback property of the iddle class ratio is the result of the assuption that iddle class flight (F(x, )) is inelastic with respect to a rise in. This appendix explores this point in ore detail. 16. The appendix provides a coplete discussion of the role of the failure rate in the analysis of local stability. 17. All of these relationships are discussed in ters of absolute values to facilitate exposition. Hence, when I speak of F rising, I ean that the relationship between the iddle class exit rate and the iddle class ratio is stronger, even though F < The governent budget constraint iplies that dγ + gdτ = 0. This relationship eans that and. d dγ. d x dγ = - (1 - ) F γ - ξ τ = - x [ ] [ ], F γ + (1 - ) ξ τ, where ξ/ τ 0 is the relationship between the educational failure rate and the teacher/student ratio. If F γ > ξ/ τ, then the teacher/student ratio has a sall influence on educational failure, which would shift lines and xx leftward because of a shift in public-sector resources fro schools to police. Cityscape 67

16 Andrews Figure 1 x x x Figure 2 x x x 68 Cityscape

17 Growth and Poverty in Cities Figure 3 x' x ' ' x' x x Cityscape 69

18 Andrews Bibliography Andrews, Marcellus Schools, Jails, and the Dynaics of an Educational Underclass: Soe Dreadful Social Arithetic, Journal of Econoic Behavior and Organization, (October) Capital, Poverty, and Growth in the City: A Model of the Urban Nightare, unpublished anuscript Meritocracy, Poverty, and Growth in a Market Econoy: Knowledge Capital and Caste Hierarchy in a Growth Model, unpublished anuscript. Beltrai, Edward Matheatical Methods for Dynaic Modeling. New York: Acadeic Press. Currie, Elliot Reckoning: Drugs, the Cities, and the Aerican Future. New York: Hill and Wang. Dahrendorf, Ralf The Modern Social Conflict: An Essay on the Politics of Liberty. Berkeley: University of California Press. Jaynes, Gerald, and Willias, Robin, eds A Coon Destiny: Blacks and Aerican Society. Washington, D.C.: National Research Council, National Acadeic Press. Jones, Jacqueline The Dispossessed: Aerica s Underclasses Fro the Civil War to the Present. New York: Basic Books. Kareit, Nancy Eleentary Education and Black Aericans: Raising the Odds. Paper prepared for the Coittee on the Status of Black Aericans. Washington, D.C.: National Research Council. Kaus, Mickey The End of Equality. New York: A New Republic Book, Basic Books. Lucas, Robert On the Mechanics of Econoic Developent, Journal of Monetary Econoics, (22), pp Marshall, Ray, and Tucker, Marc Thinking for a Living: Education and the Wealth of Nations. New York: Basic Books. Massey, Douglas, and Denton, Nancy Aerican Apartheid: Segregation and the Making of the Underclass. Cabridge, Massachusetts: Harvard University Press. Miyao, Takahiro Urban Growth and Uneployent, reprinted in Dynaic Analysis of the Urban Econoy, pp New York: Acadeic Press Dynaics of Rural-Urban Migration, reprinted in Dynaic Analysis of the Urban Econoy, pp New York: Acadeic Press. Ogbu, John The Consequences of the Aerican Caste Syste, in School Achieveent in Minority Children: New Perspectives, edited by Ulric Neisser, pp Hillsdale, New Jersey: Erlbau. Roer, Paul Increasing Returns and Long Run Growth, Journal of Political Econoy, (94), pp Cityscape

19 Growth and Poverty in Cities Schelling, Thoas Sorting and Mixing: Race and Sex, reprinted in Microotives and Macrobehavior, pp New York: Norton. Taylor, Lance Incoe Distribution, Inflation, and Growth: Lectures in Structuralist Macroeconoics. Cabridge, Massachusetts: MIT Press. Widean, John Edgar Philadelphia Fire. New York: Henry Holt. Wilson, Willia J The Truly Disadvantaged: The Inner City, the Underclass, and Public Policy. Chicago: University of Chicago Press. Cityscape 71

20 Andrews Appendix: Local Stability The governent budget constraint is θ Κ σ = Ω (1 - ) T + ω (τg + π) T, or θβ x = Ω (1 - ) + ω (τg + π) on a per capita basis. It is a siple atter to show that θ ω > 0, θ γ > 0, θ τ > 0, θ Ω > 0, that is, a rise in the real wages of public eployees (ω), per capita police spending (η), the teacher/student ratio (τ), or poor relief (Ω) increases the tax rate. A rise in the eployent rate or in the iddle class rate reduces the tax rate, that is, θ x < 0 and θ < 0, given the requireent of a continually balanced budget. The Jacobian associated with the syste coprised of (14) and (15a), given the governent budget constraint (18), is expressed as J = {. }. x.. x x x where.... [ ] = - (1 - ) F F F + F θ θ F + 1, x [ ] = - (1 - ) Fx + F θ θ x > 0, [ ] x = - x Gθρ + F + F θ + (1 - ζ) g, θ µ 2 x x [ ] = - x Gθ x ρ - F x - F θ θ x. Note that if (C1) F F + F θ θ F + 1> 0, and 2 [ ] (C2) ξ > ξ c = 1 + g Gθ ρ + F + F θ θ, 72 Cityscape

21 Growth and Poverty in Cities then.. x < 0, < 0. Condition (C1) iplies that iddle class ratio is a negative feedback process if the rate of iddle class flight is not inelastic with respect to changes in the iddle class ratio. Further, condition (C2) both defines the critical value of the failure rate and shows the condition under which the eployent rate and the iddle class ratio are negatively coupled. Finally, if Fx + F θ θ x (C3) 0 < G < ρθ x, that is, if G is sall in the sense of a relatively low sensitivity of capital flows to profit rate differentials, then. x x < 0. In that case, trace J < 0 and det J > 0, so the equilibriu point is a stable node. If ξ < ξ C and G violates (C3), then det J < 0, which eans that the equilibriu point is a saddlepoint. Further, if ξ < ξ C and G is consistent with (C3), then the equilibriu point ay still be a saddlepoint if det J < 0. The foregoing analysis suggests that a virtuous circle is a possibility if failure rates can be pushed below the critical value ξ C and if the sensitivity of capital flows to profit rate differentials is sufficiently large. Cityscape 73