Could Gentrification Stop the Poor from Benefiting from Urban

Could Gentriﬁcation Stop the Poor from Beneﬁting from Urban Improvements?

By Clare Balboni, Gharad Bryan, Melanie Morten and Bilal Siddiqi∗

When policymakers invest in urban in- I. Model frastructure – such as new train lines, parks, and schools – they provide a “place-based” The model is a standard urban commut- policy because the infrastructure is pro- ing model, based on Ahlfeldt et al. (2015). vided to a specific neighborhood and not to We augment the model to allow for several particular people. This raises an important channels through which different types of challenge: if people are mobile within cities, people (“rich” and “poor”) may differ. We an improvement in one neighborhood may then study how each of the following dif- lead to an inflow of richer people who push ferences between types affects the welfare up local prices such as rent and displace consequences of building a piece of urban the poor. This process of infrastructure in- infrastructure. duced gentrification (IIG) has led to much debate about the proper design and impact • Share of income spent on housing: if of urban investment (see, e.g., the discus- the poor spend more of their income sion in Kennedy and Leonard (2001)). on housing, they will be more exposed to endogenous rent changes. This paper investigates mechanisms that • Endogenous type-specific amenities: may lead to IIG using a general equilib- high rents may lead to an increase in rium urban commuting model. Our goal high-type amenities (such as fancy cof- is to elucidate the channels through which fee shops), which are valued less by IIG occurs and to understand how policy lower-income residents. choices mitigate or accentuate gentrification. We show that a standard urban model • Spatial comparative advantage: if it can lead to a full range of gentrification out- is less important for the poor to work comes and illustrate, through model simu- in specific locations to maximize earn- lation, which elasticities are important for ings, they will move more in response generating specific effects. We also show to infrastructure, but this does not nec- that it is important to account for gen- essarily indicate that poor incumbents eral equilibrium forces when understanding gain more than rich incumbents. the distributional impacts of urban change. Simple empirical heuristics, such as relative • City design: how heterogeneous are changes in rent or population, do not nec- neighborhoods? If IIG displaces the essarily sign the relative welfare impact be- poor, welfare impacts will depend on tween groups. Our companion paper Bal- whether they can find accommodation boni et al. (2020), lays out the theoreti- they value in other parts of the city. cal model in detail and then applies the • Housing market integration and re- method using panel data we collected in turns to scale in building high-quality Dar es Salaam, Tanzania, as the city rolled housing: if the rich consume a differ- out a Bus Rapid Transit (BRT) system. ent type of housing and the cost of building housing suitable for the rich decreases as the ratio of rich to poor in a neighborhood increases, then this ∗ Balboni: MIT. Bryan: LSE. Morten: Stanford and NBER. Siddiqi: UC Berkeley. We thank Adrien Bilal will strengthen the displacement pres- for his constructive discussion of our paper. sure. 1 2 PAPERS AND PROCEEDINGS MONTH YEAR

• Policy design: does a policy target rich the average change of welfare for people or poor residents? For example, build- (“incumbents”) who started in each loca- ing public parking lots is only valuable tion. To compute incumbent welfare we to residents who own cars, which may need to account for the fact that incum- be those who are richer. bents are both endogenously selected as well as account for the selection of which • Persistence of individual heterogene- incumbents then respond to the change in ity: incumbents chose to initially live the economic environment: in a location based on the realization of their idiosyncratic productivity shock. 1) Change in average welfare: If productivity is not persistent, in- 1 cumbency eﬀects are less relevant com- ! θτ pared with average eﬀects. τ X τ τ θτ Wc = πo0 (ˆvo0 ) 0 A. Welfare changes o

Let the indirect utility of a location o be 2) Change in incumbency welfare un- given by vτ . Individual i, who is of type der perfect persistence of shocks is a o 0 τ, chooses the location that maximizes her weighted sum of the destinations o indirect utility: that people in o choose to move to (using o → o0 to denote those that move): τ τ max vo io o P τ τ 0 τ o0 πo→o0 vô0 EF τ (io0 |o → o ) Wco = where τ is i’s idiosyncratic productivity W τ io 1 τ P τ τ θ 0 shock for location o. If is Frechet dis- 0 vˆ 0 (π 0 ) πo→o0 EF τ (o0 |o → o ) io = o o o τ τ τ tributed with shape parameter θ , then κ πo well-known results imply: which uses the property that expected 1) Commuting gravity: utility is equal across locations i.e., τ τ τ Vo E(o |o) = Wt ∀o. We show in the (vτ )θτ πτ = o paper that (a) the migration probabil- o P τ θτ o0 (vo0 ) ity depends on the relative utility gain of a location, with πo→o0 > 0 iffv ô0 > 2 2) Average welfare:1 vô, and (b) this formula can be ex- pressed in a closed form “exact hat” 1 ! θτ representation. τ τ X τ θτ W = κ (v 0 ) o 3) Change in incumbency welfare under o0 imperfect persistence of shocks is a Consider a policy shock that leads to a weighted sum of the unconditional and change in the indirect utility of a location, conditional formula. That is, if ρ ∈ and possibly, via general equilibrium ef- [0, 1] proportion of the population re- fects, the indirect utilities of all other lo- draw their idiosyncratic shock each pe- cations. Let the change in indirect utility riod, the incumbency gain is given by: be given byv ˆτ , where · denotes “change” in o b τ τ τ the notation of Dekle, Eaton and Kortum Wdo |ρ = ρWc + (1 − ρ)Wco (2008). 2This formula collapses to the standard case for the In our companion paper Balboni et al. location that has the largest gain in indirect utility. In (2020), we derive the following expressions that case, no one who initially migrated to the location for the average change across the city and choses to leave it, so πoo = πo, and so E(o|o → o) = −1 θτ E(o|o) =γπ ¯ o . In this case, the formula collapses to 1 τ τ τ κ is a type specific constant related to the Γ func- Wco =v ô i.e., the incumbents get an increase in utility tion. equivalent to the increase in indirect utility. VOL. VOL NO. ISSUE URBAN IMPROVEMENTS AND GENTRIFICATION 3

B. Indirect utility for a commuting model D. Output per unit of human capital

We assume a location specific production function To convert this model into an urban commuting model, we redefine the index o as a !α ¯ X τ τ 1−α live-work pair. We define the indirect util- Yw = Aw AwZw Tw , ity of living in location l and working in τ location w as: τ where Zw is the total amount of type τ human capital working in location w, A¯ is τ τ τ w τ τ τ τ −(β +m ) −η τ vlw = Bl ww (rl ) dlw an exogenous location w productivity, Aw τ is an exogenous location w productivity for where Bl is the (type-specific) amenity τ those of type τ and Tw is the amount of level in the live location l, ww is the (type- 4 specific) wage rate in the work location w, land available for firms in location w. This rτ is the (type-specific) rental cost in l, and production function treats L and H types as l perfect substitutes and so it will be the case dlw is the commuting cost between l and L H w. The parameter βτ represents the share thatω ˆw =ω ˆw . of income that type-τ households spend on II. Gentrification definitions housing. mτ represents the strength of endogenous amenity spillovers: we allow for We consider three related concepts: an endogenous amenity that is a function ¯ τ −mτ 1) Neighborhood composition: does the of average rents Bl = (rl ) ; we repre- sent this term by substituting it into in- ratio of low to high residents change? τ direct utility, yielding the exponent m on 2) Welfare of incumbents: do rich incum- 3 τ rent; finally, η converts minutes of com- bents gain more than poor ones? mute time to a utility cost. 3) Average welfare: across the city, do the rich gain more than the poor? C. Housing market We say that a neighborhood experiences weak gentrification if the proportion of rich H πˆl residents increases: L > 1 but welfare πˆl τ We assume that housing expenditure, Rl , gains for poor incumbents are less than for is a constant fraction of earnings. The to- rich incumbents. The neighborhood experi- tal expenditure on housing in location l de- ences strong gentrification if the number of L pends on the commuting patterns of people poor residents decreasesπ ˆl < 1. This gen- who live there: trification is compensated if the incumbents ˆ L have a net welfare gains Wo > 1 and is un- X compensated if the poor incumbents have a Rτ = βτ π earnτ . l lw lw net welfare loss Wˆ L < 1. w o We combine this with an arbitrage con- III. Model simulations dition that allows for imperfect integration (modeled by the parameter λ) between The goal of this section is to simulate the housing market and determines relative the model for different parameter values to rents: show that the model can produce a full rH πH λ range of welfare outcomes. We simulate a l = l L L simple three-location (slum, suburb, down- rl πl town) where the three locations are con- nected to enable commuting (see schematic 3This specification is closely related to the specification of endogenous amenities in Diamond (2016); Cou- θτ −1 4 τ 1 t P θτ ture et al. (2018). Zw = Γ(1 − θ )E l πlw 4 PAPERS AND PROCEEDINGS MONTH YEAR below). In this environment, we consider The welfare increase for incumbents is pos- the effect of a slum beautification project itive – 1.9% for low incumbents and 3.4% that increases the amenity in the slum. for high ones – with the high types receiving Slum ↑ amenity a larger gain because they spend a smaller proportion of their income on housing and Low amenity Low productivity so are less exposed to rent increases. Fi- nally, the policy has a small but positive welfare effect across the city. On average, low types receive a welfare gain of 0.2% and Suburb the high types a gain of 0.1%; the gain is High amenity larger for low types as they face compen- Low productivity sating general equilibrium effects through lower rents in other parts of the city.

B. Alternative simulations Downtown Low amenity We now consider a range of other al- High productivity ternatives to illustrate several mechanisms present in the model. We display the key A. Baseline economy outcome variables in Table 1. Starting with the role of preference pa- Our baseline specification considers the rameters, we first consider a case where rich effect of a policy that improves the amenity and poor spend the same share of their in- of the slum by 5% equally for both L and H come on housing. In this case, both groups types. The baseline economic environment experience the same proportional increase is: in welfare – a 3.1% gain for the incum- • Amenities: {Downtown, slum, suburb} bents and a 0.1% gain across the city as = {1,0.5,2} a whole. Next, we consider endogenous amenities that favor the rich. The impact • Productivities: {Downtown, slum, of this is to accentuate the cost of higher suburb} = {2,1,1} rents for low-income households. The wel- • Housing expenditure share: fare gain for poor incumbents falls from βL = 0.4, βH = 0.2 1.9% to 1.2%. We then consider the role of asymmetric comparative advantage by • Endogenous amenity favoring the rich: decreasing the parameter θH and increas- mL = 0.4; mH = 0 ing the parameter θL. Changing these parameters has two effects: first, it (approxi- • Integrated housing market: λ = 0 mately) increases the relative dispersion of • Equal scope for comparative advan- the productivity shocks for high types, in- tage: θL = θH creasing the importance of the match between the individual and the place for high Figure 1 plots the impact on population types. This could approximate that high- sorting and welfare after the slum improve- income workers may be more likely to have ment. The baseline economy displays weak specific skills, whereas low-income workers gentrification: as the slum becomes more are more homogenous. The second impact attractive, both low and high move in, but is that because of the greater specificity of poor incumbents see a smaller increase in skill, the migration elasticity of low-income welfare. The population of low types in- workers is higher than that of high-income creases by 6.8%, and high types by 14%. In workers. As a result, low types now move in the baseline case the rental markets are in- to benefit from the higher amenities propor- tegrated, so the increase in housing demand tionally more than high types (2.2 percent- leads to a 7.4% rise in rents for both types. age points more, compared with 7.2 per- VOL. VOL NO. ISSUE URBAN IMPROVEMENTS AND GENTRIFICATION 5

(a) Population (b) Incumbent welfare

Figure 1. : 5% improvement in slum amenity: baseline

centage points less in the baseline). Still, than that faced by low-type households the overall gain in population is smaller. (4.6% vs. 7.3%), leading to a larger gap The lower influx of people leads to a smaller in the welfare gain of high incumbents increase in rents and larger welfare gains for compared to low incumbents. low incumbents relative to baseline(2.1% vs 1.9%). Despite low types appearing to The next row considers the effects of an value the policy more than high types (they amenity improvement targeted towards the move in more), the incumbency gain is still rich. An example could be the impact of lower for low incumbents than high ones building parking garages in a setting where (2.1% compared with 3.5%). only higher-income people have cars. We model this as an improvement in the slum Next, we consider the effect of the under- amenity of 5% for the rich while leaving lying structure of the city. In our baseline the slum amenity unchanged for low types. economy, the suburb has a high amenity This policy leads to strong uncompensated value, and the initial population allocation gentrification: low-income people move out has many fewer people (both low and high) of the slum in absolute terms, and the living in the slum. If the neighborhoods are welfare of the initial low types who were more homogenous ex-ante, more of the pop- living in the slum falls by 1.5%. Across ulation is initially living in the slum. As a the city, the welfare of low types falls by result, the inflow into the slum is smaller, 0.2%, mostly reflecting the losses of poor in- and hence house prices do not rise as much. cumbents. In comparison, incumbent high This proportionally affects the low incum- types receive a gain of 4.1% (the average bents who receive a gain of 2.6% compared welfare of high types is unchanged across to 1.9% in the baseline simulation. Because the city). more people initially live in the slum, the overall benefits of the improvement are also Finally, we show the importance of the larger. On average, low-types across the persistence of the idiosyncratic shock in de- city receive a 1.6% welfare gain (compared termining the incumbency effect. If all resi- to 0.2% in the baseline). dents redraw their shock every period, then We then consider the effect of the initial location does not reveal any in- imperfectly-integrated housing mar- formation about the individual match of kets by setting λ = −0.3. This represents that location the following period. As a decreasing costs of converting land to result, an incumbent has the same average high-type housing. As a result, the rental characteristics as the average resident in the increase for high-type households is smaller city, and so the incumbency welfare gains 6 PAPERS AND PROCEEDINGS MONTH YEAR are equivalent to the average welfare gain.5 Daniel Sturm, and Nikolaus Wolf. These simulations also illustrate another 2015. “The Economics of Density: Evi- important reason to use a spatial general dence from the Berlin Wall.” Economet- equilibrium model when analyzing urban rica, 83(6): 2127–2189. investments’ impact. Simple heuristics, such as examining the relative gain in rent Balboni, Clare, Gharad Bryan, or the relative inflow of people, are not Melanie Morten, and Bilal Siddiqi. enough to sign the relative incumbency ef- 2020. “Transportation, Gentrification, fects. This is clearly seen in the counterfac- and Urban Mobility: The Inequality Ef- tual that increases the scope for compara- fects of Place-Based Policies.” Working tive advantage between low and high types. Paper. There was a larger relative inflow of low Couture, Victor, Cecile Gaubert, types than high types in that simulation, Jessie Handbury, and Erik Hurst. yet low incumbents fared worse than high 2018. “Income Growth and the Distribu- ones. In most of the other simulations, the tional Effects of Urban Spatial Sorting.” welfare gain of high incumbents was larger than the welfare gain of low incumbents, de- Dekle, Robert, Jonathan Eaton, and spite the two groups often facing the same Samuel Kortum. 2008. “Global Rebal- increase in rental rates. ancing with Gravity: Measuring the Bur- den of Adjustment.” IMF Staff Papers, IV. Conclusion 55(3): 511–540.

Across the world, especially in low- Diamond, Rebecca. 2016. “The Deter- income countries, urbanization rates are minants and Welfare Implications of US increasing. As urban density increases, Workers’ Diverging Location Choices by policy-makers invest in public infrastruc- Skill: 1980-2000.” American Economic ture such as schools, parks, and transporta- Review, 106(3): 479–524. tion routes to improve the environment. Kennedy, Maureen, and Paul However, by nature, these investments are Leonard. 2001. “Dealing With place-based: if people are mobile within Neighborhood Change: A Primer a city, improvements in one neighborhood on Gentrification and Policy Choices.” may lead to higher rental rates, pushing out Brookings Institution Center on Urban the poor and leading to gentrification. Our and Metropolitan Policy. goal in this paper was to illustrate economic channels that may lead to infrastructure in- duced gentrification through the lens of a general equilibrium spatial model. While simple, the model is rich enough to lead to a full range of equilibrium outcomes ranging from pro-poor to pro-rich outcomes. Our companion paper, Balboni et al. (2020) considers the impact of one such intervention, the introduction of the Bus Rapid Transit system in Dar es Salaam, and illustrates how to employ the theoretical model in an empirical setting.

REFERENCES

Ahlfeldt, Gabriel, Stephen Redding,

5Note that this is true in the current model because there are no costs of migrating. VOL. VOL NO. ISSUE URBAN IMPROVEMENTS AND GENTRIFICATION 7

Table 1—: Impact of slum improvement

Population Rent Incumbent welfare Avg welfare (1) (2) (3) (4) (5) (6) (7) (8) Low High Low High Low High Low High Baseline 1.068 1.140 1.074 1.074 1.019 1.034 1.002 1.001 Preference parameters Equalize housing share 1.126 1.126 1.092 1.092 1.031 1.031 1.001 1.001 Strong endog. amenities 1.009 1.190 1.022 1.022 1.012 1.045 1.009 1.000 Rich stronger comparative adv. 1.126 1.104 1.069 1.069 1.021 1.035 1.001 1.001 City design Equal baseline amenities in slum/suburb 1.042 1.090 1.057 1.057 1.026 1.038 1.016 1.016 Housing market Nonintegrated housing 1.071 1.165 1.073 1.046 1.020 1.040 1.003 1.001 Policy design Pro-rich slum improvement 0.945 1.174 1.037 1.037 0.985 1.041 0.998 1.000 Persistence Redraw idio. shock 1.068 1.140 1.074 1.074 1.002 1.001 1.002 1.001

Notes: Table shows proportional change for slum neighborhood. A value greater than 1 indicates a net gain. All simulations except for the last row assume that idiosyncratic shocks are fully persistent.