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Could Gentrification Stop the Poor from Benefiting from Urban

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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 gentrifica- tion. 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 (^vo0 ) 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 (us- ing o ! o0 to denote those that move): τ τ max vo io o P τ τ 0 τ o0 πo!o0 v^o0 EF τ (io0 jo ! 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 v^ 0 (π 0 ) πo!o0 EF τ (o0 jo ! 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 jo) = Wt 8o. 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 ^o0 > 2 2) Average welfare:1 v^o, 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 2 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 ^τ , where · denotes \change" in o b τ τ τ the notation of Dekle, Eaton and Kortum Wdo jρ = 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(ojo ! o) = −1 θτ E(ojo) =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 ^o 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 com- muting 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 hu- man 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 that! ^w =! ^w . of income that type-τ households spend on II. Gentrification definitions housing. mτ represents the strength of en- dogenous 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 π^l residents increases: L > 1 but welfare π^l 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 ^l < 1. This gen- who live there: trification is compensated if the incumbents ^ 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 W^ L < 1.
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