class: center, middle, inverse, title-slide .title[ # Neighborhood Choice ] .subtitle[ ## Set 06 ] .author[ ### Andrew Dickinson ] .date[ ### Fall 2022 ] --- class: inverse, center, middle .white[_"Love thy neighbor as yourself, but choose your neighborhood."_] .white[-Louise Beal] --- # Housekeeping .hi[Assignments:] - .hi[PS01] was due last night - Go over solutions .hi[today] - .hi[PS02] will be posted tomorrow - due date .hi-red[Sun Oct 30.] - go over solutions + review on .hi-blue[Mon Oct 31] - .hi[Reading] - finish up to chapter 5 before the midterm -- <br> .hi[Midterm:] .hi-red[Wed, Nov 2] --- # Introduction to neighborhood choice We have a fairly simple model of .hi[residential choice] (rental prices) -- .hi[Q:] What factor(s) in the model determine housing demand? -- .hi[A:] Bid-Rent model assumes commuting costs are the .hii[only factor] - this .hi[unreasonable] assumption isolates particular economic factors -- _What factors influence neighborhood decision choices?_ -- .hi-blue[Examples:] -- .pull-left[ - Schools - Demographics - Tax rates] .pull-right[ - Public safety - Air quality - Natural beauty] --- # Neighborhood choice: Amenities .hi[Definition:] .hii[Amenity] An _amenity_ is a .hi[location-specific] consumption good -- .pull-left[ - Beaches - Weather - Public transport] .pull-right[ - Parks - Restaurants - Recreation] -- Different types of .hii[amenities] - Some are nonrival^.hii[†]: Theaters, public transport - Some are nonexcludable^.hii[††]: Parks - Some are both nonrival and nonexcludable: National defense, sports teams, fireworks .footnote[.hii[†] Nonrival goods: Accessible by all; usage does limit subsequent use <br> .hii[††] Nonexcludable goods: Impossible to exclude other from consuming] --- # Neighborhood choice: Amenities .hi[Two more refined definitions:] .hi[(i) Exogenous Amenities:] Location-specific consumption good that exist .hi-red[are not] influenced by where people decide to live -- - .hi[Exogenous:] "Determined outside of the model" (fall from the sky) - Weather, geographic characteristics -- .hi[(ii)] .hii[Endogenous Amenities:] Location-specific consumption goods that .hi-blue[are] influenced by location decisions of individuals -- - .hii[Endogenous:] "Determined within the model" - School quality, crime, pollution --- # Neighborhood choice: Amenities To determine whether or not an amenity is .hi[exogenous] (.hii[endogenous]): -- .center[_"Will choosing to live here impact the amenity?"_] <br> -- - .hi[Exogenous] _Beaches exist regardless whether people live near by_ -- - .hii[Endogenous] _Crime is a function of the individuals in the area_ -- <br> Questions regarding differences between .hi[EXOGENOUS] and .hii[ENDOGENOUS?] --- # Neighborhood choice Previously we explored (broadly) a cities shape - modeled where different sectors of the economy choose to locate But we made an assumption that everyone was the .hi[same] -- <br> _Why are city neighborhoods so .hi[heterogeneous]?_ -- _What economics factor influence .hi[neighborhood sorting] within a city?_ <br> -- Model this .hi[heterogeneity] by considering a public good: .hii[Public parks] --- class: inverse, middle # Neighborhood choice + Sorting for public goods --- # Demand for public goods .hi[Consider a simple sorting model for a single, non-rival public good] -- Model a three-person city with one public good: .hi-blue[Public park] - Cost .hi[$60 per acre] to build - Cost is shared equally across all three citizens: .hi-blue[$20 per acre] each -- Of the three citizen, demand for the park varies: -- - Low demand: `\(\text{Lyla}: \color{#4c566a} {P = 30 - 2*\text{acres}}\)` - Mid demand: `\(\text{Gracie}: \color{#b48ead}{P = 40 -2*\text{acres}}\)` - High demand: `\(\text{Cooper}: \color{#bf616a} {P = 50 -2*\text{acres}}\)` -- Together they must .hi[vote] for one park size in a binary election --- # Demand for public goods <img src="06-nbhd-choice_files/figure-html/inc_plot-1.svg" style="display: block; margin: auto;" /> -- For each citizen, optimal park size is found when `\(MB_{park} = MC_{park}\)` --- count: false # Demand for public goods <img src="06-nbhd-choice_files/figure-html/demand3-1.svg" style="display: block; margin: auto;" /> If a first past the post election system is used, who wins their preferred park size? Who loses? --- # Demand for public goods: Majority rule Under .hi[majority rule] Gracie's optimal park wins -- .center[.hii[Why?]] <table class="table" style="font-size: 28px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> Election </th> <th style="text-align:left;"> 10 acre votes </th> <th style="text-align:left;"> Other votes </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 5 acres vs 10 acres </td> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Gracie and Cooper </td> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Lyla </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 15 acres vs 10 acres </td> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Gracie and Lyla </td> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Cooper </td> </tr> </tbody> </table> -- Gracie is the .hii[median voter] - Splits the voting public in half --- # Alternative to majority rule Majority rule always leave two citizens unhappy: .hi-red[Cooper] and .hi[Lyla] -- Suppose an _alternative_ is to form new municipalities <br> -- Consider a new metropolitan area with .hii[3] municipalities with 3 citizen - Each district votes on their own park - Each citizen knowns each other's preferences -- .hii[Key assumption:] Citizens pick which municipality to live in -- Implication: Similar types sort into the same neighborhood -- .pull-left[ - Lylaville: 5 acre park - Gracity: 10 acre park] .pull-right[ - Cooperstown: 15 acre park] --- # Alternative to majority rule By .hi[voting with their feet] each citizen sorts themselves into homogenous communities with their preferred public good allocation (park size) .hi[Now our city has three neighborhoods with homogenous types] - Accomodates diversity in demand -- .center[.hi[Is reality this simple?]] -- .center[.hii[Nope]] -- .hi[Let's add another layer of complexity:] .hii[Taxes] --- # Alternative: Property tax Up to this point, funding for the park is financed with a .hi[head tax] -- More realistic to model neighborhood sorting using .hi[property taxes] -- - Allow for variation in preferences + property values: - The higher your property value, the more taxes you pay for the park - `\(\tau = PV * 10\)` - .hi[3] different property values: 2, 10, 24 - .hi[9] combos: Low-Low, Low-Mid, Low-High, Mid-Low...High-High -- <table class="table" style="font-size: 18px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> Outcome </th> <th style="text-align:center;"> Tax rate per dollar in PV </th> <th style="text-align:center;"> Small PV </th> <th style="text-align:center;"> Mid PV </th> <th style="text-align:center;"> Big PV </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Mixed municipality </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $10 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $20 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $100 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $240 </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Exclusive small PV </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $60 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $120 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Exclusive mid PV </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $12 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $120 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Exclusive big PV </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $5 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $120 </td> </tr> </tbody> </table> --- # Alternative: Property tax <table class="table" style="font-size: 24px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> Outcome </th> <th style="text-align:center;"> Tax rate per dollar in PV </th> <th style="text-align:center;"> Small PV </th> <th style="text-align:center;"> Mid PV </th> <th style="text-align:center;"> Big PV </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Mixed municipality </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $10 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $20 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $100 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $240 </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Exclusive small PV </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $60 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $120 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Exclusive mid PV </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $12 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $120 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> </tr> <tr> <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> Exclusive big PV </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $5 </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> - </td> <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> $120 </td> </tr> </tbody> </table> Citizen of PV similar type have incentive to sort together to reduce tax -- In equilibrium citizen will form .hii[9 different neighborhoods] .hi[Generates a fragmented system of local government in a metro area] - Negative implications arise from this sorting --- # Neighborhood sorting: Income .center[  ] --- # Neighborhood sorting: Education .center[  ] --- # Neighborhood sorting: Atlas .center[  ] Source: [Oppurtunity Atlas](https://www.opportunityatlas.org/) --- class: inverse, middle # Neighborhood sorting: Externalities --- # Neighborhood sorting: Externalities Do you .hi[_fully_ internalize] the costs and benefits of where you decide to live? - _Is your choice of neighborhood free from externalities?_ -- .center[.hii[Nope.]] -- .hi[Examples?] -- .pull-left[ - Social networks - Jobs - Good schools - Culture] -- .pull-right[ - Noise - Drug use - Litter - Pollution ] -- Neighborhood externalities tend to be massively important for .hi[youth] .pull-left[ - Peer effects] .pull-right[ - Role models] --- # Neighborhood sorting: Externalities .hi[When your neighbor...] .pull-left[ - remodels their kitchen... - gives the scoop on a new job... - tells you how to apply for a fraudulent PPP loan... ] .pull-right[ - does a bunch of drugs... - makes a ton of noise... - is a bad role model to your children... ] -- .pull-left[ ... .hi-red[_do you pay them?_] ] .pull-right[ ... .hi[_do they pay you?_] ] -- .hi[Positive externalities] general increase with income and education level - more desirable; higher demand .center[_What does this .hi[imply?]_] --- class: inverse, middle # Becker-Murphy model --- # Becker-Murphy model In real life households compete for places in .hi[desirable] neighborhoods In the Becker-Murphy model we consider this competition - _land always goes to the highest bidder_ Focus on .hi[positive] externalities for now - assume these increase with income and education - ie desirability is a function of number of high income neighbors -- Consider a model where: - Two neighborhoods, A and B (80 lots each) - Infinite number of households on the market - Only difference between the neighborhoods is income mix --- # Becker-Murphy model Individual choices to move are determined by the _rent premium_ .hi[Rent Premium:] Difference in rent between A and B - `\(RP = R(A)-R(B)\)` (for neighborhood A) <br> -- .hi[In this model:] - Consider two types of workers: .hi[HT], .hi-red[LT] - .hi[RP] for workers (may) differ by type: `\(RP_{h} \neq RP_{l}\)` - ie benefit of living close to high types might vary by type - land will be allocated to the highest bidder - rental prices are .hi-blue[homogeneous] within a neighborhood --- # Integrated + Segregated Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/seg_eq1-1.svg" style="display: block; margin: auto;" /> ] -- .pull-right[ Suppose 40 HH's start in A - .hi[integrated] equilibrium - `\(RP_{low} = RP_{high} = 0\)` - .hi[Eq:] HH's indifferent (A ~ B) .hii[Eq "shock":] 5 high type households moves to A? - What happens? ] --- count: false # Integrated vs Segregated Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/seg_eq3-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ If 5 high types move into A - `\(RP(high) > RP(low)\)` - favorable mix of neighbors - HT WTP for A increases - cascading effect - Neighborhood A is only high income HH's .hi-red[segregated eq] - Slope .hi[blue line] `\(>\)` slope .hi-red[red line] ] -- Recall .hi[A02:] Self-reinforcing changes lead to extreme outcomes --- # Eq Defn .hi[Recall:] an .hi[locational eq] is a point at which no one wants to move - in this model, it occurs when the rent premiums are equal -- This always holds when the rent premium curves intersect -- May also occur when the do not (full segregation) - If the `\(RP\)` for the group listed on the axis is _.hi[higher]_ then this will also be an equilibrium because .hi[there is no tendency for change] - If the `\(RP\)` for the group listed on the axis is _.hii[lower]_ then population dynamics move away from this point --- # Stable vs Unstable Eq An equilibrium is .hi[stable] if a small movement away will encounter self - .hi[correcting] forces - An equilibrium is stable if when you move away from it, the pop. dynamics push you back to where you came from - Physical ex: Funnel -- A equilibrium is .hii[unstable] if a small movement away will encounter self - .hii[reinforcing] forces - That is, an equilibrium is unstable if when you move away from it, the population dynamics push you even farther than where you came from - Physical ex: Stacking golf balls --- # Integration Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/int_eq2-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ - Is the story the same here? - Now, a small movement of high income HH's into A means `\(RP(High) < RP(low)\)` - So we get pushed back to the initial equilibrium. In this case, integration is the .hi[only equilibrium] - Furthermore, integration is a .hi[stable equilibrium] ] --- # Integration Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/int_eq4-1.svg" style="display: block; margin: auto;" /> .hi[Note]: 80 high income HH's in A is not an EQ because `\(RP(low)>RP(high)\)`. So low incomes will outbid highs and move in ] .pull-right[ - Is the story the same here? - Now, a small movement of high income HH's into A means `\(RP(High) < RP(low)\)` - So we get pushed back to the initial equilibrium. In this case, integration is the .hi[only equilibrium] - Furthermore, integration is a .hi[stable equilibrium] ] --- #Mixed Eq -- .pull-left[ <img src="06-nbhd-choice_files/figure-html/mixed_eq-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ - What about a story like this? - Integration eq (40 of each type in each nbhd) is still an equilibrium. Is it .hi[stable]? - No. A small deviation away means `\(RP(high) > RP(low)\)`. So highs outbid lows until `\(RP(high) = RP(low)\)` at 45 highs in A and 35 lows. - Is 45 highs in A stable? ] --- #Mixed Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/mixed_eq4-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ - What about a story like this? - Integration eq (40 of each type in each nbhd) is still an equilibrium. Is it .hi[stable]? - No. A small deviation away means `\(RP(high) > RP(low)\)`. So highs outbid lows until `\(RP(high) = RP(low)\)` at 45 highs in A and 35 lows. - Is 45 highs in A stable? Yes (you think about why) ] --- #Mixed Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/mixed_eq5-1.svg" style="display: block; margin: auto;" /> - .hi[Note]: Full segregation here is _not_ an equilibrium for a similar reason to the last example ] .pull-right[ - What about a story like this? - Integration eq (40 of each type in each nbhd) is still an equilibrium. Is it .hi[stable]? - No. A small deviation away means `\(RP(high) > RP(low)\)`. So highs outbid lows until `\(RP(high) = RP(low)\)` at 45 highs in A and 35 lows. - Is 45 highs in A stable? Yes (you think about why) ] --- # A Heuristic 1) Draw a vertical dashed line at every intersection point 2) For every region between the vertical dashed lines, it must be the case that one of the rent premium curves is above the other - If the rent prem curve for the group listed on the axis is .hi[higher], then this group will increase in number. Draw rightward arrows on the axis - If the rent prem curve for the group listed on the axis is .hii[lower], then this group will decrease in number. Draw leftward arrows --- # A Heuristic 3) If there are rightward arrows pushing toward 100% in one nbhd, then 100% (complete segregation) is an eq even if the rent prem curves do not intersect there 4) For every eq. value, look at its immediate vicinity - If there are arrows moving towards it, it is a .hi[stable eq] - If there are arrows moving away from it on one or both sides, it is a .hi[unstable eq] --- # Neighborhood Sorting .hi[Externalities] for kids: - Good/bad role models as adults - Classmates in school: focused vs disruptive -- .hi[Externalities] for adults: - Positive: job information, property valuation - Negative: property values -- In general: positive externalities increase with income and education level. Why? --- # Neighborhood Sorting These externalities give rise to the following questions: .hi[(i)] Who gets desirable neighbors? .hi[(ii)] Will there be segregated or integrated neighborhoods? .hi[(iii)] Will there be sorting or mixing with respect to income, age, race, or some combination of those factors? .hi[(iv)] What are the implications for the price of land in various neighborhoods? --- class: inverse, center, middle # End of MT material