class: center, middle, inverse, title-slide # Econ 330: Urban Economics ## Lecture 06 ### Andrew Dickinson ### 26 October, 2021 --- class: inverse, center, middle # Lecture 06: Neighborhood Choice .white[_"Love thy neighbor as yourself, but choose your neighborhood."_ .blue[kfjlsdjgjjjjjjjg] -Louise Beal] --- class: inverse, middle # Schedule .pull-left[ .ul[.bigger[.hi-gold[Today:]]] .hi-white[(i). Amenities + Public goods] .hi-white[(ii). Neighborhood sorting model] .hi-white[(iii). Racial segregation] ] -- .pull-right[ .ul[.bigger[.hi-gold[Upcoming:]]] - .hi-white[Reading] (Chapter 4) - .hi-white[Problem set 01 due on Friday at Midnight] ] --- # Housekeeping --- # Introduction to neighborhood choice We have a fairly simple model of .hi-orange[residential choice] (rental prices) -- .qa[Q:] What factor(s) in the model determine housing demand? -- .qa[A:] Bid-Rent model assumes commuting costs are the .hi-orange[only factor] -- .hi[Is this all you consider when deciding where to live?] -- - 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 .ul[.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 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 .ul[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 .ul[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?] --- class: inverse, middle, center # Neighborhood choice + Sorting for public goods --- # Neighborhood choice .center[.hi[Why are city neighborhoods so heterogenous?]] <br> -- .center[.hi[What economics factor influence neighborhood sorting within a city?]] <br> -- .center[.hi[Let's answer these questions in a simple way.]] <br> .center[.blue[Modeling public good: Public parks]] --- # 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: `\(\text{Lyla}: \color{#34b3ff} {P = 30 - 2*\text{acres}}\)` - Mid demand: `\(\text{Gracie}: \color{#e64173}{P = 40 -2*\text{acres}}\)` - High demand: `\(\text{Cooper}: \color{#6A5ACD} {P = 50 -2*\text{acres}}\)` -- .hi-blue[Together they must 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;" /> --- # Demand for public goods <img src="06-nbhd-choice_files/figure-html/demand2-1.svg" style="display: block; margin: auto;" /> For each citizen, optimal park size is found when `\(MB_{park} = MC_{park}\)` --- # 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: Cooper and Lyla -- Suppose the city can be split into .hii[3 identical districts] with 3 citizen - Each district votes on their own park - Each citizen knowns each other's preferences -- .hii[Key assumption:] Citizens pick which district to live in -- .center[.hi[What is the implication?]] -- .center[.hi[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 .center[.hi[Do you _fully_ internalize the costs and benefits of where you decide to live?]] .center[.blue[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 ] -- .hi[Neighborhood externalities tend to be massively important for youth] .pull-left[ - Peer effects] .pull-right[ - Role models] --- # Becker-Murphy model Focus on positive externalities for now - .blue[Assume these increase with income and education] -- .hi[Q:] What is the income mix of neighborhoods - segregated or integrated? -- .ul[.hi[Becker-Murphy model:]] -- - 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) -- - Rent premiums for workers (may) differ by type: `\(RP_{high} \neq RP_{low}\)` - .qa[ie:] Benefit of living close to high types might vary by type -- .hi[Assume:] - Land will be allocated to the highest bidder - Everyone in the same neighborhood pays the same rent/price --- # Becker-Murphy model: Segregation 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 `\(\Rightarrow\)` .hi[Perfectly intergrated] equilibrium `\(RP_{low} = RP_{high} = 0\)` `\(\Rightarrow\)` HH's indifferent between A & B - .hii[EQ "Shock":] A few high income households move to A? - What happens?] --- # Segregation 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 income HH's move into A, `\(RP(high) > RP(low)\)` `\(\Rightarrow\)` More favorable mix of neighbors `\(\Rightarrow\)` High income HH's are WTP more to move to A `\(\Rightarrow\)` Even more favorable mix `\(\Rightarrow\)` Neighborhood A is only high income HH's - Slope .purple[purple line] `\(>\)` slope of .red[red line] ] -- Recall .hi[A02: Self-reinforcing changes lead to extreme outcomes] --- # Eq Defn Explicitly, an .hi[equilibrium] in this model is a point at which the rent premium is in balance across both groups -- This always holds when the rent premium curves intersect - May also occur when the do not (full segregation) -- If there is a maximum number of lots in a neighborhood then- - 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_eq_1-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ What happens in this case? Notice: Slope .purple[purple line] `\(<\)` slope of .red[red line] ] --- # Integration Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/int_eq2-1.svg" style="display: block; margin: auto;" /> ] .pull-right[ What does the shock do in this case? Notice: Slope .purple[purple line] `\(<\)` slope of .red[red line] `\(\Rightarrow RP(High) < RP(Low)\)` `\(\Rightarrow\)` Pushed back to the original EQ ] -- .hi[The starting EQ is the only EQ] `\(\Rightarrow\)` .hii[Stable EQ] --- # Integration Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/int_eq3-1.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, intergration 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.orange[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? ] --- #Mixed Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/mixed_eq2-1.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]? ] --- #Mixed Eq .pull-left[ <img src="06-nbhd-choice_files/figure-html/mixed_eq3-1.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.orange[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: 1. Who gets desirable neighbors? -- 2. Will there be segregated or integrated neighborhoods? -- 3. Will there be sorting or mixing with respect to income, age, race, or some combination of those factors? - Is this sorting _de jure_, _de facto_, or both? More on this next time -- 4. What are the implications for the price of land in various neighborhoods? --- class: inverse, middle # Checklist .pull-left[ 1) .hi[Introduction to Amenities] ✅ - Exogenous Amenities - Endogenous Amenities 2) .hi[Sorting for Public Goods] ✅ ] .pull-right[ 3) .hi[Neighborhood Sorting Intro]: ✅ ] --- <!-- --- --> <!-- exclude: true --> <!-- ```{R, generate pdfs, include = F} --> <!-- system("decktape remark 02_goodsmarket_part1.html 02_goodsmarket_part1.pdf --chrome-arg=--allow-file-access-from-files") --> <!-- ``` -->