AR 11, 12, 13 SUPP CORRESPONDENCE PART 2 — Pasadena City Council, August 8, 2022

1 Introduction
Steadily rising housing rents in many of the US’s large, productive cities has brought the issue of aﬀordable housing to the forefront of the policy debate and reignited the discussion over expanding or enacting rent control provisions. State lawmakers in Illinois, Oregon, and California are considering repealing laws that limit cities’ ability to pass or expand rent control. Already extremely popular around the San Francisco Bay Area, with seven cities having imposed rent control regulations, ﬁve additional Bay Area cities placed rent control measures on the November 2016 ballot, with two passing. Rent control in the Bay Area consists of regulated price increases within the duration of a tenancy, but no price restrictions between tenants. Rent control also places restrictions on evictions.

A substantial body of economic research has warned about potential negative eﬃciency consequences to limiting rent increases below market rates, including over-consumption of housing by tenants of rent controlled apartments ( Olsen (1972), Gyourko and Linneman (1989)), mis-allocation of heterogeneous housing to heterogeneous tenants ( Glaeser and Luttmer (2003), Sims (2011)), negative spillovers onto neighboring housing ( Sims (2007), Autor et al. (2014)) and, in particular, under-investment and neglect of required mainte- nance (Downs (1988)). Yet, due to incomplete markets, in the absence of rent control many tenants are unable to insure themselves against rent increases. A variety of aﬀordable hous- ing advocates have argued that tenants greatly value these insurance beneﬁts, allowing them to stay in neighborhoods in which they have spent many years and feel invested in.

Due to a lack of detailed data and natural experiments, we have little well-identiﬁed em- pirical evidence evaluating the relative importance of these competing eﬀects. 1 In this paper,
we bring to bear new micro data, exploit quasi-experimental variation in the assignment of rent control provided by unique 1994 local San Francisco ballot initiative, and employ struc- tural modeling to ﬁll this gap. We ﬁnd tenants covered by rent control do place a substantial 1A notable exception to this is Sims (2007) and Autor et al. (2014) which use the repeal of rent control in Cambridge, MA to study it’s spillover eﬀects onto nearby property values and building maintenance. 2 value on the beneﬁt, as revealed by their migration patterns. However, landlords of proper- ties impacted by the law change respond over the long term by substituting to other types of real estate, in particular by converting to condos and redeveloping buildings so as to ex- empt them from rent control. This substitution toward owner occupied and high-end new construction rental housing likely fueled the gentriﬁcation of San Francisco, as these types of properties cater to higher income individuals.

The 1994 San Francisco ballot initiative created rent control protections for small multi- family housing built prior to 1980. This led to quasi-experimental rent control expansion in 1994 based on whether the multifamily housing was built prior to or post 1980. To examine rent control’s eﬀects on tenant migration and neighborhood choices, we make use of new panel data sources which provide the address-level migration decisions and housing charac- teristics for close to the universe of adults living in San Francisco in the early 1990s. This allows us to deﬁne our treatment group as renters who lived in small apartment buildings built prior to 1980 and our control group as renters living in small multifamily housing built between 1980 and 1990. Using our data, we can follow each of these groups over time up until the present, regardless of where they migrate to.

On average, we ﬁnd that in the medium to long term, the beneﬁciaries of rent control are between 10 and 20 percent more likely to remain at their 1994 address relative to the control group. These eﬀects are signiﬁcantly stronger among older households and among households that have already spent a number of years at their treated address. This is consistent with the fact both of these populations are less mobile in general, allowing them to accrue greater insurance beneﬁts.

On the other hand, for households with only a few years at their treated address, the impact of rent control can be negative. Perhaps even more surprisingly, the impact is only negative in census tracts which had the highest rate of ex-poste rent appreciation. This evidence suggests that landlords actively try to remove their tenants in those areas where the reward for resetting to market rents is greatest. In practice, landlords have a few possible 3 ways of removing tenants. First, landlords could move into the property themselves, known as move-in eviction. The Ellis Act also allow landlords to evict tenants if they intend to remove the property from the rental market - for instance, in order to convert the units to condos. Finally, landlords are legally allowed to oﬀer their tenants monetary compensation for leaving. In practice, these transfer payments from landlords are quite common and can be quite large. Moreover, consistent with the empirical evidence, it seems likely that landlords would be most successful at removing tenants with the least built-up neighborhood capital, i.e. those tenants who have not lived in the neighborhood for long.

To understand the reduced form impact of rent control on rental supply, we merge in historical parcel history data from the SF Assessor’s Oﬃce, which allows us to observe parcel splits and condo conversions. We ﬁnd that the owners of exogenously rent controlled properties substitute toward other types of real estate that are not regulated by rent control.

In particular, we ﬁnd that rent-controlled buildings were almost 10 percent more likely to convert to a condo or a Tenancy in Common (TIC) than buildings in the control group, representing a substantial reduction in the supply of rental housing. Consistent with these ﬁndings, we moreover ﬁnd that, compared to the control group, there is a 15 percent decline in the number of renters living in these buildings and a 25 percent reduction in the number of renters living in rent-controlled units, relative to 1994 levels.

In order to evaluate the welfare impacts of these reduced form eﬀects, we construct and estimate a dynamic discrete choice model of neighborhood choice. Motivated by our reduced form evidence, we allow for household preferences to depend on neighborhood tenure and age, and allow for monetary "buyouts" where landlords of rent-controlled properties can pay their tenants to move out. The model features ﬁxed moving costs and moving costs variable with distance. A key contribution of the paper, relative to the existing dynamic discrete choice literature, is to show how such models can be identiﬁed in a GMM framework using quasi-experimental evidence.

We ﬁnd that rent control oﬀered large beneﬁts to impacted tenants during the 1995-2012 4 period, averaging between $2300 and $6600 per person each year, with aggregate beneﬁts totaling over $393 million annually. These eﬀects are counterbalanced by landlords reducing supply in response to the introduction of the law. We conclude that this led to a city-wide rent increase of 7% and caused $5 billion of welfare losses to all renters. We discuss how the substantial welfare losses due to decreased housing supply could be mitigated if insurance against large rent increases was provided as a form of government social insurance, instead of a regulated mandate on landlords.

Our paper is most related to the literature on rent control. Recent work by Autor et al. (2014)a n d Sims (2007) leverages policy variation in rent control laws in Cambridge, Massachusetts to study the property and neighborhood eﬀects of removing rent control regulations. Our paper studies the eﬀects of enacting rent control laws, which could have very diﬀerent eﬀects than decontrol. De-control studies the eﬀects of removing rent control on buildings which remain covered. Indeed, we ﬁnd a large share of landlords substitute away from supply of rent controlled housing, making those properties which remain subject to rent- control a selected set. Further, we are able to quantify how tenants use and beneﬁt from rent control, a previously unstudied topic due to the lack of the combination of appropriate data, natural experiments and estimation methods.

There also exists an older literature on rent control combining applied theory with cross- sectional empirical methods. These papers test whether the data are consistent with the theory being studied, but usually cannot quantify causal eﬀects of rent control. ( Early (2000), Glaeser and Luttmer(2003), Gyourko and Linneman(1989), Gyourko and Linneman (1990), Moon and Stotsky (1993) Olsen (1972)).

Our estimation methods build on the dynamic discrete choice literature. Previous work using dynamic demand for housing and neighborhoods has required strong assumptions about how agents form expectations and how all neighborhood characteristics evolve over time (Bishop and Murphy (2011), Kennan and Walker (2011), Bayer et al. (2016), Davis et al. (2017), Murphy (2017)). We relax these assumptions by building on Scott (2013). His 5 key insight is to use realized values of agents’ future expected utility as a noisy measure of agents’ expectations. This method allows us to avoid needing to make explicit assumptions about how agents form expectations. Further, we do not need to assume how all state variables transition over time. Both of these assumptions are typically needed to estimate dynamic discrete choice models. Scott leverages “renewal” actions in tenants’ choice sets which allows estimation to focus on speciﬁc actions in agents’ choice sets which exhibit ﬁnite dynamic dependence, greatly simplifying the dynamic problem (Arcidiacono and Miller (2011), Arcidiacono and Ellickson (2011)). Our contribution is to show how Scott’s method can be generalized to a set of diﬀerence-in-diﬀerence style linear and instrumental variable regressions that can be used in combination with a natural experiment to identify the model parameters.

Finally, our paper is related to a separate strand of literature on community attachment in sociology. Kasarda and Janowitz (1974) provide survey evidence that length of residence is correlated with various self-reported indicators of neighborhood attachment. We estimate households’ attachments to their neighborhoods, as revealed by their migration decisions.

Consistent with survey evidence, we ﬁnd community attachment grows with years living in one’s neighborhood, but it accumulates quite slowly over time. One additional year of residence increases one’s community attachment by the equivalent of$300.

The remainder of the paper proceeds as follows. Section 2 discusses the history of rent control in San Francisco. Section 3 discusses the data used for the analysis. Section 4 presents our reduced form results. Section 5 develops and estimates a dynamic discrete choice structural model. Section 6 discusses the welfare impacts of rent control. Section 7 concludes.
6 2 A History of Rent Control in San Francisco
Rent Control in San Francisco began in 1979, when acting Mayor Dianne Feinstein signed San Francisco’s ﬁrst rent-control law. Pressure to pass rent control measures was mounting due to high inﬂation rates nationwide, strong housing demand in San Francisco, and recently passed Proposition 13.
2 This law capped annual nominal rent increases to 7% and covered all rental units built before June 13th, 1979 with one key exemption: owner occupied buildings containing 4 units or less.
3 These “mom and pop” landlords were cast as less proﬁt driven than the large scale, corporate landlords, and more similar to the tenants who were the ones being protected. These small multi-family structures made up about 30% of the rental housing stock in 1990, making this a large exemption to the rent control law.

While this exemption was intended to target “mom and pop" landlords, small multi- families were increasingly purchased by larger businesses who would sell a small share of the building to a live-in owner, to satisfy the rent control law exemption. This became fuel for a new ballot initiative in 1994 to remove the small multi-family rent control exemption.

This ballot initiative barely passed in November 1994. Beginning in 1995, all multi-family structures with four units or less built in 1979 or earlier were now subject to rent control.

These small multi-family structures built prior to 1980 remain rent controlled today, while all of those built from 1980 or later are still not subject to rent control. 3D a t a
We bring together data from multiple sources to enable us to observe property characteristics, determine treatment and control groups, track migration decisions of tenants, and observe the property decisions of landlords. Our ﬁrst dataset is from Infutor, which provides the 2Proposition 13, passed in 1978, limited annual property tax increases for owners. Tenants felt they were entitled to similar beneﬁts by limiting their annual rent increases. 3Annual allowable rent increase was cut to 4% in 1944 and later to 60% of the CPI in 1992, where is remains today.
7 entire address history of individuals who resided in San Francisco at some point between the years of 1980 and 2016. 4 The data include not only individuals’ San Francisco addresses, but any other address within the United States at which that individual lived during the period of 1980-2016. The dataset provides the exact street address, the month and year at which the individual lived at that particular location, the name of the individual, and some demographic information including age and gender.

To examine the representativeness of the Infutor data, we link all individuals reported as living in San Francisco in 1990 to their census tract, to create census tract population counts as measured in Infutor. We make similar census tract population counts for the year 2000 and compare these San Francisco census tract population counts to those reported in the 1990 and 2000 population counts for adults 18 years old and old. A regression of the Infutor populations on census population are shown in Figures A.1 and A.2 5 Figure A.1 shows that
for each additional person recorded in the 1990 Census, Infutor contains an additional 0.45 people, suggesting we have a 45% sample of the population. While we do not observe the universe of San Francisco residents in 1990, the data appear quite representative, as the census tract population in the 1990 Census can explain 70% of the census tract variation in population measured from Infutor. Our data is even better in the year 2000. Figure A.2 shows that we appear to have 1.2 people in Infutor for each person observed in the 2000 US census. We likely over count the number of people in each tract in Infutor since we are not conditioning on year of death in the Infutor data, leading to over counting of alive people.

However, the Infutor data still track population well, as the census tract population in the 2000 Census can explain 90% of the census tract variation in population measured from Infutor. Now, Infutor matches well the level of the San Francisco population and generates an even higher R
2 of 89.9%.

We merge these data with public records information provided by DataQuick about the 4Infutor is a data aggregator of address data using many sources including sources such as phonebooks, magazine subscriptions, and credit header ﬁles.
5We only can do data validation relative to the US Censuses for census tracts in San Francisco because we only have address histories for people that lived in San Francisco at some point in their life. 8 particular property located at a given address. These data provide us with a variety of property characteristics, such as the use-code (single-family, multi-family, commercial, etc.), the year the building was built, and the number of units in the structure. For each property, the data also details its transaction history since 1988, including transaction prices, as well as the buyer and seller names. Again, we assess the quality of the matching procedure by comparing the distribution of the year buildings were built across census tracts among addresses listed as occupied in Infutor versus the 1990 and 2000 censuses. Figures A.3 and A.4 show the age distribution of the occupied stock by census tract. In both of the years 1990 and 2000, our R-squareds are high and we often cannot reject a slope of one. 6 This
highlights the extremely high quality of the linked Infutor-DataQuick data, as the addresses are clean enough to merge the outside data source DataQuick and still manage to recover the same distribution of building ages as reported in both 1990 and 2000 Censuses.

To measure whether Infutor residents were owners or renters of their properties, we compare the last names of the property owners list in DataQuick to the last names of the residents listed in Infutor. Since property can be owned in trusts, under a business name, or by a partner or spouse with a diﬀerent last name, we expect to under-classify residents as owners. Figures A.5 and A.6 plot the Infutor measure of ownership rates by census tract in 1990 and 2000, respectively, against measures constructed using the 1990 and 2000 censuses.

In 1990 (2000), a one percentage point increase in the owner-occupied rate is leads to a

0.43 (0.56) percentage point increase in the ownership rate measured in Infutor. Despite the under counting, our cross-sectional variation across census tract matches the 1990 and 2000 censuses extremely well, with R-squareds over 90% in both decades. This further highlights the quality of the Infutor data.

Next we match each address to its oﬃcial parcel number from the San Francisco Assessor’s oﬃce. Using the parcel ID number from the Secured Roll data, we also merge with any 6Since year built comes from the Census long form, these data are based only on a 20% sample of the true distribution of building ages in each tract, creating measurement error that is likely worse in the census than in the merged Infutor-DataQuick data.
9 building permits that have been associated with that property since 1980. These data come from the San Francisco Planning Oﬃce. This allows us to track large investments into renovations and changes in building use type over time based on the quantity and type of permit issued to each building over time.

The parcel number also allows us to link to the parcel history ﬁle from the Assessor’s oﬃce. This allows us to observe changes in the parcel structure over time. In particular, this allows us to determine whether parcels were split oﬀ over time, a common occurrence when a multi-family apartment building (one parcel) splits into separate parcels for each apartment during a condo conversion.

Historical data on annual San Francisco wide market rents are from a dataset pro- duced by Eric Fisher, who collected historical apartment advertisements dating back to the 1950s. See https://experimental-geography.blogspot.ca/2016/05/employment-construction- and-cost-of-san.html for further details on the construction. Figure 1 shows the time series of SF rental rates generated by this data. We use an imputation procedure to construct annual rents at the zipcode level. Speciﬁcally, using census data we construct a relationship between zipcode house price deviations from the SF mean and zipcode rent deviations from the SF mean. We then use this relationship to construct zipcode level rent measures in the years we don’t have census data.
7 Summary statistics are provided in Table 1 and Table 2. 4 Reduced Form Eﬀects
Studying the eﬀects of rent control is challenged by the usual endogeneity issues. The tenants who choose to live in rent-controlled housing, for example, are likely a selected sample. To overcome these issues, we exploit the particular institutional history of the expansion of rent control in San Francisco. Speciﬁcally, we exploit the successful 1994 ballot initiative which 7Census data reports rents paid by tenants, not asking rents. We therefore use a level adjustment to ensure that the average imputed market SF rent is equal to that reported by Eric Fisher. See the appendix for the exact details of the imputation procedure.
10 removed the original 1979 exemption for small multifamily housing of four units or less, as discussed in Section 2.

In 1994, as a result of the ballot initiative, tenants who happened to live in small mul- tifamily housing built prior to 1980 were, all of a sudden, protected by statute against rent increases. Tenants who lived in small multifamily housing built 1980 and later continued to not receive rent control protections. We therefore use as our treatment group those renters who, as of December 31 1993, lived in multifamily buildings of less than or equal to 4 units, built between years 1900 and 1979. We use as our control group those renters who, as of December 31, 1993, lived in multifamily buildings of less than or equal to 4 units, built be- tween the years of 1980 and 1990. We exclude those renters who lived in small multifamily buildings constructed post 1990 since individuals who choose to live in new construction may constitute a selected sample and exhibit diﬀerential trends. We also exclude tenants who moved into their property prior to 1980, as the none of the control group buildings would have been constructed at the time.

When examining the impact of rent control on the parcels themselves, we use small multifamily buildings built between the years of 1900 and 1979 as our treatment group and buildings built between the years of 1980 and 1990 as our control group. We once again exclude buildings constructed in the early 1990s to remove any diﬀerential eﬀects of new construction. Figure 2 shows the geographic distribution of treated buildings and control buildings in San Francisco.

4.1 Tenant Eﬀects
We begin our analysis by studying the impact of rent control provisions on its tenant bene- ﬁciaries. We use a diﬀerences-in-diﬀerences design described above, with the following exact speciﬁcation:

Y
it = δxt +αi +βt ∗Ti +γst +ϵit. (1)
11 Here, Yit are outcome variables equal to one if, in yeart, the tenant i is still living at either the same address, in the same zipcode z, or in San Francisco as they were at the end of 1993. The variables δzt and αi denote zipcode by year ﬁxed eﬀects and individual tenant ﬁxed eﬀects, respectively. The variable Ti denotes treatment, equal to one if, on December 31, 1993, the tenant is living in a multifamily building with less than or equal to four units built between the years 1900 and 1979.

We include ﬁxed eﬀects γ
st denoting the interaction of dummies for the year the tenant moved into the apartment s with calendar year t time dummies. These additional controls are needed since older buildings are mechanically more likely to have long-term, low turnover tenants; not all of the control group buildings were built when some tenants in older buildings moved in. Finally, note we have included a full set of zipcode by year ﬁxed eﬀects. In this way, we control for any diﬀerences in the geographic distribution of treated buildings vs. control buildings, ensuring that our identiﬁcation is based oﬀ of individuals who live in the same neighborhood, as measured by zipcode.
8,9 Our coeﬃcient of interest, quantifying the
eﬀect of rent control on future residency, is denoted byβt.

Our estimated eﬀects are shown in Figure3, along with 90% conﬁdence intervals. We can see that tenants who receive rent control protections are persistently more likely to remain at their 1993 address relative to the control group. Not only that, but they are also more likely to be living in San Francisco. This result indicates that the assignment of rent control not only impacts the type of property a tenant chooses to live in, but also their choice of location and neighborhood type.

These ﬁgures also illustrate how the time pattern of our eﬀects correlates with rental 8We have also ran our regressions with census tract by year ﬁxed eﬀects and our results are robust to this even ﬁner neighborhood classiﬁcation. Further, dropping the zip-year ﬁxed eﬀects also produces similar results.
9While there may be some sorting into older buildings based on personal characteristics, it seems likely that once neighborhood characteristics have been controlled for, as well as the number of years lived in the apartment as of December 31, 1993, these characteristics would not lead to diﬀerential trends in migration decisions which could contaminate our estimates. As a robustness test, we have restricted our treatment group to individuals who lived in structures built between 1960 and 1979, thereby comparing tenants in buildings built slightly before 1979 to tenants in buildings built slightly after 1979. We ﬁnd very similar results.
12 rates in San Francisco. We would expect that our results would be particularly strong in those years when the outside option is worse due to quickly rising rents. Along with our yearly estimated eﬀect of rent control, we plot the yearly deviation from the log trend in rental rates against our estimated eﬀect of rent control in that given year. We indeed see that our eﬀects grew quite strongly in the mid to late 1990s in conjunction with quickly rising rents, relative to trend. Our eﬀects then stabilize and slightly decline in the early 2000s in the wake of the Dot-com bubble crash, which led to falling rental rates relative to trend.

Overall, we measure a correlation of 49.4% between our estimated same address eﬀects and median rents, and a correlation of 78.4% between out estimated SF eﬀects and median rents.

In Table3, we collapse our estimated eﬀects into a short-term 1994-1999 eﬀect, a medium- term 2000-2004 eﬀect, and a long-term post-2005 eﬀect. We ﬁnd that in the short-run, tenants in rent-controlled housing are 2.18 percentage points more likely to remain at the same address. This estimate reﬂects a 4.03 percent increase relative to the 1994-1999 control group mean of 54.10 percent. In the medium term, rent-controlled tenants are 3.54 percent- age points more likely to remain at the same address, reﬂecting a 19.38 percent increase over the 2000-2004 control group mean of 18.27 percent. Finally, in the long-term, rent-controlled tenants are 1.47 percentage points more likely to remain at the same address. This is a 12.95 percent increase over the control group mean of 11.35 percent. These eﬀects are intuitive since we expect the utility beneﬁts of staying in a rent controlled apartment to grow over time as the wedge between controlled and market rents widen.

Tenants who beneﬁt from rent control are 2.00 percentage points more likely to remain in San Francisco in the short-term, 4.51 percentage points more likely in the medium-term, and

3.66 percentage points more likely in the long-term. Relative to the control group means, these estimates reﬂect increases of 2.62 percent, 8.78 percent, and 8.42 percent respectively.

Since these numbers are of the same magnitude as the treatment eﬀects of stay at one’s exact 1994 apartment, we ﬁnd that absent rent control essentially all of those incentivized to stay in their apartments would have otherwise moved out of San Francisco. 13 These estimated overall eﬀects mask interesting heterogeneity. We begin by cutting the data on two dimensions. First, we cut the data by age, sorting individuals into two groups, a young group who were aged 20-39 in 1993 and an old group who were aged 40-65 in 1993.

We also sort the data based on the number of years the individual has been living at their 1993 address. We create a "low turnover" group of individuals who had been living at their address for greater than or equal to four years and a "high turnover" group of individuals who had been living at their address for between four and fourteen years. Finally, we form four subsamples by taking the2×2 cross across each of these two dimensions and re-estimate our eﬀects for each subsample.

The results are reported in Figure 4. We summarize the key implications. First, we ﬁnd that the eﬀects are weaker for younger individuals. We believe this is intuitive. Younger households are more likely to face larger idiosyncratic shocks to their neighborhood and housing preferences (such as changes in family structure and employment opportunities) which make staying in their current location particularly costly, relative to the types of shocks older households receive. Thus, younger households may feel more inclined to give up the beneﬁts aﬀorded by rent control to secure housing more appropriate for their circumstances.

Moreover, among older individuals, there is a large gap between the estimated eﬀects based on turnover. Older, low turnover households have a strong, positive response to rent control. That is, they are more likely to remain at their 1993 address relative to the control group. In contrast, older, high turnover individuals are estimated to have anegative response to rent control. They are less likely to remain at their 1993 address relative to the control group.

To further explore the mechanism behind this result, we do another cut of the data, sorting individuals based on the 1990-2000 rent appreciation of their 1993 zipcode. Individ- uals are then sorted into two groups based on whether their zipcode experienced above or below median rent appreciation. We now estimate our eﬀects by age, turnover, and zipcode rent appreciation. The results are in Figure 5 and Figure 6. Among older, lower turnover 14 individuals, we ﬁnd that the eﬀects are always positive and strongest in those areas which experienced the most rent appreciation between 1990 and 2000, as one might expect. For older, high turnover households, however, the results are quite diﬀerent. For this subgroup, the eﬀects are actuallynegative in the areas which experienced thehighest rent appreciation.

They are positive in the areas which experienced below median rent appreciation. 10 This result suggests that landlords are likely actively trying to remove tenants in those areas where rent control is aﬀording the most beneﬁts, i.e. high rent appreciation areas.

There are a few ways a landlord could accomplish this. First, landlords could try to legally evict their tenants by, for example, moving into the properties themselves, known as owner move-in eviction. Alternatively, landlords could evict tenants according to the provisions of the Ellis Act, which allows evictions when an owner wants to remove units from the rental market - for instance, in order to convert the units into condos or a tenancy in common.

Finally, landlords are legally allowed to negotiate with tenants over a monetary transfer convincing them to leave. Such transfers are, in fact, quite prevalent in San Francisco.

Moreover, it is likely that those individuals who have not lived in the neighborhood long, and thus not developed an attachment to the area, could be more readily convinced to accept such payments or are worse at ﬁghting eviction. Indeed, since landlord can evict or pay tenants to move out, rent control need not ineﬃciently distort renters’ decisions to remain in their rent controlled apartments. Tenants may "bring their rent control with them" in the form of a lump sum tenant buyout. Of course, if landlords predominantly use evictions, tenants are not compensated for their loss of rent protection, weakening the insurance value of rent control.

These considerations help to rationalize some additional, ﬁnal ﬁndings. In Figure 7 and Figure 8, we examine the impact that rent control has on the types of neighborhoods tenants live in in a given year. We ﬁnd that treated individuals, i.e. those who received rent control, ultimately live in census tracts with lower house prices, lower median incomes, and lower 10A similar pattern holds for younger individuals as well, although the results are weaker. 15 college shares than the control group. As Figure9 and Figure 10 show, this is not a function of the areas in which treated individuals lived in 1993. In this ﬁgure, we ﬁx the location of those treated by rent control at their 1993 locations, but allow the control group to migrate as seen in the data. If rent-controlled renters were equally likely to remain in their 1993 apartments across all locations in San Francisco, we would see the sign of the treatment eﬀects on each neighborhood characteristic to be the same as in the previous regression.

Instead, we ﬁnd strong evidence that the out-migration of rent-controlled tenants came from very selected neighborhoods. Had treated individuals remained in the 1993 addresses, they would have lived in census tracts which had signiﬁcantly higher college shares and higher house prices than the control group. This evidence is consistent with the idea that landlords undertake eﬀorts to remove their tenants or convince them to leave in improving, gentrifying areas.

4.2 Parcel and Landlord Eﬀects
We continue our analysis by studying the impact of rent control on the structures themselves.

In particular, we examine how rent control impacts the nature of the tenants who live in the buildings, as well as its impact on investments that landlords choose to make in the properties. We run a similar speciﬁcation to that above:

Y
kt = δzt +λk +βt ∗Tk +ϵkt, (2)
where k now denotes the individual parcel andλk represent parcel ﬁxed eﬀects. The variable Tk denotes treatment, equal to one if, on December 31, 1993, the parcel is a multifamily building with less than or equal to four units built between the years 1900 and 1979. The δ
zt variables once again reﬂect zipcode by year ﬁxed eﬀects. Our outcome variablesYkt now include the number of renters and owners living in the building, whether the building sits vacant, the number of renovation permits associated with the building, and whether the 16 building is ever converted to a condo. The permits we look at speciﬁcally are addition/al- teration permits, taken out when major work is done to a property.

We begin by plotting in Figure11a the eﬀects of rent control on the number of individuals living at a given parcel, calculated as percentage of the average number of individuals living at that parcel between the years 1990-1994. We estimate a decline of approximately 10 percent over the long-run, although this eﬀect is not statistically signiﬁcant.

We next decompose this eﬀect into the impact on the number of renters and the number of owners living at the treated buildings. As shown in Figure 11b, we ﬁnd that there is a signiﬁcant decline in the number of renters living at a parcel, approximately equal to 20 percent in the late 2000s, relative to the 1990-1994 level. Figure 11c shows that the decline in renters was counterbalanced by an increase of approximately 10 percent in the number of owners in the late 2000s. This is our ﬁrst evidence suggestive of the idea that landlords redeveloped or converted their properties so as to exempt them from the new rent control regulations.

We now look more closely at the decline in renters. In Figure 12b, we see that there is an eventual decline of almost 30 percent in the number of renters living in rent-controlled apartments, relative to the 1990-1994 average.
11 This decline is signiﬁcantly larger than the
overall decline in renters. This is because a number of buildings which were subject to rent control status in 1994 were redeveloped in such way so as to no longer be subject to it.

These redevelopment activities include tearing down the existing structure and putting up new single family, condominium, or multifamily housing or simply converting the existing structure to condos. These redeveloped buildings replaced about 10 percent of the initial rental housing stock treated by rent control, as shown in Figure 12a.

A natural question is whether this redevelopment activity was a response of landlords to the imposition of rent control or, instead, if such activity was also taking place within the control group and thus reﬂected other trends. Since we have the entire parcel history 11Note here that we mean relative to the number of individuals who lived at parcels which received rent control status due to the 1994 law change.
17 for a property, we can check directly whether a multifamily property which fell under the rent control regulations in 1994 is more likely to have converted to condominium housing or a tenancy in common, relative to a multifamily property which did become subject to rent control. In Figure 12c, we show that treated buildings are 8 percentage points likely to convert to condo or TIC in response to the rent control law. This represents a signiﬁcant loss in the supply of rent controlled housing.

As a ﬁnal test of whether landlords actively respond to the imposition of rent control, we examine whether the landlords of rent-controlled properties disproportionately take out addition/alteration (i.e. renovation) permits. We ﬁnd this to strongly be the case, as shown in Figure 12d. Of course, conversions of multifamily housing to condos undoubtedly require signiﬁcant alteration to the structural properties of the building and thus would require such a permit to be taken out. These results are thus consistent with our results regarding condo conversion.

Moreover, under the San Francisco rent control regulations, capital improvements can be passed onto tenants in the form of higher rents. If the existing tenants are unable to aﬀord the higher rents, capital improvements could be one way to get new tenants in the property and reset to market rents. It is important to note that this evidence contradicts the traditional view of rent control, that landlords will be disincentivized from investing in the property. On the contrary, we ﬁnd that landlords appear to make signiﬁcant investments in their properties.

Taken together, we see rent controlled increased property investment, demolition and reconstruction of new buildings, conversion to owner occupied housing and a decline of the number of renters per building. All of these responses lead to a housing stock which caters to higher income individuals. Rent control has actually fueled the gentriﬁcation of San Francisco, the exact opposite of the policy’s intended goal. 18 5 A Structural Spatial Equilibrium Model
The reduced form shows that rent control can either increase or decreases tenancy durations depending on whether the tenant receives a buyout or eviction or instead remains at their residence at below market rents. To quantify how tenants trade oﬀ these decisions and to quantify the welfare impact of rent control to covered tenants, we estimate a dynamic discrete choice model of neighborhood choice.

5.1 Model Setup
Each year t, a household decides whether to remain in its current home, a choice which we denote as S, or to move, in which case the households chooses a neighborhoodj ∈J to live in. We denote the household’s choice as x ∈{ S }∪J. The relevant state variables for the household’s decision problem are the current neighborhood jt−1 ∈J , the number of years lived in the current neighborhood τn,t−1 ∈ N∪{0}, the number of years lived in the current house τh,t−1 ∈ N∪{0}, and whether the residence is rent-controlled dt−1 ∈{ 0,1}. We also have a state variable at−1 ∈{ Y,M } denoting whether the household is in a young (Y) or mature (M) state of life. We letθt−1 =( jt−1,τ n,t−1,τ h,t−1,dt−1,at−1) denote the household’s current state variable. The transition dynamics of the state variable are straightforward. We have j
t = j(xt), where:
j(xt)= jt−1 if xt = S
j(xt)= xt otherwise.

This equation simply says that the neighborhood remains the same if the household decides to remain in its current home. Otherwise, the new neighborhood is given by the household’s choice. The implications for years in the current neighborhood and years in the current 19 house are clearly similar, with:
τn (xt)= τn,t−1 +1 if xt ∈{ S,jt−1}
τn (xt)=0 otherwise.
and
τh (xt)= τh,t−1 +1 if xt = S
τn (xt)=0 otherwise.

Finally, we assume that each period young households transition to mature households with exogenous probability ξ. This is clearly a simpliﬁcation, made due to limitations of the data, but captures the idea that households experience certain life events such as marriage and having children at diﬀerent ages.
12 Mature households do not transition back into
young households. We denote the (probabilistic) transition function as θt =Θ (xt,θt−1).

We identify the set of neighborhood locationsJ as the San Francisco zipcodes, the counties (other than San Francisco County) in the Bay Area, and an outside option denoting any location outside of the Bay Area.

We assume that a household i has the following per-period utility from their housing decision:
u(x,ω
t,εit,θt−1)= γa expRt (j,d,τ h)+ αaτn +ϕa (x,jt−1,τ n,t−1) (3) +Λ( x,dt−1)+ ωjt +εixt,
where Rt (j,d,τ h) denotes the rent paid at the chosen location, ϕa (x,jt−1,τ n,t−1) are mov- ing costs, Δt (x,dt−1) are possible monetary transfers from landlords to tenants, ωjt is an unobservable neighborhood taste shock, and εixt is an idiosyncratic logit error taste shock 12In principle, we could tract the exact age as a stage variable, but this makes the state space very large. 20 over the possible choices which is speciﬁc to householdi.13 Note that we are suppressing the dependence of (j,τ,d ) on x. If a tenant does not live in a rent-controlled property, she pays market rents, given by Rt (j,0). Thus, there is no dependence on τh. In contrast, the rent paid by tenants in rent-controlled propertiesRt (j,1,τ h) is a function of the number of years lived in the property. Crucially, note that the household has utility over exponential rents, with coeﬃcient γa. We, of course, expect this coeﬃcient to be negative. This assumption ensures, due to the eﬀects of Jensen’s inequality, that rent control oﬀers real insurance value to tenants. We moreover allow for utility to depend on how long a household has lived in the current neighborhood, as measured by parameter α
a. Intuitively, households may build
up neighborhood capital over time which makes that location more attractive. For instance, over time people form meaningful friendships with their neighbors and acquire valuable local knowledge, such as that regarding local amenities. We allow both the rent utility parameter and neighborhood capital parameter to depend on whether the household is in the young or mature stage of life.

Households incur moving costs when they switch homes. We assume that there is a ﬁxed moving cost ϕ
0,a > 0, as well as a cost ϕd,a > 0 that is variable with distance. We allow the variable moving cost parameter to depend on current neighborhood capital τn,t−1, with the interaction eﬀect measured by ϕτ,a . This allows for the possibility that the desirability of nearby neighborhoods changes as one accrues neighborhood capital. In particular, ϕa (x,jt−1)=0 if xt = S
ϕa (x,jt−1)= ϕ0,a +ϕd,ad(jt,jt−1)+ ϕτ,a (d(jt,jt−1)×τn,t−1) otherwise, where d(jt,jt−1) denotes the distance between the old and new neighborhoods. We allow the moving costs to vary with age. For example, it seems likely that households with children will ﬁnd moving more costly than households without children, since changing schools could 13We measure rents as monthly rents divided by 3000, measured in 2010 dollars. We divide by 3000 for computational convenience.
21 prove disruptive.

We also allow for possible monetary transfers from landlords of rent-controlled properties to tenants incentivizing them to move. These may represent true tenant buyouts or the amount of buyout that would have been required to rationalize the tenant out-migration, even if in reality the migration was due to eviction. In practice, the city of San Francisco allows for such negotiations and these payments are, in practice, quite prevalent. We do not explicitly model the bargaining game between landlords and tenants. Instead, we proceed in more reduced form fashion and parameterize the transfers as:

Λ
t (x,dt−1,at−1)=0 if xt = S or dt−1 =0
Λt (x,dt−1,at−1)= λ1 [Rt (j,0)−Rt (j,1,τ h)]+ λ2τn +λY 1[at−1 = Y] otherwise.

The ﬁrst equation simply says that, if the tenant does not move or does not live in rent- controlled housing, he receives no transfers. The ﬁrst term in the second equation denotes the diﬀerence between market rents and rent-controlled rents. We would expect the coeﬃcient on this term, λ
1, to be weakly positive. Intuitively, the greater the current diﬀerence between market rents and rent-controlled rents, the greater the incentive for landlords to remove tenants and thus the more landlords should be willing to pay to convince tenants to leave.

We also allow for the outcome of the bargaining to depend on neighborhood tenureτ n, with
the impact measured by the coeﬃcient λ2. This allows for more invested tenants to receive a larger payment, since their outside option, i.e. choosing to stay, is likely better than that of a short term tenant who has not built up a large stock of neighborhood capital. Finally, we allow the level diﬀerence in transfers to diﬀer between young and mature households, measured by λ
Y .

We decompose the unobservable neighborhood amenity valueωjt into ωjt = ωj +˜ωjt,
22 where ωj is a time-invariant ﬁxed eﬀect and˜ωjt is a per-period neighborhood speciﬁc shock.

We impose no structure on the distribution of ˜ωjt beyond requiring that F(˜ωj,t+1|˜ωjt,xit)= F(˜ωj,t+1|˜ωjt). That is, the decision of any individual agent has no impact on the distribution of the neighborhood amenity value next period.

Letting β denote the common discount factor, the household’s dynamic optimization problem at time t is given by:

V (θi,t−1,ωt,εit) = max
x∗
E
( ∞∑
s≥t
βs−tu(x∗,ωt,εit,θi,t−1)|θi,t−1,ωt,εit
)
.

We next deﬁne the ex-ante value function V (θit,ωt) by integrating over the idiosyncratic errors:

Vt (θt−1)=
∫
···
∫
V (θt−1,ωt,(ε1,...,ε J+1))dF (ε1)...dF (εJ+1),
where J is the number of neighborhoods and εJ+1 it the logit error associated with staying in the current home. From this we can deﬁne the value function conditional on actions:
vt (x,θt−1)= ut (x,θt−1)+ βEt
[
Vt+1 (Θ(x,θt−1))
]
,
where ut (x,θt−1)= u(x,ωt,0,θt−1), Θ(x,θt−1) denotes the state transition function, and Et [·] denotes expectations conditional on time t information.

Since the idiosyncratic taste shocks follow a logit speciﬁcation, we get the standard results (see e.g. Hotz and Miller (1993)) relating conditional value functions to conditional choice probabilities p
t (x|θt−1):
pt (x|θt−1)= exp(vt (x,θt−1))∑
x′exp(vt (x′,θt−1)). (4)
In what follows, we denote the log of the denominator of this expression as:

It (θt−1)=l n
(∑
x′
exp(vt (x′,θt−1))
)
23 We also have that the ex-ante value function is given by:

Vt (θt−1,ωt)= It (θt−1)+Γ , (5)
where Γ is Euler’s gamma.

5.2 Renewal Actions
The key challenge in identifying dynamic discrete choice models is dealing with the ex- pected continuation values in the Bellman equation. To be able to calculate the expected continuation values, one generally must make assumptions about exactly how agents form expectations, including exactly what information is known to the agent and how they ex- pect market-level state variables to evolve. This normally requires assuming all market state variables (e.g. rents and amenities) are observed and follow assumed transition dynamics.

We build onScott (2013) and make no assumptions about how amenities evolve. We also do not assume how agents form expectations about future market states, other than that they are on average rational. Following work by Arcidiacono and Ellickson (2011)a n dArcidia- cono and Miller (2011), we make extensive use of renewal actions, or action(s) which, given current states θ
t−1 and θ′
t−1, lead to the same state in the next period. This will allow us to diﬀerence out much of the long-term continuation values in the Bellman equation, which are impossible to estimate without strong assumptions.

5.2.1 Immediate Renewals
Suppose we have two households in states θ
t−1 and θ′
t−1. In period t, these two households
take the actions x and x′respectively. Using equation (4) and diﬀerencing we ﬁnd that:
vt (x,θt−1)−vt
(
x′,θ′
t−1
)
=l n
(
pt (x|θt−1)
pt
(
x′|θ′
t−1
)
)
+It (θt−1)−It
(
θ′
t−1
)
24 Substituting in for the conditional value functions, we get:
ut (x,θt−1)−ut
(
x′,θ′
t−1
)
+βEt
[
Vt+1 (Θ(x,θt−1))
]
−βEt
[
Vt+1
(
Θ
(
x′,θ′
t−1
))]
(6)
=l n
(
pt (x|θt−1)
pt
(
x′|θ′
t−1
)
)
+It (θt−1)−It
(
θ′
t−1
)
.

Now assume x and x′are renewal actions in the sense that Θ(x,θt−1)=Θ (
x′,θ′
t−1
)
.

Note that we do not require x = x′, although this will often be the case. For example, if two households in non-rent controlled housing are living in the same neighborhood j and have the same level of neighborhood tenure, then x = S and x′= j, i.e. one household choosing to stay in the current home and the other moving to another house in the same neighborhood, constitute renewal actions. The key implication is that the future continuation values diﬀerence out, leaving:
ut (x,θt−1)−ut
(
x′,θ′
t−1
)
=l n
(
pt (x|θt−1)
pt
(
x′|θ′
t−1
)
)
+It (θt−1)−It
(
θ′
t−1
)
. (7)
If θt−1 ̸= θ′
t−1, we also need to remove the diﬀerence of log sums, which implicitly involves future continuation values as well.

To do so, suppose the households move to some neighborhood j∗ ∈J , with j∗ ̸= x and j∗ ̸= x′. This always constitutes a renewal action, so we get equation (7) again with x and x′replaced with j∗:
ut (j∗,θt−1)−ut
(
j∗,θ′
t−1
)
=l n
(
pt (j∗|θt−1)
pt
(
j∗|θ′
t−1
)
)
+It (θt−1)−It
(
θ′
t−1
)
. (8)
Diﬀerencing equations (7)a n d(8) yields:
ln
(
pt (x|θt−1)
pt
(
x′|θ′
t−1
)
)
−ln
(
pt (j∗|θt−1)
pt
(
j∗|θ′
t−1
)
)
=
[
ut (x,θt−1)−ut
(
x′,θ′
t−1
)]
(9)
−
[
ut (j∗,θt−1)−ut
(
j∗,θ′
t−1
)]
,
25 which removes the log sums. Intuitively, equation ( 9) compares the diﬀerence in utility between two diﬀerent actions a household in stateθt−1 could take versus a household in state θ′
t−1. This "diﬀerences-in-diﬀerences" approach removes all long-term utility diﬀerences since actions are selected to create renewals.

5.2.2 One Period Ahead Renewals
Now suppose that x and x′are not renewal actions in period t. Following Scott (2013), we substitute the expected diﬀerence in continuation values in equation (6) with its realization and expectational errors:
ut (x,θt−1)−ut
(
x′,θ′
t−1
)
−ln
(
pt (j|θt−1)
pt
(
j′|θ′
t−1
)
)
−
[
It (θt−1)−It
(
θ′
t−1
)]
= β
(
Vt+1
(
Θ
(
x′,θ′
t−1
))
−Vt+1 (Θ(x,θt−1))
)
+ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)
where
ξV
t (x,θt−1)= β
(
Et
[
Vt+1 (Θ(x,θt−1))
]
−Vt+1 (Θ(x,θt−1))
)
is the expectational error.

We now again make use of renewals. Suppose that at time t+1, both households move to the same neighborhood, that is xt+1 = x′
t+1 = j∗ ∈J . To see the eﬀects of this, ﬁrst
substitute out the realized ex-ante value functions using equations (4)a n d(5). We have:
ut (x,θt−1)−ut
(
x′,θ′
t−1
)
−ln
(
pt (j|θt−1)
pt
(
j′|θ′
t−1
)
)
−
[
It (θt−1)−It
(
θ′
t−1
)]
= β
(
vt+1
(
j∗,Θ
(
x′,θ′
t−1
))
−vt+1 (j∗,Θ(x,θt−1))
)
−βln
(
pt+1
(
j∗,Θ
(
x′|θ′
t−1
))
pt+1 (j∗,Θ(x|θt−1))
)
+ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1).

Since j∗ is a renewal action, the time t+2 expected value functions diﬀerence out and this 26 equation becomes:
ut (x,θt−1)−ut
(
x′,θ′
t−1
)
−ln
(
pt (j|θt−1)
pt
(
j′|θ′
t−1
)
)
−
[
It (θt−1)−It
(
θ′
t−1
)]
(10)
= β
(
ut+1
(
j∗,Θ
(
x′,θ′
t−1
))
−ut+1 (j∗,Θ(x,θt−1))
)
−βln
(
pt+1
(
j∗,Θ
(
x′|θ′
t−1
))
pt+1 (j∗,Θ(x|θt−1))
)
+ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1).

To fully remove the conditional value functions, we once again must remove the diﬀerence in log sums It (θt−1)−It
(
θ′
t−1
)
.

We follow the same procedure as previously, subtracting equation (8) from equation (10):
ln
(
pt (j|θt−1)
pt
(
j′|θ′
t−1
)
)
−ln
(
pt (j∗|θt−1)
pt
(
j∗|θ′
t−1
)
)
+βln
(
pt+1 (j∗,Θ(x|θt−1))
pt+1
(
j∗,Θ
(
x′|θ′
t−1
))
)
(11)
=
[
ut (x,θt−1)−ut
(
x′,θ′
t−1
)]
−
[
ut (j∗,θt−1)−ut
(
j∗,θ′
t−1
)]
+β(ut+1 (j∗,Θ(x,θt−1))−ut+1 (j∗,Θ(x,θt−1)))
+ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1).

Equations (9)a n d( 11) provide a linear regression framework which we can use to fully identify and estimate the parameters of the model.

5.3 Empirical Framework
We now discuss how to empirically operationalize the preceding considerations.

5.3.1 Constructing Conditional Choice Probabilities
We ﬁrst need to construct empirical estimates of the conditional choice probabilities,pt (x|θt−1).

In a given year t, we focus on those households who were part of the 1994 treatment and control groups described in the previous section and who have not moved away from their 1994 residence. Given the latter restriction, we do not need to keep track of τ h and we
therefore suppress the dependence of θt−1 on this state variable in what follows. 27 With a large enough dataset, we could simply compute empirical frequencies for all con- ditional choice probabilities. However, since there are many states, not all CCPs in our data are measured precisely. We therefore use kernel smoothing on the empirical frequencies to improve the prediction error. We smooth over distance, neighborhood tenure, and age. We use a Gaussian kernel. Distance is measured between the midpoints of zipcodes. Neighbor- hood tenure equals the number of years the renter has lived in that zipcode. Young renters are those under the age of 40, while mature/old renters are those 40 and older. We usek-fold cross validation to set the optimal bandwidths with k=5.

5.3.2 Identifying the Parameters of the Model
We set β = .85.
14 We estimate the various parameters of the model by estimating equa- tion (9)a n d(11) for appropriately chosen values of
(
θt−1,θ′
t−1
)
and (x,x′). Intuitively, by
examining the diﬀerential behavior of individuals in certain states of the world and follow- ing certain types of deviations, we can isolate the impact of the diﬀerent parameters of the model. We begin by constructing a regression equation for γ M,λ 1, and λ2. These are the
(mature) rent utility parameter and the parameters of the transfer function. Normally, we would be confronted with a signiﬁcant endogeneity problem in estimating these parameters since market rents R
t (j,0) in neighborhood j are likely correlated with the amenity value ωjt unobservable to the econometrician.

We overcome this essential endogeneity problem by exploiting the quasi-experimental na- ture of the 1994 San Francisco rent control ballot measure. This law change quasi-randomly assigned renters within a given neighborhood j to rent control status. As mentioned, we focus exclusively on this population for our regressions.

Now let θ
t−1 =( j,τ n,1,M ) and θ′
t−1 =( j,τ n,0,M ) for some j ∈J . We furthermore set
x = x′= S and letj∗ be any element ofJ . In words, we consider two mature households who both lived in neighborhood j in 1994 and have not moved as of year t. The two households 14This choice is consistent with the evidence provided in De Groote and Verboven (2016), who estimate a household discount factor of .87.
28 are of equal tenure τn. One was assigned to rent control status in 1994 and the other was not. We examine the relative probabilities of these individuals staying in neighborhoodj in year t, using neighborhood j∗ as the renewal choice in the manner described in the previous section. Under these assumptions, equation (11) gives the regression:

Yt
j,j∗ = γM [expRt (j,1)−expRt (j,0)]+
+λ1 [(βlnRt+1 (j,0)−lnRt (j,0))−(βlnRt+1 (j,1)−lnRt (j,1))] +λ2 [β(t+τn +1) −(t+τn)]
+ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)+ χt
j,j∗
Yt
j,j∗ =l n
(pt (S|j,1,τ n)
pt (S|j,0,τ n)
)
−ln
(pt (j∗|j,1,τ n)
pt (j∗|j,0,τ n)
)
+βln
(pt+1 (j∗|j,1,τ n)
pt+1 (j∗|j,0,τ n)
)
Intuitively, this regression compares the probability of staying in the neighborhood for one more year and then moving toj∗ versus moving toj∗ this year. This diﬀerence in probabilities is then diﬀerenced between treatment and control, which diﬀerences out all the utility impacts of living in j vs j
∗ other than those which are impacted by rent control.

Note that we have included an additional error term χt
j,j∗, reﬂecting measurement er-
ror in our constructed conditional choice probabilities.The key for identiﬁcation is that the unobserved amenity valueω
jt diﬀerences out. We furthermore know that:

Et
[
(Rt (j,1)−Rt (j,0))
(
ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)
)]
=0
due to rational expectations. That is, the expectational error is uncorrelated with any time t information. In general, however, we do not have:

Et
[
(Rt+1 (j,1)−Rt+1 (j,0))
(
ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)
)]
=0 .

The timet+1 rent diﬀerence may be correlated with the expectational error. This is intuitive.

For instance, neighborhood j may be better at date t +1 than was expected since market 29 rents are lower than anticipated. We, therefore, instrument for the timet+1 rent diﬀerence Rt+1 (j,1) − Rt+1 (j,0) with Zt, equal to the one-period lagged value Rt (j,1) − Rt−1 (j,0).

Since Zt is in the time t information set, we have:

Et
[
Zt
(
ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)
)]
=0 .

Thus, our exclusion restrictions are satisﬁed and the parameters are identiﬁed.

To identify the impact of tenure on utilityαM , consider two mature households living in non-rent controlled housing in neighborhood j, with diﬀerent levels of initial tenure,τn and τ′
n.Suppose both households move to j∗ after one year. We thus have θt−1 =( j,τ n,0,M ) and θ′
t−1 =( j,τ ′
n,0,M ) for some j ∈J and x = x′= S. Then equation (11) becomes:

Yt
j,j∗ = αM (τn −τ′
n)+ ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)+ χt
j,j∗
Yt
j,j∗ =l n
(pt (S|j,0,τ n)
pt (S|j,0,τ ′
n)
)
−ln
(pt (j∗|j,0,τ n)
pt (j∗|j,0,τ ′
n)
)
+βln
(pt+1 (j∗|j,0,τ n)
pt+1 (j∗|j,0,τ ′
n)
)
Since both households live in non-rent controlled housing in the same neighborhood, they pay the same rents and receive the same unobserved amenity value. Indeed, the only payoﬀ- relevant diﬀerence between the two populations is the number of years they have lived in the neighborhood. Thus, appropriately examining the relative probabilities of staying in the neighborhood is informative of the importance of tenure on utility or, in other words, of the magnitude of α
M. Intuitively, as one builds up more neighborhood capital, the beneﬁts of staying in the neighborhood an additional year. Thus, the relative probability of staying one more year versus moving away should grow if neighborhood capital is accruing.

To estimate moving costs, we consider two mature households of equal tenure τ n living
in non-rent controlled housing in neighborhood j. Suppose that one household immediately moves to another house in the same zipcode and one household stays in the same home.

Formally,θ
t−1 = θ′
t−1 =( j,τ n,0,M ), x = S,a n dx′= j. As was discussed in Section 5.2.1, this constitutes an immediate renewal since rents do not change and neighborhood tenure 30 does not change. Since one is only changing the house they live in due to the logit error and the moving costs, we can identify the ﬁxed cost of moving. If people move houses a lot within a zipcode, moving costs must be low. If they do it rarely, moving costs must be high.

Equation (9) gives the regression:

Y
t
j = −ϕ0,M +χt
j
Yt
j =l n
(pt (S|j,0,τ n)
pt (j|j,0,τ n)
)
,
which identiﬁes the ﬁxed moving cost parameter ϕ0,M . Note that there is only one log diﬀerence instead of two since the households begin in the same state.

We also need the variable moving cost parameter,ϕd,M. Consider two mature households of equal tenure τn, both living in non-rent controlled housing, one living in neighborhood j and the other in neighborhood j′. Suppose they immediately move to either neighborhood j∗ or j∗∗. Both of these are choices constitute immediate renewals. Therefore, Equation (9) gives the speciﬁcation:

Yt
j,j′,j∗,j∗∗ = ϕd,M (dj,j∗ −dj′,j∗)−ϕd,M (dj,j∗∗ −dj′,j∗∗)+ χt j,j′,j∗,j∗∗
Yt
j,j′,j∗,j∗∗ =l n
(pt (j∗|j,0,τ n)
pt (j∗|j′,0,τ n)
)
−ln
(pt (j∗∗|j,0,τ n)
pt (j∗∗|j′,0,τ n)
)
.

Intuitively, this compares the relative probabilities of moving to j∗ vs j∗∗ depending on whether one starts in j or j′.I f j is very close to j∗, but far from j∗∗, then the diﬀerence in moving costs between the moves in large. However, if j′is equidistant between the two, the moving costs between the two locations are the same. The relationship between these diﬀerences in distances and diﬀerences in migration probabilities identiﬁes the marginal cost of moving with respect to distance. Using similar considerations, one can estimate the interaction term parameter ϕ
τ,M . The equation is detailed in the appendix.

As one would expect, the equations for young households are very similar to the ones described above, but the probability of transitioning to a mature household must be taken 31 into account. Furthermore, one can use the treatment group as well as the control group to estimate the neighborhood tenure parameters and the variable moving cost parameters. All of these additional equations are detailed in the appendix. The model is then estimated via GMM.

Finally, it remains to estimate the permanent component of amenities ω j.15 We do so
after estimating the full GMM system detailed above. We once again consider two mature households of equal tenure τ
n, living in neighborhoods j and j′respectively and suppose that both households move to some neighborhood j∗ after one year. We thus have, θt−1 = (j,τ n,0,M ),θ ′
t−1 =( j′,τ n,0,M ), and x = x′= S. These choices yield the equation:

Yt
j,j′,j∗ = ωj −ωj′+˜ωjt − ˜ωj′t +ξV
t
(
x′,θ′
t−1
)
−ξV
t (x,θt−1)+ χt
j,j′,j∗
Yt
j,j′,j∗ =l n
(pt (S|j,0,τ n)
pt (S|j′,0,τ n)
)
−ln
(pt (j∗|j,0,τ n)
pt (j∗|j′,0,τ n)
)
+βln
(pt+1 (j∗|j,0,τ n)
pt+1 (j∗|j′,0,τ n)
)
−(β −1)ϕd,M (dj,j∗ −dj′,j∗)−γM [Rt (j,0)−Rt (j′,0)]
Identiﬁcation comes from the fact that, averaging over time, we average out the per-period neighborhood amenity shocks and expectational error shocks. Moreover, note that we do not have an endogeneity problem since we have already estimated γ M and can therefore
move the utility impact of the rent diﬀerence to the left hand side of the equation. We also account for the diﬀerential moving costs related to distance on the left hand side of the equation. Finally, note that we can only identify ﬁxed amenity value diﬀerences between neighborhoods. We therefore choose a normalization, letting zipcode 94110, representing the Mission District and Bernal Heights, be our baseline zipcode. We set its amenity value ﬁxed eﬀect to zero.
15We cannot identify amenities of the outside options, i.e. the rest of the Bay Area and the rest of the country, as no one in our 1994 cohorts started oﬀ living in those locations. 32 5.4 Model Estimates
Table 4 shows the parameter estimates of the model. Panel A reports the parameters mea- sured in rent equivalent dollar units, with the exception of the transfer payments, which are measured in actual dollar amounts.
16 Panel B reports the estimates in units of migra-
tion elasticities. We will focus on the estimates in Panel A. Normalizing the coeﬃcient on exponential rents to 1, we identify the standard deviation of tenants’ idiosyncratic shocks to their location preferences. We ﬁnd that young renters have annual location taste shocks with a standard deviation equivalent to $7,411. Mature renters face location shocks with a 12.7% lower standard deviation. These estimates are consistent with our previously dis- cussed hypothesis that young renters’ migration decisions are more driven by idiosyncratic shocks than older households.

Turning to the magnitudes of the tenant buyouts, we ﬁnd young renters receive $1.631 more dollars from their landlords for each additional $1 below market their rent is. Mature renters face similar impact of $1.404. We also ﬁnd buyout oﬀers are larger as tenants live in their zipcodes longer. For each additional year a young (mature) tenant lives in their zipcode, they receive $164 ($141) additional dollars in the buyout oﬀer from their landlord.

Finally, we ﬁnd mature tenants receive larger buyout oﬀers overall by $70,702. This may reﬂect that landlords expect older tenants to remain in their apartments for the very long term. Along the same lines, to the extent that these transfers reﬂect evictions, landlords would be more incentivized to evict older renters. To get a better sense of the magnitudes of these buyout payments, Figure14 plots the average buyout to young tenants oﬀered in each year in the data, across all tenants and neighborhoods. By 2010, the average oﬀer to tenants who still remain at their 1994 address is just over $30,000. Figure15 plots the heterogeneity across zipcodes in mean buyout oﬀers, highlighting that some zipcodes experience much large rent increases than others over this time period. In the most expensive zipcode, the average buyout in 2010 is just about $40,000, while in the cheapest zipcode the mean buyout oﬀer is 16These are measured at the mean rent paid by rent-controlled households, $2350. 33 around $25,000. These numbers seem very much in line with popular press anecdotes about tenant buyouts in San Francisco.

Moving along to our estimates of moving costs, we ﬁnd the ﬁxed cost of moving is equivalent, in rent-equivalent dollars, to $42,626 for young renters and $38,988 for old renters.

These estimates seem quite reasonable and actually quite below what is typically found in the literature. A main driver of the magnitude of this estimate are the short-run migration elasticities with respect to a one-year temporary change. It is often quite hard to ﬁnd a high quality instrument for rents that does not eﬀect other omitted variables such as amenities.

Likely, many instruments for rent also impact the supply and quality of amenities, leading to rent elasticities being biased towards 0. Our rent control policy experiment only aﬀects rents and cannot eﬀect amenities in our regressions, as we are comparing migration decisions between market rent and rent controlled households in the same neighborhood consuming the same amenities.

In addition to the ﬁxed costs of moving, we ﬁnd that the moving costs increase with the distance of the move. A 1 percent increase in move distance is equivalent to $114 for the young and $101 for the old. Finally, we also consider whether these variable moving costs change as households live in their zipcodes longer. One might think that the longer a household has lived in the area the more familiar they are with further and further away neighborhoods, lowering those marginal moving costs. Indeed, we ﬁnd this is the case, with each additional year a tenant has lived in their zipcode lowering the moving cost by $415 for the young and $357 for the old.

Lastly, we turn to our neighborhood capital estimates. Proponents of rent control often argue that long-term residents are the ones in the most need of rent control as migrating away from their community forces them to lose many of the connections and investments they have been in the neighborhoods over time. We do ﬁnd very statistically signiﬁcant eﬀects of neighborhood capital accumulation. However, the economic magnitude is small.

Young (mature) households increasingly value living in their zipcode by $266 ($292) in dollar 34 rent equivalent terms. However, these eﬀects can add up to a sizable eﬀect over a lifetime. 6 Welfare Eﬀects of Rent Control

6.1 Welfare Decomposition: 1994-2012
We begin our investigation of the welfare eﬀects of rent control by decomposing the impacts of the 1994 ballot initiative on its beneﬁciaries, relative to the control group. We discuss here mature households. The expressions for young households are exactly analogous.

6.1.1 Derivations
In any given yeart between the years of 1994 and 2012, the average utility diﬀerence between the treatment group and the control group is given by:

ΔU
M
t =
∑
θt−1
∑
x
(ut (x,θt−1)+ Et [εixt|x,θt−1])pt (x|θt−1)
(
pT
t (θt−1)−pC
t (θt−1)
)
(12)
=
∑
θt−1
∑
x
(ut (x,θt−1)+ Et [εixt|x,θt−1])
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
where recall ut (x,θt−1)= u(x,ωt,0,θt−1) and the utility function is deﬁned in equation (3).

The expressionpt (x|θt−1) again denotes the conditional probability of choosingx ∈{ S}∪J , given that the current state is θt−1, pT
t (θt−1),pC
t (θt−1) denote the probabilities of being in
stateθt−1 for the treatment group and control group respectively, andpT t (x,θt−1),pC
t (x,θt−1)
denote the joint probabilities. The conditional expectation Et [εit|x,θt−1] denotes the ex- pected logit error conditional on choosingx from state θt−1. Of course, equation (12) simply says that the average utility diﬀerence is the weighted average utility received by the treat- ment group minus the weighted average utility received by the control group.

We can decompose this average utility diﬀerence by substituting in for the utility function 35 from equation (3). We ﬁnd that:

ΔUM
t =Δ UM,Rent
t +ΔUM,Payoff
t +ΔUM,NC
t (13)
+ΔUM,MC
t +ΔUM,Miles
t +ΔUM,Amenity
t +ΔUM,Logit
t .

That is, the average utility diﬀerence between the treatment group and the control arises from diﬀerences in average rent paidΔUM,Rent
t , in transfers received from landlordsΔUM,Payoff
t , in
accumulated neighborhood capitalΔUM,NC
t , in ﬁxed costsΔUM,MC
t , in variable moving costs
ΔUM,Miles
t , in neighborhood amenity values ΔUM,Amenity
t , and in idiosyncratic valuations
ΔUM,Logit
t . Suppressing the dependence of j and τ on x, we can formally write these terms as:

ΔU Rent
t =
∑
θt−1
∑
x
γM exp(Rt (j,d,τ h))
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
ΔUPayoff
t =
∑
θt−1
∑
x
Λt (x,dt−1,M)
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
ΔUM,NC
t =
∑
θt−1
∑
x
αMτn
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
ΔUM,MC
t =
∑
θt−1
∑
x
ϕ0,M1[x ̸= S]
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
ΔUM,Miles
t =
∑
θt−1
∑
x
ϕd,Mdj,jt−11[x ̸= S]
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
ΔUM,Amenity
t =
∑
θt−1
∑
x
ωjt
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
.

We can measure each of these terms. 17 We recover estimates of γM,ΛM,αM,ϕ 0,M,ϕd,M, and ωjt from our structural model. We can then recover the other needed quantities from standard reduced form diﬀerences-in-diﬀerences analysis. For example, ∑
θt−1
∑
x exp(Rt (j,d,τ h))
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
is simply the average diﬀerence in
rents paid between treatment and control in yeart, ∑
θt−1
∑
x τn
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
17Since we measure rents as monthly rents/3000, we multiply by 36,000 to convert to an annual rent number.
36 is the average diﬀerence in accumulated neighborhood capital between treatment and con- trol, ∑
θt−1
∑
x 1[x ̸= S]
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
is the average diﬀerence in number of
moves between treatment and control, and
∑
θt−1
∑
x dj,jt−11[x ̸= S]
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
is the average diﬀerence in distance moved
between treatment and control. Each of these can be readily calculated using the reduced form methodology described in Section4. The average utility diﬀerence due to transfers and the average utility diﬀerence due to amenities can be similarly calculated by combining our structural estimates with reduced form diﬀerences-in-diﬀerences analysis.

Deriving an expression for the utility diﬀerence due to idiosyncratic valuationsΔU M,Logit
t
is a bit more complicated. We have that:

ΔUM,Logit
t =
∑
θt−1
∑
x
Et [εit|x,θt−1]
(
pT
t (x,θt−1)−pC
t (x,θt−1)
)
. (14)
We therefore need an expression for the conditional expectationEt [εixt|x,θt−1]. Using Bayes’ rule, we get:

Et [εixt|x,θt−1]=
∫
εixt
(∏
x′̸=x e−e−(εixt+vt(x,θt−1)−vt(x′,θt−1)) )
e−εixte−e−εixt
dεixt
pt (x|θt−1)
=
∫
εixt
(∏
x′̸=x e−e−(εixt+lnpt(x|θt−1)−lnpt(x′|θt−1)) )
e−εixte−e−εixt
dεixt
pt (x|θt−1) ,
where in the second equality we used the Hotz and Miller (1993) inversion vt (x,θt−1) − vt (x′,θt−1)=l n pt (x|θt−1)−lnpt (x′|θt−1). Substituting into equation (14), we derive:

ΔUM,Logit
t =
∑
θt−1
∑
x
{∫
εixt
( ∏
x′̸=x
e−e−(εixt+lnpt(x|θt−1)−lnpt(x′|θt−1))
)
e−εixte−e−εixt
dεixt
}
×
(
pT
t (θt−1)−pC
t (θt−1)
)
.
(15)
Since we have empirical estimates of each of the probabilities, we can estimate this utility 37 diﬀerence.

We ﬁnally convert our estimated utility diﬀerences into rent equivalent dollar amounts.

Consider an individual in the control group who pays the average San Francisco rent in year t, which we denote as
Rt. We now proceed iteratively. The dollar rent equivalent ΔW Rent t
of the utility diﬀerence ΔU Rent
t in year t due to rent diﬀerences can be calculated as the solution to :
γM exp
(
Rt +ΔW Rent
t
)
−γM exp
(
Rt
)
=Δ U Rent
t ,
which gives:

ΔW Rent
t =l n
(ΔU Rent
t
γM
+exp
(
Rt
))
−Rt.

The dollar rent equivalent incremental impact of transfers can then be calculated as:

ΔWPayoff
t =l n
(
ΔUPayoff
t
γM
+exp
(
Rt +ΔW Rent
t
)
)
−
(
Rt +ΔW Rent
t
)
.

Now letΔUM,ι
t denote the utility diﬀerences, withι ∈{ 1,..., 7} corresponding to the ordering in equation ( 13). Iterating on our procedure gives the dollar rent equivalent incremental impacts of each element of the decomposition:

ΔWι
t =l n
(
ΔUPayoff
t
γM
+exp
(
Rt +
∑
ι′<ι
ΔWι′
t
))
−
(
Rt +
∑
ι′<ι
ΔWι′
t
)
.

6.1.2 Results
The results of this decomposition are reported in Table 5. We ﬁnd that the beneﬁciaries of the 1994 rent control law received large welfare beneﬁts between the 1994-2012 period. Older households received a total rent-equivalent dollar beneﬁt of $119,625, reﬂecting an annual beneﬁt of $6,646. These beneﬁts were front loaded, with households earning a cumulative beneﬁt of $74.514 and average annual beneﬁt of $8,279 during the 1995-2003 period Cumu- lative beneﬁts equaled $45,111 during the 2004-2012 period, reﬂecting an annual average of 38 $5,012.

In terms of decomposition, most of the beneﬁts from the rent control law came from pro- tection against rent increases and transfers.18 Respectively, protection against rent increases constituted 44.2% of the total beneﬁt and transfers constituted 30.2% of the total. Lower moving costs, both ﬁxed and variable, were 13.5% of the total. Increased neighborhood capital constituted only small fraction of the total beneﬁt at 1.2%. The welfare beneﬁts from increased amenity values were negligible. Interestinly, we ﬁnd increased utility from the utility value of one’s idosyncratic preference equal to 11.2% of the welfare gain. This likely due to the fact that we found some low neighborhood capital houseohlds were more likley to move due to rent control, allowing them to over come moving costs and live in a location that best suites their idiosyncratic preference.

The beneﬁts of the rent control expansion were smaller for younger households, although still large. That they are smaller is consistent with our estimate that younger households receive larger idiosyncratic shocks, which leads to more frequent moving and thus smaller beneﬁts from rent control protections. Younger households are also estimated to receive smaller transfers. Cumulative welfare beneﬁts for these households totaled $41,121, reﬂecting an annual average of $2,285. Similar to older households, the beneﬁts were front loaded.

Younger households received cumulative beneﬁts of $32,960 during the 1995-2003 period and cumulative beneﬁts of $8,162 during the 2004-2012 period. Annual averages were $3,662 and $907 respectively.

Also similar to older households, most of the beneﬁts came from protection against rent increases and transfers, constituting 79.6% and 45.4% respectively over the total period.

The fraction due to moving costs is much smaller for younger households, at only 8%.

Note this reinforces the idea that, due to a higher variance if idiosyncratic shocks, younger 18The model assumes that all observed moves are rational choices. The transfers we estimate are those which rationalize the observed empirical frequencies. It is possible that some of the moves we see in the data are forced evictions, rather than the result of negotiations between landlords and tenants over monetary compensation. To the extent that this is the case, our welfare beneﬁts from transfer payments over overstated.

However, even in the extreme case where the welfare beneﬁts from transfers are zero, the beneﬁts from protection against rent increases would still be large. 39 households optimally choose to move more often. The fraction due to neighborhood capital is once again small, constituting just 2.6% for the average. Welfare beneﬁts due to increased amenity values now reﬂect a small, but non-negligible, fraction of the total beneﬁt at 2.6%.

Finally, the young face a substantial welfare loss due to living in places that are worse matches to their idiosyncratic preference under rent control, equal to -37.2%. This reﬂects that to stay in one’s apartment to beneﬁt from below market rents, one must give up living in the best apartment and location that suites one’s preferences. Our estiamtes shows that idosyncratice preference variaince is higher for the young, making giving up the match value a larger sacriﬁce.

We aggregate these numbers over the entire population of renters impacted by the rent control law. The aggregate welfare beneﬁts are very large. Older households received a cumulative beneﬁt of $4.440 billion dollars over the entire period, while younger households received a cumulative beneﬁt of $2.64 billion dollars. Across the entire population, the aggregate beneﬁt was $7.085 billion dollars, reﬂecting an annual average of $394 million dollars. Note also that these welfare numbers are only for the 1994 population impacted by the rent control expansion. It does not take into account the welfare beneﬁts for renters who moved into the impacted properties in later years, which presumably were also quite large.

6.2 General Equilibrium Welfare Impact of Reduced Supply We ﬁnally turn to evaluating the GE welfare impact of the landlord supply response. Intu- itively, since landlords reduced supply in response to the 1994 law, as was shown in Section

4.2, average San Francisco rents were higher than they otherwise would have been. Using our structural framework, we quantify the magnitude of this cost.

6.2.1 Derivations
We evaluate the welfare impact relative to the 1993 steady state, prior to the introduction of the law change. Aggregate welfare in this steady state is given by:
40 ∑
j
Nj ln
⎛
⎝ ∑
x∈{S}∪J
exp(v(x,j))
⎞
⎠,
where Nj is the number of people living in neighborhoodj. Note that the state variable now does not include rent control status since we are consider the pre-law steady state. Suppose that the law raises rents in zipcode j by San Francisco by a proportional amount equal to dlnR
j. Using standard calculations, we ﬁnd that the local welfare impact of a change in rents is given by:
∑
j
Nj
∑
x
p(x|j)
∑
k
∂v (x,j)
∂lnRk
dlnRk, (16)
where p(x|j) are the pre-law conditional choice probabilities To compute this quantity we thus need to calculate∂v (x,j)/dlnRk for all j, x, and k ∈J and we need to determine the zipcode level rent response to the measured reduced form supply reduction.

Steady-state in the model is characterized by the equation:
∀j : Nj (1−p(S|j)−p(j|j)) =
∑
j′̸=j
Nj′p(j|j′). (17)
This simply says that, in steady state, the number of renters ﬂowing out of neighborhood j must be equal to the number of renters ﬂowing into neighborhoodj. We now assume that the supply decrease is the same proportionally in each zipcode. Since small multifamily housing constituted 44% of 1994 non rent-controlled housing stock, our reduced form results indicate that rental supply in San Francisco decreased by 6 percent. Letting dlnN j/dΦ denote the
supply response, where Φ is simply a convenient notation indicating the impact of the law, we have
dlnNj
dΦ = dlnNSF
dΦ = −.06 for all j in SF
We determine how much rents have to change by in the new long-run steady state given this 41 supply response. Taking a derivative of equation (17) with respect to Φ gives:
dlnNj
dΦ Nj
⎛
⎝1−
∑
x∈{S,j}
p(x|j)
⎞
⎠−Nj
∑
x∈{S,j}
dp(x|j)
dΦ =
∑
j′̸=j′
[dlnNj′
dΦ Nj′p(j|j′)+ Nj′
dp(j|j′)
dΦ
]
,
(18)
for all j.

Now, in steady state, the conditional probabilities are given by:
p(x|j)= exp(v(x,j))∑
x′exp(v(x′,j)).

So:
dp(x|j)
dΦ =
∑
k
∂p(x|j)
∂lnRk
dlnRk
dΦ (19)
=
∑
k
p(x|j)
(
∂v (x,j)
∂lnRk
−
∑
x′
p(x′|j) ∂v (x′,j)
∂lnRk
)
dlnRk
dΦ .

To ﬁnish the calculation, we therefore need to determine ∂v (x,j)/∂lnRk. With these in place, we can plug equation (19) into equation (18) and solve the resulting system of equations for the rent responses dlnRk/dΦ.

We note that in steady-state:
v(x,j)= u(x,j)+ βln
(∑
x′
exp(v(x′,j (x)))
)
Taking derivatives with respect to log rents, we get:
∂v (x,j)
∂lnRk
= γexp(Rj)Rj1[j(x)= k]+ β
∑
x′
p(x′|j(x)) ∂v (x′,j (x))
∂lnRk
.

This is a system of equations which can be numerically solved for the partial derivatives. The system for young renters is similar, but takes into account the possibility of transitioning to a mature renter.
42 6.2.2 Results
We ﬁnd that 6% decrease in housing supply led to 7% increase in rental prices. These caused an aggregate welfare loss to renters of $5 Billion. This is almost as large as the beneﬁts accrued by the lucky beneﬁciaries of rent control. These GE welfare losses only account for the increased rents due to the decreased supply of housing. We also found that rent control incentivized landlords to invest in their properties by renovating and building new housing, as well as converting to owner occupancy. These eﬀects likely attached higher income tenants to San Francisco and further raised rents. It appears that the GE losses from the landlords’ response to rent control essentially completely undoes the gains accrued to the households that were lucky enough to receive rent control in 1994. 7 Conclusion
In this paper, we study the welfare impacts of rent control on its tenant beneﬁciaries as well as the welfare impacts of landlords’ responses. To answer this question, we exploit a unique rent control expansion in San Francisco in 1994 that suddenly provided rent control protections for small multifamily housing built prior to 1980. By combining new panel micro data on individual migration decisions with detailed assessor data on individual SF parcels we get quasi-experimental variation in the assignment of rent control at both the individual tenant level and at the parcel level.

We ﬁnd that, on average, in the medium to long term the beneﬁciaries of rent control are between 10 and 20 percent more likely to remain at their 1994 address relative to the control group. These eﬀects are signiﬁcantly stronger among older households and among households that have already spent a number of years at their current address. On the other hand, individuals in areas with quickly rising rents and with few years at their 1994 address are less likely to remain at their current address, consistent with the idea that landlords try to remove tenants when the reward is high, through either eviction or negotiated payments. 43 We ﬁnd that landlords actively respond to the imposition of rent control by converting their properties to condos and TICs or by redeveloping the building in such as a way as to exempt it from the regulations. In sum, we ﬁnd that impacted landlords reduced the supply the available rental housing by 15 percent. Consistent with this evidence, we ﬁnd that there was a 20 percent decline in the number of renters living in impacted buildings, relative to 1990-1994 levels, and a 30 percent decline in the number of renters living in units protected by rent control.

We develop a dynamic, structural model of neighborhood choice to translate our reduced form impacts into welfare impacts. A key contribution of the paper is to show how quasi- experimental evidence can be leveraged to estimate to dynamic discrete choice model. We ﬁnd that rent control oﬀered large beneﬁts to impacted tenants during the 1995-2012 period, averaging between $2200 and $6600 per person each year, with aggregate beneﬁts totaling over $393 million annually. Over the entire period, tenants received cumulative beneﬁts of around $7.1 billion. We ﬁnd that most of these beneﬁts came from protection against rent increases and transfer payments from landlords. However, we ﬁnd losses to all renters of $5 billion due to rent control’s eﬀect on decreasing the rental housing and raising market rents.

These results highlight that forcing landlords to provided insurance against rent increases leads to large losses to tenants. If society desires to provide social insurance against rent increases, it would be more desirable to oﬀer this subsidy in the form of a government subsidy or tax credit. This would remove landlords’ incentives to decrease the housing supply and could provide household with the insurance they desire. A point of future research would be to design an optimal social insurance program to insure renters against large rent increases. 44 References
Arcidiacono, Peter and Paul B. Ellickson , “Practical Methods for Estimation of Dy- namic Discrete Choice Models,” Annual Review of Economics , 2011, 3 (1), 363–394. and Robert A. Miller , “Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity,” Econometrica, November 2011, 79 (6), 1823–1867.

Autor, David H, Christopher J Palmer, and Parag A Pathak , “Housing Market Spillovers: Evidence from the End of Rent Control in Cambridge, Massachusetts,”Journal of Political Economy , 2014, 122 (3), 661–717.

Bayer, Patrick, Robert McMillan, Alvin Murphy, and Christopher Timmins ,“ A Dynamic Model of Demand for Houses and Neighborhoods,” Econometrica, May 2016, 84 (3), 893–942.

Bishop, Kelly C. and Alvin D. Murphy , “Estimating the Willingness to Pay to Avoid Violent Crime: A Dynamic Approach,” American Economic Review , May 2011, 101 (3), 625–629.

Davis, Morris A., Jess Gregory, Daniel A. Hartley, and Kegon Teng Kok Tan , “Neighborhood Choices, Neighborhood Eﬀects and Housing Vouchers,” 2017.

Downs, Anthony , “Residential Rent Controls,” Washington, DC: Urban Land Institute , 1988.

Early, Dirk W. , “Rent Control, Rental Housing Supply, and the Distribution of Tenant Beneﬁts,” Journal of Urban Economics , September 2000, 48 (2), 185–204.

Glaeser, Edward L and Erzo FP Luttmer , “The Misallocation of Housing under Rent Control,” The American Economic Review , 2003, 93 (4), 1027–1046.

Gyourko, Joseph and Peter Linneman , “Equity and Eﬃciency Aspects of Rent Control:

An Empirical Study of New York City,”Journal of urban Economics , 1989, 26 (1), 54–74. and , “Rent Controls and Rental Housing Quality: A Note on the Eﬀects of New York City’s Old Controls,” Journal of Urban Economics , May 1990, 27 (3), 398–409.

Hotz, V. Joseph and Robert A. Miller , “Conditional Choice Probabilities and the Estimation of Dynamic Models,” The Review of Economic Studies , 1993, 60 (3), 497–529.

Kasarda, John D. and Morris Janowitz , “Community Attachment in Mass Society,” American Sociological Review, 1974, 39 (3), 328–339.

Kennan, John and James R. Walker , “The Eﬀect of Expected Income on Individual Migration Decisions,” Econometrica, January 2011, 79 (1), 211–251. 45 Moon, Choon-Geol and Janet G. Stotsky , “The Eﬀect of Rent Control on Housing Quality Change: A Longitudinal Analysis,” Journal of Political Economy , December 1993, 101 (6), 1114–1148.

Murphy, Alvin, “A Dynamic Model of Housing Supply,” SSRN Scholarly Paper ID 2200459, Social Science Research Network, Rochester, NY February 2017.

Olsen, Edgar O , “An Econometric Analysis of Rent Control,”Journal of Political Economy, 1972, 80 (6), 1081–1100.

Scott, Paul T. , “Dynamic Discrete Choice Estimation of Agricultural Land Use,” Toulouse School of Economics Working Paper , 2013, 526.

Sims, David P , “Out of Control: What Can We Learn from the End of Massachusetts Rent Control?,” Journal of Urban Economics , 2007, 61 (1), 129–151. , “Rent Control Rationing and Community Composition: Evidence from Massachusetts,” The BE Journal of Economic Analysis & Policy , 2011, 11 (1). 46 Table 1: Sample Characteristics for Individual Regressions for Multi-Family Residence (2-4 Units)
Mean S.D
Demographics
Age in 1993 38.584 10.707
Male 0.504 0.500
Is Landlord 0.144 0.352
Residency
Living in SF 0.643 0.479
Living in Zipcode of Treated Address 0.443 0.497
Living in Treated Address 0.375 0.484
Years at 1993 Address 6.761 4.911
Years at Current Address 1.659 0.597
Observations 1508247
Notes: Sample consists of all tenants and landlords between 20 and 65 years old living in SF in 1993 and small multi-family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a landlord living there in 1993, we include it into the treatment group for rent control. Table reports the mean, standard deviation and median of demographic characteristics and various dependent variables during 1990− 2016.
47 Table 2: Sample Characteristics for Multi-Family Properties (2-4 Units) Mean S.D
Residency
Is Vacant 0.103 0.304
Population
Population/Avg Pop 90-94 2.076 3.728
Renters/Avg Pop 90-94 1.541 3.276
Renters in Covered by Rent-Control/Avg Pop 90-94 1.311 1.808 Renters in Redeveloped Buildings/Avg Pop 90-94 0.108 0.679 Owners/Avg Pop 90-94 0.535 1.467
Permits
Cumulative Add/Alter/Repair per Unit 0.256 0.487
Ever Received Add/Alter/Repair 0.336 0.472
Observations 724037
Notes: Sample consists of all parcels that are multi-family residence with fewer than four units in SF that were built during 1900− 1990. If a building associated with a parcel is constructed post 1993 and we observe someone living there before 1993, we include it into the treatment group for rent control. Table reports the mean, standard deviation and median of various dependent variables during 1990− 2016. 48 Table 3: Treatment Eﬀect for Tenants of Multi-Family Residence (2-4 Units) (1) (2) (3)
In SF Same Zip Same Address
Treat×Period
1994-1999 0.0200 ∗∗ 0.0226∗∗∗ 0.0218∗∗∗
(0.0081) (0.0087) (0.0083)
2000-2004 0.0451 ∗∗∗ 0.0355∗∗∗ 0.0354∗∗∗
(0.0115) (0.0104) (0.0088)
Post 2005 0.0366 ∗∗∗ 0.0302∗∗∗ 0.0147∗∗
(0.0109) (0.0084) (0.0063)
Control Mean 1994−1999 0.7641 0.5971 0.5410
Control Mean 2000−2004 0.5138 0.2672 0.1827
Control Mean Post 2005 0.4346 0.1801 0.1135
Adjusted R
2 0.600 0.630 0.655
Observations 1251747 1251747 1251747
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi-family residences that were built during 1900 − 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Table reports the mean of dependent variables for the control group during 1990 − 1994, 2000 − 2004 and post-2005. Standard errors are clustered at the person level. Signiﬁcance levels: * 10%,* * 5%, *** 1%. 49 Table 4: Model Estimates
A. Parameter Estimates in 2010 Dollars
St Dev of Logit Shocks Tenant Buyouts Moving Costs Neighborhood Capital Young Renters 7441.178*** Log Below Market Rent 1.631*** Fixed Cost 42626.11*** Young Renters 265.795*** (1278.596) (Young Renters) (0.092) (Young Renters) (4776.017) (52.9889) Old Renters 6496.264*** Log Below Market Rent 1.404*** Fixed Cost 38987.65*** Old Renters 291.781*** (995.629) (Old Renters) (0.101) (Old Renters) (4005.167) (47.4294) Years in Zipcode 164.222*** MC per Ln Mile 11426.11***
(Young Renters) (107.696) (Young Renters) (1816.79)
Years in Zipcode 141.439*** MC per Ln Mile 10066.49***
(Old Renters) (90.99) (Old Renters) (1437.622)
Old Renter-Direct eﬀect 70702.05*** ΔMC wrt Yrs in Zip -415.607*** (12339.43) (Young Renters) (74.24046)
ΔMC wrt Yrs in Zip -357.6618***
(Old Renters) (57.12502)
B.Demand Semi-Elasticities to Remain in Home with respect to 1 year Temporary Changes Log Rent Tenant Buyouts Moving Costs Neighborhood Capital Young Renters -0.210*** Log Below Market Rent -0.327*** Fixed Cost 0.580*** Young Renters 0.0019*** (0.040) (Young Renters) (0.068) (Young Renters) (0.003) (0.00007) Old Renters -0.244*** Log Below Market Rent -0.327*** Fixed Cost 0.580*** Old Renters 0.0024*** (0.041) (Old Renters) (0.068) (Old Renters) (0.003) (0.00008) Years in Zipcode -0.0012 MC per Mile 0.095***
(Young Renters) (0.0008) (Young Renters) (0.005)
Years in Zipcode -0.0012 MC per Mile 0.096***
(Old Renters) (0.0008) (Old Renters) (0.005)
Old Renter-Direct eﬀect -0.583*** ΔMC wrt Yrs in Zip -0.003*** (0.0082) (Young Renters) (-0.0002)
ΔMC wrt Yrs in Zip -0.003***
(Old Renters) (-0.0002)
50 Table 5: Welfare Eﬀects of 1994 Rent-Controlled Cohort in 2010 Dollars A. Old Residents (Age 40+)
1995-2003 2004-2012 1995-2012
Cumulative Per Year Share Cumulative Per Year Share Cumulative Per Year Share Rent 30,285 3,365 40.6% 22,644 2,516 50.2% 52,929 2,940 44.2% Payoﬀ 25,560 2,840 34.3% 10,511 1,168 23.3% 36,071 2,004 30.2% Neighborhood Capital 812 90 1.1% 583 65 1.3% 1,395 77 1.2% Fixed Moving Cost 8,125 903 10.9% 1,352 150 3.0% 9,477 526 7.9% Distance of Moves 3,857 429 5.2% 2,827 314 6.3% 6,684 371 5.6% Amenity -42 -5 -0.1% -276 -31 -0.6% -318 -18 -0.3%
Match Value 5,918 658 7.9% 7,470 830 16.6% 13,388 744 11.2% Total per Person 74,514 8,279 45,111 5,012 119,625 6,646 B. Young Residents (Age 20-39)
1995-2003 2004-2012 1995-2012
Cumulative Per Year Share Cumulative Per Year Share Cumulative Per Year Share Rent 20,782 2,309 63.1% 11,940 1,327 146.3% 32,722 1,818 79.6% Payoﬀ 12,537 1,393 38.0% 6,113 679 74.9% 18,650 1,036 45.4% Neighborhood Capital 431 48 1.3% 750 83 9.2% 1,181 66 2.9% Fixed Moving Cost 3,741 416 11.3% -1,643 -183 -20.1% 2,098 117 5.1% Distance of Moves 1,655 184 5.0% -949 -105 -11.6% 706 39 1.7% Amenity 243 27 0.7% 829 92 10.2% 1,073 60 2.6%
Match Value -6,428 -714 -19.5% -8,879 -987 -108.8% -15,308 -850 -37.2% Total per Person 32,960 3,662 8,162 907 41,121 2,285
C. SF Aggregate
1995-2003 2004-2012 1995-2012
Cumulative Per Year Share Cumulative Per Year Share Cumulative Per Year Share Old 2,766,989,545 307,443,283 56.6% 1,675,156,256 186,128,473 76.2% 4,442,145,875 246,785,882 62.7% Young 2,118,588,225 235,398,692 43.4% 524,611,003 58,290,111 23.8% 2,643,199,099 146,844,394 37.3% All 4,885,577,770 542,841,975 2,199,767,259 244,418,584 7,085,344,974 393,630,276 51 Figure 1: Historical Trend of Nominal Median Rent
10 100 1000 10000
Nominal Median Rent
1950 1960 1970 1980 1990 2000 2010
Year
52 Figure 2: Geographic Distribution of Treated and Control Buildings in San Francisco 53 Figure 3: Treatment Eﬀect for Tenants in Multi-Family Residence (2-4 Units) (a) Staying at Same Address
-.2 -.1 0 .1 .2 .3 .4 .5
Log Median Rent (Detrended)
-.02
0 .02
.04
.06
Treatment Effect: Same Address
1990 1995 2000 2005 2010 2015
Same Address Real Log Median Rent (Detrended)
Corr = 0.494
(b) Staying in San Francisco
-.2 -.1 0 .1 .2 .3 .4 .5
Log Median Rent (Detrended)
-.02
0 .02
.04
.06
Treatment Effect: In SF
1990 1995 2000 2005 2010 2015
In SF Real Log Median Rent (Detrended)
Corr = 0.784
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Standard errors are clustered at the person level. Signiﬁcance levels: * 10%,* * 5%, *** 1%. 54 Figure 4: Heterogeneity by Age and Tenure in Treatment Eﬀect for Tenants of Multi-Family Residence (2-4 Units)
.026
.01
-.032
.047
Young & High Turnover
Young & Low Turnover
Old & High Turnover
Old & Low Turnover
-.1 -.05 0 .05 .1
Same Address
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. We sort the sample by age group. The young group refers to residents who were aged 20-39 in 1993 and the old group are residents who were aged 40-65 in 1993. We also cut the data by number of years the individual has been living at their 1993 address. We deﬁne a "low turnover" group of individuals who had been living at their 1993 address for greater than or equal to four years and a "high turnover" group of individuals who had been living at their address for less than four years. The average treatment eﬀects in the post-1994 period along with 90% CI are plotted. Standard errors are clustered at the person level. 55 Figure 5: Heterogeneity by Rent Appreciation, Age and Tenure in Treatment Eﬀect for Tenants of Multi-Family Residence (2-4 Units)
(a) High Rent Appreciation, Young and High Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
(b) High Rent Appreciation, Young and Low Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
(c) High Rent Appreciation, Old and High Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
(d) High Rent Appreciation, Old and Low Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. We ﬁrst individuals into two groups by whether their 1993 census tract experienced above or below median rent appreciation during 1990-2000. We further sort the sample by age group and tenure following the same deﬁnitions as in Figure

4. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the person level. 56 Figure 6: Heterogeneity by Rent Appreciation, Age and Tenure in Treatment Eﬀect for Tenants of Multi-Family Residence (2-4 Units)
(a) Low Rent Appreciation, Young and High Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
(b) Low Rent Appreciation, Young and Low Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
(c) Low Rent Appreciation, Old and High Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
(d) Low Rent Appreciation, Old and Low Turnover
-.25
-.15
-.05
.05
.15
Same Address
1990 1995 2000 2005 2010 2015
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. We ﬁrst individuals into two groups by whether their 1993 census tract experienced above or below median rent appreciation during 1990-2000. We further sort the sample by age group and tenure following the same deﬁnitions as in Figure

4. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the person level. 57 Figure 7: Treatment Eﬀect at the Census Tracts level for Tenants of Multi-Family Residence (2-4 Units) – Dynamic Version
-100
-50
0 -4000
-3000
-2000
-1000
0 -.03
-.02
-.01
0 1990 2000 2010 2011 2012 2013
Median Rent
Median Household Income
Share College
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Median rent, median household income and share of residents with college education and above are measured in the census tract that an individual is living in a given year. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the person level.
58 Figure 8: Treatment Eﬀect at the Census Tracts level for Tenants of Multi-Family Residence (2-4 Units) – Dynamic Version
-30000
-20000
-10000
0 10000
0 .002
.004
.006
0 .005
.01
.015
1990 2000 2010 2011 2012 2013
Median House Value
Share Unemployed
Share in Poverty
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Median house value, share of unemployed and share of residents below poverty line are measured in the census tract that an individual is living in a given year. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the person level.
59 Figure 9: Treatment Eﬀect at the Census Tracts level for Tenants of Multi-Family Residence (2-4 Units) – Static Version
-50
0 50
-4000
-2000
0 2000
0 .02
.04
.06
1990 2000 2010 2011 2012 2013
Median Rent
Median Household Income
Share College
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Median rent, median household income and share of residents with college education and above are measured in the census tract that an individual is living in a given year for the control group, and are measured in their 1993 census tract for the treated group. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the person level.
60 Figure 10: Treatment Eﬀect at the Census Tracts level for Tenants of Multi-Family Residence (2-4 Units) – Static Version
0 50000
100000
150000
-.01
-.005
0 .005
0 .005
.01
.015
.02
1990 2000 2010 2011 2012 2013
Median House Value
Share Unemployed
Share in Poverty
Notes: Sample consists of all tenants between 20 and 65 years old living in SF in 1993 and in small multi- family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Median house value, share of unemployed and share of residents below poverty line are measured in the census tract that an individual is living in a given year for the control group, and are measured in their 1993 census tract for the treated group. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the person level.
61 Figure 11: Treatment Eﬀect for Multi-Family Residence (2-4 Units) (a) Population/Average Population 1990-1994
-.4
-.3
-.2
-.1
0 .1
Population/Avg Pop 90-94
1990 1995 2000 2005 2010
(b) Renters/Average Population 1990-1994
-.4
-.3
-.2
-.1
0 .1
Renters/Avg Pop 90-94
1990 1995 2000 2005 2010
(c) Owners/Average Population 1990-1994
-.4
-.3
-.2
-.1
0 .1
Owners/Avg Pop 90-94
1990 1995 2000 2005 2010
(d) Vacancy
-.4
-.3
-.2
-.1
0 .1
Vacant
1990 1995 2000 2005 2010 2015
Notes: Sample consists of all small multi-family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the parcel level.
62 Figure 12: Treatment Eﬀect for Multi-Family Residence (2-4 Units) (a) Renters in Rent-Controlled Buildings/Average
Population 1990-1994
-.4
-.3
-.2
-.1
0 .1
Renters in Rent-Controlled Buildings
1990 1995 2000 2005 2010
(b) Renters in Redeveloped Buildings/Average
Population 1990-1994
-.4
-.3
-.2
-.1
0 .1
Renters in Redeveloped Buildings
1990 1995 2000 2005 2010
(c) Conversion
0 .02
.04
.06
.08
.1
Conversion
1990 1995 2000 2005 2010 2015
(d) Accumulative Add/Alter/Repair per Unit
-.02
0 .02
.04
.06
.08
Accumulative Add/Alter/Repair per Unit
1990 1995 2000 2005 2010 2015
Notes: Sample consists of all small multi-family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the parcel level.
63 Figure 13: Heterogeneity by Rent Appreciation in Treatment Eﬀect for Multi-Family Resi- dence (2-4 Units)
(a) Conversion, High Rent Appreciation
0 .05
.1
Conversion
1990 1995 2000 2005 2010 2015
(b) Conversion, Low Rent Appreciation
0 .05
.1
Conversion
1990 1995 2000 2005 2010 2015
(c) Accumulative Add/Alter/Repair per Unit, High
Rent Appreciation
-.02
0 .02
.04
.06
.08
.1
Accumulative Add/Alter/Repair per Unit
1990 1995 2000 2005 2010 2015
(d) Accumulative Add/Alter/Repair per Unit, Low
Rent Appreciation
-.02
0 .02
.04
.06
.08
.1
Accumulative Add/Alter/Repair per Unit
1990 1995 2000 2005 2010 2015
Notes: Sample consists of all small multi-family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. We sort our sample by whether their 1993 census tract experienced above or below median rent appreciation during 1990-2000. The treatment eﬀects along with 90% CI are plotted. Standard errors are clustered at the parcel level.
64 Figure 14: Average Annual Tenant Buyouts
65 Figure 15: Annual Tenant Buyouts by Zipcode
A Appendix Tables
66 Table A.1: Treatment Eﬀect for Multi-Family Residence (2-4 Units) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Permanently
Vacant Vacant Population/
Avg Pop 90-94
Renters/
Avg Pop 90-94
Renters in
Rent-Controlled Buildings/
Avg Pop 90-94
Renters in
Redeveloped Buildings/
Avg Pop 90-94
Owners/
Avg Pop 90-94 Conversion
Accumulative
Add/Alter/Repair
per Unit
Ever Received
Add/Alter/Repair
Treat×Period
1994-1999 -0.0024 -0.0085 -0.0329 -0.0342 -0.0434 0.0005 0.0013 0.0100 ∗∗∗ -0.0043 0.0140 ∗ (0.0046) (0.0095) (0.0604) (0.0472) (0.0481) (0.0084) (0.0299) (0.0032) (0.0085) (0.0081) 2000-2005 0.0048 -0.0064 -0.0791 -0.1059 ∗ -0.1516∗∗ 0.0253 0.0269 0.0384 ∗∗∗ 0.0234∗ 0.0413∗∗∗ (0.0067) (0.0114) (0.0814) (0.0638) (0.0654) (0.0176) (0.0394) (0.0045) (0.0123) (0.0111) Post 2006 0.0084 -0.0076 -0.0642 -0.1453 ∗ -0.2457∗∗∗ 0.0717∗∗∗ 0.0811∗∗ 0.0793∗∗∗ 0.0459∗∗∗ 0.0552∗∗∗ (0.0094) (0.0116) (0.0933) (0.0747) (0.0773) (0.0225) (0.0409) (0.0061) (0.0144) (0.0130) Control Mean 1994−1999 0.0293 0.0800 1.8291 1.3540 1.3395 0.0232 0.4752 0.3360 0.1825 0.2352 Control Mean 2000−2005 0.0469 0.0968 2.1917 1.6278 1.5978 0.0502 0.5639 0.3460 0.2473 0.3066 Control Mean Post 2006 0.1035 0.1137 2.4287 1.8338 1.7659 0.0965 0.5949 0.3667 0.2976 0.3624 Adjusted R
2 0.565 0.354 0.600 0.569 0.555 0.404 0.603 0.747 0.803 0.763 Observations 724037 724037 643589 643589 643589 643589 643589 769181 706633 724037 Notes: Sample consists of all small multi-family residences that were built during 1900− 1990. If a building is constructed post 1993 and we observe a tenant living there in 1993, we include it into the treatment group for rent control. Table reports the mean of dependent variables for the control group during 1994− 1999, 2000− 2005 and post-2006. Standard errors are clustered at the parcel level. Signiﬁcance levels: * 10%,* * 5%, *** 1%. 67 Table A.2: Model Estimates
A. Model Parameter Estimates in Exp(Rent) Units
St Dev of Logit Shocks Tenant Buyouts Moving Costs Neighborhood Capital Young Renters 2.55*** Log Below Market Rent -17.581*** Fixed Cost 25.146*** Young Renters 0.1292*** (0.562) (Young Renters) (1.398) (Young Renters) (5.551) (0.0298) Old Renters 2.271*** Log Below Market Rent -15.658*** Fixed Cost 22.377*** Old Renters 0.1329*** (0.453) (Old Renters) (1.283) (Old Renters) (4.444) (0.0258) Years in Zipcode 0.671*** MC per Mile 4.129***
(Young Renters) (0.152) (Young Renters) (0.874)
Years in Zipcode 0.597*** MC per Mile 3.685***
(Old Renters) (0.122) (Old Renters) (0.706)
Old Renter-Direct eﬀect 4.625*** ΔMC wrt Yrs in Zip -0.1258*** (0.927) (Young Renters) (0.02515)
ΔMC wrt Yrs in Zip -0.112***
(Old Renters) (0.02029)
Notes: Model parameter estimates in the units of exponential value of monthly rent divided by $1, 500. 68 Figure A.1: Population Age 18 and above: 1990 Census 0 2000 4000 6000 8000
Infutor Population 18+
0 2000 4000 6000 8000
Census Population 18+
95% CI Fitted values
45 degree
β = 0.442 (0.026)
R
2 = 0.692
Obs = 127
Notes: The size of marker is proportional to the population of 18 and over in the Census in each census tract.

The ﬁtted line is by weighted least square using the population of 18 and over in the Census as weights.

Figure A.2: Population Age 18 and above: 2000 Census
0 2000 4000 6000 8000 10000
Infutor Population 18+
0 2000 4000 6000 8000
Census Population 18+
95% CI Fitted values
45 degree
β = 1.145 (0.029)
R
2 = 0.898
Obs = 175
Notes: The size of marker is proportional to the population of 18 and over in the Census in each census tract.

The ﬁtted line is by weighted least square using the population of 18 and over in the Census as weights. 69 Figure A.3: Age of Occupied Housing: 1990 Census
(a) Built 1970 to 1990: 1990 Census0 .2 .4 .6 .8 1
Infutor Fraction Built 1970-1990
0 .2 .4 .6 .8 1
Census Fraction Built 1970-1990
95% CI Fitted values
45 degree
β = 0.639 (0.046)
R
2 = 0.667
Obs = 100
(b) Built 1950 to 1969: 1990 Census0 .2 .4 .6 .8 1
Infutor Fraction Built 1950-1969
0 .2 .4 .6 .8
Census Fraction Built 1950-1969
95% CI Fitted values
45 degree
β = 0.928 (0.046)
R
2 = 0.807
Obs = 100
(c) Built 1940 to 1949: 1990 Census0 .2 .4 .6 .8
Infutor Fraction Built 1940-1949
0 .2 .4 .6
Census Fraction Built 1940-1949
95% CI Fitted values
45 degree
β = 1.111 (0.035)
R
2 = 0.911
Obs = 100
(d) Built 1939 or earlier: 1990 Census0 .2 .4 .6 .8 1
Infutor Fraction Built 1939 and earlier
0 .2 .4 .6 .8
Census Fraction Built 1939 and earlier
95% CI Fitted values
45 degree
β = 1.024 (0.040)
R
2 = 0.872
Obs = 100
Notes: The size of marker is proportional to the number of occupied housing units in each census tract. The ﬁtted line is by weighted least square using the number of occupied housing units as weights. 70 Figure A.4: Age of Occupied Housing: 2000 Census
(a) Built 1980 to 2000: 2000 Census
0 .2 .4 .6 .8 1
Infutor Fraction Built 1980-2000
0 .2 .4 .6 .8
Census Fraction Built 1980-2000
95% CI Fitted values
45 degree
β = 0.813 (0.024)
R
2 = 0.876
Obs = 159
(b) Built 1960 to 1979: 2000 Census
0 .2 .4 .6 .8 1
Infutor Fraction Built 1960-1979
0 .2 .4 .6 .8 1
Census Fraction Built 1960-1979
95% CI Fitted values
45 degree
β = 1.083 (0.036)
R
2 = 0.853
Obs = 159
(c) Built 1950 to 1959: 2000 Census
0 .2 .4 .6 .8
Infutor Fraction Built 1950-1959
0 .2 .4 .6
Census Fraction Built 1950-1959
95% CI Fitted values
45 degree
β = 0.955 (0.049)
R
2 = 0.711
Obs = 159
(d) Built 1940 to 1949: 2000 Census
-.2 0 .2 .4 .6 .8
Infutor Fraction Built 1940-1949
0 .2 .4 .6
Census Fraction Built 1940-1949
95% CI Fitted values
45 degree
β = 1.323 (0.042)
R
2 = 0.863
Obs = 159
(e) Built 1930 or earlier: 2000 Census
0 .2 .4 .6 .8 1
Infutor Fraction Built 1939 and earlier
0 .2 .4 .6 .8
Census Fraction Built 1939 and earlier
95% CI Fitted values
45 degree
β = 1.144 (0.036)
R
2 = 0.863
Obs = 159
Notes: The size of marker is proportional to the number of occupied housing units in each census tract.

The ﬁtted line is by weighted least square using the number of occupied housing units as weights. 71 Figure A.5: Ownership Rate at Person Level: 1990 Census 0 .2 .4 .6 .8 1
Infutor Ownership Rate
0 .2 .4 .6 .8 1
Census Ownership Rate
95% CI Fitted values
45 degree
β = 0.432 (0.014)
R
2 = 0.910
Obs = 100
Notes: Plot shows the ownership rate at the person level from our Infutor sample in 1990 against the ownership rate of occupied housing units in 1990 Census. The size of marker is proportional to the number of occupied housing units in each census tract. The ﬁtted line is by weighted least square using the number of occupied housing units as weights.

Figure A.6: Ownership Rate at Person Level: 2000 Census 0 .2 .4 .6 .8 1
Infutor Ownership Rate
0 .2 .4 .6 .8 1
Census Ownership Rate
95% CI Fitted values
45 degree
β = 0.562 (0.011)
R
2 = 0.939
Obs = 159
Notes: Plot shows the ownership rate at the person level from our Infutor sample in 1990 against the ownership rate of occupied housing units in 1990 Census. The size of marker is proportional to the number of occupied housing units in each census tract. The ﬁtted line is by weighted least square using the number of occupied housing units as weights.
72

Pasadena City CouncilAugust 8, 2022

Pasadena City Council
August 8, 2022