Limitations

QSMs are inherently quite limited. The authors of the QSM which I am building upon (the Cities Spatial Model) name several considerations which limit whole-cloth application of this methodology to real-world cities. They mention(Cole et al. 2024):

• A lack of a time component to the results. My findings therefore represent an eventual “settling point” once the imbalances generated by the Midline are internalized in the price of land and housing as well as the distribution of workers and households across the metropolitan area. One can assume that it will take multiple decades for this process to be fully realized.

• Like most basic economic models, this QSM has a representative agent, meaning that all individuals are assumed to have the same basic preferences. In real life, this is obviously a gross simplification. For the purposes of high-level modelling, however, it may make more sense to assume the vast majority of individuals are broadly trying to get the most they can out of a limited salary or wage and will move wherever they assess has the highest economic promise and amenities within the constraints of their budget.

• This model assumes a single production sector, meaning that all industries combine labor and capital in similar ways. This allows us to generate a homogeneous measure of total factor production (TFP), but it is not terribly realistic. Consider the measures of productivity below as a composite of the various economic activities present in the Cleveland area.

• This model assumes full employment and freedom of movement. Given Cleveland’s history of prolonged, elevated unemployment, as well as the challenges which segregation and information asymmetries have posed, these assumptions also seem unrealistic, though it should be noted that unemployment in the Cleveland-Elyria MSA is now in line with national averages (U. S. Bureau of Labor Statistics, n.d.) and that many areas which were hitherto off-limits to Black Clevelanders due to racial covenants and other manifestations of systemic racism are now rapidly diversifying. (Keating 1994)

• Finally, as with many classical economic models, this QSM assumes perfect competition and rationality. This assumption lies at the crux of many critiques of quantitative economics, and is worth taking seriously, but at the level of abstraction this model operates at, competition and rationality isn’t far off mark. The market for housing and urban land in the US is by and large a free market, and self-interest is a chief concern of most actors involved.

Why use a QSM despite these limitations? As I have argued, none of these are fatal for the purposes of this back-of-the-napkin report. Furthermore, it is my view that having some sort of grounding scenario is better than none, even if there are obvious flaws. We may answer basic questions regarding the proposal (e.g. Will there be any appreciation in property values? Will there be any population growth?) while also understanding that all exact figures are meant to be interpreted with a grain of salt.

1. Residential Population

I derive residential population by census tract from the 2023 American Community Survey (accessed via IPUMS). (Ruggles et al., n.d.) The population of tracts is heterogeneous across the metropolitan region since they are reapportioned periodically to ensure they average about 4,000 residents, though suburban tracts are generally more populous than urban tracts due to continued depopulation and lagged reapportionment.

2. Workplace Population

The Census Bureau tracks workplace population with its LEHD Origin-Destination Employment Statistics (LODES) survey, the most recent of which was published in 2023. (U. S. Census Bureau, n.d.) Workplace population is far more concentrated than residential population with particular clusters in Downtown, University Circle, along Euclid Avenue, and in suburban industrial/business parks.

3. Area

This was calculated easily by downloading a Census tract shapefile, reprojecting to an Ohio-specific projection, and then using QGIS to determine the area. As one would expect, the largest tracts are in the rural fringes of the metropolitan area while the smallest are in dense urban cores.

4. Floorspace Price per Square Foot

I was able to impute price per square foot (PPSF) by using data from Redfin, a real estate listing website. (Redfin, n.d.) For the purpose of this report, I assume that the relative inter-neighborhood price of residential floorspace is similar to that of commercial and industrial buildings. One could question this assumption, but unfortunately there few public sources of going rates for commercial floorspace in the region. Redfin publishes longitudinal data in various geographies, but not Census tracts. I therefore downloaded the most recent price per square foot data (generally from the first quarter of 2025) for Cleveland area neighborhoods and ZIP codes. Redfin defines “neighborhoods” in a unique and unreliable manner, meaning that determining their boundaries required scraping Redfin and searching raw HTML for Google Polylines, a compact system of storing spatial data. ZIP code geographies were easier to attain and I eliminated those which were almost entirely covered by neighborhoods.

Median PPSF by neighborhood

Median PPSF by ZIP code

Since neighborhoods are generally contained within ZIP code regions, this presented an opportunity to impute more granular data on floorspace prices using a technique called areal weighted interpolation. This involves leveraging discrepancies in areal statistics between overlapping geographies with known population densities to estimate statistics where the geographies do and do not overlap. The way this works is simple: imagine there is a neighborhood completely enclosed within a ZIP code. The number of households in the neighborhood is 500 versus 1000 in the ZIP code as a whole. Suppose we know that average household income is $750 within the neighborhood but $1000 in the ZIP code. We can estimate the average household income in the “remainder” of the ZIP code by solving for \(x\) within the expression \(pop_n*income_n+(pop_z-pop_n)x=pop_z*income_z\). In this example, the average household income in the remainder is $1250.

Using IPUMS, I was able to access block-level (very granular) counts of housing units, which then functioned as my “population” layer. This allowed me to impute (using the method discussed above) PPSF for the ZIP code areas outside of Redfin-identified neighborhoods. It bears noting that Redfin tracks median rather than mean PPSF, a distinction which means that this model assumes property values in a given neighborhood are normally distributed, something which seems more plausible in certain areas than others.

Median PPSF by neighborhood/ZIP code remainder

Instead of performing areal weighted interpolation again, this time with Census tracts, I instead chose to convert average PPSF figures into a point layer and used inverse distance weighted (IDW) interpolation to transform these data into a continuous raster. I chose to do this because the interpolated neighborhood/ZIP code data was sufficiently granular, and market-rate property values generally change gradually, barring a significant gap in the urban fabric (such as a controlled-access highway or a river). With this raster layer I then calculated the mean PPSF per tract. Familiar patterns emerge from a visualization of these data, namely low prices along the East Side corresponding to Cleveland’s most impoverished neighborhoods and higher prices in the direction of Shaker Heights, Lakewood, and other wealthier enclaves.

5. Commute Time Matrix

The final necessary ingredient is a matrix of commute times (ostensibly in minutes) between every possible combination of spatial units. Ideally, there are routing algorithms which could perform these sorts of calculations, but given the number of paths this would involve—\(166*166=27,556\)—it will take a lot of computing power to generate a full matrix. I am working on figuring out how to efficiently carry out this task, but in the meantime I use distance as a proxy, assuming an in-town average driving speed of 30 km/h. This is likely to differ a good deal from actual driving times, as the Cleveland area is connected by highways which hinder movement between adjacent neighborhoods even as they facilitate movement between suburbs and the city center, a dynamic which aggravates the region’s spatial inequalities.

Total Factor Productivity

The first of these is total factor productivity (TFP). In short, TFP is the ratio of outputs to inputs, or how efficiently a given firm, polity, or place combines labor and capital to create value. Generally this is expressed as the value \(A\) which solves the expression (a Cobb-Douglas production function, to be more precise) \(Y=A*K^\alpha*L^\beta\) where \(Y\) is output, \(K\) is capital input, and \(L\) is labor input. IGCities breaks TFP down into two main components: endogenous TFP and exogenous/baseline TFP. The first of these takes into account all factors which shape productivity, including externalities/spillovers generated by adjacent places, such as the knowledge agglomerating around universities or the enhanced access to labor markets provided by highway access. The latter speaks to the “inherent” productivity specific to the place, including infrastructure, capital stock, and local workforce.

The spatial pattern of \(A\) (taking into account externalities) and \(a\) (baseline) are generally similar. Poorer areas on the East Side and rural areas on the margin of the metropolitan area have lower productivity. That being said, subtracting \(a\) from \(A\) demonstrates that spillovers play a crucial role in the enhancing local output in Downtown and along several corridors radiating from the central business district. Interestingly, the model picks up on the presence of key transportation corridors (I-271, I-77, I-90, Euclid Avenue) without these explicitly being in the input data!

Amenities

Another crucial factor which determines the spatial composition of an urban area is the presence of amenities, that is, anything which creates value which might be crystallized in market value but is not directly related to production. Households may place a premium on living close to a park, good schools, diverse restaurants, and natural beauty, to give a few examples. As with productivity, the amenities may spillover into nearby areas. \(B\) therefore represents total amenities, including endogenous factors. The two most striking factors are the high level of amenities on the West Side versus the East and the prominence of rural tracts. Comparing this with \(b\), however, one realizes that there are actually two distinct dynamics at play. The West Side boasts high baseline amenities, likely due to the presence of the lake, public beaches, and ample parks. Places like Lakewood are nice in and of themselves. In rural areas, however, the amenities are almost entirely spillovers. In other words, the premium is the result of being far from undesirable areas with bad externalities. This dynamic represents the driving force behind historic and continuing flight, especially among White residents, from Cleveland proper.

Density of Development and Floorspace Use

Model inversion also conjectures the density of development (the density of floorspace brought to bear for residential and commercial uses), signified by the letter \(\phi\) and the share of that space under commercial/industrial use (\(\theta\)). The first map below shows the natural log of \(\phi\), demonstrating—as one would expect—more floorspace in urban areas with especially high values in Downtown, Euclid Avenue, and University Circle. These specific areas actually have several times more floorspace than any other tract in the area, which is the reason why I logged the data. Otherwise, the subtle distinctions between urban and rural would be illegible.

The following map shows that commercial development is especially prevalent along the Cuyahoga River, the I-271 corridor, outer Euclid Avenue, and Downtown. Again, it is impressive that a model with simple inputs is able to correctly identify individual industrial/business parks as well as the airport and important logistical hubs.

Wages

Finally, inverting the model generates a vector of wages paid out in each work location. Again, places with large amounts of workers and high productivity are prominent. Those with high amenities do not necessarily pay out the highest wages. These figures are important, however, as this model simulates individual workers’ attempts to maximize utility given their budget. Locations where individual workers can live cheaply while earning high wages and enjoy good amenities will quickly be arbitraged away by higher prices and the disamenities of congestion.

Baseline

Below, I call IGCities’ solveModel method to generate the baseline scenario. This requires our original inputs as well as values generated by inverting the model. This simulation quickly converges (155 iterations) on an equilibrium because Cleveland, as a real-life city, contains few opportunities for spatial arbitrage. This generates a list of matrices with the new, post-equilibrium population, wage, floorspace data, etc.

model_baseline <- IGCities::solveModel(
            N=N,
            L_i=L_i,
            L_j=L_j,
            K=K,
            t_ij=t_ij,
            a=a,
            b=b,
            varphi=varphi,
            w_eq=w,
            u_eq=u,
            Q_eq=Q_norm,
            ttheta_eq=ttheta
)

Counterfactual (closed)

Having generated the baseline scenario, I will now simulate the impact of the Midline. Ideally, I would have more exact data on how the project would modify the amenities, floorspace, and productive capacity, but for the purpose this rough simulation, I choose to increase \(\phi\), \(a\), \(b\), and \(\theta\) by a standard deviation in all of the tracts which intersect with the site. This approximates the combination of parks, industrial/commercial facilities, and improved infrastructure implied by the Site Fund’s plan.

midline_tracts <- which(current_data$GISJOIN %in% c("G3900350114501","G3900350197200","G3900350198400","G3900350114800"))

a_ <- a
b_ <- b
varphi_ <- varphi
ttheta_ <- ttheta

varphi_[midline_tracts, ] <- varphi[midline_tracts, ] + sd(inverted_values$varphi)
a_[midline_tracts, ] <- a[midline_tracts, ] + sd(inverted_values$a)
b_[midline_tracts, ] <- b[midline_tracts, ] + sd(inverted_values$b)
ttheta_[midline_tracts, ] <- ttheta[midline_tracts, ] + sd(inverted_values$ttheta)

Unmodified, IGCities does not allow migration into and out of a given urban area. This implies the city is a closed system. This may not matter for interventions which fail to significantly alter the attraction of Cleveland versus other cities. For example, the opening of a new park may lead more people to move to a neighborhood, but it is unlikely to cause many people to move to the Cleveland area who would otherwise live in a different state. In equilibrium, metropolitan populations are balanced apart from natural change. The aggregate utility within Cleveland would equal that of its outside options, meaning that individuals (on average, individual experiences may differ) do not gain from moving to Columbus or Detroit. This may actually be a reasonable assumption (at least regarding Cleveland vs. the rest of the world) because the metropolitan area’s population has varied within a band of ~150,000 residents since at least 1960, making it one of the most “stable” metro regions in the country despite dramatic internal shifts, most prominently the rapid development of the suburbs at the expense of Cleveland itself.

model_closed <- IGCities::solveModel(
            N=N,
            L_i=L_i,
            L_j=L_j,
            K=K,
            t_ij=t_ij,
            a=a_,
            b=b_,
            varphi=varphi_,
            w_eq=w,
            u_eq=u,
            Q_eq=Q_norm,
            ttheta_eq=ttheta_
)

Counterfactual (open)

That being said, the scale of the Midline project means that there is a strong chance that it could meaningfully increase Cleveland’s aggregate utility, generating in-migration. This requires modifying IGCities’ solveModel function to increase the metro area’s population until this spread is closed. Since adding 1 individual per iteration will not capture the full extent of the population increase associated with the Midline, I modify the function call to increment population by 200 every step. This prevents the model from precisely reaching a level of aggregate utility which equals outside utility, so the model never properly converges. We can tolerate an error of ±200, so this isn’t a terrible fault. I choose to cut off the model after 300 iterations, since errors fail to shrink after this point.

This modification incorporates two new inputs: U_bar (the outside option utility) and step (the amount of inhabitants to add or subtract in each iteration). Since Cleveland might already be in equilibrium with the outside world (meaning that its utility matches the outside option), my simulation uses the baseline scenario’s aggregate utility as the outside option. Since the Midline’s interventions increase utility, the model will increase population until outside and inside utility is equalized.

model_open <- solveModel_open(N=N,
            L_i=L_i,
            L_j=L_j,
            K=K,
            t_ij=t_ij,
            a=a_,
            b=b_,
            varphi=varphi_,
            w_eq=w,
            u_eq=u,
            Q_eq=Q_norm,
            ttheta_eq=ttheta_,
            maxiter=300,
            step=200,
            U_bar = model_baseline$U)

Population

The open city model projects a metropolitan population 4.11% larger than the baseline scenario. Given a 2024 estimate of 2,171,877 residents (US Census Bureau), we might therefore expect an overall population gain of about 90,000 residents across the entirety of the region.

This gain would be distributed throughout Cleveland, with most neighborhoods only gaining a couple dozen residents. Most of the action is adjacent to the Midline itself, with the area between Opportunity Corridor and Central/Quincy Avenues gaining several thousand residents. Interestingly, some of the tracts near but not directly abutting the Midline lose a couple hundred residents. In the closed city model, a broader pattern emerges which sees suburbs lose population as population rises in Cleveland proper.

Regarding jobs, the open city model sees the creation of 41,800 direct and indirect jobs, the majority of which are concentrated in one area: the northern part of Fairfax and the Euclid Avenue corridor. A smaller (but still significant) cluster emerges along the Opportunity Corridor between the East 79th and Woodhill Green/Blue Line stations. Few new jobs are created elsewhere, and in the closed city scenario Downtown, University Circle, and several industrial parks actually lose jobs due to firms relocating to the Midline.

Wages

In the open city model, wages in the average neighborhood increase by only 0.1% whereas in the closed city model wages increase by 1.3%. This discrepancy is due to the impact of in-migration driving down wages. Such an outcome may not result from outright wage decreases but may function as it does in other high-cost cities—employers let real wages fall by failing to compensate workers for higher prices elsewhere in the economy.

In the both the open and the closed city models, wages increase by 7%-28% along the Midline, with the strongest gains in the southern sections of the site. Wages increase less along Euclid Avenue because this is already an area with comparatively high wages (the Cleveland Clinic, among other important employers, are in this area). In the open city model, everywhere beyond about a half-hour drive from the Midline experiences slight wage declines.

Floorspace Prices

Price per square foot, in general, increases rapidly along the northern section of the Midline, moderately along the middle, and actually decreases towards the south. This is likely due to very high demand for living and working space at the north as well as a slight oversupply problem at the south. Otherwise, floorspace gets more expensive in the swath surrounding the Midline, cheaper in a band encompassing the West Side and the outer East Side, and then expensive again in further areas.

Summary

As the table below demonstrates, the Midline would have a significant impact on the economy of the Cleveland region, though the areas which would see the most dramatic changes would be concentrated in the immediate vicinity of the project, namely, Fairfax and Central. In the open city scenario, many of the benefits generated by new development would be diminished by new entries into the labor market. Wages, floorspace prices, and consumer market access would remain stagnant as competition heats up for jobs and places to live, leading to congestion in the market. That being said, the impact on Fairfax’s Census tracts are more potent, especially in directly impacted areas. The table below also includes a measure of commuter market access (CMA)—that is, a composite measure of access to employment. In both the open and closed city scenarios, workers’ access to jobs increases, which is to be expected, though only modestly.

It is important with these projections to note that these are all relative impacts due specifically to the modifications described above. Cleveland is already undergoing significant change due to new developments, the shifting attraction of other metropolitan regions, and broader changes in the economy as a whole. Therefore, one should think of the values in the table below as changes above the “do nothing” scenario in which the Midline never existed. Price per square foot may therefore (and probably will) increase by more than 13%, but that the Midline’s presence means that prices are 13% higher than what they would be otherwise.

Future Directions

Moving forwards, I hope to use these results as part of a financial model which will explore the possibility of pooling land bank holdings in Fairfax and creating a trust which raises capital for investment into housing construction/repair while returning most of its proceeds to current residents of the community, thus averting the threat of displacement in the face of steep property value appreciation. I already have access to detailed data on local land banks’ holdings, including appraisals, the condition of individual properties, etc., and applying these results (especially PPSF) to this data could be a first step in estimating a cap rate for the trust. This could also involve imputing appreciation in land values (rather than merely home values) using a regression on the existing relationship between PPSF and land value in the region. Plugging projected PPSF would generate the future value of publicly-held buildable land under a variety of scenarios, especially different zoning regimes.