Stranded: The Effects of Inaccessible Public Land on Local Economies in the American West

Sources of Stranded Land

The spatial distribution of public land ownership in the western United States is more an accident of history than the result of careful resource management and planning. Land policy focused on disposal and privatization for most of the nineteenth century, and originally most of the western United States was intended for private ownership and opened for settlement (Hibbard 1939; Gates 1968; Libecap 2018). Policy priorities slowly shifted toward preservation beginning with the first national parks in the 1870s and forest preserves in the 1880s and eventually culminated in the end of most homesteading under the Taylor Grazing Act in 1934 (Loomis 1993).

The Homestead Act of 1862 set the terms for much of the settlement in the West, granting 160 acres for free to parties that made improvements to the land and occupied it for five years.11 Claimants could select any available land that had been surveyed and not previously set aside for another purpose. Much of the land managed by the USFS was set aside between 1890 and 1920, after the first wave of homesteading had passed through. Similarly, most land managed by the BLM is what was left over and never claimed prior to the Taylor Grazing Act (Loomis 1993; Libecap 2018). In some cases, homesteads failed, and the land reverted to the government. The result is public land scattered among private land holdings across much of the West.

The federal government’s policy for granting land to states is a second source of fragmented and inaccessible land in the West. The 11 western states received 71 million acres from the federal government as grants to support funding for public education (Loomis 1993). States were granted specific 1 × 1 mile sections of land in each township of the Public Land Survey System (e.g., sections 16 and 36), resulting in a scattered pattern of state landholdings (Hibbard 1939; Gates 1968; Loomis 1993). As a result, most states own scattered square-mile sections that are often surrounded by private land, although they are sometimes adjacent to federally owned land.

The final and most significant source of stranded land is the system of railroad land grants, which made up roughly 10% of the land privatized by the federal government (Loomis 1993). The government subsidized the construction of seven transcontinental railroads beginning in the 1860s by granting land adjacent to the track as it was completed.12 In an effort to avoid monopoly control of valuable land by the railroad, grants were given to alternating square-mile sections in a 20–40-mile checkerboard along each of the land grant railroads. The government hoped to recoup its losses by selling the land it retained in the checkerboard at a “double minimum” price that was twice the going cash rate, but often the land did not sell (Hibbard 1939; Paul 2006).13 Because many of the federal sections were never purchased, these checkerboards of private and public land persist today in many places.

Measuring Stranded Land

We combine GIS data on public land ownership and easements from the Protected Areas Database of the United States (PAD-US) with data on public roads from the U.S. Census TIGER/Line shapefiles to quantify the extent of stranded public land in each county in the 11 western states.14 We focus on land that is designated as public access and managed by a state government, the BLM, USFS, FWS, NPS, or Bureau of Reclamation.15 We aggregate the public land layers so that each contiguous unit of public land is a unique feature and then determine which land units are intersected by a public road or accessible via an easement across private land. From TIGER/Line roads data, we include all primary, secondary, local neighborhood, and rural roads; city streets; and vehicular (4WD) trails. USFS roads are retained, but private roads are excluded.

We call a tract of public access land stranded if it does not touch a public road or easement. After determining which larger tracts of public land lack direct or indirect road access, we disaggregate them into tracts managed by individual agencies (or states) and quantify the total acreage of stranded land by agency in each county in the 11 western states. Table 1 reports state-level totals of our estimates for total public access acres, stranded (inaccessible acres), and share of stranded land managed by the BLM, USFS, NPS, FWS, or states. The information presented in Table 1 and the underlying data represent the first systematic measure of access for public land in the academic literature.16

Our approach, which estimates fine-scale differences in accessibility across a large area, may understate the number of stranded public acres for two reasons. First, landowners may try to restrict access to adjacent public land by blocking roadways or other access points that show up in our data as unrestricted (Center for Western Priorities 2013). Second, our approach treats land as accessible if it is connected in some way to another tract of public access land with road access. In practice, some areas that are indirectly accessible via other public landholdings may be so remote as to be functionally inaccessible.

Figure 2

Stranded Land as a Percentage of County Area

But there are two reasons our estimates may overstate actual stranded land. First, some public land may have access via private roads that are in reality used by the public. Second, there may exist informal arrangements or prescriptive easements across private land that grant access to public land but are not recorded in our data. While these caveats are important, we emphasize that our estimates are the first systematic attempt to quantify public access at the county level and for the western United States as a whole.

Distribution of Stranded Land

We estimate that 6,019,305 acres of public access land in the West are inaccessible. Figure 2 is a map of western counties shaded by the total share of the county that is stranded public land. Darker counties have larger shares of stranded land. Strandedness varies substantially in and between states. The average share of county land that is stranded is 0.73%. Only seven counties have no stranded land, and some counties have stranded percentages as high as 10%.

Table 1 also reports the share of stranded land managed by each agency in each state. In most states, the BLM manages most stranded land. Notable exceptions include Arizona and Washington, where most stranded land is owned by the state. The patterns in Table 1 illustrate the legacy of uncoordinated nineteenth-century land policies. In contrast to the national parks that were always intended for access, public land initially intended for other purposes—homesteads, railroad grants, or state trust land—now face barriers to accessibility.

We calculate and report stranded land as a share of public land in each county. Appendix Figure A1 shows the results, which reveal interesting contrasts to Figure 2. Some counties have a relatively large amount of stranded land, even though the share of public land that is stranded is relatively low, owing mostly to the large federal land holdings in some western counties. Of public access land in the average county, 4.6% is inaccessible to the public. Some counties lack access to as much as 75% of their public land.

Conceptual Framework

Our empirical estimation is based on the Roback (1982) model, which characterizes the equilibrium sorting of workers and firms. Each location in the model is a separate land and labor market with a fixed set of unpriced amenities. These amenities affect the utility of workers and the production costs of constant-returns-to-scale firms. In equilibrium, land rents and wages adjust to make mobile workers and firms indifferent to locations. Using Roback’s notation, the equilibrium conditions for each location are 1 and 2 where w is the wage rate, r is the land rent, s is the amenity level, k is the equilibrium utility level, and 1 is the normalized price of the firm’s output. The equilibrium conditions imply, respectively, that the utility of workers (V) and the marginal costs of firms (C) are equalized across local economies. The power of the Roback model is that it predicts how land rents and wages will differ between markets with different local amenities. In particular, the conditions in equations [1] and [2] can be used to derive the following comparative statics results: 3 and 4 where ∆ > 0, and V_i and C_i are partial derivatives of the indirect utility and cost functions with respect to the ith variable. In general, the marginal effect of the amenity on rents and wages is of ambiguous sign, as it depends on whether it increases or decreases the utility of workers (the sign of V_s) and whether it is productive or unproductive for firms (the sign of C_s).

The Roback model provides a useful framework for understanding the estimated effects of public land on local economies. In our empirical application, we treat public land in a county as an unpriced amenity (or disamenity) that affects the utility of residents and the productivity of firms in the respective county.17 Appendix Table A1 summarizes the four possible sets of comparative statics results from the Roback model, based on whether public land is an amenity for consumers (V_s > 0) and productive (C_s < 0) for firms. As discussed below, public land can produce a variety of amenities, which can affect rents in various ways and may differentially affect the value of individual land parcels (e.g., if the effects are moderated by distance to public land). We assume that counties define distinct land and labor markets, a designation that we acknowledge is imperfect but argue is the best available alternative.

We measure the overall average effect of public land on rents in a county by specifying the dependent variable as the county average farmland value per acre in the main empirical model. Farmland value proxies for the average price of undeveloped private land in the county. An advantage of farmland values is that they reflect not only current effects of public land but also expected changes in future rents. There is evidence from previous studies that farmland value capitalizes the expected growth in rents from higher future demand for urbanization (Plantinga, Lubowski, and Stavins 2002; Isgin and Forster 2006) as well as benefits from proximity to recreation and natural amenities (Bastian et al. 2002; Wasson et al. 2013; Borchers, Ifft, and Kuethe 2014).

Figure 3 illustrates the empirical approach. Figure 3a shows a county with only private land. The essence of our empirical strategy is to compare this county with otherwise identical counties with stranded and nonstranded public land to determine the effect on per acre farmland value. Figure 3a and Figure 3b are deliberately drawn to be the same size, as we control for total county area in the empirical model. However, because the dependent variable is defined as the total value of farmland divided by total farmland area, not total county area, our estimates capture amenity effects of public land but not the acreage effect of a smaller private land base.

In Figure 3b, a positive share of the county’s land base is in stranded public land, which for several reasons is likely to be a disamenity relative to private land. Although public access to private land is often restricted, private land may offer more recreational opportunities to residents and visitors than stranded public land. Regional managers from the USFS and BLM indicate that strandedness can be especially problematic for recreational activities such as hunting, hiking, and off-road vehicle use (U.S. General Accounting Office 1992). Accordingly, a county with stranded public land would be less attractive to residents compared with an otherwise identical county with only private land. Holding wages constant, equilibrium rents would have to be lower to compensate residents for the disamenity. These effects are captured in farmland values because they capitalize rents from future uses of the land (e.g., housing). In contrast to these market-wide effects on farmland values, stranded public land could have offsetting positive effects on the value of adjacent land parcels if landowners are afforded exclusive access to stranded land for grazing, recreation, and other activities or if they obtain easement payments from others seeking access. This could make stranded land a consumption (or a production) amenity for some landowners. More broadly, the amenities associated with open space may capitalize at a variety of spatial scales (Abbott and Klaiber 2011). Thus, the net effect of stranded land on rents that comes through the utility channel is of ambiguous sign.

Figure 3

Empirical Approach

Stranded public land may be unproductive for firms compared with private land. First, strandedness may limit traditional extractive resource uses, such as timber harvest or oil and gas development. Although these activities may be allowed on stranded land, resource developers would need to contract with adjacent private landowners for access. This is likely to raise costs for firms because these landowners do not benefit directly from production on adjacent public land and may hold up development. As with disamenities, lower rents would be needed to induce firms to locate in the county with stranded public land (holding wages constant). Second, stranded public land may limit efficient use of private land (e.g., by preventing consolidation of land parcels), especially in checkerboarded areas. Third, stranded land may be associated with higher rates of trespass by members of the public seeking access to public land. This may lead to underinvestment in the land itself because of less secure property rights, further dampening land values (Hornbeck 2010).

The inability of public agencies to access and manage stranded land may also adversely affect landowners. The U.S. Supreme Court held in Leo Sheep Co v. United States in 1979 that government officials cannot use eminent domain to cross private land without permission, even to access land under their jurisdiction (Chavez 1987). This makes management activities such as invasive species control and fire prevention difficult or impossible (U.S. General Accounting Office 1992).18 In all these cases, stranded land raises costs for firms and private landowners, putting downward pressure on farmland values.19

The county in Figure 3c has a positive share of accessible public land (but no stranded land). There are numerous hedonic price studies that find a positive effect on housing value of proximity to federal land such as national forests (e.g., Stetler, Venn, and Calkin 2010; Liu et al. 2013; Wasson et al. 2013). However, these studies typically measure the marginal effect of distance to federal land in a given land market, which is not directly comparable to our approach. Rather, the comparison of the county in Figure 3c to the county in Figure 3a measures the land market effects of shifting land from private uses to accessible public uses. Several of the studies reviewed in Section 2 (e.g., Duffy-Deno 1998; Lewis, Hunt, and Plantinga 2002; Eichman et al. 2010) are designed in the same way but measure effects on employment and migration rather than on rents.

As with stranded land, we expect accessible public land to affect recreational opportunities of residents and the production costs of firms. When easily accessed, public land is more likely to provide better recreational activities than private land and thus be an amenity for residents and visitors.20 Finally, a comparison of the county in Figure 3d to the county in Figure 3a measures the combined effect of stranded public and accessible public land on per acre farmland values. We also estimate alternative models with per capita income as the dependent variable. Given the estimated effects on farmland values and income, results from the Roback model provide insights into whether public land is an amenity or disamenity to residents and whether it is productive or unproductive for firms. We explore these implications of our results in Section 6.

For firms, costs of extractive resource uses may be higher on accessible public land than on private land due to greater regulation but still lower than on stranded land because of easier access. Accessible public land may be a net amenity for firms if it forms the basis for a local recreation economy, as discussed in Walls, Lee, and Ashenfarb (2020). Moreover, the accessibility of public land limits trespass on private land and negative spillovers from unmanaged stranded land. In sum, accessible public land is more likely to be an amenity for consumers than stranded public land. Whether accessible public land raises costs for firms compared with private land depends on the relative importance of resource extraction versus recreation in the local economy.

Econometric Framework

We begin with the empirical model of farmland value per acre. Farmland value is from the U.S. Census of Agriculture and represents the average owner-estimated per acre value of private farmland in a county.21 The use of county data has the advantage that we can measure effects of public land that are common to all properties in the market (e.g., lower rents in an area that are the result of higher costs for natural resource extraction). As with all aggregate data, a disadvantage is that we cannot characterize within-county heterogeneity (e.g., we measure the average of spatially varying effects of public land). In addition, counties may not accurately represent distinct land and labor markets. Studies of urban amenities have used cities, or metropolitan statistical areas, as the definition of a market area (Roback 1982; Albouy 2016). This is not appropriate for this application because it would exclude rural areas, where most stranded land is found. In the end, counties are a convenient way to define markets because so much other data are reported at this scale. This likely explains why many previous studies have used this designation (Carlino and Mills 1987; Mendelsohn, Nordhaus, and Shaw 1994; Chay and Greenstone 2005).

We focus on farmland value in 2017 for counties in the 11 western states.22 The estimating equation is 5 where i indexes counties, %NonStranded_i is the percentage of total county acres inaccessible public land, %Stranded_i is the percentage of total county acres in inaccessible public land, and is a vector of geographic and economic controls. Although land value data are available for multiple years, we do not estimate equation [5] using panel data because our public land measure is time-invariant, making county fixed effects infeasible. As described below, we also estimate a version of equation [5] with per capita income as the dependent variable.

Equation [5] is directly linked to the conceptual model in Figure 3. The coefficient on accessible public land (β₂) is estimated by comparing counties with different shares of private and accessible public land, holding all other factors constant (e.g., Figures 3a and 3c), whereas the coefficient on stranded public land (β₃) is estimated by comparing counties with different shares of private and stranded public land (e.g., Figures. 3a and 3b). We test several hypotheses. The first is whether the effects of public land are significantly different from zero: β₂ = 0, β₃ = 0. The second is whether the effects are different for stranded and nonstranded land: β₂ = β₃. The comparison of β₂ to β₃ provides insight about whether access has an impact on the amenities associated with public land. If access is important, we predict β₂ ≠ β₃.

There are several concerns for identifying β₂ and β₃ in equation [5]. First, the extent and configuration of public land in each county is likely endogenous to a variety of unobservable factors that influenced settlers’ decisions about where to establish homesteads as well as decisions about which land to set aside as national forests or parks. In particular, the amenity value of public land may be confounded by the fact that public land tends to be highly correlated with high elevations, rugged terrain, and other geographic features that are consumption amenities.

Second, given some initial configuration of public land, there may be factors that affect the selection of land into stranded versus nonstranded status. Whether a specific tract of public land is stranded ultimately comes down to ability to access that land by road. Hence, stranded land is likely endogenous to factors that affect the construction of public roads. Moreover, the accessibility of public land as measured in 2017 is endogenous to past attempts to improve public access through land exchanges and acquisitions, which were especially common in the 1990s (U.S. General Accounting Office 2000). If the USFS or BLM targeted acquisitions in counties with relatively high gains from improving access, OLS estimates of β₃ will be biased toward zero. Selection on the potential benefits of access would lead to lower strandedness in high-value areas relative to areas that received few or no exchanges as of 2017. Moreover, counties that received more land exchanges may have experienced an artificial increase in land values if land deeded to private parties was systematically worth more than the land conveyed to the government during the 1990s, as opponents of land exchanges have claimed (U.S. General Accounting Office 2000).

We address these selection concerns using the approach developed by Oster (2019) to diagnose potential selection on unobservables. Specifically, Oster (2019) shows how to calculate the proportional degree of selection on unobservables that would have to be present for β₂ or β₃ to be zero, based on the selection on observables estimated from the data. For example, if Oster’s δ = 5, selection on unobservables would have to be five times as large as the selection on observables measured in the data for the true β to be equal to zero. Hence, a larger value of δ implies that selection on unobservables is relatively less likely to undermine a statistically significant result because it would have to be larger relative to the measured selection in the data. We characterize the potential for different types of selection by estimating the Oster δ across the following sets of control variables:

• Geographic controls: These include elevation, ruggedness, soil quality, precipitation, and stream density. They are the most clearly exogenous and are likely to strongly affect selection into public versus private ownership. They may also affect the selection into stranded versus nonstranded public land.

• 1934 economic controls: These include the total number of manufacturers in a county in 1934 and the percentage of the population living in urban areas in 1934. They capture how developed and populous a county was when the process of selection into private and public ownership became fixed with the passage of the Taylor Grazing Act. Importantly, these controls are measured before the development of major road infrastructure that could have affected which land became stranded or nonstranded.

• New Deal controls: These include the total spending in a county by the Public Works Administration, the Works Progress Administration, and the Public Roads Administration, which are direct measures of funding for building roads after 1934. Although much of this spending was driven by national political factors (Fishback, Horrace, and Kantor 2005), they may be endogenous to the existing distribution of public land.

• Modern controls: These include modern railroad miles, road density, and an indicator for the presence of a major urban area. They capture key determinants of land value that may be mechanically related to stranded land, though they are the least likely to be exogenous.

We also use several sets of spatial fixed affects to nonparametrically absorb unobserved differences between counties. In all models, we include fixed effects for the Amenity Index Ranking assigned to a county by the USDA. The USDA’s Amenity Ranking is based on a variety of factors, including winter sun and temperature, summer temperatures and humidity, topography, and water area. Appendix Figure A5 shows the Amenity Ranking for each county. We report results that add either state fixed effects or state-by-ecoregion fixed effects, using Level 2 ecoregions obtained from the EPA. According to the EPA, ecoregions are areas where the type, quality, and quantity of environmental resources are generally similar and reflect “similarity in the mosaic of biotic, abiotic, terrestrial, and aquatic ecosystem components with humans being considered as part of the biota” (EPA 2023).

Finally, we conduct a variety of robustness checks by including other individual control variables: Native American reservations, land exchanges, universities, net primary productivity, and irrigation. We then assess the potential for selection on unobservables across different sets of controls and fixed effects.

Data for Covariates

For our geographic controls, we collect elevation data at 30 × 30 m resolution from the USGS National Elevation Dataset and calculate the mean and standard deviation of elevation for each county. The latter serves as our measure of topographic roughness (Ascione et al. 2008). We calculate average precipitation and temperature over 1980–2010 using the PRISM climate dataset. We use a soil quality index from Schaetzl, Krist, and Miller (2012) to calculate acres of high-quality land in each county.23 We use the USGS National Hydrography Dataset to calculate the density of perennial streams in each county (stream miles per square mile).

For the 1934 economic controls, we obtain data on total population, urban population, and the number of manufacturers from the U.S. Census. For the New Deal controls, we obtain county-level measures of total infrastructure expenditures during the New Deal by the Public Works Administration, Works Progress Administration, and the Public Roads Administration (Fishback, Horrace, and Kantor 2005). For the modern controls, we obtain data on urban areas from the U.S. Census TIGER/Line shapefiles. We use the TIGER/Line transportation database to measure the miles of railroad track and roads in each county in 2017.

In addition, we create an indicator for the presence of a Native American reservation in a county using U.S. Census TIGER/Line shapefiles. We also count the number of higher education institutions with at least 5,000 students using U.S. Census data. We measure the share of farmland irrigated in 2017 based on the U.S. Census of Agriculture as well as average net primary production.24 Finally, we estimate the total acreage of land that changed hands as a part of land exchanges or federal acquisition in each county using recently digitized patent data from the General Land Office.25 Appendix Table A2 provides summary statistics and variable definitions.

OLS Results for Land Values

Table 2 presents the results of estimating equation [5] using OLS, where the dependent variable is the natural log of land value per acre in 2017. Panel A uses state fixed effects, and panel B uses state-by-ecoregion fixed effects. Both panels include USDA Amenity Ranking fixed effects. Column (1) reports the baseline results with no controls, column (2) adds the geographic controls, column (3) adds the 1934 economic controls, column (4) adds the New Deal spending controls, and column (5) adds the modern controls. Standard errors are clustered by arbitrary 150-square-mile grid cells (N = 62) and reported in parentheses.26

Across all specifications in both panels, stranded land has a negative and statistically significant effect on land values. In panel A, the effect of stranded land is much larger without including controls but falls by 25% after including just geographic controls and continues to fall as additional controls are included. The estimates are more stable to the inclusion of controls in panel B, which includes the finer spatial fixed effects in all specifications.

Consistent with the coefficient stability, the Oster δ for stranded land is significantly larger in the panel B specifications. In panel A, selection on unobservables would need to be roughly twice the magnitude of selection on observables for the true effect of stranded land to be zero. In contrast, in panel B, selection on unobservables would need to be 7–24 times as severe as selection on observables to fully explain the estimated effect of stranded land (depending on the specification). The upshot is that including state-by-ecoregion fixed effects substantially helps address potential selection on unobservables.

The results for nonstranded land in Table 2 also reveal important effects of including covariates. When no controls are included, the effect of nonstranded land on land values is not statistically distinguishable from zero. However, adding basic geographic controls causes the effect of nonstranded land to triple (panel A) or double (panel B) in size. Across columns (2)–(5), which include various sets of controls, the effect of nonstranded public land is positive and statistically significant. The Oster δ’s for nonstranded land tell a slightly different story, peaking in column (2) with only geographic covariates and then declining as additional, potentially endogenous controls are added. Consistent with this, the estimated effect of nonstranded land is less stable across specifications in panel B than the effect of stranded land.

In summary, the selection of land into nonstranded status appears to be primarily driven by fixed geographic features that can be readily controlled for. Adding more economic controls actually reduces the confidence that the model adequately addresses selection on unobservables, suggesting that these measures may be “bad controls” for nonstranded land. In contrast, the coefficient on stranded land is more stable to the inclusion of these controls, which reduce the scope for selection on unobservables. This implies that the “best” model may depend on whether one is primarily interested in the effect of stranded or nonstranded land. In the discussion that follows, we focus on the estimates in column (3), which produces the largest δ for stranded land.

The estimates in Table 2, panel B, column (3) indicate that a 1 percentage point increase in stranded land would lead to a 10% decrease in land value per acre. For context, the average county has 0.7% stranded land, with a standard deviation of 1.1 percentage points. Hence, a 1 percentage point increase in stranded land represents more than double the mean amount of stranded land in a county. Mean farm value per acre in 2017 was $4,490, with a standard deviation of $7,377. Hence, a 1 standard deviation increase in stranded land leads to a decrease in land value of roughly 1.1 × 0.0997 × $4,490 ≈ $490 per acre, or about 1/14th of the standard deviation in land value.

Turning to the effect of nonstranded land, Table 2, panel B, column (3) indicates that a 1 percentage point increase in nonstranded land leads to a 0.8% increase in land value per acre. The average county in our sample is 41% nonstranded land, with a standard deviation of 27 percentage points. For nonstranded land, a 1 standard deviation increase would lead to an increase in land value of 27 × 0.00766 × $4,490 ≈ $930 per acre, which is about 1/7th of the standard deviation in land value. Ultimately, it is difficult to interpret these effects without also understanding the impact of public land on wages.

OLS Results for per Capita Income

The Roback (1982) model implies that equilibrium wages, such as land rents, are a function of local amenities. Uncovering the effect of public land on wages can help us distinguish among the possible scenarios described in Appendix Table A1 and draw conclusions about the net welfare effects of public land for both consumers and firms.

Table 3 presents the results of estimating equation [5] using OLS, where the dependent variable is the natural log of per capita income in 2017. The structure of the table is analogous to Table 2. The results reveal starkly different patterns than the land value results. To begin with, the effect of stranded land is positive across all specifications and statistically significant in five (α = 0.05) and nine (α = 0.10) specifications. The coefficients are also fairly stable across the specifications that include controls in columns (2)–(5) and across both sets of fixed effects. Finally, the Oster δ’s in panel B suggest that selection on unobservables would have to be anywhere from 4.4 to 59 times the selection on observables for the effect of stranded land to be zero.

In contrast, the effect of nonstranded land is extremely small in magnitude and never statistically significant. Unsurprisingly, the Oster δ’s for nonstranded land are also quite small. Taken together, the results in Table 3 provide fairly clear evidence that there is not a relationship between nonstranded land and per capita income at the county level.

Turning to magnitudes, the estimates in Table 3, panel B, column (3) indicate that a 1 percentage point increase in stranded land is associated with a 1.75% increase in per capita income. The average per capita income across our sample of counties is $27,664 with a standard deviation of $7,212. Hence, a 1 standard deviation increase in stranded land (1.1 percentage points), would imply an increase in income of 1.1 × 0.0175 × $27,664 ≈ $530 per capita, roughly 1/13th of the standard deviation in income. Before interpreting these coefficients in the context of the Roback (1982) model, we assess the robustness of our core results and provide estimates obtained from an alternative identification strategy.

Robustness of OLS Results

Appendix Table A3 presents a series of robustness checks for the effect of stranded and nonstranded land on land values. Each column adds a potential confounding variable individually, and the final column includes all the variables in combination. All models include all four sets of primary controls (geographic, 1934 economic, New Deal spending, and modern) as well as state-by-ecoregion and USDA Amenity Ranking fixed effects.

Column (1) includes an indicator for whether there is a federally recognized Native American reservation in a portion of county, as incomes and land values tend to be lower on reservations (Leonard, Parker, and Anderson 2020). Column (2) includes the percentage of land in a county that was part of a federal land exchange, a measure of concentrated attempts to reduce stranded land. Column (3) includes the number universities in a county with more than 5,000 students because the economic development prospects may be fundamentally different in “university towns” in rural parts of the western United States. Column (4) includes a control for net primary production, a measure of agricultural suitability that could impact land values and incomes. Column (5) includes a control for the percentage of farmland in a county that is irrigated, which could also affect farm values.

Across all specifications, the effect of stranded land on land values remains negative and statistically significant. The estimates in columns (1)–(3) are very similar in magnitude to those in Table 2. The agricultural controls included in columns (4)–(6) do reduce the estimated impact of stranded land somewhat, though the magnitude of the Oster δ’s across these columns suggest that the scope for selection on unobservables is minimized when the agricultural controls, which may be endogenous, are not included. The estimated effect of nonstranded land on land values is also robust to the inclusion of the various controls and is quite similar in magnitude to the estimates in Table 2.

Appendix Table A4 presents the robustness results for per capita income. As with land values, the effect of stranded land on per capita income is robust to including the various controls, and the magnitudes are fairly stable across all six specifications. The estimated effects for nonstranded land remain small and statistically insignificant in three of five specifications, but including the control for irrigation leads to a marginally significant positive coefficient on nonstranded land.

IV

An alternative approach is to instrument for the %NonStranded and %Stranded variables in equation [5]. To do this, we develop several instruments that measure the extent and distribution of public land based on predetermined spatial variation in the original land grants to the transcontinental railroads and states. The intuition behind this approach is to use historical variation in the planned land grant policies as a source of identifying variation in the modern distribution of public land. The combination of planned land grants to railroads and states leads to modern fragmentation in public land that is predetermined with respect to subsequent patterns of settlement and deviations from the policies as originally designed. Figure 4 provides an example of the influence of historical land grants on modern stranded land.

We create several county-level variables summarizing potential sources of strandedness. First, we calculate the total distance of land grant and checkerboard edges in a county, denoted GrantBorders_i. For instance, each square-mile section of state land that is not contiguous with any other public land adds four miles (6,437 m) of land grant edges. Second, we calculate the share of county land that was composed of land grants or retained portions of the railroad checkerboards (%Grants_i). Third, we create a measure of land grant fragmentation based on the ratio of the perimeter-to-area ratio of planned public land grants in a county to the potential minimum perimeter-to-area ratio if all public land in the county was contiguous (Fragmentation_i).27

These three variables capture the overall extent and fragmentation of land exposed to spatially random designation. These measures should mechanically increase the amount of accessible and inaccessible land in a county because each additional parcel of checkerboarded land contributes to the total amount of public land, while the degree of fragmentation in the retained land also drives modern access problems. Details on the development of our instruments are provided in the Appendix.

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Figure 4

Land Grants and Access in Pershing County, Nevada: top, Planned Land Grants; bottom, Modern Land

Appendix Table A5 presents the IV results for the land value (panel A) and per capita income (panel B) models specified in equations [A1]−[A3]. Because we have multiple endogenous regressors and multiple instruments, we estimate all models using limited-information maximum likelihood rather than generalized method of moments. All models include state-by-ecoregion and USDA Amenity Rank fixed effects. The different sets of controls are added sequentially as in Table 2. We report the partial F-statistics for both stranded and nonstranded land in Appendix Table A5, and Appendix Table A6 shows the full first-stage results.

The estimates in panel A of Appendix Table A5 indicate substantially larger coefficients on stranded land than in the OLS estimates. The estimates in column (3), for instance, imply that a 1 percentage point increase in stranded land is associated with a 47% decrease in land value per acre. These results are also much more sensitive to the different sets of controls than the OLS results. For nonstranded land, the IV estimates are negative and statistically significant across all specifications, in contrast to the positive estimates for nonstranded land in Table 2. Column (3) results suggest that a 1 percentage point increase in nonstranded land leads to a 3% decrease in land value per acre in a county. Turning to the per capita income estimates in panel B, we find a negative and marginally significant effect of stranded land on per capita income (in contrast to the positive effects in Table 3). For nonstranded land, we find a negative and marginally significant effect (in contrast to null effects in Table 3).

Ultimately, the OLS estimates are our preferred results for two reasons. First, as we discuss in the Appendix (where we interpret the IV diagnostic tests reported in Appendix Table A5), our IV estimates may be subject to weak instrument problems. Second, differences between the OLS and IV estimates may be driven by crucial differences in the identifying variation in public land that underlies each approach. The IV estimator delivers a local average treatment effect based on the identifying variation in the instruments. That is, we identify the effect of stranded land that is caused specifically by checkerboarding from historic land grant policies.28 That this can produce an especially severe form of strandedness may explain why the IV estimates are larger than the OLS estimates. It could also explain the sign changes. Even when it is accessible, fragmented public land is much less likely to support recreation or large-scale production, which could explain the negative impacts of nonstranded land on land values and income. Therefore, while we think the IV results help to inform the different drivers of the spatial distribution of public land, they may be less useful for quantifying the overall average effect of public land on local economies.