Roads & SDGs, tradeoffs and synergies: learning from Brazil’s Amazon in distinguishing frontiers

To reduce SDG tradeoffs in infrastructure provision, and to inform searches for SDG synergies, the authors show that roads’ impacts on Brazilian Amazon forests varied significantly across frontiers. Impacts varied predictably with prior development – prior roads and prior deforestation – and, further, in a pattern that suggests a potential synergy for roads between forests and urban growth. For multiple periods of roads investments, the authors estimate forest impacts for high, medium and low prior roads and deforestation. For each setting, census-tract observations are numerous. Results confirm predictions for this kind of frontier of a pattern not consistent with endogeneity, i.e., short-run forest impacts of new roads are: small for relatively high prior development; larger for medium prior development; and small for low prior development (for the latter setting, impacts in such isolated areas could rise over time, depending on interactions with conservation policies). These Amazonian results suggest ‘SDG strategic’ locations for infrastructure, an idea the authors note for other frontiers while highlighting major differences across frontiers and their SDG opportunities. (Published in Special Issue The Sustainable Development Goals—Assessing interlinkages, tradeoffs and synergies for policy design) JEL O12 O13 H23 H41 Q23 Q24 Q56


Introduction
Infrastructural investments that lower transport costs can have considerable impacts on many elements of economic development. In terms of Sustainable Development Goals (SDGs), while #9 directly recognizes the roles of infrastructure -also bringing in industrialization and innovation, linked with cities as in #11 -SDGs #1, #2, #3 and #8 all highlight elements of economic development that we would expect to improve via trade, specialization, and improved public service delivery if roads networks expand to further connect cities and rural areas (see van de Walle 2002, Andersen et al. 2002, Khandker et al. 2009, Warr 2005, Bell and Van Dillen 2012, Aggarwal 2014, Gollin and Rogerson 2014. This drives planned road expansions. Expansions of roads networks also have impacts on land use that affect not only life on land (#15) but also life below water (#14) given strong direct connections via runoff, plus enormous impacts through atmospheric conditions including those likely to influence the climate (#13). Thus, SDG tradeoffs -and potential synergies -for road infrastructure are considerable. So, too, is planned future road investment, globally, of up to 25m km by 2050 (Caro et al. 2014;Laurance et al. 2014Laurance et al. , 2015Wade 2017 on OBOR).
Scanning empirical impact literatures suggests SDG tradeoffs for roads are obvious and constant. Roads are found to be one of the most consistent and largest factors in deforestation in the studies to date, in particular concerning tropical frontiers (Angelsen and Kaimowitz 1999, Pfaff 1999, Pfaff et al. 2007, Geist and Lambin 2001, Rudel et al. 2009, Ferretti-Gallon and Busch 2014. That could make sense for the settings considered, in which roads lowered input costs and raised farmgate prices for agropastoral outputs (see, e.g., von Thünen 1826). The expansion of agriculture was profitable and feasible, leading to deforestation. This paper's goal is to empirically distinguish settings, even within a single large forest frontier. We highlight that the forest losses societies incur as the tradeoff for economic gains are not constant but, instead, vary considerably. We analyze the forest impacts from roads on a specific large forest frontier -the Brazilian Amazon early in its development. This informs infrastructure choices for specific other sites and generally demonstrates the value of distinguishing settings in terms of their SDG tradeoffs and synergies. We conclude, within our Discussion, by distinguishing this particular forest frontier from other key forest frontiers that seem different a priori and for some of which the impacts of new roads are being examined.
For Brazil's Amazon, tensions between the foci now represented within different SDGs have long been clear, for a region of high biodiversity whose forests play key roles in carbon and hydrologic cycles. In the early 1960s, the Brazilian government began to build roads to link to other parts of Brazil and, within decades, over 10% of this forest was cleared with annual loss in the millions of hectares (Laurance et al. 2004). From the early 2000s, there have also been calls to pave roads for development objectives, including the expansion of soybean exports (Laurance et al. 2001, Fearnside 2001, Nepstad et al. 2002. 1 Here, instead of simply estimating average impacts of such new road investments upon the forest, we model the variation in road impacts on deforestation as a function of prior development. The differentiated predictions guide empirical tests of significant variations in _________________________ road impacts on this important forest frontier as the region developed. Such variations in road impact would suggest that shifting road locations could generate less deforestation for the same development.
For early frontier days, we believe the classic von Thunen market-center model is appropriate for consideration of three different contexts that are distinguished by their market distance and profitability. Others have long used this model for early frontier development 2 , though not for variation in road impact.
This model predicts that new deforestation due to a road investment is low if, given other factors, prior development already led to high prior deforestation. For intermediate levels of prior development, roads are predicted to generate more deforestation, given more parcels 'at the margin' of profitability. Finally, the model predicts little short-run deforestation impact of new roads within the distant, isolated and currently undeveloped frontiers (for this setting, we discuss long versus short run and consider interactions with other policies 3 ).
Moving away from market center, this model predicts lower, then higher, then lower road impact. Such a pattern would not be generated by the endogeneity of roads' locations to more profitable locations. If new roads go to sites with unobservable drivers of deforestation, that could bias each of our estimates, yet such location biases for road investments would not predict the patterns of road impacts we highlight.
Unlike almost all of the work in this literature to date (though fortunately this is being remedied), our data include roads changes over time and, in fact, two such sets of roads investments that were made before the periods (1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1986)(1987)(1988)(1989)(1990)(1991)(1992) of deforestation that we are trying to explain. The periods are, by design, part of early development on this Amazon frontier. They permit results concerning dynamics in early growth, i.e., for one important type of frontier dynamic (our discussion considers other frontiers with different dynamics).
To have sufficient observations for each prior-development setting on this early Amazon frontier, as observations we use census tracts -considerably smaller than the county units often studied for Brazil. For 1976-1987 clearing, they confirm the short-run predictions from our model. Forest impact is close to zero from the new roads in the regions with the highest prior development. In regions with intermediate levels of prior development, however, the deforestation following the new road investments is significant. Finally, for regions of low prior development, new roads generate little deforestation across this period.
For 1986-1992 deforestation, again we can confirm predicted spatial variations in roads' impacts. Specifically, for higher past development again we see low impact. For intermediate past development -more common with ongoing development -again we see higher impact. For 'low prior development', our results for this time period depend on how we define 'low development'. Using zero prior deforestation, which summarizes all influences, again new roads have small, even statistically insignificant impacts on deforestation. To stress the importance of understanding evolutions during ongoing development, though, we also show that if defining 'low prior development' using low prior roads alone, i.e., ignoring other relevant elements of _________________________ 2 Given other settings of economic development and deforestation we must mention analyses such as Mather (1992), Foster and Rosenzweig (2003), Chomitz (2006) and recently, adding road empirics to their overlaps, Kaczan (2017).
3 For a few years to a decade, i.e., the typical time period for deforestation studies, far out on the frontier labor and other inputs can be insufficient to permit large rapid changes. The long run can be much the same or very different.
Economics: The Open-Access, Open-Assessment E-Journal 12 (2018-11) www.economics-ejournal.org 4 ongoing development, then we find new road impacts are as high as the road impacts with intermediate prior development. Thus, we can see that any region, such as the Brazilian Amazon, will evolve over time in ways that affect the SDG tradeoffs involved in infrastructure investments. That said, the policy relevant differences in roads' impacts by level of prior development are quite robust over time. The rest of the paper is as follows. Section 2 reviews prior work concerning impacts of roads -for SDG purposes including economic effects, both aggregate and on poverty, as well as forest impacts. Section 3 presents our derivation, based on the von Thunen (1826) model, of predicted impacts variations. Section 4 presents our data and specification, Section 5 discusses all our results, then Section 6 concludes.

Varied Development Benefits of Roads
If roads' economic or, more generally, development or SDG benefits were uniform across the landscape, roads' deforestation impacts might determine optimal locations. However, benefits vary. For the Brazilian Amazon, e.g., Andersen et al. (2002) find in census data that economic impacts may be higher where prior development is higher, e.g., near cities. This opens the door to SDG synergies from the choice of new roads' locations: if forest loss is lower in such areas, new roads near prior development may maximize total gains in SDGs. Varied rural road benefits are a focus in van de Walle (2002). Evaluations that study travel time or output without distinguishing groups by poverty are criticized for leaning toward the developed areas. Rural roads may generate less of the kinds of benefits that tend to be counted officially, yet more social benefits that tend not to be. Illustrating this for Vietnam stresses the value of identifying, with sufficient resolution (a data point in our conclusion), whether a new road improves access for each group. Gibson and Rozelle (2003) also ask where benefits are high. They consider Papua New Guinea, where terrain and history yield transport gaps, and stress that understanding where road access is a factor in poverty helps to target impact. Their focus on access, and their poverty objective, motivate attention to rural frontiers. Examining areas with relatively low prior development, with or without an instrument for roads, their evidence suggests that roads reduce poverty if the prior access to infrastructure has been low. Warr (2005)'s evidence for rural road benefits highlights a positive interaction between economic reforms and access to markets. It distinguishes year-round market access from only during dry seasons, finding that raising access in wet seasons lowers poverty. Reducing poverty is again the central objective, which is noted to differ from maximizing benefits in the aggregate, such that the objective affects relative measured benefits across the road options in question. Methodologically, the use of road changes is suggested for addressing endogeneities in road siting -in agreement with our emphasis upon building up intertemporal data.

Varied Ecological Costs of Deforestation
If economic benefits and deforestation impacts were uniform across the landscape, then arguments about variations in ecological costs of forest loss might determine optimal road locations. A brief review of early literature on conservation and species, e.g., could highlight 'scoring', 'iterative', and 'programming' approaches to maximization of species benefits. 'Scoring' ranks each site by contribution to the objective, then proceeds down a ranked list. 4 This allows inefficient duplication, however. 'Iterative' analyses avoid duplication by ranking marginal contributions conditional on prior protection: the top-ranked site is protected; and then all the other sites are re-ranked. 5 'Programming' approaches uses standard operations-research techniques. 6 Unlike sequential approaches, they compare entire choice sequences so that earlier choices are evaluated in light of later choices of site. Generalizing, weights on forest loss could differ across sites.

Varied Deforestation Impacts of Roads 7
For the Brazilian Amazon, Almeida (1992) examine colonization and migration, while Reis and Margulis (1991) and Reis and Guzman (1992) also find roads to be key drivers of deforestation. Pfaff (1999) adds that population's spatial distribution (and thus urbanization) is critical, while roads matter not only within but also across counties. 8 Laurance et al. (2001)'s discussion of deforestation from roads has an 'optimistic' scenario with loss of 28% of pre-Columbian forest by 2020 (but with 42% lost in a 'non-optimistic' scenario). Such work stimulated debate about assumptions for average and heterogeneous roads impacts. Heterogeneous impacts can explain why average impact estimates have not always been large (Chomitz and Thomas 2003 for Brazilian Amazon). Nelson and Hellerstein (1997) explicitly suggested that impacts may vary across space. For central Mexico, they find that the existence of prior roads in an area influences road impact. Thus, average impact could misrepresent every setting. Alongside Chomitz and Thomas (2003)'s observations, we must ask if average impacts understate some higher roads impacts. Andersen et al. (2002) pursue heterogeneous impacts of roads by studying Brazilian census data. They ask if impacts vary with past deforestation, using an interaction effect so that high _________________________ past deforestation has monotonic impact. This contributed as an approach and the result is consistent with one of our results.
That estimated interaction also means that high enough prior deforestation implies that new roads reduce deforestation. Weinhold and Reis (2008) extend this claim empirically and by suggesting spatial intensification: development is drawn to roads, so it falls in places near to but without an own new road. Refuting that hypothesis, Pfaff et al. (2007) show that nearby census tracts 9 not receiving new roads, yet in the same county as a census tract that did receive a new road, actually increased in their deforestation.
Another economic interaction that might underlie such empirical associations for forests is trade. In the New England region within the United States (Pfaff 2000 andWalker 2010), for instance, investing in railroad connections to the Midwest raised New England forest, as agricultural production fell in the latter given more efficient Midwest production. Pfaff and Walker (2010) suggest that analogous rising net imports will not soon save Amazon forests. Our model is a different economic story for forest impacts of roads, one conditioned on prior development and not suggesting that roads lower deforestation.

3
Modeling Road Impacts

Prior Development Landscapes
Our modeling follows von Thunen (1826) in terms of where we expect clearing for agricultural development. One agricultural good is produced. All land extends out from a market, is originally forested, and remains so until cleared for agriculture. One unit of agricultural good is produced in each location, i, yielding agricultural profit π i = P -t i -c iε i, where: P is the output price at market; t i is transport costs to market from parcel i; c i is the cost of production per unit of output in parcel i; and ε i is an identically and independently distributed random term that represents unobservable factors favoring forest profits over clearing profits. For modeling deforestation empirically, the random term provides an indication of factors beyond market price and transport costs. Key factors include soil quality, land slope and local policy. Above, c i indicates observable elements of those determinants, some of which we include in our empirical analyses. Unobservable elements are denoted by the random term ε i . For our empirical work, that motivates error terms. We reflect their potential importance in model predictions (Figures 2 and 3) and in interpretations.
Profit maximization implies a probability of any given parcel being cleared in static equilibrium: Lacking census-tract detail implies at most 300 municipio or "county" units for study over time. That limits study of heterogeneity, in particular for Brazilian Amazon counties that can be huge, making the data for county units misleading for census tracts. Figure 1 shows how different are the census tract and county representations of a road. 2). It is clear in this example that the counties are much larger than census tracts. Thus, as can be seen with this example of a road linking to Manaus, a market center, census tracts allow more spatially precise testing.
where Φ is the cumulative function for a single-peaked distribution with mean and peak at zero. Figure 2 -assuming a common c i -shows how the probability of deforestation falls as t i rises. Highly varied prior development and deforestation are seen in three zones distinguished by 'Expected Profits': 1) high prior development near market center; 2) forest margin where expected profits are zero and parcels are near the margin; and 3) low prior development farther from the market center on isolated, less developed frontiers.  (1826) idea, these zones 1, 2 and 3 are increasingly distance from a market center which is at the intersection of the two bold black axes. At that market center, expected profits are positive. However, they fall (the blue line) with distance from the center, eventually becoming negative on average. Yet with heterogeneity of parcels at any given distance (colored distributions), some parcels are profitable.

Short-Run Road Impacts
Road investments lower transport costs, so that we expect land-use change. The first derivative of the probability of deforestation at i in (1) with respect to t i indicates heterogeneous deforestation impacts: Figure 3 conveys (2)'s prediction. The impact of a transport-cost reduction isφ . It depends on the density of parcels that become profitable with a road and, thereby, on where the prior land-use equilibrium stood.  (2) and refer to the variance of the epsilon term in that equation (as well as (1)). Simply put, the greater is the single-peakedness of the distribution of unobservable factors, the stronger will be the prediction of non-monotonicity for the impacts of new roads investments, as they sweep through that distribution.
Most striking is the non-monotonicity of the impacts of new roads. Impact is low where there was higher prior development and deforestation, nearer to the market center (low transport costs in Figure 3), since most forest is cleared before the investment. Impact is low also for low prior development and low prior deforestation, farther from market (to the right in Figure 3), since marginally reducing transport costs makes newly profitable only the few parcels with random terms that highly favor profit in clearing.
Near 'the von Thunen forest margin', where expected net profits are close to zero and there is an intermediate level of prior development and deforestation, many parcels may become newly profitable due to a road investment, yielding higher road impact. Such a pattern of new roads' marginal impacts on deforestation follows directly from single-peaked distributions of the random term. A uniform distribution yields zero impact in either tail but a positive and uniform impact within the support (relative to which a standard von Thunen model, with no land-quality variation, simply shrinks the range with impact). Thus, for many settings, roads' predicted short-run impacts will vary non-monotonically with past development.

Longer-Run Development Dynamics
After a road better connects a frontier, public and private investments may follow (yet data sets may well not include them). Settlers will lobby locally for additional roads, schools, agricultural subsidies and other investments that raise their quality of life. Investments, in turn, affect decisions by migrants and producers. Dynamic interactions, likely with path dependence between public and private decisions, then affect forest outcomes -and such processes could have impact beyond the location of the road investment (which empirically means beyond a unit such as a census tract in which investment occurs (Pfaff et al. 2007)). Thus, frontier conditions change as development unfolds, again perhaps in ways not captured in data sets. Prior road investment nearby, e.g., may lead to unpaved road extensions that we do not observe in our data set even though they influence deforestation. Nearby prior roads may indicate such processes. By our second time period, we might expect more unobserved improvements that facilitate development. Thus, we want to examine new roads' impacts by time period.

Data
We use census tracts to have more observations than the counties in many Brazilian Amazon analyses (Reis and Guzman 1992, Pfaff 1999, Andersen et al. 2002, Weinhold and Reis 2008. This increases our cross-sectional units from under 300 to over 6000 -which is extremely helpful because to address spatial variation in road impacts, our intended focus, we want to be able to estimate more than just a single average road impact. Table 1 presents statistics for these smaller sampling units that, on average, are under 1000 km 2 .

Deforestation
We examine measures of the deforestation during 1976-1987 and 1986-1992. For the first period, the maps we used were produced in 1997 by the IBGE (Instituto Brasileiro de Geografia e Estatistica) for their "Diagnostico Ambiental da Amazonia Legal" data product. Our 1976 forest cover is from RADAM Project vegetation maps. The forested area information for 1987 is from IBAMA/INPE maps based upon Landsat imagery. For our second time period, the 1986 and the 1992 forest observations were generated by the TRFIC (Tropical Rain Forest Information Center, www.trfic.msu.edu/products/amazon_products/), located at Michigan State University, and are derived from Landsat data with a spatial accuracy of 1km. For a given census tract, at any point in time we know the fraction of area in forest. To compute deforestation by 1976 required a map of the original extent of forest in each census tract (as noted earlier, significant areas were not originally forest). Our 'Deforestation 1976' variable is the fraction of original forest area gone by 1976. Similarly, for each period, our dependent variable (fraction of the forest cleared during the period) is computed from the loss of the forest area that was present at the start of the period.

Roads
We tracked roads changes over time from highly spatially specific maps. Digital road maps were developed at the Department of Geography at Michigan State University from paper maps  1968, 1975 and 1985, we measure paved-road and unpaved-road density, i.e., length divided by the census tract's area. This permits initial road measures before investments and two periods of changes. We emphasize that our time periods for measuring road changes each come before the periods of deforestation. As Warr (2005) notes, using road changes is particularly useful for helping to address the issue of endogenous road placement. Having road changes come before forest changes helps even more. We had measures of road investments in neighboring census tracts for our first investments, i.e., the 1968-1975 roads changes. To check robustness, to this we added neighboring-tract road investments for 1975-1985. For each census tract, and time period, we have indicators for whether a tract in the same county received road investments (in 100km rings around the tract in question). These help to distinguish where the new investments in roads truly are the most isolated, from among many census tracts that have relatively low prior development (which, again, is measured using the prior roads and prior deforestation).

Factors
We control for distances from the census-tract centroids to cities. We use both a set of 19 large cities ('large' defined as a density over 100 people/km 2 ) as well as another set of 270 medium and large cities ('medium' defined as a density over 11 people/km 2 ). We include these urban or market distances as variables in our regressions -but also, wanting to focus upon the settings where deforestation is highly relevant, we use the city distances in various ways to drop some urban areas in order to check robustness.
We have maps of biophysical conditions. The variables we employ are an index of soil quality, a continuous measure of rainfall data (see Laurance et al. 2002 for discussion, as well as the original extent of the forest) and binary variables that indicate categories for land slope (e.g., whether land is 'steeply sloped' land or 'rolling hills'). Finally, we also include county indicator variables to help to control for all of the unobservable county characteristics. This provides controls for the many possible differences, such as price and production costs, which vary by county but are common across the census tracts in a county. These controls are made possible by the census-tract data and are very useful given the size of this region.

Core Specification
Since the census tracts are quite varied in their areas, and we want results for an average forest parcel facing the threat of clearing, we weighted the following regression using census tracts' forest areas: %Deforestation t to t +1 = β 0 + β 1 *Roads Investment t-1 to t + β 2 *Prior Roads t-1 + β 3 *Prior % Deforestation by t β 4 * City Distance + β 5 *Soil + β 6 *Rain + β 7 *Slope + β 8 *County + ε Per (3), it is worth reiterating how our data permit progress on identification of roads' impacts. Deforestation is change over time in the forest outcome of interest, measured across each of our two time periods. However, while many analyses have used forest-change measures, many fewer have had in hand changes in the roads over time, i.e., road investments as opposed to just a road's presence within a unit. Without such changes, i.e., with just a snapshot of a road at a point in time, we do not know when any given road came to be present and, thus, whether we should expect its presence to have ongoing effects.
Our roads-changes measures are for periods before our forest-changes measures, eliminating the possibility that roads responded to the deforestation we explain. It is, of course, possible that road creation was forward-looking, e.g., developers picked regions where future economic activity and deforestation were expected. However, even if so, county dummies provide a partial remedy. Because road-investment impacts are estimated using within-county variation across tracts, in order to bias our roads coefficients such endogeneity driving road location would have to be picking out particular census tracts in a county.

Prior Development
Our specification above indicates that we always control for prior roads and deforestation. When we move to a focus on heterogeneous impacts, we expect road impacts to vary with prior development. Here we discuss the rules we use to split levels of prior development. We can use them to split our sample or to interact prior development categories with roads investments. All our rules are based on prior roads and prior deforestation, noting that prior deforestation is a more comprehensive summary of the settings.
We chose initial definitions of higher, intermediate and lower prior development a priori, without looking at the data, i.e., simply trying to think about what might characterize such levels of development. One natural option was that 'lower prior development' would mean no prior roads or prior deforestation, while 'higher prior development' would mean somehow having both prior roads and prior deforestation.
To better distinguish settings, we defined 'higher prior development' as tracts with prior roads, plus prior deforestation of over 25%. Correspondingly, we defined 'lower development' as no prior roads but deforestation up to 25%. For results tables, we arrange the census-tract groups from highest prior development to lowest. Thus, "High Prior Dev1" is the stricter definition above that requires greater prior deforestation. For our ordering, the smaller strictly defined group of low tracts will be "Low Prior Dev2".
For robustness, we also considered other rules such as 12.5% prior deforestation for both ends of the spectrum and, as always, 'intermediate' in the middle (i.e, the tracts with no prior roads above 12.5% prior deforestation and the tracts with prior roads below 12.5% prior deforestation). For all these divisions to check robustness we used different rules to drop tracts based on distance to city including: within 30km of a city; within 5km of a medium city; and within 10km of a large city. All our broad patterns are robust.
Finally, we note that our 'lower prior development' range had many tracts (i.e., over two thirds). To distinguish among these tracts, we shrank the 'lower prior development' category by including only tracts with no prior neighboring investments either. This makes the 'intermediate' category larger, since some relatively higher 'lower prior development' tracts move up. This sometimes shifted the impacts but often did not. Importantly, it dramatically shrunk the 'lower' group, often to reveal a smaller road impact.

Average Impacts of 1968-1975 Road Investments
On average, road investments increase deforestation in this time period, with a highly significant impact from increases in road density, even controlling for the prior road density before road investment ( Table 2, 1 st column). The prior road density is highly significant as well, as is total prior deforestation. We stress that these two indicators of prior development provide quite strong controls for road impacts. The analysis also confirms important controls for inferences concerning new road investments, as greater market distance discourages deforestation while higher soil fertility increases it. Rainfall and slope also significantly constrain economic production, and thus deforestation, yet we highlight that the county dummies absorb much of the spatial variation that could be used for estimating effects of those factors (e.g., without counties all the rainfall terms are significant, with linear terms positive and quadratic terms negative). Therefore, across our tables we simply indicate that we control for counties, rainfall and slopes.

Road Impact by Prior Development
For the small set of 'higher prior development' tracts, road investments did not significantly raise deforestation (Table 2, 2 nd & 3 rd columns). That holds for both definitions of 'higher prior development' (Table 2), as well as for the robustness check that employed 12.5% for prior deforestation (not shown).
The early state of this frontier had few 'higher prior development' tracts. That limits our tests yet, as a robustness check, we can interact continuous 'prior development' with road investment (Table 3, 1 st & 2 nd columns). Given our non-monotonic prediction, we interact with the road investments both linear and quadratic prior road density, plus linear and quadratic prior deforestation. Neither prior-deforestation term is significant, nor is the quadratic prior-roads term (1 st column). Thus, for easier interpretation, we include only the significantly negative linear term for the interaction of the prior road density with these roads investments (Table 3, 2 nd column). The result supports our conjecture that higher prior development reduces new roads' impacts. (We cannot test the low category this way as many tracts had no prior roads.) For 'intermediate prior development', we find quite robust results (Table 2, 4 th & 5 th columns). Generally, we find new roads' impacts similar to the average impact for the entire set of census tracts. Supporting our model, 'intermediate' impact is above the 'lower' impact (6 th and 7 th columns) and also above the 'higher' impact (2 nd and 3 rd columns but, again, better illustrated by Table 3's columns 1 and 2).
We highlight the lack of significant impact even for the large groups of census tracts that qualify under our two definitions of lowest prior development (Table 2, 6 th & 7 th columns). If we use absence of prior roads and prior deforestation for this definition, over two-thirds of our sample qualified. Thus, to identify some census tracts with even lower relative prior Table 2. Explaining 1976-1987Deforestation with 1968-1975    Weights are tracts' initial forest areas. Coefficients are presented with standard errors (asterisks for significance). Dropping all of the census tracts with centroids within 5km of any of the locations that we define as a large city.
b High Prior Development: in Dev1, prior roads and prior deforestation is > 25%; in Dev2, any prior deforestation.
Intermediate Prior Development: always defined as all of the tracts with lower than 'High' but higher than 'Low'. Low Prior Development: in Dev1, no prior roads, prior deforestation up to 25%; in Dev2, no prior deforestation. For neighbor investment: in Dev 1, none in tracts with centroids <= 100km; in Dev2, none in tracts out to 200km.      Weights are tracts' initial forest areas. Coefficients are presented with standard errors (asterisks for significance). Dropping all of the census tracts with centroids within 5km of any of the locations that we define as a large city. b High Prior Development: in Dev1, prior roads and prior deforestation is > 25%; in Dev2, any prior deforestation.
Intermediate Prior Development: always defined as all of the tracts with lower than 'High' but higher than 'Low'. Low Prior Development: in Dev1, no prior roads, prior deforestation up to 25%; in Dev2, no prior deforestation. For neighbor investment: in Dev 1, none in tracts with centroids <= 100km; in Dev2, none in tracts out to 200km. c coefficient multiplied by 1000 (per kilometer instead of per meter) development, we dropped those tracts that had any neighbor-tract road investments, out to 100km (6 th column) or even 200km (7 th column) from a tract. For this time period, then, we have sufficient observations to test impact for very low prior development.

Average Impacts of 1975-1985 Road Investments
In this period too, new roads increased deforestation on average (Table 4, like Table 2). New roads are significant on average even with controls for prior road densities and deforestation (1 st column), and with many other variables as controls (Table 4 -again much like Table 2 for our earlier time period). Thus, for our second time period, we find impacts from road investments even with very strong controls. Yet we would also highlight that this average impact estimate for new road investments (Table 4) is one-eighth the magnitude of the previous impact estimate (Table 2). This supports our conjecture about the potential challenge when comparing across different time periods in development, given significant shifts that are common within any given development setting, including shifts common across this region such as exchange rates, diseases such as hoof-andmouth, and the status of national and global economies. Below, we examine further within this second deforestation time period, across prior development levels.

Road Impact by Prior Development
For the stricter definition of 'high prior development', we can see that development has occurred simply through the number of observations (Table 4, 2 nd column). The set of census tracts that qualify for the stricter 'high prior development' category is roughly five times as large as it was for the first period. Supporting the strongest version of our predictions, even for this larger strict group in the second period we find that roads have little or no impact. This supports that high prior development lowers new roads' forest impacts, as was suggested by negative new-road interactions with prior roads (Table 3, 3 rd column).
The less strictly defined 'high prior development' category also conveys development over time via its number of observations (Table 4, 3 rd column). For this category, roughly ten times as many tracts now qualify. Within this larger group with a less strict definition, though, we find significant new road impact -although lower than the average impact, still consistent with a weaker version of our predictions.
Our prediction about the significant impacts of new roads in the 'intermediate prior development' category is confirmed as well (Table 4, 4 th & 5 th columns). As before, this group of tracts has an impact similar to average impact (Table 4, 1 st column). Our 'middling prior development' result is quite robust.
Our definitions of 'lower prior development' (Table 4, 6 th & 7 th columns) tell different stories and the difference in estimated impacts suggests rises across time in unobservable elements of development. When 'lower prior development' is defined solely by lower prior road density, development can be driven ahead by varied factors, including ones we do not observe.
Despite the observed lower prior road density, other factors could raise impact and we find an impact similar to 'intermediate', despite no prior roads (6 th column). Yet if zero prior deforestation defines 'lower', then the result still fits a prediction of no impact (7 th column). The set of such census tracts is shrinking, showing the value of studying early development.
Further support for our predictions is provided by interactions (within the 3 rd column of Table 3). Both interactions with prior deforestation are significant (and prior deforestation's greater influence in the 2 nd period supports conjectures above). The positive linear interaction and negative quadratic interaction suggest exactly that new-road investments raise deforestation most for 'intermediate' prior deforestation. Finally, with sufficient observations in each 'prior development' category for this period, we supplement results from Table 4 by interacting categories with roads in Table 3 and we find support across the tables.

Discussion
To illustrate variation in roads' SDG tradeoffs and to inform the search for synergies, we tested a prediction of heterogeneity in roads' impacts on deforestation across Brazilian Amazon frontiers, early in the region's economic development. We show that the deforestation generated by new roads investments rises then falls with the level of prior development: smaller impact where high prior development already occurred; larger impact at the forest margin; but smaller impact again for isolated, undeveloped frontiers. Since our indicators of prior development are easily observable by policy makers, such results suggest that strategic siting choice for transport infrastructure could considerably reduce tradeoffs between SDGs. Further policy suggestions can arise from combining our results, for roads' varied forest impacts, with complementary perspectives concerning spatial variation in other types of costs or benefits of roads. If roads have more impact on economic growth when prior development is significant, such as near cities (Anderson et al. 2002 find this for the Brazilian Amazon), then perhaps both urban economic growth and standing forests could benefit from patterns of investment in transport that are oriented around big cities. If roads cause greater damage to ecosystems on isolated, currently intact frontiers, that too could guide road siting away from rural spaces (see, e.g., Mahmoud et al. 2017 about a proposed highway in Nigeria).
Our specific results for relatively isolated frontiers are relevant for some other sites, though they also show that the specific processes generating spatial allocations of new roads affect both impacts and the challenge of controlling for heterogeneity across frontiers in order to correctly estimate roads' impacts (for instance, if roads are built to connect distant large cities, across large rural spaces, average impact is potentially very different from when roads extend slowly outwards while around urban areas). While we highlighted that our particular estimates of roads' impacts show an opportunity for 'SDG strategic' siting, also we emphasize that opportunities for SDG optimization in road location vary with the type of frontier (our results support this idea through a shift in whether low prior roads identify 'low prior development'). More such empirical work for other locations will be welcome, yet here we can speculate across frontiers.
As does much of the empirical literature on roads to date, our results for early Brazilian Amazon development concern frontiers relatively low both in population density and in the presence of the state. They would also be characterized as being early within the common 'structural transition' of an economy, with a high share of the economy being in the agricultural sector versus, e.g., in the manufacturing sector.
Such features definitely are not fixed across all of space and time. For instance, it is clear that in some countries, environmental governance is significantly stronger than in others. Indeed, regions within a country can vary considerably (see, e.g., Rico-Straffon et al. 2017 per concessions in the Peruvian Amazon). For the Brazilian Amazon, states vary considerably in environmental orientation (e.g., Rondonia versus Acre) while, in addition, at the regional and the national level environmental governance has shifted across time. This is relevant because such differences affect the forest impacts of roads. As one simple example, it is clear that protected areas located near to roads can greatly constrain their forest impacts (Pfaff et al. 2015 show that such forest impacts are a joint product of the governance and regional development). A striking case to show this in the Brazilian Amazon is Acre's Chico Mendes Extractive Reserve (Pfaff et al. 2013).
Returning to varied economic dimensions along which developing forested frontiers might differ, SDG tradeoffs for roads are likely to differ if considering locations with considerable prior development. For instance, Kaczan (2017) considers India and a post-2000 program of investment in rural roads. There, not only has forest been rising across decades but also, on average, new roads slightly raised forest cover. That too can make sense, given completely different mechanisms or behaviors (e.g., using natural gas in place of fuelwood or going to work in cities) affected by transport costs within more developed frontiers.
Even after we have dealt with average differences across frontiers, distinguishing via key details of specific sub-frontiers again provides additional information relevant for policies, such as road location. For the locations in India that are more isolated, i.e., more like some of the Latin American forest sites of focus in much past roads literature, new roads actually lower forest cover. Yet within those parts of India that feature much greater ongoing development, road investments more significantly raised forest cover. Going forward, such distinctions across forested frontiers will be critical within the pursuit of the SDGs.