*Ecological Archives* A025-123-A1

Ashley E. Larsen, Steven D. Gaines, and Olivier Deschênes. 2015. Spatiotemporal variation in the relationship between landscape simplification and insecticide use. *Ecological Applications* 25:1976–1983. http://dx.doi.org/10.1890/14-1283.1

Appendix A. Methodological background and details.

*Fixed Effects Model Background*

The pooled model is represented by the following equation:

where Y_{i} is the response variable, the proportion of the county *i* treated with insecticides. X represents the vector of covariates including proportion of county in cropland, proportion of cropland in corn, soybeans and small grains, vegetables, fruit and nut orchards, and income per harvested hectare in each county *i*, and u represents the random error term for each county, *i*. In order to obtain an unbiased estimate of the vector b, the error must be uncorrelated with the vector of covariates X (Wooldridge 2002). If an unobserved variable is not included in the regression it is in effect is incorporated into the error term. Thus if that unobserved variable is correlated with one or more variables in X and the dependent variable, the estimate of the vector b will be biased (Wooldridge 2002).

The fixed effects model can greatly reduce omitted variable bias by controlling for time invariant unobserved effects unique to an area (e.g., soil quality) or shocks unique to a year (e.g., technological improvements) (Wooldridge 2002). Omitted variable bias occurs when variables that are predictive of the outcome and correlated with other covariates are not included in the regression. For instance, characteristics such as soil fertility or cultural practices are important determinants of agricultural land-use decisions (Deschênes and Greenstone 2007), but are not easily measured. Locational fixed effects, such as state or county fixed effects, isolate variation in land use to that which occurs within an individual location over time and thus can be very powerful when omitted variable bias is suspected. Due to low levels of within-county variation in the proportion of county in cropland in some ERS regions, we use state and region-by-year fixed effects rather than the county and year fixed effects. State fixed effects control for time invariant characteristics shared by counties within a state such as soil quality or farming practices, and region-by-year effects control for time trends or year shocks shared by all counties in a region, and thus will lead to more reliable estimates and inference. However, to the extent that the unobserved factors that cause omitted variables bias are not distributed evenly across counties, the state fixed effects model remains inferior to a model with county fixed effects. As noted above, the county fixed effect model is not possible in the current setting. State fixed effects still remove potentially important sources of unobserved variation such as state farming practices and historical legislation, and in this case preserve sufficient year-to-year variation in cropland at the state level for the fixed-effects estimation to be reasonably statistically precise.

*Additional Econometric Models*

To account for the possibility large farms use more insecticides, we reran the region-by-year model including proportion of harvested cropland in large farms as a covariate. We allowed this variable to vary regionally, but not annually. To further parse the observed spatiotemporal variability we included growing season degree-days and precipitation, Julian date of first fall frost and last spring frost, as well as first fall frost of the previous year as covariates in the region-by-year model to assess the possibility that these weather variables modified the relationship between landscape simplification and insecticide use. We calculated degree-days as follows: days with mean temperature below 46.4F (8C) contributed zero degree-days, days with mean temperature between 46.4F and 89.6F (32C) contributed the difference between mean temperature and 46.4F degree-days and days above 89.6F contributed 43.2 degree-days (Deschênes and Greenstone 2007). We calculated Julian date of last spring frost as the last date the minimum temperature dropped to or below 32F prior to July 1, and date of first fall frost as the first freezing temperature after July 1.We did not interact weather variables with region or year. Finally, we included a quadratic term on proportion of county in cropland allowing for a nonlinear relationship between landscape simplification and insecticide use. Again, we allowed this variable to vary regionally, but not annually.

To control for autocorrelation we used cluster robust standard errors clustered at the Agricultural Statistics District (ASD). We tested addition spatial autocorrelation models including Conley standard errors (Conley 2008, Hsiang 2010) as well as spatial error models at varying distances (300 km, 400 km). For computational ease, the spatial error models were run by individual region-year, using the same distance band for all regions and years. It is important to note there are limitations to this approach. In particular, using individual region models we cannot account for spatial autocorrelation between counties in different regions, even if counties are in close geographical proximity. Further, using a uniform distance band does not encapsulate differences in the extent of spatial autocorrelation known (from variograms) to be present in different regions. Despite these shortcomings, overall regional and temporal patterns were similar among the ASD, Conley and spatial error models. We leave it to future research to further investigate the nature of spatial autocorrelation in the landscape simplification-insecticide use relationship across regions.

Literature cited

Conley, T. G. 2008. in *The New Palgrave Dictionary of Economics*, Spatial econometrics, eds Durlauf SN, Blume LE (Palgrave Macmillan, New York)., pp 741–747.

Deschênes, O. and M. Greenstone. 2007. The economic impacts of climate change: evidence from agricultural output and random fluctuations in weather. The American Economic Review 97:354–385.

Hsiang, S. M. 2010. Temperatures and cyclones strongly associated with economic production in the Caribbean and Central America. Proceedings of the National Academy of Science 107:15367–15372.

Wooldridge, J. M. 2002 *Econometric Analysis of Cross Section and Panel Data*. First edition. MIT Press. Cambridge, Massachusetts, USA.