National Academies Press: OpenBook

Improving Crop Estimates by Integrating Multiple Data Sources (2017)

Chapter: 4 Sources of Data for Cash Rents

« Previous: 3 Multiple Data Sources for Crops: Challenges and Opportunities
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

4

Sources of Data for Cash Rents

Because land is the primary input to agricultural production, its value and the rent it garners are key indicators of the financial health of the farm sector. According to the 2012 Census of Agriculture, almost 40 percent of agricultural land is rented.1 The National Agricultural Statistics Service (NASS) estimates thus provide reference points for transactions in a significant market for farmland. Accordingly, NASS has regularly sought to improve the quality of its cash rent estimates and, as with crop yields, has sought additional sources of data to bolster its predictions.

The current NASS Cash Rents Survey is sponsored by the Farm Services Agency (FSA), which uses the results in determining payments to farmers under the Conservation Reserve Program. In its surveys, NASS asks respondents to report acres rented and either the cash rental rate or the total dollars of rent paid. NASS computes cash rental rates as the ratio of total dollars paid in rent within a geographic area to total acres rented in that area based on responses to the Cash Rents Survey (used for county-level estimates) or the annual June Area Survey (used for state-level estimates). The methodology for these surveys is described in Appendix A. The Cash Rents Survey is sent to about 275,000 farms every other year, while the June Area Survey results in about 35,000 interviews.2

This chapter summarizes the auxiliary data available for improving the estimation of county-level cash rents, describes the model for cash rents

___________________

1 See https://www.agcensus.usda.gov/Publications/2012/Online_Resources/Highlights/Farms_and_Farmland/Highlights_Farms_and_Farmland.pdf [July 2017].

2 See https://www.nass.usda.gov/Surveys/Guide_to_NASS_Surveys/June_Area [July 2017].

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

that currently provides input to the Agricultural Statistics Board (ASB), and summarizes how NASS might transition the ASB process for estimation of cash rents to one that is more transparent and reproducible.

AUXILIARY DATA FOR CASH RENTS

Auxiliary data for cash rents are potentially valuable for improving estimates derived through models. NASS has noted that spatial and temporal relationships of cash rents are quite stable and that cash rent values may be related to land values, soil productivity, yield, and climate. Cash rents reflect the value of the farmland asset in crop production, a relationship that can be modeled statistically. A number of sources of auxiliary data for use in a cash rents model are available.

First, the U.S. Department of Agriculture’s (USDA) Economic Research Service (ERS) and NASS jointly sponsor the Agricultural Resource Management Survey (ARMS), which, among other things, collects land value information from farms annually. The sample size of the ARMS is about 30,000 farms and ranch operations each year. The ARMS Tenure, Ownership, and Transition of Agricultural Land (TOTAL) survey collected cash rental rates and farmland values in 2014 from landlord owners of agricultural land, including nonfarm operators of agricultural land, as a follow-on component of the Census of Agriculture program. Data are available only for the U.S. total and 25 states. The U.S. sample size was 41,205.3 A similar survey, the Agricultural Economics and Land Ownership Survey, was conducted in 1999. Farm real estate values (land and buildings) are collected in the Census of Agriculture.4

Second, county tax offices may have tax information on land values and real estate transactions. However, the definitions and formats they use are inconsistent. Commercial vendors have compiled tax information and made it publicly available for purchase. Examples include the following:

  • Core Logic has data on land values and geospatial parcels.
  • Boundary Solutions Inc., another parcel data company (a competitor of Core Logic, states on its home page that it is the custodian of the national Parcelmap Data Portal, which also includes extensive tax roll attributes).
  • Acrevalue by Granular advertises on its website that users can “view GIS [geographic information systems] maps that compile

___________________

3 See https://www.agcensus.usda.gov/Publications/2012/Online_Resources/Highlights/TOTAL/TOTAL_Highlights.pdf [July 2017].

4 See https://www.agcensus.usda.gov/Publications/2012/Online_Resources/Highlights/Farm_Land_and_Buildings/Highlights.pdf [July 2017].

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
  • agricultural data, including farmland values, soil productivity ratings, crop mix, and parcel ownership information.”

Third, many, if not all, of the Federal Reserve Banks, including the Chicago, Kansas City, Dallas, and Minneapolis Federal Reserve Banks, conduct agricultural credit surveys. Additionally, land grant universities such as Iowa State and Michigan State collect information on and prepare estimates of cash rents and land values. The Purdue farmland value survey collects information from rural appraisers, commercial bank and agricultural loan officers, FSA personnel, farm managers, and farmers. These private surveys tend to be collected during the spring of the year and published in August, timing similar to that of the NASS Cash Rents Survey.

Finally, land values are a function of characteristics of the land itself, geographic location, market prices, and eligibility for government payments. Nickerson and colleagues (2012) document a trend and correlation analysis of farmland values and the related macroeconomic and parcel-specific factors. For this analysis, they used estimates for cropland and pastureland values from the NASS June Area Survey. In particular, because the June Area Survey is an area survey, they were able to use its GIS identification of farm parcels to develop linkages to such parcel-specific (spatial) factors as soil quality, access to market terminals, government payments, proximity to development potential, distance to population concentrations, access to roads, and the land’s amenity value. Data available from the June Area Survey include cash rental rates, land values, irrigation status, and planted acres by crop. Among the variables found by the authors to affect farmland values were proximity to urban areas, soil quality, and irrigation status. Of note, they found that relationships between land values and the factors they considered were complex and varied in importance across location and time. For example, they found that the relationship between land value and soil quality was fairly consistent for farms that were at least 25 miles away from a city of at least 50,000, and was even stronger for parcels at least 40 miles from a population center. They also observed that patterns varied substantially across regions, with positive correlation between soil quality and cropland values in the Corn Belt, Lake States, and North Dakota (in the Northern Plains region), but a negative or insignificant correlation in the Appalachian region.

While the analysis of Nickerson and colleagues (2012) was intended to illuminate land values, a similar approach could be used to evaluate the factors associated with cash rents. In particular, the authors’ Appendix A provides a detailed description of the preparation of the input variables and indices used in the study. The examination and development of parcel-specific variables is of particular importance since the addition of Common Land Units (CLUs) to the NASS list frame would make the development

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

of unit-level models for cash rents feasible in the future. Currently, as described in the next section, NASS makes use of a cash rents model that considers previous-year rents but also a limited set of covariates that relate mainly to yield and soil productivity. Recruiting additional sources of data for the modeling effort and tying estimates to specific parcels of land could potentially improve prediction results.

RECOMMENDATION 4-1: The National Agricultural Statistics Service should work with the Economic Research Service to extend the Nickerson and colleagues (2012) analysis of parcel-specific variables that influence farm values to parcel-specific variables that influence cash rental rates. The results of this effort would illuminate the potential for additional modeling of cash rental rates once geospatial identifiers are available.

MODEL-BASED INDICATIONS FOR CASH RENTS

Berg and colleagues (2014) developed a model for producing county-level estimates for cash rents based on the (then) annual Cash Rents Survey, and illustrated the approach by applying it to estimation of cash rents for irrigated cropland, nonirrigated cropland, and pastureland in six diverse states. A primary motivation for investigating model-based estimates of cash rental rates was to guide ASB with a transparent and reproducible method for developing county-level estimates for cash rents in the above three categories, along with mean squared error estimates of those rents.

NASS first incorporated the Berg and colleagues (2014) model for cash rental rates into its official estimation process in 2013. In addition to direct estimates obtained from the Cash Rents Survey, which serve as the primary basis for setting official estimates, the Berg and colleagues (2014) model-based estimates were supplied as additional indications for ASB’s consideration in 2013, 2014, 2016, and 2017 (because, as described in Chapter 2, the survey was not conducted in 2015). See Bellow et al. (2017) for a summary of the impacts of the skipped year on the performance of the cash rents model. For now, NASS will likely need to maintain two versions of the model, one for the situation when surveys are conducted in adjacent years, and one for the situation when there is a 2-year gap between surveys.

The model described by Berg and colleagues (2014) consists of two univariate Fay-Herriot models—one for the average of the two yearly means and the other for the difference between the two yearly means—each with an auxiliary input index, as described below. The estimate of cash rents for the current year is then the sum of the average cash rents from the first model and half of the average cash rents difference from the second

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

model. The procedure recognizes the correlation between cash rents in the two consecutive years but assumes equality of variances in these two years.

The auxiliary input index is based on the county-level total dollar value of agricultural production from the 2007 Census of Agriculture; NASS’s published county yields for 2004–2009 to reflect the quality of the land in the county; one of four yield indices described below, depending on the county; and National Commodity Crop Productivity Indices (NCCPIs) for corn, wheat, and cotton from the Natural Resources Conservation Service. The yield indices include one based on combined yield from irrigated and nonirrigated croplands in states where these yields are not split, two indices for states where yields are split by irrigated and nonirrigated, and a separate hay yield index used to exclude hay crops from the irrigated and nonirrigated croplands.

Although this model meets many of the salient challenges that arise in actual operations, the simplifying assumption of equality of variances in the two years may not always hold and merits further investigation. The assumption is less likely to hold when surveys are conducted every other year rather than annually. A panel member discussed with NASS staff a bivariate hierarchical Bayesian model that circumvents this difficulty and warrants evaluation. Porter and colleagues (2015) provide another possibility, as do Bradley and colleagues (2015a). An evaluation of the model is described below.

RECOMMENDATION 4-2: The National Agricultural Statistics Service should develop and evaluate a bivariate hierarchical Bayesian model for cash rents that does not rely on the assumption of equal variances in two survey years. The intent would be to improve model performance, especially when surveys are conducted 2 years apart.

Benchmarking

The model of Berg and colleagues (2014) implements two-stage benchmarking that enables benchmarking the Agricultural Statistics District (ASD) estimates to the corresponding aggregated state estimates, and the county-level estimates to the corresponding benchmarked ASD estimates. The proposed method benchmarks the county cash rental rates to the average cash rental rate for the state, with weights based on the fraction of rented acres in the county, a procedure more sophisticated than the ratio adjustment currently used by NASS. The latter adjustment suffers from the drawback that all units are equally benchmarked to the corresponding aggregated unit and that the variation introduced by this process is not included in measures of uncertainty.

The current NASS procedure constrains the model’s predictions because they are benchmarked to survey results. Such benchmarking might appear

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

logical in the context of crop production estimates, when county and state estimates must sum to a preset, finite total of national output. But it is not obvious that the cash rents model should be treated similarly, as there is no analogous constraint on what could be spent on cash rents. NASS could develop unconstrained estimates using models that include the auxiliary data on land characteristics, geographic location, and subsidy eligibility discussed earlier. The performance of the two modeling approaches could then be compared. However, several references describe potential advantages to benchmarking. Pfeffermann (2013), for example, notes that benchmarking to higher levels when design-based estimates are deemed reliable may provide some protection against cases in which the model is misspecified. This benefit is especially important for time series models since they are “slow to adapt to abrupt changes.” Additionally, as observed by Berg and colleagues (2014, p. 23), benchmarking can reduce bias that may result from the modification of outliers, as noted by Gershunskaya and Lahiri (2010).

NASS Evaluation of Model-Based Estimates

At its January 2017 meeting, the panel heard a presentation by Cruze, Erciulescu, and Bellow, that has since been published in Bellow et al. (2017), assessing the suitability of the model of Berg and colleagues (2014) adjusted to accommodate survey data collected every 2 years. They described a careful evaluation of the model and its performance, expressing some frustration that the model did not always appear to result in improvements. They observed that, according to the 2012 Census of Agriculture, there were 2,764 counties with 20,000 or more acres of combined cropland and pasture. Cash rents are intended to be published for these counties. A cash rental rate for at least one of the categories (nonirrigated, irrigated, pasture) has been published for 93–95 percent of these counties since 2009.

The model is a clever way to gain strength by combining survey estimates for 2 years. However, it relies on the difference between individual farm-level survey responses in the 2 years as part of computing the estimate for the difference between the 2 years. This approach has obvious benefits except in counties for which the sample is thin, in which case there may be no or few such matched observations. Berg and colleagues (2014) note that the average number of respondents per year was approximately the same when the Cash Rents Survey was conducted annually. However, the average response rate in both years was 25–50 percent. The average number of farms responding in both survey years is a key indicator of the quality of the resulting model-based indications. Table 1 in Berg et al. (2014) illustrates that irrigated and nonirrigated cropland and pastureland have very different error characteristics. For example, that table shows that there was an average of less than one matched respondent for irrigated

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

cropland in four states, fewer than two in another state, and fewer than three in another state. If this characteristic persists, it may be unreasonable to expect to make much use of model-based indications for irrigated cropland. Results were somewhat better for pastureland, with only two states having an average of fewer than three matched respondents. Results were most promising for nonirrigated cropland. Because of the low match rate between respondents in the two survey years, the revised model using data from 2014 and 2016 could not produce an estimate for all counties for which ASB produced estimates.

The analysis presented to the panel displayed model results versus ASB estimates (indicating those suppressed for confidentiality purposes). The straight-line plots looked promising, but there were outliers, some of the most egregious of which were suppressed in ASB estimates. The model indication looked most like the Board estimate (adherence to a straight line) for nonirrigated cropland and irrigated cropland (except for suppressed values). Pastureland followed a line with outliers and variance clearly increasing with cash rent per acre.

A final table presented to the panel showed the number of times the ASB estimate fell within the 95 percent confidence interval of the model-based estimate. This table showed that 92–95 percent of the ASB estimates fell within the model’s 95 percent confidence interval.

NASS needs to determine how the model can help in providing high-quality estimates, and in which counties (or for which the characteristics of those counties) it will help the most. The model might be useful to NASS in two key ways. First, by combining 2 years of survey data and using covariates, the model may provide publishable estimates for some of the counties that are not currently publishable. Second, in some counties that pass the current publication standard, the model-based indications may have lower mean squared error, leading one to think that they would provide higher-quality estimates. This model is unlikely to support estimates of cash rents for irrigated cropland in counties where the sample is already thin.

The panel proposes that NASS prepare a summary illustrating the root mean square error or other summary uncertainty measure of the model-based indication versus the design-based indication for several categories of counties (a county that has between 3 and fewer than 30 respondents but accounts for more than 25 percent of acreage, a county that has fewer than 30 respondents and accounts for less than 25 percent of acreage, and a county that has 30 or more respondents). Within the latter two groups, some classification based on the number of matched respondents might also be useful to help in determining the characteristics associated with the best model performance. Summary statistics for the uncertainty measures might include the maximum, 75th percentile, median, 25th percentile, and minimum, as well as the average number of matched responses in the county.

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

Matched respondent groups might be 10 to 19, 20 to 29, 30 to 50, and more than 50. Ideally, this table would indicate where the model provides the greatest (or least) improvement. A similar table using counties published only because respondents cover 25 percent of acreage might indicate how well the model does for this set of counties.

This analysis would represent only a starting point. The intent would be to identify where the model works best and hence where and how it should be used, as well as where the model does not work well. Note that this model requires matched responses in two subsequent years to produce useful estimates, and cannot be expected to perform well in all counties for all land use categories. It may, however, provide improved estimates in some counties, and its ability to do so needs to be ascertained.

RECOMMENDATION 4-3: The National Agricultural Statistics Service should work with the Agricultural Statistics Board (ASB) and stakeholders to determine the circumstances in which the model of Berg and colleagues (2014) performs best and develop guidance on how the model indications should be used by ASB. In particular, tables illustrating uncertainty estimates for counties not currently publishable, those publishable only because respondents cover 25 percent of acreage, and those currently meeting publication standards would be most valuable.

THE AGRICULTURAL STATISTICS BOARD’S PROCESS FOR REVIEWING ESTIMATES FOR CASH RENTS

The remaining challenge is that, although model-based indications for cash rents are now available to ASB, there is no public information on how (or whether) they are used. NASS’s estimates are derived through its ASB process. The panel was told that the primary inputs to the determination of cash rental rates for irrigated and nonirrigated cropland and pastureland are direct indications from the Cash Rents Survey. Indications of total rented acres by category for ASDs are ratio benchmarked to add to the state totals used to prepare published estimates of cash rents at the state level. Next, county-level indications are ratio benchmarked to sum to ASD totals.

The panel was told that ASB strives for consistency in its estimates and makes use of all available indications (direct survey indications, past-year cash rents estimates, and model-based indications). Edit guidelines are described in the NASS Estimation Manual. The guidelines state, for example, that the current-year estimate should be between or on the current survey indication and the previous-year estimate. If the direct survey estimate has a sufficient number of reports and satisfies this inequality, it is likely to be used. The panel is unaware of guidance on specifically what is to be done if the inequality does not hold. The panel was told that large

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

counties with good reports are typically not adjusted by the ASB review process. Adjustments are made more often in smaller counties to make them consistent and fill in gaps so as to match the state total. Year-to-year outlier changes are verified with reports, historical knowledge, and field staff notes. Field offices are instructed to comment on, document, and justify changes to the survey-based indications. In 2014, 34,452 county-level estimates were developed with 939 (8.2%) ASB changes.

While the process is not particularly transparent and reproducible, the panel’s interpretation of the ASB changes is that the direct survey estimate was used for more than 90 percent of the county-level estimates. There is also evidence that NASS is keeping good records of decisions made as part of the process of selecting estimates. ASB’s cash rents estimation process would likely be the easiest to use as an example for converting to a transparent and reproducible process.

NASS already has established some rules for review of estimates that it uses to assist in ASB’s deliberation process. This experience can be used in creating formal and well-documented guidelines that would lead to a more transparent review process.

RECOMMENDATION 4-4: The National Agricultural Statistics Service should use its experience with the cash rents model results and other model-based approaches as a starting point for establishing a set of clear guidelines and rules for review of estimates before they are released for publication.

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×

This page intentionally left blank.

Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 79
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 80
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 81
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 82
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 83
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 84
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 85
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 86
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 87
Suggested Citation:"4 Sources of Data for Cash Rents." National Academies of Sciences, Engineering, and Medicine. 2017. Improving Crop Estimates by Integrating Multiple Data Sources. Washington, DC: The National Academies Press. doi: 10.17226/24892.
×
Page 88
Next: 5 Implementing the Vision and Beyond »
Improving Crop Estimates by Integrating Multiple Data Sources Get This Book
×
Buy Paperback | $65.00 Buy Ebook | $54.99
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

The National Agricultural Statistics Service (NASS) is the primary statistical data collection agency within the U.S. Department of Agriculture (USDA). NASS conducts hundreds of surveys each year and prepares reports covering virtually every aspect of U.S. agriculture. Among the small-area estimates produced by NASS are county-level estimates for crops (planted acres, harvested acres, production, and yield by commodity) and for cash rental rates for irrigated cropland, nonirrigated cropland, and permanent pastureland. Key users of these county-level estimates include USDA’s Farm Services Agency (FSA) and Risk Management Agency (RMA), which use the estimates as part of their processes for distributing farm subsidies and providing farm insurance, respectively.

Improving Crop Estimates by Integrating Multiple Data Sources assesses county-level crop and cash rents estimates, and offers recommendations on methods for integrating data sources to provide more precise county-level estimates of acreage and yield for major crops and of cash rents by land use. This report considers technical issues involved in using the available data sources, such as methods for integrating the data, the assumptions underpinning the use of each source, the robustness of the resulting estimates, and the properties of desirable estimates of uncertainty.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

    « Back Next »
  6. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  7. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  8. ×

    View our suggested citation for this chapter.

    « Back Next »
  9. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!