FAI locational research

Using FSRDC microdata, Dunn and Hueth (Reference Dunn and Hueth2017) show the number of crop services establishments is in secular decline, but the number of employees per establishment is growing. The authors also show that multi-unit establishments make up a relatively constant and small proportion of that sector and that business establishment births are in decline. Consolidation to exploit economies of scale in FAI is therefore likely an ongoing process that involves firms deciding to stay in business at their current location, to grow at their current location, go out of business, or move. This observation has two implications for FAI location research:

1. 1. The classic location question from industrial recruitment literature, that is, how to attract a branch plant, takes on a slightly different form with FAI, implying a need to explore fully characteristics associated with viability of existing locations rather than focusing exclusively on decisions involving new locations.

2. 2. A secular trend towards fewer and larger FAI establishments translates into more counties with suppressed data, leading to a need to aggregate across industries for a full data set. Aggregation can produce important shortcomings in estimations, as critical locational factors for one industry may be very different than another, even if they occupy the same two-digit NAICS sector. Thus, over time, as the number of suppressions grows, models based on public data may become less accurate.

Modeling approaches from industrial recruitment inform our analytical choices in exploring determinants of FAI firm locations. In the context of rural areas (non-FAI), manufacturing arises from several conditions. Importantly, the location choice literature reveals that rural areas can be attractive to manufacturing firms because wages, property taxes, and land costs can be lower than in metro areas, though rural workforce size can be a limitation. Unfortunately, research into rural manufacturing locational outcomes remains hamstrung by rural data suppression, which worsen with industry disaggregation.

A demand threshold is defined as the minimum market size (population) required to support a particular type of retail or service business and still yield a rate of return such that the business will continue to operate (Berry and Garrison Reference Berry and Garrison1958a and Reference Berry and Garrison1958b; Parr and Denike Reference Parr and Denike2016). In examining off-farm FAI service industries, such as agricultural support services, we draw on past retail and service industry demand threshold analysis. Cleary et al. (Reference Cleary, Bonanno, Chenarides and Goetz2018) adapt Bresnahan and Reiss (Reference Bresnahan and Reiss1991) to estimate the minimum market size (population thresholds) that imply profitability for one or more large grocery stores in non-metro U.S. counties. The intuition is straightforward, with lower population thresholds implying store profitability in less populated areas. Their results suggest that the cost-effectiveness of broad-based policy solutions to improve physical access to large food stores or to stimulate demand may be limited. Similarly, threshold analyses could serve as a useful tool to highlight over-investment in off-farm FAI, such as may be the case with food hubs (Cleary et al. Reference Cleary, Goetz, Mcfadden and Ge2019). More specific FAI and FAI-related threshold analyses and more precise policy implications are now possible with the FSRDC system.

For off-farm FAI manufacturing, most research focuses on the locational determinants of food processing and food manufacturing. Typically, these studies only examine a specific geographic region, probably due to non-disclosures. Food manufacturing locations tend to occur in counties with access to input and product markets, developed transportation networks, agglomeration economies (efficiencies that occur when industries locate near each other and industrial clusters), favorable fiscal policies, and low wages (Davis and Schluter Reference Davis and Schluter2005; Henderson and McNamara Reference Henderson and McNamara1997, Reference Henderson and McNamara2000). Particularly, important factors include proximity of agricultural commodities and low-cost labor. Rural counties tend to historically have a comparative disadvantage for attracting food processors, though non-metropolitan counties adjacent to urban areas may have an advantage for some food manufacturers (Lambert and McNamara Reference Lambert and McNamara2009). Studies enhancing the understanding of agglomeration economies may be particularly important for rural areas, where there may be possible negative effects of competition from growing concentrations of firms (Schmit and Hall Reference Schmit and Hall2013). Consolidation under spatial monopsony may also result in unserved areas.

Less discussed in prior location modeling efforts is the role of industry aggregation from nesting more refined industry categories in limiting the accuracy of model outcomes. This may be a function of prior limits on alternative levels of aggregation. In contrast, aggregation bias is familiar to analysts working in international trade (Feenstra and Hanson Reference Feenstra and Hanson2000; Hillberry Reference Hillberry2002) or regional economic models using input-output or CGE approaches (Miller and Blair Reference Miller and Blair2009). Wensley and Stabler (Reference Wensley and Stabler1998) refer to this industry aggregation issue as the product mix effect. They find that their demand threshold models on subsector classifications within the NAICS system that include many more narrowly defined industries more often exhibit increasing establishment multiplication rates. Despite Wensley and Stabler’s (Reference Wensley and Stabler1998) comment on the potential issue of the product mix effect from industry aggregation, most demand threshold studies count establishments at the subsector or industry group levels (Chakraborty Reference Chakraborty2012; Mushinski and Weiler Reference Mushinski and Weiler2002; Reum and Harris Reference Reum and Harris2006; Shonkwiler and Harris Reference Shonkwiler and Harris1996).

Clearly, there are also disadvantages in finer levels of disaggregation. No two businesses are alike; at some point of disaggregation, more output becomes cumbersome, suggesting diminishing marginal returns from disaggregation, particularly in sector classifications with small product mixes. The number of zero values across geography will also grow with greater sectoral detail. Within the FSRDC system, it becomes more feasible to test various levels of aggregation. In the analysis that follows, we explore results associated with two levels of NAICS code aggregation. The next section provides a basis for the model structure used in our analysis.

Estimation methods in the context of FAI

This section first outlines estimation methods of traditional locational choice and demand threshold literatures before weighing the trade-offs with several different estimators, largely following the recent review by Carpenter, Van Sandt, and Loveridge (Reference Carpenter, Van Sandt and Loveridge2021) and applying their guidance to the FAI context.

Carlton (Reference Carlton1983) and Bartik (Reference Bartik1985) are among the first to model the determinants of business location using multinomial logit (McFadden Reference McFadden and Zarembka1973). Limitations of this approach include an excessive number of alternatives and violation of the independence of irrelevant alternatives (IIA) assumption, given the location alternatives are likely correlated, even when conditioning on observable characteristics (Wooldridge Reference Wooldridge2010). Researchers aggregated alternatives to address the excessive alternatives problem and attempted to control for the IIA violation by introducing spatial group indicator variables (Bartik Reference Bartik1985).Footnote ⁶ Despite these efforts, the limitations led to use of nested logit, which uses a smaller sample of alternatives randomly drawn from the full set of alternatives (Friedman et al. Reference Friedman, Gerlowski and Silberman1992; Woodward Reference Woodward1992). This approach faces limitations both in the imposition of an arbitrarily limited and hierarchical choice set on firms, and the implied reduction in information. Furthermore, both approaches are limited because they are only consistent if the IIA assumption holds within subsets of the alternatives, that is, various hierarchies for the nested logit and spatial groups for the multinomial logit.

Given these limitations, others model establishment location by using count data models to examine locational outcomes in a particular area (Coughlin and Segev Reference Coughlin and Segev2000; Guimarães, Figueiredo, and Woordward Reference Guimarães, Figueiredo and Woodward2004; Papke Reference Papke1991; Wu Reference Wu1999). Importantly, Guimarães, Figueiredo, and Woodward (Reference Guimarães, Figueiredo and Woodward2003, Reference Guimarães, Figueiredo and Woodward2004) demonstrate not only that the Poisson count model presents a more tractable approach than conditional logit approaches but also that the coefficients of the Poisson model can be given an economic interpretation compatible with the framework of random utility (profit) maximization. Conveniently in the context of FAI, which include both services/retail and manufacturing, count data models are also compatible with the Central Place Theory (CPT) theoretical perspective, which researchers use in demand threshold analysis of retail and service sectors (Carpenter, Van Sandt, and Loveridge Reference Carpenter, Van Sandt and Loveridge2021). Furthermore, the count data regression is preferred when dealing with large sets of alternatives, since each spatial alternative becomes an observation, and thus, the excessive choice set problem faced by logit models becomes an advantage (Guimarães, Figueiredo, and Woodward Reference Guimarães, Figueiredo and Woodward2003).

When modeling demand threshold and business location using count data, multiple theoretical dimensions can be considered. First, the location or “participation” decision $\left\{ {0,\;1} \right\}$ and the establishment count or “amount” decision $\left\{ {0,\;1,\;2,\;3,\; \ldots } \right\}$ may be separate for FAI (and understanding each decision may be of interest), so a flexible estimator that models the decisions separately (with a zero-inflated estimator) is preferable. Relatedly, the effect of explanatory variables on the respective participation and amount decisions may have different partial effects, and there may be conditional correlation between the participation distribution and the amount distribution. Finally, both the participation and amount decision allow for the possibility of zero values. For establishment location data, there may be two types of zeros: (1) structural zeros – locations that establishments will never choose for participation; and (2) non-structural zeros – locations that establishments could potentially choose but are not chosen.

Review of corner response and count data models

Given the nature of the establishment data, $y \in \left\{ {0,\;1,\;2,\;3,\; \ldots } \right\}$ , count data models are most appropriate for empirical estimation.Footnote ⁷ Indeed, count data estimators have become common in locational and threshold models, though researchers often fail to appropriately apply and compare the various models, as we will demonstrate. For non-FAI establishments, applications of Poisson, Negative Binomial (NB), Hurdle Poisson (HP), and Zero-Inflated Poisson (ZIP) are numerous with Carpenter, Van Sandt, and Loveridge (Reference Carpenter, Van Sandt and Loveridge2021) providing a near comprehensive review for each. They also show a place for the Zero-Inflated Negative Binomial (ZINB), especially when using an expanded geographic scope.

The Poisson model remains useful at least as a starting point for comparison to other estimation procedures. However, the Poisson model’s assumption that the conditional variance of the dependent variable is equal to the conditional mean is often violated in practice due to multiple potential sources of overdispersion. If the conditional distribution is overdispersed, the NB will be more efficient than Poisson. The NB allows for unobserved heterogeneity between subjects that implies overdispersion. Specifically, the NB assumes the Poisson parameter is Gamma distributed and allows the amount of overdispersion to increase with ${\rm{E}}\left( {{y_i}|{x_i}} \right)$ (Wooldridge Reference Wooldridge2010). ^{Footnote 8} Although this likely holds when modeling FAI employment (e.g., due to rare large FAI manufacturers), this relationship is unlikely to hold when measuring FAI establishments due to excess zeros driving much of the overdispersion while decreasing ${\rm{E}}\left( {{y_i}|{x_i}} \right)$ . Hence, zero-inflated and hurdle versions of the Poisson model are often used to account for excess zeros in the data. Zero-inflated models add a logit link function which allows for an inflation stage in which the probability of an outcome being a structural zero is estimated, while still allowing for the estimation of (non-structural) zeros in the typical Poisson.Footnote ⁹ This results in two sets of estimates: (1) coefficients describing the likelihood of an observation being a structural zero and (2) coefficients describing changes in the level of the dependent variable given the observation is not a structural zero. Conversely, HP only assumes one type of zero by truncating the Poisson distribution after the zero-generating process. Such a restriction would be difficult to justify for any off-farm FAI under consideration here, so we do not test the HP. See Carpenter, Van Sandt, and Loverdige (Reference Carpenter, Van Sandt and Loveridge2021) for more details.

Finally, previous research failed to account for overdispersion that remains after the zero inflation in ZIP (Carpenter, Van Sandt, and Loveridge Reference Carpenter, Van Sandt and Loveridge2021). This remaining overdispersion may result from unobserved heterogeneity between subjects and excessive concentration of firms, which itself increases in economies of scale and agglomeration. Such economies are common to off-farm FAI. Thus, ZINB is underutilized in the current literature, with examinations of FAI typically using NB due to overdispersion, but failing to test for the source of that overdispersion (Bhattacharya and Innes Reference Bhattacharya and Innes2016; Henderson and McNamara Reference Henderson and McNamara2000; Lambert and McNamara Reference Lambert and McNamara2009; Weiss and Wittkopp Reference Weiss and Wittkopp2005). Indeed, we highlight that ZINB is the preferred model for numerous off-farm FAI.

Review of off-farm FAI data sources and issues

As noted above, researchers typically measure industry size in a location with establishment counts. Despite the growing body of literature highlighting effective econometric methods to measure demand thresholds on establishment counts in rural areas, extant demand thresholds research focuses on retail businesses almost exclusively and is limited in detail, or limited in industrial and geographic scope due to data limitations (Chakraborty Reference Chakraborty2012). Indeed, many demand threshold analysis and locational analysis studies use the publicly available County Business Patterns (CBP) data, resulting in several limitationsFootnote ¹⁰ and biased estimates (Carpenter, Van Sandt, and Loveridge Reference Carpenter, Van Sandt and Loveridge2022c).

Other federal data programs publish information about the economic activity in FAI, including the National Establishment Time-Series (NETS), Quarterly Census of Employment and Wages (QCEW), the Quarterly Workforce Indicators (QWI), and Non-employer Statistics (NS).Footnote ¹¹ Although versions of the QCEW, QWI, and NS are available publicly, researchers encounter the same problem as the CBP data: the exact counts of a particular NAICS code are often suppressed. While the NETS data avoid issues with suppressions and include non-employers, it remains a smaller sample (while the LBD is essentially the universe of establishments in its frame), and thus, researchers often must pool NETS observations across multiple years to reach sufficient observations of FAI (Low et al. Reference Low, Bass, Thilmany and Castillo2020). Isserman and Westervelt (Reference Isserman and Westervelt2006) provide methods to improve over simply taking the midpoint from suppressed CBP data and numerous proprietary data sets exist that estimate suppressed cells. However, these data sets remain substantially biased, with estimates ranging from 30% attenuation bias in 3-digit NAICS county-level data to being unreliable in 5- and 6-digit NAICS data (Carpenter, Van Sandt, and Loveridge Reference Carpenter, Van Sandt and Loveridge2022c). Suppressions are particularly prevalent in some FAI due to their relatively small count in rural counties. Given the extensiveness of disclosure limitations, exact counts yield more precise models. Finally, the LBD includes all off-farm FAI establishments with paid employees without regard to whether any employees are engaged in agricultural production. An FSRDC is thus a natural place to make improvements to existing research.

Example empirical approach

In support of the objective of this paper – to demonstrate the potential value of federal administrative data for food and agricultural industry (FAI) locational outcome research – we conduct an example empirical approach. First, we compare results and model diagnostics from the Poisson, NB, and their zero-inflated counterparts to provide robust results across NAICS 115, 1151, 1152, and 1153. This flexible approach takes advantage of the count nature of the data and allows for the separate analysis of factors contributing to both structural zeros and non-structural, while also addressing the multiple potential sources of overdispersion. We selected the data generation process underlying each industry by first testing for overdispersion in the data to select between the Poisson and negative binomial distributions. After checking for zero inflation, the alpha parameter was double-checked to ensure that overdispersion was still present in the data after accounting for excess zeros.

The log-likelihood function for ZIP may be written as:

\begin{align}\ln L &= \mathop \sum \limits_{i \in {\rm{S}}} {\rm{ln}}\left\{ {{\rm{F}}\left( {\gamma '{Z_i}} \right) + \left[ {1 - {\rm{F}}\left( {\gamma '{Z_i}} \right)} \right]\ {\rm{exp}}\left( { - {\lambda _i}} \right)} \right\}\\ &\quad + \mathop \sum \limits_{i \notin {\rm{S}}} \left\{ {\ln \left[ {1 - {\rm{F}}\left( {\gamma '{Z_i}} \right)} \right] - {\lambda _i} + {y_i}\beta '{X_i} - \ln \left( {{y_i}!} \right)} \right\}\end{align}

where S is a set of observations where ${y_i} = 0$ , ${\rm{F}}$ is the logit link function (for zero inflation), $Z$ is a vector containing covariates in the participation decision, and $X$ is a vector containing covariates in the amount decision. The log-likelihood function for ZINB differs from this by allowing the Poisson parameter to be Gamma distributed thereby relaxing the assumption of equidispersion.

To choose among the various count data models empirically, much previous work has incorrectly used Vuong’s Statistic to test for zero inflation (Wilson Reference Wilson2015).Footnote ¹² To provide a consistent comparison to evaluate the various count data models, we focus on graphical distribution analysis and comparison of the Akaike and Bayesian information criteria (AIC and BIC, respectively) as suggested in Greene (Reference Greene1994). If an industry follows a zero-inflated data generation process, we retest the overdispersion parameter again to ensure the overdispersion was not solely a product of the zero-inflation process.

Off-Farm FAI data

We use restricted access establishment-level data from the Census’ LBD and ILBD for the year 2014, along with secondary data sources to econometrically estimate the locational outcomes for the more-aggregated Support Activities for Agriculture and Forestry (NAICS 115), along with its (less-aggregated) sub-industries Support Activities for Crop Production (NAICS 1151), Support Activities for Animal Production (NAICS 1152), and Support Activities for Forestry (NAICS 1153). Table 1 provides summary statistics for these industries.

Table 1. Food and agricultural industry summary statistics

Note: Due to disclosure concerns, these statistics come from publicly available census county business patterns and non-employer statistics data.

Despite the inclusion of all businesses within the LBD and the ILBD, the U.S. Census Bureau requires us to conduct our analysis at an aggregated county level due to the sensitivity of the data. This unit of analysis is also necessary for including important secondary data sources that capture the potential influence of internet access, travel infrastructure, labor characteristics, urban influence, and other demographic and location variables. Further, county-level aggregation facilitates the implementation of the previously discussed methods. Table 2 provides descriptive statistics for the publicly available county-level FAI data and sources. A subset of FAI is selected to demonstrate the empirical implications of industry aggregation and size measurement in the results section.

Table 2. Covariate descriptive statistics and sources

Note: Table provides some descriptive statistics for model covariates and their respective sources. Local food farms are defined by USDA NASS (direct to consumer/retailer, agritourism, and value-added products). Descriptive statistics for the LQ are reproduced using publicly available U.S. Census County Business Pattern to assuage disclosure concerns.

Abbreviations: ACS: American Community Survey; BLS: Bureau of Labor Statistics; FCC: Federal Communications Commission; LQ: Locational Quotient; NASS: National Agricultural Statistics Service; NERCRD: Northeast Regional Center for Rural Development at Pennsylvania State University; SA: SmartAsset.com; USDA: United States Department of Agriculture.

This article does not estimate the locational outcomes of farms and ranches, but rather agricultural support services (i.e., 115, 1151, 1152, and 1153). As we describe in the next section, results vary by industry and sub-industry.

While FAI includes dozens of industry types spanning many sectors of the economy, we focus on investigating this subset of these industries with a 2014 cross section of the data using every county in the continental U.S. With the intention of highlighting the multitude of potential directions of FAI location outcomes research in the FSRDC system, we provide a diverse and large set of covariates routinely found in the location determinants literature (Carpenter, Dudensing, and Van Sandt Reference Carpenter, Dudensing and Van Sandt2022a; Carpenter et al. Reference Carpenter, Van Sandt, Dudensing and Loveridge2022b; Henderson, Kelly, and Taylor Reference Henderson, Kelly and Taylor2000; Lambert and McNamara Reference Lambert and McNamara2009; Van Sandt et al. Reference Van Sandt, Carpenter, Dudensing and Loveridge2021a; Reference Van Sandt, Carpenter, Dudensing and Loveridge2021b) and to facilitate comparisons across different measures of industry size (e.g., non-employer establishments and employer establishments), covariates are the same across industries. More specifically, each model uses 2014 county-level data and includes production variables (crop farm counts, livestock farm counts, and share local food farms), place-based factors (population density and internet service providers), labor-force characteristics (social capital index, share with a bachelor’s degree or higher, share in poverty, and the unemployment rate), industrial sector interdependencies (manufacturing location quotient, and transportation and wholesale location quotient), and factor costs (property tax rate and highway density).Footnote ¹³