Earlier versions of this paper presented at the North American Regional Science Association Annual Conference, November, 2013, Atlanta, GA and Ottawa, Canada, November 2012 as well as the Mid Continent Regional Science Association, Kansas City, MO, June 2013 . This work has benefited from seminar participants at the University of Wisconsin-Madison and Cornell University. Support for this work was provided in part by the Wisconsin Agricultural Experiment Station, University of Wisconsin-Madison, the University of Wisconsin-Extension, Cooperative Extension and the North Central Regional Center for Rural Development.
2 | P a g e
The Robustness of Local Foods and Economic Growth Abstract
In this paper we explore the impact of local foods on economic growth using a Barro-type framework. We address model uncertainty by using a Spatial Bayesian Model Averaging (SMBA) approach and check for robustness of results on local foods by employing several metrics of local foods. Results suggest that higher levels of local foods weakly lead to lower levels of income growth. The results are not robust implying that our thinking about how to define and quantify local foods needs further attention. Introduction
Concerns over a rash of food-borne illnesses, the rise of obesity across America and the
sustainability of modern agricultural practices have sparked a “push back” against industrial agriculture.
These concerns are best expressed in populist research such as Michael Pollan’s In Defense of Food.
There appears to be a growing pool of evidence that this “push back” may be sufficient to open new and
meaningful markets for local food systems and small and medium scale agriculture (Lyson and Guptill
2004; Tropp 2008; King, et al. 2010). Brown and Miller (2008, p.1296) point to the rapid growth in the
number of farmers markets, perhaps the “historical flagship of local food systems” over the past ten
years. Hardesty (2008) notes the growth in the number of local institutions such as hospitals, schools
and even prisons expressing interest in purchasing from local farmers. At the same time Greene, et al.
(2009) note that U.S. organic food markets have quintupled from sales of $3.6 billion in 1997 to $21.1
billion in 2008. Despite this tremendous growth, direct sales by organic farmers to consumers only
accounted for 0.4 percent of total agricultural sales in 2007 (Martinez, et al. 2010).
The rapid growth of interest in what has been called “civic agriculture” in both the sociology
(DeLind 2002; Lyson and Guptill 2004) and planning (Lapping 2004) literatures is captured in the Obama
Administration’s “Know Your Farmer, Know Your Food” initiative. In the past, small and medium scale
agriculture has generally been dismissed by economists as a viable rural economic growth and
development strategy (Henry 1986; Barkley and Wilson 1992). More recently, however, there has been
a resurgence of interest in revisiting this strategy (King, et al. 2010). Within the context of “Rural Wealth
Creation” Pender, Marré and Reeder (2012) talk in terms of an entrepreneurial class of farmers who can
take advantage of these shifts in the market demand for local foods. This movement is generally based
on smaller and medium scale farms.
There are theoretical justifications for promoting local foods as a rural growth and development
strategy. Marsden, Banks and Bristow (2000) and King, et al. (2010) note that shortening the supply
chain between farmers and consumers could create additional value opportunities for rural areas. Ikerd
(2005) describes how farmers are able to retain a larger share of the consumer dollar which maximizes
the injection of money into the rural economy. Zepeda and Li (2006) and Starr et al. (2003) speak in
3 | P a g e
terms of retaining money that traditionally goes to “middlemen” as a possible benefit. Darby et al.
(2008) suggests that farmers may be able to charge a premium for local foods which translates into
potentially higher incomes for rural residents through higher margins.
Writing more than 60 years ago, Goldschmidt (1947) suggested that the movement away from
small family farms to larger industrial or commercial farms may be detrimental to the economic well-
being of rural residents. Originally focused on the concept of large absentee-owner farms in California,
Goldschmidt expressed concern about the outflow of profits from local communities, low pay for farm
workers, and weaker production ties to the local community. The negative elements of the
“Goldschmidt hypothesis” could be minimized by the movement to a model of “civic agriculture”
embodied in local foods and smaller scale agriculture.
Unfortunately, there is a lack of rigorous evidence that supports the notion that a movement to
“civic agriculture” via local foods is a viable rural economic growth and development strategy. Indeed,
small and medium scale agriculture has generally been dismissed as a viable rural economic growth and
development strategy (Henry 1986). Barkley and Wilson (1992, p.239) “conclude that alternative
agriculture may be viable in select rural areas. However, total employment generation potential is too
small and diffused to provide significant rural development impacts.” Today the question is if the push-
back on large scale agriculture embodied in the local foods movement has created sufficiently thick
markets to affect rural economic growth and development.
This study is aimed at exploring the impact of local foods on economic growth. A Barro’s-type
model is used to test the robustness of results across a range of local foods metrics. We employ a
Spatial Bayesian Model Averaging (SBMA) approach to address the issue of model uncertainty in
establishing a set of control variables. The paper is composed of four sections after these modest
introductory comments. First we outline the theoretical and empirical framework with a special
attention to model uncertainty that has proven to be a weakness of Barro-type models. We then
document our measures of local foods followed by the empirical results. By using a range of local foods
metrics, we address the robustness of our results and highlight the difficulty in quantifying local foods.
We conclude the study with a discussion of future steps.
Modeling Framework
A traditional neoclassical model of regional economic growth, as presented by Barro (1991,
1997), Barro and Sala-i-Martin (1992), Nijkamp and Poot (1998) and Keely and Quah (2000), is adapted
to test the research question as discussed above: how are higher concentrations of local foods activity
related to economic growth? In neoclassical theory for closed economies developed by Ramsey (1928),
Solow (1956), Cass (1965) and Koopmans (1965), growth rates in per capita income are inversely related
to the initial levels of per capita income, and over time, economies should see a convergence in per
capita income. If economies are similar in terms of preferences and technology, poorer regions should
grow faster than richer ones. In other words, there are natural economic forces that promote
convergence which is generally referred to as β converge within the literature.
4 | P a g e
Following Smith (1975), a closed national economy is composed of n regions (states) with
competitive markets exhibiting constant returns to scale with reproducible capital. The national output
(Y) or income can be expressed as a function of labor (L) and capital (K):
Yt = KtαLt
1-α (1)
for a given point in time (t). National growth (ΔYt) is driven by changes in capital (ΔKt) and labor (ΔLt):
ΔKt = sYt – δKt +ρ(r-rA)Kt (2a)
ΔLt = L0ent + ϕ(w-wA)Lt. (2b)
Here changes in capital can come from two sources: net capital investment which is the difference
between new investments (sYt) and depreciation (δKt) plus net capital movement between regions
within the national economy (ρ(r-rA)Kt). Here capital moves to regions that offer the highest rate of
return (r). Changes in labor are a function of the natural growth rate in labor supply (L0ent) as well as net
migration (ϕ(w-wA)Lt) where labor moves between regions in search of the highest wage rate (w).
Substituting eqs.(2a) and (2b) into eq.(1) yields the general growth framework:
ΔYt = {sYt – δKt +ρ(r-rA)Kt }α{L0e
nt + ϕ(w-wA)Lt}1-α. (3)
In this framework there are three mechanisms that lead to convergence: (1) constant returns
results in investment in capital moving toward a steady state; (2) capital movement (mobility) will drive
rates of return on capital to a national average (r→rA); and (3) labor movement (mobility) will drive
wages to a national average (w→wA).
We employ a traditional empirical specification of the neo-classical model, which has become
widely known within the literature as a Barro-type model:
ΔYt = o + 1Yt-1 + I=1…mIXit-1 + θLFt-1 + t (4)
Here Y is per capita income and X is a set of control variables and LF is our local foods metrics. The
parameter of interest is 1 (= (ΔYt)/1Yt-1) or the β-convergence parameter. Unfortunately, the
robustness of the results of the traditional neoclassical empirical growth model has been at the center
of a large literature (Pack 1994; Durlauf and Quah 1999; Brock and Durlauf 2001; Beugelsdijk, de Groot
and van Schaik 2004; Durlauf, Johnson and Temple 2005; Brock, Durluaf and West 2007). In the end,
theory tells us that everything matters and this results in a laundry list approach to which control
variables to include in the analysis. Levine and Renelt (1992), in particular, are very critical of this
laundry list approach to the Barro-type neoclassical based regression model and maintain that the rate
of β-convergence is very sensitive to model specification. Small changes in the design matrix of control
variables (i.e., the laundry list) can alter the rate of β-convergence parameter, thus introducing the
notion of “conditional convergence”. Here the rate of convergence is conditional on the specification of
the set of control variables. The argument that modest changes in the set of control variables (X) could
alter the policy conclusions of the analysis cast a shadow over the entire line of research.
5 | P a g e
An alternative way of thinking about the problem is within the framework of model uncertainty.
If everything matters and if there are multiple means of measuring different elements, this situation
creates uncertainty about what to include and exclude in a model. More formally, model uncertainty
may be the result of the openendness of the theory from which those models are built. Openendness, as
described in Brock and Durlauf (2001), is related to the idea that one causal theory does not imply the
falsity of another. It may also be the result of theory contingency, sensitivity of theoretical predictions,
for instance, and/or historical or geographical contexts.1 For linear regression models, theory
openendness can be described as uncertainty regarding the appropriate set of specific variables that
should be included in the model, whereas theory contingency can be reduced to the uncertainty about
how the values of such parameters should vary for a given sample either over time or within units of
analysis. Testing a theoretical hypothesis in this case is often reduced to test the statistical significance
of variable parameters.
The conventional (and frequentist) approach has usually bypassed the issue of openendness
while totally ignoring the issue of contingency. Their treatment of model uncertainty has consisted of
the imposition of some information criteria in order to select a single “best” model regarded as the true
model from which variable parameters are estimated. Comparing determination criteria, such as
changes in the equation F statistic, ̅ or Mallows’ statistic, are tracked across alternative linear
regressions for the purpose of identifying a “best” model. Other criteria include the Amemiya criteria
(PC), Akaike Information Criteria (AIC), Sawa Bayesian Information Criterion and/or the Schwarz
Bayesian Information Criterion (BIC) as well as the Jeffreys-Bayes posterior odds ratio, among others
(see Burnham and Anderson 2004; Judge et al., 1985; Kuha 2004; Posada and Buckley 2004 for formal
discussions). Here models with different variable specifications yield some type of selection criteria
metric (e.g., F, ̅ , , AIC, BIC, etc.) and the model with the highest (or lowest depending on the criteria
metric) is selected as the “correct” model. Or, even more crudely, a process of elimination based on
individual variable t statistics can be used.
The problem with this approach in the selection of a set of control variables is that it ignores
model uncertainty. Analysts typically select a model from some class of models then proceed as if the
model generated the data. In addition to problems of vague theoretical foundations for selecting one
method over another, critical values of these model selection methods, or rules to follow when methods
provide inconsistent results, ignores a component of uncertainty leading to an increase in Type I error
and/or over-confident inferences. In the case of a relatively large number of potential variables this can
be a very cumbersome and time consuming process.
Within the economic growth literature Bayesian model averaging (BMA) has been introduced to
provide a coherent mechanism to account for model uncertainty in terms of what variables should be
1 Brock and Durlauf (2000) refers to the first type of uncertainty as theory uncertainty and to the second
as heterogeneity uncertainty.
6 | P a g e
included in the final specification of the model (Durlauf and Quah 1999; Durlauf, Johnson and Temple
2005). Suppose that there is a set of models all of which may be “reasonable” based on the theory for
estimating θ from a given data set y. Suppose further that a particular parameter θ has a common
interpretation across all possible models M1,…,Mk. Instead of using one single model for making
inferences about θ, Bayesian model averaging constructs , the posterior density of θ given the
data and is not conditional on any specific model (Mi).
Following the lead of LeSage and Parent 2007) and Cuaresma, Doppelhofer and Feldkircher
(2009) specify the general growth model (eq.(4)) as a spatial lag model:
(5)
where is an n by 1 vector of ones, . The number and identity of variables in is
unknown so the columns in are taken to be k variables from a larger set (K) of potential explanatory
variables contained in with . Any potential model specification is contained in the set of all
model possibilities (i.e., ). The potential number of possible model combinations is which
can become very large in practice.
Inference on the parameters attached to the variables in can be based on the weighted-
average parameter estimates of individual models,
( | ) ∑
(6)
with denoting the data. The spatial lag vector Wy appears in all models as does the intercept term,
leaving only the variable vectors in the matrix X subject to change as we compare alternative models.
This approach mirrors the one developed by Fernández, Ley, and Steel (2001a), where the intercept
term appears in all models.
Posterior model probabilities are given by
( | )
∑
(7)
Model weights can be obtained using the marginal likelihood of each individual model after eliciting a
prior over the model space. The marginal likelihood of model is given by
( | )
(8)
Given a model ( of dimension k) we can use a noninformative prior on and and a g -prior on the
coefficients we have
(9)
with . Fernández, Ley, and Steel (2001) shows that a great deal of computational
simplicity can be found by using Zellner’s g-prior (Zellner 1986) for the parameters b in the SAR model.
7 | P a g e
In addition to simplifying matters, Fernández, Ley, and Steel (2001) provide a theoretical justification for
use of the g-prior as well as Monte Carlo evidence comparing nine alternative approaches to setting the
hyperparameter g.
The posterior distributions of the coefficients for the spatial autoregressive specification are
calculated as the which maximizes the likelihood calculated over a grid of values. Building on the
prior work of Raftery, Madigan and Hoeting (1997) as well as Fernandez, Ley and Steel (2001) LeSage
and Parent (2007) adopts a Markov Chain Monte Carlo Model Composite (MC3) method modeling
composition approach introduced by Madigan and York (1995). Using a random-walk step in every
replication of the MC3 procedure, one can construct an alternative model to the active one in each step
of the chain by adding or removing a regressor from the active model. The chain then moves to the
alternative model with probability given the product of Bayes factor and prior odds resulting from the
beta-binomial prior distribution. The posterior inference is based on the models visited by the Markov
chain instead of on the complete model space which is untraceable given a large K (recall the full model
space is 2K, if, for example if K=10, then the full model space has a dimension of 1,024). We can
more formally define a neighborhood for each (the set of all possible models). From
there we can define a transition matrix q by setting and
. If the chain is currently in state M, we can proceed by drawing M’ from
. M’ is accepted with probability
( | )
. (10)
Otherwise the chain remains in state M. Using a Metropolis-Hastings sampling scheme, LeSage and
Parent (2007) were able to implement a Markov Chain Monte Carlo routine to move through the
modeling space.
There are three ways to use the Spatial Bayesian Model Averaging approach to identify the final
set of control variables to include in the Barro-type growth model (Eq.(4)). First, use the single model
with the highest posterior probability to determine which variables are to be included in the
final set of control variables. Second, look at the frequency of variables entering the top ten models
( ) ranked by their posterior probability. If a particular variable appears more than, say seven
times, in the top ten models, that variable could be included in the final set of control variables. Finally,
examine the posterior probability of individual variables and, if the variable has a posterior probability
above some threshold, the variable is included in the final set of control variables. In most cases the
three criteria are generally in agreement and the choice of variables is clear. There are, however, a
handful of cases where the three methods do not concur and a judgment call is required. For this study
we use each of the three criteria: (1) the variable must be contained in the single model with
the highest posterior probability; (2) the variable must be contained in at least eight of the top ten
models ( ) ranked by their posterior probability; and (3) the posterior probability of the single
variable must be greater than 0.75.
8 | P a g e
While the use of a Spatial Bayesian Model Averaging is a step above the use of more ad hoc
criteria metrics (e.g., F, ̅ , , AIC, BIC, etc.) to select the “correct” set of control variables, there are
still judgment calls to be made. For example, why is there a threshold of eight of the top ten models,
furthermore, why ten models and not twenty or thirty, or why posterior probabilities of a single variable
greater than 0.75 and not 0.85 or 0.95? The Spatial Bayesian Model Averaging approach provides a
more solid theoretical foundation for model comparisons and variable selection. Specifically, the
approach is more theoretically consistent with notions of model uncertainty than the more ad hoc
criteria metrics.
Once the SBMA approach identifies the set of control variables (X) in the Barro-type growth
model (Eq.(4)), we then introduce lagged per capita income and the set of local food indices (LF). As
outlined in LeSage and Pace (2009) we use a Bayesian heteroskedastic spatial autoregressive (SAR) model:
The set of variance scalars (v1, v2, . . . , vn) are unknown parameters that need to be estimated. The prior
distribution for the vi terms takes the form of an independent χ2(r)/r distribution where χ2 is a single
parameter distribution with r as the parameter. By adding the single parameter r this allows the
estimation of the n parameters vi. The prior distributions are indicated using (π ), a normal-gamma
conjugate prior for σ and a uniform prior for ρ.
Model Specification
The specification of the model involved two distinct steps. The first is to create a set of variables
to introduce into the Spatial Bayesian Model Averaging filtering process outlined above and the second
is to design a set of local food metrics. We do each in turn but first consider the data sources. We
model growth in per capita income from 2000 to 2011. Unless otherwise noted, much of the data
comes from the 2000 Census as well as the Bureau of Economic Analysis, Regional Economic
Information System (BEA-REIS), and County Business Patterns. The non-profit data used in one of the
social capital metrics comes from the National Center for Charitable Statistics. All data are at the county
level.
We introduce 27 variables across eight groupings into the SBMA process. Given the
computational parameters of SBMA a total of 1.34e+8 (=227) model combinations were explored with
10,000 draws using the Gibbs sampling procedure. The six variable groupings include: (1) deep lags, (2)
(6) social capital. The deep lags include growth rates in two general economic metrics (per capita
income and employment) from 1990-2000 to capture growth momentum. Demographic characteristics
include age and ethnic characteristics and voting preferences to reflect political attitudes. Economic
structure includes share of total employment in the public sector which can also serve as a simple proxy
for state and local fiscal policies. Population density captures scale of the economy. Poverty rates and
income distribution captures income characteristics of the county. Housing characteristics are aimed at
reflecting the age and stability of the community and the rental pricing a simple measure of cost of
living. Income characteristics are aimed at capturing patterns in poverty and income distributions. The
amenity characteristics are drawn from Deller, et al. (2001) and are aimed at capturing both natural and
built amenities including climate characteristics. Social capital measures include the concentration of
non-profits and a broader index developed by Rupasingha and Goetz (2008).
Deep Lags:
Deep Lag: percent change in per capita income 1990 to 2000
Deep Lag: percent change in employment 1990 to 2001
Demographic:
Percent of the population under age 18
Percent of the population over age 65
Percent of population African American
Percent of the population Latino
Ethnic diversity Index
Percent of population speaks a language other than english at home
Percent voting Democratic in 2000 Presidential Election
Economic:
Poverty rate for those over age 65
Poverty rate for those under age 18
Unemployment rate
Population density
Percent of employment in state government
Gini Coefficient of income distribution
Housing:
Percent of housing stock built before 1939
Percent of homes owner occupied
Percent of population in same house 1995-2000
Percent of rental units with monthly rent under $200
Percent of rental units with monthly rent over $1000
Amenity:
10 | P a g e
Climate Index
Urban Index
Land Index
Water Index
Winter Index
Social Capital:
Social Capital Metric (Deller)
Social Capital Metric (Goetz)
The second challenge we face is the construction of a set of local food metrics. This
unfortunately, is easier stated than accomplished as noted by Martinez et al. (2010) in their
comprehensive review of local foods literature. For example, it is not clear what defines “local”. Are
apples grown in southwestern Wisconsin considered “local” to consumers in Milwaukee, Chicago or the
Twin Cities of Minneapolis – St. Paul? While the 2008 Farm Bill may provide a legal definition of “less
than 400 miles from its origin, or within the State in which it is produced,” how consumers or retailers
define “local” in their mind is not clearly understood. Studies attempting to identify the demand for
local foods are finding significant heterogeneity in consumer opinions (e.g., James, Rickard and Rossman
2008). Durham, et al., (2009), for example, found that many consumers disagree that food produced
beyond a 100-mile designation could be considered local foods. In a study of food retailers Dunne, et al.
(2011) found that grocers’ perceptions of local food varied significantly from one another. Martinez and
his colleagues (2010) find that what constitutes local foods varies not only across rural and urban
consumers, but also by the agricultural product being considered. For researchers who are interested in
studying local foods concerns over conceptual definitions have direct implications on measurement.
The most widely used measure is direct-to-consumer sales from the Census of Agriculture. Low
and Vogel (2011) observe that over the years 1978 and 2007 farms with any level of direct-to-consumer
food sales represented 5.5 percent of all farms and 0.3 percent of total farm sales. Between 1992 and
2007 the number of farmers participating in direct-to-consumer sales increased by 58 percent from
86,000 to 136,000 with the constant dollar value of direct sales increasing by 215 percent from $558
million to $1.2 billion. Low and Vogel (2011) further note that direct-to-consumer sales, such as through
farmers’ markets and community supported agricultural (CSA) farms, captures a small part of the local
foods market. Using the 2008 Agricultural Resource Management Survey (ARMS) they found that when
intermediated sales (direct-to-grocer, restaurant or other local institutions such as hospital and schools)
are combined with direct sales, local food is closer to a $4.8 billion dollar market with the majority of the
market in the form of intermediate sales. They also find that the direct-to-consumer market is
dominated by smaller farms (less than $50,000 in sales) while the intermediated market is dominated by
larger farms (more than $250,000 in sales). Unfortunately, at the county level intermediate sales data
are not available. As such the study of local foods and economic growth is limited to data available from
the Census of Agriculture.
11 | P a g e
Given this serious limitation we move forward along three fronts. First, we use direct
agricultural sales as a benchmark metric. This is done using the number of farms with direct sales per
1,000 persons within the county and the dollar value of direct sales per capita. We treat these two our
benchmarks. Second, what farm characteristics are most closely associated with direct sales? For
example, we know that local food producers tend to be smaller, produce fruits and vegetables and/or
specialty livestock, and follow organic practices, characteristics for which we have data from the Census
of Agriculture, we can build proxy metrics of local foods activity. But the challenge is which
characteristics? We use a range of methods to identify which characteristics are most closely tied to
direct sales. Third, we use principal component analysis to build a set of local food indices along
different dimensions. If we know the characteristics of local food producers, we can build county
profiles (principal component derived indices) along those characteristics.
Thirteen different farm characteristics are considered in our attempts to find a reasonable proxy
measure of local foods:
Farms by value of sales Less than $100,000
Total sales $100,000 to $249,999
Vegetables, melons, potatoes, and sweet potatoes
Sheep, goats, and their products
Poultry and eggs
Fruits, tree nuts, and berries
Value of certified organically produced commodities
Vegetable and melon farming
Greenhouse, nursery, and floriculture production
Beef cattle ranching and farming
Dairy cattle and milk production
Animal aquaculture and other animal production
Colonies of bees Inventory Farms
Each of these are correlated with our two measures of direct sales (number of farms with direct sales
per 1,000 population and value of direct sales per capita) to identify which characteristics are most
associated with local foods.
In addition to using the principal component approach to think about how best to measure local
foods using a set of different metrics in the growth model, we are indirectly testing the robustness of
our results. Specifically if the growth results vary by local foods metrics, then the robustness of the
overall result comes into question. The pattern in these results can also shed light on the underlying
relationship between local foods and economic growth.
Empirical Results
The research results proceed in four steps: (1) what farm characteristics are most closely tied to
local foods; (2) how are those characteristics combined into a proxy measure; (3) what is the
12 | P a g e
appropriate set of control variables that should be retained in the final growth models; and (4) what
impact does local foods measured by our proxies have on economic growth (growth in per capita
income). We address each in turn.
Local Foods Characteristics We use five methods to examine patterns in farm characteristics and
local foods measured by direct sales: the Spatial Bayesian Model Averaging (SBMA) approach, a simple
step-wise selection criteria based on stepped in F-statistics, the Mallows C(p) criterion, simple ordinary
least squares (OLS), and a simple spatial autoregressive estimator (SAR). We “regress” each of the 13
characteristics listed above on number of farms with direct sales per 1,000 population and the value of
direct sales per capita using these five methods. The results of this analysis are provided in Table 1. The
statistical significance of the spatial parameter ρ in the SAR model (last two columns of Table 1) suggests
that spatial dependency is within the data and the three non-spatial estimators (step-in F, Mallows C(p)
and OLS) should be viewed with skepticism.
Taking the results presented in Table 1, the following nine characteristics are included for
further consideration:
Vegetables, melons, potatoes, and sweet potatoes
Poultry and eggs
Fruits, tree nuts, and berries
Value of certified organically produced commodities
Greenhouse, nursery, and floriculture production
Dairy cattle and milk production
Animal aquaculture and other animal production
Colonies of bees Inventory Farms
Farms by value of sales Less than $100,000
Based on prior work on measuring local foods, most of these are intuitive and consistent with
expectations. Only poultry and eggs along with dairy cattle and milk production are somewhat
surprising.
The second step involves using the nine characteristics identified above and aggregating them
with number of farms with direct sales per 1,000 population and the value of direct sales per capita,
respectively. To accomplish this we use factor analysis. The basic idea is that these farm characteristics
should move together or are correlated. Using the information in that correlation or covariance matrix a
weighting scheme to combine the variables into a single index can be identified. We use four different
approaches to factor analysis: a common factor analysis, a Harris component analysis, an alpha
component analysis and a principal component analysis using the correlation matrix. We use these four
different approaches to examine the robustness of the final local food indices. The results of this factor
analysis are provided in Table 2. A simple scatter plotting (Appendix A) of the different eigenvector
weighting schemes reveals little if any real differences across the four factor analysis approaches.
Therefore, to be consistent with prior rural economic growth work (e.g., Deller et al. 2001) we elect to
13 | P a g e
use the principal component approach. The final weighting schemes of our two local food indices (one
based on concentration of farmers with direct sales and one based on direct sales per capita) are
provided in Table 3. Organic production, aquaculture and other animal (other than cows, hogs and
chicken) production, and smaller scale production appear to be the primary characteristics that drive
our local food indices.
A simple mapping of our four measures of local foods provides an interesting picture of spatial
concentrations of activities. The spatial distribution of number of farms with direct sales per 1,000
population is provided in Map 1a. Here we can see what appear to be concentrations in parts of Texas
and north along the Mississippi River valley area to the Upper Midwest and then west to the Pacific
Coast. But this casual observation can be tested using the Getis-Ord Gi* statistic of spatial
concentration (Getis and Ord 1992; Ord and Getis 1995).2 This spatial statistics look for “hot” and “cold”
places on the spatial map. “Hot” places are where neighboring counties have similar characteristics
while “cold” places have dissimilar characteristics. Across places where the statistic is insignificant the
spatial distribution of the variable of interest, local foods, appears to be random. The mapping of the
Getis-Ord Gi* statistic (Map 1b) we can find that the casual observation concerning Texas, the
Mississippi River Valley north and then west to the Pacific appears to be statistically significant. We also
identify “cold” spots particularly in the southeastern U.S. ranging as far north as Michigan. Somewhat
surprising is the lack of a “hot” spot in the northeastern U.S. One must keep in mind that these are data
for 2002 and does not reflect any rapid growth in local foods over the past ten years. Rather these data
reflect the base year for our growth analysis. A mapping of direct sales per capita (Maps 2a and 2b)
reveals a similar overall pattern with subtle difference. In particular parts of northern New England
become “hot” spots along with an area around Denver. Parts of Texas, Wisconsin and the Dakotas west
to the Pacific coast remain “hot” spots and the southeastern US remains a “cold” spot.
A mapping of the two principal component derived local food indices reveal consistent overall
patterns (Maps 3a, 3b 4a and 4b). For the farm concentration based index (Maps 3a and 3b) parts of
Texas, New England and Wisconsin west to the Pacific coast remain “hot” spots and much of the
southeastern US remains a “cold” spot. A mapping of the direct sales per capita based index (Maps 4a
and 4b) supports the overall pattern of the previous local foods measures, but the specific geographic
areas are altered slightly. For example, the previous “hot” spot in Texas is much smaller as is the band
from Wisconsin to the Pacific coast. Here we see much smaller geographic “hot” spots centered around
2 The Getis-Ord Gi* is computed as 1 1*
2
2
1 1
1
n n
ij j ij
j j
i
n n
ij ij
j j
w X X w
G
n w w
Sn
where
2
21
n
j
j
X
S Xn
and X is a
the variable of interest, or in this case local foods, and w is a spatial weight matrix as described elsewhere in the manuscript.
14 | P a g e
Washington State and Oregon, part of Montana, Wisconsin and now part of Michigan. In the three prior
metrics, the local foods concentration in Michigan was either random or identified as a “cold” spot. We
also see the New England “hot” spot expanded to much of the Northeast. The southeastern US remains
a “cold” spot for local foods activity.
This mapping exercise tells us several things about the spatial distribution of local foods. First,
there are spatial patterns in the data suggesting that the use of traditional non-spatial statistical
methods may lead to biased and inconsistent estimates. Second, the consistent finding of “cold” spots
in the southeastern US and “hot” spots in parts of the Upper Midwest, New England and Pacific
Northwest strongly implies that the error structure is not homoscedastic across space and the Bayesian
heteroskedastic spatial autoregressive is appropriate. Third, while the overall spatial pattern is consistent
across the four local foods metrics, there are unique subtle differences, such as the much smaller spatial
clusters identified with the per capita direct sales based index. This suggests that our thinking about
what defines local foods and how we measure it may influence the overall growth results and
subsequent policy implications. Thus, in our growth modeling we use all for measures of local foods to
assess the stability or robustness of the local foods and economic growth relationship.
Spatial Bayesian Model Averaging The results of the Spatial Bayesian Model Averaging process are
provided in Table 4. Recall that there are three criteria: (1) the variable must be contained in the single
model with the highest posterior probability (m10); (2) the variable must be contained in at
least some minimum number of the top ten models ( ) ranked by their posterior probability;
and (3) the posterior probability of the single variable must be greater than 0.8. Of the 27 variables
introduced into in the SBMA nine variables are identified and used as the set of control variables in
subsequent modeling
Based on the overall probability five variables should be retained (ranked on highest
probability):
Population Density
Percent of population in same house 1995-2000
Deep Lag: percent change in per capita income 1990 to 2000
Poverty rate for those under age 18
Social Capital Metric (Goetz)
This set of results is consistent with prior studies of rural economic growth (e.g., Deller et al. 2001; Deller
and Lledo 2007). Population density captures potential agglomeration effects, the deep lag on income
growth reflects long-term growth patterns, residential stability and the Goetz measure of social capital
reflect stability and proactive attitudes of the community. All these are expected to have a positive
influence on income growth. Youth poverty rates are expected to have a drag on income growth.
15 | P a g e
The model with the highest overall probability of being “correct” ( ) also contains four
additional variables:
Percent of population speaks a language other than English at home
Percent of housing stock built before 1939
Percent voting Democratic in 2000 Presidential Election
Percent of the Population Latino
The share of the population that speaks a language other than English at home reflects the growing
migrant population which tends to be attracted to growing areas. This is also a reflection of the larger
share of the population that is Latino. One would expect for rural areas in the US these two variables
should be highly correlated, and to some extent they are. But there is evidence that the overlap
between these two groups is most evident in first or second generation migrants. Latinos who have
been in the US for more than two generations are generally English speakers at home. It is not clear if a
higher concentration of these types of these two variables will have a positive or dampening effect on
income growth (reinforcing growth or lower paying jobs). Age of the housing stock generally reflects the
age of the community and older communities are expected to experience slower income growth rates
then communities that have seen more recent growth in their housing stock. The Presidential elect
results are intended to capture the broad political philosophies of the community and it is not clear
what impact they may or may not have on income growth. It is important to note that these last four
variables has relatively low overall probability levels and it is not clear if they will contribute to the
overall performance of the final model.
Growth Models The results of five versions of the growth model are presented in Table 5: a base
model with local foods removed, then one additional model with each of our four separate local foods
indicators included. In general, the growth model explains almost 38 percent of the variation in the
growth of per capita income from 2000 to 2011. As expected, the spatial parameter ρ is also statistically
significant across all five specifications of the model. The lagged level of per capita income (introduced
into the model independent of the SBMA analysis above) had a dampening effect on subsequent income
growth rates. This is the “convergence” result that has been documented in so many regional growth
studies that employ the neo-classical based Barro’s-type growth framework. The implication is that per
capita incomes across US rural counties are moving toward a national average. This does not address or
provide any insight into what is happening to the distribution of income within counties (i.e., the well
documented widening income gap).
The deep lag growth in per capita income has a positive impact on income growth which can be
considered consistent with the convergence result: poorer rural counties in 1990 that experienced faster
growth rates in the 1990s have established a momentum that is carrying through to the 2000s. Also,
because poorer counties have a lower starting point the rates of increase will by definition be faster
than richer rural counties. Rural counties that have a higher population density in 2000 experienced
16 | P a g e
slower growth in per capita income. This may be that more sparsely populated counties tend to start
with lower incomes which would again be consistent with the convergence hypothesis. The results on
percent of the population that is Latino and the percent of the population that is non-English speakers at
home appear to be contradictory. The larger the share Latino the slower the growth rate in per capita
income. This result could be explained by Latinos being concentrated in rural counties with lower
paying jobs. But the higher the share of the population that speaks a language other than English at
home has a positive impact on rural income growth. While the Latino and non-English variables tend to
move together they are not perfect substitutes. Many rural Latinos are multigenerational residents who
tend to speak English and many foreign in-migrants who are non-English speakers at home are not
necessarily Latinos. The latter group could include migrants from Asia, Eastern Europe, the Middle East
or India among others. There is some evidence that suggests that the injection of foreign migrants into
some rural communities can spark creative change within the community (Longworth 2008). The
percent of the votes casted for President in 2000 that were for the Democrat had a dampening effect on
income growth, but the result is not statistically significant. Recall from the SBMA variable selection
process, this was one of the variables selected on the second criteria ( ). Of the control
variables this is the only one that is statistically insignificant. Rural counties that tend to have an older
stock of housing and higher levels of residential stability experienced faster income growth. Finally,
rural communities that had a higher level of social capital as measured by Goetz and his colleagues also
experienced higher rates of income growth. This latter result is as expected.
Now turn attention to the variables of interest related to local foods. Of the four measures,
three have a negative coefficient suggesting that higher levels of local foods activity have a dampening
effect on rural income growth. But none of the four measures are statistically significant suggesting that
local foods does not influence economic growth and if there is a relationship it might be a negative one.
If we look at the traditional metrics of the overall performance of the growth model, including local
foods does not improve the performance of the model.
Discussion and Conclusions
In this work we explore the argument that the promotion of local foods is a viable community
economic growth strategy. Given the slow pace of recovery from the Great Recession local foods
advocates have moved the argument that local foods is an economic growth strategy front and center.
The problem is that there is scarce research supporting this argument and the limited and somewhat
dated work suggests that the small scale agriculture commonly associated with local foods is not a viable
growth strategy. While some individual entrepreneurs may find success it is not sufficiently large to
impact the overall growth patterns of local communities.
The work here attempts to revisit this older limited literature given the modern widespread
interest in local foods. We use a Barro-type model of growth in per capita income and address the issue
of model uncertainty (e.g., selecting the “correct” set of control variables) by employing a Spatial
Bayesian Model Averaging approach suggested by LeSage and Parent (2007). The second step is to
17 | P a g e
explore the robustness of our results by employing multiple measures of local foods. The results on
local foods suggests that higher levels of local food production activity does not contribute to income
growth and there is very weak evidence that it may lead to slower levels of economic growth. But the
results are not robust.
In conducting the work it became readily clear that quantitative metrics of local foods are in
need of substantial additional work. From the work on modeling the demand for local foods it is clear
that the very definition of local foods is not clear in the eyes of consumers. This makes developing
quantitative models of local foods from the production or supply side very difficult. In addition, our
analysis is limited to the data available through the Census of Agriculture which ignores the metrics of
what Low and Vogel (2011) refer to as intermediate sales to restaurants and local institutions such as
hospitals and schools. This latter market has been estimated to be three to five times the size of direct
sales for human consumption. As such, much of our future work will be to refine our metrics of local
foods.
Another limitations to this line of work is the timeframe of the analysis. First, while the local
foods movement has seen rapid growth from 1992 with much of that growth occurring over the past
five years. Using measures from the 2002 Census may not be adequately capturing the most recent
rapid growth in local foods. Second, the significant effects of the Great Recession make the model of
community economic growth difficult. It could be that the very slow recovery from the Great Recession
coupled with much of the job growth occurring in lower paying occupations and/or part-time work, is
masking the local foods and growth relationship. If we model growth from 2000 to 2007 to side-step
this very real problem, we are capturing only the beginning phases of the local foods movement. This is
a similar argument to using the 2002 Census of Agriculture noted above.
While the line of work outlined in this particular study is encouraging, much additional work is
required. While we have attempted to test the robustness of our results using different metrics of local
foods future work should explore how different elements of local foods drives economic growth.
Further, while we have a lagged growth model with deep lags, there could be issues around causation or
endogeneity. Is it the case that areas that are experiencing faster growth see growth in the demand for
local foods? Here growth in income is driving the local foods movement through demand structures.
While our hands are somewhat tied with the county as a unit of measurement, county boundaries do
not coincide with functioning economic areas. Such one use the USDA’s definition of 400 miles to group
counties into a series of overlapping spatial observations? But why 400 miles and not 100 miles, or 200?
This goes back to the challenge in defining what we mean by local foods.
In the end, one must take great care in making the policy argument that local foods could be an
engine of rural revitalization and economic growth. The evidence is just not there to support the claim.
18 | P a g e
References Barkley, D.L. and P.N. Wilson. 1992. “Is Alternative Agriculture a Viable Rural Development Strategy?” Growth and Change. Spring:239-253.
Barro, R. (1991). “Economic Growth in a Cross Section of Countries.” Quarterly Journal of Economics. 106(2):407-443. Barro, R. (1997). Determinants of Economic Growth, Cambridge: MIT Press.
Barro, R.J. and X. Sala-i-Martin. "Converge." Journal of Political Economy. 100(2, 1992):223-251. Beugelsdijk, S., H.L.F. de Groot and A.B.T.M. van Schaik. (2004). “Trust and Economic Growth: A Robust Analysis.” Oxford Economic Papers. 56:118-135. Brock, W. and S. Durlauf. (2001). “.What Have We Learned from a Decade of Empirical Research on Growth? Growth Empirics and Reality.” The World Bank Economic Review. 15(2):229-272.
Brock, W., S. Durlauf and K. West. (2007). “Model Uncertainty and Policy Evaluation: Some Theory and Empirics.” Journal of Econometrics. 136(2):629-664. Burnham, K.P. and D.R. Anderson. 2004. “Multimodel Inference: Understanding AIC and BIC in model selection.” Sociological Methods & Research. 33(2):261-304.
Cass, D. (1965). “Optmum Growth in an Aggregate Model of Capital Accumulation.” Review of Economic Studies. 32(3):233-240. Cuaresma, J.C., G. Doppelhofer and M. Feldkircher. (2009). “The Determinants of Economic Growth in
European Regions.” CESIFO Working Paper No. 2519.
http://www.cesifo-group.de/portal/pls/portal/docs/1/1186586.PDF (Accessed October 10, 2012)
Durlauf, S., P. Johnson and J. Temple, (2005),”Growth Econometrics,” in Handbook of Economic Growth, P. Aghion and S. Durlauf eds., Amsterdam: North Holland. Durlauf, S. and D. Quah. (1999). “The New Empirics of Economic Growth.” In Handbook of Macroeconomics. (eds) J. Taylor and M. Woodford. Amsterdam: North Holland. Fernández, C., E. Ley, and M. F. J. Steel. (2001). ‘‘Model Uncertainty in Cross-Country Growth Regressions.’’ Journal of Applied Econometrics 16, 563–76. Henry, M. 1986. “Agriculture’s Stake in Rural Economic Development.” Northeast Journal of Agricultural and Resource Economics. 75-85. Ikerd, J. 2005. Eating Local: A Matter of Integrity, presentation at The Eat Local Challenge kickoff event, Portland, OR, June 2. http://www.tierramiguelfarm.org/files/20081126_Eating%20Local.pdf Judge, G.G., W.E. Griffiths, R.C. Hill, H. Lutkepohl and T.C. Lee. 1985. The Theory and Practice of Econometrics, Second Edition, New York: John Wiley & Sons.
Keely, L.C. and Quah, D. (2000). “Technology in growth”, in Economic Growth and its Determinants, ed. Thijs Ruyter van Steveninck (Amsterdam: Kluwer) chapter 3, pp. 75–99.
King, R.P., M.S. Hand, G. DiGiacomo, K. Clancy, M.I. Gomez, S.D. Hardesty, L.Lev and E.W. McLaughlin. 2010. Comparing the Structure, Size and Performance of Local and Mainstream Food Supply Chains. Report Number 99. USDA ERS: Washington DC. Koopmans, T.C. (1965). “On the Concept of Optimal Economic Growth.” In The Econometric Approach to Development Planning. Amsterdam: North Holland. Kuha, J. 2004. AIC and BIC: Comparisons of assumptions and performance. Sociological Methods and Research. 33(2):188-229. James, J.S., B.J. Rickard and W.J. Rossman. 2009. “Product Differentiation and Market Segmentation in Applesauce: Using a Choice Experiment to Assess the Value of Organic, Local, and Nutrition Attributes.” Agricultural and Resource Economics Review. 38(3):357-370. Lapping, M.B. 2004. “Toward the Recovery of the Local in the Globalizing Food System: The Role of Alternative Agricultural and Food Models in the US.” Ethics, Place and Environment. 7(3):141-150. LeSage, J. and R.K. Pace 2009. Introduction to Spatial Econometrics. Boca Raton, FL: Taylor and Francis Group. LeSage, J. P. and Parent, O. 2007. Bayesian model averaging for spatial econometric models. Geographical Analysis. 39:3:241-267. Longworth, R.C. 2008. Caught in the Middle: America’s Heartland in the Age of Globalism. NY: Bloomsbury. Low, S.A., and S. Vogel. 2011. Direct and Intermediated Marketing of Local Foods in the United States, Research Report Number 128. USDA ERS: Washington DC. Lyson, T.A. and A. Guptill. 2004. “Commodity Agriculture, Civic Agriculture and the Future of U.S. Farming.” Rural Sociology. 69(3):370-385. Marsden, T., J. Banks and G. Bristow. 2000. “Food Supply Chain Approaches: Exploring their Role in Rural Development.” Sociologia Ruralis. 40(4):424-438. Martinez, S., M. Hand, M. Da Pra, S. Pollack, K. Ralston, T. Smith, S. Vogel, S. Clark, L. Lohr, S. Low, and C. Newman. 2010. Local Food Systems: Concepts, Impacts, and Issues, ERR 97, U.S. Department of Agriculture, Economic Research Service. Nijkamp, P. and J. Poot. (1998). “Spatial Perspectives on New Theories of Economic Growth.” Annals of Regional Science. 32:7-37. Pack, H. (1994). “Endogenous Growth Theory: Intellectual Appeal and Empirical Shortcomings.” Journal of Economic Perspectives. 8:55-72.
20 | P a g e
Posada, D. and T.R. Buckley. 2004. Model selection and model averaging in phylogenetics: Advantages of Akaike Information Criterion and Bayesian approaches over likelihood ratio tests. Systematic Biology. 53(5):793-808. Ramsey, F. (1928). “Empirics for Economic Growth and Convergence.” European Economic Review. 40:543-559.
Smith, D.M. (1975). “Neoclassical Growth Models and Regional Growth in the U.S.” Journal of Regional Science. 15(2):165-182.
21 | P a g e
Table 1: What goes into the local foods index (marginal significance)
SBMA Step-in on F test Mallows C(p) OLS SAR
Farms
with
Direct
Sales
Per
Capita
Direct
Sales
Farms
with
Direct
Sales
Per
Capita
Direct
Sales
Farms
with
Direct
Sales
Per
Capita
Direct
Sales
Farms
with
Direct
Sales
Per
Capita
Direct
Sales
Farms
with
Direct
Sales
Per
Capita
Direct
Sales
Total sales $100,000 to $249,999 0.7995 0.3514 (0.0011) (0.0228) (0.0021) (0.0039) (0.0014) (0.0039) (0.0058) (0.0034)
