An Estimated Structural Model of
Entrepreneurial Behavior
John Bailey Jones
Department of Economics
University at Albany - SUNY
jbjones@albany.edu
Sangeeta Pratap
Department of Economics
Hunter College & Graduate Center - CUNY
sangeeta.pratap@hunter.cuny.edu
April 12, 2016
Abstract
Using a rich panel of owner-operated New York dairy farms, we provide new
evidence on entrepreneurial behavior.
We formulate a dynamic model of farms
facing uninsured risks, …nancial constraints and liquidation costs. Farmers derive
nonpecuniary bene…ts from operating their businesses.
We estimate the model
via simulated minimum distance, matching both production and …nancial data. We
…nd that …nancial factors play an important role at both the extensive and intensive
margins. Collateral constraints and liquidity restrictions inhibit borrowing and the
accumulation of capital. Debt renegotiation allows productive farms to continue
operating despite temporary setbacks. Farms with high productivity are more constrained than low productivity farms. The nonpecuniary bene…ts to farming are
large and keep small, low productivity farms in business. Although farmers are risk
averse, eliminating uninsured risk has only modest e¤ects on capital and output.
We are grateful to Paco Buera, Lars Hansen, Boyan Jovanovic, Todd Keister, Vincenzo Quadrini,
Todd Schoellman, Fang Yang and seminar participants at Emory University, the Federal Reserve Bank
of Richmond, LSU, University at Albany, University of Connecticut, Université Paris I, the Midwest
Macro Meetings, and the ITAM-PIER conference on Macroeconomics for helpful comments. Cathryn
Dymond and Wayne Knoblauch provided invaluable assistance with the DFBS data. Jones gratefully
acknowledges the hospitality of the Federal Reserve Bank of Richmond. The opinions and conclusions
are solely those of the authors, and do not re‡ect the views of the Federal Reserve Bank of Richmond or
the Federal Reserve System.
1
1
Introduction
Entrepreneurs di¤er from other economic agents in many ways. They tend to be
wealthier, save at higher rates, and invest much of their wealth in their own businesses
(Quadrini, 2000, 2009; Cagetti and De Nardi, 2006; Herranz et al., 2015). On the other
hand, Moskowitz and Vissing-Jorgenson (2002) …nd that the returns to undiversi…ed entrepreneurial investments are no higher than the returns to public equity, while Hamilton
(2000) …nds that self-employment yields lower earnings than wage work. Hall and Woodward (2010) …nd that the “risk-adjusted payo¤s to the entrepreneurs of startups are
remarkably small.”
Several mechanisms are probably at work. The propensity of entrepreneurs to reinvest in their own …rms suggests the presence of …nancial constraints, as does evidence
that inheritances improve their chances of survival (Holtz-Eakin et al., 1994), and evidence that wealthier individuals are more likely to become entrepreneurs (Evans and
Jovanovic, 1989).1 Returns that are risky and low relative to other investments suggest
that entrepreneurs receive signi…cant non-pencuniary bene…ts from running their own
…rms. Alternatively, Vereshchagina and Hopenhayn (2009) show that limited liability
can encourage entrepreneurs to take risks, while Kihlstrom and La¤ont (1979) argue that
risk-loving individuals are more likely to become entrepreneurs.
In this paper we evaluate the importance of each of these considerations by building
and estimating a rich model of entrepreneurial behavior. Risk-averse entrepreneurs make
debt, investment, production, dividend and liquidation decisions. They face uninsured
risk, along with collateral and liquidity constraints, but also receive nonpecuniary bene…ts
from operating their businesses. Older entrepreneurs retire, and entrepreneurs of any age
can exit to wage work, albeit with liquidation costs. They can also seek to renegotiate
their debt. Limited liability and the outside option of wage work create incentives for risk
taking.
We estimate the model’s parameters using a detailed panel of family-owned and operated dairy farms in New York State. These farms face substantial uninsured risk. The
dataset contains comprehensive information on the farms’ real and …nancial activities,
including input use, revenue, investment, borrowing and equity. Since they are drawn
from a single region and industry, our data are less vulnerable to issues of unobserved
heterogeneity. The panel spans a decade (2001-2011), which allows us to measure …rm1
Hurst and Lusardi (2004) argue that a positive relationship between wealth and business creation
exists only at the top of the wealth distribution. Buera (2009) argues that in a dynamic model the
relationship is not monotonic.
2
level …xed e¤ects, and sharpens the identi…cation of the model’s dynamic mechanisms.
We are therefore able to disentangle the e¤ects of real and …nancial factors on …rms’
operating decisions, the key issue in the voluminous and often contentious literature on
investment-cash ‡ow regressions.2 We can also estimate the degree of risk-taking behavior
and the magnitude of the nonpecuniary bene…ts of being an entrepreneur.
Our paper combines two distinct strands of research. The …rst is the literature on
entrepreneurship. In contrast to our work analyzing established businesses, many studies
in this literature examine the decision to become an entrepreneur (Evans and Jovanovic,
1989; Hurst and Lusardi, 2004; Buera, 2009; Hurst and Pugsley, 2011). The studies that
focus on established …rms are typically calibrated to match cross-sectional data such as
the distribution of household wealth (Quadrini, 2000; Cagetti and De Nardi, 2006), or the
distribution and composition of entrepreneurial wealth (Herranz et al., 2015).3 The second
strand of research is the literature on structural corporate …nance (Pratap and Rendon,
2003, Hennessey and Whited, 2007; Strebulaev and Whited, 2012), which analyzes the
real and …nancial decisions of large publicly-traded corporations.
Our study does not …t neatly into either of these categories. Less than half of our …rms
would be considered “small” by the Small Business Administration de…nition.4 On the
other hand, they are family-owned and operated, and hence not comparable to …rms listed
on the stock market. In contrast to the data used in most studies of entrepreneurship,
such as the Survey of Consumer Finances or the Survey of Small Business Finances,
our dataset allows us to estimate …nancial constraints from investment dynamics, rather
than cross-sectional features. This is a quite di¤erent and arguably more direct source of
identi…cation. The closest counterparts to our approach are in the development literature,
where structural models of entrepreneurship have been estimated with …rm-level panel
data, often from Townsend’s Thai surveys.5
We estimate our model using a simulated minimum distance estimator, matching both
the production and the …nancial side of the data. Information on output and input use
identify the parameters of the production function, which in turn allows us to back out
2
Key papers in this literature include Fazzari, Hubbard and Peterson (1988) and Kaplan and Zingales
(1997). Bushman et al. (2011) provide a review. Of note for this study are Bierlen and Featherstone
(1998), who estimate investment-cash ‡ow sensitivities for a dataset of Kansas farms.
3
Quadrini (2009) provides a review of this literature. An interesting outlier is Abbring and Campbell
(2004), who study the …rst year of operation among a collection of Texas bars.
4
The Small Business Administration de…nes enterprises with annual revenues of $500,000 as small in
the dairy industry. As Table 1 shows, the median enterprise in our sample has revenues of $700,000.
5
Townsend et al. (1997) and Samphantharak and Townsend (2010) provide a description of the data.
A recent study especially relevant to ours is Karaivanov and Townsend (2014), which also contains a
literature review.
3
a series for total factor productivity (TFP) for each farm. These TFP estimates in turn
can be decomposed into a permanent farm-speci…c component, an aggregate shock and
an idiosyncratic component. We …nd that high-productivity farms (as measured by the
permanent farm-speci…c component) operate at much larger scales, invest more and pay
down their debt more quickly than low productivity farms. High productivity farms also
operate further below their optimal levels of capital stock than low productivity farms.
This justi…es their higher investment rates and suggests that …nancial constraints may be
important in explaining their distance from the optimum.
Aggregate productivity is closely related to the price of milk. We …nd that periods of
high aggregate productivity are also periods of high investment. Since aggregate productivity appears to be uncorrelated over time, this suggests that the cash ‡ow generated by
higher milk prices facilitates investment.
Our model …ts the data in the time series and the cross section. The parameter estimates show that entrepreneurs are extremely risk averse, and derive a large nonpecuniary
bene…t from operating their own business. These two features combine to mitigate the
appetite for risk-taking, despite limited liability and the ability to exit into wage work.
Counterfactual experiments allow us to quantify the e¤ects of relaxing the …nancial
constraints. We …nd that these constraints exert a signi…cant in‡uence on both the intensive and the extensive margin. The intensive margin of operation, i.e., investment
and output, is strongly a¤ected by the collateral constraints. Liquidity constraints that
force businesses to hold cash and divert resources from investment have similar e¤ects.
The ability to renegotiate debt is important for the extensive margin, in that it allows
productive farms to continue operating despite temporary setbacks. Liquidation costs
likewise a¤ect the extensive margin by impeding the exit of small, unproductive farms,
thus creating …nancial ine¢ ciencies. We also …nd that liquidation costs amplify the effect of nonpecuniary bene…ts. Both work in the direction of discouraging exit of small,
marginal farms. Taken together, their e¤ects are much larger than each in isolation.
Our framework also allows us to assess the importance of risk. We …nd that eliminating risk allows farms to expand along the intensive margin, although the e¤ect is
quantitatively modest, especially compared to the e¤ect of relaxing …nancial constraints.
The extensive margin is virtually una¤ected. Understanding the e¤ects of risk is essential
to understanding the e¤ects of the USDA’s dairy policies, which seek to limit the downside risk faced by dairy farms. Prior to 2014, the main program for the dairy industry
was the Dairy Price Support Program, which provided a price ‡oor of $9.90 per hundred
pounds (cwt) of milk. This ‡oor, however, had been below the market price of milk and
4
largely irrelevant since the mid-1990s (Schnepf, 2014). The 2014 Farm Bill replaced price
supports with margin support, providing a ‡oor on milk margins (milk prices net of feed
costs). We estimate what the impact of this program would have been if it had existed
during our 2001-2011 sample period. Consistent with our results on risk in general, we
…nd that the insurance provided by the margin support program has a minor e¤ect on
farm operations. The premium charged for the margin support has much larger, and
negative, consequences.
The rest of the paper is organized as follows. In section 2 we introduce our data
and perform some diagnostic reduced form exercises. Section 3 sets out the model and
section 4 describes our estimation procedure. Section 5 presents our parameter estimates
and assesses the model’s …t. In section 6 we discuss issues of identi…cation. Section 7
elaborates on the mechanisms of the model, considering nonpecuniary bene…ts, …nancial
constraints, and their interactions. Section 8 evaluates the e¤ects of uninsured risk in
general, and the e¤ects of the 2014 Farm Bill in particular. We conclude in section 9.
2
Data and Descriptive Analysis
2.1
The DFBS
The Dairy Farm Business Summary (DFBS) is an annual survey of New York dairy
farms conducted by Cornell University. The data include detailed …nancial records of
revenues, expenses, assets and liabilities. Physical measures such as acreage and herd
sizes are also collected. Assets are recorded at market as well as book value. The data
allow for the construction of income statements, balance sheets, cash ‡ow statements,
and a variety of productivity and …nancial measures (Cornell Cooperative Extension,
2006; Karzes et al., 2013). Participants can then compare their management practices to
those of their peers. These diagnoses are an important bene…t of participation, which is
voluntary (Cornell Cooperative Extension, 2015). Given such considerations, the DFBS
data are not representative,6 but they are quite likely to be of high quality.
Our dataset is an extract of the DFBS covering the calendar years 2001-2011. This is
6
Farms in our sample have larger revenues and herd sizes than the average New York State diary
farm. In 2011, average revenue in our sample was $2,285,000, compared to the state average of $520,000.
In the same year, the average herd size of New York State dairy farms was 209 cows, while our sample
had an average herd size of 403. In demographic terms the sample is very similar to state averages: the
principal operator statewide has an average age of 51, as in our sample. All the farms in our sample are
family-owned, as are virtually all (97 percent) of the dairy farms in New York state. (New York State
Department of Agriculture and Markets, 2012).
5
an unbalanced panel of 541 distinct farms, with approximately 200 farms surveyed each
year. We trim the top and bottom 2.5 percent of the size distribution; the remaining
farms have time-averaged herd sizes ranging between 34 and 1,268 cows. Since our model
is explicitly dynamic, we also eliminate farms with observations for only one year. Finally
we eliminate farms for which there is no information on the age of the operators. Since
these are family-operated farms, we would expect retirement considerations to in‡uence
both production and …nance decisions. These …lters leave us with a …nal sample of 338
farms and 2,037 observations. During the same period, the number of dairy farms in
New York State fell from 7,180 to 5,240 (New York State Department of Agriculture and
Markets, 2012), so that our sample contains roughly 5 percent of all New York dairy
farms.
Table 1 shows summary statistics. A detailed data description is provided in Appendix A. The median farm is operated by two operators and more than 80 percent of farms
have two or fewer operators. The average age of the main operator is 51 years. For multioperator farms, however, the relevant time horizon for investment decisions is the age of
the youngest operator, who will likely become the primary operator in the future. On
average, the youngest operator tends to be about 8 years younger than the main operator.
In our analysis we will consider the age of the youngest operator as the relevant one for
age-sensitive decisions.
Table 1 also illustrates that these are substantial enterprises: the yearly revenues of the
average farm are in the neighborhood of 1.5 million dollars in 2011 terms. The distribution
of revenues is heavily skewed to the right, with median farm revenues equal to about half
the mean. A large part of farm expenses are accounted for by variable inputs: intermediate
goods and hired labor. Of these labor expenses are relatively small, accounting for about
14 percent of all expenditures on variable inputs. The remainder consists of intermediate
goods and services such as feed, fertilizer, seed, pest control, repairs, utilities, insurance,
etc. We also report the amounts spent on capital leases and interest, which are less than
10 percent of total expenditures on average.
Capital stock consists of machinery, real estate (land and buildings) and livestock, of
which real estate is the most valuable. Most of the capital stock is owned, but the median
farm leases about 14 percent of its capital, mostly real estate. (See Appendix A.) The
majority of farms lease less than 20 percent of their machinery and equipment. Livestock
is almost always owned. Capital is by far the predominant asset, accounting for more
than 80 percent of farm assets.
6
Standard
Variable
Mean Median Deviation Maximum Minimum
No. of Operators
1.82
2
0.93
6
1
Operator 1 Age
51.04
51
10.68
87
16
43
10.60
74
12
Youngest Operator Age 43.04
Herd Size (Cows)
302
169
286
1,268
34
2,793
1,802
2,658
15,849
212
Total Capital
654
446
606
4,164
13
Machinery
Real Estate
1,443
924
1,451
10,056
0
Livestock
696
394
700
5,215
39
Owned Capital
2,267
1,496
2,132
14,286
83
Machinery
490
331
461
2,895
3
1,097
710
1,103
9,100
0
Real Estate
680
390
674
3,467
39
Livestock
Owned/Total capital
0.84
0.86
0.12
1.00
0.26
Revenues
1,417
726
1,490
8,043
68
1,199
608
1,278
6,296
57
Total Expenses
Variable Inputs
1,098
553
1,177
5,846
55
101
52
120
1,026
0
Leasing and Interest
Total Assets
2,707
1,738
2,565
16,134
103
Total Liabilities
1,302
710
1,346
7,560
0
Net Worth
1,404
824
1,597
12,951
-734
Notes: Financial variables are expressed in thousands of 2011 dollars.
Table 1: Summary Statistics from the DFBS
7
Gross Investment /
Variable
Owned Capital
Average investment rate
0.086
Inaction rate (< abs(0.01))
0.097
Fraction of observations < 0
0.087
Positive spike rate (>0.2)
0.074
Negative spike rate (<-0.2)
0.002
Serial correlation
0.097
CooperHaltiwanger
LRD
0.122
0.081
0.104
0.186
0.018
0.058
Table 2: Investment Rates
Farm liabilities include accounts payable, debt, and …nancial leases on equipment and
structures. For the median farm, this accounts for about 70 percent of total liabilities.
Deferred taxes constitute the remainder. Combining total asssets and liabilities reveals
that the average farm has a net worth of 1.4 million dollars. Only 28 (or 1.4 percent) of
all farm-years report negative net worth.
The DFBS reports net investment for each type of capital. It also reports depreciation, allowing us to construct a measure of gross investment. Following the literature,
we focus on investment rates, scaling investment by the market value of owned capital
at the beginning of each period. Table 2 describes the distribution of investment rates.
Cooper and Haltiwanger (2006) show, using data from the Longitudinal Research Database (LRD), that plant-level investment often occurs in large increments, suggesting a
prominent role for …xed investment costs. Table 2 shows statistics comparable to theirs,
and for reference reproduces the statistics for gross investment rates shown in their Table 1. Investment spikes are much less frequent in the DFBS than in the LRD. The
average investment rate is also a bit lower, and the inaction rate is slightly higher. These
suggest that …xed investment costs are less important in the DFBS, and in the interest
of tractibility we omit them from our structural model.
Farm technologies can be divided into two categories: stanchion barns and and milking
parlors, the latter considered the newer and larger-scale technology. About two-thirds
of the farms in our sample are parlor operations. Table 3 displays summary statistics
by size and technology splits. Large farms are de…ned as those whose time-averaged peroperator herd sizes are larger than the median. As the table shows, large farms have
higher investment and debt to asset ratios, hold more cash, and pay higher dividends
than small farms. Interestingly, large operations also use more variable inputs per unit of
capital, which suggests that their technology may di¤er from that of small operations.
The small-large distinction does not perfectly coincide with the stanchion-parlor dis8
All Farms
Stanchion Barns Milking Parlors
Small Large Small
Large
Small Large
Total Capital
544
1,915
476
779
707
2,461
Intermed. Goods/Capital 0.28
0.39
0.26
0.27
0.33
0.41
0.39
0.51
0.36
0.37
0.44
0.53
Output/Capital
Investment/Capital
0.04
0.07
0.03
0.03
0.05
0.08
0.43
0.50
0.39
0.46
0.46
0.51
Debt/Assets
Cash/Assets
0.11
0.16
0.09
0.12
0.14
0.17
Dividends
18.03 40.54 14.71
23.79
23.60
44.24
51
203
41
76
78
277
Cows
Notes: Financial variables normalized by family size and expressed in thousands of 2011 dollars.
A large farm has a per-operator herd size larger than the median for its technological category.
Table 3: Medians by Technology and Size
tinction. Although parlor operations are typically larger, about 30 percent of parlors can
be classi…ed as small farms, and 10 percent of the stanchion operations can be classi…ed as
large. Moreover, as Table 3 shows, di¤erences between small and large operations within
each technology group are quite substantial. Along many dimensions small parlor operations are closer to large stanchion operations than to large parlor operations. Alvarez
et al. (2012), who sort farms using a latent class model, also …nd the stanchion-parlor
distinction to be inadequate. Accordingly, in our estimation we will allow the production
function to vary by farm size, rather than by milking technology.
2.2
2.2.1
Productivity
Our Productivity Measure
We assume that farms share the following Cobb-Douglas production function
Yit = zit Mi Kit Nit 1
;
where we denote farm i’s gross revenues at time t by Yit and its entrepreneurial input,
measured as the time-averaged number of operators, by Mi .7 Kit denotes the capital
stock; Nit represents expenditure on all variable inputs, including hired labor and intermediate goods; and zit is a stochastic revenue shifter re‡ecting both idiosyncratic and
7
More than two thirds of all farms and 90 percent of farm-years display no change in family size.
9
systemic factors.8 With the exception of operator labor, all inputs are measured in dollars. Although this implies that we are treating input prices as …xed, variations in these
prices can enter our model through changes in the pro…t shifter zit .
In per capita terms, we have
yit =
Yit
= zit kit nit 1
Mi
:
In this formulation, returns to scale are 1
, with measuring an operator’s “span of
control”(Lucas, 1978).
Following Alvarez et al. (2012) and based on the descriptive statistics in the previous
section, we allow for two production technologies. Using the structural estimation procedure described below, we …nd that for small-herd operations b = 0:141 and b = 0:160,
and for large-herd operations b = 0:144 and b = 0:116. In other words, large farms have
similar returns to scale and lower returns to capital than small farms. These estimates
allow us to calculate total factor productivity as
zit =
yit
kitb nit 1
b b
:
(1)
We assume that the resulting TFP measure can be decomposed into the individual …xed
e¤ect i ; a time-speci…c component, common to all farms, t , and the idiosyncratic i.i.d
component "it :
ln zit = i + t + "it :
(2)
A Hausman test rejects a random e¤ects speci…cation. Regressing zit on farm and time
dummies yields estimates of all three components. The …xed e¤ect has a mean of 0.976,
but ranges from 0.13 to 1.42 with a standard deviation of 0.19, implying signi…cant timeinvariant di¤erences in productivity across farms. The time e¤ect t is constructed to be
zero mean. This series is e¤ectively uncorrelated,9 and has a standard deviation of 0.060.
8
The assumption of decreasing returns to scale in non-management inputs is not inconsistent with the
literature. Tauer and Mishra (2006) …nd slightly decreasing returns in the DFBS. They argue that while
many studies …nd that costs decrease with farm size: “Increased size per se does not decrease costs— it is
the factors associated with size that decrease costs. Two factors found to be statistically signi…cant are
e¢ ciency and utilization of the milking facility.”
9
It is often argued that milk prices follow a three-year cycle. Nicholson and Stephenson (2014) …nd
a stochastic cycle lasting about 3.3 years. While Nicholson and Stepheson report that in recent years a
“small number”of farmers appear to be planning for cycles, they also report (page 3) that: “the existence
of a three-year cycle may be less well accepted among agricultural economists and many ... forecasts ...
do not appear to account for cyclical price behavior. Often policy analyses ... assume that annual milk
prices are identically and independently distributed[.]”
10
Figure 1: Aggregate TFP, real Milk Prices, and Cash Flow
The idiosyncratic residual "it can also be treated as uncorrelated (the serial correlation is
-0.009), with a standard deviation of 0.069.
To provide some insight into this productivity measure, Figure 1 plots the aggregate
component t against real milk prices in New York State (New York State Department
of Agriculture and Markets, 2012). The aggregate component of TFP follows milk prices
very closely – the correlation is well over 90 percent – which gives us con…dence in our
measure. On the same graph we plot the average value of the cash ‡ow (net operating
income less estimated taxes) to capital ratio. Aggregate cash ‡ow is also closely related
to our aggregate TFP measure. Cash ‡ow varies quite signi…cantly, indicating that farms
face signi…cant …nancial risk.
2.2.2
Productivity and Farm Characteristics
How are productivity and farm performance related? Figures 2 and 3 illustrate how
farm characteristics vary as a function of the time-invariant component of productivity,
i . We divide the sample into high- and low-productivity farms, splitting around the
median value of i , and plot the evolution of several variables. To remove scale e¤ects, we
either express these variables as ratios, or divide them by the number of operators. More
than 90 percent of the low productivity farms are small, and about 60 percent of them
are stanchion barn operations. A very small fraction (10 percent) of the high productivity
farms are stanchion barns. About 90 percent of high productivity farms are large.
Our convention will be to use thick solid lines to represent high-productivity farms
11
Figure 2: Production and Inputs by TFP and Calendar Year
and the thinner dashed lines to represent low-productivity farms. Figure 2 shows output
(revenues) and input choices. The top two panels of this …gure show that high-productivity
farms operate at a scale 4-5 times larger than that of low-productivity farms.10 This
size advantage is increasing over time: high productivity-…rms are growing while lowproductivity …rms are static. The bottom left panel shows that high-productivity farms
lease a larger fraction of their capital stock (18 percent vs. 8 percent). The leasing
fractions are all small and stable, however, implying that farms expand primarily through
investment.
The bottom right panel of Figure 2 shows that the ratio of variable inputs – feed,
fertilizer, and hired labor –to capital is also higher for high productivity farms (40 percent
vs. 30 percent). This could be due to di¤ering production functions between small and
large farms, as described earlier, since larger farms also tend to be higher productivity
farms. Another explanation for this di¤erence in input use could be …nancial constraints
10
Using the 2007 U.S. Census of Agriculture, Adamopoulos and Restuccia (2014) document that farms
with higher labor productivity are indeed substantially larger.
12
on the purchase of variable inputs. We will account for both possibilities in our model.
Figure 3 shows …nancial variables. The top two panels contain median cash ‡ow
and gross investment. These variables are positively correlated in the aggregate; for
example, the recession of 2009 caused both of them to decline. Given that the aggregate
shocks are not persistent, the correlation of cash ‡ow and investment suggests …nancial
constraints, which are relaxed in periods of high output prices. The middle left panel
shows investment as a fraction of owned capital, and con…rms that high-productivity
farms generally invest at higher rates. The middle right panel shows dividends, which are
also correlated with cash ‡ow. Dividend ‡ows are in general quite modest, especially for
low-productivity farms.
The bottom row of Figure 3 shows two sets of …nancial ratios. The left panel shows
debt/asset ratios.11 Although high-productivity farms begin the sample period with
more debt, over the sample period they rapidly decrease their leverage. By 2011, the
debt/asset ratios of high and low-productivity farms are much closer. This suggests that
the high-TFP …rms are using their pro…ts to de-lever as well as to invest.
In a static frictionless model, the optimal capital stock for a farm with productivity
level i is given by ki = [ exp( i )]1= , where is a positive constant.12 The bottom right
panel of Figure 3 plots median values of the ratio kit =ki , showing the extent to which
farms operate at their e¢ cient scales. The median low-productivity farm is close to the
optimal capital stock until the very end of the sample period. In contrast, the capital
stocks of high-productivity farms are initially well below their optimal size, but grow
rapidly. This suggests that …nancial constraints hinder the e¢ cient allocation of capital.
Midrigan and Xu (2014) …nd that …nancial constraints impose their greatest distortions
by limiting entry and technology adoption. To the extent that high-productivity farms
are more likely to utilize new technologies, such as robotic milkers (McKinley, 2014), our
results are consistent with their …ndings. Our results also comport with Buera, Kaboski
and Shin’s (2011) argument that …nancial constraints are most important for large-scale
technologies.
Finally we consider the empirical correlates of investment. In the standard investment
regression, investment-capital ratios are regressed against a measure of Tobin’s q and
a measure of cash ‡ow. While our farms are not publicly traded …rms and we cannot
11
To ensure consistency with the model, and in contrast to Table 1, we add capitalized values of leased
capital to both assets and liabilities.
12
This expression can be found by maximizing E(zit )kit n1it
nit (r +
$)kit . In contrast to
the construction of capital stock described in Appendix A, here we use a single user cost for all capital.
+
Standard calculations show that
=
r+
$
(1
13
)
1
E(exp(
t "it )):
Figure 3: Investment and Finances by TFP and Calendar Year
14
Dependent Variable: Gross Investment/Capital
Coe¢ cient Std. Error Coe¢ cient Std. Error
Operator Age
-0.002*
0.000
-0.007*
0.002
Cash Flow/Capital Small
-0.188
0.146
1.050*
0.329
0.430*
0.108
0.729*
0.244
Cash Flow/Capital Large
zit Small
-0.526*
0.139
-0.160
0.142
zit Large
0.199*
0.058
i Small
Large
0.121*
0.040
i
Fixed E¤ects
No
Yes
Time E¤ects
Yes
Yes
Table 4: Investment-Cash Flow Regressions
construct Tobin’s q, we can use zit or one of its components as a substitute. Table 4
reports the coe¢ cient estimates.
The …rst column of Table 4 shows that farms with higher values of the TFP …xed e¤ect
i have higher investment rates. Decreasing returns to per-operator inputs are manifested
in the larger responsiveness of small farms to i . Investment rates also decline with age,
although the coe¢ cient is small. This shows (weak) evidence of life cycle behavior on the
part of the farmers. Investment is positively related to cash ‡ow for large operations, but
does not seem to be so for small ones.
The results change once we introduce …xed e¤ects in the third column. Investment
is now positively related to cash ‡ow for both small and large operations.13 Our results
contrast to those of Weersink and Tauer (1989), who estimate investment models using
DFBS data for 1973-1984. Weersink and Tauer …nd that investment levels are decreasing
in cash ‡ow and increasing in asset values (which proxy for pro…tability).
3
Model
Consider a farm family seeking to maximize expected lifetime utility at “age”q:
Eq
Q
X
h q
[u (dh ) +
1ffarm operatingg] +
h=q
13
Q q+1
!
VQ+1 (aQ+1 ) ;
A larger coe¢ cient on cash ‡ow for small …rms need not indicate tighter …nancial constraints, as
documented by Kaplan and Zingales (1997). Pratap (2003) shows that in the presence of adjustment
costs the investment of constrained …rms may be less responsive to cash ‡ow.
15
where: q denotes the age of the principal (youngest) operator; dq denotes farm “dividends”
per operator; the indicator 1ffarm operatingg equals 1 if the family is operating a farm and
0 otherwise, and measures the psychic/nonpecuniary gains from farming; Q denotes the
retirement age of the principal operator; a denotes assets; and Eq ( ) denotes expectations
conditioned on age-q information. The family discounts future utility with the factor
0 < < 1. Time is measured in years. Consistent with the DFBS data, we assume
that the number of family members/operators is constant. We further assume a unitary
model, so that we can express the problem on a per-operator basis. To simplify notation,
throughout this section we omit “i”subscripts.
The ‡ow utility function u( ) and the retirement utility function VQ+1 ( ) are specialized
as
u(d) =
VQ+1 (a) =
1
1
(c0 + d)1
1
1
c1 +
a
;
1
;
with
0, c0 0, c1 c0 and
1. Given our focus on farmers’business decisions, we
do not explicitly model the farmers’personal …nances and saving decisions. We instead
use the shift parameter c0 to capture a family’s ability to smooth variations in farm
earnings through outside income, personal assets, and other mechanisms. The scaling
parameter re‡ects the notion that upon retirement, the family lives for years and
consumes the same amount each year.
Before retirement, farmers can either work for wages or operate a farm. While working
for wages, the family’s budget constraint is
aq+1 = (1 + r)aq + w
dq ;
(3)
where: aq denotes beginning-of-period …nancial assets; w denotes the age-invariant outside
wage; and r denotes the real risk-free interest rate. Workers also face a standard borrowing
constraint:
aq+1 0:
Turning to operating farms, recall that gross revenues per operator follow
yq = zqt kq nq 1
;
(4)
where kq denotes capital, nq denotes variable inputs, and zqt is a stochastic income shifter
16
re‡ecting both idiosyncratic and systemic factors. These factors include weather and
market prices, and are not fully known until after the farmer has committed to a production plan for the upcoming year. In particular, while the farm knows its permanent TFP
component , it makes its production decisions before observing the transitory e¤ects t
and "q .
A farm that operated in period q 1 begins period q with debt bq and assets a
~q . As
a matter of notation, we use bq to denote the total amount owed at the beginning of
age q: rq is the contractual interest rate used to de‡ate this quantity when it is chosen
at age q 1. Expressing debt in this way simpli…es the dynamic programming problem
when interest rates are endogenous. At the beginning of period q, assets are the sum of
undepreciated capital, cash, and operating pro…ts:
a
~q
(1
+ $)kq
1
+ `q
1
+ yq
1
(5)
nq 1 ;
where: 0
1 is the depreciation rate; $ is the capital gains rate, assumed to be
constant; and `q 1 denotes liquid (cash) assets, chosen in the previous period.
A family operating its own farm must decide each period whether to continue the
business. The family has three options: continued operation, reorganization, or liquidation. If the family decides to continue operating, it will have two sources of funding: net
worth, eq a
~q bq ; and the age-q proceeds from new debt, bq+1 =(1 + rq+1 ). (We assume
that all debt is one-period.) It can spend these funds in three ways: purchasing capital;
issuing dividends, dq ; or maintaining its cash reserves:
eq +
bq+1
=a
~q
1 + rq+1
bq +
bq+1
= kq + dq + `q :
1 + rq+1
(6)
Combining the previous two equations yields
iq
1
= kq
= [yq
(1
1
+ $)kq
nq
1
1
dq ] + [`q
1
`q ] +
bq+1
1 + rq+1
bq :
(7)
Equation (7) shows that investment can be funded through three channels: retained
earnings (dq is the dividend paid after yq 1 is realized), contained in the …rst set of
brackets; withdrawals from cash reserves, contained in the second set of brackets; and
additional borrowing, contained in the third set of brackets.
17
Operating farms face two …nancial constraints:
bq+1
(8)
kq
nq
(9)
`q ;
with
0 and
1. The …rst of these constraints, given by equation (8), is a
collateral constraint of the sort introduced by Kiyotaki and Moore (1997). Larger values
of imply a tighter constraint, with farmers more dependent on equity funding. The
second constraint, given by equation (9), is a cash-in-advance or working capital constraint
(Jermann and Quadrini, 2012). Larger values of imply a more relaxed constraint, with
farmers more able to fund operating expenses out of contemporaneous revenues. Because
dairy farms receive income throughout the entire year, in an annual model is likely to
exceed 1.
As alternatives to continued operation, a farm can reorganize or liquidate. If it chooses
the second option, reorganization, some of its debt is written down.14 The debt liability
bq is replaced by ^bq
bq and the restructured farm continues to operate. Finally, if
the family decides to exit – the third option – the farm is liquidated and assets net of
liquidation costs are handed over to the bank:
kq = 0;
aq = max f(1
)~
aq
bq ; 0g :
We assume that the information/liquidation costs of default are proportional to assets,
with 0
1. Liquidation costs are not incurred when the family (head) retires at
age Q.
The interest rate realized on debt issued at age q 1, rbq = rbq (sq ; rq ), depends on the
state vector sq (speci…ed below) and the contractual interest rate rq . The function rb( )
emerges from enforceability problems of the sort described in Kehoe and Levine (1993).
If the farmer to chooses to honor the contract, rbq = rq . If the farmer chooses to default,
rbq =
min f(1
)~
aq ; bq g
bq =(1 + rq )
1 = (1 + rq )
min f(1
The return on restructured debt is rbq = (1 + rq )^bq =bq
14
bq
)~
aq ; bq g
1:
1. We assume that loans are
Most farms have the option of reorganizing under Chapter 12 of the bankruptcy code, a special
provision designed for family farmers. Stam and Dixon (2004) review the bankruptcy options available
to farmers.
18
supplied by a risk-neutral competitive banking sector, so that
(10)
Eq 1 (b
rq (sq ; rq )) = r;
where r is the risk free rate. While we allow the family to roll over debt (bq can be bigger
than a
~q ), Ponzi games are ruled out by requiring all debts to be resolved at retirement:
bQ+1 = kQ+1 = 0;
aQ+1
0:
To understand the decision to default or renegotiate, the family’s problem needs to be
expressed recursively. To simplify matters, we assume that the decision to work for wages
is permanent, so that the Bellman equation for a worker is:
VqW (aq ) =
max
0 dq (1+r)aq +w
W
u(dq ) + Vq+1
(aq+1 );
s:t: equation (3):
The Bellman equation for a family who has decided to fully repay its debt and continue
farming is
VqF (eq ; ) =
fdq
max
c0 ;bq+1 0;nq 0;kq 0g
u(dq ) +
+ Eq (Vq+1 (~
aq+1 ; bq+1 ; )) ;
s:t: equations (4) - (6), (8) - (10);
where Vq ( ) denotes the continuation value prior to the age-q occupational choice:
Vq (~
aq ; bq ; ) =
max VqF (~
aq
minfbq ; ^bq g; ); VqW (max f(1
)~
aq
bq ; 0g) :
We require that the renegotiated debt level ^bq be incentive-compatible:
^bq = maxfb ; (1
q
VqF (~
aq
bq ; )
VqW (max f(1
)~
aq g;
)~
aq
bq ; 0g);
so that ^bq = ^bq (sq ), with sq = f~
aq ; bq ; g. The …rst line of the de…nition ensures that ^bq
is incentive-compatible for lenders: the bank can always force the farm into liquidation,
bounding ^bq from below at (1
)~
aq . However, if the family …nds liquidation su¢ ciently
unpleasant, the bank may be able to extract a value of bq that is larger. The second line
19
ensures that such a payment is incentive-compatible for farmers, i.e., farmers must be
no worse o¤ under this deal than they would be if they liquidated and switched to wage
work. (We assume that once a farm chooses to renegotiate its debt, the bank holds all
the bargaining power.)
A key feature of this renegotiation is limited liability. If the farm liquidates, the bank
at most receives (1
)~
aq , and under renegotiation dividends are bounded below by
c0 . Our estimated value of c0 is small, implying that new equity is expensive and not
an important source of funding. Coupled with the option to become a worker, limited
liability will likely lead the continuation value function, Vq ( ), to be convex over the regions
of the state space where farming and working have similar valuations (Vereshchagina and
Hopenhayn, 2009).
The debt contract also bounds repayment from above: the farm can always honor its
contract and pay back bq . Solving for ^bq (sq ) allows us to express the …nance/occupation
indicator IqB 2 fcontinue, restructure, liquidateg as the function IqB (sq ). It immediately
follows that
1 + rbq (sq ; rq )
= 1fIqB (sq ) = continueg +
1 + rq
minf(1
1fIqB (sq ) = liquidateg
1fIqB (sq ) = restructureg
bq
)~
a; bq g
+
^bq (sq )
:
bq
Inserting this result into equation (10), we can calculate the equilibrium contractual rate
as15
1 + rbq (sq ; rq )
1 + rq = [1 + r] = Eq 1
:
(11)
1 + rq
4
Econometric Strategy
We estimate our model using a form of Simulated Minimum Distance (SMD). In
brief, this involves comparing summary statistics from the DFBS to summary statistics
calculated from model simulations. The parameter values that yield the “best match”
15
1+b
r (s ;r )
q
q q
The previous equation shows that the ratio
is independent of the contractual rate rq .
1+rq
Finding rq thus requires us to calculate the expected repayment rate only once, rather than at each
potential value of rq , as would be the case if debt incurred at age q 1 were denominated in age-q 1
terms. (In the latter case, bq would be replaced with (1 + rq )bq 1 .) This is a signi…cant computational
advantage.
20
between the DFBS and the model-generated summary statistics are our estimates.
Our estimation proceeds in two steps. Following a number of papers (e.g., French,
2005; De Nardi, French and Jones, 2010), we …rst calibrate or estimate some parameters
outside of the model. In our case there are four parameters. We set the real rate of return
r to 0.04, a standard value. We set the outside wage w to an annual value of $15,000,
or 2,000 hours at $7.50 an hour. To a large extent, the choice of w is a normalization
of the occupation utility parameter , as the parameters a¤ect occupational choice the
same way. From the DFBS data we calculate the capital depreciation rate to 5.56
percent and the appreciation rate $ to 3.59 percent as described in the appendix. The
liquidation loss, , is set to 35 percent. This is at the upper range of the estimates found
by Levin, Natalucci and Zakrajšek (2004). Given that a signi…cant portion of farm assets
are site-speci…c, high loss rates are not implausible. We discuss alternative values of
below.
In the second step, we estimate the parameter vector = ( , , c0 , , c1 , , , , n0 , ,
, ) using the SMD procedure itself. To construct our estimation targets, we sort farms
along two dimensions, age and size. There are two age groups: farms where the youngest
operator was 39 or younger in 2001; and farms where the youngest operator was 40 or
older. This splits the sample roughly in half. We measure size as the time-averaged herd
size divided by the time-averaged number of operators. Here too, we split the sample in
half: the dividing point is between 86 and 87 cows per operator. As Section 2 suggests,
this measure corresponds closely to the …xed TFP component i . Then for each of these
four age-size cells, for each of the years 2001 to 2011, we match the following sample
moments:
1. The median value of capital per operator, k.
2. The median value of the output-to-capital ratio, y=k.
3. The median value of the variable input-to-capital ratio, n=k.
4. The median value of the gross investment-to-capital ratio.
5. The median value of the debt-to-asset ratio, b=~
a
6. The median value of the cash-to-asset ratio, `=~
a.
7. The median value of the dividend growth rate, dt =dt 1 .16
16
Because pro…tability levels, especially for large farms, are sensitive to total returns to scale 1
,
we match dividend growth, rather than levels. Both statistics measure the desire of farms to smooth
dividends, which in turn a¤ects their ability to fund investment through retained earnings.
21
For each value of the parameter vector , we …nd the SMD criterion as follows. First,
we use and to compute zit for each farm-year observation in the DFBS, following
equation (1). We then decompose zit according to equation (2). This yields a set of
…xed e¤ects f i gi and a set of aggregate shocks f t gt to be used in the model simulations,
and allows us to estimate the means and standard deviations of i , t , and "iq for use in
…nding the model’s decision rules. Using a bootstrap method, we take repeated draws
from the joint distribution of si0 = ( i ; ai0 ; bi0 ; qi0 ; ti0 ), where ai0 , bi0 and qi0 denote the
assets, debt and age of farm i when it is …rst observed in the DFBS, and ti0 is the calendar
year it is …rst observed. At the same time we draw #i , the complete set of dates that farm
i is observed in the DFBS.
Discretizing the asset, debt, equity and productivity grids, we use value function iteration to …nd the farms’decision rules. We then compute histories for a large number
of arti…cial farms. Each simulated farm j is given a draw of sj0 and the shock histories
f t ; "jt gt . The residual shocks f"jt gjt are produced with a random number generator,
using the standard deviation of "iq described immediately above. The aggregate shocks
are those observed in the DFBS. Combining these shocks with the decision rules allows
us to compute that farm’s history. We then construct summary statistics for the arti…cial data in the same way we compute them for the DFBS. Let gmt , m 2 f1; 2; :::; M g,
t 2 f1; 2; :::; T g, denote the realization of summary statistic m in calendar year t, such
as median capital for young, large farms in 2007. The model-predicted value of gmt
is gmt ( ). We estimate the model by minimizing the squared proportional di¤erences
between fgmt ( )g and fgmt g.
Because the model gives farmers the option to become workers, we also need to match
some measure of occupational choice. We do not attempt to match observed attrition,
because the DFBS does not report reasons for non-participation, and a number of farms
exit and re-enter the dataset. In fact, when data for a particular farm-year are missing in
the DFBS, we treat them as missing in the simulations, using our draws of #i . However,
we also record the fraction of farms that exit in our simulations but not in the data. We
use this fraction to calculate a penalty that is added to the SMD criterion, ( ).
Our SMD criterion function is
M X
T
X
m=1 t=1
@2m
gmt ( )
gmt
2
1
+ ( ):
Our estimate of the “true” parameter vector 0 is the value of
that minimizes this
criterion. Appendix B contains a detailed description of how we set the weights f@m g
22
and calculate standard errors.
5
Parameter Estimates and Goodness of Fit
5.1
Estimates
Table 5 displays the parameter estimates and asymptotic standard errors. The estimated values of the discount factor , 0.996, and the risk aversion coe¢ cient , 3:3,
are both within the range of previous estimates (see, e.g., the discussion in De Nardi et
al., 2010). The retirement parameters imply that farms greatly value post-retirement
consumption; in the period before retirement, farmers consume only 1.8 percent of their
wealth and save the rest.17 The nonpecuniary bene…t of farming , is expressed as a
consumption increment to the non-farm wage w. With w equal to $15,000, the estimates
imply that the psychic bene…t from farming is equivalent to the utility gained by increasing consumption from $15,000 to $100,000. Even though the outside wage is modest,
the income streams from low productivity farms are so small and uncertain that some
operators would exit if they did not receive signi…cant psychic bene…ts.
The returns to management and capital are both fairly small, implying that the returns
to intermediate goods, 1
, are between 70 and 74 percent. Table 1 shows that
variable inputs in fact equal about 77:5 percent of revenues. The collateral constraint
parameter is 1:026, implying that each dollar of debt must be backed by an almost
equivalent amount of capital. The liquidity constraint parameter is estimated to be
about 2.6, implying that farms need to hold liquid assets equal to about 5 months of
expenditures. Although these two constraints together signi…cantly reduce the risk of
insolvency, farms with adverse cash ‡ow may …nd themselves extremely illiquid.
17
This can be found by solving for the value of the optimal retirement assets ar in the penultimate
period of the operator’s economically active life, max
r
a
0
1
1
(c0 + x
1
ar )
+
1
c1 +
ar (1+r)
1
,
and …nding @ar (x)=@xjar =(ar ) . A derivation based on a similar speci…cation appears in De Nardi et al.
(2010).
23
Parameter Description
Discount factor
Risk aversion
Consumption utility shifter (in $000s) c0
Retirement utility shifter (in $000s)
c1
Retirement utility intensity
Nonpecuniary value of farming
(consumption increment in $000s)
Returns to management: small herds
Returns to management: large herds
Returns to capital: small herds
Returns to capital: large herds
Strength of collateral constraint
Degree of liquidity constraint
Parameter Standard
Estimate
Error
0.996
3.72 10 6
3.299
0.013
4.177
0.001
23.64
1.490
58.11
0.365
84.77
202.60
0.141
0.144
0.160
0.116
1.026
2.64
1.09 10
4.89 10
3.08 10
0.0004
0.082
3.08 10
5
5
5
5
Table 5: Parameter Estimates
5.2
Goodness of Fit
Figures 4 and 5 compare the model’s predictions to the data targets. To distinguish
the younger and older cohorts, the horizontal axis measures the average operator age of
a cohort at a given calendar year. The …rst observation on each panel starts at age 29:
this is the average age of the youngest operator in the junior cohort in 2001. Observations
for age 30 correspond to values for this cohort in 2002. When …rst observed in 2001, the
senior cohort has an average age of 48. As before, thick lines denote large farms, and thin
lines denote smaller farms. For the most part the model …ts the data well, although it
understates the capital holdings of large farms and overstates dividend growth. However,
it captures many of the di¤erences between large and small farms, and much of the yearto-year variation.
Our estimation criterion includes a penalty for “false exits:” simulated farms that exit
when their data counterparts do not. False exit is uncommon, with a frequency of less
than 0.6 percent.
24
Figure 4: Model Fits: Production Measures
25
Figure 5: Model Fits: Financial Measures
To assess the cross sectional variation generated by the model, we repeat the regressions in Table 4 on simulated data. The results are presented in Table 6. The table shows
that our model generates a positive relation between cash ‡ow and investment, even after
controlling for productivity. Smaller farms have a greater investment cash ‡ow sensitivity
than large farms as in the data. The …xed component of productivity i is an important
determinant of investment.
6
Identi…cation
The model’s parameters are identi…ed from aggregate averages. Some linkages are
straightforward. For example, as discussed in the previous section, the production coef…cients and are identi…ed by expenditure shares, and the extent to which farm size
varies with productivity. The cash constraint is identi…ed by the observed cash/asset
ratio.
Table 7 shows comparative statics for our model, computed from model simulated
26
Dependent Variable: Gross Investment/Capital
Coe¢ cient Std. Error Coe¢ cient Std. Error
Operator Age
-0.001*
0.000
-0.007*
0.000
Cash Flow/Capital Small
1.297*
0.005
2.269*
0.011
0.659*
0.001
0.508*
0.022
Cash Flow/Capital Large
zit Small
-3.240*
0.043
2.321*
0.025
zit Large
0.060*
0.002
i Small
Large
0.120*
0.002
i
No
Yes
Fixed E¤ects
Time E¤ects
Yes
Yes
Table 6: Investment-Cash Flow Regressions with Simulated Data
data where we change parameters in isolation. The numbers in the table are averages
of the model-simulated data over the 11-year (pseudo-) sample period. Row (1) shows
the statistics for the baseline model associated with the parameters in Table 5, while
subsequent rows show the statistics that arise as we vary di¤erent parameters or features of
the model. The statistics shown in Table 7 serve two purposes. First they provide insight
into the identi…cation of the model’s parameters. Second, they illustrate the mechanisms
of the model and help us assess the importance of …nancial frictions, nonpecuniary bene…ts
and risk.
Row (2) shows the averages that result when the discount factor is lowered to 0:975.18
Farms hold less capital and invest less, as they place less weight on future returns. In
addition, is identi…ed by the dividend growth rate rate, as lower values of imply slower
growth of dividends for the average farm.
Rows (3) and (4) show the e¤ects of changing the risk coe¢ cient . With risk neutrality
( = 0:0), farmers hold less debt, as the borrowing rate r = 0:04 exceeds the discount rate
of 0:004, and the opportunity cost of retained earnings –unsmoothed dividends –is zero.
Dividends are initially negative, as farmers acquire funds any way possible. Risk-neutrality
also leads farmers to invest more aggressively in capital, as they are less concerned about
its stochastic returns. The investment rate rises from 10.7 to 16.2 percent, while the
average capital stock increases from $1.32 to $1.61 million. These high rates of growth
of dividends and capital is at odds with the data. Under risk neutrality, the baseline
consumption value of being a farmer, $85,000, is enough to induce all farms to remain in
operation: relative to its baseline value the fraction of farms operating (and observed in
18
We restrict
to lie in the (0; 1) interval.
27
the DFBS) is at its highest possible level, 1.006. In contrast, increasing to 4:0 (row (4))
leads a few farms to exit the industry. The utility shifter c0 in line (8) is identi…ed by
similar mechanics.
The retirement parameters c1 and are identi…ed by life cycle variation not shown
in Table 7. As goes to zero and retirement utility vanishes, older farmers will have
less incentive to invest in capital, and their capital stock falls relative to that of younger
farmers. Setting to zero also increases debt-holding, as farmers become more inclined
to carry debt into retirement.
The parameter , measuring the strength of the collateral constraint, is identi…ed by
several factors. Tighter collateral constraints reduce debt holdings, induce greater exit,
reduce the average capital stock and force farmers to build up their capital stock gradually
over time, rather than acquiring it immediately, resulting in higher investment rates.
The data show that farmers have fairly ‡at dividend trajectories, but accumulate capital
rapidly. These behaviors are hard to reconcile in a consumption-smoothing framework
without a borrowing constraint. We will discuss the e¤ects of , and the other …nancial
constraints, in more detail in Section 7.2 below.
7
7.1
Model Mechanisms
Nonpecuniary bene…ts
Our estimates imply that the nonpecuniary bene…t from farming is equivalent to the
utility gained by increasing consumption from $15,000 to $100,000. The parameter is
identi…ed by occupational choice, namely the estimation criterion that farms observed in
the DFBS in a given year also be operating and thus observed in the simulations. While
the standard errors suggest weak local identi…cation of , row (5) of Table 7 shows that
the e¤ect of setting to zero is large. Eliminating psychic bene…ts leads some farms
to liquidate, so that the average number of farms operating drops by 7 percent. Not
surprisingly, it is the smaller, low-productivity farms that exit: the survivors in row (5)
have more assets, debt and capital. Their optimal capital stock (recall Figure 3) rises from
$1.80 to $1.92 million. Hamilton (2000) and Moskowitz and Vissing-Jørgensen (2002)
…nd that many entrepreneurs earn below-market returns, suggesting that nonpecuniary
bene…ts are large. (Also see Quadrini, 2009, and Hall and Woodward, 2010.) Similarly,
Figure 3 and Table 3 show that many low-productivity farms have dividend ‡ows around
the outside salary of $15,000. Moreover, these ‡ows are uncertain, while the outside
28
salary is not. This is consistent with a high value of .19 The high estimated value of
also implies that large increases in consumption have only modest e¤ects on ‡ow utility,
implying that the consumption increment underlying will be large.
The high value of may re‡ect other considerations, such as e¢ ciencies in home production, tax advantages to continued operations,20 or limited employment opportunities in
rural areas.21 On the other hand, there is evidence suggesting that farming provides large
nonpecuniary rewards. Recent surveys of national well being, published by the O¢ ce for
National Statistics in the U.K., show that the levels of life satisfaction of farmers and farm
workers rank among the highest for all occupations, and are substantially higher than the
levels of life satisfaction reported by individuals in occupations with similar incomes such
as construction and telephone sales (O’Donnell et al., 2014). Hurst and Pugsley (2011)
…nd that non-pecuniary considerations “play a …rst-order role in the business formation
decision” and that many small businesses have “no desire to grow big.” Both attitudes
appear consistent with the behavior of the small farms in our sample.
Row (5) also shows that eliminating nonpecuniary bene…ts raises the N=K ratio from
0.349 to 0.353. This likely re‡ects selection e¤ects, as the production technology for large
farms places more weight on intermediate goods.22 On the other hand, the cash/assets
ratio falls, even though larger farms tend to hold more cash (see Figure 5). With nonpecuniary bene…ts, small farms hold cash reserves to avoid being forced out of business.
Setting = 0 removes this precautionary motive. It also raises the debt/asset ratio from
0.466 to 0.486. In addition to composition e¤ects, some of this increase may re‡ect a
greater willingness to take on debt.
7.2
Financial Constraints
Our model contains …ve important …nancial elements: liquidation costs, limits on new
equity, collateral constraints, liquidity constraints, and the ability to renegotiate debt.
We consider the e¤ects of each element on assets, debt, capital, investment, and exit.
19
Notice that our estimate of the nonpecuniary bene…t is conservative, as we assign a low value to the
outside option; $15,000 is roughly equivalent to the Federal poverty line for a household of two individuals.
A higher value of the outside option would require an even higher nonpecuniary bene…t to explain the
continued operation of low-productivity farms.
20
We are indebted to Todd Schoellman for this point.
21
Poschke (2012, 2013) documents that the probability of entrepreneurship is “U-shaped” in an individual’s prior non-entrepreneurial wage, and argues that many low-productivity entrepreneurs start and
maintain their businesses because their outside options are even worse.
22
In a frictionless static world, with full debt …nancing (r = 0:04), the N=K ratio would be 0.261 for
small-herd farms and 0.368 for large farms.
29
30
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
No
No
No
No
Assets
1,650
1,615
1,930
1,625
1,758
1,738
2,080
2,139
1,997
1,273
1,468
1,688
1,731
2,017
1,682
1,708
Debt
865
866
810
844
929
1,053
1,118
881
1,208
506
703
895
903
856
895
932
Debt/
Assets
0.466
0.468
0.395
0.454
0.486
0.474
0.522
0.349
0.525
0.353
0.424
0.475
0.468
0.404
0.474
0.485
Cash/
Assets
0.122
0.125
0.125
0.123
0.120
0.117
0.120
0.109
0.125
0.140
0.237
0.089
0.120
0.120
0.125
0.123
Capital
1,319
1,279
1,606
1,290
1.404
1,399
1,681
1,824
1,635
942
973
1,410
1,394
1,690
1,341
1,373
0.349
0.354
0.345
0.351
0.353
0.331
0.354
0.290
0.316
0.448
0.349
0.369
0.324
0.313
0.363
0.361
N=K
Investment/
Capital (%)
10.66
9.46
16.18
9.99
10.57
8.87
9.49
9.01
3.28
11.79
10.10
11.52
7.62
11.78
10.86
10.76
Table 7: Comparative Statics
Relative to baseline cace. y Mean growth rates. N.A. indicates negative initial dividends.
Renegotiation
Reneg., = 0
Aggregate Shocks
Transitory Shocks
= 0:975
= 0:0
= 4:0
=0
=0
= =0
c0 = 2; 000
= 0:5
= 1:5
=1
=4
Baseline Model
Fraction
Operating
1.000
0.999
1.006
0.990
0.927
0.934
0.728
1.006
1.006
0.998
0.975
1.000
0.950
0.971
1.000
0.998
Dividendy
Growth (%)
4.45
4.03
N.A.
4.23
4.55
4.31
3.75
N.A.
3.10
4.88
4.65
4.39
4.26
29.0
4.62
4.57
Optimal
Capital
1,803
1,805
1,796
1,816
1,920
1,837
2,241
1,796
1,796
1,806
1,815
1,803
1,804
1,798
1,803
1,802
7.2.1
Liquidation Costs
Row (6) shows the e¤ects of setting the liquidation cost to zero. Eliminating the
liquidation cost reduces the number of operating farms, by allowing farmers to retain more
of their wealth after exiting.23 Liquidation costs thus provide another explanation of why
entrepreneurs may persist despite low …nancial returns. The e¤ect of setting = 0 is in
many ways similar to that of eliminating the psychic bene…t . This lack of identi…cation
is one reason why we calibrate rather than estimate . Row (7) shows that nonpecuniary
bene…ts and liquidation costs reinforce each other; setting = = 0 leads over a quarter
of farms to exit.
Comparing row (6) to row (1), and row (7) to row (5), shows that the farms that remain
after the elimination of liquidation costs are signi…cantly larger and more productive.
Liquidation costs thus lead to …nancial ine¢ ciency, by discouraging the reallocation of
capital and labor to more productive uses.
7.2.2
Equity Injections
In addition to serving as a preference parameter, c0 limits the ability of farms to
raise funds from equity injections. Row (8) shows the e¤ects of increasing c0 to 2,000,
allowing farmers to inject up to $2 million of personal funds into their farms each year.24
Because farmers have a discount rate of 0:4 percent, as opposed to the risk-free rate of
4 percent, they greatly prefer internal funding to debt. Increasing c0 to 2,000 thus results
in a dramatic decrease in debt, along with signi…cant increases in capital and assets. The
reduced cost of funds also leads to a di¤erent input mix. Because capital becomes cheaper
relative to intermediate goods, the N=K ratio falls from 35 to 29 percent. Greater access
to equity also raises the value of farming, so that no operators exit.25
7.2.3
Collateral Constraints
Row (9) shows the e¤ects of setting the collateral constraint to 0:5, allowing each
dollar of capital to back up to 2 dollars of debt. Farms respond to the relaxed constraint
by borrowing more and acquiring more capital, with mean capital rising from $1.32 million
to $1.64 million. Much of this additional capital is purchased up front; the investment
23
Recall that we assume that liquidation costs are not imposed upon retiring farmers.
We also increase the retirement shifter c1 by an equivalent amount.
25
Increasing c0 also reduces ‡uctuations in the marginal utility of consumption, u0 (c0 + d), making
farming a more appealing choice. On the other hand, c0 decreases the incremental utility associated with
farming, which is calculated as u(w + c0 + 85) u(w + c0 ).
24
31
rate falls from 10.7 percent to 3.3 percent. Background results reveal that the increase
in initial capital is concentrated in the large/high productivity farms, suggesting again
that borrowing constraints are causing capital to be misallocated across farms. As with
equity, expanding access to debt raises the value of farming, and virtually all farmers stay
in business.
Row (10) shows the e¤ects of the opposite experiment, setting to 1.5. Tightening
the constraint this much leads farms to drastically reduce their capital stock, by 29 percent
of its baseline value. Farms accumulate their capital through retained earnings. With
capital more di¢ cult to fund, farms use more intermediate goods, so that the fall in
output, 17 percent, is much smaller than the fall in capital. All of these changes make
farming less pro…table, and fewer farms remain in operation.
7.2.4
Liquidity Constraints
Rows (11) and (12) illustrate the e¤ects of the liquidity constraint, given by equation (9). Row (11) of Table 7 shows what happens when we tighten this constraint by
reducing to 1. Even though fewer farms remain in business, the average scale of operations declines. While total assets fall by around 11 percent, capital falls by over 26
percent, and the cash/asset ratio jumps from 0.122 to 0.237. Rather than holding their
assets in the form of capital, farms are obliged to hold it in the form of liquid assets used
to purchase intermediate goods. Output falls by nearly 25 percent.
Loosening the liquidity constraint ( = 4) allows farms to hold a larger fraction of
their assets in productive capital, raising the assets’overall return. Total assets rise from
their baseline value by 2.3 percent, while capital rises even more, by 7 percent. Needing
fewer liquid assets, intermediate goods are more desirable, and the N=K ratio rises.
7.2.5
Renegotiation of Debt Contracts
Finally we explore the role of contract renegotiation. Row (13) of Table 7 shows the
e¤ects of eliminating renegotiation and requiring farms with negative net worth to liquidate. The fraction of farms operating and observed drops by 5 percent. Any farms that
enter the DFBS with negative net worth are forced out immediately in our simulations.
In addition, the inability to renegotiate signi…cantly reduces the value of farming, causing
a number of farms to exit voluntarily. Notably, the optimal capital stock increases only
slightly, from $1.803 to $1.804 million, revealing that some of the exiting farms are not
from the bottom of the productivity distribution. Renegotiation can therefore play an
important role in keeping productive farms alive.
32
Row (14) shows the e¤ects of jointly eliminating renegotiation and setting the risk
coe¢ cient to zero. Without consumption smoothing motives, farming becomes much
more desirable, and farms exit primarily when their net worth is negative. Comparing
this experiment to the one in row (3) shows that over 3 percent of farms are forced out
by a strict default requirement. (Some of these farms also exit in the baseline case.) The
ability to renegotiate is less valuable when there are no dividend smoothing motives.
7.3
Overview
To sum up: our estimates and comparative statics exercises indicate that …nancial
factors play an important role in farm outcomes both at the intensive and extensive
margin. The collateral and liquidity constraints both hinder capital investment and reduce
output and assets.26 The ability to renegotiate debt allows productive farms to remain
operational despite temporary setbacks. On the other hand, liquidation costs impede
the exit of low productivity farms, by reducing the wealth they can carry into their new
occupation.
Our analysis also reveals that nonpecuniary bene…ts are a signi…cant motivating force.
They keep farms in operation, despite low and uncertain revenue ‡ows. Coupled with
the high discount factor, they encourage cautious …nancial behavior and discourage risk
taking. Nonpecuniary bene…ts reinforce the e¤ects of liquidation costs. When both mechanisms are in place, only a few highly unproductive farms choose to exit.
8
The E¤ects of Uninsured Risk
As discussed in Sections 5 and 6, our estimates suggest that our entrepreneurs are
very risk averse, with a coe¢ cient of relative risk aversion ( ) of about 3.3. This parameter is identi…ed by the low observed dividend growth rates, as higher values of
make entrepreneurs less willing to substitute dividends across time. Table 7 shows that
risk neutrality would lead farmers to choose negative dividends at the beginning of the
estimation period, resulting in counterfactually high dividend growth.
Section 2 showed that farmers face signi…cant uninsured risk, which can be decomposed into an aggregate and an idiosyncratic component. Aggregate risk in turn, is
closely related to ‡uctuations in milk prices. This suggests a potentially useful role for
government programs that insure farmers against milk price ‡uctuations, as envisaged by
26
Similar borrowing constraints have been shown to play an important role in …nancial crises in Latin
America and East Asia (see for example Pratap and Urrutia, 2012; or Mendoza, 2010).
33
various dairy support programs. Before considering the speci…c provisions of the latest
program, as formulated in the 2014 Farm Bill, we …rst examine the e¤ects of aggregate
and idiosyncratic risk in general.
8.1
Full Insurance
Comparing row (15) of Table 7 to the baseline model in row (1) shows the e¤ects of
shutting down aggregate risk, keeping mean productivity constant. Such a change can be
viewed as the introduction of complete insurance against aggregate shocks. Farms expand
operations by increasing debt, and using it to …nance purchases both …xed and variable
inputs. The average capital stock increases by about 1.7 percent. The use of intermediate
goods increases as well, and the intermediate goods to capital ratio increases from 35 to
36 percent. These increases are modest, as the farms are still subject to idiosyncratic
shocks and operators are risk averse.
Like the aggregate shock, the idiosyncratic shock is also i.i.d and has a similar standard
deviation (6.9 percent compared to 6 percent for the aggregate shock). The e¤ects of
shutting down the idiosyncratic shock are therefore very similar to the results shown in
row (15). Row (16) shows that the e¤ects of eliminating all transitory shocks (aggregate
and idiosyncratic) are larger, but qualitatively similar. The average operation increases
its capital stock by 4 percent, and its debt by almost 8 percent.
It is worth noting that the elimination of transitory risk, aggregate or idiosyncratic,
has little e¤ect on the extensive margin. The fraction of farms operating is virtually
unchanged, as is their time-invariant productivity level, as measured by the optimal capital
stock. In fact, risk increases the number of operating farms, by allowing a few lowproductivity farms to “get lucky”with high idiosyncratic shocks.
Rows (15) and (16) suggest that risk discourages investment, as reducing risk leads
to higher capital. In addition to preferences, …nancial incentives induce farms to behave
this way. Although our model includes limited liability and occupational choice, most
low-productivity farms enter our sample with low levels of indebtedness and (relative to
the productivity …xed e¤ect i ) high capital stocks (see Figures 2 and 3). In such circumstances the risk-taking incentives described by Vereshchagina and Hopenhayn (2009) are
less likely to apply. Vereshchagina and Hopenhayn also argue that patient …rms are less
likely to seek risky investment projects; our estimated discount rate is 0.4 percent. Our
data do not reject Vereshchagina and Hopenhayn’s proposed mechanisms, but they reveal
an environment where the mechanisms are unlikely to arise. Moreover, while risk discourages investment and production, the reductions are modest. As the previous section
34
12
14
16
24
19
Milk M argins
8
10
Milk Price
4
6
14
r
2014
a
2012
e
2010
Y
2008
2006
2004
2002
2000
2014
r
2012
a
2010
e
2008
2006
2004
2002
2
9
2000
Y
Figure 6: Milk Prices and Margins
shows, collateral and liquidity constraints have larger e¤ects.
8.2
The Farm Bill of 2014
The dairy provisions of the Farm Bill of 2014 replaced a largely defunct dairy price
support program. Although the former program guaranteed a statutory price for milk,
either through direct purchase or through the purchase of other dairy products,27 the support price of $9.90 per hundred pounds (cwt.) of milk was widely considered inadequate.
As the left panel of Figure 6 shows, by 2000 the national average milk price, to which
the support price was indexed, was always substantially higher than $9.90 per cwt., while
still volatile.
This situation, coupled with an increase in feed costs, provided the impetus for a policy
change towards margin support, rather than price support. The milk margin is de…ned
as the di¤erence between the price of milk and the weighted average of the prices of corn,
soybean and alfalfa. The program o¤ers a baseline margin support of $4.00 per cwt. for
all participants, and higher support levels in exchange for a premium. The right panel of
Figure 6 shows nominal milk margins, as calculated by Schnepf (2014), between January
2000 and September 2014. Margin supports in the range of $4 to $8 would have kicked
in several times in our sample period.
The close correlation between milk prices and the aggregate TFP shock, along with
the assumption of constant input prices, imply that within our framework the aggregate
TFP shock acts as a margin shock. We therefore model margin ‡oors by eliminating the
left-hand tail of the aggregate shock distribution. As Schnepf (2014) notes, the premium
structure encourages farmers to choose a margin support level of $6.50 per cwt. This
27
Our description of the dairy provisions of the 2014 Farm Bill and its predecessors borrows heavily
from the discussion in Schnepf (2014).
35
Capital
1,321
1,336
1,244
Debt
867
882
796
Debt/
Assets
0.468
0.469
0.449
Cash/
Assets
0.122
0.122
0.118
Investment/
Capital (%)
10.66
10.75
11.16
(1) Baseline Model
(2) Margin Support, No Premium
(3) Margin Support, Full Premium
No Idiosyncratic Risk
(4) No Margin Support
1,351
902
0.476
0.125
11.18
(5) Margin Support, No Premium
1,362
914
0.481
0.124
11.10
(6) Margin Support, Full Premium
1,276
835
0.466
0.121
10.50
Shock process revised to accommodate Farm Bill experiments. See Appendix C.
Optimal
Capital
1,803
1,803
1,614
1,803
1,803
1,614
Table 8: E¤ects of the 2014 Farm Bill
translates into truncating the aggregate shock distribution at the 9th percentile. Appendix C provides more details on the margin support program, the calculation of the
truncation level, and the computational mechanics of truncating the distribution.
Table 8, shows the e¤ects of a margin support program of $6.50. The …rst row of
the table shows the no-farm bill benchmark.28 The second row shows the e¤ect of a $6.50
margin support that is provided to farmers for free. The e¤ects of the margin support
are modest. The capital stock increases by about 1 percent and debt by 1.7 percent.
The extensive margin – the number of farms operating, not reported in the table – is
unchanged. Recalling row (15) of Table 7 shows that the e¤ects of the margin support,
which eliminates the worst downside risk, are similar to those of completely eliminating
aggregate TFP risk. If anything, the margin support has smaller e¤ects.
Row (3) of Table 8 shows the e¤ects of coupling the margin support with the legislated
premium (for large volumes) of $0.29 per cwt. Even though this premium equals only
about 1.6 percent of the average milk price, it signi…cantly reduces the scale of operations.
Under our speci…cation, returns to scale per operator are given by 1
, with estimated
to be around 0.14 (see Table 5). This means that in the absence of frictions, the optimal
scale of operations is quite sensitive to productivity, so that even a small fee can generate
a signi…cant contraction. The …nal column of Table 8 shows that the margin support
premium reduces the optimal capital stock by more than 10 percent. The actual capital
stock falls by about 6 percent, however, as most farms are below their e¢ cient size. The
28
Assessing the Farm Bill requires that we use a discretized shock process with many more grid points
than in the baseline speci…cation used to estimate the model. See Appendix C. Using a …ner shock grid
signi…cantly increases computation time. However, the simulations generated by this case di¤er little
from those of the baseline speci…cation.
36
premium for a $6.50 margin support that would, in combination with the margin supports,
leave the average capital stock unchanged from the baseline level of $1.321 million turns
out to be around $0.05 per cwt.
In short, we …nd the negative e¤ects of the margin support premium on production
outweigh the small positive e¤ects of the support itself. This does not mean that farmers
would not purchase margin support at this price, as they are risk averse, but only that the
premium/support combination discourages production. It is also possible that our model,
which is calibrated to an annual frequency, understates the e¤ects of the margin support
program, which operates at a two-month frequency. Schnepf (2014) shows that milk
margins change signi…cantly from month to month. Moreover, the cash holdings observed
in the DFBS, recorded at the beginnings and ends of calendar years, may understate
farms’actual liquidity needs, which tend to be highest in the summer.29 The combination
of seasonal cash shortages and monthly margin ‡uctuations may enhance the impact of
margin support.
Another potential reason for the small e¤ects of the (free) margin support program
could be the presence of idiosyncratic risk, which, as we have seen earlier, is as large as
aggregate risk. To consider this possibility we eliminate idiosyncratic risk and then repeat
the margin support experiments. The results are shown in rows (4)-(6), and indicate that
idiosyncratic risk does not signi…cantly a¤ect the impact of the margin support program.
9
Conclusions
In this paper we assess the importance of …nancial constraints, nonpecuniary bene…ts
and attitudes to risk in determining entrepreneurial behavior. We build a life-cycle model
that incorporates all these considerations and estimate it with a rich panel of owneroperated dairy farms in New York State. Using a simulated minimum distance estimator,
we …t the model to real variables such as input use, capital and revenues, and to …nancial
variables such as debt, dividends and cash holdings. Matching both production and
…nancial variables allows us to identify the parameters of the model and to disentangle
the e¤ects of real and …nancial factors. It also allows us to assess the nonpecuniary
bene…ts of entrepreneurship, and the propensity of entrepreneurs to take risks.
Our results indicate that …nancial constraints a¤ect farm behavior on both the extensive and the intensive margins. Collateral constraints on investment and liquidity
constraints on the purchase of intermediate goods reduce the scale of operations by re29
Conversation with Wayne Knoblauch, April 20, 2015.
37
stricting capital holdings, input purchases and output. The ability of farms to renegotiate
debt allows productive farms to remain in business despite temporary setbacks.
We …nd that the nonpecuniary bene…ts of farming are considerable and an important reason why many low productivity farms remain operational. Liquidation costs also
discourage exit. Our estimates also reveal that farmers are risk averse. Taken together,
these features discourage risk taking of the sort envisaged by Vereschagina and Hopenhayn
(2009). More generally, …nancial constraints and non-…nancial considerations interact in
important ways.
In addition to being risk averse, farmers face signi…cant uninsured risk. Using our
model to infer TFP, we …nd that movements in aggregate farm productivity closely mirror
the volatile movements in the price of milk. Nonetheless, eliminating aggregate risk has
very modest e¤ects on farm decisions, with very small increases in the capital stock of
the average farm. The insurance provided by the milk margin support program of the
2014 Farm Bill also has similar modest e¤ects. On the other hand, the premium for this
margin support program has a signi…cant contractionary e¤ect on investment and capital.
Broadly speaking, our results show that nonpecuniary bene…ts and …nancial constraints have signi…cant e¤ects on entrepreneurial decisions. We do not …nd evidence
of risk-taking behavior. This is not to suggest that such behavior does not exist in general. But in our data the nonpecuniary bene…ts from operating a business signi…cantly
outweigh the incentives to take risk, despite limited liability and the ability to exit into
secure wage work.
Many of our …ndings follow directly from our data. The data show that some farms
remain in operation in spite of low and uncertain income ‡ows. This indicates that
nonpecuniary bene…ts, or a mechanism that acts similarly, must be present. The data
also reveal that times of high productivity and cash ‡ow are times of high investment
even though productivity shocks are serially uncorrelated. High productivity operations
have ‡at dividend streams but expand their capital rapidly. These features indicate
the presence of borrowing constraints. A productive area of future research would be
to apply our framework, modi…ed accordingly, to other datasets, to see if they support
similar conclusions.
38
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43
For Online Publication: Appendices
A
Data Construction
Sample Selection: The table below describes the …lters used to construct the sample.
The outlier farms eliminated were those whose time-averaged herd size was in the top
and bottom 2.5th percentile respectively. Since we are interested in the dynamic
behavior of the enerprises, we also eliminate farms with only one observation. Finally,
we drop farms with missing information on the age of the youngest operator.
# of Farms # of Observations
Original Sample
Trim top and bottom 2.5%
Drop farms with one observation
Drop farms with missing age
541
508
357
338
2461
2261
2110
2037
Owned Capital: The sum of the beginning of period market value of the three
categories of capital stock owned by a farm: real estate and land, machinery and
equipment and livestock.
Depreciation and Appreciation Rates: The depreciation rate
capital stock j is calculated as
j
j
for each type of
P
1
i Depreciationjit
= P
T i Market Value of Owned Capitaljit
where i indexes farms and T = 11 (2001-2011).
Analogously, the appreciation rate $j for each type of capital stock j is given by
P
1
i Appreciationjit
$j = P
T i Market Value of Owned Capitaljit
The actual depreciation rate is the weighted average of each j ;the weights being the
average share of each type of capital stock in owned capital. The appreciation rate $ is
calculated similarly.
44
Leased Capital: The market value of leased capital (M V LK) of type j for farm i at
time t is calculated as
M V LKjit =
Leasing Expendituresjit
r + j $j +
where r is the risk free rate of 4 percent and is the average in‡ation rate through the
period. The market value of all leased capital is the sum of the market value of all types
of leased capital.
Total Capital : Owned Capital + Leased Capital
Investment: Sum of net investment and depreciation expenditures in real estate,
livestock and machinery.
Total Output: Value of all farm receipts.
Total Expenditure: Expenses on hired labor, feed, lease and repair of machinery and
real estate, expenditures on livestock, crop expenditures, insurance, utilities and interest.
Variable Inputs: Total expenditures less expenditures on interest payments and
leasing expenditures on machinery and real estate
Total Assets: Beginning of period values of the current assets (cash in bank accounts
and accounts receivable), intermediate assets (livestock and machinery) and long term
assets (real estate and land).
Total Liabilities: Beginning of period values of current liabilities (accounts payable
and operating debt), intermediate and long term liabilities.
Dividends: Net income (total receipts-total expenditures) less retained earnings and
equity injections.
Cash: Total assets less owned capital.
45
B
Econometric Methodology
We estimate the parameter vector = ( , , c0 , , c1 , , , , n0 , , , ) using a
version of Simulated Minimum Distance. To construct our estimation targets, we sort
farms along two dimensions, operator age and size (cows per operator). Along each
dimension, we divide the sample in half. Then for each of these four age-size cells, for
each of the years 2001 to 2011, we match:
1. The median value of capital per operator, k.
2. The median value of the output-to-capital ratio, y=k.
3. The median value of the variable input-to-capital ratio, n=k.
4. The median value of the gross investment-to-capital ratio.
5. The median value of the debt-to-asset ratio, b=~
a
6. The median value of the cash-to-asset ratio, `=~
a.
7. The median value of the dividend growth rate, dt =dt 1 .
Let gmt , m 2 f1; 2; :::; M g, t 2 f1; 2; :::; T g, denote a summary statistic of type m in
calendar year t, such as median capital for young, large farms in 2007, calculated from
the DFBS. The model-predicted value of gmt is gmt ( ). We estimate the model by
minimizing the squared proportional di¤erences between fgmt ( )g from fgmt g. Because
the model gives farmers the option to become workers, we also need to match some
measure of occupational choice. We thus record the fraction of farms that exit in our
simulations but not in the data, and the fraction to calculate a penalty, I ( ), that is
added to the SMD criterion.
Our SMD criterion function is
QI ( ) =
M X
T
X
m=1 t=1
@2m
gmt ( )
gmt
2
1
+
I(
);
(12)
where ( ) is a penalty imposed when farms exit in the simulations, but not in the
DFBS. The weights f@m g are normalized to 1, with one exception. We set the weight
on dividend growth rates to 2. The dividend growth rate measures the willingness of
farmers to fund investment internally by withholding dividends. If the dividend
smoothing motive is strong, equity funding will be driven by cash ‡ow rather than
46
variations in dividends. Given the paper’s focus on the links between …nancial
conditions and investment, we place a high priority on matching the dividend smoothing
motive, and have thus placed additional weight on deviations in dividend growth rates.
Our estimate of the “true”parameter vector 0 is the value of that minimizes the
criterion function QI ( ). Let I denote this estimate. Our approach for calculating the
variance-covariance matrix of 0 follows standard arguments for extremum estimators.
Suppose that
p @QI ( 0 )
p
N (0; );
IDI ( 0 )
I
@
so that the gradient of QI ( ) is asymptotically normal in the number of cross-sectional
observations. With this and other assumptions, Newey and McFadden (1994, Theorem
3.1) show that
p
I( I
N (0; H 1 H 1 );
(13)
0)
where
@QI ( 0 )
:
@ @ 0
We estimate H as HI , the numerical derivative of QI ( ) evaluated at I .
Unfortunately, there is no analytical expression for for the limiting variance . We
instead …nd via a bootstrap procedure. In particular, we create S arti…cial samples of
size I, each sample consisting of I bootstrap draws from the DFBS. Each draw contains
the entire history of the selected farm. In this respect, we follow Kapetanios (2008),
who argues that this is a good way to capture temporal dependence in panel data
bootstraps. Our bootstrap procedure does not account for aggregate shocks, and thus
our standard errors abstract from aggregate variation. For each bootstrapped sample
s = 1; 2; : : : ; S, we generate the arti…cial criterion function Qs ( I ), in the same way we
constructed Qs ( I ) using the DFBS data. The function Qs ( I ) is then run through a
numerical gradient procedure to …nd Ds ( I ). The estimated parameter vector I is
used for every s, but the simulations used to construct Qs ( ) employ di¤erent random
numbers, to incorporate simulation error.30 Finding the variance of Ds ( I ) across the S
subsamples yields S , an estimate of =I (not ).
An alternative interpretation of our approach is to treat it as an approximation to the
“complete”bootstrap, where is re-estimated for each arti…cial sample s.31 Let GI
H = plim
30
Because gmt () is found via simulation rather than analytically, the variance
must account for
simulation error. In most cases the adjustment involves a multiplicate adjustment (Pakes and Pollard,
1989; Du¢ e and Singleton, 1993; Gouriéroux and Monfort, 1996). Because each iteration of our bootstrap
employs new random numbers, no such adjustment is needed here.
31
We are grateful to Lars Hansen for this suggestion.
47
denote the vector containing all the summary statistics used in QI ( ). The …rst-order
condition for minimizing QI ( ) implies that
DI (
I)
= D(
I ; GI )
= 0;
Implicit di¤erentiation yields
@ I
@GI
HI
1 @D(
I ; GI )
@GI
:
Because the mapping from GI to I –the minimization of QI ( ) –is too
time-consuming to replicate S times, we replace it with its linear approximation:
V(
C
I)
@ I
@ I
@D( I ; GI )
@D( I ; GI )
V (GI ) 0 = HI 1
V (GI )
HI
@GI
@GI
@GI
@G0I
HI 1 S HI 1 :
1
Modelling the 2014 Farm Bill
The 2014 Farm Bill program replaces the previous dairy support program, which
guaranteed a minimum price for milk, with a guarantee of the milk margin, the
di¤erence between the price of milk and a weighted average of the prices of corn,
soybean and alfalfa. As described by Schnepf (2014), the program provides a baseline
margin support of $4.00 per cwt. for all participants. Higher support levels (in $0.50
increments) can be acquired in exchange for a premium. For the …rst 4 million lbs of
output, the premium ranges from $0.01 per cwt. for a margin of $4.50 to $0.475 for a
$8.00 margin. For additional output the premium ranges from $0.02 to $1.36 per cwt.
As discussed in the main text, we model margin ‡oors by eliminating the left-hand tail
of the aggregate shock distribution. Schnepf (2014) notes that the premium structure
encourages farmers to choose a margin support level of $6.50 per cwt. In the
implementation of the margin support program, the milk margin is computed and
compared to the margin ‡oor every two months. At this frequency, during our sample
period of 2001 to 2011 nominal milk margins fell beneath $6.50 about 13.6 percent of
the time. Real milk margins, measured in September 2014 dollars, fell beneath the ‡oor
about 7.6 percent of the time. At the annual frequency used in our model, both
nominal and real milk margins fell below the $6.50 ‡oor once, in 2009, a rate of 1/11 =
9.09 percent. We choose this annual …gure as our truncation level.
48
Following standard practice, when solving the model numerically we replace the
continuous processes for the TFP shocks with discrete approximations. We use the
approach developed by Tauchen (1986) for discretizing Markov chains, simpli…ed here to
i.i.d. processes. Under Tauchen’s approach one divides the support of the underlying
continuous process into a …nite set of intervals. The values for the discrete
approximation come from the interiors of the intervals (demarcated by the midpoints,
except at the upper and lower tails), and the transition probabilities are based on the
conditional probabilities of each interval. To impose the cuto¤, we construct the
discretization for the aggregate shock so the bottom two states/intervals have a
combined probability of 9.09 percent. We then set the truncated value for these states
to equal the 9.09th percentile of the underlying continous distribution.
When …nding the decision rules, we combine the aggregate and idiosyncratic shocks into
a single transitory shock. In the baseline speci…cation, which we use when estimating
the model, we approximate the sum of the two shock processes with a 8-state
discretization. To model the elimination of certain shocks, we simply change the
standard deviation of this combined process. However, to capture the Farm bill, we
need to alter the distribution of the aggregate shock in isolation. We thus model the
aggregate shock with its own 8-state discretization. To get the joint shock, we
approximate the idiosyncratic shock with a 4-state distribution, and convolute the
aggregate and idiosyncratic shocks into a 32-state distribution. We construct the
4-state discretization so that the standard deviation of the convoluted 32-state process is
the same as the standard deviation of the 8-state shock used in the baseline model.
Switching between the two discrete approximations a¤ects the model’s results only
modestly (compare the …rst lines of Tables 7 and 8). Under either approximation, the
shocks used in the simulations are a combination of idiosyncratic shocks from a random
number generator and the aggregate shocks estimated from data. To simulate the Farm
Bill, we simply truncate the aggregate shock for 2009 to the 9.09th percentile.
For large volumes, the premium for a margin support of $6.50 is $0.290 per cwt. This
equals about 1.58 percent of the average real milk price over the 2001-11 interval
($18.34). We impose the premium by incrementing the logged TFP process by
ln(0:9842), that is, by reducing the TFP level by 1.58 percent.
49