Replaced with revised version of poster 08/03/10.Farm size, farm performance, SEM models, Agricultural Finance, Farm Management,

Hadrich, Joleen C.

Olson, Frayne E.

English

Research Papers in Economics

 
 
 
 
 
 
 
Confirmatory Factor Analysis of Farm Size and Performance 
 
 
Joleen C. Hadrich and Frayne Olson 
 
Department of Agribusiness & Applied Economics 
North Dakota State University 
Fargo, ND 58103 
Email:  Joleen.Hadrich@ndsu.edu / Frayne.Olson@ndsu.edu 
Phone: 701-231-5721 / 701-231-7377 
 
 
 
 
 
Poster prepared for presentation at the Agricultural & Applied Economics Association 2010 
AAEA, CAES, & WAEA Joint Annual Meeting, Denver, Colorado, July 25-27, 2010 
 
 
 
 
 
 
 
 
 
Copyright 2010 by Joleen C. Hadrich and Frayne Olson.  All rights reserved.  Readers may 
make verbatim copies of this document for non-commercial purposes by any means, provided 
that this copyright notice appears on all such copies. Confirmatory Factor Analysis of Farm Size and Performance
Joleen C. Hadrich and Frayne Olson, Department of Agribusiness & Applied Economics, North Dakota State University, Fargo, ND  58103
joleen.hadrich@ndsu.edu, frayne.olson@ndsu.edu
Introduction
• 2007 Census of Agriculture reported that 8% of the principal  farm 
operations surveyed were under the age of 35.  It is estimated that by 
2012, 51% of the principal farm operators will be over the age of 65.  
• What does this mean for production agriculture?
*New and beginning farmers will be managing one  or more of 
the farms exiting the industry.  This may  lead to increased 
farm size, but may also play a role  in farm performance.  
•How do we measure farm size and performance? 
*Agricultural Economics literature uses farm size to define the 
farm life cycle as the following, but does not specify the 
measures to define “farm size”: 
•Rather than using one indicator to define “farm size” a combination 
of size indicators may be more appropriate and provide a more 
accurate estimation of the farm business life cycle.  Secondly, “farm 
performance” may also provide a source for defining the farm business 
life cycle.
• Understanding the indicators defining “farm size” and “farm 
performance” and the relationship between them will lay the 
foundation for estimating and further analyzing the farm business life 
cycle. 
Research Objective
• Determine the set of underlying indicators that define “farm size” 
and “farm performance”
Methods
• Confirmatory Factor Analysis (CFA)
•What is CFA?
 Type of SEM estimation
 Researcher defines the relationship between indicator 
variables based upon theoretical justification and tests  how 
well the relationships assumed in the model reproduces the 
observed relationships in the data.
 Estimates factor loadings (statistical estimates of direct 
effects) to determine the explanatory power of individual 
indicator variables for the latent variable.  
Factor Loadings
Independent 
Latent Variable #2
ξ2
Independent 
Latent Variable #1
ξ1
x2 x4 x3 x1 x5
δ1
x6 x9 x7 x8
δ2 δ3 δ4 δ5 δ6 δ7 δ8 δ9
λ1 λ2
λ3 λ4 λ5 λ6 λ7 λ8 λ9
θ1
ξ1 = Farm Size ξ2 = Farm Performance
X1= Acres X5= Operating Expense Ratio
X2 = Gross Sales X6 = Current Ratio
X3= Pounds of Output produced  X7 = Rate of Return on Assets (ROA)
X4 = Total Farm Assets X8 = Debt-to-Equity Ratio
X9 = Gross Sales/Labor hours
X1…. X4  = Size Indicator Variable                     X6…. X9 = Performance Indicator Variables
λ1…. λ4  = Size Factor Loadings                           λ6…. λ9= Performance Factor Loadings
δ1…. δ4 = Error Terms                                           δ6…. δ9  = Error Terms
θ1  = Correlation term between farm size and performance
Path Diagram for Farm Size and Performance Confirmatory Factor Analysis
Data/Summary Statistics
Results
• A set of statistically significant indicators define farm size and 
performance, rather than just one indicator.  The set of indicators 
provide a more complete measure of size and performance.
•Estimated factor loadings for farm size and performance are similar 
from 2008 to 2009 even though returns varied greatly between the 
two years.  Therefore, indicators are measuring multiple dimensions 
of the latent variables consistently.  
• Gross Sales and Farm Assets are the strongest indicators of farm 
size.  Acres is statistically significant, but the weakest indicator for 
farm size.  This is surprising since acres are typically the “standard” 
for measuring farm size.
•Gross sales/labor hour is the strongest indicator of farm 
performance emphasizing the importance of labor efficiency.  Asset 
management as measured by the ROA is the second strongest 
indicator of farm performance.
•As hypothesized, there is a negative relationship between farm 
performance and the operating expense ratio and debt-to-equity 
ratio.  
•Correlation between farm size and farm performance is positive 
and significant.  This indicates that both factors must be considered 
jointly in order to appropriately estimate the farm business life 
cycle.
Kay, Edwards, and Duffy.  Farm Management, 2008).
Further Considerations
• Results from CFA will be used to 
estimate the farm business life 
cycle over time.  
•Up to 15 years of consecutive data 
is available for ND farms.
 Provide estimation of farm business life cycle over time 
considering the correlation between farm size and 
performance.
 Evaluate how farm business life cycle differs by livestock 
enterprises grown, farm tenure, and location.
www.ndtourism.com
www.ndtourism.com
www.ndtourism.com
• 2008 & 2009 Farm Financial and demographic data collected,  532 North Dakota Farms, 270 Crop Farms, 262 Crop & Livestock Farms
2008 2009
Size Indicator Symbol Average Std. Dev. Average  Std. Dev.
Acres X1  2,589 2,167 2,522 2,143
Gross Sales X2  607.623 581,739 559,739 544,680
Pounds Output produced X3 4,647,770 5,873,148 4,808,542 5,532,919
Farm Assets X4 1,305,773 1,248,256 1,545,789 1,508,008
Performance Indicators
Operating Expense Ratio X5 0.89 0.40 0.92 0.35
Current Ratio X6 3.75 7.58 4.12 15.02
ROA X7 13.22 15.81 6.32 11.09
Debt-equity ratio X8 1.26 1.89 1.39 2.15
Gross Sales/Labor Hours X9 206.48 132.18 107.29 68.33
Graphical Summary
2008 2009
Size Indicators
Factor 
Loadings
P-value Factor 
Loadings
P-value
Acres 0.57 0.0000 0.59 0.0000
Gross Sales 0.99 0.0000 0.98 0.0000
Pounds of Output produced 0.79 0.0000 0.80 0.0000
Farm Assets 0.86 0.0000 0.86 0.0000
Performance Indicators
Operating Expense Ratio -0.35 0.0000 -0.38 0.0000
Current Ratio 0.16 0.0016 0.11 0.0173
ROA 0.41 0.0000 0.27 0.0000
Debt-equity ratio -0.24 0.0000 -0.21 0.0000
Gross Sales/Labor Hours 0.82 0.0000 0.94 0.0000
θ1  (Correlation term) 0.64 0.0000 0.73 0.0000
Goodness of Fit Statistic Fit Statistic Fit
RMSEA 0.1226 Moderate 0.1348 Moderate
NFI 0.8807 Good 0.8688 Good
CFI 0.8915 Good 0.8786 Good
TLI 0.8122 Moderate 0.7899 Moderate
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•The graphical summary depicts the relationship between selected indicators of farm size and farm 
performance for the 2008 and 2009 data sets.  The relationships are similar but the magnitudes differ 
between 2008 and 2009.  This suggests that these selected indicators are closely related, but not 
substitutes for each other.

Confirmatory Factor Analysis of Farm Size and Performance

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