land values, almon lag, farm profitability, Agribusiness, Agricultural Finance, Farm Management, Financial Economics, Production Economics,

Dahl, Cody P.

Gunderson, Michael A.

Moss, Charles B.

English

Research Papers in Economics

Using Land Values to Predict Future Farm Income 
Cody P. Dahl 
Ph.D. Student 
Department of Food and Resource Economics 
University of Florida 
Gainesville, FL 32611 
 
Michael A. Gunderson 
Assistant Professor 
Department of Food and Resource Economics 
University of Florida 
Gainesville, FL 32611 
 
Charles B. Moss 
Professor 
Department of Food and Resource Economics 
University of Florida 
Gainesville, FL 32611 
 
 
 
 
 
Selected Paper prepared for presentation at the Southern Agricultural Economics Association 
Annual Meeting, Orlando, FL, February 6-9, 2010  
 
Copyright © 2010 by Dahl, Gunderson, Moss. All rights reserved. Readers may make verbatim 
copies of this document for non-commercial purposes by any means, provided this copyright 
notice appears on all such copies Background 
The value of an asset should be equal to the discounted future cash flows generated by 
that asset. Research in agricultural finance has attempted to explain agricultural land prices based 
on the simultaneous movement of land prices and another measure of cash flow (usually land 
rents or income per acre including crop sales, other revenues and government payments). Some 
increasingly sophisticated models have attempted to integrate spatial correlation to account for 
the possibility of future development of agricultural lands.  
Featherstone and Baker identified land price bubbles in their model. In the paper the 
model defines real asset values based on lagged returns and previous asset values (1987). That is 
they are using previous cash flows to explain today’s asset value. This formulation is directly 
counter to the efficient market hypothesis.  
Indeed, accounting research has shown that Price-to-Earnings (P/E) ratios can predict 
future earnings as reported in GAAP based accounting statements. This model reflects that some 
information regarding companies’ operating performance becomes public and is incorporated 
into stock prices months before the officially audited financial statements required by the SEC. 
Thus, the model uses current P/E ratios to explain future cash flows.  
Objectives 
The goal of this paper is to understand the relationship between current land prices and 
future returns to agricultural assets. With the understanding that purchasers of agricultural land 
are best suited to determining the expected returns, this analysis should identify the extent to 
which purchasers are correct in their expectations. In addition, it might help to uncover some of 
the inconsistencies between land values and the discounted cash flows that have existed in the 
literature.  It is expected that the price of land will be a good predictor of future returns to 
agricultural land. This assumes that buyers of agricultural land are building their future 
expectations into prices paid rather than simply using historical returns as a guide for pricing. 
There might be some limitations to the estimates as the model is based on annual data. The 
accounting research uses quarterly or monthly data on stock returns for their models, which may 
provide more robust results.  
Literature Review 
The accounting literature has provided evidence that a firm’s stock price tends to lead 
accounting earnings (Ou and Penman). The consensus suggests that information embedded in the 
stock price has already realized much of the information reported in quarterly accounting 
statement. Operating performance is revealed as it occurs to market participants with information 
regarding the firm. The information is accordingly built into the price of the stock, even in the 
absence of audited financial statements. Market participants may revise the stock price if the 
audited statements reveal inconsistencies in the performance. Evidence exists that market 
participants are knowledge of operating performance before audited statements are released, as 
participants often release guidance reports before the date of release.  
 
Data and Methods 
Following Schmitz (1995), the economic relationship we seek to model is 
 
in which in which   represents the expected return on farmland in period t given 
information at the beginning of period t,  signifies the observed 
change in logarithmic farmland values, and rt is the discount rate for the farm sector in period t. We model the influence of farmland values on expected returns using an ordinary least 
squares estimator (OLS), a restricted least squares estimator (RLS), and a restricted generalized 
method of moment (RGMM) estimator. 
Letting  and , the OLS estimator is a finite 
distributed lag model in which expected returns are a function of the current change in farmland 
values and three prior changes in farmland values, or  .   
The statistical model with n=3 lags becomes 
 
where  is the change in the value of land at time t,  is the change in the value of land at 
time t-1, etc.,  T-n vector of ones,   denotes the intercept, and  are the distributed lag weights. 
It is likely that decision makers consider only a finite number of previous changes in land 
values when formulating their expectations of returns to farmland.  Following the method 
developed by Almon (1965), we approximate the true lag structure by a second order 
polynomial.  Our RLS is thus a finite polynomial distributed lag model where we restrict the 
estimated coefficients to lie along a second degree polynomial:  
.  
If we let 
 , where , and , and s denotes explanatory 
parameters, then we estimate first estimate 
  ,  and recover the restricted least squares estimates using   . 
The estimated error variance  is obtained using   
and .  Finally, 
 . 
The OLS and RLS estimators are biased and inefficient if any explanatory variable 
correlates to the model’s error term.  To circumvent distributional assumptions, we employ the 
use of GMM and instrumental variables to recoup the population moments.   
For our GMM estimator we set   to eliminate the influence of lags beyond three 
periods,  
 . 
 
This also reduces the number of estimated parameters by one since  
 
.  
 
Having made this substitution, the estimated RGMM model is  
  
  
For convenience, it is necessary to change notation for the RGMM estimator.  Let  
  
  
  
where   
  
The first order conditions require   
The RGMM estimator 
  
where Z is a T x q matrix of instruments containing   
Based on distribution theory, Hall (Year) demonstrates the asymptotic variance of the 
GMM estimator can be obtained by 
,  
which converges in distribution to 
  
 
Results 
An initial and brief interpretation of the results from the RGMM estimator suggests that if 
the value of agricultural land increases by a percent for three consecutive years, and is expected 
to increase a percent during the current year, expected return will increase by approximately .26 
percent (≈ .013 + .095 + .066 + .048 + .04).  The OLS and RLS models would expect to see a 
.25% increase in returns under the same scenario.  
Discussion  
This is an alternative way to look at agricultural land prices, given that traditionally 
agricultural finance researchers have used current or previous earnings to explain current 
agricultural land values. This paper uses current agricultural prices to explain future earnings. 
The results will be meaningful for agricultural policy which may aim to reduce the volatility of 
agricultural asset prices. 
 
 
 
 
 
 
 
 
Parameters OLS RLS RGMM
Intercept -0.00302 -0.00304 0.01274 ***
(0.00367) (0.02621) (0.00417)
Xt 0.08634 *** 0.08334 *** 0.09458 ***
(0.02565) (0.02621) (0.01266)
Xt-1 0.05872 ** 0.06683 *** 0.06615 ***
(0.02752) (0.02370) (0.01511)
Xt-2 0.06236 ** 0.05438 ** 0.04769 ***
(0.02760) (0.02399) (0.01499)
Xt-3 0.04257 0.04599 * 0.03921 ***
(0.02709) (0.02757) (0.01146)
Numbers in parentheses are standard errors
*** Indicates statistical significance at the α = .01
** Indicates statistical significance at the α = .05
* Indicates statistical significance at the α = .10Citations 
Almon S. 1965. “The Distributed Lag Between Capital Appropriations and Expenditures,” 
Econometrica, Jan., pp. 178-96. 
Featherstone A. and T.G. Baker. 1987. “An Examination of Farm Sector Real Asset Dynamics: 
1910-85,” American Journal of Agricultural Economics, 69(3)(Aug., 1987), pp. 532-546 
Hall, A.R. 2005. Generalized Method of Moments, Oxford University Press, Oxford. 
Ou, J. and Penman, S. 1989. “Accounting Measurement, Price–Earnings Ratios, and the 
Information Content of Security Prices,” Journal of Accounting Research 27:111–52. 
Schmitz, A. 1995. “Boom-Bust Cycles and Ricardian Rents,” American Journal of Agricultural 
Economics 77(5):1110-25. 

Using Land Values to Predict Future Farm Income

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