Is Farm Real Estate The Next Bubble?

Is Farm Real Estate The Next Bubble?

Brett C. Olsen & Jeffrey R. Stokes

# Springer Science+Business Media New York 2014

Abstract The recent increase in farmland prices leads many to conjecture that a pricebubble exists. A dataset of Iowa farmland prices for three grades of quality over the last60 years is examined to address the question whether the conditions for a rationalexpectations bubble are evident. An abnormal component in the change in farmlandprices is found during the most recent sub-period of the sample. A novel valuationmodel that measures the speculative component of farmland value as a function of cashrents shows no speculative component is present. An additional test of the time seriescharacteristics of the data provides no evidence of negative duration dependence.However, analysis of transition probabilities shows asymmetry exists most notably inthe low quality farmland data series. Finally, time irreversibility is shown to be presentat different lags for only the lowest farmland quality grade. Overall, the results implythat the low quality grade farmland is the most likely candidate to exhibit the conditionsnecessary to support a rational expectations bubble. In general, however, the data offerweak support of a bubble in farmland prices.

Keywords Farmland . Bubbles . Valuation . Abnormal returns

Introduction

The sharp increase in farmland prices over the last few years has led many to believethere may be a bubble forming in farmland markets. This belief naturally leads to theprediction that the bubble will burst. Indeed, the recent price increase, in nominal terms,is distinctively more pronounced than the price increase that occurred in the 1970s,which was then followed by the farmland crash in the early to mid-80s. While a cursorylook at farmland prices may support the presence of a farmland price bubble, thedeterminants of farmland value have also dramatically changed over the past fewdecades. As shown in Fig. 1, while farmland prices have increased (Panel A), produc-tivity has nearly doubled (Panel B), and crop prices have risen sharply as well (Panel C).The coincident recent rise in farmland prices and corn prices is difficult to ignore.

J Real Estate Finan EconDOI 10.1007/s11146-014-9469-9

B. C. Olsen (*) : J. R. StokesDepartment of Finance, University of Northern Iowa, Cedar Falls, IA 50614-0124, USAe-mail: [email protected]

A

B

C

Fig. 1 The average farmland price per acre (Panel A), corn yield per acre (Panel B), and corn price per bushel(Panel C) for Iowa farmland from 1950 through 2012

B.C. Olsen, J.R. Stokes

Increased world demand for grain and domestic demand for corn in ethanol productionare two key contributors to the recent increase in corn prices, as argued by (Stokes andCox 2014), who identify low interest rates as another contributor. These drivers offarmland prices likely constitute a significant portion of the farmland’s fundamentalvalue. Perhaps the rise in farmland values is related to an increase in the returns on thefarmland’s fundamental value and not speculation at all. While identifying a bubble orthe timing of its end is challenging at best, understanding the increase in returns and thepotential for a valuation bubble and its bursting is extremely important for existing andprospective buyers and sellers, including farmers and investors.

This study examines rational expectations bubbles as studied by (Shiller 1978) and(Blanchard and Watson 1982) and further examined by (McQueen and Thorley 1994).Within rational expectations bubbles, asset prices may deviate from the asset’s funda-mental value. The bubble component of the fundamental value relation grows in eachperiod that it survives. As the bubble component gets larger, it dominates the funda-mental component, reducing the likelihood of a negative innovation. Investors realizethat prices are overvalued, but they believe that prices will continue to increase. Theprobability of a high return compensates for the probability of a crash. Thus, investorswill remain in overvalued markets. Rational expectations bubbles imply a nonlinearpattern in prices. Previous studies examine nonlinear price patterns within the stockmarket ((Shiller 1981); West 1987), the gold market (Blanchard and Watson 1982), andthe forex market (Evans 1986).

Speculative bubbles within the farmland market are also the topic of interest forresearchers, especially during periods of sharply increasing prices as seen in the 1970sand 2000s (see Fig. 1). The farmland market is a good candidate for bubbles due tosignificant transaction costs (Chavas and Thomas 1999) and overreaction to changes inmarket fundamentals ((Featherstone and Baker 1987); (Lloyd 1994); (Schmitz andMoss 1996)). (Clark et al. 1993) consider the pattern in farmland values, testing thenecessary condition that the time-series properties of farmland values and cash rentshave equal time series representations. Their results do not support this condition, andthey recommend that models that allow for complexities such as rational bubbles beused in future studies. One of the likely reasons for their conclusion is that whilefarmland prices can be observed and potentially change every time farmland is sold,cash rents tend to be negotiated at infrequent intervals and are sluggish to adjust tochanging economic conditions. For example, a farmland owner and tenant mightnegotiate a 3-year lease contract indicating that cash rent will remain fixed over the3-year period. In addition, tenants tend to have an informational advantage about theproductivity of the farmland that they can exploit. Given these features of the landowner-tenant relationship, it is not surprising that cash rents and farmland values do nothave the same time series representation.

(Tegene and Kuchler 1993) investigate the existence of bubbles in farmland prices inthree Midwest regions using stationarity and cointegration tests. The authors find nosupport for the presence of a speculative bubble in farmland prices or cash rents for theperiod 1921–1989. (Power and Turvey 2010) find that farmland values have deviatedfrom fundamental values during the last few years of their 1949–2006 samples. Theyuse wavelet-based statistical methods and tests on long memory estimation to show thatprice volatility increased and that a short-term bubble exists over the final 10 years oftheir sample period. (Lavin and Zorn 2001) produce mixed results after employing


different tests to determine if a rational expectations bubble exists in Iowa andNebraska farmland prices from 1910 through 1995. Examining agricultural commodityprices rather than farmland prices, (Liu et al. 2013) find evidence of prices deviatingfrom fundamental values, but the authors do not find the traits of speculative bubbles infive of the six commodities they test.

This paper contributes to the real estate literature and to contemporary analysis ofasset bubbles. The study extends the knowledge of farmland pricing and returns byincluding varying qualities of farmland in an updated dataset and directing focus to theabnormal returns provided by farmland ownership rather than prices alone. Thecontribution of production advances and crop prices as drivers of abnormal returnsfrom farmland are also considered.

Following a description of the dataset, this study considers the rational expectationsbubble and its conditions. Next, the change in the value of Iowa farmland across thesample period and during various sub-periods provides an initial step towards under-standing the determinants driving any abnormal component of the change in value. Amodel is then developed that examines the fundamental and speculative component infarmland value. Finally, several tests scrutinize the pattern of the farmland returns,looking for evidence of the characteristics required for a rational expectations bubble inIowa farmland returns.

Data

The analysis that follows uses annual average Iowa farmland prices from 1950through 2012 available from Iowa State University Extension and Outreach.Farmland price data is obtained through annual surveys of real estate brokersand other experts. Survey respondents provide an estimate of the value offarmland based on the three grades of quality – high, medium, and low.Farmland quality is measured using the Corn Suitability Rating (CSR), anindex that rates the soil based on its productivity in yielding row-crops. Theaverage CSR for a tract of farmland may vary based on soil type, the slope ofthe farmland, and erosion susceptibility. Figure 2 illustrates the variation innominal farmland prices based on production quality. The prices correspondingto the three quality grades of high, medium, and low exhibit little variationduring the first 20 years of the sample. In the 1970s, the prices noticeablydisperse, rising sharply until reaching a peak in 1981, followed by a drop to alow point 5 years later. Prices quickly turn upward from the low in 1986,climbing higher and faster through 2012 when high quality farmland reached$10,181 per acre. The sharp rise in prices since the farmland crisis in the 1980sis feeding the recent interest in research by academics and in speculation bymedia outlets regarding the presence of a farmland price bubble.

Risk-free rates are from the St. Louis Federal Reserve, while annual average cornyields (bushels/acre), corn prices (dollars/bushel), and cash rents are obtained from theUnited States Department of Agriculture National Agricultural Statistics Service(USDA-NASS). Cash rent data, reflecting the average dollar payment per acre forirrigated cropland, is obtained through the annual Cash Rents Survey conducted by theUSDA. Unfortunately, the cash rent data includes only average cash rents unrelated to


farmland quality. The arithmetic average is greater than the USDA-NASS averagesuggesting that Iowa farmland quality is skewed toward the high grade.

To disaggregate the average cash rent data and provide better estimates of the cashrents for each quality grade, an entropy model is employed to estimate the cash rents forthe three farmland quality grades based on the dispersion of farmland prices amongthese grades. The Entropy Concentration Theorem (Jaynes 1957, 1979) states that outof all of the distributions that satisfy the observed data (i.e., the moments); a signifi-cantly large proportion of these distributions will be concentrated sufficiently close tothe one with maximum entropy. The entropy analysis is discussed in more detail in theAppendix and uses the average farmland price for each year of the sample. Applyingthe entropy method to the cash rent data produces the series depicted in Fig. 3. Sincethe cash rents are loosely based on the farmland price data, the pattern over time is quitesimilar to the farmland price series.

Determinants of Farmland Price Changes

The rise in farmland prices in the 1970s eventually ended in the early part of thefollowing decade as interest rates doubled and debt tied to farmland became increas-ingly difficult to service. While the recent increase in Iowa farmland prices is effec-tively illustrated in Fig. 1 Panel A as a distinctively larger increase than the run-upexperienced in the 1970s, consideration of the possible similarities of the two time

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

High land quality

Medium land quality

Low land quality

Fig. 2 Nominal farmland prices for Iowa farmland from 1950 through 2012 for the three quality grades offarmland: high, medium, and low quality


periods should be made to determine if another correction in farmland values isimminent. An OLS regression that controls for several determinants of the change infarmland prices is used to better understand how the recent increase in farmland pricescompares to historical trends. The basic model is:

ΔPt ¼ at þ btXt þ εt ð1ÞThe dependent variable, ΔPt, is the change in average value of Iowa farmland, and

Xt represents a vector of determinants that may influence the value change. Thedeterminants used include the changes in corn yields and prices, the change in theaverage cash rents, and the change in the risk-free rate, which should be highlycorrelated to the borrowing costs available to potential farmland buyers.

Table 1 provides the regression results. Across the entire period, the changes in cornprice and average cash rents are significantly related (positive) to the change infarmland price. Using sub-period regressions where the period is split into overlapping20-year sub-periods, a significant intercept in (1) occurs in the latter periods of thesample and corresponds closely with the increase in farmland prices seen since the1990s. These results imply that farmland produced abnormal positive increases inprices only during the most recent portion of the sample period after controlling forkey determinants. The change in average price per acre during the 1990 to 2009 sub-period is driven by the changes in corn prices, average rents, and the risk-free rate. Theperiods that include the 1970s show that the change in average cash rents has a strongpositive relation to the change in farmland price, but the farmland price change does nothave an abnormal component (the intercepts are negative and not significant). Whileone cannot conclude from these results that a bubble currently exists in Iowa farmland,the findings do show that farmland prices are increasing at a higher rate than expected.

$0

$50

$100

$150

$200

$250

$300

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

High qualityMedium qualityLow quality

Fig. 3 Nominal cash rents per acre, developed using an entropy model, for Iowa farmland from 1950 through2012 for the three quality grades of farmland: high, medium, and low quality


The Speculative Component of Farmland Returns

While the OLS analysis above indicates that there may be an abnormal component thatdrives farmland price changes in recent years, a more rigorous examination of the issueis necessary. Several researchers have shown that the price of an asset includes afundamental component and a rational expectations component (e.g., (Shiller 1978);(Blanchard and Watson 1982)).1 The price of an asset can deviate from its fundamentalvalue by a rational expectations component, or bubble. With the equilibrium conditionthat the value of an asset is equal to the expected future cash flows discounted at therequired rate of return r, the bubble component must grow every period at the rate r.Examining farmland, a very simple valuation model is used to consider the presence ofa speculative component, i.e., a bubble, in the price of the farmland.

Let Ct=C(t) be time t cash rent per acre where Ct evolves according to a geometricBrownian motion: dCt=μCtdt+σCtdzt. Here, μ is the expected rate of growth in cashrent, σ is the volatility in cash rent, and dzt~N(0,dt) is the increment of a ℙ -Brownianmotion. The value of farmland per acre, Vt=V(Ct), can be found by equating theexpected capital gain on the farmland plus the flow of cash rent with an equilibriumreturn on the farmland. 2 Mathematically, E dV tð Þ þ Ctdt ¼ ρV tdt; where ρ is theequilibrium rate of return. Rearranging terms results in the following second-orderordinary differential equation:

σ2C2t

2

� �V

0 0t þ μCtV

0t þ Ct ¼ ρV t

Table 1 OLS regressions of change in farmland value

Full sampleperiod

1950 to1969

1960 to1979

1970 to1989

1980 to1999

1990 to2009

2000 to2012

Intercept 0.013 0.006 −0.010 −0.006 −0.004 0.044 *** 0.076 **

Corn yield 0.018 0.073 0.314 * −0.065 −0.068 0.036 −0.044Corn price 0.190 *** 0.108 0.231 * 0.041 0.141 0.126 ** 0.220 *

Average rents 0.811 *** 0.515 1.086 *** 1.019 ** 0.632 0.824 *** 0.462

Risk-free rate 0.002 −0.026 −0.049 0.112 0.149 0.035 *** 0.019

Adj R2 0.429 0.032 0.462 0.383 0.214 0.671 0.539

This table provides the OLS regression results wherein the dependent variable is the change in the averageprice per acre of Iowa farmland. Corn yield is the change in the yield of corn, in bushels per acre; Corn price isthe change in the per bushel price of corn; Average rents is the change in cash rent received per acre; and Risk-free rate is the change in the rate of return on the 10-year Treasury. The change in each variable from period t-1to period t is calculated as ln(Xt/Xt−1).

*** (** * ) indicates significance at the 1 % (5 % 10 %) level

1 (Camerer 1989) provides a thorough review of asset bubbles and provides a more explicit definition of therational speculative bubble model.2 While it is theoretically possible to develop the appropriate hedging arguments to cast the pricing modelpresented here in the context of risk-neutral pricing, the approach used here opts for a simpler pricing modelthat does not depend on such assumptions.


The general solution to this equation is

V Ctð Þ ¼ K1Cβ1t þ K2C

β2t þ K3Ct

where K1, K2, K3, β1>1, and β2<0 are all constants and

β1;2 ¼− μ−

σ2

2

� ��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ− σ2

2

� �2 þ 2ρσ2

qσ2

As Ct→0, it should be the case that Vt→0, which will happen if and only if K2=0since β2<0. Using similar reasoning, as Ct→∞, a bounded solution representingfundamental value will happen if and only if K1=0 since β1>0.

However, (Dixit and Pindyck 1994) have shown that capital gain speculation canresult for some Ct≫0 in equilibrium. If capital gain speculation is present, an investorcould buy farmland at a price above fundamental value in anticipation of a large capitalgain. This would result in a farmland valuation model where

V Ctð Þ ¼ K1Cβ1t þ K3Ct ð2Þ

With the interpretation that the first term is a speculative component of farmlandvalue while the second term is the fundamental value taken as a perpetuity. Theparameter K3 in this case can be shown to equal (ρ−μ)−1. It follows that byregressing observed farmland values on observed cash rents, the significance of K1

can be empirically tested under the null hypothesis that K1=0 and there is nocomponent of farmland value attributable to speculation.

A nonlinear least squares approach estimates the parameters from the value relation(2), and the results are presented in Table 2. As shown, the parameter K1 is notstatistically significant for any farmland quality although the parameters β1 and K3

are highly significant at the 1 % level. The Wald, F, and Likelihood Ratio (LR) teststatistics also confirm that there is no statistical evidence of a speculative component in

Iowa farmland prices. Capitalization rates (i.e., ρ−μ ¼ bK−13 ) are also shown from OLS

Table 2 Nonlinear Least Squares and Ordinary Least Squares parameter estimates for low, medium, and highquality Iowa farmland

Nonlinear Least Squares Test statistics Ordinary Least Squares

Farmland Quality K1 β1 K3 Wald F LR K3 Cap rate

Low 0.000240 3.25476 *** 6.9318 *** 0.19466 136.4 107.1 15.6292 *** 6.398 %

Medium 0.000016 3.73286 *** 11.8710 *** 0.13256 135.7 106.8 19.6264 *** 5.095 %

High 0.000017 3.59539 *** 14.1488 *** 0.10677 108.0 95.4 22.0974 *** 4.453 %

This table provides (1) the parameter estimates from the farmland value relation V Ctð Þ ¼ K1Cβ1t þ K3Ct

using nonlinear least squares; (2) the Wald, F, and Likelihood Ratio (LR) test statistics; and (3) the estimatedcapitalization rates (Cap Rate) from the relation V(Ct)=K3Ct, where ρ−μ ¼ bK−1

3 . *** indicates significance atthe 1 % level


regressions with the restriction that K1=0 in (2), and the results are consistent withhigher (lower) quality farmland having a lower (higher) cap rate.

It is important to note that while these results are inconsistent with speculation infarmland, they cannot be unencumbered from the pricing model itself. That is, thestatistical tests are a joint test of the efficacy of the structural model and the hypothesisin question. This means that rejecting speculation may just be a rejection of thestructural model. The results of efforts to this point to determine the potential for aspeculative bubble in the Iowa farmland market are insufficient. Therefore, additionaltests are proposed to eliminate the potential influence of the structural model. In whatfollows, as shown in (2), the fundamental value of farmland is assumed to be perpe-tuity, namely,

V Ctð Þ ¼ K3Ct ¼ Ct

ρ−μð3Þ

implying that the perpetuity grows exponentially at rate μ and is discounted atequilibrium rate ρ. Also, it follows directly that

dV Ctð Þ ¼ dCt

ρ−μ¼ μV tdt þ σV tdzt

As shown, when cash rents follow geometric Brownian motion, the fundamental valueof farmland also follows geometric Brownian motion. The implication here is thatfarmland values are assumed to be lognormally distributed, and the time series offarmland values is necessarily nonstationary.

As noted above, hedging arguments may make it possible to unencumber thefundamental value from the unobservable parameter ρ. However, the selected approachhere estimates ρ from observable data by noting that it is akin to a weighted averagecost of capital. Most farmland is financed with a mixture of debt and equity capital.More specifically, farmland purchases typically require about one-third of the purchaseprice as down payment so that ρ=(1/3)Re+(2/3)i, where Re (i) represents the cost ofequity (debt) capital. Stock market returns are assumed to represent the opportunity costof investing equity capital in farmland, and the cost of debt capital is assumed toapproximate 10-year Treasury bond yields plus a premium. The premium is estimatedto be 1.73 % using Farm Credit System data on interest rates charged for loanscollateralized by farm real estate.

Patterns in the Time Series Data

Additional tests that are not influenced by the structural models studied above aredeployed to evaluate the patterns in the time series data. These tests examine differenttraits of the time series to determine if the conditions for a rational expectations bubbleare present. Previous studies focus on the capital gains earned on farmland. Thisperspective ignores the income received from owning, i.e., cash rents, which representa significant component of the total return. The OLS regressions performed above thatfound cash rents are a significant determinant of changes in farmland prices supportsthe total return perspective of farmland ownership. The data series is further refined by


calculating the excess abnormal returns from farmland, defined as the returns providedby the capital gain and income yield over the change in the fundamental value of thefarmland minus the return on a risk-free asset. More formally, excess abnormal returns,RtA, in period t are defined as:

RAt ¼ ln

Pt

Pt−1

� �þ Ct

Pt

� �−ln

V t

V t−1

� �−Rf ;t ð4Þ

where ln(Pt/Pt−1) is the nominal capital gains yield based on the change in farmlandprice from period t−1 to t; (Ct/Pt) represents the income yield, measured as the currentcash rent divided by the farmland price; ln(Vt/Vt−1) represents the discrete change infundamental value, found using (3) above; and Rf,t is the risk-free rate in period t, whichis obtained from CRSP.3 It is important to note that previous studies such as (Lavin andZorn 2001) examine only the capital gains yield (the first term in (4)), while this studyfocuses on the excess abnormal returns.

Runs

Within the rational expectations bubble structure, the probability of a negative returnconditional on a series of prior positive returns decreases with the length of the run. Inother words, the longer the bubble continues over time, the less likely that a crash willoccur. This phenomenon is called negative duration dependence. Alternatively, positiveduration dependence contends that the probability of a run ending increases with thelength of the run (Kiefer 1988). (McQueen and Thorley 1994) examine the durationdependence of stock price patterns, stating that the duration dependence pattern test isunique to bubbles. Bubbles can induce positive autocorrelation, skewness, and kurtosis,but these parameters are also associated with the fundamental component of prices.(Lavin and Zorn 2001) find evidence of positive duration dependence with their Midwestfarmland price data, a result inconsistent with the presence of a rational expectationsbubble. Examining 28 different commodities, (Went et al. 2009) test the durationdependence and find eleven that exhibit the traits of rational expectations bubbles.

The duration dependence method used here applies the methods of (McQueen andThorley 1994) and (Lavin and Zorn 2001) to the three quality grades of farmland inIowa, testing for negative duration dependence using a hazard-function specification,which measures the probability of an unexpected return decrease given a sequence ofprior return increases. From the annual abnormal return data, a series of positive andnegative run lengths is constructed. The resulting dataset is a set (St) of J observationsof random run length T. The hazard rate, ht, represents the probability that a run ends atperiod t given that the run lasts until t, or [ht≡Pr(T=t|T≥t)]. For rational expectationsbubbles, ht+1<ht for all T, which implies that as a positive run increases in length, theprobability of the run ending in the next period decreases?

To estimate the hazard rate, the Weibull model, a commonly used parametricrepresentation of the hazard, is used. The Weibull model is given as

ht ¼ λp λtð Þp −1 ð5Þ

3 Obtained fromKen French’s website at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.


http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

where λ and p are parameters to be estimated. The parameter p takes on particularimportance in that its magnitude determines the type of duration exhibited by the data.For p>1 (p=1) positive (constant) duration dependence results, while p<1 is indicativeof negative duration dependence. Also, when p=1, the Weibull model reduces to theexponential model, another frequently used parametric (constant) duration model.

As shown in Table 3, low quality farmland exhibits the longest runs of positiveabnormal returns (median=3.82 years). Also shown in the table and consistent with pastresearch on farmland price changes, the parameter p from the Weibull model in (5) isstatistically significantly greater than one for all farmland qualities, providing evidence ofpositive duration dependence. The results in Table 3 clearly show that negative durationdependence, a characteristic of rational expectations bubbles, is not present in the data.

Transition Probabilities

If farmland returns follow a random walk, the probability of an increase in returns willnot depend on the previous year’s return. To evaluate the null hypothesis that excess

Table 3 Run frequencies and tests of duration dependence

Land Quality

Run Length Low Medium High

1 9 11 13

2 8 8 9

3 5 6 6

4 5 4 2

5 4 4 2

6 4 3 2

7 3 2 2

8 2 2 1

9 2 1 1

10 2 1 1

11 1 – –

12 1 – –

Median run length (years) 3.82 3.09 2.60

Weibull parameters and standard errors:

λ 0.2049 0.2546 0.2944

σλ 0.0213 0.0276 0.0397

p 1.4906 1.5041 1.3762

σp 0.2400 0.2601 0.2673

H0:p=1 2.0442 ** 1.9379 ** 1.4071 *

H0:p≤0 6.2105 *** 5.7825 *** 5.1475 ***

This table provides run frequencies for positive excess abnormal returns across the three farmland qualitygrades. The estimated Weibull model is: ht=λp(λt)

p−1 where ht is the hazard rate at time t, λ and p areparameters, and σλ and σp are standard errors for the parameter estimates. *** (** * ) indicates rejection of thenull hypothesis at the 1 % (5 % 10 %) level


abnormal returns follow a random walk, a Markov chain technique is used. TheMarkov chain approach requires that the abnormal return series is stationary but doesnot restrict the series to be normally distributed as do regression tests. For a randomwalk series, the transition probabilities from one period to the next will be statisticallyidentical, resulting in a symmetrical pattern. In a Markov chain setting, the transitionprobabilities may vary based on the sequence of prior returns, an advantage over othertime series tests.

(Lavin and Zorn 2001) find asymmetry in the transition probabilities from oneperiod to the next for capital gains. Their two-state Markov chain examining farmlandprices for Iowa and Nebraska show asymmetry for sequences of farmland price changesover 3 years. In other words, the probability of a price increase following two periods ofprice decreases differs from the probability of a price decrease after two price increases.A finite two-state Markov process {It}, based on previous work ((Neftçi 1984);(McQueen and Thorley 1991); (Lavin and Zorn 2001)), is used and is defined as:

I t ¼ 1 if RAt > 0

0 if RAt ≤ 0

�

where RtA represents the excess abnormal returns in period t. The derived series {It}

represents 1 for return increases, and 0 for non-positive return changes. If returns followa random walk, then the probability of a return increase or decrease does not depend onthe previous sequence of returns, providing the following transition probabilities for afirst-order Markov chain.

λ00 ¼ Pr I t ¼ 0��I t−2 ¼ 0; I t−1 ¼ 0

h iλ01 ¼ Pr I t ¼ 0

��I t−2 ¼ 0; I t−1 ¼ 1h i

λ10 ¼ Pr I t ¼ 0��I t−2 ¼ 1; I t−1 ¼ 0

h iλ11 ¼ Pr I t ¼ 0

��I t−2 ¼ 1; I t−1 ¼ 1h i

Of course, there is no particular reason to believe that abnormal returns follow a first-order Markov chain. (McQueen and Thorley 1991) use a second-order representation forannual stock returns, noting the consistency with previous studies ((Fama and French1988); (Poterba and Summers 1988)) and the results of identification tests (e.g.,Likelihood Ratio). (Lavin and Zorn 2001) assume that capital gains follow a second-order Markov chain based on the large proportion of one- and 2-year run lengths in theirsample of Iowa and Nebraska farmland prices. Examining the nature of the data series,this study estimates transition probabilities for the three farmland qualities for first-,second-, and third-order Markov chains using the Akaike Information Criterion (AIC)and LR tests to determine the appropriate order of the chain. In each case, the transitionprobabilities are chosen to maximize the log of the likelihood function as shown by(Neftçi 1984). The criterion statistics are presented in Table 4 Panel A. The AIC statisticssuggest that, in general, low quality farmland is best modeled as a first-order Markovchain. For medium quality farmland, the order of the Markov chain is most likely third-


order. For high quality farmland, the order of the Markov chain is most likely second-order, but the AIC for the first-order chain is only slightly larger.

Table 4 Panel B presents the results of more rigorous tests of the order of the Markovchains, including the LR test statistics under various hypothesis tests. These resultsshow that the first-order Markov chain cannot be rejected in favor of the second-orderor third-order Markov chain at any reasonable significance levels for low qualityfarmland. For medium quality farmland, the first-order chain is rejected in favor ofthe second-order (third-order) chain at the 10 % (5 %) level. At the 10 % level ofsignificance, the second-order Markov chain can be rejected in favor of the third-orderMarkov chain. For high quality farmland, the first-order chain cannot berejected in favor of the second-order, and the first-order Markov chain isrejected in favor of the third-order Markov chain, yet only at the 10 % levelof significance. Based on the results in both panels of Table 4, the followingMarkov chains are investigated: the first-order Markov chain for low qualityfarmland, the second- and third-order Markov for medium quality, and the first-and third-order for high quality.

Next, tests of symmetry and the random walk hypothesis are conducted for eachfarmland quality grade using the appropriate Markov chain order. Shown in Table 5 arethe estimated transition probability matrices for each farmland quality grade and corre-sponding Markov chain order. Symmetry implies that the probability that the abnormalreturn of farmland increases given a previous increase is the same as the probability that theabnormal return of farmland decreases given a previous decrease. Thus, in the case ofsymmetry, the diagonal elements of the transition probabilitymatrix would be identical. Forlow quality farmland and assuming a first-order Markov chain, as shown in Table 5, theprobability of a(n) decrease (increase) in excess abnormal returns following a(n) decrease(increase) is 42.18% (83.37%). A similar disparity in the transition probabilities is seen forhigh quality farmland if a first-order Markov chain (39.33 % vs. 68.86 %) is assumed.Using a third-order Markov chain, the disparity is much smaller and not statistically

Table 4 Markov chain order for abnormal returns

Panel A: Akaike Information Criterion

1st order 2nd order 3rd order

Low quality 66.52 67.49 67.93

Medium quality 77.22 74.87 73.50

High quality 82.98 82.66 83.73

Panel B: Likelihood Ratio tests

H0: 1st orderH1: 2nd order

H0: 1st orderH1: 3rd order

H0: 2nd orderH1: 3rd order

Low quality LR=3.0257 LR=10.5916 –

Medium quality LR=6.3477 * LR=15.7227 ** LR=9.3750 *

High quality LR=4.3231 LR=11.2502 * –

This table provides results of tests to determine the rank order of the Markov Chains for the abnormal returnsseries of Iowa farmland by farmland quality. Panel A presents the Akaike Information Criterion. Panel Bpresents the Likelihood Ratio (LR) test statistics. *** (** * ) indicates significance at the 1 % (5 % 10 %) level


significant. The transition probabilities for medium quality farmland, regardless of theMarkov chain order, are also not significantly different.

LR tests are performed, testing the null hypothesis that the transition prob-abilities are equal, and the results are reported in Table 6 Panel A. For low(high) quality farmland, the null is rejected at the 1 % (5 %) level ofsignificance, implying that the excess abnormal returns series appears to beasymmetric. For medium quality farmland, however, the null hypotheses thatthe transition probabilities are identical cannot be rejected, indicating symmetry.The results from the Markov chain analysis examining symmetry suggest thatthe conditions required for a rational expectations bubble are present for lowand high quality farmland, but not present for medium quality farmland.

In Table 6 Panel B LR statistics are presented for the test of the random walkhypothesis, which implies that all of the transition probabilities are equal. As shown,this hypothesis is rejected for all three levels of farmland quality at the 1 % significancelevel. A review of the transition probabilities in Table 5 support this finding. The resultsfrom the Markov chain analysis testing the random walk theory suggest that theconditions required for a rational expectations bubble are present for all three farmlandqualities, but the conditions are most prominent for the low and high farmland qualitygrades.

Time Reversibility

Another symmetry application is the “time reversible” nature of the data series.(Ramsey and Rothman 1996) introduce time reversibility as a unified frame-work for the alternative definitions of data series asymmetry. A data series is“time reversible” if the covariance relationship of the series is the same goingforward in time as it is going backward in time. If true, the data series issymmetrical and would not be conducive to the formation of bubbles. Withinthe Markov chain framework above, asymmetric transition probability matricesimply time irreversible processes. The analysis begins with the null hypothesisthat abnormal returns data series are time reversible. (Ramsey and Rothman1996) develop a time reversibility test and apply the test to several economicdata series. (Lavin and Zorn 2001) use the time reversibility method to examinethe patterns of farmland prices in Iowa and Nebraska, finding irreversibilitypatterns at different lags in the time series.

The equality of individual moments from the joint probability distribution ofthe data series, {Xt}, are tested, following the approach of (Ramsey andRothman 1996) and (Lavin and Zorn 2001). The symmetric-bicovariance func-tion, γ2,1, of a stationary data series {Xt} is defined as the difference betweentwo bicovariances, or γ2,1(k)=E[Xt

2Xt−k]−E[XtXt−k2 ] for all integer values of lag

k. The data series {Xt} is time reversible if γ2,1 = 0 for all lags k in ℕ, i.e., themoments are equal. Sample estimates of the bicovariances for the stationaryseries {Xt} with T observations are

bB2;1 ¼ 1

T−k

Xt¼kþ1

T

X 2t X t−k


Tab

le5

Transition

probability

estim

ates

1storder

2ndorder

3rdorder

Low

quality

p dd¼

0:4218

p di¼

0:5782

p id¼

0:1663

p ii¼

0:8337

––

Medium

quality

–

p ddd

¼0:6973

p ddi¼

0:3027

p did¼

0:1751

p dii¼

0:8249

p idd

¼0:1857

p idi¼

0:8143

p iid¼

0:2485

p iii¼

0:7515

2 6 43 7 5

p dddd¼

0:6000

p dddi¼

0:4000

p ddid¼

0:0000

p ddii¼

1:0000

p didd¼

0:5000

p didi¼

0:5000

p diid

¼0:2222

p diii¼

0:7778

p iddd¼

1:0000

p iddi¼

0:0000

p idid¼

0:1250

p idii¼

0:8750

p iidd¼

0:1250

p iidi¼

0:8750

p iiid

¼0:2609

p iiii¼

0:7391

2 6 6 6 6 6 6 6 6 6 4

3 7 7 7 7 7 7 7 7 7 5

Highquality

p dd¼

0:3933

p di¼

0:6067

p id¼

0:3114

p ii¼

0:6886

–

p dddd¼

0:6000

p dddi¼

0:4000

p ddid¼

0:0000

p ddii¼

1:0000

p didd¼

0:3333

p didi¼

0:6667

p diid

¼0:3000

p diii¼

0:7000

p iddd¼

0:6667

p iddi¼

0:3333

p idid¼

0:2222

p idii¼

0:7778

p iidd¼

0:2222

p iidi¼

0:7778

p iiid

¼0:3529

p iiii¼

0:6471

2 6 6 6 6 6 6 6 6 6 4

3 7 7 7 7 7 7 7 7 7 5

Thistableprovides

transitio

nprobability

estim

ates

foreach

farm

land

quality

gradeapplying

theappropriateorderMarkovchains

identifiedin

Table4.

Subscriptsianddreferto

anincrease

ordecrease

inexcess

abnorm

alreturns


bB1;2 ¼ 1

T−k

Xt¼kþ1

T

X tX2t−k

The test statistic, bγ2;1 kð Þ , which is the difference between the sample bicovarianceestimates, is estimated as

bγ2;1 kð Þ ¼ bB2;1 kð Þ−bB1;2 kð Þ ð6Þ

for various integer values of k.To estimate the test statistic in (6), a time series model is fit to each data series. While

prior studies fit ARMA models to their data ((Ramsey and Rothman 1996), e.g.), thepossibility of heteroscedastic error variances should be considered. (Engle 1982, 1983),among others, show that variances may cluster, requiring a different approach to analyzingtime series data. (Serrano and Hoesli 2010) focus on the heteroscedastic nature of securi-tized real estate returns relative to stock prices. As prices change rapidly, the variance of theprices is most likely not constant. To capture the effects of this excess volatility, eachfarmland quality data series is tested for ARCH effects using the white-noise test for thesquared time series. The null hypothesis is that the population autocorrelation functions forthe squared time series are equal to zero. Examining the p-value for the Ljung-Boxmodified statistic within the Chi-square distribution, both the high and medium qualityfarmland data series are found to exhibit ARCH effects, while the low quality farmlanddata series does not. An EGARCH framework from (Nelson 1991) is applied torecognize the potential for an asymmetric property of the volatilities. An EGARC

Table 6 Markov chain tests for excess abnormal returns

Panel A: Tests of symmetry and transition probabilities

1st orderH0: pdd=piiH1: pdd≠pii

2nd orderH0: pddd=piiiH1: pddd≠piii

3rd orderH0: pdddd=piiiiH1: pdddd≠piiii

Low quality LR=9.0708 *** – –

Medium quality – LR=0.0914 LR=0.3706

High quality LR=4.9761 ** – LR=0.0366

Panel B: Tests of the random walk assumption

1st orderH0: all pjk=pkjH1: not all pjk=pkj

2nd orderH0: all pjkl=plkjH1: not all pjkl=plkj

3rd orderH0: all pjklm=pmlkj

H1: not all pjklm=pmlkj

Low quality LR=23.4306 *** – –

Medium quality – LR=19.0789 *** LR=24.2950***

High quality LR=6.9706 *** – LR=14.062***

This table provides tests of symmetry and transition probabilities (Panel A) and tests of the random walkassumption (Panel B). Subscripts i and d refer to an increase or decrease in excess abnormal returns. Subscriptsj, k, l, andmmay represent an increase or decrease in excess abnormal returns. *** (** * ) indicates significanceat the 1 % (5 % 10 %) level and rejection of the null


H(2,1) provides the best model structure for both the high and medium quality farmlandseries.4 An ARMA(1,1) provides the best fit to the low quality farmland series.

Armed with the time series models for the data, a Monte Carlo simulation isperformed, and the sample bicovariance estimates from (6) are calculated. Next, a plotis constructed comparing the sample bicovariance, bγ2;1 kð Þ , which is calculated directlyfrom each data series, to the boundary conditions of +/− two standard deviations of thesample bicovariance determined by the Monte Carlo simulations (N=10,000 iterations).The comparison is illustrated in Fig. 4. The high and medium farmland quality dataseries are clearly time reversible time series as the +/− two standard error boundaries arenot breached. These two farmland qualities, then, are time reversible to order 3 anddegree 20.5 However, the low quality farmland plot shows that the test statistic exceedsthe boundaries at lags k=2, 3, 4, and 5. Only the abnormal returns series from lowquality farmland exhibits evidence of time irreversibility, or asymmetry. The standard-

ized time reversibility statistic, bγ2;1 kð Þ=Var bγ2;1 kð Þ� �1=2(Ramsey and Rothman 1996),

provided in Table 7, corroborates the Fig. 4 illustrations. Applying an EGARCH(2,1) tothe low quality farmland data series provides very similar results.

Conclusions

Farmland prices in recent years have risen sharply, inviting speculation of the presenceof a bubble in the farmland market. While there have been many studies of the behaviorof farmland prices, most concentrate on the capital gains associated with farmland inthe 1970s, a period of well documented farmland price increases. Using an updatedsample (1950–2012) of Iowa farmland prices and cash rents segregated by farmlandquality, several empirical tests are deployed using farmland capital gains and excessabnormal returns to determine whether the more recent increases in farmland value areconsistent with the formation of a bubble in rural Iowa farmland markets.

From OLS regressions, after controlling for crop prices, crop yields, cash rents to theowners, and interest rates, a significant intercept is produced only during the mostrecent portion of the data sample. Despite the abnormal change in farmland prices (theintercepts) in recent years, no statistically significant evidence is found to support aspeculative component in the value of Iowa farmland. This finding, however, cannot beunencumbered from the specified structural model. Therefore, additional empirical testsare necessary to examine patterns in the excess abnormal returns data for the conditionsthat support the existence of a rational expectations bubble. Negative duration depen-dence, a characteristic of rational expectations bubbles, is not evident for the excessabnormal returns series of any of the three farmland quality grades. Markov chainanalysis finds that the pattern of excess abnormal returns is asymmetric for low andhigh quality farmland, although the high quality farmland results are not persistentacross higher order Markov chains. The null hypothesis that excess abnormal returnsfollow a random walk is rejected for all farmland quality grades. Lastly, only the lowquality farmland data series exhibits time irreversibility patterns at different lag points.

4 Details for the models for all three farmland quality data series are available from the authors.5 Describing the time reversibility results, the order refers to i+j for γi,j, and the degree refers to the maximumlag, which is 20.


A

B

-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0 5 10 15 20

Lag

High quality land

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0 5 10 15 20

Lag

Medium quality land

C

-0.002

-0.001

-0.001

0.000

0.001

0.001

0 5 10 15 20

Lag

Low quality land


The key finding of this study is that in general, Iowa farmland markets, despite thestrong increases in farmland prices in recent years, is likely not consistent with theformation of a farmland market bubble. At best, if a bubble has formed or is forming, itis more likely to be in the market for low quality Iowa farmland and not the higherquality grades. This could occur because of the much greater values being placed on thehigher quality grades. More participants are able to bid on the lowest farmland quality,increasing the likelihood of the rational expectations bubble, while fewer playersbidding on the higher quality grades lowers the bubble probability.

One potential weakness of this study, indeed a weakness of potentially all farmlandvalue studies, is the aggregate nature of the data. Increasing the frequency of the returns

�Fig. 4 The results of testing the null hypothesis that the excess abnormal return data series are time reversible.The solid line represents the sample bicovariance estimate, γ2; 1k , for lags k=1–20. The dotted lines identifythe upper and lower boundaries at +/− two standard deviations of the bicovariance estimate calculated fromMonte Carlo simulations. Points above the upper boundary or below the lower boundary indicate lags at whichthe data series is time irreversible

Table 7 Time reversibility test statistics

High quality farmland Medium quality farmland Low quality land

k

1 −0.0158 −0.0430 −0.76202 −0.1634 −0.2852 −2.9420 ***

3 −0.3780 −0.6428 −4.1240 ***

4 −0.2379 −0.3590 −1.9581 *

5 −0.3491 −0.6243 −2.8628 ***

6 −0.0757 −0.1310 −1.38047 0.1429 0.1160 −0.91238 0.1556 0.1610 −0.32549 0.4974 0.7290 0.7533

10 0.0827 −0.1337 −1.171511 0.0794 0.1118 0.0004

12 −0.0363 −0.1234 −0.632813 −0.2204 −0.4008 −1.334914 −0.1610 −0.2275 −0.864315 −0.1055 −0.1373 −0.449316 −0.0866 −0.1223 −0.291917 −0.0505 −0.1041 −0.136118 −0.3506 −0.5074 −1.232619 −0.6328 −0.8934 −1.383720 −0.6405 −0.7820 −1.4247

This table provides the results from testing whether the three data series are time reversible to order 3 anddegree 20. The test statistic, bγ2;1 kð Þ=Var bγ2;1 kð Þ� �1=2

is generated from the Gaussian innovations from thetime series models. The numerator is the sample bicovariance estimate calculated directly from the time series.The denominator is the standard deviation of the sample bicovariance estimates calculated using Monte Carlosimulations. k represents the lag. *** (** * ) indicates significance at the 1 % (5 % 10 %) level and rejection ofthe null that the time series is reversible


data would add statistical power to the tests examining the patterns. A second potentialweakness is the source of the farmland value data, the surveys of real estate brokers andother related experts. Requesting an assessment of farmland values only once eachcalendar year may introduce a familiarity bias, for example, related to chronology (theease of recallingmore recent information). Although elusive, high frequency, transactions-level farmland price data would allow for a more comprehensive farmland value analysis.

Acknowledgments The authors wish to thank C.F. Sirmans (editor) and the reviewer for their helpfulcomments, as well as seminar participants at the University of Northern Iowa.

Appendix

Since only annual average cash rent is reported, an entropy-based model, based on(Golan 2006), is used to determine likely cash rents for low, medium, and high qualityfarmland using the most likely distribution of farmland by quality. Most of Iowafarmland is medium to high quality and, as a result, the simple average of farmlandvalues is not the same as the reported average value. Therefore, the following optimi-zation model is specified to recover the most likely proportion of farmland of eachquality grade that would constitute the reported average. More clearly, the followingframework is solved for each t:

max E sð Þ ¼Xi

sit ln sitð Þs.t.

Xi

sitPit ¼ P̄t;

Xi

sit ¼ 1;

sit ≥0

Where i is an index of farmland quality, and sit is the time t proportion or share oftotal Iowa farmland that is categorized by quality i. E(s) is the entropy of the distribu-tion of the unobserved proportions. The first constraint is a moment matching equationwherein the weighted average farmland value is forced to equal the reported average,Pt. The second constraint ensures that the proportions sum to one, while the third set ofconstraints ensures the proportions are non-negative. If the reported average appearingin the right-hand side of the first constraint is the simple average, the entropy would bemaximized with a uniform distribution of proportions equal to one-third each.

Once the proportions are uncovered, they are applied to the reported average cashrent per acre. However, it is typically the case that cash rent for high (medium) qualityfarmland is about 20 % higher than cash rent for medium (low) quality farmland.Applying this simple rule allows for the development of cash rent data for eachfarmland quality that is consistent with the distribution of farmland prices by quality.One drawback of this construction is the fact that μ, the rate of growth in cash rents,


will not vary by farmland quality even though it likely does in reality. However, theobvious advantage is that reported farmland values by quality can be fully utilized toconstruct excess abnormal returns.

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