120 Week 6 F /For WIZARD KIM

Is Farm Real Estate The Next Bubble?

Brett C. Olsen & Jeffrey R. Stokes

Published online: 28 May 2014 # Springer Science+Business Media New York 2014

Abstract The recent increase in farmland prices leads many to conjecture that a price bubble exists. A dataset of Iowa farmland prices for three grades of quality over the last 60 years is examined to address the question whether the conditions for a rational expectations bubble are evident. An abnormal component in the change in farmland prices is found during the most recent sub-period of the sample. A novel valuation model that measures the speculative component of farmland value as a function of cash rents shows no speculative component is present. An additional test of the time series characteristics of the data provides no evidence of negative duration dependence. However, analysis of transition probabilities shows asymmetry exists most notably in the low quality farmland data series. Finally, time irreversibility is shown to be present at different lags for only the lowest farmland quality grade. Overall, the results imply that the low quality grade farmland is the most likely candidate to exhibit the conditions necessary to support a rational expectations bubble. In general, however, the data offer weak 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 believe there may be a bubble forming in farmland markets. This belief naturally leads to the prediction 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 cursory look at farmland prices may support the presence of a farmland price bubble, the determinants of farmland value have also dramatically changed over the past few decades. 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 Econ (2015) 50:355–376 DOI 10.1007/s11146-014-9469-9

B. C. Olsen (*): J. R. Stokes Department of Finance, University of Northern Iowa, Cedar Falls, IA 50614-0124, USA e-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

356 B.C. Olsen, J.R. Stokes

Increased world demand for grain and domestic demand for corn in ethanol production are two key contributors to the recent increase in corn prices, as argued by (Stokes and Cox 2014), who identify low interest rates as another contributor. These drivers of farmland prices likely constitute a significant portion of the farmland’s fundamental value. Perhaps the rise in farmland values is related to an increase in the returns on the farmland’s fundamental value and not speculation at all. While identifying a bubble or the timing of its end is challenging at best, understanding the increase in returns and the potential for a valuation bubble and its bursting is extremely important for existing and prospective 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 each period that it survives. As the bubble component gets larger, it dominates the funda- mental component, reducing the likelihood of a negative innovation. Investors realize that prices are overvalued, but they believe that prices will continue to increase. The probability of a high return compensates for the probability of a crash. Thus, investors will remain in overvalued markets. Rational expectations bubbles imply a nonlinear pattern in prices. Previous studies examine nonlinear price patterns within the stock market ((Shiller 1981); West 1987), the gold market (Blanchard and Watson 1982), and the forex market (Evans 1986).

Speculative bubbles within the farmland market are also the topic of interest for researchers, especially during periods of sharply increasing prices as seen in the 1970s and 2000s (see Fig. 1). The farmland market is a good candidate for bubbles due to significant transaction costs (Chavas and Thomas 1999) and overreaction to changes in market fundamentals ((Featherstone and Baker 1987); (Lloyd 1994); (Schmitz and Moss 1996)). (Clark et al. 1993) consider the pattern in farmland values, testing the necessary condition that the time-series properties of farmland values and cash rents have equal time series representations. Their results do not support this condition, and they recommend that models that allow for complexities such as rational bubbles be used in future studies. One of the likely reasons for their conclusion is that while farmland 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 to changing economic conditions. For example, a farmland owner and tenant might negotiate a 3-year lease contract indicating that cash rent will remain fixed over the 3-year period. In addition, tenants tend to have an informational advantage about the productivity of the farmland that they can exploit. Given these features of the land owner-tenant relationship, it is not surprising that cash rents and farmland values do not have the same time series representation.

(Tegene and Kuchler 1993) investigate the existence of bubbles in farmland prices in three Midwest regions using stationarity and cointegration tests. The authors find no support for the presence of a speculative bubble in farmland prices or cash rents for the period 1921–1989. (Power and Turvey 2010) find that farmland values have deviated from fundamental values during the last few years of their 1949–2006 samples. They use wavelet-based statistical methods and tests on long memory estimation to show that price volatility increased and that a short-term bubble exists over the final 10 years of their sample period. (Lavin and Zorn 2001) produce mixed results after employing

Is Farm Real Estate The Next Bubble? 357

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

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

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

Data

The analysis that follows uses annual average Iowa farmland prices from 1950 through 2012 available from Iowa State University Extension and Outreach. Farmland price data is obtained through annual surveys of real estate brokers and other experts. Survey respondents provide an estimate of the value of farmland based on the three grades of quality – high, medium, and low. Farmland quality is measured using the Corn Suitability Rating (CSR), an index that rates the soil based on its productivity in yielding row-crops. The average CSR for a tract of farmland may vary based on soil type, the slope of the farmland, and erosion susceptibility. Figure 2 illustrates the variation in nominal farmland prices based on production quality. The prices corresponding to the three quality grades of high, medium, and low exhibit little variation during the first 20 years of the sample. In the 1970s, the prices noticeably disperse, rising sharply until reaching a peak in 1981, followed by a drop to a low 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 1980s is feeding the recent interest in research by academics and in speculation by media outlets regarding the presence of a farmland price bubble.

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

358 B.C. Olsen, J.R. Stokes

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

To disaggregate the average cash rent data and provide better estimates of the cash rents for each quality grade, an entropy model is employed to estimate the cash rents for the three farmland quality grades based on the dispersion of farmland prices among these grades. The Entropy Concentration Theorem (Jaynes 1957, 1979) states that out of 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 to the one with maximum entropy. The entropy analysis is discussed in more detail in the Appendix and uses the average farmland price for each year of the sample. Applying the entropy method to the cash rent data produces the series depicted in Fig. 3. Since the cash rents are loosely based on the farmland price data, the pattern over time is quite similar 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 the following 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-up experienced 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 of farmland: high, medium, and low quality

Is Farm Real Estate The Next Bubble? 359

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

ΔPt ¼ at þ btXt þ εt ð1Þ The 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. The determinants used include the changes in corn yields and prices, the change in the average cash rents, and the change in the risk-free rate, which should be highly correlated to the borrowing costs available to potential farmland buyers.

Table 1 provides the regression results. Across the entire period, the changes in corn price and average cash rents are significantly related (positive) to the change in farmland price. Using sub-period regressions where the period is split into overlapping 20-year sub-periods, a significant intercept in (1) occurs in the latter periods of the sample and corresponds closely with the increase in farmland prices seen since the 1990s. These results imply that farmland produced abnormal positive increases in prices only during the most recent portion of the sample period after controlling for key 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. The periods that include the 1970s show that the change in average cash rents has a strong positive relation to the change in farmland price, but the farmland price change does not have an abnormal component (the intercepts are negative and not significant). While one 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 quality Medium quality Low quality

Fig. 3 Nominal cash rents per acre, developed using an entropy model, for Iowa farmland from 1950 through 2012 for the three quality grades of farmland: high, medium, and low quality

360 B.C. Olsen, J.R. Stokes

The Speculative Component of Farmland Returns

While the OLS analysis above indicates that there may be an abnormal component that drives farmland price changes in recent years, a more rigorous examination of the issue is necessary. Several researchers have shown that the price of an asset includes a fundamental component and a rational expectations component (e.g., (Shiller 1978); (Blanchard and Watson 1982)).1 The price of an asset can deviate from its fundamental value by a rational expectations component, or bubble. With the equilibrium condition that the value of an asset is equal to the expected future cash flows discounted at the required 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 of a 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 geometric Brownian motion: dCt=μCtdt+σCtdzt. Here, μ is the expected rate of growth in cash rent, σ is the volatility in cash rent, and dzt~N(0,dt) is the increment of a ℙ -Brownian motion. The value of farmland per acre, Vt=V(Ct), can be found by equating the expected capital gain on the farmland plus the flow of cash rent with an equilibrium return on the farmland.2 Mathematically, E dVtð Þ þ Ctdt ¼ ρVtdt; where ρ is the equilibrium rate of return. Rearranging terms results in the following second-order ordinary differential equation:

σ2C2t 2

� � V

00 t þ μCtV

0 t þ Ct ¼ ρVt

Table 1 OLS regressions of change in farmland value

Full sample period

1950 to 1969

1960 to 1979

1970 to 1989

1980 to 1999

1990 to 2009

2000 to 2012

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 −0.044 Corn 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 average price per acre of Iowa farmland. Corn yield is the change in the yield of corn, in bushels per acre; Corn price is the 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-1 to 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 the rational speculative bubble model. 2 While it is theoretically possible to develop the appropriate hedging arguments to cast the pricing model presented here in the context of risk-neutral pricing, the approach used here opts for a simpler pricing model that does not depend on such assumptions.

Is Farm Real Estate The Next Bubble? 361

The general solution to this equation is

V Ctð Þ ¼ K1Cβ1t þ K2Cβ2t þ K3Ct where K1, K2, K3, β1>1, and β2<0 are all constants and

β1;2 ¼ − μ−

σ2

2

� � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μ− σ2

2

� �2 þ 2ρσ2q σ2

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

However, (Dixit and Pindyck 1994) have shown that capital gain speculation can result for some Ct≫0 in equilibrium. If capital gain speculation is present, an investor could buy farmland at a price above fundamental value in anticipation of a large capital gain. 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 farmland value while the second term is the fundamental value taken as a perpetuity. The parameter K3 in this case can be shown to equal (ρ−μ)

−1. It follows that by regressing 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 no component 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 not statistically 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) test statistics 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 high quality 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 estimated capitalization rates (Cap Rate) from the relation V(Ct)=K3Ct, where ρ−μ ¼ bK−13 . *** indicates significance at the 1 % level

362 B.C. Olsen, J.R. Stokes

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

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

V Ctð Þ ¼ K3Ct ¼ Ct

ρ −μ ð3Þ

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

dV Ctð Þ ¼ dCt ρ−μ

¼ μVtdt þ σVtdzt

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

As noted above, hedging arguments may make it possible to unencumber the fundamental value from the unobservable parameter ρ. However, the selected approach here estimates ρ from observable data by noting that it is akin to a weighted average cost 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 purchase price as down payment so that ρ=(1/3)Re+(2/3)i, where Re (i) represents the cost of equity (debt) capital. Stock market returns are assumed to represent the opportunity cost of investing equity capital in farmland, and the cost of debt capital is assumed to approximate 10-year Treasury bond yields plus a premium. The premium is estimated to be 1.73 % using Farm Credit System data on interest rates charged for loans collateralized by farm real estate.

Patterns in the Time Series Data

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

Is Farm Real Estate The Next Bubble? 363

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

RAt ¼ ln Pt Pt−1

� � þ Ct

Pt

� � −ln

Vt Vt−1

� � −Rf ;t ð4Þ

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

Runs

Within the rational expectations bubble structure, the probability of a negative return conditional on a series of prior positive returns decreases with the length of the run. In other words, the longer the bubble continues over time, the less likely that a crash will occur. This phenomenon is called negative duration dependence. Alternatively, positive duration dependence contends that the probability of a run ending increases with the length of the run (Kiefer 1988). (McQueen and Thorley 1994) examine the duration dependence of stock price patterns, stating that the duration dependence pattern test is unique 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 Midwest farmland price data, a result inconsistent with the presence of a rational expectations bubble. Examining 28 different commodities, (Went et al. 2009) test the duration dependence and find eleven that exhibit the traits of rational expectations bubbles.

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

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

ht ¼ λp λtð Þp −1 ð5Þ

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

364 B.C. Olsen, J.R. Stokes

where λ and p are parameters to be estimated. The parameter p takes on particular importance 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 indicative of negative duration dependence. Also, when p=1, the Weibull model reduces to the exponential model, another frequently used parametric (constant) duration model.

As shown in Table 3, low quality farmland exhibits the longest runs of positive abnormal returns (median=3.82 years). Also shown in the table and consistent with past research on farmland price changes, the parameter p from the Weibull model in (5) is statistically significantly greater than one for all farmland qualities, providing evidence of positive duration dependence. The results in Table 3 clearly show that negative duration dependence, 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 will not 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 quality grades. The estimated Weibull model is: ht=λp(λt)

p−1 where ht is the hazard rate at time t, λ and p are parameters, and σλ and σp are standard errors for the parameter estimates.

*** (** * ) indicates rejection of the null hypothesis at the 1 % (5 % 10 %) level

Is Farm Real Estate The Next Bubble? 365

abnormal returns follow a random walk, a Markov chain technique is used. The Markov chain approach requires that the abnormal return series is stationary but does not restrict the series to be normally distributed as do regression tests. For a random walk series, the transition probabilities from one period to the next will be statistically identical, resulting in a symmetrical pattern. In a Markov chain setting, the transition probabilities may vary based on the sequence of prior returns, an advantage over other time series tests.

(Lavin and Zorn 2001) find asymmetry in the transition probabilities from one period to the next for capital gains. Their two-state Markov chain examining farmland prices for Iowa and Nebraska show asymmetry for sequences of farmland price changes over 3 years. In other words, the probability of a price increase following two periods of price 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:

It ¼ 1 if R A t > 0

0 if RAt ≤ 0

�

where Rt A 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 follow a random walk, then the probability of a return increase or decrease does not depend on the previous sequence of returns, providing the following transition probabilities for a first-order Markov chain.

λ00 ¼ Pr It ¼ 0 ���It−2 ¼ 0; It−1 ¼ 0h i

λ01 ¼ Pr It ¼ 0 ���It−2 ¼ 0; It−1 ¼ 1h i

λ10 ¼ Pr It ¼ 0 ���It−2 ¼ 1; It−1 ¼ 0h i

λ11 ¼ Pr It ¼ 0 ���It−2 ¼ 1; It−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 for annual stock returns, noting the consistency with previous studies ((Fama and French 1988); (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 their sample 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 transition probabilities 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 statistics suggest that, in general, low quality farmland is best modeled as a first-order Markov chain. For medium quality farmland, the order of the Markov chain is most likely third-

366 B.C. Olsen, J.R. Stokes

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 Markov chains, including the LR test statistics under various hypothesis tests. These results show that the first-order Markov chain cannot be rejected in favor of the second-order or third-order Markov chain at any reasonable significance levels for low quality farmland. For medium quality farmland, the first-order chain is rejected in favor of the second-order (third-order) chain at the 10 % (5 %) level. At the 10 % level of significance, the second-order Markov chain can be rejected in favor of the third-order Markov chain. For high quality farmland, the first-order chain cannot be rejected in favor of the second-order, and the first-order Markov chain is rejected in favor of the third-order Markov chain, yet only at the 10 % level of significance. Based on the results in both panels of Table 4, the following Markov chains are investigated: the first-order Markov chain for low quality farmland, 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 each farmland quality grade using the appropriate Markov chain order. Shown in Table 5 are the estimated transition probability matrices for each farmland quality grade and corre- sponding Markov chain order. Symmetry implies that the probability that the abnormal return of farmland increases given a previous increase is the same as the probability that the abnormal return of farmland decreases given a previous decrease. Thus, in the case of symmetry, the diagonal elements of the transition probability matrix would be identical. For low quality farmland and assuming a first-order Markov chain, as shown in Table 5, the probability 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 for high 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 order H1: 2nd order

H0: 1st order H1: 3rd order

H0: 2nd order H1: 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 returns series of Iowa farmland by farmland quality. Panel A presents the Akaike Information Criterion. Panel B presents the Likelihood Ratio (LR) test statistics. *** (** * ) indicates significance at the 1 % (5 % 10 %) level

Is Farm Real Estate The Next Bubble? 367

significant. The transition probabilities for medium quality farmland, regardless of the Markov 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 of significance, implying that the excess abnormal returns series appears to be asymmetric. For medium quality farmland, however, the null hypotheses that the transition probabilities are identical cannot be rejected, indicating symmetry. The results from the Markov chain analysis examining symmetry suggest that the conditions required for a rational expectations bubble are present for low and 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 walk hypothesis, 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 % significance level. A review of the transition probabilities in Table 5 support this finding. The results from the Markov chain analysis testing the random walk theory suggest that the conditions required for a rational expectations bubble are present for all three farmland qualities, but the conditions are most prominent for the low and high farmland quality grades.

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 going forward in time as it is going backward in time. If true, the data series is symmetrical and would not be conducive to the formation of bubbles. Within the Markov chain framework above, asymmetric transition probability matrices imply time irreversible processes. The analysis begins with the null hypothesis that abnormal returns data series are time reversible. (Ramsey and Rothman 1996) develop a time reversibility test and apply the test to several economic data series. (Lavin and Zorn 2001) use the time reversibility method to examine the patterns of farmland prices in Iowa and Nebraska, finding irreversibility patterns at different lags in the time series.

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

2Xt−k]−E[XtXt−k 2 ] 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., the moments are equal. Sample estimates of the bicovariances for the stationary series {Xt} with T observations are

bB2;1 ¼ 1 T−k

X t¼kþ1

T

X 2t X t−k

368 B.C. Olsen, J.R. Stokes

T ab

le 5

T ra ns it io n pr ob ab il it y es ti m at es

1s t or de r

2n d or de r

3 rd

or de r

L ow

qu al it y

p dd

¼ 0 :4 2 1 8

p di ¼

0 :5 7 8 2

p id ¼

0 :1 6 6 3

p ii ¼

0 :8 3 3 7

– –

M ed iu m

qu al it y

–

p dd d ¼

0 :6 9 7 3

p dd i ¼

0 :3 0 2 7

p di d ¼

0 :1 7 5 1

p d ii ¼

0 :8 2 4 9

p id d ¼

0 :1 8 5 7

p id i ¼

0 :8 1 4 3

p ii d ¼

0 :2 4 8 5

p ii i ¼

0 :7 5 1 5

2 6 4 3 7 5

p d dd d ¼

0 :6 0 0 0

p d dd i ¼

0 :4 0 0 0

p dd id ¼

0 :0 0 0 0

p dd ii ¼

1 :0 0 0 0

p di dd

¼ 0 :5 0 0 0

p d id i ¼

0 :5 0 0 0

p di id ¼

0 :2 2 2 2

p di ii ¼

0 :7 7 7 8

p id dd

¼ 1 :0 0 0 0

p id di ¼

0 :0 0 0 0

p id id ¼

0 :1 2 5 0

p id ii ¼

0 :8 7 5 0

p ii dd

¼ 0 :1 2 5 0

p ii di ¼

0 :8 7 5 0

p ii id ¼

0 :2 6 0 9

p ii ii ¼

0 :7 3 9 1

2 6 6 6 6 6 6 6 6 6 4

3 7 7 7 7 7 7 7 7 7 5

H ig h qu al it y

p dd

¼ 0 :3 9 3 3

p di ¼

0 :6 0 6 7

p id ¼

0 :3 1 1 4

p ii ¼

0 :6 8 8 6

–

p d dd d ¼

0 :6 0 0 0

p d dd i ¼

0 :4 0 0 0

p dd id ¼

0 :0 0 0 0

p dd ii ¼

1 :0 0 0 0

p di dd

¼ 0 :3 3 3 3

p d id i ¼

0 :6 6 6 7

p di id ¼

0 :3 0 0 0

p di ii ¼

0 :7 0 0 0

p id dd

¼ 0 :6 6 6 7

p id di ¼

0 :3 3 3 3

p id id ¼

0 :2 2 2 2

p id ii ¼

0 :7 7 7 8

p ii dd

¼ 0 :2 2 2 2

p ii di ¼

0 :7 7 7 8

p ii id ¼

0 :3 5 2 9

p ii ii ¼

0 :6 4 7 1

2 6 6 6 6 6 6 6 6 6 4

3 7 7 7 7 7 7 7 7 7 5

T h is ta bl e p ro vi de s tr an si ti on

pr ob ab il it y es ti m at es

fo r ea ch

fa rm

la nd

qu al it y gr ad e ap pl yi ng

th e ap pr op ri at e or de r M ar ko v ch ai ns

id en ti fi ed

in T ab le 4 . S u bs cr ip ts i an d d re fe r to

an in cr ea se

o r d ec re as e in

ex ce ss

ab no rm

al re tu rn s

Is Farm Real Estate The Next Bubble? 369

bB1;2 ¼ 1 T−k

X t¼kþ1

T

X tX 2 t−k

The test statistic, bγ2;1 kð Þ , which is the difference between the sample bicovariance estimates, 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.), the possibility of heteroscedastic error variances should be considered. (Engle 1982, 1983), among others, show that variances may cluster, requiring a different approach to analyzing time 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 the prices is most likely not constant. To capture the effects of this excess volatility, each farmland quality data series is tested for ARCH effects using the white-noise test for the squared time series. The null hypothesis is that the population autocorrelation functions for the squared time series are equal to zero. Examining the p-value for the Ljung-Box modified statistic within the Chi-square distribution, both the high and medium quality farmland data series are found to exhibit ARCH effects, while the low quality farmland data series does not. An EGARCH framework from (Nelson 1991) is applied to recognize 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 order H0: pdd=pii H1: pdd≠pii

2nd order H0: pddd=piii H1: pddd≠piii

3rd order H0: pdddd=piiii H1: 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 order H0: all pjk=pkj H1: not all pjk=pkj

2nd order H0: all pjkl=plkj H1: not all pjkl=plkj

3rd order H0: 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 walk assumption (Panel B). Subscripts i and d refer to an increase or decrease in excess abnormal returns. Subscripts j, k, l, and m may represent an increase or decrease in excess abnormal returns. *** (** * ) indicates significance at the 1 % (5 % 10 %) level and rejection of the null

370 B.C. Olsen, J.R. Stokes

H(2,1) provides the best model structure for both the high and medium quality farmland series.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 is performed, and the sample bicovariance estimates from (6) are calculated. Next, a plot is constructed comparing the sample bicovariance, bγ2;1 kð Þ , which is calculated directly from each data series, to the boundary conditions of +/− two standard deviations of the sample bicovariance determined by the Monte Carlo simulations (N=10,000 iterations). The comparison is illustrated in Fig. 4. The high and medium farmland quality data series are clearly time reversible time series as the +/− two standard error boundaries are not breached. These two farmland qualities, then, are time reversible to order 3 and degree 20.5 However, the low quality farmland plot shows that the test statistic exceeds the boundaries at lags k=2, 3, 4, and 5. Only the abnormal returns series from low quality 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) to the low quality farmland data series provides very similar results.

Conclusions

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

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

Is Farm Real Estate The Next Bubble? 371

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 maximum lag, 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

372 B.C. Olsen, J.R. Stokes

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

One potential weakness of this study, indeed a weakness of potentially all farmland value 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 identify the upper and lower boundaries at +/− two standard deviations of the bicovariance estimate calculated from Monte Carlo simulations. Points above the upper boundary or below the lower boundary indicate lags at which the 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 −0.7620 2 −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 −1.3804 7 0.1429 0.1160 −0.9123 8 0.1556 0.1610 −0.3254 9 0.4974 0.7290 0.7533

10 0.0827 −0.1337 −1.1715 11 0.0794 0.1118 0.0004

12 −0.0363 −0.1234 −0.6328 13 −0.2204 −0.4008 −1.3349 14 −0.1610 −0.2275 −0.8643 15 −0.1055 −0.1373 −0.4493 16 −0.0866 −0.1223 −0.2919 17 −0.0505 −0.1041 −0.1361 18 −0.3506 −0.5074 −1.2326 19 −0.6328 −0.8934 −1.3837 20 −0.6405 −0.7820 −1.4247

This table provides the results from testing whether the three data series are time reversible to order 3 and degree 20. The test statistic, bγ2;1 kð Þ=Var bγ2;1 kð Þ� �1=2 is generated from the Gaussian innovations from the time 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 Carlo simulations. k represents the lag. *** (** * ) indicates significance at the 1 % (5 % 10 %) level and rejection of the null that the time series is reversible

Is Farm Real Estate The Next Bubble? 373

data would add statistical power to the tests examining the patterns. A second potential weakness is the source of the farmland value data, the surveys of real estate brokers and other related experts. Requesting an assessment of farmland values only once each calendar year may introduce a familiarity bias, for example, related to chronology (the ease of recalling more 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 helpful comments, 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 quality farmland using the most likely distribution of farmland by quality. Most of Iowa farmland is medium to high quality and, as a result, the simple average of farmland values 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 each quality grade that would constitute the reported average. More clearly, the following framework is solved for each t:

max E sð Þ ¼ X i

sitln sitð Þ s.t.

X i

sitPit ¼ P̄t;

X i

sit ¼ 1;

sit ≥0

Where i is an index of farmland quality, and sit is the time t proportion or share of total 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 equation wherein 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 of constraints ensures the proportions are non-negative. If the reported average appearing in the right-hand side of the first constraint is the simple average, the entropy would be maximized with a uniform distribution of proportions equal to one-third each.

Once the proportions are uncovered, they are applied to the reported average cash rent per acre. However, it is typically the case that cash rent for high (medium) quality farmland 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 each farmland 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,

374 B.C. Olsen, J.R. Stokes

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

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