Farmland prices, structural breaks and panel data

European Review of Agricultural Economics Vol 34 (2) (2007) pp. 161–179 doi:10.1093/erae/jbm018 Advance Access Publication 14 July 2007

Farmland prices, structural breaks and panel data Luciano Gutierrez University of Sassari, Italy

Joakim Westerlund Lund University, Sweden

Kenneth Erickson US Department of Agriculture, Economic Research Service, Washington, DC, USA Received February 2006; final version received March 2007

Summary Previous time series evidence has indicated that farmland prices and cash rents are not cointegrated, a finding at odds with the present value model of farmland prices. We argue that this failure to find cointegration may be due to low power of tests and to the presence of structural change representing a shifting risk premium on farmland investments. To accommodate this possibility, we use panel unit root and cointegration methods that are more powerful than conventional time series methods and allow for breaks in the cointegration relationship. Our results, based on a large panel covering 31 US states between 1960 and 2000, suggest that the present value model of farmland prices cannot be rejected. Keywords: farmland prices, present value model, non-stationary panel data analysis, structural breaks

JEL classification: C23, G12, Q14

1. Introduction During the last decade, there has been much research focusing on the long-run relationship between farmland prices and the expected future returns on this asset (see, for example, Falk, 1991; Engsted, 1998; Falk and Lee, 1998; Lence and Miller, 1999; Roche and McQuinn, 2001). Even with the rapid advances in technology in agriculture during the 20th century, farmland remains a critical production factor. The importance of farmland is underscored by its dominant position in the agricultural balance sheet over time. Nonetheless, and despite the vast amount of research effort # Oxford University Press and Foundation for the European Review of Agricultural Economics 2007; all rights reserved. For permissions, please email [email protected]

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spent on explaining the behaviour of land prices, most economic models of land prices have met with only limited empirical success. One of the most popular theoretical models for explaining land price behaviour over long-time horizons is the present value model. As is well known, the present value model of real land prices requires that, if the real rent possesses a unit root, then so must the price of land itself. Moreover, assuming a fixed discount rate, land prices and rents must be cointegrated with a unit coefficient on rents. Because of its strong theoretical appeal, the present value model has also been subject to much empirical scrutiny. Unfortunately, the results show that although the movements of land prices and rent are highly correlated in the short run, they may not be in the long run (see, for example, Moss and Schmitz, 2003). For example, Falk (1991) analysed Iowa farmland prices and ended up rejecting the present value model. Similar results were reported for Illinois by Clark et al. (1993). Tegene and Kuchler (1993) and Engsted (1998) examined three US regions—the Lake States, the Corn Belt and the Northern Plains—and found no evidence supporting the present value model. The main objective of this study is to investigate whether this absence of empirical support for the present value model can be attributed to the restrictiveness and poor precision of conventionally employed unit root and cointegration methods. In particular, using a simple theoretical model we show that a change in the required risk premium on farm investments can induce a level shift in the estimated regression. Thus, in cases such as this, the present value model no longer implies cointegration in the usual sense, and the appropriate empirical test is therefore not a conventional cointegration test, but rather a test for cointegration with structural breaks. However, it is well known that the presence of such breaks may induce serial correlation properties in the residuals that are akin to those of a random walk. Therefore, the conventional tests may incorrectly indicate the absence of cointegration when the series are in fact cointegrated around a level shift. Another possible explanation for the absence of empirical support for the present value model is that standard unit root and cointegration tests may not be powerful enough to detect cointegration when applied to single time series of small to moderate length, especially when the series are cointegrated but with persistent equilibrium errors. To overcome both these problems, this paper applies recently proposed unit root and cointegration methods to a panel of multiple time series. These methods are not only able to take into account structural shifts in the cointegration relation, but are also expected to be more accurate than conventional methods based on single time series. The remainder of this paper is organised as follows. In Section 2, we show how structural shifts in the premium on farm investments can affect the test of the present value model by inducing breaks in the level of the relationship between farmland prices and rents. To allow for this possibility, we use panel cointegration methods that can be implemented even in the presence

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of structural breaks. In Section 3, these methods are applied to a panel of 31 US states, for which time series data on farmland prices and cash rents are available for 1960–2000. The results show that while conventional unit root and cointegration tests tend to reject the present value model, this model cannot be rejected once level shifts in a panel of multiple time series are allowed for. Section 4 concludes the paper.

2. Testing the present value model The empirical literature has developed several empirical tests of the present value model. The particular test used in this paper is that of Campbell and Shiller (1988), who suggested testing the present value model by using cointegration techniques. This section gives a brief account of this test and then discusses some of its problems. Finally, we present one possible solution to these problems. 2.1. A time series cointegration test

The Campbell and Shiller (1988) version of the present value model relates, Pit, the real price per acre of farmland in state i ¼ 1, . . . , N at period t ¼ 1, . . . ,T, to Citþ1, the real rent per acre of farmland paid at beginning of time tþ1 for the land held from the beginning of time t to the beginning of time tþ1. In this notation, the log of the gross real rate of return on an acre of land in state i from period t to tþ1, Ritþ1 say, may be defined as logðRitþ1 Þ ¼ logðPitþ1 þ Citþ1 Þ  logðPit Þ; or, equivalently ritþ1 ¼ logð1 þ expðSitþ1 ÞÞ þ pitþ1  pit ;

ð1Þ

where the lowercase letters are the logs of the corresponding uppercase variables and Sitþ1 ¼ citþ1 2 pitþ1 is the log of the ratio of rents to prices, usually referred to as the ‘spread’ in the financial literature. The objective here is to write log returns as a linear function of log prices and log rents, which is complicated by the first term on the right-hand side of equation (1). Fortunately, as shown by Campbell and Shiller (1988), this problem can be readily resolved by linearising log(1þexp(Sitþ1)) around the time series mean of Sitþ1, Si say. With this modification, equation (1) can be written approximately as ritþ1  ki þ Sit  ri Sitþ1 þ Dcitþ1 ;

ð2Þ

where ki ¼ 2log(ri) 2 (1 2 ri) log(1/ri 2 1) and ri ¼ 1/(1 þ exp(Si)) are parameters of the linearisation.

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Equation (2) is basically an ordinary difference equation, which can be solved forward indefinitely to obtain the following approximation for Sit:

Sit  ki =ð1  ri Þ 

1 X

rsi ðDcitþ1þs  ritþ1þs Þ þ lim rsi Sitþs : s!1

s¼0

ð3Þ

Now, consider taking expectations conditional on all the information available at time t. Since Sit is known at t, and if the standard transversality condition holds, so that the expected value of the last term on the right-hand side of equation (3) is zero, then the above equation can be rewritten as

Sit þ ki =ð1  ri Þ  Et

1 X

!

rsi ðDcitþ1þs

 ritþ1þs Þ :

ð4Þ

s¼0

This equation encapsulates the notion of the present value model. It expresses the current value of Sit in terms of the present discounted value of expected future values of Dcitþ1 and ritþ1. In order to derive testable predictions of this model, assume that the expected excess return to an acre of land, over some alternative asset with return git, is constant over time so that Et ðrit Þ  Et ðgit Þ ¼ ri ; where ri is the risk premium on farm investments. With this assumption, the present value model reduces to

Sit þ ðki  ri Þ=ð1  ri Þ  Et

1 X

!

rsi ðgitþ1þs  Dcitþ1þs Þ :

ð5Þ

s¼0

Suppose further that the expected rate of return on the alternative asset is stationary, and that log rents and prices are non-stationary such that their first differences are stationary. If this is the case, then the right-hand side of equation (5) must be stationary, which implies that the left-hand side must be stationary too, in which case the constant expected excess returns version of the present value model might be said to hold. As pointed out by Campbell and Shiller (1988), a test of this model can be readily implemented using conventional cointegration techniques, which amounts to first estimating and then testing the following regression for cointegration pit ¼ ai þ bi cit þ eit ;

ð6Þ

where ai ¼ 2(ki 2 ri)/(1 2 ri) and bi are state-specific intercepts and slopes, respectively, and eit is a zero-mean disturbance. To see what this means for

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the test of the present value model, note that equation (6) can be rewritten as Sit  ai ¼ ð1  bi Þcit  eit :

ð7Þ

Next, suppose that log prices and rents are cointegrated. In this case, the disturbance eit must be stationary, so the order of integration of the spread depends only on the order of integration of the term (1 2 bi)cit. If bi ¼ 1, then this term vanishes, so variations in the spread reflect only temporary deviations from its mean value, ai. Intuitively, because log prices move one-for-one with log rents in the long run, their unit root components cancel out, leaving the spread unaffected. In contrast, if bi is different from one, then (1 2 bi)cit will not vanish, which suggests that the spread must contain the same unit root component as log rents. Of course, log rents and prices may still be cointegrated even though the spread is non-stationary. But since bi is not one, cointegration is by itself insufficient to ensure that the present value model too holds. The conventional way in which earlier studies have tried to test the present value model within this regression framework involves first estimating equation (6) individually for each state i by least squares (LS), and then testing whether the residuals from those regressions can be regarded as stationary or not by using any conventional cointegration test. Studies based on this approach are generally unable to reject the null hypothesis of no cointegration, which is seen to imply that the present value model of farmland prices should be rejected; see, for example, Engsted (1998), Clark et al. (1993) and Tegene and Kuchler (1993).

2.2. Some empirical problems

Most attempts to reconcile the failure of the present value model of farmland prices have taken the empirical evidence more or less at face value and have then modified the theoretical arguments. For example, De Fontnouvelle and Lence (2002) argued that the presence of market frictions can drive a wedge between the price at which outsiders are willing to buy land and the price at which landowners are willing to sell it. To study the effects of such frictions, the authors introduced a new theoretical framework that allows for the presence of transaction costs. Using different arguments, Shiha and Chavas (1995) postulated that farmland markets are influenced by barriers that alter the flow of non-farm equity capital into farm real-estate markets. Taking another approach, Hanson and Myers (1995) argued that the existence of a time-varying risk premium could explain the failure of the present value model. In this paper, we take the alternative route and focus instead on the econometric methodology used for testing the present value model. We argue that the existing empirical evidence concerning farmland prices is flawed in at least two respects, and that this may at least partially explain the weak

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results previously obtained. It therefore seems reasonable to investigate these problems before embarking on further revisions of economic theory. One problem is that the empirical relationship between rents and farmland prices that is being estimated need not be invariant to structural changes, which may lead to shifts in both rents and prices, and hence in the relationship between them. To understand better how such breaks can affect the test of the present value model, suppose that the premium on farm investments is given by Et ðrit Þ  Et ðgit Þ ¼ rij ;

t ¼ tij1 ; . . . ; tij ;

where j ¼ 1, . . . , mi þ 1 indexes the break regimes, while ti0 ¼ 0 and timi þ 1 ¼ T. Thus, in this setup, there are mi breaks, or mi þ 1 break regimes, for each state i with the jth regime running from tij21 to tij time series observations. Thus, although constant within regimes, the premium jumps from rij21 to rij at time t ¼ tij. If this is the case, then equation (4) can be rewritten as

Sit þ ki =ð1  ri Þ  

1 X

rsi Et ðDcitþ1þs  ritþ1þs Þ

s¼0

¼

1 X

rsi Et ðgitþ1þs  Dcitþ1þs Þ þ rij =ð1  ri Þ:

s¼0

Thus, by rearranging the terms, we obtain

Sit þ ðki  rij Þ=ð1  ri Þ 

1 X

rsi Et ðgitþ1þs  Dcitþ1þs Þ:

s¼0

Hence, a shifting farm investment premium translates into a shifting intercept in the cointegrating relationship, which will henceforth be written as

aij ¼ ðki  rij Þ=ð1  ri Þ: A shifting aij is problematic in the sense that, if these shifts are not appropriately accounted for, this will create breaks in the estimated residuals. In particular, the problem is that breaks and unit roots share many qualitative features, so that most residual-based tests that attempt to distinguish between a spurious and a cointegrated process will tend to favour the spurious model when the true process is subject to structural breaks but is otherwise cointegrated within the break regimes. The presence of structural breaks is therefore one possible explanation for the failure of the present value model. Another related problem is that most, if not all, studies employ methods that are designed to test the null hypothesis of no cointegration, and these are

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known to suffer from low power when the equilibrium errors are highly persistent under the alternative of cointegration, especially when there are breaks present. Thus, low power of the tests could be another explanation of why cointegration has been so difficult to find. In a situation like this, it is essential to use tests with higher power. A promising approach would be to combine the sample information from the time series dimension with that from the cross-sectional. This not only increases the power of the test by taking the total number of observations and their variation into account, but also increases the precision of the test by effectively reducing the noise coming from the individual time series regressions. Therefore, one way to augment the power of univariate tests would be to subject the residuals from (6) to a panel data cointegration test. Unfortunately, most existing tests of this kind rely critically on assuming that the states are independent of each other, which is unlikely to hold in the present application because, for example, of common boom-bust cycles. Another limitation of most panel cointegration tests is that they ignore the possibility of structural change, which, as explained earlier, is likely to be a critical issue in the current application. Thus, a first crucial step in testing the present value model of farmland prices using panel data is to employ tests that allow for structural breaks, and that do not rely to such a large extent on the states being independent. Another desirable requirement is the ability to test whether all N states are cointegrated or not, which is usually not possible because of the way that panel tests of this kind are constructed. In fact, most tests take no cointegration as the null hypothesis, meaning that a rejection can be due to a single cointegrated unit, which is not very interesting.

2.3. Testing for cointegration in panels with breaks and cross-section dependence

The previous section suggests that testing for cointegration in cross-section dependent data with structural change is particularly important when investigating the present value model of farmland prices. In this section, we outline a test that fits this description, and that is general enough to allow for both crossstate dependence and an unknown number of breaks that may be located at different dates for different states. Since the breaks are of particular interest, special attention will be paid to their treatment. Consider the following break-augmented panel regression pit ¼ aij þ bi cit þ eit ;

ð8Þ

where bi is again a state-specific slope that is assumed to be constant over time, while aij ( j ¼ 1, . . . , mi þ 1) is a state-specific intercept that is subject to mi structural breaks. The present value model requires that equation (8) is cointegrated. If there is no structural change, then this hypothesis can be

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readily tested by using existing tests for cointegration in panel data. If there are breaks, however, then this test procedure is no longer valid since the relationship in equation (8) is no longer linear in aij. As mentioned earlier, this poses a serious problem, as most tests cannot be used to discriminate between cointegration with structural shifts and the absence of cointegration. In order to account for these shifts, we invoke some recent advances in the area of non-stationary panel data. In particular, the panel Lagrange multiplier test for cointegration developed by Westerlund (2006) is general enough to allow for multiple breaks, which makes it suitable for our purposes. The null hypothesis is that cointegration holds in all states in the panel, while the alternative is that cointegration does not hold in one or more states. The test statistic for this hypothesis is given by

ZðmÞ ¼

tij N m i þ1 X X 1X S2 =½ðtij  tij1 Þ2 s^ i2 ; N i¼1 j¼1 t¼tij1 þ1 it

P where Sit ¼ ts¼tij21þ1eˆis and eˆit is any efficient estimate of the regression error in equation (8), which, in the presence of endogenous regressors, can be obtained using the fully modified LS (FM) estimator of Phillips and Hansen (1990). The quantity sˆ2i is the usual Newey and West (1994) long-run variance estimator based on eˆit. Note also that although Z(m) might look complicated at first, closer inspection reveals that it is actually nothing but the cross-sectional average of mi þ 1 regime-specific statistics tij X

S2it =½ðtij  tij1 Þ2 s^ i2 ;

t¼tij1 þ1

which are computed for subsamples of length tij 2 tij21. These regimespecific statistics are in turn nothing but the usual Kwiatkowski et al. (1992) stationarity test applied to the estimated regression residuals. Now, given that the states are independent, Westerlund (2006) showed that Z(m) reaches the following sequential limit as T ! 1 and then N ! 1 under the null hypothesis: pffiffiffiffi N ðZðmÞ  EðZðmÞÞÞ pffiffiffiffiffiffiffi ) Nð0; 1Þ; varðZðmÞÞ where ) signifies convergence in distribution, while the mean and variance adjustment terms E(Z(m)) and var(Z(m)) are defined in Westerlund (2006). Thus, by standardising Z(m) by its mean and standard deviation, we obtain a new test statistic that has a limiting standard normal distribution under the null hypothesis. Under the alternative hypothesis, the statistic diverges to

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positive infinity, suggesting that the right tail of the normal distribution should be used to reject the null. For the estimation of the number of breaks and their locations, Westerlund (2006) suggested using the LS approach of Bai and Perron (2003), which is based on solving the following minimisation problem

ðt^i1 ; . . . ; t^imi Þ ¼ argmin

m i þ1 X

tij X

ti1 ;...;timi j¼1 t¼t þ1 ij1

e^ 2it ;

where eˆit is again the estimated regression error in equation (8) based on the partition tij with j ¼ 1, . . . , mi and a trimming parameter of tmin such that tij 2 tij21 . tmin, which imposes a minimum length for each subsample. The estimation is performed in two separate steps. In the first, the minimisers of the sum of squared residuals are estimated and stored together with the associated breaks tij for each possible break number mi ¼ 1, . . . , mmax, where mmax , mi is some predetermined upper boundary. In the second step, the number of breaks is estimated for each i using an information criterion. The purpose of the first step is to estimate the aij and bi together with the unknown break points when T observations are available for each state. This can be done by using the dynamic programming algorithm developed by Bai and Perron (2003). In our case, however, since the slope parameters bi are not subject to shift and are estimated using the full length of the time series dimension, the algorithm cannot be applied directly. This is so because the estimate of bi associated with the minimum of the sum of squared residuals depends on the breaks that we are trying to estimate, which means that we cannot concentrate out bi from the objective function. Therefore, the minimisation of the sum of squared residuals cannot be done with respect to tij directly but must be carried out iteratively. The iterative procedure suggested by Bai and Perron (2003) proceeds in the following fashion. Given a starting value for bi, initiate the procedure by minimising the objective function with respect to aij and tij, while keeping bi fixed. This requires an evaluation of the optimal break partition for all subsamples that admit the possibility of mi breaks. Because bi is held fixed, this stage amounts to minimising the objective function of a pure structural change model to which the dynamic programming algorithm applies. The next stage is to minimise with respect to aij and bi simultaneously while keeping tij fixed. The idea is then to iterate until the marginal decrease in the objective function converges. The first step yields estimated break partitions and sum of squared residuals for each number of breaks that lie between zero and mmax. The second step uses these sums of squared residuals to estimate mi, which is done as suggested by Bai and Perron (2003) using the Schwarz Bayesian information criterion. The estimated breakpoints tˆij are then obtained as the partition associated with the particular number of breaks that minimises the criterion. These steps

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are then repeated N times, which produces a set of estimated breakpoints for each state i in the sample. The Z(m) statistic can then be constructed using these estimates in place of their true values. One problem with this test procedure is that it is based on the assumption of cross-section independence, which, as argued earlier, is unlikely to hold in the present application. To handle the impact of deviations from this assumption, Westerlund (2006) suggested using the bootstrap approach. The particular bootstrap scheme opted for in this paper uses the sieve approach of Westerlund and Edgerton (2007), who proposed a bootstrap version of the Westerlund (2006) test in the absence of breaks, but that can be easily modified to allow for breaks. The underlying idea here is that the cross-sectional and time series dependence of the disturbances can be approximated by means of a panel vector autoregressive model, from which the bootstrap innovations are then drawn.1 Finally, before reporting the empirical results, we would like to stress one last time the generality and flexibility of the testing approach just described. Not only are all parameters of the model free to vary over the cross-section, but there is also the allowance for an unknown number of breaks as well as cross-state dependence. In fact, the only information that is actually pooled here is that all states are cointegrated under the null hypothesis.

3. Empirical results This section first briefly describes the data, and then presents the empirical cointegration test results. Finally, some results on the estimated cointegration vectors are given. 3.1. Data

Annual observations for 31 US states2 between 1960 and 2000 are used for this study. The availability of data for cash rents turned out to be a critical constraint, and determined which states were included. Farmland prices are based on estimates of the value of land and buildings per acre, obtained from the US Department of Agriculture, National Agricultural Statistics Service and the Economic Research Service. Net cash rents per acre come from the same sources. Both series are based on opinion surveys. Finally, all the series were deflated using the aggregate consumer price index, obtained from the US Department of Commerce, Bureau of Economic Analysis. The reference year is 1996. This sample differs from those used by other studies in two important respects. First, the time series are longer than most other studies, and the number of states is much larger than in any existing study on the present value model of farmland prices.3 Second, in contrast to many other studies on farmland prices, we use raw net cash rents, which are less prone to measurement error than estimated returns. 1 See Westerlund and Edgerton (2007) for more details. 2 See Table 2 for a complete list of the included states. 3 For example, the sample used by Alston (1986) covers only eight states between 1963 and 1982.

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3.2. Panel stationarity testing

Before testing for cointegration, we first establish the order of integration of farmland prices and cash rents. This is done using the panel stationary test of Carrion-i-Silvestre et al. (2005), which is similar to the Westerlund (2006) test in that it uses the Bai and Perron (2003) procedure to allow for structural breaks and a sieve-type bootstrap approach to allow for crossstate dependence. It is therefore an appropriate test for our purposes. Since none of the variables appear to be trending, the test is implemented with an individual-specific constant only, and the bootstrap is carried out using a sieve lag of five and 1,000 replications. The Bai and Perron (2003) procedure is implemented with a maximum of three shifts, which seems sufficient to capture all major breaks in the data. Also, to ensure that the break date estimator works properly, we follow Bai and Perron (2003) and set tmin, the minimum length of each break regime, equal to 0.1 T, which means that each segment has at least four observations.4 The results obtained from applying the Carrion-i-Silvestre et al. (2005) test to the farmland data are reported in the first two rows of Table 1. Note that since some of the breaks in the raw data will tend to cancel out in the cointegrating relationship, all break estimation results are postponed to the next section where we test for cointegration. For each variable, the fourth column of Table 1 contains the test value, while the fifth and sixth columns contain the asymptotic and bootstrapped p-values, respectively. The results from the asymptotic p-values suggest that the null hypothesis of stationarity can be safely rejected at all conventional levels of significance. However, these values assume that the states are independent, which, as argued before, is unlikely to hold. In order to account for Table 1. Panel stationarit and cointegration tests Test

Model

Variable

Value

p valuea

p valueb

Unit root

Level break

Cointegration

Fixed intercept Intercept break

Cash rents Farmland prices — —

9.074 5.657 8.413 9.563

0.000 0.000 0.000 0.000

0.000 0.032 0.031 0.548

Note: All test results allow for up to three structural breaks for each state, which were estimated using the Bai and Perron (2003) procedure. The only exception is the fixed intercept model, which refers to a cointegrated regression with a non-breaking intercept. To handle the serial correlation, the Newey and West (1994) long-run variance estimator was used. a The p value is based on the asymptotic normal distribution. b The p value is based on the bootstrapped distribution. The number of lags in the sieve approximation is five and we made 1,000 bootstrap replications.

4 Note that there is a direct correspondence between mmax and tmin in that if one increases, then the other must in general decrease. Our choice of this variable is motivated by the usual trade-off between the number of breaks to include and the accuracy with which each break can be estimated. Setting tmin equal to 0.1 T is a usual choice, because it allows for some observations within each regime, while simultaneously permitting ample freedom for mmax.

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this dependence, we used the bootstrapped p-values instead. The results suggest that the conclusions are not altered by taking the cross-state correlations into account, at least not at the 5 per cent level. Thus, since the overall evidence in favour of a rejection is quite overwhelming, we chose to proceed as if the variables are in fact non-stationary.5

3.3. Panel cointegration testing

Having verified that the variables are indeed non-stationary, we then tested for cointegration. To do so, we began by estimating the number of breaks and their location using the Bai and Perron (2003) procedure, which was implemented exactly as described in the previous section. The results are reported in Table 2. Many interesting points emerge. The first thing to notice is that all states have at some point been subject to breaks, which confirms our claim that accounting for structural change is key in testing the present value model. The fact that the breaks are not synchronised across the states is probably due to local changes in market fundamentals, which are then reflected in the cash rent-to-value relationship. In particular, we need to differentiate between the Northeast, which is relatively more urbanised, and the Corn Belt and Lake, Plains, Southeast, Appalachia and Delta, which are largely influenced by farm-related factors. In the Northeast, for example, cash rents are not only influenced by expected returns, but also by the non-farm demand for farmland. However, the purpose here is not to identify every single break but rather to determine whether these breaks can be attributed to the farm financial crisis that affected the whole country. In doing so, we concentrated on identifying periods where many states were affected. There are three such periods. The first period covers roughly the years 1964– 1969, whereas the second covers 1973– 1976. More than half of the states registered a break in the cointegration relationship in at least one of these periods and one-third of the states registered a break in both periods. This seem very reasonable given the exceptionally rising land values of that time, which Just and Miranowski (1993) attributed to higher inflation and changes in the real rate of return on alternative uses of capital. In particular, while the first period was mainly characterised by high farm income growth, and low real agricultural interest rates and rates of return on farm assets, the events that shaped the second period include oil price shocks, an unusually large farm income following the growth of agricultural exports due to devaluation of the dollar and bad weather conditions in competing production regions overseas, and a rise of the rate of return on farm assets. The perceived profit opportunities allowed farmers to increase production by bringing more land under cultivation and by investing in more efficient technologies.6 5 We also used a battery of panel unit root tests, which led to the same conclusion (see Gutierrez, 2006). 6 See USDA, Agricultural Outlook, various issues.

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Table 2. Estimated breaks Region

Northeast

Lake States and Corn Belt

Northern and Southern Plains

Appalachia

Southeast

Delta

State

Delaware Maryland New Jersey New York Pennsylvania Illinois Indiana Iowa Michigan Minnesota Missouri Ohio Wisconsin Kansas Nebraska North Dakota Oklahoma South Dakota Texas Kentucky North Carolina Tennessee Virginia West Virginia Alabama Florida Georgia South Carolina Arkansas Louisiana Mississippi

No.

2 1 3 2 3 3 3 1 2 3 3 3 3 2 3 2 2 3 3 3 2 1 2 2 3 1 3 2 3 2 3

Breakpoint 1

2

3

1969 1985 1967 1964 1967 1976 1968 1984 1973 1964 1965 1964 1968 1973 1969 1980 1975 1964 1966 1966 1973 1981 1982 1964 1967 1985 1964 1972 1965 1968 1972

1982 — 1973 1973 1973 1980 1981 — 1984 1973 1985 1973 1980 1984 1984 1984 1984 1969 1973 1972 1984 — 1986 1973 1981 — 1972 1988 1969 1973 1984

— — 1984 — 1984 1984 1985 — — 1984 1991 1982 1984 — 1994 — — 1988 1982 1981 — — — — 1990 — 1982 — 1973 — 1995

Note: The breakpoints were estimated using the Bai and Perron (2003) procedure, while the number of breaks to use for each state was determined using the Schwarz Bayesian information criterion with a maximum of three breaks. The minimum length of each break regime was set to 0.1 T.

The third period covers the second half of the 1980s, in which more than 80 per cent of the states registered a break in the cointegration relationship. These breaks may be explained by increased uncertainty in expected returns on farmland investments, by high real interest rates, and low commodity prices that have created financial problems for many US farmers, especially for those in highly leveraged positions. The falling incomes and rising interest rates pressured farm asset values, which fell dramatically during this period (see Moss et al., 2003).

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In synthesis, it seems reasonable to expect that these events, although not perfectly synchronised across states, were able to change the required risk premium on farmland investments and consequently the level of the cointegration relationship between farmland prices and cash rents, as explained in Section 2. Thus, given these estimated breaks, we then proceeded to test for cointegration using the Westerlund (2006) Z(m) test. The results are presented in the last two rows of Table 1. Looking at the p-values, the model with a fixed constant provides very little evidence in support of cointegration. However, these results ignore the possibility of structural breaks, and are therefore prone to erroneous conclusions. Indeed, if we allow for structural shifts and crossstate correlation as in Table 1, then the null hypothesis of cointegration cannot be rejected at any conventional significance level when using the bootstrapped p-values. We therefore conclude that the variables appear to be cointegrated around a broken intercept. Summarising the results so far, all states appear to have been affected by at least one break, which confirms our assertion that structural change is a key issue when testing the present value model of farmland prices. Moreover, there is a preponderance of breaks occurring in the middle of the 1980s, which seems to coincide with the farm financial crisis period. Thus, although there is some variation among the states, the results seem largely consistent with the structural changes in the US farm production sector, particularly during the first half of the 1980s. Finally, once allowing for structural breaks, land prices and rents are cointegrated. 3.4. Panel cointegration estimation

Since the variables appear to be cointegrated, it is possible to estimate and test whether the cointegrating slope is indeed equal to one as predicted by the present value model. Before we discuss the estimation results, however, there are a few issues that need to be addressed, namely, endogeneity, homogeneity and cross-state dependence. It is well known that the LS estimator is consistent under fairly general conditions when applied to the cointegrated regression in equation (8). Unfortunately, if the regressor is endogenous, then this estimator suffers from nuisance-parameter dependencies even asymptotically, which makes it a very poor candidate for inference. To account for this, we employed the same FM estimation technique used in constructing the Z(m) test. All results reported up to this point were based on allowing for a perfectly heterogeneous cointegrating relationship, pooling only the information available regarding the cointegration hypothesis. Thus, when we turned to estimating and inferring the cointegrating slope, it was desirable to pool the information regarding this parameter instead. This can essentially be done in two ways depending on how the data are aggregated, which we will describe here briefly. For more details, we refer to Pedroni (2000). Within-estimation is based on pooling, and is appropriate

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for testing the null hypothesis that bi ¼ 1 for all i against the alternative hypothesis that bi is equal to some common value, which is different from unity. In contrast, between-estimation is based on averaging, and is appropriate for testing the null that bi ¼ 1 for all i versus the alternative that bi = 1 for some i. Accordingly, between-estimation provides a basis for a consistent test of the unit coefficient hypothesis against coefficient values that need not be common under the alternative hypothesis. Note that, if the true slopes are not equal, between-estimation provides consistent estimates of the sample mean of the individual coefficients, while within-estimation does not. Similarly, applied studies using panel data (see Baltagi, 2005, for a recent survey) have found that the between-estimator tends to give better long-run estimates than the within-estimator. This was quite important in our case, because we were interested in estimating the long-run relationship between farmland prices and cash rents. Thus, among the two approaches considered, between-estimation seemed preferable. The third and final issue is that of cross-sectional dependence. As when testing for stationarity and cointegration in panel data, dependence of this kind means that inference based on the asymptotic normal distribution is likely to be inappropriate, and that bootstrap inference might be better. The particular bootstrap opted for this section was again taken from Westerlund and Edgerton (2007), which is appropriate in the sense that it allows for both serial and cross-state correlation. As an indication of the severity of the cross-correlation problem, we applied the Pesaran (2004) test of crosssection correlation to the LS residuals of the estimated cointegrated regression. The computed test value was 18.755, which, when compared to the right tail of the asymptotic normal distribution, clearly rejected the ‘no correlation’ null at all conventional significance levels. Thus, as expected, cross-state correlation is indeed a problem that needs to be addressed. The results from the estimated coefficients using both LS and FM techniques are reported in Table 3.7 We began the analysis by considering the results of the estimated slopes together with the double-sided p-values for the unit coefficient hypothesis, which are reported in the first four rows of Table 3. The first thing to notice is that the estimated slopes lie close to their hypothesised values of one. The range of the estimated slopes is 0.781 to 0.853 for the within-type estimators, and 0.859 to 1.064 for the betweenestimators. The closeness of the latter estimates to their expected value based on the present value model is supported by the p-values. Indeed, given the p-values based on the asymptotic normal distribution, the null hypothesis of a unit slope cannot be rejected at the 1 per cent level for any of the estimators. At the 5 per cent level, there is one rejection, for the FM type within-estimator, while at the most liberal 10 per cent level, there are only two rejections, for both the within estimators. The results from the bootstrapped p-values are also supportive of the unit slope null for the between-estimates. 7 Because of limited space, the estimated intercepts and break dummies are not reported.

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Table 3. Panel cointegration slope estimates Method

Estimator

Value

p valuea

p valueb

Within

LS FM LS FM LS FM

0.781 0.853 0.859 1.064 206.774 202.625

0.052 0.033 0.259 0.106 0.000 0.000

0.000 0.000 0.637 0.129 0.002 0.003

Between Wald test

Note: All results allow for up to three structural breaks in the intercept for each state. The p values for the between and within estimates are for the null of a unit slope against the alternative that the slope is different from unity. The Wald tests are for the null of a homogeneous slope, not necessarily equal to one. a The p value is based on the asymptotic normal distribution. b The p value is based on the bootstrapped distribution. The number of lags in the sieve approximation is five and we made 1,000 bootstrap replications.

Thus, based on the p-values of the t-tests, it seems that the slopes can be regarded as homogeneous and equal to one, just as one would expect based on the present value model. Unfortunately, this is not what we observe when testing, in isolation, the null of homogeneous slopes. In order to carry out this test, the Wald approach was employed. The results, which are presented in the last two rows of Table 3, suggest that there is little support for the null of homogeneity, regardless of whether the asymptotic or bootstrapped p-values are used. Thus, we find that while the Wald tests reject the null of a homogeneous slope, the t-tests, especially the between-type tests, support the null of a homogeneous slope equal to one. Although this might seem strange at first, conflicting results of this kind are in fact very common in the empirical literature. For example, Baltagi et al. (2000) estimated the demand for cigarettes using a panel of US states. They found that, while the pooled estimates are well in line with theory, most of the heterogeneous estimates are economically implausible. Moreover, using the same Wald test approach as we do, the authors rejected the null hypothesis that the slopes are the same across the states. Despite the rejection, however, Baltagi et al. (2000) recommended pooling because, in addition to being economically more plausible, the pooled estimates are able to generate superior out-of-sample forecasts. That is, they argued that the superior forecast performance of the pooled estimates makes them more reliable. To check whether this is the case also in our panel, we undertook a similar out-of-sample forecasting exercise, in which we compared the restricted homogeneous, unit estimate with the heterogeneous state-by-state estimates. The forecast performance was measured in terms of the root mean squared prediction error, and we combined all the forecast errors in order to compute the root mean squared prediction error for the the heterogeneous estimates. We then computed one- and three-year-ahead forecasts for both the homogeneous and heterogeneous estimates. In both cases, the regressions were estimated without using the last three observations. The ratio of the

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homogeneous to the heterogeneous root mean squared prediction error was 0.9 for the one-year horizon and 0.88 for the three-year horizon.8 This means that the homogeneous estimates are in fact able to generate better forecasts compared to the heterogeneous estimates. Thus, adopting the stance of Baltagi et al. (2000), we conclude that the results favour a unit slope in the panel, and therefore also the present value model. Summarising this section, we find that farmland prices and cash rents appear to be cointegrated around a breaking intercept with a cointegrating slope equal to one. This leads us to the conclusion that the present value model cannot be rejected.

4. Concluding remarks Earlier results indicated that farmland prices and cash rents are non-stationary and non-cointegrated, a finding that seems directly at odds with the implications of the present value model. In fact, this is a quite common finding in the empirical literature on farmland prices, and although there are many theoretical explanations for these results, such as the presence of transaction costs, none has been very convincing. The results reported in this paper suggests that the inability to find a stable cointegration relationship between farmland prices and rents may be due to inadequate econometric methods. In particular, we argue that a failure to account for structural breaks and the poor precision of commonly applied time series tests are likely to result in a rejection of the present value model. To circumvent these problems, we exploited some recent advances in the area of non-stationary panel data in order to show that the present value model of farmland prices cannot be rejected, when a whole panel of data covering 31 US states between 1960 and 2000 is used and the possibility of structural breaks is also allowed for. Moreover, after controlling for breaks, consistent with the present value model, we found that a one per cent increase in the cash rents increases farmland prices by the same amount. We also provide some evidence suggesting that the estimated breaks may be partly attributed to changes in the required risk premium on farmland investments during the US farm financial crisis of the early 1980s. Of course, since farmland prices are affected by many factors, we recognise that this may not be the only explanation. We leave this important question as a potential avenue for further research. Another possible extension of this work involves determining to what extent various forms of government transfers to the agricultural sector are capitalised into the value of farm assets. The panel non-stationary analytical approach used in this paper provides a powerful framework within which these issues can be investigated. 8 In the interest of comparability, we did not compute any forecasts for longer horizons, as this would have consumed a disproportionate number of degrees of freedom for the heterogeneous estimates.

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Acknowledgements The authors would like to thank the editor and three anonymous referees for many valuable comments and suggestions. An earlier version of this paper was presented at the XI EAAE Congress on ‘The Future of Rural Europe in the Global Agri-Food System’ in Copenhagen, Denmark, and the Department of Agricultural and Food Economics at the University of Reading, United Kingdom. The authors thank the participants for their valuable comments and suggestions. Gutierrez gratefully acknowledges financial support from MIUR, and Westerlund thanks the Jan Wallander and Tom Hedelius Foundation for their financial support under research grant number W2006 –0068 : 1. The views expressed in this paper are those of the authors and do not necessarily represent the views or policies of the Economic Research Service or the US Department of Agriculture.

References Alston, J. M. (1986). An analysis of growth of U.S. farmland prices, 1963– 1982. American Journal of Agricultural Economics 68: 1 – 9. Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18: 1 – 22. Baltagi, B. H. (2005). Econometric Analysis of Panel Data. Chichester: John Wiley & Sons. Baltagi, B. H., Griffin, J. M. and Xiong, W. (2000). To pool or not to pool: homogeneous versus heterogenous estimators applied to cigarette demand. Review of Economics and Statistics 82: 117–126. Campbell, J. and Shiller, R. (1988). The dividend-price ratio and expectations of future dividends and discount factors. The Review of Financial Studies 1: 195– 228. Carrion-i-Silvestre, J. L., Del Barrio-Castro, T. and Lopez-Bazo, E. (2005). Breaking the panels: an application to GDP per capita. Econometrics Journal 8: 159–175. Clark, J. S., Fulton, M. E. and Scott, J. T. (1993). The inconsistency of land values, land rents and capitalization formula. American Journal of Agricultural Economics 75: 147– 155. De Fontnouvelle, P. and Lence, S. (2002). Transaction costs and the present value. Southern Economic Journal 68: 549– 565. Engsted, T. (1998). Do farmland prices reflect rationally expected future rents? Applied Economics Letters 5: 75 –79. Falk, B. (1991). Formally testing the present value model of farmland prices. American Journal of Agricultural Economics 73: 1 – 10. Falk, B. and Lee, B. S. (1998). Fads versus fundamentals in farmland prices. American Journal of Agricultural Economics 80: 696– 707. Gutierrez, L. (2006). Panel unit root tests for cross-sectional correlated panels: a Monte Carlo comparison. Oxford Bulletin of Economics and Statistics 68: 519– 540. Hanson, S. D. and Myers, R. J. (1995). Testing for a time-varying risk premium in the returns to U.S. farmland. Journal of Empirical Finance 2: 265– 276. Just, R. E. and Miranowski, J. A. (1993). Understanding farmland price changes. American Journal of Agricultural Economics 75: 156– 168. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? Journal of Econometrics 54: 159– 178.

Farmland prices, structural breaks and panel data

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Lence, S. H. and Miller, D. J. (1999). Transaction costs and the present value model of farmland, Iowa, 1900– 1994. American Journal of Agricultural Economics 81: 257– 272. Moss, C. B. and Schmitz, A. (2003a). Government Policy and Farmland Market. Ames: Iowa State Press. Moss, C. B., Shonkwiler, J. S. and Schmitz, A. (2003). The certainty equivalence of farmland values: 1910 to 2000. In C.B. Moss and A. Schmitz (eds), Government Policy and Farmland Markets: The Maintenance of Farmer Wealth. Ames: Iowa State Press. Newey, W. and West, K. (1994). Autocovariance lag selection in covariance matrix estimation. Review of Economic Studies 61: 613– 653. Pedroni, P. (2000). Fully modified LS for heterogeneous cointegrated panels. In B. H. Baltagi (ed.), Advances in Econometrics: Nonstationary Panels, Panel Cointegration, and Dynamic Panels. New York: JAI Press. Pesaran, H. (2004). General diagnostic tests for cross section dependence in panels. Cambridge Working Paper in Economics 435. Phillips, P. C. B. and Hansen, B. E. (1990). Statistical inference in instrumental variables regression with I(1) process. Review of Economics Studies 57: 99 – 125. Roche, M. J. and McQuinn, K. (2001). Testing for speculation in agricultural land in Ireland. European Review of Agricultural Economics 28: 95 – 115. Shiha, A. N. and Chavas, J. P. (1995). Capital market segmentation and U.S. farm real estate pricing. American Journal of Agricultural Economics 77: 397– 407. Tegene, A. and Kuchler, F. (1993) A regression test of the present value model of US farmland prices. Journal of Agricultural Economics 44: 135– 143. Westerlund, J. (2006). Testing for panel cointegration with multiple structural breaks. Oxford Bulletin of Economics and Statistics 68: 101– 132. Westerlund, J. and Edgerton, D. L. (2007). A panel bootstrap cointegration test. Forthcoming in Economics Letters.

Corresponding author: Luciano Gutierrez, Department of Agricultural Economics, University of Sassari, Via E. De Nicola 1, Sassari 07100, Italy. E-mail:[email protected]