What moves farmland markets: decomposing the price surge in eastern Germany

Abstract

Farmland prices have been surging worldwide; yet little is known about the particular strong surges in the upper quantiles of price distribution. We investigate by quantile how the composition of the farmland sales and agents’ valuation of land characteristics contribute to these price developments. Using farmland transactions from Brandenburg, Germany, we decompose the price surges between 2008–09 and 2017–18 by combining unconditional quantile regressions with propensity score reweighting. Our results show an increased valuation of land characteristics, e.g. soil quality, and their responsibility for about 25% of the price surges in the upper (>75%) quantiles of price distribution.

1. Introduction

Land is the key production factor for producing food, fuel and fibre. It is also an important component for climate change mitigation, given its high potential for carbon sequestration and for ensuring the climate regulating functions of the natural ecosystem. Thus, farmland and its value play a key role in the sustainable future of food systems. Moreover, incomes of rural areas and farms are directly related to farmland values, which thereby also concern the social dimension of sustainability. Under climate change and contested land resources, the growing importance and surging prices of farmland (Eurostat, 2021) have therefore triggered policy debates about market regulation (e.g. Jauernig, Brosig, and Hüttel, 2023). In particular, price caps have been proposed to protect local farmers from being priced out of the market. Price caps address the upper parts of the price distribution. Yet little is known about the magnitude and potential drivers of the upper quantiles—topics of this paper.

The surge in farmland prices has been attributed to various potential drivers. Some have pointed to rising commodity prices, which stimulate higher crop production profitability and thereby increase the valuation of farmland (Miao, Khanna, and Huang, 2016; Jouf and Lawson, 2022). Other researchers and policymakers blame the continuing spike in demand following the global financial crisis in 2008 as both agricultural and non-agricultural investors have been looking for hard assets as aids in managing portfolio risks or hedging against inflation (e.g. Olsen and Stokes, 2015; Clapp and Isakson, 2018). Other experts point to the promotion of renewable energy (RE), where fixed feed-in tariffs may capitalise into land values (e.g. Haan and Simmler, 2018; Ifft and Yu, 2021) or rental rates (e.g. Hennig and Latacz-Lohmann, 2017). Also, it has been argued that global trends of urbanisation limit the availability (supply) of farmland and intensify competition for scarce farmland, particularly at the rural-urban fringe (e.g. Guiling, Brorsen, and Doye, 2009; Zhang and Nickerson, 2015; Borchers, Ifft, and Kuethe, 2014). Climate change effects may also increasingly influence land values with ambiguous outcomes. For example, rising temperatures may have a positive (Chatzopoulos and Lippert, 2015; Ortiz-Bobea, 2020) or hill-shaped (Massetti and Mendelsohn, 2020) impact on returns. Negative effects may result from declining spring precipitation and the increasing likelihood of droughts (Lippert, Krimly, and Aurbacher, 2009).

In our study region of Brandenburg, Eastern Germany, the farmland price surge was particularly pronounced: prices more than doubled on average during the past two decades and even more than tripled in the upper price quantiles.¹ The aim of this paper is to disentangle what part of this price surge at the upper quantiles stems from changes in the land and regional characteristics of the plots traded (composition effect) and what part is due to altered valuations of these characteristics over time (pricing effect). In our empirical model, composition effects refer to changing characteristics (‘Xs’) over time, while pricing effects refer to changing regression coefficients (‘βs’) over time. We rely on farmland transaction data to answer this question and decompose the changes in upper quantiles of farmland prices between 2008–09 and 2017–18 in two steps. First, we run unconditional quantile regressions (Firpo, Fortin, and Lemieux, 2009) on transactions data from 2008–09 and 2017–18 at the 75, 90 and 95 per cent quantiles of the farmland price distribution. Second, we use the estimated coefficients of each characteristic together with propensity score reweighting to divide the changes in upper quantiles of farmland prices over time into a pricing effect and composition effect of each individual characteristic.

By analysing farmland values over time (see Deaton and Lawley, 2022: for an overview), using aggregated data, price developments were for instance decomposed into short- and long-run components (Falk and Lee, 1998). Using transaction or region-specific (aggregated) data in a hedonic regression framework (Nickerson and Zhang, 2014), changes in farmland prices over time can be attributed to changes in the land and regional characteristics (the regressors) or to altered valuations of given characteristics (the coefficients). Hanson, Sherrick, and Kuethe (2018), for instance, point to an increased valuation of agricultural productivity over time, while Buck, Auffhammer, and Sunding (2014) document a time-invariant positive valuation of water availability. Ortiz-Bobea (2020) finds that damages from extreme degree-days increased between 1950 and 2012 in the USA and that farmland valuation is less and less driven by soil quality. None of these papers, however, quantify the contribution of these factors to the observed price change within a decomposition.

Our paper examines the surge in the upper part of the price distribution and thus also contributes to the growing literature on the determinants of farmland prices away from the mean. By applying conditional (on the model covariates) quantile regressions, for instance, effects of higher off-farm income (Mishra and Moss, 2013), natural amenities (Uematsu, Khanal, and Mishra, 2013), relative population change and loss of utilised agricultural area (Lehn and Bahrs, 2018b) on farmland price quantiles have been documented. Different effects at the upper part of the conditional distribution are also reported for the rental rate distribution (März et al., 2016). Time effects were typically captured by dummy variables and represent ceteris paribus effects for a given quantile, indicating a potential outward or inward shift of the price distribution over time.

Conditional quantile regressions, however, are not suitable for our aim—to decompose the observed increase in a given quantile into a pricing and a composition effect. This is because the conditional quantiles do not average up to the corresponding unconditional quantile. We therefore base our approach on an unconditional quantile regression, which is the first step of the decomposition method developed by Firpo, Fortin, and Lemieux (2018) (hereafter FFL) as a generalisation of the well-known Oaxaca–Blinder (OB) decomposition (Blinder, 1973; Oaxaca, 1973) of a difference in means. In contrast to the alternative quantile decomposition procedures (DiNardo, Fortin, and Lemieux, 1996; Machado and Mata, 2005; Melly, 2005; Chernozhukov, Fernandez-Val, and Melly, 2013), the FFL approach has the advantage of allowing us to explicitly quantify the individual contribution of each land and regional characteristic to the pricing and composition effects, respectively. While this type of decomposition analysis of price changes over time has been applied to the housing market (McMillen, 2008; McMillen and Shimizu, 2021), to our knowledge, this paper is the first to apply it to farmland markets.

Our results show that hedonic land characteristics such as soil quality are even more valuable at the upper part of the distribution than at the mean. The increased valuation has further increased over our study period, leading to the pricing effects that have been driving the surge. Rather than capping prices or excluding buyer groups, we recommend fostering transparency in the farmland market as a potential remedy for potential overbidding (Humpesch et al., 2022; Seifert and Hüttel, 2023).

Our paper contributes in several ways: first, we decompose farmland price increases by quantile using a novel approach in this field of literature. Second, we add to the scientific discussion by quantifying the specific contributions of individual land and regional characteristics to the surge in the upper quantiles. By this, we can identify main drivers for our study region. Based on the unconditional quantile regressions, we also enhance the literature on the determinants of farmland prices away from the mean.

The remainder of this paper is organised as follows. Section 2 explains the methodology. Section 3 describes Brandenburg’s farmland market and the dataset. Section 4 discusses the empirical results. In Section 5, we discuss our findings and conclude.

2. Methodology

As a starting point of our analysis, Figure 1 shows kernel density estimates of our dependent variable, price per square metre for our two periods of study.² Note that the price distribution moves towards higher prices. This is demonstrated here by the difference in the 90 per cent quantiles (marked by the dashed vertical lines) of the two distributions. The aim of the paper is to decompose this outward shift of the upper quantiles, which we also investigate for the τ = 75 and τ = 95.

2.1. Aggregate decomposition

We let |$Q_{08\_09}(\tau)$| and |$Q_{17\_18}(\tau)$| denote the τ-th quantile of the population land price distribution in 2008–09 and 2017–18, respectively. We focus on their difference |$Q_{17\_18}(\tau)-Q_{08\_09}(\tau).$| Our aim is to decompose this difference into two components: (1) the part solely attributable to the difference in distribution of the characteristics of the plots and (2) the part solely attributable to different valuation of a given characteristic in the two periods. Part (1) should capture, for instance, if plots traded in 2017–18 were of better quality on average than those in 2008–09. We denote the resulting component of the quantile difference as |$\Delta^{\tau}_{\text{characteristics}}$| and refer to it as the ‘composition effect’. Part (2) should capture if, for instance, plots of a given quality were valued more in 2017–18 than in 2008–09. We denote the resulting component of the quantile difference as |$\Delta^{\tau}_{\text{pricing}}$| and refer to it as the ‘pricing effect’. We formulate the decomposition of the quantile difference as

Even though our dataset contains measures of several important characteristics for each plot, invariably, other characteristics remain unobserved. Like most empirical studies, we thus invoke an ignorability assumption: that the distribution of unobservable characteristics does not differ between 2017–18 and 2008–09 for each given combination of observable characteristics |$X.$| In particular, this assumption rules out that |$\Delta_{\text{characteristics}}$| is driven by differences in the composition of unobserved characteristics between plots in the two periods. Accordingly, we rewrite the decomposition as

where

Here, |$\Delta^{\tau}_{X}$| is the component of the quantile difference due to differences in the distribution of observable characteristics X between both periods. |$\Delta^{\tau}_{S},$| on the other hand, presents the ‘structural’ part of the quantile difference due only to changes in the valuation of given characteristics. To achieve strict separation between the contributions of X and |$S,$|  |$\Delta^{\tau}_{X}$| and |$\Delta^{\tau}_{S},$| we compare |$Q_{17\_18}(\tau)$| and |$Q_{08\_09}(\tau),$| the quantiles of the actual price distributions in 2017–18 and 2008–09, to |$Q_{C}(\tau)$|⁠, the τ quantile of a counterfactual distribution. It is the distribution of prices that would have prevailed under the pricing structure of 2008–09, but with the distribution of characteristics in 2017–18 (see Appendix B.1 and Appendix C.1 for details). Identification of this counterfactual distribution from the available data will be discussed later.

2.2. Detailed decomposition

Our aim is to not only decompose the quantile difference |$Q_{17\_18}(\tau) - Q_{08\_09}(\tau)$| into the two aggregate components |$\Delta^{\tau}_{X}$| and |$\Delta^{\tau}_{S}.$| We would also like to quantify the contribution of individual characteristics to these components such as estimating what part of |$\Delta^{\tau}_{X}$| is due to plots traded in the two periods having different average soil quality or what part of |$\Delta^{\tau}_{S}$| is due to plots with a given soil quality being differently valued in the two periods.

To quantify the specific contribution of each characteristic to |$\Delta^{\tau}_{X}$| and |$\Delta^{\tau}_{S}$|⁠, we make the following linearity assumption about the relationship between observable characteristics and the prices:

where the vectors |${\beta}_{j}, j \in \{{17\_18},{08\_09}\}$| collect the coefficients in 2017–18 and 2008–09, respectively. Linearity is sufficient to yield a detailed composition in the form of the well-known OB decomposition of the difference in the means of both distributions:

with

where |$E[\mathbf{x}|{17\_18}]$| and |$E[\mathbf{x}|{08\_09}]$| denote the vectors of average characteristics in 2017–18 and 2008–09.

We estimate the coefficient vectors by running separate least squares regressions of prices Y on the set of characteristics x in both subsamples, yielding |$\hat{\beta}_{17\_18}$| and |$\hat{{\beta}}_{08\_09}$|⁠, and we replace the population averages of prices and characteristics in (3) and (4) by sample averages to obtain the estimated OB decomposition:

with

where the right-hand sides of (5) and (6) show how contributions of individual characteristics to |$\hat{\Delta}^{\mu}_{X}$| and |$\hat{\Delta}^{\mu}_{S}$| are estimated. To illustrate, if X_k is soil quality, we compute its contribution to |$\hat{\Delta}^{\mu}_{X}$| by taking the difference in average soil quality in 2017–18 and 2008–09, weighted by the estimated coefficient of soil quality in 2008–09, and compute its contribution to |$\hat{\Delta}^{\mu}_{S}$| by taking the difference in its estimated coefficients in 2017–18 and 2008–09, weighted by its sample average in 2017–18. We estimate and use this OB decomposition at the mean as a point of reference for the quantile results, which are the focus of our paper.

For quantiles, the decomposition takes the following form:

where |${\gamma}^{\tau}_{08\_09},$|  |${\gamma}^{\tau}_{17\_18}$| and |${\gamma}^{\tau}_{C}$| are coefficient vectors and R^τ is a remainder term defined as |$R^{\tau}=E[\mathbf{x}|{17\_18}]^{T} \{{\gamma}^{\tau}_{C}-{\gamma}^{\tau}_{08\_09}\}$|⁠. There are three differences in the OB decomposition defined earlier: (i) the coefficient vectors will not be obtained by regressing prices on characteristics but rather by using a transformation of prices as the dependent variable known as the Recentred Influence Function; (ii) the quantile decomposition requires to explicitly estimate coefficients |${\gamma}^{\tau}_{C}$| in the counterfactual situation that would have prevailed under the pricing structure of 2008–09, but with the distribution of characteristics in 2017–18; and (iii) the composition effect |$\Delta^{\tau}_{X}$| includes the remainder term |$R^{\tau}.$| Each of these issues will be explained in the following paragraphs.

The need in the quantile case to work with transformed prices is due to the fact that for quantiles, there is no equivalent to the law of iterated expectations (LIEs). The LIE is underlying the OB decomposition at the mean because it provides a simple connection of the unconditional means on the left-hand side of the decomposition to the conditional means of Y given X on the right hand side. However, in the quantile case, Firpo, Fortin and Lemieux (2018) (hereafter FFL) have shown that an equivalent formula holds for a transformation of Y, the recentred influence function (RIF). The RIF transformation is defined as follows:

where |$I(\bullet)$| denotes the indicator function and f_Y denotes the density of prices evaluated at the |$\tau-$| quantile. For a given |$\tau,$| constructing RIF-transformed prices thus requires estimating the desired quantile |$Q_{j}(\tau)$| from the price distribution, checking whether the price of a particular observation is below the quantile (⁠|$I(y\leq Q_{j}(\tau))$|⁠) and using kernel density estimation to estimate |$f_{Y}(Q_{j}(\tau)),$| the value of the price density at the particular quantile.³

Once we have computed RIF-transformed values of all prices and thus constructed the transformed dependent variables |$RIF(Y_{j,i},\tau)$| we relate them to the observed characteristics via the following regressions:

We refer to them as the RIF regressions. They are the equivalent of (2) in the OB decomposition, except that they postulate that the characteristics linearly relate to RIF-transformed prices in both periods. We estimate their coefficients by least squares. They can be interpreted as the effect of a change in the respective characteristic on the unconditional quantile of interest (see Firpo, Fortin, and Lemieux, 2009).

The structural component |$\Delta^{\tau}_{S}$| of the quantile decomposition includes |${\gamma}^{\tau}_{C},$| the coefficient vector from the counterfactual situation that would have prevailed under the pricing structure of 2008–09, but with the distribution of characteristics in 2017–18. In the OB decomposition at the mean, there is a straightforward solution to the counterfactual situation that simply combines averages from 2017–18 with coefficients from 2008–09. For quantiles, this shortcut is not available and |${\gamma}^{\tau}_{C}$| needs to be inferred from the following counterfactual RIF regression:

We estimate |${\gamma}^{\tau}_{C}$| by using the data from 2008–09 but reweighting observations such that a characteristic’s distribution as in 2017–18 is achieved. The resulting weighted least squares is defined as

The weights |$\hat{w}_{C}(\mathbf{x}_{i})$| are based on the estimated probability that an observation with characteristics x_i belongs to the 2017–18 period group and are defined as

where |$p(\mathbf{x}_{i})$| denotes this ‘propensity score’. We estimate the propensity score |$p(\mathbf{x}_{i})$| from a logit model that relates a 2017–18 indicator to all explanatory variables and calculate the weights |$\hat{w}_{C}(\mathbf{x}_{i})$|⁠.⁴

Finally, we combine the estimated coefficient vectors from the RIF regressions with the sample averages of characteristics to obtain the elements of the following estimated FFL decomposition:

Comparing equations (12) and (13) of the FFL decomposition to the corresponding equations (3) and (4) from the OB decomposition illustrates their basic similarity. First of all, both provide an overall answer to the question of whether the observed price increase (at the mean or |$\tau-$|quantile) is due to changing characteristics (‘Is it the X?’) or changing coefficients (‘Is it the β?’), in the form of |$\hat\Delta_{X}$| and |$\hat\Delta_{S}$| on the left-hand sides. Second, in the terms on the right-hand side, they also quantify how much each individual variable is contributing to both the overall composition effect and the pricing effect on the left.

We close this section, by using equations (12) and (13) to highlight the main difference to an alternative approach that would also estimate a separate regression in each time period in order to explore the changing patterns of coefficients but without subjecting them to a decomposition calculation. The key advantage of a decomposition approach is that each coefficient difference |$\hat{\gamma}^{\tau}_{\text{k,17\_18}}-\hat{\gamma}^{\tau}_{\text{k,C}}$| is ‘weighted’ by the average level of the variable in the second period (⁠|$\bar{X}_{k,17\_18}$|⁠) to precisely give a variable’s contribution to the pricing effect |$\hat\Delta_{S}.$| Similarly, each difference in average levels of a characteristic |$\{\bar{X}_{k,17\_18}-\bar{X}_{k,08\_09})$| is ‘weighted’ by the base period coefficient |$\hat{\gamma}^{\tau}_{k,08\_09}$| to precisely yield a variable’s contribution to the composition effect |$\hat\Delta_{X}.$| Finally, in this more coherent and structured approach, the pricing and composition effects exactly add up to the quantile increase that was the starting point of the analysis.

2.3. Robustness analysis

The FFL decomposition relies on the assumed linearity of the RIF regressions both in its aggregate and individual forms. We investigate the viability of the linearity assumption at both levels: (i) by using an estimator of the aggregate decomposition that is not built from the RIF regressions and their assumed linearity and (ii) by estimating the RIF regression as a probability model that does not impose linearity on the data.

For the aggregate decomposition of equation (1), an alternative estimator has been proposed that does not aim at also delivering an individual decomposition and thus does not use (linear) RIF regressions at all. It is directly built on the basic definitions of the aggregate decomposition in equation (1), where only the counterfactual quantile |$Q_{C}(\tau)$| presents a challenge for estimation. Firpo, Fortin, and Lemieux (2018) have shown that under the ignorability assumption the cumulative distribution function (cdf) of the counterfactual distribution of prices that would have prevailed under the pricing structure of 2008–09 but with the distribution of characteristics in 2017–18 can be estimated if the observations from 2008–09 are reweighted by the propensity score:

Here, |$D_i=1$| for observations from 2017 to 2018 and zero otherwise and |$\hat{p}$| is the sample fraction of observations from 2017 to 2018. From this cdf, any τ quantile can be obtained, yielding |$\hat{Q}_{C}(\tau).$| Because this reweighting procedure had first been proposed by DiNardo, Fortin, and Lemieux (1996), we refer to the resulting decomposition as the DFL approach:

As these component estimators are not built on RIF regressions, comparing them with their counterparts from (12) and (13) amounts to a specification test of the linearity assumption of the RIF regression approach from an aggregate perspective.

To assess the linearity assumption at the level of individual characteristics, we use the fact that in the case of quantiles, the conditional expectations of RIF-transformed prices are equal to the conditional probability of a farmland’s price to be above a respective quantile of interest, rescaled by a factor and recentred by a constant (see Firpo, Fortin, and Lemieux, 2009). That is

where |$c_{1,\tau}=1/f_y(Q(\tau))$| and |$c_{2,\tau}=Q(\tau)-c_{1,\tau} \cdot (1-\tau)$|⁠. The RIF regressions assume that the left-hand side of (16) is a linear function of the characteristics (i.e. |$E[\text{RIF}(Y, Q(\tau)) | X=x]={\gamma}^{\tau}\mathbf{x}$|⁠): Using this assumption and rearranging gives

The RIF regressions can thus be seen as assuming a linear model for the conditional probability of a farmland’s price to be above a quantile of interest.

As an alternative, we use the backfitting algorithm (see Hastie and Tibshirani, 1990) to estimate the following additive, non-parametric model of this conditional probability:

where no particular functional form for the component functions |$m_k(X_{k})$| is assumed. For any characteristic k, the estimated linear component estimate from (17) can then be compared to its non-parametric alternative |$\hat{m}_k(x_{k}).$|

3. Empirical approach

3.1. Background

Brandenburg is a federal state located in northeastern Germany, covering a total area of 2,965,416 ha. Eastern Germany has experienced the same sharp increases in farmland prices observed in other post-socialistic European countries (Ciutacu, Chivu, and Vasile, 2017). Figure 2 (left) shows the moving averages of quarterly farmland prices from 2000 through 2018.

Historically, expropriation, land collectivisation and socialist policies shaped its agricultural structure and farmland market (cf. Wolz, 2013; Lerman, 2001). After reunification in 1990, Bodenverwertungs- und Verwaltungs GmbH (BVVG) began to privatise and manage substantial amounts of restituted land on behalf of the Federal Ministry of Finance. In 2007–08, BVVG started to conduct first price, sealed bid auctions with public tenders, offered special tenders for young and organic farmers and sold directly to former owners and tenants (Balmann et al., 2021). Between 2008 and 2018, BVVG sold 35 per cent of the total transacted land in Brandenburg. In 2022, privatisation ended, and BVVG now leases only to organic farms to meet federal initiatives for promoting organic farming.

Brandenburg’s agricultural land covers roughly 1,323,500 ha, with an average of 1.6 per cent being traded annually between 2008 and 2018 (Amt für Statistik Berlin-Brandenburg, 2020). Figure 2 (right) shows that the observed farmland transactions are widely distributed over the entire study region for both time periods. All land transactions continue to need approval by local authorities of the federal state. Reasons for denial may include a transaction’s price level, i.e. if assessed as far too high compared to the average local levels provided by Oberer Gutachterausschuss im Land Brandenburg (local committee of land valuation experts). A non-local buyer may be denied if the committee determines that the land supports local farming and a local farmer-buyer is willing to match the non-local buyer’s offer. In our study region, we observe intense debates about tightening regulation intensity to protect local farmers. This has resulted in two regulatory initiatives, released in 2019 and 2023, respectively (Jauernig, Brosig, and Hüttel, 2023; MLUK Brandenburg, 2023), but both failed to achieve the necessary implementation majorities.

Like many countries, Germany has been subsidising RE production (Renewable Energy Act, first implemented in 2000) through, among other measures, fixed feed-in tariffs for RE from wind, solar and biogas. Particularly, the subsidised biogas production alters the return structure from using the land (level and risk) and thus affects land price formation. By 2019, our study region achieved about two-thirds of the state’s electricity consumption from renewable sources (Schill, Diekmann, and Püttner, 2019).

Large, cash crop-oriented commercial farms characterise Brandenburg’s agricultural sector. The average farm size increased from 200 ha in 2008 to 249 ha in 2018, and the number of farms decreased from 6,624 in 2008 to 5,320 in 2018, respectively (Amt für Statistik Berlin-Brandenburg, 2010; Amt für Statistik Berlin-Brandenburg, 2020). The major cultivated crops were rye (22 per cent, 16 per cent of arable land in 2008 and 2018, respectively), maize (13 per cent, 20 per cent), wheat (14 per cent, 17 per cent) and oil seeds (14 per cent, 13 per cent) (Destatis, 2008; Destatis, 2018). The substantial increase in maize cultivation can in fact be attributed to RE policy and farms investing or delivering to biogas operations.

During our study period, the European Union’s Common Agricultural Policy (CAP) underwent fundamental reforms. We cover the later years of the Fischler reform (2003), funding period 2004–2013, and the later years of the greening reform (2013), funding period 2013–2020. After the Fischler reform, where Germany opted for a hybrid model with a phasing-out of coupled payments, farms faced increasing price risk. Biogas operations can provide lower-risk returns for farming and potentially increase a buyer’s willingness to pay (Towe and Tra, 2013; Haan and Simmler, 2018). The capitalisation of the direct payments on land values was noted as small and non-robust across the European Union (Baldoni and Ciaian, 2023). Initial evidence on the capitalisation of the latter policy (greening) also suggests overall small effects, including on farm performance (Varacca et al., 2023). Despite the interesting question of whether CAP-related capitalisation rates altered over time, studying one region in Germany means insufficient cross-sectional variation in the payments for empirical identification.

3.2. Data

We collect 9,861 transactions in 2008–09 and 2017–18 provided by Oberer Gutachterausschuss im Land Brandenburg. This committee is mandated by law to request and collect information on all farmland transactions in Brandenburg. For each transaction, we use plot size, contract date, price and location (geographical coordinates), federal characteristics (Germany’s official soil quality index combines pedologic, scientific and agro-economic considerations within one measure for arable land and grassland), regional characteristics (variables describing the local land market’s micro-structure) and agent type (professional or private seller, farmer or non-farmer buyer) (see Balmann et al. (2021) for the details).

We limit the present study to arms-length transactions by removing 2,225 transactions with missing values for the relevant variables (the numbers in parentheses denote the total amount of observations removed when we do not delete previous observations): 1,195 (1,195) plots not designated for agricultural uses after transaction; 588 (632) with unusual or personal relationships among the transaction parties; 275 (312) that are not purchases; 106 (168) with missing or declared, unusual price origins; 27 (33) package sales; 4 (4) with a price of zero; 0 (4) with a plot size of zero; 4 (15) with missing information on soil quality; and 26 (26) with missing values for the relevant variables from the merged data. We use a second outlier detection based on the minimum covariance determinant estimator (Rousseeuw and van Driessen, 1999) to delete another 217 observations (see Appendix Table A.1 for details). Our final dataset contains 5,003 and 2,416 arms-length arable farmland transactions in 2008–09 and 2017–18, respectively.

3.3. Hedonic pricing model

To investigate the quantile-specific price increases between the two periods, we use a hedonic pricing approach (Rosen, 1974) typically used in farmland price analyses (Nickerson and Zhang, 2014; Seifert, Kahle, and Hüttel, 2021). Per square metre prices are modelled as a function of land and regional characteristics, including the market micro-structure.

Land characteristics

Land characteristics include plot size and Germany’s official soil quality index. Low (high) numbers indicate low (high) productivity (Deutscher Bundestag, 2007). A higher soil quality index thus indicates higher expected returns. Therefore we expect positive effects across all price quantiles.

Larger plots may be valued higher due to the potential of economies of size related to farm machinery use and land management (Ritter et al., 2020). However, also smaller lots may be attractive, for instance, if property boundaries can be realigned or because they offer opportunities for non-agricultural land uses such as recreational farming (Brorsen, Doye, and Neal, 2015). This is why plot size and soil quality are often modelled in a flexible manner in hedonic regressions (Seifert, Kahle, and Hüttel, 2021; Humpesch et al., 2022). Given the limitations to model non-linearities in the decomposition approach, we restrict our attention to net pricing and composition effects on the respective price quantile.

Market micro-structure

The immobility of land makes each transaction unique, and markets appear thinly traded (Bigelow, Ifft, and Kuethe, 2020). In the recent decade, less than 2 per cent of the farmland in our study region was transacted on average per year. This is why we include the regional market micro-structure in the price function (Balmann et al., 2021; Piet, Melot, and Diop, 2021; Seifert, Kahle, and Hüttel, 2021). For instance, different types of buyers and sellers face different search, information and bargaining costs (Harding, Knight, and Sirmans, 2003; King and Sinden, 1994). Agents with lower search and bargaining cost, i.e. preferable bargaining position, may achieve a price markup or markdown (Balmann et al., 2021; Curtiss et al., 2021), noted as price dispersion for the same fundamental (Seifert, Kahle, and Hüttel, 2021). We therefore consider variables indicating buyer and seller types, because each type may reflect different information costs. For instance, farmers may benefit from better knowledge of current and potential sales and the competition in the market or from a special relationship such as that between the seller and the current tenant (Perry and Robison, 2001; Taylor and Featherstone, 2018), thereby negotiating a price markdown (Balmann et al., 2021; Curtiss et al., 2021).

On the buyer side we distinguish former tenants, farmers and non-agricultural buyers. On the seller side, we use indicator variables to distinguish between sales by BVVG using public tenders, professional real estate agents and private sellers, where we expect private sellers to suffer most from information disadvantages and highest search cost finding buyers with the maximum willingness to pay. We are interested in composition and pricing effects related to these variables by quantile and not in identifying the relation of information deficiency and buyer/seller types. We thus restrict our attention to average impacts of information deficiency in either direction that can be captured by these indicators (Kumbhakar and Parmeter, 2009; Kumbhakar and Parmeter, 2010).

Regional characteristics

To account for price effects due to agro-climatic conditions we add regional long-run precipitation and short-term soil moisture information. For each transaction, we project the central coordinate of a plot on to a 1-km raster of publicly available precipitation data and extract the mean yearly precipitation in the 30 years prior to the transaction (DWD, 2018). Because yield potential and its stability can be subject to climate change (e.g. Ortiz-Bobea, 2020) and transaction parties could pay particular attention to the short-term weather conditions in a region (Tabetando et al., 2023), we additionally consider a drought indicator. This indicator comprises the number of months with a drought during the 3 years prior to a transaction according to a soil moisture index.⁵

To reduce bias from omitted variables, we add spatial dummy variables that absorb the price effect of spatially clustered omitted variables (Kuminoff, Parmeter, and Pope, 2010). We include a county dummy variable for each of the 18 counties in Brandenburg, with the exception of the reference county.

For the potential effects of urbanisation due to urban sprawl and the potential demand effects for alternative land uses (Sklenicka et al., 2013; Delbecq, Kuethe, and Borchers, 2014; Zhang and Nickerson, 2015), we use car travel time from each plot to Berlin’s central business district (CBD).⁶

To account for the regional-specific effects related to subsidised RE production from biogas, we use the municipal-level data on installed biogas capacity in kilowatts per hectare (Bundesnetzagentur, 2020).

3.4. Preliminary analysis

Table 1 lists the summary statistics of the 13 variables for 2008–09 and 2017–18. A particular focus in our decomposition analysis lies on the change in the means of characteristics over time. While the plots traded in 2017–18 did not have better soil quality or different sizes on average than those traded in 2008–09, we found that other variables, e.g. the fraction of plots sold by BVVG and the share of BVVG transactions in the 3 years prior to a transaction, substantially decreased by about 50 and 42 per cent, respectively. Two-sample t-tests on a significance level of 1 per cent for each variable suggest statistically different means for all variables except for the soil quality index, log of plot size, the share of agricultural area and car travel time to Berlin. The summary statistics only give a starting point. To understand what drives increases in farmland prices, a joint investigation of prices and related land and regional characteristics is necessary.

4. Results and discussion

4.1. Aggregate decomposition

Table 2 reports the results of our aggregate decomposition. Comparing quantiles in the right tail of the price distribution with τ = 75, τ = 90 and τ = 95, respectively, reveals that, regardless of the position, pricing effects dominate observed price increases between 2008–09 and 2017–18. As the quantile differences increase, so does |$\hat\Delta^{\tau}_{S,\text{FFL}}.$| Finding that the composition effect plays virtually no role suggests that we can rule out differently characterised plots and regions as major sources of price increases. The very small remainder term |$\hat{R}^{\tau}$| in all instances indicates the adequacy of our linear RIF regression specification.

4.2. RIF regressions

Table 3 reports the results of our RIF regressions for observations of 2008–09 and 2017–18. Since a change in coefficients between the RIF regressions in the two periods (see Equation (13)) reflects an increase in valuation (pricing effect), we start with the coefficient estimates of the RIF regressions.

As a point of reference, Table 3 lists the standard ordinary least squares (OLS) coefficients for the regression at the mean. We interpret all coefficients as the effect of a location shift in the respective land and regional characteristic (X-variable) on the unconditional mean or quantile of interest (Firpo, Fortin, and Lemieux, 2009). For instance, consider the estimated regression coefficients for soil quality in 2008–09. If there is a positive location shift of the distribution of soil quality by 10 index points, the unconditional mean of farmland prices would increase by approximately 0.042€/m² and the unconditional upper quantiles would increase by approximately 0.052–0.080€/m².

Table 3 lists the positive effects across all regressions of soil quality (cf. Nilsson and Johansson, 2013; Hüttel, Wildermann, and Croonenbroeck, 2016), plot size (cf. Nilsson and Johansson, 2013; Lehn and Bahrs, 2018b), plots sold within public tenders (Peeters, Schreurs, and van Passel, 2017; Balmann et al., 2021), share of utilised agricultural area (Lehn and Bahrs, 2018a) and share of transactions by BVVG in 2017–18 (Seifert, Kahle, and Hüttel, 2021) on farmland prices at the mean and the upper quantiles. Both car travel time to Berlin’s centre and months of drought prior to a transaction in 2017–18 show negative effects, as in Sklenicka et al. (2013) and Seifert, Kahle, and Hüttel (2021), respectively. For the remaining variables, the implied interval estimates firmly cover the ‘no effect’ value of zero (see Appendix Table D.2).

The effects at the quantiles show similar signs for most variables as those at the mean. However, the magnitude of the effects generally gets larger as we move along the distribution towards the upper tail. Focusing on OLS estimates at the mean would therefore tend to mask this pattern of increasing effects and would underestimate the impact that characteristics have at the upper quantiles of farmland prices (cf. Peeters, Schreurs, and van Passel, 2017). For instance, the price increasing effects of soil quality and plot size are more pronounced in the high-price segment of the land market during both time periods. This suggest that, while holding other factors constant, there is an upward shift in the upper quantiles of farmland prices for plots with higher soil quality (larger plot size) relative to plots with lower soil quality (smaller plot size), with a larger shift at the upper end of the distribution. We also observe this pattern for plots sold by BVVG and those located in regions with higher shares of utilised agricultural area, shorter travel times to Berlin’s CBD and lower numbers of months of drought (in 2017–18).

4.3. Detailed decomposition

Table 4 lists the detailed decomposition of Equations (12) and (13) (see Appendix Table E.1 for counterfactual RIF regressions). The upper part shows the individual contributions to the aggregate pricing effect |$\hat\Delta^{\tau}_{S}$| for each characteristic, and the lower part shows the contributions to the aggregate composition effect |$\hat\Delta^{\tau}_{X}.$| The second column of Table 4 shows the results of an OB decomposition at the mean serving as reference for the reweighted RIF decompositions at the upper quantiles.⁷

Pricing effects

There are several variables (soil quality, plot size, plots sold by BVVG, share of utilised agricultural area and share of BVVG transactions) with pronounced positive pricing effect estimates. For these variables, the implied interval estimates are strictly positive at the mean and for most or even all quantiles (see Appendix Table D.1). This means that, for comparable plots, their positive coefficients in the RIF regressions (i.e. their unconditional quantile effects) are larger in 2017–18 than in 2008–09, leading to an overall positive pricing effect throughout the upper quantiles of the price distribution. To gauge their size, we interpret these pricing effects relative to the total price increase. To illustrate, the estimated contribution of soil quality to the pricing effect at the 75 per cent quantile (0.1815) amounts to 20 per cent of the total price increase (0.93, see Table 2). Towards the top end of the price distribution, these pricing effects roughly increase in proportion to total price increases.

Table 4 implies that the contributions of the increased valuation of soil quality relative to the total price increase are 21 per cent for the mean and 20, 11 and 30 per cent for the upper quantiles. However, these relative contributions of about one fifth on average are compatible with a wide range of possible contributions: the implied confidence intervals range from 12 per cent to 30 per cent for the mean and from 5 to 55 per cent for the 95 per cent quantile. One explanation for the increased valuation of soil quality may be attributable to climate change and the resulting increases in the valuations of higher-quality plots with higher field capacity potential. Compared to other federal states, Brandenburg has a lower percentage of high-quality land, and areas with less favourable soils already face more drought risk (Grundmann and Klauss, 2014). Investing in higher-quality farmland could therefore be a production risk mitigation strategy of farmers and could have intensified demand particularly for highly productive farmland. According to Hanson, Sherrick, and Kuethe (2018), the strong increase in crop prices during their investigated period (2000–10) was advantageous for highly productive farmland, where high-quality crops such as wheat are typically grown. However, as crop prices remained relatively stable during our study period (Eurostat, 2024), this explanation does not apply in our case.

The contributions of the increase in valuations of plot sizes relative to the increase in total prices are 5 per cent for the mean and 7, 5 and 4 per cent for the upper quantiles. Larger plots may offer higher returns due to increased economies of scale (see Seifert, Kahle, and Hüttel, 2021) over time.

The contributions of the increase in price markups of plots sold by BVVG relative to the increase in total prices are 5 per cent for the mean and 4, 5 and 7 per cent for the upper quantiles. This may indicate that price markups in auctions compared to other sales mechanisms, such as private bargaining, have increased over time. This could relate to learning effects, but could also indicate trends towards potential overbidding (Seifert and Hüttel, 2020), or point to anchoring effects in bidding behaviour, given that BVVG publishes regularly most recent auction results (Holst, Hermann, and Musshoff, 2015). Positive pricing effects of the share of BVVG transactions of 4–9 per cent support the idea of increased market transparency and more competitive prices (Curtiss et al., 2021). For instance, reduced information gathering, search and even bargaining costs may have reduced bargaining power imbalances.

Positive pricing effects of the share of utilised agricultural area indicate that the price markups due to scarcity of land in a given region increased over time, supporting the previous argumentation. Related to that, we find an increased discount of prices with increasing car travel time to Berlin. That is, the relative value placed on the accessibility regarding Berlin increased over time. This suggests an increased competition for scarce farmland near Berlin for residential, commercial or infrastructural use, contributing further to overall scarcity of fertile farmland.

Plots located in regions affected by droughts prior to a transaction have larger price discounts in 2017–18 compared to similar plots in 2008–09. As a result, we find negative pricing effects across the upper half of the price distribution. These negative pricing effects indicate that, without the altered perception of drought events, price increases in the upper quantiles would have been 24, 5 and 6 per cent larger. This suggests that the sensitivity of market agents towards droughts increase. However, the implied confidence intervals for the 90 and 95 per cent quantiles are compatible with an effect in the opposite direction. The growing sensitivity towards droughts may stem from an increased awareness, possibly influenced by a heightened frequency and duration of drought periods in Brandenburg in the last two decades (Markonis et al., 2021). It provides indirect evidence of the effects of a changing climate on land values, aligning with findings in several studies (e.g. Ortiz-Bobea, 2020; Chatzopoulos and Lippert, 2016; Massetti, Mendelsohn, and Chonabayashi, 2016).

Composition effects

Most of the individual contributions to the composition effect reported in the lower panel of Table 4 are small and economically irrelevant. Moreover, their implied interval estimates generally cover the no-effect value of zero (see Appendix Table D.1). Individual composition effects reflect the change in averages of a characteristic over time. For most characteristics, the 2008–09 averages are close to the 2017–18 averages (see Table 1), which might explain the small size of these effects.

The main exception are the variables pertaining to the activity of the privatisation agency BVVG. For the variable indicating a sale by BVVG, we find a composition effect of about −4 per cent for the upper quantiles of the price distribution. The negative sign can be explained by the drop in the fraction of plots sold by BVVG from 28 per cent in 2008–09 to 14 per cent in 2017–18. Its size, though, is small because this change in means is weighted by relatively small effects of the variable in 2008–09. For the variable measuring BVVG’s regional transaction share, the implied interval estimate of the composition effect is not only strictly positive at the mean and at τ = 90 and τ = 95 but also small in size (see Appendix Table D.1). It is positive, despite the reduction in the average regional transaction share of the BVVG from 2008–09 to 2017–18, because it is counteracted by the negative estimated effect of the variable in 2008–09.

4.4. Robustness analysis

Both our aggregate and detailed decomposition results are derived from the linear RIF regressions. The results of our two robustness checks regarding the linearity assumption are as follows.

At the aggregate level, we compare our results of the FFL approach with those of the DFL approach, which does not use RIF regressions (see Appendix Table F.1). The comparison shows only small deviations between the FFL and DFL results.⁸

To assess the assumed linearity of the RIF regressions at the level of individual variables, we compare them to non-parametric estimates of the component functions of the variables. Although the non-parametric estimates do not allow us to calculate a detailed decomposition as listed in Table 4, they are useful for gauging the assumed linearity. For example, Figure 3 illustrates our variable-specific robustness with the component function estimates for soil quality in 2008–09.

Each panel shows the non-parametric estimates |$\hat{m}_k(x_{k})$| as a dashed line, where x_k denotes soil quality, the corresponding 95 per cent confidence intervals are given as a grey area, and the linear estimate |$\hat{\beta}_{k}x_{k}$| is given as a black line.⁹ The estimated impact of soil quality on |$ \text{Pr}[Y\gtQ(\tau) | X=x]$| for τ = 75, |$\tau=90,$|  τ = 95 and the mean (µ) in 2008–09 indicates that the linear estimate is a good approximation of the non-parametric component estimate over the major part of the domain of soil quality and usually well within the non-parametric confidence intervals. Differences only occur at the fringes. We find similar results for the other variables in both periods of study.¹⁰

5. Concluding remarks

This paper investigated the strong prices surges of arms-length transactions of farmland in Brandenburg, an important agricultural state of Germany. Given farmland’s role as a key production base, a popular investment to hedge against inflation and a still largely unused carbon sink, increasing prices are a key concern to farmers, investors and policy makers. Our aim was to improve the understanding of what has been driving the strong price surges in the upper quantiles of farmland prices to inform the policy debate, e.g. about price caps or favouring the farmer buyer group. In a two-step decomposition approach based on unconditional quantile regressions we aimed to find out how pricing and composition effects contributed to the price surge in the upper quantiles overall and for each of the considered land and regional characteristics.

The results show that price increases in our study region can be mainly attributed to the pricing effect, due to increased valuations of characteristics such as soil quality and plot size. This suggests that price increases were particularly strong for plots of high soil quality and of larger size and those sold using auctions as an efficient sales mechanism (Seifert, Kahle, and Hüttel, 2021). The price increases in the upper quantiles for plots sold through BVVG auctions could even indicate potential overbidding in this segment of the market (Seifert and Hüttel, 2023).

Our results indicate pronounced price surges for plots in regions near Berlin, characterised by urban sprawl, as well as for plots with stable soil moisture conditions. The demand for fertile land is typically high. However, both cases share a shrinking supply of fertile land, leading to an increased scarcity-induced competition and subsequent price increases. Such shifts in local farmland market demand and supply conditions may reflect market functioning across a wide range of price quantiles.

The results of our (first-step) unconditional quantile regressions show that the magnitude of the estimated effects of key land and regional characteristics on the price quantiles tends to increase towards the upper tail of the price distribution—a pattern that is masked by conventional hedonic price regressions. This finding is in line with other papers studying the determinants of farmland prices beyond the mean (Mishra and Moss, 2013; März et al., 2016; Lehn and Bahrs, 2018b; Peeters, Schreurs, and van Passel, 2017). Regarding the influence of RE policy, our results show small pricing and composition effects of the variable biogas density with high statistical uncertainty. That is, while several studies report that it is actually the landlords who benefit by capitalisation of the RE policy in farmland rental prices ( e.g. Hennig and Latacz-Lohmann, 2017) our results are in line with the small and statistically uncertain RE policy effects reported for our study region ( e.g. Balmann et al., 2021)

Turning to the policy implications of our research, they are based on possible explanations for the estimated changes in valuation of land and regional characteristics, which have contributed to the price surge in the upper quantiles and not on causal claims.

Recent calls for more rigorous farmland price regulation in Germany (cf. Appel et al., 2023; Jauernig, Brosig, and Hüttel, 2023) have proposed price caps, i.e. denying transactions with negotiated or search market prices considerably exceeding the locally common (mean) price. Our research suggests that such price caps are problematic for two reasons. First, defining price caps (as suggested) based on local mean prices will be difficult. Our results show that price distributions have long right tails, with tail behaviour varying substantially across plot types, locations or time periods. Identifying an accurate local base price will thus be challenging.¹¹ Second, given that our results could demonstrate market functioning, with price signals adapting over time to changing local conditions, they cast doubt on the necessity to regulate farmland prices by caps—in order to protect local farmers from being priced out of the market or for other reasons such as promoting sustainable land ownership and land use allocation.

Based on our empirical results, we suggest alternatively to increase market transparency. In line with Balmann et al. (2021), Humpesch et al. (2022) and Seifert and Hüttel (2023), our evidence regarding BVVG auctions underscores the necessity for policy makers to shift their attention to counteract potential overbidding by promoting market transparency and providing information about the market mechanism, demand (potential buyers and bidders) and the bid vector. We recommend to expand suggested transparency measures by reporting prices, their development over time and quantile,¹² since reported prices serve as core information for forming not only future bids but also collateral estimates, value estimates for negotiations or compensation matters.

Dovetailing with Lehn and Bahrs (2018b), we further recommend to counteract future scarcity as a source of price surges in upper quantiles of the price distribution, for instance, due to reduced supply of fertile farmland attributable to urbanisation and climate change. Our results underscore the necessity to sustain land fertility and to mitigate climate change impacts and vulnerability of the farming sector (Brill et al., 2024). If the sensitivity towards droughts had remained constant over time, price increases in the upper quantiles over time likely would have been even stronger. Thus, a possible idea to counteract price surges in the upper quantiles could be mitigating the loss of highly fertile agricultural land by implementing policies that actively manage urban sprawl and guide land use change in a coordinated fashion. For instance, local governments could enact zoning regulations that prioritise the preservation of agricultural areas by restricting residential and commercial development on prime farmland. Additionally, incentives could be provided to developers who choose to build within existing urban areas or on brownfield sites rather than expanding into agricultural land.

As in any study, we acknowledge several limitations: First, some variables used in the hedonic regression may not accurately measure the underlying hypothesised effect. For instance, population growth and quality of public transportation (Sklenicka et al., 2013; Delbecq, Kuethe, and Borchers, 2014) may be more accurate measures of the effect of urban sprawl than the car travel time to the next CBD. Likewise, our climate and weather variables do not capture expectation about future climate and related anticipations for land returns, and our model does not acknowledge adaptations in farming to a changing climate, e.g. higher frequencies of extreme hydro-meteorological events, and related impacts on future returns (Severen, Costello, and Deschênes, 2018). For instance, in an adapted agricultural production system, climate effects might be of lower relevance for upper quantiles. This offers a promising avenue for future research. Second, we relied on a parsimonious model to keep the decomposition results interpretable, instead of modelling potential non-linear effects of lot and deal characteristics on farmland prices, e.g. polynomials and interaction terms (Seifert, Kahle, and Hüttel, 2021; Balmann et al., 2021; Curtiss et al., 2021). For instance, the pricing of soil quality may be influenced by the RE policy as farms with biogas operations may bid higher for prime farmland in proximity to their plant. Third, we could not account for any potential effects related to the debates about intensifying farmland market regulation, as documented and thus measurable initiatives were released in 2019 and 2023, which are out of our sample. New data could be available, and text-mining approaches from local media could offer a basis for identifying such effects. Fourth, reweighting of the observations needed to disentangle pricing and composition effects relies on the adequacy of the estimated logit model.

Regarding possible extensions, our approach could serve as a foundation for identifying the effect of specific policies on quantiles of the price distribution. Under conditional independence, |$\Delta^{\tau}_{S},$| the ‘structural’ part of the aggregate decomposition, can be interpreted as a causal quantile effect of a binary treatment (Fortin, Lemieux, and Firpo, 2011). While such an interpretation is inappropriate for our two-period comparison, it may be considered for discrete policy interventions. Such an analysis would not require the first-step unconditional quantile regressions but would crucially depend on the propensity score reweighting step to estimate the counterfactual quantile (Firpo, 2007). It may be used to investigate whether agricultural, energy and environmental policies capitalise differently by quantile. Differences over time and across regions are well noted (O’Neill and Hanrahan, 2013; Ciaian, Kancs, and Espinosa, 2018; Graubner, 2018; Varacca et al., 2022), yet identified capitalisation rates remain low, particularly when contrasted with rental rates (see Latruffe and Le Mouël, 2009). Differences by quantile could explain why smaller mean policy capitalisation rates for land values are often reported. Moreover, extending the decomposition method to incorporate implicit spatial effects and spatial correlation could offer another promising path for future research. Finally, our results call for replication in other study regions to ensure external validity.

Data availability

Our article is based on data provided by Brandenburg’s surveyor commission (Oberer Gutachterausschuss im Land Brandenburg). Unfortunately, these data are confidential and cannot be published. Publishing detailed information on farmland transactions, such as geographic coordinates, dates or whether the buyer is a farmer and former tenant, could enable specific agricultural land transactions to be traced and potentially linked to individuals or other legal entities, thereby violating confidentiality rules. To gain access to similar data or inquire about the necessary procedures to replicate the study under legal and institutional guidelines, one should contact the Oberer Gutachterausschuss im Land Brandenburg (https://geobasis-bb.de/lgb/de/aufgaben/oberer-gutachterausschuss/) and submit a formal request explaining the purpose of the research and how one intends to use the data in a confidential manner.

Footnotes

References

Appendix A. Outlier Detection and Removal

We conduct a yearly outlier detection analysis to remove transactions with unusual lot sizes and prices per square meter. Specifically, we split the sample by years, and calculate each observation’s Mahalanobis distance regarding the natural logarithm of lot size and price per square meter. We apply the outlier-robust method based on the minimum covariance determinant estimator by [1]. For each year, we remove observations which provide Mahalanobis distances having a probability of less than 0.1% under the hypothesis of normally distributed input distributions. In consequence, we remove 96 (2008-09) and 71 (2017-18) observations and 50 observations (upper 1% for each period) located in small municipalities having very high values for the installed biogas capacity per hectare.

Appendix B. Counterfactual Price Density Estimation

Figure B.1 shows the kernel density estimates of farmland prices per square meter for 2008-09 and 2017-18 and the kernel density estimate of the counterfactual distribution, i.e., the distribution of farmland prices that would have prevailed in 2008-09, if the characteristics were priced as in 2008-09, but if the plots would have had a similar distribution of characteristics as the plots sold in 2017-18. The similarity of the kernel density estimates of the counterfactual distribution and the distribution in 2008-09 indicates that changes in the distribution of price drivers only account for a minor part of the shift toward higher farmland prices over time. The increase in farmland prices would be similar throughout the price distribution if the characteristics of farmland were the same in both periods of study.

Appendix C. Balance Statistics

Table C.1 presents the improved balance of the plot characteristics in 2008-09 and 2017-18 following the reweighting of observations from 2008-09. This reweighting aims to ensure that the distributions of plot characteristics closely resemble those observed for plots sold in 2017-18. Utilizing a propensity score reweighting approach based on a logit model, the differences in averages for 10 out of 12 variables have been reduced. Post-reweighting, the number of variables exhibiting statistically significant mean differences based on two-sample t-tests at a significance level of 1% decreases from 8 to 4.

Appendix D. Interval Estimates for Decomposition and Regressions Interval Estimates for Decomposition and Regressions

Appendix E. Counterfactual RIF-regressions

Table E.1 lists the estimates of the counterfactual regression relationship between RIF-transformed prices and the characteristics that would have prevailed in 2008-09 if they had been distributed as in 2017-18.

Appendix F. Robustness Check at the Aggregate Level