Determinants of farmland values in the Campine region (Belgium): Conditional and unconditional quantile regression estimates

Ludo Peeters

Eloi Schreurs

Steven Van Passel

Hasselt University, Belgium

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General purposes

Estimation of the determinants of farmland prices realized in a particular area in Belgium (Flanders) = identification of sources of the variation in observed farmland prices

Using a hedonic price-function framework

Our (initial) focus (was) is on the impact of heavy-metal (cadmium) soil pollution on the valuation of agricultural land

In terms of estimation strategy, we attempt to go beyond standard mean regression (OLS) and to resort to quantile regression (QR)

Our work is still in an early stage, and only some preliminary results will be presented

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Contributions

• First study (curiously…) aimed at estimating the impact of heavy-metal = Cd soil pollution on values of farmland

• Spillover effects/spatial effects:

– Spillovers from prices of developed/developable land (municipal effects)

– Spillovers from prices realized by nearby transactions in recent past (spatiotemporal effects)

• Quantile regressions (QR):

– Heterogeneity and heteroskedasticity

– Beyond conventional mean (OLS) regression

– Both conditional and unconditional QR

Specific contributions

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Contributions

Mean regression (OLS) (effect on average)

Quantile regression (effect on entire distribution)

Conditional quantile regression (CQR)

Unconditional quantile regression (UQR)

Problems:

Mean regression has both a conditional and unconditional interpretation

Quantile regression has not !

Therefore, results from OLS and CQR are not directly “comparable”, whereas OLS and UQR can be compared

Something that has been generally overlooked in the literature…

Estimation strategies

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Differences between OLS, CQR, and UQR

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Difference between CQR and UQR

To make a long story short…

In the case of OLS, we have (if all usual assumptions are satisfied)

OLS: 𝐸 b X = 𝐸𝐗[𝐸 𝐛 𝐗 ] = 𝐸(𝐛)

In most cases, conditional QR (CQR) generates results that are not always generalizable or interpretable in a policy of population context “within-group” effect of a given covariate; so, we have

CQR: 𝐸 𝐛𝜏 X ≠ 𝐸(𝐛𝜏) limited importance

In contrast, unconditional QR (UQR) provides more easily interpretable results as it marginalizes (integrates) the effect over the distributions of the other covariates in the model “between-group” effect of a given covariate; so, we have

UQR: 𝐸 𝐛𝜏 X = 𝐸(𝐛𝜏)

Key reference: Firpo-Fortin-Lemieux (2009)

For a gentle introduction, see Borah-Basu (2013)

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Implementation/estimation: RIF-OLS

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OLS, CQR, and UQR impact of union status on earnings (Firpo, Fontin, Lemieux, Econometrica, 2009)

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CQR

UQR

OLS

Empirical application (case study)

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Determinants of farmland values in the Campine region in Belgium (Flanders)

Hedonic (implcit) prices of heavy-metal pollution = Cd contamination of agricultural land

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Empirical application (case study)

Data

Micro-data on individual sales transactions were available from the Belgian Land Registry Office

We have a sample of 599 farmland parcels sold during the period 2004–2011…

…in the Campine region (in the northern part of Belgium, along the Dutch border)

The region is known to have a legacy of heavy-metal (Cd) pollution of the soil

The parcels are spread out over 14 municipalities of the study area

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Study area: Campine region, 14 municipalities

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Dependent variable

Sales prices per m2 for 599 farmland parcels (€) sold during the period 2004–2011

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Independent variables

Transaction (parcel) characteristics Public vs. private sale (1/0)… [gray market… envelop… common…] Parcel size (1,000 m2) Structure vs. vacant (1/0) Pasture land (1/0) Arable land (1/0) Residential zoning (1/0) Natural/forest zoning (1/0) Distance to Dutch border (km)… [much higher prices in The NL…]

Neighborhood (municipality) characteristics Average prices of developable land (€) Farming density (# farms per km2) Spatiotemporally lagged farmland prices (€)

Environmental variable Cd concentration (ppm = parts per million)

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Neighborhood (municipality) characteristics

Average prices of developable land (€/m2)

Farming density (# farms per km2)

Spatiotemporally lagged farmland prices (€/m2)

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Average prices of developable land

Developable land = land for other land agricultural uses (residential, commercial/industrial, etc., uses)

Idea = to capture “urban/development pressure”

Developed space is always nearby, due to Scattered housing

Ribbon development

Markets for agricultural land and developable land are cl:osely linked prices of developable land may spill over to farmland market

Every reasonably accessible patch of land (farmland) is a potential building site, considering also that zoning and land-use regulations are poorly enforced in Belgium/Flanders…

We use 5-year moving averages, for each of the 14 municipalities, as a crude measure

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Ribbon development in Belgium (Flanders)…

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Capitalization of prices of developable land

• Urban sprawl pressure on land values

• Distance to urban center (e.g., CBD) is most common approach (model of Alonso,…)

• Not particularly relevant to an area such as the “rural” Campine region (small towns) – Low-density/large-lot and ribbon development across the landscape

(scattered residential and agricultural land)

– Landowners may increasingly resort to speculative motives for holding (hoarding) land, in anticipation of potential land-use conversions from farming to residential, commercial and/or industrial uses

• Zoning of land not always strictly enforced in Belgium (Flanders)

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Farming density

We use the number of farms per km2, for each of the 14 municipalities

Idea = to capture the degree of “rural-ness” of the various municipalities

The higher the farming density in a municipality, the better are local conditions for farming and, therefore, the higher the demand for farmland—hence, potentially giving rise to higher prices

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Spatiotemporal lag of farmland prices (1/4)

In constructing the spatiotemporal lag of farmland prices, two issues have to be addressed:

how to define the relevant “neighborhood”

how to determine the “recent past”

We conducted a preliminary covariance analysis,

on the basis of which we decided to focus on within-municipality (average) prices realized in earlier sales transactions

We have chosen a 12-month time window

The specifics of the variable construction follow…

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Spatiotemporal lag of farmland prices (2/4)

The spatiotemporal weights matrix W is obtained from the Hadamard (element-by-element) multiplication of the spatial weights matrix S and the “temporal-dependence” matrix T

W = S ⊙ T = 𝑠𝑖𝑗𝑡𝑖𝑗 = 𝑤𝑖𝑗

As a measure of proximity, we use the (inverse) distances between farmland parcels

S = 𝑠𝑖𝑗 = 1 𝑑𝑖𝑗

with diagonal elements set to zero

Note: inverse distances imply 50% decay of spatial weight at distance of 2 km

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Spatiotemporal lag of farmland prices (3/4)

If sales are ordered by their time of occurrence (from the most recent one (in 2011) to the first one (in 2004)), the temporal-dependence matrix 𝐓 is specified as the Hadamard product of three different matrices

T = U ⊙ B ⊙ M = 𝑡𝑖𝑗

U = upper-triangular matrix of 1s

B = matrix containing blocks of 1s to identify parcels sold on an earlier date within the 12-month time window (where the 1s are replaced by 0s for those transactions that took place on the same day)

M = matrix of interspersed 1s to identify within-municipality sales

The resulting spatiotemporal matrix W is row-standardized 22

Spatiotemporal lag of farmland prices (4/4)

Our procedure relies on specific choices (as theory provides no clear guidance

Our choice of the inverse distances is based on the observation that spatial correlations are far much stronger among sales prices within a short-distance range, and particularly for those sales occurring within the same municipality

Our choice of the length of the time period over which agents are assumed to base their (imperfect) information is partly motivated by the modest size of our dataset: 599 observations over a period of 8 years. We decided to choose a 12-month time window, which implies that we lose the first 64 observations of our dataset (about 11% of the original sample). If we had chosen 24 months, we would have lost already 160 observations (about 27% of the original sample)

Without a far longer time period, it is not possible to examine how far back in time buyers make comparisons. Yet, buyers may take relatively greater notice of more recent sales in addition to taking greater notice of nearby sales

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Environmental variable (Cd): Practical issue

Water pollution you can see it

Air pollution you can smell it (e.g., odor)

Noise pollution you can hear it

Heavy-metal (Cd) pollution of land

you cannot see, smell, or hear it

Additional problem = actual (objective) pollution vs. perceived (subjective) pollution

to what extent are buyers aware of the actual

pollution?

most researchers would find significant explanatory

power from subjective measures of pollution

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Objective measures (no subjective measures avaliable)

Based on examination of about 12,000 geo-referenced soil samples

Spatial interpolation was used to assign Cd contamination level to geo-referenced farmland parcels in our sample

Issues: Objective (scientific) vs. subjective (perceptive) measures of soil

pollution

To what extent are market participants aware of Cd contamination?

Environmental variable (Cd): Measurement

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Environmental variable (Cd) and study area

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Environmental variable (Cd): Estimation of effect

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ln 𝑝𝑖 = 𝛼 + 𝛽𝑐𝑖𝐼(𝐶𝑑𝑖 ≤ 2) + other factors + 𝑢

where

𝑝𝑖 = price of parcel 𝑖 𝐶𝑑𝑖 = Cd concentration of parcel 𝑖

𝑐𝑖 = ln𝐶𝑑𝑖

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𝐼 • = indicator function, such that

𝐼 = 0 if 𝐶𝑑𝑖 ≤ 2 1 if 2 < 𝐶𝑑𝑖 ≤ 4.5

with critical “threshold value” of Cd = 2 ppm, and

∆ ln(𝑝)

∆ ln(𝑐)≡

∆ ln 𝑝

∆ ln 𝐶𝑑= 2𝛽 ln 𝐶𝑑𝑖 − ln(2)

Estimation results: OLS and median regression

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Estimation results: Marginal effects of Cd

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Estimation results: Impact of Cd

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Estimation results: Q plots

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Diagnostics: Error autocorrelation

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“within-municipality” and “between-municipality” [unconditional] covariances among farmland prices

within some bandwidth h of a given distance d

where 𝑝 𝑖 and 𝑝 𝑗 are the “demeaned” farmland prices

Ref.: Barrios-Imbens-Koselár (2012)

Importance of municipal boundaries (1/2)

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Importance of municipal boundaries (2/2)

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Barrios T., Diamond R., Imbens G.W., Koselár M. (2012). Clustering, spatial correlations, and randomization inference, Journal of the American Statistical Association, 107, 578–591

Borah, B.J., Basu A. (2013). Highlighting differences between conditional and unconditional quantile regression approaches through an application to assess medication adherence, Health Economics, 22, 1052–1070.

Firpo, S., Fortin, N.M., Lemieux, T. (2009). Unconditional quantile regressions, Econometrica, 77, 953–973.

Geniaux G., Ay J.-S., Napoléone C. (2011). A spatial hedonic approach on land use change anticipations, Journal of Regional Science, 51, 967–986.

Maddison D. (2009). A spatio-temporal model of farmland values, Journal of Agricultural Economics, 60, 171–189.

Moulton B.R. (1990). An illustration of a pitfall in estimating the effects of aggregate variables on micro units, The Review of Economics and Statistics, 72, 334–338.

Patton M., McErlean S. (2003). Spatial effects within the agricultural land market in Northern Ireland, Journal of Agricultural Economics, 54, 35–54.

Some key references

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