Estimating the Value of Foregone Rights on Land. A Working Paper Prepared for the Vermillion River Watershed Joint Powers Organization 1.

Transcription

1 . Estimating the Value of Foregone Rights on Land A Working Paper Prepared for the Vermillion River Watershed Joint Powers Organization 1 July 2008 Yoshifumi Konishi Department of Applied Economics University of Minnesota Supervised by Jay S. Coggins Associate Professor, Department of Applied Economics University of Minnesota and, Steven J. Taff Associate Professor, Department of Applied Economics University of Minnesota 1 Funding support from an Environmental Protection Agency 2005 Targeted Watershed Grant.

2 1. Introduction and Summary This document (i) describes methods for estimating the value of foregone rights on land induced from voluntary land use restrictions, and (ii) presents the summary of preliminary estimation results using these methods. Estimation of the value of foregone rights on land is of interest to both public and private agents involved in the Vermillion River Watershed Thermal Trading program. First, it allows us to construct an empirical regional supply function for thermal credits. Landowners may reduce thermal loads from their land by changing their land use, say, from agricultural use to wetlands, and sell the estimated thermal reductions as credits to developers, who need the credits to meet the temperature standards. In many cases, landowners do not need to forego the ownership of their land, but simply sell their rights to use the land for certain purposes such as development or agricultural production. Thus, the full market price of land may not be used for transactions of partial land use restrictions. Estimation of the empirical supply function requires estimation of the ex ante value of foregone rights using appropriate econometric techniques. Once we obtain the estimated supply curve, we can use it to simulate trades and the equilibrium effects of, say, alternative trading rules. We may also use the estimated supply curve and the predicted equilibrium price of credits to facilitate transactions between buyers and sellers, who are often unsure about the fair price of those restrictions. Second, more generally, estimation of the value of foregone rights on land is, and has been, of considerable interest to governments. Today, governments have a variety of voluntary land use restriction programs, such as Conservation Reserve Program, Agricultural Reserve Program, and Green Acres Program. Governments need to know not only "fair" compensation payments for such land use restrictions but also the appropriate compensation levels to maximize the voluntary enrollment given the budget (i.e. it is more cost-effective if the government offers the exact amount that matches landowner s willingness-to-accept). A number of studies have attempted to estimate the effect of land use restrictions on the market price (Anderson and Weinhold, 2005; Brimlow, 2008; Lynch and Lovell, 2002; Mashour et al., 2005; Nickerson and Lynch, 2001; Plantinga and Miller, 2001; Plantinga, Lubowski, and Stavins, 2006; Plantinga, 2006; Shoemaker, 1989; Shultz and Taff, 2004; Taff and Wiesberg, 2007; and Vitaliano and Hill, 1994). My approach differs significantly from these studies. 2 First, I use only the data on the estimated market value of land itself, not the data on actual easement payments by governments. This is because analyzing the data on actual easement payments suffers significantly from sample selection bias. Often, the observations for which easement payments data are available represent a very small subset of the land price data. Second, I explicitly incorporate the structural model of random-utility-theoretic land use decision-making into estimation. In many studies, some structural decision-making process is theoretically modeled, but estimation is done in a reduced form hedonic analysis. I explain below why the structural model needs to be incorporated into estimation. Third, after estimation of the main model is done, I estimate the value of foregone rights using the asset valuation theory precisely. The asset valuation theory states that the change in the market price of a parcel of land by foregoing certain land uses (which equals lost value and option values) must equal the value of changes in the expected probabilities of land uses for that parcel of land. This identity is also consistent with my econometric strategy to control for the endogeneity of land use decisions. The main results are as follows. First, using the proposed method, the value of foregone rights by changing the land use from agricultural use to forestry (and keeping that use) is estimated 2 I may need to read through these cited papers again to be more cautious. Thus this and the following statements are subject to change. 1

3 to be at $6,919 (at mean), $864 (at minimum), and $60,068 (at maximum). Second, the value is highly negatively associated with the distance to Twin City, but weakly negatively associated with productivity index. This finding implies that the value of foregone rights is driven more by foregoing future development rights than by foregoing agricultural production The Econometric Model Conventional wisdom suggests that the observed value of a land property reflects the present discounted sum of the stream of expected future rents. Thus, the value of the property that is currently in corn production should reflect the fact that it is in agricultural use, and therefore, the stream of expected net returns from the corn production. It follows then that the current land use must in part influence property values. However, economists would also argue that the value of a property is not only driven by the current use per se, but also by the suitability of the land for potential land use(s) it is in a certain land use because it is best suited for that use. This argument further implies that the property value may be driven not only by the current use, but also by its suitability for future land use(s). This is certainly the case for land parcels on the urban fringe. Land parcels near the urban boundary that are currently in agricultural use may become a residential area. The property values of these parcels would be certainly higher than those of similar parcels that are far from the urban boundary, precisely because the values reflect suitability for residential developments. Converting an agricultural field into prairie or forests would mean restrictions land uses on that land. It then follows that the value of the foregone rights equals the portion of the property value that is driven not only by the economic rent associated with current land use, but also by the economic rents of all possible future land uses. This is indeed the asset valuation theory: the price or value of an asset equals the expected return of the asset. I use the asset price theory in modeling land property values in a hedonic-like equation. There are k land use options (e.g. residential, corn, prairie, and forest). ln p i = x 0 i α + β d ji β j + ξ i, (1) j=1 where i indexes land parcels, x 0 i is a vector of exogenous variables, d ji is an indicator variable, which equals 1 if parcel i is in use j and 0 otherwise, and ξ i is an unobserved error term. I assume that each landowner faces an unconstrained decision problem and chooses a particular land use if and only if that use generates the highest economic rent for that landowner. I model this decisionmaking process in the random-utility-theoretic framework: y ji = z0 ji θ 1 + ɛ ji, (2a) 1 if and only if y d ji = ji y ki for all k 0 o.w., (2b) where y ji is a latent variable that describes the parcel i s economic rent if it is in use j, z 0 ji is a vector of independent variables, and ɛ ji is an unobserved error term. Note that the economic rent y ji may also include the landowner s unobserved utility term for certain land uses. It is reasonable to presume that ɛ ji s will be in general correlated with each other and with the error ξ i in (1), with a joint density, h(ξ i,ɛ 1i,ɛ 2i,ɛ 3i ) and a variance-covariance matrix,. The question is how one can obtain consistent estimates of coefficients in (1). Note that the standard hedonic approach, including all land characteristics as independent variables in (1), does 3 All results in this document are preliminary. 2

4 not give us consistent estimates. This is because y ji (and ɛ ji) influences the probability of observing d ji so that d ji is likely correlated with ξ i to the extent that ɛ ji and ξ i are correlated. Thus, simply running regression of ln p i on these variables does not result in consistent estimates. Traditionally, a hedonic approach was used without dummies d ji, and all that analysts care about is to obtain consistent estimates on site-specific characteristics. We are interested in estimating the value of changes in land use, incorporating the fact that land use changes are endogenous. To consistently estimate (1), one could use (i) two-step instrumental variable approach or (ii) full-information maximum-likelihood approach. Both methods are outlined in Heckman (1978). In this paper, I use the first approach. To do (i), first fit a multinomial logit or probit to the probabilistic-choice model (2) and (3), and obtain estimated probabilities ˆP ji. Substitute these out for d ji, and obtain the equation of interest (1) becomes ln p i = x 0 i α + β j=1 ˆP ji β j + ξ i, (1 0 ) Note that this equation precisely captures the idea of the asset valuation theory. That is, (ignoring other covariates) the price of parcel i is the expected value of the economic rent, with β j being the economic rent associated with each land use j. Note that all the estimated economic rents will be relative to the base land use. We could drop the intercept term β 0 and include all land use dummies in equation (1). It is straightforward to show that the estimated values of foregone rights will be the same either way. Furthermore, ˆP ji is the (estimated) implicit probability of parcel i to be in use j given the current economic conditions captured by covariates z 0 ji. One caveat is that as Heckman pointed out, the standard formula for asymptotic variance would be inappropriate, and the correct formula may be difficult and computationally burdensome. 3. Data The study area is the major subsection of the Vermillion River Watershed (see Map). Map. Vermillion River Watershed All data used in this document are based on 30x30-meter cell in GIS database. The land prices per acre used in this analysis are based on the estimated market value of land excluding the value 3

5 of structures. I plan to also analyze the actual sales prices when the data become available. I categorize 12 land covers into one of the five land use class: use = 1 if developed, =2 if agricultural use, = 3 if tall grass, = 4 if forest, and = 5 if undevelopable lands (e.g. pond, reservoir). This data set contains 494,680 observations. From this, I randomly drawn 20,000 observations. The distributions of land covers and land use class with full sample and reduced sample are presented in Tables A1-A5 in Appendix. Based on the analysis of the distribution, land values below $2,000 or above $500,000 appear to be extreme values. Thus I decided to curtail these observations. Table 1-3 present summary statistics of land values by land cover, by land use, and by community. It is reasonable to expect that landowners of undevelopable land parcels (i.e. reservoirs and ponds) do not have a free choice in deciding optimal land use. Thus I exclude observations with this land use class. After these adjustments, my sample reduces to 12,627 observations. Table 1. Property Value Per Acre by Land Cover Table 2. Property Value Per Acre by Land Use Surprisingly, parcels in agricultural use have lower market values on average than those in tall grass and forest (Table 2). This is probably because other variables (e.g. distance to city or to river, community, and watershed) may make those lands in tall grass and forest more attractive on average than those in agricultural use. This is precisely the reason why a simple OLS regression 4

6 would unlikely elicit the correct economic rent associated with land use. Moreover, many of the agricultural lands in this watershed are enrolled in Agricultural Preserve Program or Green Acres Program, which tend to lower their market values. Table 3. Property Value Per Acre by Community The property values vary significantly by community (Table 3). Parcels in Rosemount, Burnsville, and Apply Valley have significantly higher market values than in other communities. It is reasonable to expect that there are unobserved "community" effects on land values. Therefore, I include community fixed effects in the regression analysis. In the future, we might attempt to collect information on quality of school district, zoning, and other community variables to control these effects better. 4. Two-step Instrumental Variable Estimation As discussed in Section 2, I use the two-step instrumental variable (IV) approach: I first estimate the expected probabilities of different land use given observed covariates in (2), using either multinomial probit or multinomial logit, and then substitute out the estimated probabilities ˆP ji with each land use into (1). As discussed in Section 3, I use four land use classes, instead of 3 as described in (1) and (2): j = 1 if developed; = 2 if ag. use; = 3 if tall grass; and = 4 if forest. The base land use is j = 4, forest. As with the standard procedure, I use two normalizations in the first-step maximum likelihood estimation: let y 4i = 0 and estimate the standardized latent variable y ji =σ j. A. OLS Regression Results For comparison purposes, I run a basic OLS regression, regressing ln p on all right-hand-side variables. Not surprisingly, all variables except distance to river and slope are significant at less than 5% levels. More importantly, the results indicate that developed lands have associated with significantly higher market values relative to forest while agricultural use and prairie are associated with lower market values relative to forest. The results are not surprising given that parcels in agricultural use or tall grass have lower market values on average than those in forest as shown in (Table 2). As we will see, these results significantly change once we account for the bias that stems from endogenous land use decisions. 5

7 Table 4. Fixed-Effect Regression Results B. First-Step Estimation Results For the first step estimation, land use variable was regressed on distance to river, distance to highway, distance to city, productivity index, and slope, using the multinomial logit procedure. Essentially all variables were significant and have signs consistent to expectations. Land development is significantly positively associated with distance to river and distance to highway, but is 6

8 negatively associated with distance to city, productivity index, and slope. Agricultural land use is significantly positively correlated with distance to highway, distance to city, and productivity index, but is negatively correlated with distance to river and slope. The results are presented in Tables 5 and 6. Table 5. Multinomial Logit Estimation - First-Step Estimation Furthermore, Figure 1 contains six graphs analyzing the relationships between the estimated probabilities, the estimated economic rents (= linear predictions), and the land values. The shapes of the graphs on the left of Figure 1 appear to suggest that land use decisions (i.e. probabilities of different land uses) are essentially driven by the decisions as to whether to develop and whether to use lands for agricultural purposes. The probability of development has a clear S-shape in the estimated (normalized) latent economic rent for development. A similar comment applies to the probability of agricultural use. Also the graphs on the right of Figure 1 suggest that logged land values are essentially positively associated with the (normalized) latent economic rent. A jump in the middle graph (for agricultural use) simply indicates that there is a threshold effect in the probability (and the rent) of agricultural use. I also ran the multinomial probit and confirmed that the results are essentially the same as the multinomial logit model. 7

9 Table 6. Predicted Probabilities and Latent Values Figure 1. Relationships between Predicted Probabilities, Predicted Rents, and Land Prices 8

10 C. Second-step IV Estimation Results In the second step, I regress ln p i on the estimated probabilities ˆP ji along with other relevant covariates. Note that the estimated coefficient captures the economic rent relative to the base land use, "forest," since we cannot include ˆP 4i in the estimation, as long as we keep a constant term in the regression, for otherwise the variable is linearly dependent with other three land use probabilities (i.e. it is the same as "dummy variable trap"). The regression results are presented in Tables 7. Comparing the results of the base OLS regression (Table 4) and the two-step IV regression tells us an important and interesting point. Without controlling for endogeneity, land use classes, ag. use (cover2) and tall grass (cover 3), have significantly negative coefficients. This means that land values are, on average, lower if land is used for ag. use or tall grass than if it is used for forest. This result is essentially driven by the fact that average land values for ag. use and tall grass are lower than those for forest (see Table 2). However, after controlling for endogeneity of land use decisions, both ag. use and tall grass have positive economic rents relative to forest (see the results in Table 7). The lower average land values for ag. use and tall grass are simply associated with the covariates (i.e. distance to city etc) that drive land use choices, but not the higher economic rents associated with land uses. This finding is consistent with the asset price theory that the price of an asset is driven by the expected economic rent and our expectation that lands in agricultural use and tall grass have higher economic rents, on average, than being left as natural forest. D. Estimating the Value of Foregone Rights Now the question becomes, how to estimate the ex ante value of foregone rights on land. For concreteness, I consider the case of converting land i from the agricultural use to forest and keeping that land use effectively. From the first-step multinomial logit regression, I estimated the expected probabilities of four land uses associated with each land i: f ˆP 1i, ˆP 2i, ˆP 3i, ˆP 4i g. This means that even if i is currently in agricultural use, it has the expected probability of ˆP 1i to be developed, ˆP 2i to be in agricultural production, and ˆP 3i to be in prairie. The land use restriction scenario above would change these probabilities to f0, 0, 0, 1g. That is, this land i has to be in forest, forever, with a 100% chance, at least for as long as the restriction is effective. According to the asset price theory, this change in these expected probabilities should change the value of the land price. Given my interpretation that β j is the estimate of expected (relative) economic rent associated with land use j, we can estimate the value of foregone rights from this scenario as follows. E[p i jp i = f ˆP 1i, ˆP 2i, ˆP 3i, ˆP 4i g] E[p i jp i = f0, 0, 0, 1g] = exp(x 0 i α + ˆP 1i β 1 + ˆP 2i β 2 + ˆP 3i β σ 2 ) exp(x 0 i α + 0.5σ 2 ), The term 0.5σ 2 must be used to adjust for the variance of the log-normal distribution. Because the estimated rents are relative to the base land use, we do not need to consider the effect of changes in the expected probability of the base land use. 4 4 To see this, consider the asset value equation, p i = j ˆP ji R ji, where R ji is the economic rent associated with use j. If we include a constant term β 0, exclude the base use 4, and estimate coefficients β j on ˆP ji, we would have β 0 = R 4i and β j = R ji R 4i. Thus, we have: p i = ˆP 1i β 1 + ˆP 2i β 2 + ˆP 3i β 3 + β 0, = ˆP 1i (R 1i R 4i ) + ˆP 2i (R 2i R 4i ) + ˆP 3i (R 3i R 4i ) + R 4i = ˆP 1i R 1i + ˆP 2i R 2i + ˆP 3i R 3i + (1 3 j=1 ˆP ji )R 4i = j ˆP ji R ji. 9

11 Some summary statics and preliminary characterization of the estimated values are given in Table 8 and Figure 2. First, the value of foregone rights by changing the land use from agricultural use to forestry (and keeping that use) is estimated to be at $6,919 (mean), $864 (minimum), and $60,068 (maximum). Second, the value is highly negatively associated with the distance to Twin City, but weakly negatively associated with productivity index. This finding implies that the value of foregone rights is driven more by foregoing future development rights than by foregoing agricultural production. Table 7. Two-step IV Estimation Results 10

12 Table 8. Summary of Estimated Value of Foregone Rights From Agricultural Use to Forest Figure 2. Characteristics of Estimated Values of Foregone Rights 11

13 Appendix Table A1. Distribution of Land Cover, Full Sample Table A2. Distribution of Land Use, Full Sample Table A3. Distribution of Land Cover, 20,000 Sample 12

14 Table A4. Distribution of Land Use, 20,000 Sample Table A5. Percentile Distribution of Land Value Per Acre 13

15 References [1] Anderson, K. and D. Weinhold (2005), Do Conservation Easements Reduce Land Prices? Staff Paper No. 484, Agricultural and Applied Economics, University of Wisconsin. [2] Brimlow, Jake (2008), Voluntary Land Use Restrictions and Agricultural Property Values, mimeo. [3] Hajavassiliou, Vassilis A., Paul A. Ruud (1994), Classical Estimation Methods for LDV Models Using Simulation, in Handbook of Econometrics, IV, ed. R.F. Engle and D.L. McFadden. [4] Heckman, James J. (1978), Dummy Endogenous Variables in a Simultaneous Equation System, Econometrica, 46(4), [5] Glewwe, Paul (1992), The Three-Choice Multinomial Probit with Selectivity Corrections, Econometric Theory, 8(2), [6] Glewwe, Paul (1993), The Three-Choice Multinomial Probit with Selectivity Corrections, Econometric Theory, 9(2), [7] Lynch, Lori and Sabrina J. Lovell (2002), Hedonic Price Analysis of Easement Payments in Agricultural Land Preservation Programs. Working Paper #02-13, Dept. of Agricultural and Resource Economics, University of Maryland. [8] Mashour, Terri, J. Alavalapati, R. Matta, S. Larkin, and D. Carter (2005), A Hedonic Analysis of the Effect of Natural Attributes and Deed Restrictions on the Value of Conservation Easements, Forest Policy and Economics, [9] Nickerson, C.J. and L. Lynch (2001), The Effect of Farmland Preservation Programs on Farmland Prices, Americal Journal of Agricultural Economics, 83(2), [10] Plantinga, Andrew J. and Douglas J. Miller (2001), Agricultural Land Values and the Value of Rights to Future Land Development, Land Economics, 77(1), [11] Plantinga, Andrew J., Lubowski, R.N., and R. Stavins (2002), The Effects of Potential Land Development on Agricultural Land Prices, Journal of Urban Economics, 51, [12] Plantinga, Andrew J. (2006), The Economics of Conservation Easements, Paper prepared for the Lincoln Institute of Land Policy Land Policies for Urban Development Conference. [13] Shoemaker, Robbin (1989), Agricultural Land Values and Rents under the Conservation Reserve Program, Land Economics, 65(2), [14] Shultz, S. and S.J. Taff (2004), Implicit Prices of Wetland Easements in Areas of Production Agriculture, Land Economics, 80(4), [15] Taff, S.J. and Sanford Weisberg (2007), Compensated Short-term Conservation Restrictions May Reduce Sale Prices, The Appraisal Journal, [16] Train, Kenneth E. (2003), Discrete Choice Methods with Simulation. Cambridge University Press: New York. [17] Vitaliano, D.F. and C. Hill (1994), Agricultural Districts and Farmland Prices, Journal of Real Estate Finance and Economics 8(3):