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A direct test of hyperbolic discounting using market asset data
Economics Letters 112 (2011) 290–292
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
A direct test of hyperbolic discounting using market asset data Matthew J. Salois a,∗ , Charles B. Moss b a
Department of Food Economics and Marketing, University of Reading, UK
b
Food and Resource Economics Department, University of Florida, USA
article
info
Article history: Received 5 February 2010 Received in revised form 17 May 2011 Accepted 24 May 2011 Available online 31 May 2011
abstract This paper introduces a framework that generalizes exponential discounting in a net present value model by including a quasi-hyperbolic discount parameter in the asset valuation equation. Using observed market asset data, a statistically significant quasi-hyperbolic parameter is obtained, thus rejecting exponential discounting. © 2011 Elsevier B.V. All rights reserved.
JEL classification: C23 D90 G12 Q15 Q24 R14 Keywords: Exponential discounting Farmland values Generalized method of moments Net present value Quasi-hyperbolic discounting Time preferences
1. Introduction The net present value model dominates the literature on asset valuation, in which the value of an asset is determined by the stream of discounted expected future returns. A number of empirical concerns have arisen from the use of the present value model, calling its validity into question (Campbell and Shiller, 1987; Barsky and De Long, 1993). Overwhelmingly, the a priori assumption of an exponential discount factor is relied upon. While this assumption invokes intertemporal consistency in preferences and constant discounting, evidence confirms that declining discount rates (e.g., hyperbolic discounting) are more descriptive of actual investment decisions. (Laibson, 1997; Frederick et al., 2002). This paper relaxes the assumption of exponential discounting in a net present value model for a market investment good that allows for hyperbolic discounting. A hypothesis test is derived, permitting
∗ Corresponding address: University of Reading, PO Box 237, Reading, Berkshire, RG6 6AR, UK. Tel.: +44 0 118 378 7702; fax: +44 0 118 935 2421. E-mail address: [email protected] (M.J. Salois). 0165-1765/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2011.05.029
a direct test on the discount parameters. A statistically significant hyperbolic discount parameter is obtained using observed market data for an illiquid asset. Results of the hypothesis tests imply a formal rejection of exponential discounting. 2. Theoretical and empirical model Financial theory stipulates an investment project is undertaken if the net present value of the project is positive. Under risk neutrality and time-consistency, the value of an investment today is written as the discounted stream of expected future returns: Vt =
∞ −
δt +s Et [Rt +s ].
(1)
s=1
The price or value of the investment at time t is Vt . The expected return at time t + s is Et [Rt +s ] and is based on the information available in period t. The standard exponential discount factor is:
δ t +s =
s ∏ i=1
(1 + ρt +i )−1 ,
(2)
M.J. Salois, C.B. Moss / Economics Letters 112 (2011) 290–292
where δ ∈ [0, 1]. The rate of time preference in period t is the constant rate of discount, ρt +i . While alternative forms of declining discount rates exist, quasi-hyperbolic discounting is of interest. Quasi-hyperbolic discounting is a discrete time-value function incorporating the declining value property of generalized hyperbolic discounting:
β=
if t = 0 if t > 0.
1
β · δt
The parameter δ behaves similarly to the exponential discount factor, while the parameter β captures an immediacy effect in time preference (Loewenstein and Prelec, 1992). The short-run discount factor is β · δ while the long-run discount factor is δ . Incorporating quasi-hyperbolic discounting into Eq. (1) yields: Vt = β ·
∞ −
δt +s Et [Rt +s ].
(3)
s =1
Values of β determine the extent discounting deviates from exponential discounting. Discounting is exponential if β = 1 and is quasi-hyperbolic if β ∈ (0, 1). Eq. (3) is modified to derive a model for asset values based on changes in the asset value over time:
1Vt = Vt − Vt −1 = β ·
∞ −
δt +s Et [Rt +s ]
s=1
− βδ ·
∞ −
δt +s Et −1 [Rt +s ].
(4)
s=0
Under rational expectations there is a forecast error, meaning Et [Rt +s ] = Et −1 [Rt +s ] + et +s , where et +s is an uncorrelated residual term representing ‘‘white noise’’. Equation (4) is rewritten by aggregating over like exponents and simplifying:
1Vt = −βδ · Et −1 [Rt ] + (1 − δ)β ·
∞ −
δt +s Et [Rt +s ] + et +s .
The observed cash flow in the next period is assumed to proxy the expected return in the next period, that is, Et −1 [Rt ] → Rt , and Eq. (3) is substituted in: (6)
To test for quasi-hyperbolic discounting, a linear panel regression is parameterized:
1Vit = α0 + α1 · Rit + α2 · Vit + eit .
(7)
Eq. (7) contains a constant term, which is included in most net present value regressions, and is extended to account for observations over time and space. Eq. (7) nests both the exponential and quasi-hyperbolic discount factors. The discount parameters are obtained from the estimated coefficients. Since α1 = −βδ and α2 = (1 − δ), then δ = (1 − α2 ) and:
β=
−α1 1 − α2
.
(8)
Based on the parameter estimates, a hypothesis test is devised to test for quasi-hyperbolic discounting. A direct nonlinear hypothesis test on Eq. (8) has the null hypothesis of Ho : −α1 / (1 − α2 ) = 1 against the alternative of Ha : −α1 / (1 − α2 ) < 1.1 3. Data and estimation method The availability of a rich set of data on US farmland motivates empirical examination of the possibility of quasi-hyperbolic discounting in the farmland market. Additional motivation stems
1 Standard errors computed using the delta method.
from the considerable attention that net present value models for farmland receive (Falk, 1991; Lloyd, 1994). Moreover, justification for using a declining discount rate in land investment models is given by Shoup (1970) in the context of optimal conversion.2 Given the uncertain nature of conversion times, the discount rate used in the present value formulation of undeveloped lands may be higher in time periods closer to the present. The discount rate falls as the conversion time advances, implying the value of land will appreciate faster in time periods before development. The argument by Shoup (1970) makes a case for a discount rate that declines over time and highlights the inadequacy of exponential discounting in the context of farmland investment. The data consist of annual observations on farmland values and returns and represent a 43-year panel from 1960 to 2002 of the eight major agricultural regions of the United States.3 The data are obtained using farm balance sheets and income statements reported by the USDA’s Economic Research Service and National Agricultural Statistics Service. The dependent variable is the first difference of farmland values, which represents the annual change in the value of farmland for each state. Farmland values are defined as the value of farmland per acre, excluding the value of operator dwellings. The definition of farmland returns is gross revenues per acre less expenditures on variable inputs. Given the nature of the data, using a simple estimator such as least squares for estimating Eq. (7) would not be ideal. First, while the error term, eit , is assumed to be independently and identically distributed with zero mean, heteroskedasticity across years and farms remains a possibility. Second, while the error term is not correlated with the dependent variable 1Vit , the first difference of farmland values, eit is serially correlated across time. Estimation is based on the Generalized Method of Moments (GMM).4 Proposed by Hansen (1982), GMM provides consistent estimates of the parameters. A fixed effects dummy variable approach is used.
(5)
s=1
1Vt = −βδ · Rt + (1 − δ) · Vt + et .
291
4. Results Table 1 summarizes the GMM estimates of the asset valuation equation for agricultural land and reports the J-statistic.5 Based on the GMM estimates, the null hypothesis that the over-identifying restrictions hold is not rejected. Moreover, consistent with rational expectations, none of the constant terms are statistically significant. Table 2 reports the exponential and quasi-hyperbolic discount parameters values, along with the F -statistic for the direct test of quasi-hyperbolic discounting. Results for the Appalachian panel indicate an estimated exponential discount factor of δˆ = 0.939 and an estimated quasi-hyperbolic discount factor of βˆ = 0.060. Enacting the nonlinear hypothesis test derived earlier, a value of 102.152 is obtained for the F -statistic. The null hypothesis of exponential discounting is rejected in favor of quasi-hyperbolic discounting.
2 Justification is described by Arnott and Lewis (1979) in the context of rural land and by Grenadier and Wang (2007) in the context of commercial land development. 3 Regions include the Appalachian (Kentucky, North Carolina, Tennessee, Virginia, West Virginia), Corn Belt (Illinois, Indiana, Iowa, Missouri, Ohio), Delta (Arkansas, Louisiana, and Missouri), Great Plain (Kansas, Nebraska, North Dakota, Oklahoma, South Dakota, Texas), Lake (Michigan, Minnesota, Wisconsin), Mountain (Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah, Wyoming), Pacific (California, Oregon, Washington), and Southeast states (Alabama, Florida, Georgia, South Carolina). 4 In addition to the regressors, the instrument set includes square-root terms and lagged terms of state population and farmland acreage, for a total of four overidentifying restrictions. 5 Estimates obtained using R© version 2.6.0 software.
292
M.J. Salois, C.B. Moss / Economics Letters 112 (2011) 290–292 Table 1 GMM parameter estimatesa .
Appalachia Corn belt Delta Great plains Lake Mountain Pacific Southeast a b
Constant (α0 )
Asset-values (α1 )
Asset-returns (α2 )
Observations
J-statisticb
−0.168 (10.807)
−0.056 (0.080) −0.0543 (0.316) −0.150 (0.240) −0.472 (0.195) −0.486 (0.191) −0.571 (0.173) −0.337 (0.224) −0.280 (0.142)
0.061 (0.011) 0.071 (0.020) 0.037 (0.028) 0.071 (0.019) 0.110 (0.019) 0.103 (0.013) 0.067 (0.027) 0.078 (0.021)
210 210 126 252 126 336 126 168
0.024 0.053 0.119 0.106 0.069 0.064 0.102 0.046
19.499 (17.525) 3.306 (15.068) 0.242 (5.472) 0.163 (14.588) −1.865 (5.707) 18.803 (16.802) 10.841 (11.657)
Standard errors in parentheses; dummy variable coefficient estimates are suppressed. Critical value is 9.488 based on a 5% level of significance.
Table 2 Estimated discount factorsa .
Appalachia Corn Belt Delta Great Plains Lake Mountain Pacific Southeast a b
δ Factor
β Factor
F -statisticb
0.939 (0.011) 0.929 (0.020) 0.963 (0.028) 0.929 (0.19) 0.890 (0.019) 0.897 (0.013) 0.933 (0.027) 0.922 (0.021)
0.060 (0.086) 0.584 (0.349) 0.155 (0.252) 0.508 (0.218) 0.546 (0.222) 0.637 (0.200) 0.361 (0.249) 0.304 (0.161)
120.152 1.420 11.199 5.064 4.187 3.305 6.563 18.733
Standard errors in parentheses. Critical value of the F -statistic is 3.840 based on a 5% level of significance.
For the Corn Belt states, the nonlinear hypothesis test results in an F -statistic of 1.417, implying the null hypothesis of βˆ = 1 cannot be rejected. For the Mountain states, δˆ = 0.897 and βˆ = 0.637, with an F -statistic of 3.305 unable to reject the null hypothesis of exponential discounting at the 5% level (but can reject at the 10% level). For the remaining panel regions (Great Plains, Lake, Pacific, and Southeast) the result of the hypothesis test results in the rejection of exponential discounting at the 5% level. In six out of the eight panel regions, exponential discounting is rejected at the 5% level. Quasi-hyperbolic discounting is generally more descriptive of farmland investment decisions than exponential. Results are relevant to models of land development. Agricultural land is increasingly being converted to urban uses and is the subject of policy debate (Capozza and Li, 1994; Plantinga et al., 2002). The presence of quasi-hyperbolic discounting suggests a tendency to let the short-run dominate land-use decisions leading to over-development of agricultural land. 5. Conclusions A model for depicting changes in asset valuation over time is derived for the net present value model in which the diametrically polar cases of exponential discounting and quasi-hyperbolic discounting are nested. Previous research exploits the computationally convenient assumption of exponential discounting while
failing to acknowledge evidence suggesting a declining discount rate, such as a quasi-hyperbolic one, may be more realistic. This paper estimates the parameters of time preferences in the asset valuation equation of an important market asset (US agricultural land), generalizing the model to include both exponential and quasi-hyperbolic discounting. Evidence of quasi-hyperbolic discounting is found, which propagates three conclusions. First, evidence of hyperbolic discounting can be tested using actual market investment data using the approach derived in this paper. Second, the assumption of exponential discounting does not adequately describe time preferences in the farmland market. Third, results are relevant to models of land development; quasi-hyperbolic discounting suggests the propensity to overdevelop land in the short-run. References Arnott, R.J., Lewis, F.D., 1979. The transition of land to urban use. Journal of Political Economy 87, 161–169. 1, February. Barsky, R.B., De Long, J.B., 1993. Why does the stock market fluctuate? Quarterly Journal of Economics 108, 291–311. 2, May. Campbell, J.Y., Shiller, R.J., 1987. Cointegration and tests of present value models. Journal of Political Economy 95, 1062–1088. 5, October. Capozza, D., Li, Y., 1994. The intensity and timing of investment: the case of land. American Economic Review 84, 889–904. 4, September. Falk, B., 1991. Formally testing the present value model of farmland pricing. American Journal of Agricultural Economics 73, 1–10. 1, February. Frederick, S., Loewenstein, G., O’Donoghue, T., 2002. Time discounting and time preference. Journal of Economic Literature 40, 351–401. 2, June. Grenadier, S.R., Wang, N., 2007. Investment under uncertainty and timeinconsistent preferences. Journal of Financial Economics 84, 2–39. 1, April. Hansen, L.P., 1982. Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054. 4, September. Laibson, D., 1997. Golden eggs and hyperbolic discounting. Quarterly Journal of Economics 112, 443–477. 2, May. Lloyd, T., 1994. Testing a present value model of agricultural land. Oxford Bulletin of Economics and Statistics 56, 209–223. 2, May. Loewenstein, G., Prelec, D., 1992. Anomalies in intertemporal choice: evidence and an interpretation. Quarterly Journal of Economics 107, 573–597. 2, May. Plantinga, A.J., Lubowski, R.N., Stavins, R.N., 2002. The effects of potential land development on agricultural land prices. Journal of Urban Economics 52, 561–581. 2, November. Shoup, D.C., 1970. The optimal timing of urban land development. Papers in Regional Science 25, 33–44. 1, April.
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
A direct test of hyperbolic discounting using market asset data Matthew J. Salois a,∗ , Charles B. Moss b a
Department of Food Economics and Marketing, University of Reading, UK
b
Food and Resource Economics Department, University of Florida, USA
article
info
Article history: Received 5 February 2010 Received in revised form 17 May 2011 Accepted 24 May 2011 Available online 31 May 2011
abstract This paper introduces a framework that generalizes exponential discounting in a net present value model by including a quasi-hyperbolic discount parameter in the asset valuation equation. Using observed market asset data, a statistically significant quasi-hyperbolic parameter is obtained, thus rejecting exponential discounting. © 2011 Elsevier B.V. All rights reserved.
JEL classification: C23 D90 G12 Q15 Q24 R14 Keywords: Exponential discounting Farmland values Generalized method of moments Net present value Quasi-hyperbolic discounting Time preferences
1. Introduction The net present value model dominates the literature on asset valuation, in which the value of an asset is determined by the stream of discounted expected future returns. A number of empirical concerns have arisen from the use of the present value model, calling its validity into question (Campbell and Shiller, 1987; Barsky and De Long, 1993). Overwhelmingly, the a priori assumption of an exponential discount factor is relied upon. While this assumption invokes intertemporal consistency in preferences and constant discounting, evidence confirms that declining discount rates (e.g., hyperbolic discounting) are more descriptive of actual investment decisions. (Laibson, 1997; Frederick et al., 2002). This paper relaxes the assumption of exponential discounting in a net present value model for a market investment good that allows for hyperbolic discounting. A hypothesis test is derived, permitting
∗ Corresponding address: University of Reading, PO Box 237, Reading, Berkshire, RG6 6AR, UK. Tel.: +44 0 118 378 7702; fax: +44 0 118 935 2421. E-mail address: [email protected] (M.J. Salois). 0165-1765/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2011.05.029
a direct test on the discount parameters. A statistically significant hyperbolic discount parameter is obtained using observed market data for an illiquid asset. Results of the hypothesis tests imply a formal rejection of exponential discounting. 2. Theoretical and empirical model Financial theory stipulates an investment project is undertaken if the net present value of the project is positive. Under risk neutrality and time-consistency, the value of an investment today is written as the discounted stream of expected future returns: Vt =
∞ −
δt +s Et [Rt +s ].
(1)
s=1
The price or value of the investment at time t is Vt . The expected return at time t + s is Et [Rt +s ] and is based on the information available in period t. The standard exponential discount factor is:
δ t +s =
s ∏ i=1
(1 + ρt +i )−1 ,
(2)
M.J. Salois, C.B. Moss / Economics Letters 112 (2011) 290–292
where δ ∈ [0, 1]. The rate of time preference in period t is the constant rate of discount, ρt +i . While alternative forms of declining discount rates exist, quasi-hyperbolic discounting is of interest. Quasi-hyperbolic discounting is a discrete time-value function incorporating the declining value property of generalized hyperbolic discounting:
β=
if t = 0 if t > 0.
1
β · δt
The parameter δ behaves similarly to the exponential discount factor, while the parameter β captures an immediacy effect in time preference (Loewenstein and Prelec, 1992). The short-run discount factor is β · δ while the long-run discount factor is δ . Incorporating quasi-hyperbolic discounting into Eq. (1) yields: Vt = β ·
∞ −
δt +s Et [Rt +s ].
(3)
s =1
Values of β determine the extent discounting deviates from exponential discounting. Discounting is exponential if β = 1 and is quasi-hyperbolic if β ∈ (0, 1). Eq. (3) is modified to derive a model for asset values based on changes in the asset value over time:
1Vt = Vt − Vt −1 = β ·
∞ −
δt +s Et [Rt +s ]
s=1
− βδ ·
∞ −
δt +s Et −1 [Rt +s ].
(4)
s=0
Under rational expectations there is a forecast error, meaning Et [Rt +s ] = Et −1 [Rt +s ] + et +s , where et +s is an uncorrelated residual term representing ‘‘white noise’’. Equation (4) is rewritten by aggregating over like exponents and simplifying:
1Vt = −βδ · Et −1 [Rt ] + (1 − δ)β ·
∞ −
δt +s Et [Rt +s ] + et +s .
The observed cash flow in the next period is assumed to proxy the expected return in the next period, that is, Et −1 [Rt ] → Rt , and Eq. (3) is substituted in: (6)
To test for quasi-hyperbolic discounting, a linear panel regression is parameterized:
1Vit = α0 + α1 · Rit + α2 · Vit + eit .
(7)
Eq. (7) contains a constant term, which is included in most net present value regressions, and is extended to account for observations over time and space. Eq. (7) nests both the exponential and quasi-hyperbolic discount factors. The discount parameters are obtained from the estimated coefficients. Since α1 = −βδ and α2 = (1 − δ), then δ = (1 − α2 ) and:
β=
−α1 1 − α2
.
(8)
Based on the parameter estimates, a hypothesis test is devised to test for quasi-hyperbolic discounting. A direct nonlinear hypothesis test on Eq. (8) has the null hypothesis of Ho : −α1 / (1 − α2 ) = 1 against the alternative of Ha : −α1 / (1 − α2 ) < 1.1 3. Data and estimation method The availability of a rich set of data on US farmland motivates empirical examination of the possibility of quasi-hyperbolic discounting in the farmland market. Additional motivation stems
1 Standard errors computed using the delta method.
from the considerable attention that net present value models for farmland receive (Falk, 1991; Lloyd, 1994). Moreover, justification for using a declining discount rate in land investment models is given by Shoup (1970) in the context of optimal conversion.2 Given the uncertain nature of conversion times, the discount rate used in the present value formulation of undeveloped lands may be higher in time periods closer to the present. The discount rate falls as the conversion time advances, implying the value of land will appreciate faster in time periods before development. The argument by Shoup (1970) makes a case for a discount rate that declines over time and highlights the inadequacy of exponential discounting in the context of farmland investment. The data consist of annual observations on farmland values and returns and represent a 43-year panel from 1960 to 2002 of the eight major agricultural regions of the United States.3 The data are obtained using farm balance sheets and income statements reported by the USDA’s Economic Research Service and National Agricultural Statistics Service. The dependent variable is the first difference of farmland values, which represents the annual change in the value of farmland for each state. Farmland values are defined as the value of farmland per acre, excluding the value of operator dwellings. The definition of farmland returns is gross revenues per acre less expenditures on variable inputs. Given the nature of the data, using a simple estimator such as least squares for estimating Eq. (7) would not be ideal. First, while the error term, eit , is assumed to be independently and identically distributed with zero mean, heteroskedasticity across years and farms remains a possibility. Second, while the error term is not correlated with the dependent variable 1Vit , the first difference of farmland values, eit is serially correlated across time. Estimation is based on the Generalized Method of Moments (GMM).4 Proposed by Hansen (1982), GMM provides consistent estimates of the parameters. A fixed effects dummy variable approach is used.
(5)
s=1
1Vt = −βδ · Rt + (1 − δ) · Vt + et .
291
4. Results Table 1 summarizes the GMM estimates of the asset valuation equation for agricultural land and reports the J-statistic.5 Based on the GMM estimates, the null hypothesis that the over-identifying restrictions hold is not rejected. Moreover, consistent with rational expectations, none of the constant terms are statistically significant. Table 2 reports the exponential and quasi-hyperbolic discount parameters values, along with the F -statistic for the direct test of quasi-hyperbolic discounting. Results for the Appalachian panel indicate an estimated exponential discount factor of δˆ = 0.939 and an estimated quasi-hyperbolic discount factor of βˆ = 0.060. Enacting the nonlinear hypothesis test derived earlier, a value of 102.152 is obtained for the F -statistic. The null hypothesis of exponential discounting is rejected in favor of quasi-hyperbolic discounting.
2 Justification is described by Arnott and Lewis (1979) in the context of rural land and by Grenadier and Wang (2007) in the context of commercial land development. 3 Regions include the Appalachian (Kentucky, North Carolina, Tennessee, Virginia, West Virginia), Corn Belt (Illinois, Indiana, Iowa, Missouri, Ohio), Delta (Arkansas, Louisiana, and Missouri), Great Plain (Kansas, Nebraska, North Dakota, Oklahoma, South Dakota, Texas), Lake (Michigan, Minnesota, Wisconsin), Mountain (Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah, Wyoming), Pacific (California, Oregon, Washington), and Southeast states (Alabama, Florida, Georgia, South Carolina). 4 In addition to the regressors, the instrument set includes square-root terms and lagged terms of state population and farmland acreage, for a total of four overidentifying restrictions. 5 Estimates obtained using R© version 2.6.0 software.
292
M.J. Salois, C.B. Moss / Economics Letters 112 (2011) 290–292 Table 1 GMM parameter estimatesa .
Appalachia Corn belt Delta Great plains Lake Mountain Pacific Southeast a b
Constant (α0 )
Asset-values (α1 )
Asset-returns (α2 )
Observations
J-statisticb
−0.168 (10.807)
−0.056 (0.080) −0.0543 (0.316) −0.150 (0.240) −0.472 (0.195) −0.486 (0.191) −0.571 (0.173) −0.337 (0.224) −0.280 (0.142)
0.061 (0.011) 0.071 (0.020) 0.037 (0.028) 0.071 (0.019) 0.110 (0.019) 0.103 (0.013) 0.067 (0.027) 0.078 (0.021)
210 210 126 252 126 336 126 168
0.024 0.053 0.119 0.106 0.069 0.064 0.102 0.046
19.499 (17.525) 3.306 (15.068) 0.242 (5.472) 0.163 (14.588) −1.865 (5.707) 18.803 (16.802) 10.841 (11.657)
Standard errors in parentheses; dummy variable coefficient estimates are suppressed. Critical value is 9.488 based on a 5% level of significance.
Table 2 Estimated discount factorsa .
Appalachia Corn Belt Delta Great Plains Lake Mountain Pacific Southeast a b
δ Factor
β Factor
F -statisticb
0.939 (0.011) 0.929 (0.020) 0.963 (0.028) 0.929 (0.19) 0.890 (0.019) 0.897 (0.013) 0.933 (0.027) 0.922 (0.021)
0.060 (0.086) 0.584 (0.349) 0.155 (0.252) 0.508 (0.218) 0.546 (0.222) 0.637 (0.200) 0.361 (0.249) 0.304 (0.161)
120.152 1.420 11.199 5.064 4.187 3.305 6.563 18.733
Standard errors in parentheses. Critical value of the F -statistic is 3.840 based on a 5% level of significance.
For the Corn Belt states, the nonlinear hypothesis test results in an F -statistic of 1.417, implying the null hypothesis of βˆ = 1 cannot be rejected. For the Mountain states, δˆ = 0.897 and βˆ = 0.637, with an F -statistic of 3.305 unable to reject the null hypothesis of exponential discounting at the 5% level (but can reject at the 10% level). For the remaining panel regions (Great Plains, Lake, Pacific, and Southeast) the result of the hypothesis test results in the rejection of exponential discounting at the 5% level. In six out of the eight panel regions, exponential discounting is rejected at the 5% level. Quasi-hyperbolic discounting is generally more descriptive of farmland investment decisions than exponential. Results are relevant to models of land development. Agricultural land is increasingly being converted to urban uses and is the subject of policy debate (Capozza and Li, 1994; Plantinga et al., 2002). The presence of quasi-hyperbolic discounting suggests a tendency to let the short-run dominate land-use decisions leading to over-development of agricultural land. 5. Conclusions A model for depicting changes in asset valuation over time is derived for the net present value model in which the diametrically polar cases of exponential discounting and quasi-hyperbolic discounting are nested. Previous research exploits the computationally convenient assumption of exponential discounting while
failing to acknowledge evidence suggesting a declining discount rate, such as a quasi-hyperbolic one, may be more realistic. This paper estimates the parameters of time preferences in the asset valuation equation of an important market asset (US agricultural land), generalizing the model to include both exponential and quasi-hyperbolic discounting. Evidence of quasi-hyperbolic discounting is found, which propagates three conclusions. First, evidence of hyperbolic discounting can be tested using actual market investment data using the approach derived in this paper. Second, the assumption of exponential discounting does not adequately describe time preferences in the farmland market. Third, results are relevant to models of land development; quasi-hyperbolic discounting suggests the propensity to overdevelop land in the short-run. References Arnott, R.J., Lewis, F.D., 1979. The transition of land to urban use. Journal of Political Economy 87, 161–169. 1, February. Barsky, R.B., De Long, J.B., 1993. Why does the stock market fluctuate? Quarterly Journal of Economics 108, 291–311. 2, May. Campbell, J.Y., Shiller, R.J., 1987. Cointegration and tests of present value models. Journal of Political Economy 95, 1062–1088. 5, October. Capozza, D., Li, Y., 1994. The intensity and timing of investment: the case of land. American Economic Review 84, 889–904. 4, September. Falk, B., 1991. Formally testing the present value model of farmland pricing. American Journal of Agricultural Economics 73, 1–10. 1, February. Frederick, S., Loewenstein, G., O’Donoghue, T., 2002. Time discounting and time preference. Journal of Economic Literature 40, 351–401. 2, June. Grenadier, S.R., Wang, N., 2007. Investment under uncertainty and timeinconsistent preferences. Journal of Financial Economics 84, 2–39. 1, April. Hansen, L.P., 1982. Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054. 4, September. Laibson, D., 1997. Golden eggs and hyperbolic discounting. Quarterly Journal of Economics 112, 443–477. 2, May. Lloyd, T., 1994. Testing a present value model of agricultural land. Oxford Bulletin of Economics and Statistics 56, 209–223. 2, May. Loewenstein, G., Prelec, D., 1992. Anomalies in intertemporal choice: evidence and an interpretation. Quarterly Journal of Economics 107, 573–597. 2, May. Plantinga, A.J., Lubowski, R.N., Stavins, R.N., 2002. The effects of potential land development on agricultural land prices. Journal of Urban Economics 52, 561–581. 2, November. Shoup, D.C., 1970. The optimal timing of urban land development. Papers in Regional Science 25, 33–44. 1, April.