The Effect of Agricultural Policy on Farmland Values.
The transfer efficiency of an agricultural support program is usually measured by its effectiveness in distributing benefits within the agri-food sector. While most farm programs are directed at farmers in terms of income support, not all of this money remains with the farmers for consumption or reinvestment. Some program benefits may be transferred from farmers to suppliers of inputs, processors, distributors in the product market, and final consumers; or from future farmers to those presently farming. Other responses may include increased production of supported commodities relative to non-supported commodities or increased prices for the assets used in production. These adjustments result in an economy-wide adjustment that may or may not have been intended by the policy initiative.
The increase in the value of assets used in agricultural production is considered to be one of the major outflows from government support payments. Capitalizing the full benefits of a support program will not affect net farm income in the short run. There are also negative distributional consequences associated with the capitalization of government support payments. Current asset owners obtain the present values of future income transfers while beginning farmers received little or no benefit from the transfers.
Since the mid 1980s, a limited number of studies have empirically examined the effect of government programs on the price of land and agricultural assets with mixed results. Using a partial equilibrium model of the U.K. agricultural sector, Traill (1985) estimated a 1% increase in support prices would increase net farm income by 9%, but this increase in income was largely capitalized into land values. Using a recursive econometric model of cast rents and land values, Featherstone and Barker (1988) estimated that a move to a more free market scenario from the 1985 farm program would reduce land prices in the United States by about 13% in five years. Veeman, Dong, and Veeman (1993) determined that the abolition of direct government transfer payments in Canada would reduce total farm cash receipts by 13%, and consequently lead to a decline in land prices of 5% in the short run and 18.5% in the long run. Clark, Klein, and Thompson (1993) also found that subsidies as well as market-based income were capitalized into land values for Saskatchewan using a cointegration approach. Just and Miranowski (1993) estimated that government payments account for approximately 15 to 25% of the capitalized value of land in the United States, but only a small part of their fluctuations. Examining the effects of government subsidies on land values across regions, Goodwin and Ortalo-Magne (1992) found that a 50% reduction in Producer Subsidy Equivalents for wheat producers would have a significant negative effect on land values in the EC and a small positive effect on land values in the United States and Canada as prices would tend to equalize under conditions of free trade.
Studies on aggregate farm land prices have generally focused on how demand forces determine equilibrium prices. The basic premise has been that the price of an income earning asset should follow the present value model in which a stream of discounted net returns drive the price of that asset. Traditional time series regression analyses have supported the underlying basis of the capitalization model in which changes in returns to farming explain changes in farmland prices (e.g., Alston (1986), Burt (1986), Weisensel, Schoney, and van Kooten (1988), and Veeman, Dong, and Veeman (1993)). However, recent studies using cointegration analysis have found that land rents and prices do not have the same time series properties, thereby suggesting that the present value method may not be appropriate for examining land price movements (e.g., Featherstone and Baker (1987), Baffes and Chambers (1989), Falk (1991), Clark, Fulton, and Scott (1993), and Tegene and Kuchler (1993)). The rejection of the capitalization approach could be linked to parameter instability originating from inappropriate modeling of the underlying expectations.
Another possible reason for the rejection of the capitalization approach suggested by Falk (1991) may the presence of a time varying discount rate. The only formal analysis of the subject is by Hanson and Myers (1995) who test alternative theories of time-varying discount rate and factors contributing to the generation of such rates. Depending on circumstances and how farmers view them, the two streams of farm income, market income and government payments, can have very different projected rates of growth in the future. If for example, government payments are considered to be transitory compared to income from the market, as suggested by Schmitz (1995) for Saskatchewan, income from this source will be discounted more heavily than income from the market. Should this happen, the impact of government payments on land prices will be minimal. The reverse could also be true if the nature of government programs is different and viewed as less transitory than income from the market.
The purpose of this paper is to estimate the separate effects of market returns and government support programs on agricultural land values. An attempt is also made to investigate if income from government programs is, indeed, discounted more heavily than income from the market. The next section of the paper reviews the development of various approaches to land valuation from the demand and supply models of the 1960s, to the extensions of the capitalization model evaluated using traditional time series regression, to the recent cointegration studies which generally question the application of the basic capitalization model. A structural model is then developed which decomposes rents into two sources (market-based returns and government payments) and allows for differences in potential growth rates between these sources and thus, differences in how those rents are discounted. The model is then estimated for Ontario land prices and the results compared for consistency with the time series approach. The paper concludes with a brief discussion of the policy implications stemming from the estimated results.
II. REVIEW OF LAND VALUATION STUDIES
There is no general consensus as to the exact influence of government transfer payments on land prices because researchers have yet to agree on how cash flows impact land price over time. Land price studies have evolved dramatically with positions accepted by some and subsequently restated by others. The following review provides a chronology of thought on this subject and is presented to outline the complexities involved in researching the subject matter of this paper, as well as offering some caveats to the process.
Early studies assumed net farm income-per-acre as the most appropriate variable against which to measure land value and that the present value of land is equal to its annual earnings divided by a discount rate (Doll, Widdows, and Velde 1983). This capitalization formula is derived under the assumption that the value of an income-producing asset is the capitalized value of the current and future stream of earnings from owning the asset,
[L.sub.t] = [summation of] E([R.sub.t+i])/(1 + [r.sub.t+1])(1 + [r.sub.t+2])...(1 + [r.sub.t+i]) where [infinity] to i=0 
where [L.sub.1] is the equilibrium asset price at the beginning of time period t; [R.sub.1] is the residual real return generated from owning the asset measured at the end of time period t; [r.sub.1] is the time varying real discount rate for year t; and E is the expectation on returns conditional on information in period t. The maximum bid price that a buyer would offer and the minimum asking price that a seller would accept will converge to the unique equilibrium price in equation  assuming symmetry in the market between the opportunity cost for a seller and the returns to a buyer (Robison, Lins, and VenKataraman 1985). If it is assumed that the discount rate is constant, agents are risk neutral, and differential tax treatments of capital gains and rental income are ignored (Hamilton and Whiteman 1985), then the asset valuation model given by equation  becomes:
[L.sub.t] = [(1 + r).sup.-1] [summation of] E([R.sub.t+i]/[(1 + r).sup.i] where [infinity] to i=0. 
Assuming the residual return is constant in each period, [R.sup.*], equation  simplifies further to the traditional capitalization formula:
[L.sub.t] = [R.sup.*]/r. 
The inclusion of ordinary income taxes do not change this capitalization formula in the absence of income growth (Baker, Ketchabaw, and Turvey 1991).
The capitalization formula given by equation  has formed the foundation for most studies on asset values with residual returns measured by net farm income. However, the divergence of asset values from farm income trends forced researchers to examine the validity of the capitalization formula and assumptions used in its derivation. A number of alternative explanations were proposed including productivity increases, government programs, and urban pressures. In the 1960s, these variables were introduced in land pricing through a supply and demand framework. Studies using a simultaneous equation framework for farmland values (demand) and farmland transfers (supply) include Herdt and Cochrane (1966), Tweeten and Martin (1966), and Reynolds and Timmons (1969). Although these supply and demand models explained farmland price variations reasonably well within the period for which they were estimated, Pope et al. (1979) reestimated them using more recent data and found the models to be ineffective in explaining the divergence between farm income and land values in the 1970s. The most important problem with the supply and demand framework is that a classic supply function for farmland does not exist due to the highly inelastic nature of farmland quantity (Burt 1986). Due to a number of unresolved theoretical and empirical questions surrounding the simultaneous demand and supply analysis of the farmland market, most recent studies of farmland price movements focus exclusively on the role of demand side forces.
One of the restrictive assumptions prompting the questioning of the capitalization formula was addressed in a study on the causes of asset appreciation by Melichar (1979). Melichar pointed out the inappropriateness of net farm income as a measure of the return to land. He also noted that current returns to farm assets grew rapidly over a 25-year period beginning in the mid 1950s and that resulted in the large annual real capital gains and a low real rate of current return to assets actually experienced by the farm sector. On the basis of this historical experience, Melichar modified the capitalization formula to account for growth so that
[L.sub.t] = (1 + g)R/(r - g) 
where g is the annual growth rate of the current return, R. Thus, land values can change with changes in the returns and in the discount rate, plus the growth rate in returns (deemed to be the driving force behind increasing land values throughout the 1970s). If the growth rate is greater than zero, the equilibrium land price will increase each year even if the growth rate and discount rate remain unchanged from year to year. This idea can be incorporated into the traditional capitalization formula (equation ) by solving the following equation recursively:
[L.sub.t] = E([L.sub.t+1] + [R.sub.t]/(1 + r), 
which shows Melichar's point that capital gains can be explained in theory as the capitalization of expected future rents (Falk 1991).
Alston (1986) also assumed that rental income grows exponentially at a constant nominal rate, but differs from the approach of Melichar by distinguishing between the tax rate on income ([T.sub.y]) versus capital gains ([T.sub.c]). The distinction between tax rates results in modifying the capitalization formula given in equation (4) to:
[L.sub.t] = (1 - [T.sub.y])[R.sub.t]/(r - (1 - [T.sub.c])g). 
Alston then decomposes the discount rate into a risk premium for land (c) and the nominal market interest rate (i) which earns interest income that is taxable (r = c + (1 Ty)i). Substituting this definition of the discount rate into equation  results in an asset price which is still equal to current expected rental income divided by a discount rate, however the discount rate is now adjusted for income growth (capital gains) and taxes. Alston empirically estimated a version of equation  which allowed him to examine two competing hypotheses. One put forward by Melichar, who asserted that land prices grow at the same rate as returns to land, and the other advanced by Feldstein (1980), who suggested that increases in expected inflation cause a decrease in the discount factor due to the preferential treatment given to capital gains income thereby leading to an increase in real land prices. Alston concluded that most of the growth in real land prices for several countries can be explained by growth in real net rental income and that inflation has had only a small statistically insignificant negative effect on real land prices. Rose and LaCroix (1989) also found that Feldstein's hypothesis could not be taken as a general model of land price movements.
The present value model also formed the basis of a study by Burt (1986). Burt noted that there are two sources of dynamic behavior in the basic model given in equation . Burt approximated the composite effects of both expectations with regard to rents and the adjustment mechanism for land price with a multiplicative distributed lag specification on net rents which encompasses a family of alternative dynamic structures. In addition, Burt assumes a constant real discount rate since investors in land are concerned with the long run equilibrium rate and do not account for yearly movements in the real rate. The difference between the specification used by Burn and Alston is that the former study uses an explicit but robust lag specification, while the latter uses a tightly parameterized model of thirteen lags on past land prices and no lags on net real returns. However, Aliston does allow more flexibility on the capitalization rate which is assumed to be constant by Burr. Burt concludes that the annual percentage change in Illinois land prices is due to, (a) the percentage difference between the capitalized value of current expected rent and expected land price the previous year (13%); and, (b) the percentage change in expected land prices (75%). However, Burt notes that the latter component is not the traditional measure of capital gains but rather an exogenous measure which is implicitly a function of lagged rents. He concludes that land prices are driven mostly by changes in net rents and not by the speculative forces driving the values of non-income earning assets as has been suggested in the literature.
Burt also tested a hypothesis originating in the theoretical model of Shalit and Schmitz (1982) in which the assumption of credit rationing forces the accumulated debt level to be a major determinant of farmland. Shalit and Schmitz (1982) suggest the desired rate of land purchases by an individual farmer increases with rising land prices because those higher prices provide extra equity for loan collateral. Therefore, the higher accumulated per acre debt on farmland, the higher the land price. However, Burt found debt-per-acre to have a very small effect. Weisensel, Schnoney, and van Kooten (1988) also refute the Shalit and Schmitz hypothesis and suggest to the contrary that increased land values may be a determinant of increased credit use. Just and Miranowski (1993) also found debt to have little influence on land values since debt levels are a relatively small value of land holdings, implying that credit is not a major constraint to land purchases.
Featherstone and Baker (1988) also start from the capitalization formula with dynamics entering into the market through the expectations of returns to land and the adjustment mechanism for land prices. However, they assume an ad hoc adaptive process in which cash rent is a weighted average of current and past residual returns to farmland. Past and historical cash rents then determine land value in the recursive system.
The empirical finding that net real returns is the major factor explaining land values was brought into question in a series of articles beginning with Featherstone and Baker (1987). Their study covered a much longer time frame than that of Burt and used vector autoregression (VAR) in which equations for asset values, returns to assets, and interest rates are all estimated simultaneously. Lags of each variable were used as regressors in each equation. By specifying lagged asset values, in addition to the expectations processes for rents and interest rates as explanatory variables in the reduced form equation for asset values, Featherstone and Baker (1987) were able to test for the presence of an asset price bubble. Such a bubble may arise if the market participants focus on irrelevant aspects such as past capital gains, rather than movements in returns and real interest rates. Their results suggest that speculative forces may have played a major role in determining U.S. farmland prices. The propensity for large and random price responses is inconsistent with a present value formulation.
Previous literature in support of the present value method used traditional time series regression analysis. However, if the data are characterized by non-stationarity, such methods may suffer from the spurious regression problem originally studied by Granger and Newbold (1974). In addition, the concept of cointegration in the sense of Engle and Granger (1987) between land price and a set of explanatory variables becomes an important empirical consideration when unit roots characterize the data. Indeed, the appropriateness of the use of the traditional capital asset pricing model to determine land price was brought into question by a number of studies using cointegration methodology. For example, Campbell and Shiller (1987) show that if the present value model is correct, then, (a) net rents and land prices should have the same time series properties; and, (b) past values of the spread between land prices and rents add useful information in forecasting future changes in rents given past changes in net rents. These restrictions were tested in a number of studies investigating farmland price movements in North America and Europe.
Using Campbell and Shiller's procedures, Falk (1991) found that although Iowa farmland price and rent movements are highly correlated, price movements are more volatile than rent movements. Thus, talk rejects the present value model on the basis of the second set of restrictions as formulated by Campbell and Shiller. Using the same procedures but with the data employed by Featherstone and Baker (1987), Clark, Fulton, and Scott (1993) also found that the simple asset pricing model did not hold. However, unlike Falk (1991), they found the time series representations of rents and land prices were inconsistent as did Baffes and Chambers (1989). Tegene and Kuchler (1993) also rejected the present value method as a means of approximating U.S. farmland price movements using a slightly different time series method employed previously to study stock price movements. Possible reasons for rejection of the present value model include: (a) the presence of speculative bubbles; (b) time varying discount rates: and (3) nonmonetary returns to farmland. In contrast to these studies, Clark, Klein, and Thompson (1993) found some support for the capitalization formula model using Saskatchewan data. Hanson and Myers (1995) do allow for a time-varying risk premium, but reject the present value model of farmland returns as well as the CAPM model.
In a return to a structural model, as opposed to the recent free-form econometric investigations just mentioned, Just and Miranowski (1993) present a framework for analyzing the relative importance of factors determining farmland prices. If inflation taxes, credit market imperfections, transactions costs, and risk aversion are eliminated, the land value equation reduces to the standard discounting equation. Just and Miranowski (1993) found government payments are a minor factor in explaining year-to-year changes in land prices, and that land price expectations are the most important explanatory variable that is driven by inflation and the real return on alternative uses of capital.
Land value studies can thus be summarized into two camps: those that rely on the present value model of asset pricing with traditional time series analysis, and those that use cointegration analysis to examine the validity of the capitalization model and particularly the assumption of a constant discount rate. What has not been considered by the latter group of studies is that land rents are derived from two sources, market income and government payments. These two streams of income can have very different projected growth rates due to different discount factors implicit in the expectations of economic agents and thus can have differing impacts on land prices. A modification of the traditional capitalization model is necessary to incorporate this idea of decomposing land rents into two sources. Such a modification may improve the performance of the CAPM in explaining farmland prices. We introduce such a modification in the following section.
III. THEORETICAL MODEL
The present value model of land valuation without government payments can be summarized in the following equation:
[L.sub.t] = [summation of] [b.sub.j][E.sub.t-1][R.sub.t+j] where j=1 to [infinity] 
where [L.sub.t] is current nominal land price at the beginning of the period t; b is the nominal discount factor; and [R.sub.t] is the nominal net cash rental income to land in period t as expected on the basis of information available in period t - 1 (E). The nominal discount factor can be decomposed into b = 1/(1 + i + c) where i is the nominal rate of interest, and c is a nominal risk premium for land. A real version of equation  would have land price and rent in real rather than nominal terms and have the expected growth rate in nominal cash rent, ([Pi]), subtracted from the interest rate, (i). No differential tax rates are assumed.
The present value model given by  can be rewritten if the stochastic process driving nominal rents is known. Suppose this process is described by:
[R.sub.t] = (l + [Pi])[R.sub.t-1] + [w.sub.t], 
where w is a white noise error term. Solution of the infinite prediction problem from equation  (except for the first step ahead prediction) using equation  results in the following specification of the present value model:
[L.sub.t] = [E.sub.t-1][R.sub.t]/(i + c - [Pi]).
Equation  can be interpreted as a short-run equilibrium formula. If the nominal rate, risk premium, and growth rate in returns are time varying then equation  can be written as:
[L.sub.t] = [E.sub.t-1][R.sub.t]/(i, + [c.sub.t] - [[Pi].sub.t]) + [[Mu].sub.i], 
where u is an error term capturing deviations around the equilibrium.
In order to assess the effects of government programs on land values, two modifications are introduced to the existing capitalization formula given by equation . First, economic rents are decomposed into those derived from the market and those derived from government programs. Second, the discount rate varies depending upon the source of economic rents, thereby allowing for the testing of the hypothesis that income from government programs is more likely to be transitory, and thus discounted more heavily than market income.
The first modification separates returns from the land base, (R), into its two possible sources, production, (P), and government, (G), so that, [Mathematical Expression Omitted]. Many studies have specified an economic rent that includes returns from both sources, but only Goodwin and Ortalo-Magne (1992) and Just and Miranowski (1993) have isolated the two sources. The separation allows for the testing of the hypothesis that land prices respond differently to anticipated changes in the alternative sources of economic rents (i.e., Ho: ([Delta]L/ [Delta][R.sup.*] [multiplied by] ([Delta][R.sup.*]/[Delta]P) = ([Delta]L/[Delta][R.sup.*]) [multiplied by] ([Delta][R.sup.*]/[Delta]G)). This modification is incorporated into our model by rewriting equation  as:
[Mathematical Expression Omitted], 
where [b.sub.j] and [b.sub.2] are the respective discount factors for market returns and government payments.
The second modification relates to the discount rate which is decomposed into two separate rates for each income source to allow for differences in potential growth rates in those sources. The growth rates for farm market income and government transfers are denoted by p and g respectively. It is assumed that both sources of returns follow similar stochastic processes given by:
[P.sub.t] = (1 + p)[P.sub.t-1] + [w.sub.1t] [14a]
[G.sub.t] = (1 + g)[G.sub.t-1] + [w.sub.2t] [14b]
Retracing the steps involved in solving for equation , the land value equation incorporating these two modifications can be expressed as
[L.sub.t] = [E.sub.t-1][P.sub.t]/[i.sub.1t] + [c.sub.1t] - [p.sub.t] + [E.sub.t-1][G.sub.t]/[i.sub.2t] + [c.sub.2t] - [g.sub.t] 
The hypothesis that market income is discounted less heavily than income from government programs (p, [greater than] g,) can now be tested. Empirical support for the specification is provided by Schmitz (1995), who notes that Saskatchewan land prices fell much faster than total returns during the early periods of the farm financial crisis since most of these returns were composed of heavily discounted government payments.
The responsiveness of land prices to the alternative sources of returns, as indicated by elasticity measures, are complicated by the fact that the capitalization formula is solved using prediction equations. These prediction coefficients are not needed for the calculation of certain elasticities. For example, a long-run elasticity of land values to market-based returns or government payments would presumably measure the percentage response of land values to a permanent percentage response in market based returns or government payments. If indeed the responses are permanent, then these permanent responses would be known to economic agents and there would be no need to predict them. Under these circumstances, the long-run elasticity to a permanent change in either return can be calculated directly from equation  by imposing the steady state and converting it to an elasticity. The resulting long-run elasticity measures of land values to market-based income [16a] and government payments [16b] are thus:
[Mathematical Expression Omitted] [16a]
[Mathematical Expression Omitted] [16b]
where [[Xi].sup.LR] is the long-run elasticity of land values with respect to market-based income or government payments, [P.sub.B] is the mean of market-based returns, [G.sub.B] is the mean of government payments, and [L.sub.B] is the mean of land values.
Defining appropriate short-run elasticities is more problematic since one can legitimately speak of a one-year response to both expected as well as unexpected changes in market-based returns and government payments. Presumably, for policy purposes, the response to expected changes is more relevant since most policies are based on known responses and not "surprises." Once the long-run elasticities are estimated, the relevant short-run elasticities can be derived from them. Thus, the one-year elasticity of land values to a 1% change in market based income, [Mathematical Expression Omitted], and in government payments,
[Mathematical Expression Omitted]. are given by:
[Mathematical Expression Omitted]. [17a]
[Mathematical Expression Omitted]. [17b]
A number of important empirical issues need to be resolved before generating the estimates of long-run and short-run elasticities of land prices with respect to market income and income from government payments. We focus on these issues in the next section.
IV. EMPIRICAL ISSUES
The present value model for land valuation with two sources of income (market and government payments) summarized by,
[Mathematical Expression Omitted], 
cannot be solved in its present form because it involves unobservable expectations on future market returns and government payments by farm operators. The model can be empirically estimated however, if it is assumed that farm operators have rational expectations and that the time series models generating market returns and government payments are known.
The previous section assumed a general explosive time series for the two income sources (equations [14a] and [14b]) to obtain a land price equation that can be estimated. Suppose the stochastic process driving both sources of income can be represented by a first order autoregressive trend stationary series, so that equations [14a] and [14b] can be empirically specified as,
[P.sub.t] = [[Alpha].sub.0] + [[Alpha].sub.1]t + [[Alpha].sub.2][P.sub.t-1] + [v.sub.2t], 
[G.sub.t] = [[Beta].sub.0] + [[Beta].sub.1]t + [[Beta].sub.2][G.sub.t-1] + [v.sub.3t], 
where [Alpha] and [Beta] are parameters and v are error terms. Empirical justification for the choice of a trend stationary series for both market-based returns and government payments is provided in the next section. Combined with the assumption of rational expectations, equations  and  deliver an equation for the determination of land values based on observable market-based returns, government payments and a time trend which can be estimated and subjected to empirical testing. By applying the Wiener/Kolmogorov prediction formula to equations  and  and substituting them into equation  yields:
[L.sub.t] = [[Gamma].sub.0] + [[Gamma].sub.1]t + [[Gamma].sub.2][P.sub.t-1] + [v.sub.tt], 
[Mathematical Expression Omitted]
[[Gamma].sub.2] = [[Alpha].sub.2][b.sub.1]/1 - [[Alpha].sub.2][b.sub.1]), [[Gamma].sub.3] = [[Beta].sub.2][b.sub.2]/(1 - [[Beta].sub.2][b.sub.2]). 
The trend, (t), in land price equation  is generated from the existence of a trend in the stochastic processes generating market-based returns and government payments. Therefore, any growth in land prices must come from the growth in at least one of the forcing variables, P and G. If both [[Alpha].sub.1] and [[Beta].sub.1] are zero, then [[Gamma].sub.1] is also zero in equation  thereby eliminating the trend from the land price equation providing an example of what Granger calls balancing of stochastic processes.(2) Similar arguments can also be made for any of the variables on the right-hand side of the stochastic processes driving either market-based returns (equation ) or government payments (equation ).
Derivation of equation  explicitly recognizes the importance of expectations concerning the stochastic processes for the two sources of income in the generation of a reduced-form land price model. For example, the existence of a trend term in  is due entirely to the existence of a trend in either market returns  or government payments . If expectations concerning the stochastic processes generating either source of income were to change, then this in turn would affect the [Gamma] coefficients of the land price equation. This phenomenon is known as the Lucas  critique. For example, suppose that market-based returns were not a trending process (i.e., [[Alpha].sub.1] = 0). In this case, the coefficient on the trend in  reduces to [[Gamma].sub.1] = [[Beta].sub.1] [b.sub.2]/(1 - [[Beta].sub.2][b.sub.2])(1 - [b.sub.2]) so that the trend in land prices would be completely driven by the trend in government payments. Now suppose there is a policy change and governments decide not to increase farm support payments. Assuming this policy change is known by farm operators (or at least farmers can learn the policy change has taken place), then [[Beta].sub.1] in  is zero, and the trend is eliminated from the government payments equation. This in turn implies [[Gamma].sub.1] = 0 in  and thereby eliminates the trend from the land price equation. Land values would no longer be a trending process because neither sources of income are characterized by trending processes.
The results imply, that if one were to estimate the land price equation without also examining the income prediction equations given by  and , one may observe parameter instability if expectations are changing over the sample period. Parameter instability is sometimes interpreted as rejection of the theory presented. However, the model setup in this study discounts such an interpretation since it may simply be due to changes in expectations related to changes in the stochastic processes generating either source of income.
Estimation of the system of equations given by equations , , and  can deliver estimates of the model parameters. The parameters of the stochastic process given by equations  and  together with the discount factors [b.sub.1] and [b.sub.2] are embedded within the land price equation via the restrictions given in equation . These are known as the cross-equation restrictions implied by rational expectations (e.g., Sargent 1979). The cross-equation restrictions together with the (non-linear) system of equations defined by equations , [201, and  identify a total of eight parameters; three from equation  ([[Alpha].sub.0], [[Alpha].sub.1], and [[Alpha].sub.2]), three from equation  [[[Gamma].sub.0], [[Beta].sub.1], and [[Beta].sub.2]) and two from equation  ([b.sub.1] and [b.sub.2]). If, instead, the (linear) system given by equations , , and  were estimated without imposing the restrictions given by , then a total of ten parameters would have been estimated; three from equation  ([[Alpha].sub.0], [[Alpha].sub.1], and [[Alpha].sub.2] three from equation  [[[Beta].sub.0], [[Beta].sub.1], and [[Beta].sub.2]) and four from equation  [[[Gamma].sub.0], [[Gamma].sub.1], [[Gamma].sub.']2, and [[Gamma].sub.3]). The difference between the number of parameters estimated in the unrestricted linear model and the restricted non-linear model are known as the cross-equation restrictions and can be tested using standard non-linear methods such as a likelihood ratio test (e.g., Gallant 1987).
Further testing can be done on the system of equations , , and  with restrictions  imposed. The first of these is a test that market-based returns and government payments are discounted at the same rate ([b.sub.1] = [b.sub.2]). Rejection of this hypothesis would imply that these two sources of income are viewed differently when capitalization decisions are made. Other hypotheses of interest include that the trend in land values is completely driven by the trend in either market-based returns ([[Alpha].sub.1] = 0) or government payments ([[Beta].sub.1] = 0).
The effects of government programs on farmland prices was assessed for the province of Ontario. Annual observations on direct government subsidies (both federal and provincial) per acre, income from farm operations (on cash basis) per acre, and land values per acre from 1947 to 1993 were obtained for Ontario from Statistics Canada Catalogue #21-603E (Agricultural Economic Statistics). Data on direct subsidies include payments under: (a) crop insurance program, (b) ASA-Price Stabilization, (c) ASA-Tripartite plans, (d) provincial stabilization programs, (e) dairy subsidy, (f) NISA, (g) GRIP, and (h) other federal and provincial programs designed to deal with unusual climate (e.g., drought or frost etc.) or economic conditions (e.g., very low commodity prices, trade war, etc.) affecting agriculture. Data are deflated by the Canadian implicit GNP price deflator (1987 = 100), taken from the Canadian Statistical Observer 1993. The subsidy data were subtracted from the income data to arrive at the provincial income figure that does not include subsidies.
Ontario farmland prices per acre are plotted in Figure 1. Land values generally increased steadily through time with a rapid increase beginning in the early 1970s until the beginning of the next decade. Prices started to rebound in the late 1980s and have now approached the previous peak levels. In contrast to the general upward trend in land prices, farm income per acre in Ontario has fluctuated around the $90 level with the exception of the peak in the mid 1970s and the fall since 1986 (Figure 1). There has been a strong trend in government payments over time. The subsidy series increased slowly during the first part of the sample and then rose rapidly during the 1980s. Since 1990, however, the rate of growth has declined (see Figure 1). Government payments have also been relatively more stable around this trend than have farm income levels which have fluctuated significantly over the last 40 years.
VI. EMPIRICAL RESULTS
The methods of the theoretical and empirical issue sections are heavily dependent upon the assumption that the various series are trend stationary. If the non-stationarity in the series were difference stationary, a different statistical approach would be required (e.g., Campbell and Shiller (1987) and Clark and Klein (1993)). Justification for the choice of a trend stationary model of land prices is provided in Table 1 which presents the results of the application of Dickey-Fuller [[Tau].sub.t], tests to the three data series. For both land prices and government payments, the difference stationary model is strongly rejected in favor of the trend stationary specification. Although the Dickey-Fuller test could not be rejected at the usual level of significance for market-based returns, this particular unit root test of difference stationarity series has low power against plausible trend stationary alternatives (e.g., Dejong et al. (1990). Since market-based returns as a difference stationary process is inconsistent with the trend stationarity of land prices and the Dickey-Fuller test has low power in identifying difference stationary series, we will assume that market returns is also a trend stationary series.
The Box-Q statistics for both market-based returns and government payments are not significant when no lagged differences are included in the regression. This implies that the first order autoregressive models presented in equations  and  as the stochastic processes generating market-based returns and government payments are consistent with the data. Additional lagged terms would be required if significant lagged difference were found in the data.(3)
Since all of the series are likely to be trend stationary series, the next step is to estimate the system of equations given by equations , , and  and test the various restrictions. This system is estimated using Non-Linear Seemingly Unrelated Regression (NSUR). Results of the various tests performed on the system of equations using NSUR are presented in Table 2. The cross-equation restrictions implied by rational expectations are rejected.
Test statistics for equality of discount factors and significance of trend variables in driving land prices, land rents and government payments are also presented in Table 2. The null hypothesis that the discount factors [TABULAR DATA FOR TABLE 1 OMITTED] are equal for both market based returns and government payments is rejected (F-value of 4.75 with (2, 128) degrees of freedom) indicating that these two income streams are viewed differently when capitalization decisions are made. In addition, the asymptotic t-value on the trend variable in the market returns equation was not significantly different [TABULAR DATA FOR TABLE 2 OMITTED] from zero in the system of equations with the cross equation restrictions imposed (this amounts to a Wald test on the parameter (e.g., Gallant 1987). This hypothesis that the trend in market-based returns is zero was tested using the more powerful likelihood ratio test and is presented as the last test in Table 2. The hypothesis was not rejected implying that the trend in land prices in Ontario is driven by the trend in government payments and not the trend in market returns.
Estimates of the parameters of the model with the trend in market-based returns set equal to zero are presented in Table 3. The model delivers a reasonable fit for all three equations, although the [R.sup.2] value for the prediction equation of market-based returns is somewhat low. All t-values, with the exception of the intercept terms, indicate the estimated parameters are significantly different from zero at the 5% level of significance. Average annual absolute difference between actual and predicted was approximately 9% with the model under-estimating land prices in the late 1970s and over-estimating them in the mid 1980s.
TABLE 3 RESTRICTED NON-LINEAR SEEMINGLY UNRELATED REGRESSION RESULTS FOR ONTARIO LAND PRICE MODEL, 1949-1993(*) Dependent Variable Repressor Land Price (L) Income (P) Subsidies (G) Intercept -227.492 2.695 -3.083 (-1.44) (0.47) (-2.19) Trend 43.030 - 0.419 (17.04) (4.60) Lagged P 4.461 0.953 - (2.59) (14.04) Lagged G 0.494 - 0.335 (210.04) (2.45) [R.sup.2] 0.85 0.53 0.75 Estimated Discount Factors P 0.857 (25.98) G 0.986 (313.77) * Values underneath parameter estimates are asymptomatic t-values.
Government payments are discounted less than are market based returns in Ontario. The [TABULAR DATA FOR TABLE 4 OMITTED] estimated discount factor for government payments (0.986) is greater than that estimated for market-based returns (0.857). This would imply that government payments have been viewed as a more stable source of income to farm operators in Ontario during the last half century than market-based returns. The result contradicts the suggestions by Schmitz (1995) that Saskatchewan farmers discount government payments more heavily than farm income when pricing land. The difference is due to the nature of the stabilization programs between the two provinces. Ad-hoc government transfers have been common in Saskatchewan whereas the payments to Ontario producers have been largely based on defined stabilization programs. As farm incomes have fallen, these payments have increased and provided the returns necessary to maintain an overall increasing trend in Ontario land prices over time.
Short-run and long-run elasticities of land values to market-based returns and government payments are presented in Table 4. Short-ran elasticities to both sources of income are quite small with the response of market-based returns being the larger of the two responses. The long-run response of land values to the two income returns is inelastic. However, the elasticity of land values to government payments is approximately 50% higher at 0.625 than the corresponding elasticity with respect to production income (0.433). The difference between these elasticity measures is growing over time with the increasing importance of government transfers to total net farm income (Table 4). These results suggest that land values are more responsive to government payments, especially when these payments are perceived to be permanent in nature.
The extent to which agricultural support programs have been capitalized into farmland prices, and the subsequent efficiency loss with those programs, has been examined in this study. A present value land price model was developed which decomposes returns to the land based into its two possible sources (farm production and government subsidies) and allows the associated discount rates with these two income sources to vary. The results indicate that the two income streams are viewed differently when capitalization decisions are made by Ontario farmers. Government payments are discounted less than are market based returns in Ontario suggesting that government payments have been viewed as a more stable source of income to farm operators in Ontario during the last half century than market-based returns. Suggestions for future research include examining the generality of the results. For example, the ad-hoc nature of stabilization programs in Saskatchewan may lead to the opposite results where farmers discount government payments more heavily than farm income (Schmitz 1995). In addition, the influence of changing expectations regarding transfers in an era of government austerity should also be examined.
1 An exception is the recent study by Lopez, Shah, and Altobello (1994) who develop a supply-demand model of the amount of land in agriculture to determine the optimal allocation of land among competing uses.
2 The balancing of stochastic processes was first pointed out in the land price literature by Clark et al. (1992).
3 Lag length tests were undertaken on the market returns series and the government payment series including a trend and a lag length of one was found.
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Alfons Weersink, Steve Clark, Calum G. Turvey, and Rakhal Sarker are, respectively, professor, Department of Agricultural Economics and Business, University of Guelph, Guelph, Ontario; associate professor, Department of Economics and Business Management, Nova Scotia Agricultural College, Truro, Nova Scotia; associate professor and assistant professor, Department of Agricultural Economics and Business, University of Guelph, Guelph, Ontario. Financial support for the project was gratefully received from the Ontario Ministry of Agriculture, Food, and Rural Affairs.
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|Author:||Weersink, Alfons; Clark, Steve; Turvey, Calum G.; Sarker, Rakhal|
|Article Type:||Statistical Data Included|
|Date:||Aug 1, 1999|
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