The Impacts of Different Farm Programs on Cash Rents

Farmland is the main asset of the U.S. agricultural sector's balance sheet, accounting for an average of 68% of U.S. agricultural assets between 1960 and 2001. This is important for at least three reasons. First, the sector's solvency is intimately linked to the value of farmland. Second, the opportunity cost of farmland represents a major production expense from the perspective of individual farmers. Finally, related to the opportunity cost of farmland, farmland values have a significant effect on the estimation of productivity and competitiveness measures across regions.

The significance of farmland values for the agricultural sector's economic performance has made factors determining farmland values a frequent subject of research. Studies of farmland values have typically emphasized expected returns, interest rates, and government payments to farmers, among other factors. In a recent comparison of rates of return between farm and nonfarm businesses, Hopkins and Morehart show that nonfarm businesses generate much higher sales from their assets than farm businesses do. They suggest that farmland may be responsible for this perceived inefficiency, through the capitalization of payments from government programs into farmland prices. The capitalization of farm program payments into land values has often been discussed in the literature (e.g., Just and Miranowski, Tweeten and Martin, Herdt and Cochrane, Melichar). However, these studies were limited in the way returns to farmland were measured. For example, returns to farmland were estimated as the residual return remaining after paying for all other factors. Additionally, some studies include farm payments as explanatory variables of land prices or returns, without providing a theoretical foundation to include them in the analysis and to interpret the results in economic terms.

The present study is unique in several ways. First, unlike previous related research, the focus is on the impact of government payments on cash rental rates, which are representative of the observed price of land as an input in the production process (Alston). Second, a theoretical model is developed to investigate the effect of government payments on cash rental rates. Third, government payments are disaggregated into four distinct categories: (1) deficiency payments (DEF), (2) payments associated with the market loss assistance program (MLA), (3) production flexibility contract (PFC) payments, and (4) conservation reserve program (CRP) payments. This disaggregation of government payments allows us to test whether they exert different impacts on cash rental rates. Finally, because of the geographic nature of the data used for the empirical analysis, the econometric estimation specifically allows for spatial autocorrelation.

Theoretical Model

Consider a farmer whose profits equal the revenues obtained from producing two crops (e.g., corn and soybeans) plus government payments, minus costs:

(1)

In (1), variables with a tilde denote variables that the farmer takes as random from the perspective of planting time. Random variables include crop prices ( and) and environmental conditions during the growing season (e.g., weather and the like) ( and), and may be correlated with each other. Yields per acre [y₁(·) and y₂(·)] are determined by the acres planted (a₁ and a₂) and the levels of other variable inputs (b₁ and b₂), and are random because they are affected by the environmental conditions. Government payments per acre [g(·)] may also be random because they may depend on crop prices and environmental conditions, in addition to planted acres and input levels. Finally, r denotes the rental rate per acre, s is the per unit cost of other variable inputs, and C represents fixed costs.

Let the effect of acres on yields and on government payments be represented by the Cobb-Douglas functions, as in (2) and (3), respectively:¹

(2)

(3)

In (2), α_ii is the elasticity of yield for crop i with respect to its own acreage, and α_ij is the cross elasticity of crop i yield with respect to the acres planted with crop j. In (3), γ_i is the elasticity of government payments (per acre) with respect to the acres planted with crop i. Functions f_i(·) and h(·) are also assumed to satisfy standard regularity conditions so that the optimization problem discussed below is well behaved.

Assuming that the agent's decision problem at planting time consists of selecting the number of acres and the levels of other variable inputs so as to maximize expected profits, the optimization's objective function consists of

(4)

where E(·) denotes the expectation operator (i.e., the agent's expectations about the random variables conditional on information at the time of decision making). For an interior solution, the first-order necessary conditions corresponding to the planted acreages are given by (5):

(5)

where, and asterisks are used to denote optimal levels of the decision variables.

If there is a relatively small geographical area, say, a county, where farmers face the same prices, all farmers are alike and represented by 1-5, and the total supply of tillable land is fixed at some level A, equilibrium land rents (r_equilibr) will satisfy expression (6):

(6)

In (6), A^*_i denotes the total number of acres planted with crop i in the area, so that A = A^*₁ + A^*₂. Expression (6) is obtained by multiplying (5) by a^*_i/(a^*_i + a^*_j), adding to it the analogous expression for crop j, substituting A^*_i/A for a^*_i/(a^*_i + a^*_j), and rearranging. Of particular interest to us is the impact of government payments on land rents. According to (6), a one-dollar increase in expected (optimum) government payments per acre increases the equilibrium rental rate by (1 + γ₁ + γ₂) dollars. Estimation of (6) is the object of the discussion in the next section.

Estimation Methods

Equation (6) can be put in a regression framework as (7):

(7)

where subscripts n and t denote county and time, respectively. Given (6), the regression parameters in (7) are defined as β₁ ≡ 1 + α₁₁ + α₁₂, β₂ ≡ 1 + α₂₂ + α₂₁, and β₃≡ 1 + γ₁ + γ₂, regression variables are, and. The ε term is a zero-mean regression error uncorrelated with x₁, x₂, and x₃. Note that a testable restriction of (7) is that the intercept should equal zero. In the context of (7), the effect of government payments on land rents can be obtained as the estimate of coefficient β₃.

Unfortunately, it is impossible to fit (7) using standard regression techniques, because the explanatory variables x₁, x₂, and x₃ are not observable.² Our proposed solution to this problem is to use the actual realizations of the random variables in lieu of their conditional expectations. To explain the issues involved in the proposed solution, it is convenient to use an alternative notation. More specifically, let, and, so that. That is, E(· | φ_t) denotes the expectation operator conditional on information at time t. Because it is always possible to write provided does exist,³ it follows that. Therefore, x_int = z_int+1 − ν_int+1, where z_int+1 and ν_int+1 (without tildes) denote actual realizations of and, respectively. Since z_int+1 is observable, in principle, the advocated solution consists of estimating regression (8) instead of (7):

(8)

where.

Compared with (7), the key feature of (8) is that the residual is correlated with the regressors (because z_int+1 measures x_int+1 with error). This causes ordinary least squares estimates of βs in (8) to be biased. To control for this problem, we use the generalized method of moments (GMM) with lagged realizations (z_int) as instruments. Since lagged realizations are in the information set available at the time of decision making, they are uncorrelated with the difference between the conditional expectation and the actual realization (i.e., z_int and are uncorrelated because).

Estimating the coefficients of (7) by applying GMM to (8) is straightforward if one uses time series data for a particular county n. This is true because the unconditional expectation of in the time dimension is zero, so that its sample counterpart tends to zero as the time series becomes infinitely long:

(9)

Therefore,

(10)

(11)

for i = 1, 2, 3. Condition (11) justifies the use of the three sample moments to estimate the three coefficients β₁, β₂, and β₃. Condition (10) shows that the intercept in (8) should equal zero.

In contrast, the cross-sectional average of ν_int+1 need not converge to zero as the number of counties increases, because shocks may be correlated across counties (i.e., there may be systemic risks) (Altuğ and Labadie, p. 300):

(12)

where Κ_it+1 may be different from zero in any particular year t + 1. For example, if crop-1 prices and weather shocks are highly correlated across counties, one would observe Κ_1t+1 › 0 in a year with unexpectedly high prices and favorable weather conditions. For this reason, it is necessary to allow for the possibility of a nonzero intercept in (8).

Allowing for a nonzero intercept means that the GMM regression to be estimated with cross-sectional data is (13) instead of (9):

(13)

where ≡−(β₁ν_{1 t+1} + β₂ν_2t+1 + β₃ν_3t+1) and.⁴ The cross-sectional counterparts of (10) and (11) are (14) and (15), respectively,

(14)

(15)

for i = 1, 2, 3. The four coefficients, β₁, β₂, and β₃ are estimated from the four sample counterparts of (14) and (15).

With the kind of cross-sectional data used in the present study, it is realistic to assume not only that residuals are correlated across counties, but also that residuals of neighboring counties are more correlated than residuals of counties far apart from each other.⁵ For this reason, it is important to allow for spatial error dependence as well. Succinctly, defining the (N × 1) cross-sectional vectors r_t ≡ [r_1t, …, r_Nt]′, r_it+1 ≡ [z_i1t+1, …, z_iNt+1]′, and, autoregressive spatial error dependence means that (Anselin and Bera):

(16)

where ρ is the spatial autoregression coefficient, W̱ is an (N × N) positive matrix with spatial weights, and ξ̱_t+1 ≡ [ξ_1t+1, …, ξ_Nt+1]′ is an uncorrelated and (without loss of generality) homoskedastic (N × 1) error vector. The spatial weight matrix W has elements w_nm = 0 for m = n and w_nm ≡ d^−δ_nm/∑_j≠nd^−δ_nj otherwise, where δ > 0 is a constant and d_nm is the distance between the centroids of counties n and m. Matrix W̱ is row-standardized so that the sum of its elements equals one for each row, that is, (Anselin and Bera).

Since (16) implies that, where I̱ is the (N × N) identity matrix, it follows from (13) that the uncorrelated error vector ξ̱_t+1 can be expressed as

(17)

That is, given (17), the spatial-lag-dependence regression equation analogous to (13) is

(18)

where, and z_i(−n)t+1 ≡ ∑_m≠nw_nmz_imt+1.

From the earlier discussion about (8), residual ξ_nt+1 in (18) is correlated with both z_int+1 and z_i(−n)t+1 because they measure, respectively, x_int+1 and x_i(−n)t+1 with error. Residual ξ_nt+1 is also correlated with r_(−n)t becauser_nt and r_(−n)t are simultaneously determined.⁶ This means that the desired coefficient β₃ in (7) can be estimated from cross-sectional data by applying GMM to (18) and using as instruments the lagged values of the regressors (and a constant). If panel data are available, (18) can be estimated in the form of a system of equations, each of them corresponding to each cross-section available, restricting all coefficients other than the intercept to being the same across equations.

Data

The model was estimated using county-level annual panel data for the state of Iowa. Lack of county-level price and/or cash-rental information prevented us from fitting the model with data from other states. Data were obtained from various sources. Cash rental rates were the average typical cash rental rates per acre of cropland reported in publication FM 1851 of the Iowa State University Cooperative Extension Service. Prices received by farmers for corn and soybeans data were downloaded from the Iowa Agricultural Statistics Service's website. Corn and soybean yields were calculated by dividing county output by the respective planted areas. Output and area planted data were furnished by the National Agricultural Statistics Service of the U.S. Department of Agriculture (USDA).

County-level government payments were obtained from the Farm Service Agency of the USDA. The database contained forty different categories of government payments. Because of the substantially different nature of many of such payments, for estimation purposes they were aggregated into four broad types rather than pooling all of them into a single series. In this manner, differential effects across types of government payments may be uncovered while maintaining a parsimonious model. The four types of government payments are deficiency payments and payments associated with price support programs (z_DEF), market loss assistance payments for corn and soybeans (z_MLA), production flexibility contract payments (z_PFC), and payments corresponding to the conservation reserve and related programs (z_CRP). The composition of each type of government payment is shown in table 1.

Payments z_DEF, z_MLA, and z_PFC were converted to a per acre basis by dividing the total county-level payments by the respective county-level sum of the areas planted with corn and soybeans. By contrast, to express z_CRP payments on a per acre basis, total county-level CRP payments were divided by the corresponding county-level CRP acreages (Farm Service Agency, USDA). The reason for this is that CRP acres cannot be planted with corn or soybeans.

During the period 1996–2000, the ninety-three Iowa counties under study received a total of $6.54 billion in farm program payments, comprising $1.80 billion in DEF payments, $1.35 billion in MLA payments, $2.56 billion in PFC payments, and $0.71 billion in CRP payments. That is, the categories included in the analysis accounted for 98.2% of the total farm program payments. The remaining 1.8% comprised the miscellaneous programs described in table 1.

The period used for estimation was 1996–2000, because government payments were greatly affected by the Federal Agricultural Improvement and Reform Act of 1996, and no price data for 2001 were available. The estimated model involved equations analogous to (18) only for years 1997 through 2000, because the 1996 equation could not be estimated, as lagged values were used as instruments. Summary statistics for the basic variables are shown in table 2. The distance matrix was constructed using the distances between the centroids for every pair of counties in Iowa. Distances were obtained from the Economic Research Service of the USDA.

Results and Discussion

The model was estimated by means of the econometric program TSP^TM version 4.4, using the GMM command under the default options. The instruments used for each equation were the values of the corresponding explanatory variables lagged one year. The fact that the market loss assistance program started in 1998 was problematic for the estimation of the 1998 equation. The reason for this is that z_MLA,n,1997 = z_{MLA,(−n),1997} = 0, and therefore, they provide very poor instruments for z_MLA,n,1998 and z_{MLA,(−n),1998}, respectively. For this reason, two alternative specifications were estimated. In the MLA98-N (MLA98-Y) specification, the 1998 equation excluded (included) z_MLA,n,1998 and z_{MLA,(−n),1998} as explanatory variables.

The results are summarized in tables 3 through 5. Table 3 shows the results obtained by performing an iterative search over the power factor used to compute the spatial weights (δ) so as to maximize the model's p-value (as implied by the test of overidentifying restrictions). The results in table 3 are very consistent across the MLA98-N and MLA98-Y specifications. More important, the tests of overidentifying restrictions have very high p-values, providing support for the advocated model. The pseudo-R²s imply that the model can explain between 51% and 71% of the variability in cash rental rates.

As expected, acreage-weighted corn and soybean revenues are found to have a positive and significant impact on cash rental rates. The coefficients on the alternative types of government payments suggest that cash rental rates are affected very differently according to the type of payment. The coefficients corresponding to the MLA payments (β_MLA) and the PFC payments (β_PFC) are both positive and significant in an economic as well as a statistical sense. The point estimates of β_MLA and β_PFC suggest that cash rental rates increase by about 85 cents for each dollar paid per acre under the MLA and PFC programs. The coefficient associated with CRP payments (β_CRP) is positive but economically and statistically insignificant. The most surprising result is the negative and statistically significant estimated effect of DEF payments. The point estimate of β_DEF is considerably smaller in absolute terms than any of the other statistically significant farm payment coefficients, but its negative value is difficult to rationalize.

The point estimates of the spatial autoregression coefficient are close to one and highly significant. This confirms the existence of important spatial dependencies in the data. Given the large and significant spatial autoregression coefficients found, it is of interest to see how different the estimated model would be if spatial dependency were neglected. To this end, specifications MLA98-N and MLA98-Y were estimated under the restriction ρ = 0. Since this constraint eliminates variables r_(−n) and z_(−n) from the basic estimation model (18), their lagged values were also omitted from the set of instrumental variables.

Results from the GMM estimation with ρ= 0 are shown in table 4. Compared with the models that allow for spatial correlation, the models with ρ = 0 have much smaller p-values. Indeed, both the MLA98-N and MLA98-Y specifications with ρ = 0 are rejected at the 5% significance level, indicating that misspecification problems are likely to be present. Another hint of the poorer fit of the models with ρ= 0, compared with the models allowing for spatial correlation, is that the former exhibit notoriously smaller pseudo-R²s.

Several of the coefficient estimates in table 4 are quite different from the coefficients in table 3. Setting ρ= 0 leads to much larger intercepts.⁷ More important, the point estimates of the acreage-weighted corn revenue coefficient (β_CORN) under ρ= 0 are about one-fourth the size of the respective estimates obtained when ρ is unrestricted. Further, the estimate of β_CORN in the MLA98-Y specification is not significant under ρ= 0. Similarly, neglecting spatial autocorrelation yields smaller estimates of β_MLA (which is not significant in the case of the MLA98-Y specification). Also, the β_DEF estimates under ρ = 0 are considerably smaller in absolute magnitude and are not significant. In contrast, the restriction ρ = 0 results in appreciably larger estimates for β_PFC and, especially, β_CRP. Unlike the scenario allowing for spatial autocorrelation, CRP payments are statistically significant under ρ = 0.

In summary, a comparison of the results in table 4 with the results in table 3 provides strong indications of misspecification problems with the specifications that ignore spatial autocorrelation. Such a comparison highlights the need to account for spatial autocorrelation to avoid faulty inferences regarding the effect of government payments on cash rental rates.

For completeness, the model without disaggregating among the various types of farm program payments was also estimated. Results for a specification using the aggregate farm program payments variable z_GOV≡z_DEF + z_MLA + z_PFC + z_CRP are shown in table 5. The power factor for spatial weights that yielded the largest p-value was δ = 3.45. The model's p-value is large and the pseudo-R²s are similar to the pseudo-R²s corresponding to the specifications with disaggregated farm payments. The estimates of β_CORN and β_BEAN in table 5 are comparable to their counterparts in table 3. More important, the effect of government payments on cash rental rates (β_GOV) is found to be statistically significant but economically small, with one additional dollar per acre in government payments increasing cash rental rates by only 13 cents per acre.

An issue with the model reported in table 5 is that the point estimate of the spatial autoregression coefficient (ρ) is considerably greater than one. Although such an estimate is computationally feasible, it does not seem reasonable and cannot be interpreted in terms of the advocated model. The point estimate of ρ greater than one is also the reason why the intercepts in table 5 bear opposite signs with respect to the intercepts in table 3. This is true because the intercept in equation (18) is a function of (1 − ρ).

Concluding Remarks

Farmland values are intrinsically associated with the economics of the farm sector. Also, government programs have played a major role in U.S. agriculture since the 1920s (Kohls and Uhl, p. 369). This explains why there exists a large body of research addressing the effect of government programs on land values. The present study departs from the previous literature in that it focuses on the impacts of government program payments on cash rental rates. Another innovation is that the econometric analysis allows for different impacts across farm programs. In addition, econometric methods are used to account for potential spatial dependencies in the data.

County-level annual observations for Iowa from 1996 through 2000 were used to measure the impacts of the main types of farm program payments on cash rental rates. The data were found to exhibit strong geographic dependency. Accounting for spatial autocorrelation in the econometric analysis was shown to be crucial to avoid misleading inferences.

Results reveal important differences in the effects of alternative farm programs on cash rental rates. Cash rental rates were found to increase by almost one dollar per acre for each additional dollar per acre paid for market loss assistance and production flexibility contracts, whereas conservation reserve program payments appear to exert no effect on cash rental rates. A counterintuitive finding that warrants further examination is the negative impact of deficiency payments on cash rental rates.