Empirical Results

The TSLS estimation method was used to estimate the demand for corn. By transforming the variables via the natural log, coefficient estimates can be read as elasticities. The most important of the elasticities for this research is the cross price elasticity of corn demand with respect to the price of ethanol. Through the estimation of this cross price elasticity, a more thorough understanding of the relationship between ethanol and corn can be realized.

Descriptive statistics of all variables used in the study can be found in Table 4.1.

Table 4.1 Descriptive Statistics

         The estimation results, shown in Table 4.2, depict statistical significance at conventional confidence levels for some of the variables in the regression. The coefficient of P^D_CN is significant and negative as expected, complying with the law of demand. The estimated coefficient of P_EN, the price of ethanol, was both positive and significant. Estimation also produced unanticipated results for both the livestock index and sugarcane The estimation of the livestock price index, P_LVI, was insignificant and negative, a contrary relationship to that developed in the theoretical framework presented in previous sections. Also, the estimated coefficient of the price of sugarcane, P_SC, was not significant and positive, denying the claim that sugarcane and corn are substitutes.

Table 4.2 Estimation Output

         One potential cause for the two curious results could be a number of statistical issues. The TSLS estimation method, and indeed any instrumental procedure, is sensitive to the choice of instruments. Conditions for valid instruments are captured in the principles of instrumental relevance and instrument exogeneity:

       1. Instrument relevance: corr(Z,X) ≠ 0.

       2. Instrument exogeneity: corr(Z,µ_i) = 0.

That is, the chosen instrumental variables must harbor some relation to the independent variable of concern. Furthermore, the instruments must not be correlated with the error term µi¬. Some of the questionable estimation results may be due to failure of instrumental variables to adhere to these two conditions. For example, the variable QHK, the quantity harvested in the previous year, has a very low correlation with several of the independent variables. The correlation matrix, showing the correlation between all of the variables, is presented in Table 4.3. In addition, there could be instrumental variables not considered in this research that better separate out the portion of Xi that is correlated to the error term.

Table 4.3 Correlation Matrix

         Another potential reason for the two estimated coefficients being contrary to the theoretical framework is multicollinearity. Kennedy (2003) defines multicollinearity as a phenomenon marked by approximate linear relationships between independent variables. These approximate linear relationships are in fact very common in economic variables. The correlation matrix can be used to detect the presence of multicollinearity and the extent to which it may present difficulties in estimation. Kennedy (2003) explains that multicollinearity becomes an issue of concern when the simply correlation between two independent variables is 0.8 or greater in absolute value. Examining the correlation matrix, several variables show a simple correlation coefficient exceeding the 0.8 benchmark. The most satisfactory way to solve issues of multicollinearity is to include more information, to formalize the relationships among regressors, to specify the relationships between parameters, to remove some variables, to incorporate estimates from other studies, to form a principle component (such as the livestock index), or to use a factor analysis. It is important to keep these potential pitfalls in mind in the ensuing discussion.

        As noted previously, the estimated coefficients can be directly interpreted as elasticities. The cross price elasticity of corn demand with respect to ethanol then is 0.80; that is, a 1% change in the price of ethanol creates a 0.8% change, in the same direction, in the demanded for corn. The elasticity of demand for corn, given by the estimated coefficient of PCN, is 0.66. This elasticity of demand is in fact quite reasonable. Shonkwiler and Manddala (1985) found the elasticity of demand for corn to be 0.72, while Taylor and Frohberg (1997) found the elasticity of demand for corn to be 0.50. The elasticity of the supply of corn will be taken from Shonkwiler and Maddala (1985), who found the estimated value to be 0.392. These elasticities are summarized in equation 4.1:

        To understand how much the price of corn will change due to a change in the price of ethanol, a simple microeconomic relationship found in some principles textbooks ⁽³⁾ will be used. (O’Sullivan & Sheffrin, 112). This price-change formula is written as follows:

     

The numerator captures the rightward shift of the demand curve in percentage terms, counterbalanced by the sum of the elasticity of demand and supply in the denominator. This is reasonable because, if consumers and producers are very responsive to changes in prices, excess demand will be eliminated with a relatively small increase in price. In addition, the percentage change in price will be positive in the case presented because the demand shift is positive. Using the equation 4.2 and the elasticities presented in equation 4.1, a 1% increase in the price of ethanol creates a 0.76% increase in the equilibrium price of corn.

Figure 4.1 Demand Shift Figure

Figure 4.1 shows how the equation captures the 0.76% change represented by the movement from E₁ to E₂. The movement from E₁ to P₁ represents the shift in demand of corn from the increase in the price of ethanol. At point P₁ there is a shortage of corn which places upward pressure on the price of corn. As the quantity supplied of corn increases to accommodate the increased demand, the price of corn rises from p₁ to p₂ bringing about equilibrium at point E₂. It is the percentage change from p₁ to p₂ that is then given by equation 4.2.

            This equation can be used to examine current trends in ethanol production and what effects this might have on the equilibrium price of corn. During the period 2000 through 2007, the price of ethanol increased by an average of 13.18% per year, which at the 2007 price of ethanol represents a $.30 change. Using this average price increase and the estimated cross price elasticity of demand for corn with respect to ethanol, a 10.544% increase in the demand for corn is obtained; at 2007 corn production levels, this increase represents nearly 1.4 billion additional bushels. Then using equation 4.2, a 13.18% increase in the price of ethanol will increase the equilibrium price of corn by 10.023%. Using the February 2008 price of corn, $4.25 per bushel, a 10.023% increase as a result of the average yearly increase in the price of ethanol increases corn prices by $.43.

            The conclusions to be drawn from these empirical results follow directly from the established relationships between corn and ethanol. The estimated demand function for corn, coupled with the price change formula, suggest that an increase in the price of ethanol will increase the equilibrium price of corn as the markets adjust. Costs of corn production, on the other hand, have grown at a low and stable rate over the past decade. The total costs of production in the corn industry, including inputs, taxes, and opportunity costs, have grown an average of 2% over the past decade (ERS, Commodity Costs and Returns 2008). The conclusion then follows that with the likely trends in ethanol markets leading to increased ethanol prices and thus increased corn prices, and with the cost structure of farmers remaining stable, subsidies for corn production are unwarranted. Assuming the growth rate of costs remains constant, the increase in the price of corn represents an increase in the profitability of the corn industry. Intuitively, increasing profitability is not a sign of a struggling industry in need of a transfer of wealth from taxpayers to firms.

           Agricultural subsidies are meant to control prices and stabilize farming income. As ethanol is forced upon refiners as a blending agent to address environmental concerns, corn farmers’ income will stabilize itself through market mechanisms. The theoretical rationale behind the general form of subsidies is to capture some sort of social benefit or loss that is not manifested in the private sector’s cost-benefit structure. If nothing else, the effects of ethanol on corn markets would at the very least decrease the need for subsidies in the short run, thereby allowing the market mechanism to dictate the most beneficial use of resources. The reallocation of crops resulting from the increase in demand for corn will take time. Once the new equilibrium price is reached, the adjustment of input markets could lead to increase costs, thus returning corn farmer profitability to its original state. In this way subsidies in the long run may be justified, given an agenda of price and quantity control.

           As stated above, some of the endogenous variables returned questionable relationships to the quantity of corn. These problematic relationships may be a sign of inadequate instrumental variables. Estimation errors may also contribute to the existence of multicollinearity. Additional information could be added to the model to decrease the effects of said statistical issues. One such piece of information could be a variable that fully captures the opportunity cost of farmland. A farmer who grows corn may switch to some other commodity if doing so would maximize profits. This underlying opportunity cost of farmland may include a copious amount of other crops that could potentially grow on the land. The number and type of substitute crops then would depend on the geographical region. Mapping these opportunity costs across farms may be the subject of further research.

Conclusion