Table 1: Unit Root Tests KPSS Test Augmented Dickey-Fuller Test with Time Trend

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1 Table 1: Unit Root Tests KPSS Test Augmented Dickey-Fuller Test with Time Trend with Time Trend test statistic p-value test statistic Corn Soy Corn Soy Corn acreage Soy acreage Farmland Noncrop Corn yield Soy yield Supply Diffusion Index Supply Diffusion Index Demand Diffusion Index Demand Diffusion Index Notes: All tests use one lag. The null hypothesis of the ADF test is that the variable contains a unit root. The null hypothesis of the KPSS test is that the variable is trend stationary. A Phillips-Perron test with time trend gives similar results, as do ADF and PP tests without time trends. Exceptions are, where the null is (not surprisingly) not rejected in the tests without trends. The 5% critical value for the null hypothesis in the KPSS test with time trend is

2 response variable response variable Table 2.1: Forecast Error Variance Decompositions (One-Step Ahead) Scenario 1, impulse variable acreage Notes: Forecast error variance decomposition tells us the percentage of the forecasting error for a variable due to a specific shock at a given horizon. For instance, the estimate of.68 in the acreage column, row, tells us that shocks to acreage explain 6.8% of the one-step ahead forecast error in s. Note that, since this FEVD is structural, the shocks are orthogonalized. Table 2.2: Forecast Error Variance Decompositions (One-Step Ahead) Scenario 2, impulse variable 1 1 6E acreage non-crop Notes: Forecast error variance decomposition tells us the percentage of the forecasting error for a variable due to a specific shock at a given horizon. For instance, the estimate of.4 in the non-crop column, row, tells us that shocks to non-crop explain 4% of the one-step ahead forecast error in s. Note that, since this FEVD is structural, the shocks are orthogonalized. 2

3 response variable response variable Table 2.3: Forecast Error Variance Decompositions (One-Step Ahead) Scenario 1, impulse variable acreage E Notes: Forecast error variance decomposition tells us the percentage of the forecasting error for a variable due to a specific shock at a given horizon. For instance, the estimate of.86 in the acreage column, row, tells us that shocks to acreage explain 8.6% of the one-step ahead forecast error in s. Note that, since this FEVD is structural, the shocks are orthogonalized. Table 2.4: Forecast Error Variance Decompositions (One-Step Ahead) Scenario 2, impulse variable acreage E non-crop.19 3E-5 1E Notes: Forecast error variance decomposition tells us the percentage of the forecasting error for a variable due to a specific shock at a given horizon. For instance, the estimate of.17 in the non-crop column, row, tells us that shocks to non-crop explain 1.7% of the one-step ahead forecast error in s. Note that, since this FEVD is structural, the shocks are orthogonalized. 21

4 change in bean, dollars per change in bean, dollars per 22 change in, dollars per change in, dollars per Figure 1: Impulse Response Functions Scenario 1: negative shock (1 million acres) to acreage Scenario 2: negative shock (1 million acres) to non-crop farm acreage Scenario 1: negative shock (1 million acres) to bean acreage Scenario 2: negative shock (1 million acres) to non-crop farm acreage Notes: Impulse response functions trace out the effect of exogenous shocks on realizations of the random variables across time. Since the system is structural, the shocks are orthogonalized. The y-axis shows the change in the U.S. or bean, and the x-axis shows the period following the shock (which occurs in period zero). Confidence intervals are at the 95% level.

5 change in, dollars per change in bean, dollars per 23 change in, dollars per change in, dollars per Figure 2: Cumulative Impulse Response Functions Scenario 1: negative shock (1 million acres) to acreage Scenario 2: negative shock (1 million acres) to non-crop IRF CIRF IRF CIRF Scenario 1: negative shock (1 million acres) to acreage Scenario 2: negative shock (1 million acres) to non-crop IRF CIRF IRF CIRF Notes: Impulse response functions trace out the effect of exogenous shocks on realizations of the random variables across time. Since the system is structural, the shocks are orthogonalized. The cumulative IRF shows the path of the crop over time for repeated acreage shocks. The y-axis shows the change in the U.S. or bean, and the x-axis shows the period following the first shock (which occurs in period zero).

6 24 Figure 3: Robustness Checks Scenario 1, : negative shock (1 million acres) to acreage Scenario 2, : negative shock (1 million acres) to non-crop Full, Two Lags Full, Three Lags Full, Secondary DIs Full, log/log Full, Yields per ed acre Full, Rotation Full, Cropland Full, Principal crops Sparse Sparse, Two Lags Sparse, Three Lags Sparse, log/log Sparse, Rotation Sparse, Cropland Full 1 Scenario 1, : negative shock (1 million acres) to acreage.2 Scenario 2, : negative shock (1 million acres) to non-crop Notes: Impulse response functions trace out the effect of exogenous shocks on realizations of the random variables across time. Since the system is structural, the shocks are orthogonalized. The y-axis shows the change in the U.S. or bean, and the x-axis shows the period following the shock (which occurs in period zero).

7 change in, dollars per change in, dollars per 25 change in, dollars per change in, dollars per Figure 4: Rolling Time Frame Scenario 1, : negative shock (1 million acres) to acreage.15 Scenario 2, : negative shock (1 million acres) to non-crop Scenario 1, : negative shock (1 million acres) to acreage Scenario 1, : negative shock (1 million acres) to non-crop Notes: The estimated IRF for the entire sample is shown with a dashed line. The rolling window estimation results are shown in gray. The same SVAR is estimated ten times, with 41 s included in each estimation (i.e., 1958 to 1998, 1959 to 1999, etc.). The y-axis shows the change in the U.S. or bean, and the x-axis shows the period following the shock (which occurs in period zero).

8 26 Appendix A.1: Estimated SVAR Coefficients Scenario 1, contemporaneous linear trend acreage Corn and and s in 27 dollars per. Farmland and acreage in million acres. Intercept estimated but not reported. one period lag In our notation, contemporaneous effects make up the A matrix, on the right-hand side of the set of equations. Moving these effects to the left-hand side reverses the signs. Thus, have a positive effect on the contemporaneous (with a coefficient of.35), and have a negative effect on the contemporaneous (with a coefficient of -.17), etc. Note also that these coefficients must be interpreted with care because of the recursive nature of the system. For instance, contemporaneously effect the, which in turn contemporaneously affects. Thus the coefficient on in the equation is only part of the total effect, which also includes effects that feed through the.

9 27 Appendix A.2: Estimated SVAR Coefficients Scenario 2, contemporaneous linear trend acreage Corn and and s in 27 dollars per. Farmland and acreage in million acres. Intercept estimated but not reported. one period lag In our notation, contemporaneous effects make up the A matrix, on the right-hand side of the set of equations. Moving these effects to the left-hand side reverses the signs. Thus, have a positive effect on the contemporaneous (with a coefficient of.3), and have a positive effect on the contemporaneous (with a coefficient of.21), etc. Note also that these coefficients must be interpreted with care because of the recursive nature of the system. For instance, contemporaneously effect the, which in turn contemporaneously affects. Thus the coefficient on in the equation is only part of the total effect, which also includes effects that feed through the.

10 28 Appendix A.3: Estimated SVAR Coefficients Scenario 1, contemporaneous linear trend acreage Corn and and s in 27 dollars per. Farmland and acreage in million acres. Intercept estimated but not reported. one period lag In our notation, contemporaneous effects make up the A matrix, on the right-hand side of the set of equations. Moving these effects to the left-hand side reverses the signs. Thus, have a positive effect on the contemporaneous (with a coefficient of.21), and have a negative effect on the contemporaneous (with a coefficient of -.13), etc. Note also that these coefficients must be interpreted with care because of the recursive nature of the system. For instance, contemporaneously effect the, which in turn contemporaneously affects. Thus the coefficient on in the equation is only part of the total effect, which also includes effects that feed through the.

11 29 Appendix A.4: Estimated SVAR Coefficients Scenario 2, contemporaneous linear trend acreage Corn and and s in 27 dollars per. Farmland and acreage in million acres. Intercept estimated but not reported. one period lag In our notation, contemporaneous effects make up the A matrix, on the right-hand side of the set of equations. Moving these effects to the left-hand side reverses the signs. Thus, have a positive effect on the contemporaneous (with a coefficient of.26), and have a positive effect on the contemporaneous (with a coefficient of.14), etc. Note also that these coefficients must be interpreted with care because of the recursive nature of the system. For instance, contemporaneously effect the, which in turn contemporaneously affects. Thus the coefficient on in the equation is only part of the total effect, which also includes effects that feed through the.

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