Determinants of land value volatility in the U.S. Corn Belt

Figures & data

Figure 1. Land values in the Corn Belt in 2017 prices.

Figure 2. Land value to cash rent ratio and the 10-year constant maturity treasury rate.

Table 1. Mean and standard deviation of the variables.

	Land Value Volatility (%)		Interest Rate (%)		Cash Rent ($)		Land Value ($)		Population Density (%)		Consumer Price Index
Corn Belt States	Mean	Standard Deviation	Mean	Standard Deviation	Mean	Standard Deviation	Mean	Standard Deviation	Mean	Standard Deviation	Mean	Standard Deviation
Iowa	0.08	0.03	6.2	2.9	102.94	64.75	2089.98	2211.98	0.082	0.003	31.3	30.5
Ohio	0.06	0.04	6.2	2.9	66.59	36.97	1950.57	1581.48	0.919	1.232	31.3	30.5
Illinois	0.07	0.03	6.2	2.9	101.82	58.02	2281.57	2036.90	0.332	0.021	31.3	30.5
Indiana	0.06	0.03	6.2	2.9	88.18	48.90	2113.55	1924.10	0.250	0.023	31.3	30.5
Missouri	0.07	0.07	6.2	2.9	52.69	32.16	1087.26	920.93	0.121	0.010	31.3	30.5

Land value volatility is defined as the variance of the unpredictable component of the appreciation rate for land values.

Table 2. Panel unit root tests of Corn Belt land value series and of the VAR variables.

Variable	Augmented Dicky-Fuller		Phillips-Perron		Harris-Tzavalis
GARCH modelling variables
Land values per State
Illinois	−3.536**		−48.481***
Iowa	−3.997**		−45.043***
Ohio	−3.408*		−57.52***
Missouri	−3.484**		−53.52***
Indiana	−3.861**		−43***
VAR variables
Land Value Volatility					0.483***
Consumer Price Index					0.813***
Constant Maturity Rate					−0.038***
Population Density					−0.075***
Land Values					0.597***
Cash Rents					0.388***

Statistical significance level: ***1%, **5% and *10%.

Table 3. ARCH LM tests for the residuals from an ARCH model.

State	ARCH-LM test	p-values
Indiana	47.46	0.000***
Illinois	74.16	0.000***
Ohio	79.48	0.000***
Missouri	48.69	0.000***
Iowa	40.13	0.003***

LM tests presented are with 4 lags. Comparable results were also obtained with 8 lags. ***indicates 5% level of statistical significance.

Table 4. Asymmetric effects from the univariate EGARCH volatility models.

State	Model		Asymmetric Coefficient (${\gamma }_{\mathrm{i}})$
Indiana	EGARCH(1,1)	lag1	0.88***
Iowa	EGARCH(1,2)	lag1	0.69***
Illinois	EGARCH(3,2)	lag1	0.70***
		lag2	−0.07
		lag3	0.67**
Ohio	EGARCH(1,1)	lag1	0.90***
Missouri	EGARCH(2,1)	lag1	1.55***
		lag2	−0.20

*indicates 10%, ** indicates 5% and ***indicates 1% level statistical significance.

Table 5. Results from the pooled vector auto-regression model.

Coefficients	POP	CMT	CR	LV	CPI	VLY
pop-t-1	−0.253*	5.140**	−0.231	0.568*	0.056***	−0.071
cmt-t-1	0.002	−0.826***	0.011*	0.022***	0.0003	0.008**
cr-t-1	0.009	−5.397*	−0.168	−0.218	−0.013	0.032
lv-t-1	0.012	12.059***	0.427***	0.150	0.025**	−0.480***
cpit-1	−0.042	26.271***	0.336	−0.861*	0.526***	0.312
pop+t-1	−0.002	−8.314***	−0.257	−0.347**	−0.115***	−0.235**
cmt+t-1	−0.003	−0.016	−0.014**	−0.016**	−0.0001	−0.002
cr+t-1	−0.016	−0.940	−0.080	0.002	−0.017**	0.017
lv+t-1	−0.029	1.862*	0.327***	0.495***	0.009	0.115***
vlyt-1	0.007	0.476	0.009	0.130	0.014*	0.271***
R-Squared	0.079	0.337	0.418	0.548	0.802	0.502
Observations:				56 years and 280 observations

The coefficients of the time and state dummies were supressed.

Codes: *** indicates 1%, ** 5% and * 10% level of statistical significance.

POP: Population density growth rate; CMT: Interest rate growth rate; CR: cash rents growth rate; LV: land value growth rate; CPI: consumer price income growth rate; VLY: volatility.

Table 6. Results from the Dumitrescu and Hurlin Granger causality test.

Hypothesis	$\bar{Z}$	$\tilde{z}$	Hypothesis	$\bar{Z}$	$\tilde{z}$
vlyt-1 -> vly	46.6***	43.4***	pop^− -> cr	6.3***	5.8***
cmt^− -> vly	1.2	1.0	pop^+ -> cr	−0.8	−0.8
cmt^+ -> vly	−0.5	−0.5	cmt^− -> cr	5.8***	5.3***
cpi -> vly	5.4***	5.0***	cmt^+ -> cr	−0.5	−0.6
lv^− -> vly	10.9***	10.1***	cpi -> lv	−0.9	−0.9
lv^+ -> vly	7.5***	6.9***	cr^− -> lv	0.4	0.4
cr^− -> vly	2.7***	2.5**	cr^+ -> lv	−0.6	−0.6
cr^+ -> vly	2.4**	2.2**	pop^− -> lv	−0.7	−0.7
pop^− -> vly	2.6***	2.4**	pop^+ -> lv	−1.3	−1.3
pop^+ -> vly	0.5	0.4	cmt^− -> lv	−1.0	−1.0
vly -> cmt	1.3	1.2	cmt^+ -> lv	8.7***	8.0***
vly -> cpi	0.9	0.8	lv^− -> cpi	−0.7	−0.7
vly -> lv	0.8	0.7	lv^+ -> cpi	2.1**	1.9*
vly -> cr	0.1	0.1	cr^− -> cpi	−1.3	−1.3
vly -> pop	−0.6	−0.6	cr^+ -> cpi	−0.5	−0.5
cpi -> cmt	5.5***	5.1***	pop^− -> cpi	−1.2	−1.2
cr^− -> cmt	−0.9	−0.9	pop^+ -> cpi	−0.5	−0.5
cr^+ -> cmt	−0.9	−0.9	cmt^− -> cpi	−1.3	−1.3
lv^− -> cmt	6.9***	6.3***	cmt^+ -> cpi	−1.2	−1.2
lv^+ -> cmt	0.9	0.8	lv^− -> pop	−1.4	−1.3
pop^− -> cmt	−1.5	−1.4	lv^+ -> pop	1.3	1.2
pop^+ -> cmt	−1.1	−1.1	cr^− -> pop	−1.4	−1.4
cpi -> cr	2.1	0.1	cr^+ -> pop	−0.4	−0.4
lv^− -> cr	8.1***	7.5***	cpi -> pop	−0.6	−0.6
lv^+ -> cr	7.2***	6.7***	cmt^− -> pop	−1.3	−1.3
			cmt^+ -> pop	−0.7	−0.7

*indicates 10% **5% and ***indicates 1% level of statistical significance.

$\bar{Z}=\sqrt{\frac{\mathrm{N}}{2K}}\cdot \left(\bar{W}-K\right)\underset{T,\mathrm{N}\to \mathrm{\infty }}{\to }\left(0,1\right)$ and $\tilde{Z}=\sqrt{\frac{\mathrm{N}}{2K}\cdot \frac{T-3K-5}{T-2K-3}}\cdot \left[\frac{T-3K-3}{T-3K-1}\cdot \bar{W}-K\right]\underset{\mathrm{N}\to \mathrm{\infty }}{\to }N\left(0,1\right)$ where, N is the sample size, K is the lag order, $\bar{W}$ the average number of the N individual Wald statistics (Lopez and Weber 2017).

Figure 3. Impulse response functions: The response of land value volatility to exogenous shocks.

Table A1. AIC statistics for each ARMA model specification.

Gray shaded areas indicate the ARMA model chosen.

Table A2. EGARCH Model specification selection.

Model	Akaike information criterion
Indiana
EGARCH(1,1)	−2.635
EGARCH(1,2)	−2.6226
EGARCH(1,3)	−2.6573 (C)
EGARCH(2,1)	−2.6021
EGARCH(2,2)	−2.5864
EGARCH(3,1)	−2.5892
EGARCH(3,2)	−2.5703
Illinois
EGARCH(1,1)	−2.427
EGARCH(1,2)	−2.4681
EGARCH(1,3)	−2.5389 (C)
EGARCH(2,1)	(Did not converge)
EGARCH(2,2)	−2.4812
EGARCH(3,1)	−2.5113
EGARCH(3,2)	(Did not converge)
Iowa
EGARCH(1,1)	−2.2452
EGARCH(1,2)	−2.2281
EGARCH(1,3)	(Did not converge)
EGARCH(2,1)	−2.2633
EGARCH(2,2)	−2.2599
EGARCH(3,1)	−2.3905
EGARCH(3,2)	−2.4301 (C)
Ohio
EGARCH(1,1)	−2.6305 (C)
EGARCH(1,2)	(Did not converge)
EGARCH(1,3)	(Did not converge)
EGARCH(2,1)	−2.6259
EGARCH(2,2)	(Did not converge)
EGARCH(3,1)	(Did not converge)
EGARCH(3,2)	(Did not converge)
Missouri
EGARCH(1,1)	−2.7543
EGARCH(1,2)	−2.7419
EGARCH(1,3)	−2.7264
EGARCH(2,1)	−2.7495
EGARCH(2,2)	−2.8384 (C)
EGARCH(3,1)	−2.7485
EGARCH(3,2)	−2.8086

(C) indicates the chosen specification. AIC from models that did not converge were not reported. Different solvers were tried but failed in solving the non-convergence issue.

Table A3. Results of the EGARCH models for each state.

	Illinois	Ohio	Indiana	Iowa	Missouri
Mean equation
E[lvi,t|Ii-1]	0.04***	0.05***	0.06***	0.04**	0.05***
	(0.011)	(0.006)	(0.011)	(0.018)	(0.006)
Variance Equation
omega	−4.50**	−1.78***	−1.73**	−1.57***	−1.04**
	(1.845)	(0.642)	(0.829)	(0.400)	(0.501)
alpha1	−0.18	0.25**	0.05	−0.04	−0.14
	(0.183)	(0.117)	(0.133)	(0.106)	(0.152)
alpha2	0.50***				0.61***
	(0.173)				−0.167
alpha3	−0.25
	(0.198)
gamma1	0.70***	0.90***	0.69***	0.69***	1.55***
	(0.226)	(0.193)	(0.147)	(0.199)	(0.203)
gamma2	−0.07				−0.20
	(0.311)				(0.244)
gamma3	0.67**
	(0.294)
beta1	0.07	0.67***	0.88***	1.00*	0.82***
	(0.275)	(0.113)	(0.228)	(0.563)	(0.083)
beta2	0.10			−0.31
	(0.164)			(0.502)
Log-Likelihood	144.83	148.98	148.29	126.89	163.06
AIC	−2.49	−2.66	−2.64	−2.22	−2.87
LB	0.00[0.997]	0.73[0.394]	1.16[0.281]	2.13[0.144]	0.00[0.965]
LB^2	0.02[0.878]	0.20[0.179]	0.12[0.728]	0.02[0.887]	0.05[0.826]

Standard errors are displayed in the brackets. LB and LB2 are the (Ljung and Box 1978) tests for the standardized residuals and the squared standardized residuals. [] displays the p-values. *, ** and *** indicate 10%, 5% and 1% levels of statistical significance, respectively.

Lopez, L., and S. Weber. 2017. “Testing for Granger Causality in Panel Data.” IRENE Working paper 17-03. Switzerland: University of Neuchatel. https://www.unine.ch/files/live/sites/irene/files/shared/documents/Publications/Working%20papers/2017/WP17-03.pdf

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