**3. Results and discussion**

#### **3.1 TAR model results**

LLCUL\_CAP is the threshold variable and is separated into two regimes with observations. The TAR model shows the threshold value for both regimes to be 2.09%, with the first regime consisting of 16 observations (*Zt*<sup>1</sup> < *λ*) and the second regime having 22 observations (*Zt*<sup>1</sup>>*λ*). The threshold level is negative in the analysis because arable land is a fixed asset that cannot be increased, while the South African population growth is increasing. The relationship between the threshold variables and the explanatory variables (price per ton and consumption per ton) is differentiated into the different regimes. In the first regime with 16 observations, the price per ton shows a coefficient of 0.1365 and carries a negatively related coefficient against the cultivated land/area, which means that an increase in LPRCE\_TON has the effect of decreasing LLCUL\_CAP (per capita maize-cultivated land) with a margin of 13.7%; this is shown in **Table 1**.

Consumption per ton (LCONSUPTION\_TON) also carries a negatively related coefficient of 0.8236 against the threshold variable (cultivated land) which suggests that increases in consumption per ton put downwards production pressure on cultivated land area, with a margin of 82.4%. The denoted relationship therefore resulted in 16 observations that are less than the threshold value which suggests that during the pre-1994 apartheid era, the negative relationship was sustainable and did not go past the threshold level of 2.09%; in the first regime, the LPRCE\_TON is not statistically significant with t-statistics and p-value that are above the 5% significance level, while LCONSUPTION\_TON is reported to be statistically significant as p-values are less than 5%; this is shown in **Table 1**.

**Threshold**

**LLCUL\_CAP(**

**29**

**3) < 2.09 with 16** 

Zt**1** <λ **(first regime)**

**Coefficient**

0.136533

0.823665

Non-threshold

5.621432

2.146702

 2.618636

0.0132

 variable

 0.280937

 0.085868

LPRCE\_TON

LCONSUPTION\_TON

C **Table 1.** *TAR model estimates.*

 **Std. error**

 **t-statistics** 1.590037

2.931847

 0.0061

 0.1214

 **p-values**

 **Coefficient**

0.265049

0.690729

 0.257767

 0.042998

 **Std. error**

 **t-statistics** 6.164189

2.679666

 0.0114

 0.0000

 **p-values**

*Regime Switch and Effect on Per Capita Food Security Issues in South Africa*

*DOI: http://dx.doi.org/10.5772/intechopen.86931*

**observations**

 **variables** **LLCUL\_CAP(**

**3) = > 2.09 with 22** 

Zt**1**>λ

**(second regime)**

**observations**

In the case of the second regime, both explanatory variables are statistically significant, with p-values that are below 5%. The threshold variable (cultivated land) has 22 observations that are below the threshold value indicating unsustainable per capita food security. The coefficient for both price per ton and consumption per ton is still negatively related in the regime, with LPRCE\_TON shown as 0.265 and LCONSUPTION\_TON as 0.6907. These values suggest that an increase in LPRCE\_TON and LCONSUPTION\_TON results in decreasing cultivated area/land of maize. The results suggest the cultivated land area of maize was not sustainable at the threshold value of 2.09% for food security and imply that the cultivated land area has diminished beyond the negative threshold value with at least 22 observations.

A more descriptive observation of the result is shown by **Figure 1** for actual, fitted and residual model for the transformed data. More specifically, attention is given to the actual and fitted model in the figure. As from 1970 to 1988, the first regime is observed, while the second regime continues from 1989 to 2010, where the first regime with 16 observations shows the cultivated land remains sustainable even though it negatively slopes and decreases. However, in the second regime, as located from 1989, the behaviour changes, because the actual and fitted models show a further decline in cultivated land area beyond the threshold value at 22 observations; this makes the second regime unsustainable.

The results of per capita consumption and the change in consumption trend over the period of analysis from 1970 to 2010 are indicated in **Figure 1**. The food security indicators (per capita land cultivated and per capita consumption) presented in **Figure 1** indicate the validity of food sovereignty theory with the evidence that



*TAR model estimates.*
