Different modes of land reform and their performances were discussed in the literature review section. The census survey of all farmland transactions involving transfer of ownership in five South African provinces during 2006 and 2007 was conducted to determine the rate of land redistribution in South Africa. The main purpose for conducting the survey was to estimate the demand for land in South Africa where land reform measures are employed in farmland transactions. Fifty observations from five provinces were drawn from the DLA provincial lists of properties financed with grant and loans. The provinces were selected randomly and they are KZN, Mpumalanga, Free State, North West and Limpopo. The logit model described below is used to estimate the impact of land reform grant on the demand for land.
6.11.1 The Logit Model
The logit model is a non-linear probability model based on a logistic curve designed to estimate the conditional probability of a positive response or presence of characteristic (Hill et al, 1997).
Parameter estimates and their variances give information for investigation of statistical association among variables. The other two equally important purposes of empirical research in logit models are selection and prediction (Cramer, 2003). In application of discrete probability for selection, the estimates of β serve to calculate predicted probabilities for individuals or items with covariates.
The probabilities are then used for classification, identification or segmentation of target groups (Cramer, 2003:27-28).
Examples of target groups as listed by Cramer are prospective customers who are interested in a particular product or item and potential borrowers who are likely to default; these examples are consistent with the logit study pursued because previously disadvantaged grant applicants and/or recipients are prospective customers who are interested in a particular product (farmland), and are also potential borrowers who are likely to default, hence, have to be assessed for selection purpose.
D = f(Debt/Equity Ratio)
D = 1 if D/E ratio is ≥ 1.5, 0 otherwise
Where: D/E is the ratio of loan to LRAD grant used to finance property
As theory suggests, the greater the collateral a household possesses, the greater is the credit worthiness of that household. Putting a greater amount of deposit on purchases enhances the transaction deal. The likelihood for the financial provider that the borrower will not default is also increased. Hill et al (1997: 203) argue that banks, prior to approving loans predict the probability
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that an applicant will default. If the probability of default is high, the loan is not approved or additional conditions such as extra collateral is imposed.
In this study, at least 40 percent of LRAD grant is perceived as a good deposit to secure a loan. It is thus argued that a positive relationship is expected between the demand for land and the increase in LRAD grant obtained. A second implication is that a meaningful grant plus the loan secured increase the willingness and the ability of a household to purchase farmland. It is therefore argued that a positive relationship holds for reasonable solvency ratio and chance to purchase farmland. In the study the logistic function can be specified as:
;
Where the variable (z) can be regarded as an input and f(z) as an output. The control variable (z) can be of any value from negative to positive, (Cramer, 2003). The control or independent variable (z) measures the aggregate contribution of all control variables (if they are many) used in the model. The final outcome f(z) is confined to any values between zero and one.
The control variable (z) is normally specified as:
Where is the intercept; , are the regression coefficients of respectively.
If the contribution control variables equals zero, the intercept is the value of control variables.
An increase in the probability of the outcome is explained by a positive coefficient ( , ) whereas a negative coefficient implies that the probability of outcome is reduced by the control variable whose coefficient is negative. The logit model describes the potential relationship between one or more control variables (for example, success, failure, live, dead, age, sex, and so on) and an outcome that is expressed as a probability with alternatives such as success or failure.
The model analyses binomial distribution of data in the form:
Where the numbers of Bernoulli trials are known and the probabilities of outcome are not known. In this study, the binomial distribution is the fraction of LRAD grant holders that are successful in farmland markets after combining their LRAD grants and mortgage loans. The natural logs of the log of odds of the unknown probabilities are then modelled as a linear function of the ( .) depicted below:
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Pi is the probability of competing fairly well in the property market and (1 – Pi) is the probability of no strong competition offered by the previously disadvantage grant holders in farmland market.
The ratio is the odds ratio or the odds in favour of successful biding by grant holders, and therefore increasing the demand for land. The natural log of this odds ratio is called the logit and the model is called the logit model (Gujarati, 1999: 449).
The logit model informs us that the log of odds ratio is a linear function of explanatory variable D/E in the present case. In this model, for example, the slope coefficient β2 estimates the change in the log of odds ratio per unit change in the amount of credit obtained by grant holders.
6.11.2 Special features of the logit model
Probabilities estimated from the model will always lie within the logical bounds of 0 and 1. The probability of competing fairly strong does not increase linearly or by a constant amount with a unit change in the value of any explanatory variable (Gujarati, 1999:449).
Since data on individual observation was collected, the method of maximum likelihood (ML) will be used to estimate the model. The logit ML estimation routine of the SHAZAM computer programme will be used to estimate the model. For the logit model, the usual R² is not meaningful.
Alternatives such as Maddala and McFadden R²s are used for validation.
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