Dependent variables

As discussed in Chapter Three, landholders’ behaviour about land use change relies on the decision of whether to change land use, and then the extent to which the change is made. This reflects that a two-step decision process or double hurdle is appropriate (Moffat, 2005). The first step models the decision about whether to change land use from forestry (

𝛅𝛅

3-10). If the decision to change from forestry is adopted, the second step is to determine the proportion of forest land reduced (FLir) (Equation 3-11). Literature suggests these types of data have a better fit in the limited dependent variable models such as probit and double hurdle model (Kimhi, 1999; Moffat, 2005; Verbeek, 2012). As it was assumed that the two decisions (whether to reduce and how much to reduce) are independent to each other, the double hurdle model (often termed two-part model) is better than the Tobit model. The parameters of the first decision were modelled with probit regression, and the parameters of the second decision were modelled with truncated regression using LIMDEP software.

6.3.2

Data related to how many landholders increased forest land area, decreased forest area, and did not change forest area was gathered. The first three time periods shown in Table 6-4 have land use information of what landholders actually did; the rest are related to what they might do about land use change in the future. As there is a socioeconomic risk in the carbon bank model (section 3.2.2, Chapter Three), the dependent variable is related to decreased forest land area. Data in Table 6-4 is used to analyse the number of landholders who decreased their forest land area in different time periods. Thus, from all time periods the largest number of landholders (27) who decreased forest area was in time period 3. This time period encompasses 10 years of land use change. Because the bank pays annual rental payments, the likely proportion of forest carbon lost by socioeconomic risk needs to be converted to per year (see section 6.6 of this chapter for details).

The reductions in forest land in different time periods (Table 6-4) were tested using probit and truncated model. Because there were only 11 and 12 small landholders reducing forest land use in time periods 1 and 2, respectively, these observations were not enough to test 2 or 3 explanatory factors explaining landholders’ decisions about forestry land use change. The importance of the explanatory factors, in both probit and truncated models, for the bank is that it would help to set up decision-making criteria and identify who (landholders) might represent

98 a risk in reducing forest land. The statistical information derived from these explanatory factors with a small sample of observations would have provided a low level of confidence to analyse landholders’ decisions about reducing forest land. Therefore, this research excluded time periods 1 and 2 from the modelling process. In time periods 4, 5 and 6, observations were also not enough to explain landholders’ decisions about land use; therefore, these time periods were also dropped from the modelling process.

Table 6-4. Number of landholders tending to increase, decrease or not change forest cover

All continuous variables without zero values in Table 6-2 were tested in logarithmic and quadratic functional forms in the regression model (Verbeek, 2012). These transformations gave statistically higher log likelihood value of the estimated model which indicates a better fit in the model. The fit of these variables in both the probit and truncated regression models was examined by running the model with the non-logged variables gathered through the questionnaire (raw field data). Explanatory variables with continuous values were tested on log function forms and standard forms. The most appropriate fit of these functional forms of data was determined by using Chi-Square test for the ratio of log likelihood values of the log transform and non-transform models. In addition, based on the Chi-Square likelihood ratio test of the restricted (variable dropped) and unrestricted models, some explanatory variables listed in Table 6-1 were dropped from the probit and truncanted models because they were not significant. Only significant variables were included in the final model (see Table 6-5 for descriptive statistics of significant variables).

The Z statistics values of STAP, CASH, FORES, PASTR variables of the model estimate were unusually inflated (too large) and the signs of some variables contrasted with what was expected. The results indicated endogeneity32 _{and misspecification}33 _{problems in the models.}

32 _{Correlation between an independent variable and the error term. This implies that the regression coefficient in}

an Ordinary Least Squares (OLS) regression may be biased (Verbeek, 2012).

33_{A deviation from the true population in the sample model means that the sample model is misspecified. This}

indicates that the inferences from the sample model about the population are suspect (Verbeek, 2012).

Forest tendency

Time period of change/Number of landholders

1 2 3 4 5 6

2003-2008 2008-2013 2003-2013 2013-2018 2013-2023 2018-2023

Increased 12 12 36 18 18 7

No change 62 61 22 50 54 60

It was found that some of the explanatory variables were correlated with the error term in both models (probit and truncated). These variables would have created a misleading output of the model. Following Verbeek (2012), these problems were solved by estimating and using predicted values of the endogenous variables in both probit and truncated models. After correcting the endogeneity problem by plotting the dependent variable against residuals in the model, no heteroscedasticity34 _{was found. Table 6.5 provides descriptive statistics of the} variables calculated from model data and fitted in the probit and truncated models.

Table 6-5. Descriptive statistics of significant variables for probit and truncated model

6.4

Analysis of landholders’ decisions on selecting the option of the