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# COLLEGE OF SOCIAL SCIENCE

COLLEGE OF SOCIAL SCIENCE

## Heckman Selection Model

Heckman Selection Model for Ratio of Large to Small Scale Amendments of Future Land Use 63 Table 13 and 14 report parameter estimates for four with and without interaction models. Table 13 reports the selection equation stage while Table 14 shows the outcome equation 64 . The likelihood ratio test (LR test) reported at the bottom of the table 14 is an equivalent test for ρ = 0 and the comparison of the joint likelihood of an independent probit model for the selection equation and a regression model on the observed ratio data against Heckman model likelihood. Since χ2 = 7.50 for the without interaction model, this justifies the Heckman selection equation with these data. The rests of LR tests are χ2 = 8.50 (Mayor interaction with community interests), χ2 = 8.83 (Election interaction with community interests), χ2 = 7.63 (RPC interaction with community interests) justifying the appropriateness of using Heckman selection model. The model fits of all estimating models are statistically significant at the 1% level (χ2 is significantly different from zero). Physical characteristics of communities at the selection equation 65 have very similar influence on whether cities offer amendments for the future land use map in both without interaction terms model and with interaction terms models. While other variables are constant, population has positive relationship with cities offering amendments of future land use map, which means larger communities are more likely to offer future land use map change. As the table shows, cities with higher population density and more shoreline are less likely to offer future land use map change amendments. This result could be possible since most amendment packages have a pro-developmental nature. Another possible explanation of this is the data’s time-invariant nature. For example, in a small city, one development may make the city more populous. The population change and water/land ratio variables are not statistically significant at all. Further, population change has negative relationship with future land use change amendments. These results can be explained also in the above way. 63 Before running the model, I ran the regression model with panel standard error corrected. The result is reported in Appendix. The result does not show much difference from the Heckman model except some community interest variables. 64 For the convenience purpose, I split the Heckman selection results into selection and outcome parts. Thus, I report Wald test, rho, sigma, lamda statistics in only outcome equation table. 65 The selection equation model is related to why a city offered future land use map amendment whether or not an amendment is small or large. Thus, the direct interpretation of direction is not straight forward. 81

Table 13. Heckman Selection Model of Ratio of Large/ Small Scale 1 (Selection Equation) Variables Population Popchange Density Water Land Ratio Shoreline Constant Without Interaction .99 (.09)*** -.0004 (.0008) -.0001 (.0000)*** .001 (.002) -.003 (.000)*** -3.81 (.34)*** 1 robust standard error clustered at city level Interaction with Mayor .99 (.09)*** -.0004 (.0008) -.0001 (.0000)*** .001 (.002) -.003 (.000)*** -3.81 (.34)*** Interaction with District Election .99 (.09)*** -.0004 (.0008) -.0001 (.0000)*** .001 (.002) -.003 (.000)*** -3.81 (.34)*** Interaction with RPC .99 (.09)*** -.0004 (.0008) -.0001 (.0000)*** .001 (.002) -.003 (.000)*** -3.81 (.34)*** While the physical characteristic variables produced mixed results, institutional variables are mostly in the hypothesized directions. In column 1 of without interaction model, strong mayor form of government has statistically significant direct effects in proenvironmental land use policy change. Strong mayor presents a ratio of large/small scale amendments of 8.65% 66 higher than the other forms of government. District election also confirms the hypothesized direction showing significant positive effects on proenvironmental land use policy change. 1% increase of council members elected by district is correlated to the .1% increase of the ratio of large/small scale amendments. Another important finding is that turnover rates of council members are also confirming my hypothesis showing negative relationship with pro-environmental land use policy change. 1% increase of council member turnover rates is correlated to the 0.09 % decrease of the ratio of large/small scale amendments. Unlike the analysis of conservation amendments, administrative capacity variable (expenditure) is statistically significant at p=.10 level in a positive direction. This means that the bigger a city’s planning capacity the higher the ratio of large/small scale amendments is. However, informal institutional variables (RPC and ILA) have no significant direct effects in this analysis. 66 In the Heckman Selection Model, the coefficient value is same as marginal effect (Wooldridge 2002). Thus, this type of interpretation can be allowed in this analysis 82

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