Solving Problems in the Panel Regression Model for Truncated
Dependent Variables: A Constrained Optimization Method
4.1 Model Assumptions
In Section 4, we apply constrained optimization to the panel regression by replicating Hansford and Gomez's (2010) model as mentioned at the beginning of Section 2. Five different models that use various settings will be presented. Each model has different assumptions in model specification or parameter estimation, or both. Model I and Model II differ in the centering methods in model specification, while they share the least-squares objective function. Additionally, neither model applies constrained optimization in parameter estimation. Model II and III adopt the same model specification, but they differ in whether or not to apply constrained optimization. Model III and IV both apply constrained optimization, but they differ in the specification of least-squares or maximum likelihood objective functions. Model IV and V share all the assumptions in parameter estimation, but they differ in whether to correct the demeaning bias in model specification. Table 1 sums up the similarities and differences for the five models' assumptions.
Table 1 Model Assumptions
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