Final answer:
The statement that pooled OLS estimation requires a constant regression function shape over time is false. While it assumes constant slope coefficients, it does not necessitate a constant function shape. Instead, it handles differences with intercept shifts, but other models may be preferred if the assumption of homogeneity is violated.
Step-by-step explanation:
Pooled OLS estimation does not require the assumption that the shape of the regression function is constant over time.
The assumption related to Ordinary Least Squares (OLS) regression is that the relationship between the independent variables and the dependent variable is linear and homoscedastic, meaning that the error terms have a constant variance. Pooled OLS models are often used in panel data analysis where we have multiple observations for each cross-sectional unit (such as a person, company, country, etc.) across time. However, pooled OLS does not necessitate a constant shape of the regression function over time; rather, it assumes that differences across these units can be captured by intercept shifts, while the slope coefficients, which represent the effect of the independent variables on the dependent variable, are generally assumed to be constant.
Nonetheless, when the assumption of homogeneity over time is strongly violated, alternative estimation methods such as fixed effects or random effects models may provide a more appropriate analysis as they can account for time-invariant characteristics of the individuals or entities being studied, potentially leading to better inference about the data.