Strengths of the pooled approach include the following:
- For a given time period and data periodicity there are up to 51 times as many observations as in the national time series or the time series for a single state. This helps solve the multicollinearity problems that are common to national time-series models and allows for a richer specification of the model. Subject to availability, more variables can be included in the model;
- As with national or individual state time-series data, the dynamic impacts of explanatory variables can be explored, and the relatively large number of observations allows for richer dynamic specifications than are possible with a single time series;
- In comparison to national or state time-series estimates, it is feasible to control for all changes in national program policy or other national factors, at least to the extent that they have the same effects on participation in all states, by using time fixed effects. In the time-series approach, sample-size restrictions severely limit the number of dummy variables that can be used to estimate the effects of such changes without obscuring the effects of other variables;
- In comparison to national time-series analysis, the prospects for obtaining strong estimates of the impacts of program variables are much better because there is much more variation in individual state program variables than in weighted national averages of these variables. This applies to AFDC and other state programs, such as Medicaid and general assistance. The studies discussed above provide examples of multiple AFDC program variables used in the same model (Moffitt (1986) uses a maximum benefit variable and the earned income reduction rate, and Cromwell et al. (1986) use a maximum benefit variable and an UP dummy);
- The pooled methodology creates opportunities to test the validity of the model that are not possible with individual time series. Perhaps most importantly, we can test a set of constraints that is implied by the methodology itself -- identical coefficients for every state. Failure to reject the constraints would bolster confidence in the validity of the model. We could also test whether some or all coefficients are the same across two sample subperiods -- something which is difficult with a single time series because of limited observations. It is also possible to learn from comparing findings for various pooled specifications (e.g., fixed effects versus random effects), and to test whether the coefficients based on, say, cross-section relationships in the levels are the same as those based on cross-section relationships in changes of the variables.
The pooled methodology does have its limitations, however:
- It is methodologically more complex than the national time-series approach, which makes it more difficult both to implement and to describe the findings.
- Cross-state relationships between participation measures and explanatory variables in the model may in part reflect substantial cross-state variation in variables that have not been included, thereby biasing estimated coefficients for the included variables. State fixed-effects may need to be used to control for such factors;
- Collecting state level data requires more effort than collecting national level data. Data for some variables may not be available and the quality of other data may be poor. Data quality is particularly problematic when state fixed effects are used because measurement error bias is exacerbated by the use of the fixed effects;
- The estimated model is likely to track the participation measure for each state less well than a state time-series model, and the sum of the simulated series (i.e., across states) may track the national series less well than a simulation from a national time-series model. The reason for this is that the pooled methodology constrains explanatory variable coefficients to be the same in all states. If the constraints are valid, however, the pooled methodology should perform relatively well.