Using 2007 to 2011 quarterly SEDS data, we estimate separate regression models for total Medicaid/CHIP enrollment and for Medicaid enrollment only, where the dependent variable is the log transformation of children’s enrollment in each state and quarter. We estimate two-way fixed effect difference-in-difference equations with balanced panels as our main models for this analysis, where the eight ELE states constitute the treatment group (with the intervention occurring at different points in time) and matched non-ELE states with similar pre-2009 enrollment trends comprise the comparison group. The main estimation equations are the following:
(1) Log(McaidCHIP)i,t = ∝ + β1ELEi,t+ β2OTHERPOLICYi,t + β3COVARIATESi,t + υi + δt + ∈i.t
(2) Log(Medicaid)i,t = ∝ + β1ELEi,t+ β2OTHERPOLICYi,t + β3COVARIATESi,t + υi + δt + ∈i.t
where ∝ is the intercept term, i is an index for state, t is an index for unique quarter, υ is a set of state dummy variables (state fixed effects), δt is a set of quarter-specific dummy variables (quarter fixed effects), and isin;i,t is a random error term. The dependent variable, Log(McaidCHIP)i,t, is the log of the number of children ever enrolled in Medicaid or CHIP in state i during quarter t, and corresponds Log(McaidCHIP)i,t to the number of children ever enrolled in Medicaid. We log transform enrollment so that the dependent variable has a normal distribution; otherwise the distribution of the untransformed variable is heavily skewed. We report robust standard errors clustered at the state level to correct for possible heteroskedasticity and autocorrelation (White 1980; Bertrand et al. 2004).
The key independent variable of interest is ELTi,t, which is set to one when the observation is an ELE state and the quarter either contains the month when ELE was implemented or is after ELE implementation. This variable measures the effects of ELE on Medicaid/CHIP or on Medicaid-only enrollment, depending on the model. With a log-transformed dependent variable, the estimated ELE coefficient reflects the percentage change in total enrollment associated with ELE implementation. We anticipate that ELE will have a positive impact on Medicaid/CHIP enrollment—that is, β1 is greater than zero.
Compared with the simple descriptive comparisons, findings from this model offer more rigorous evidence of the effects of ELE because they control for many sources of potential confounding factors. The state fixed effects ϒi help control time-invariant differences across states that could be correlated with the ELE variable, such as inherent differences between ELE and non-ELE states, for example, potential differences in reporting accuracy of the SEDS data. The quarter fixed effects βt control for factors common to all states that vary from quarter to quarter.
By including indicators for other state policy changes and time-varying covariates, we control for other factors that change over time, which could also contribute to differences in aggregate Medicaid and CHIP enrollment numbers. OTHERPOLICY is a series of state policy variables and COVARIATES is a series of other state-level controls that vary over time and that could influence Medicaid/CHIP enrollment. In the combined Medicaid/CHIP model—Equation (1)—OTHERPOLICY includes the simulated Medicaid/CHIP eligibility threshold for children;53 the simulated Medicaid eligibility threshold for parents; and dummy indicators for the presence of a separate CHIP program, joint applications for Medicaid and CHIP, presumptive eligibility for Medicaid, administrative verification of income for Medicaid, no in-person interview for Medicaid, continuous eligibility for Medicaid, presumptive eligibility for CHIP, administrative verification of income for CHIP, no in-person interview for CHIP, elimination of asset test for CHIP, and continuous eligibility for CHIP. In the Medicaid-only model—Equation (2)—we use the simulated child Medicaid eligibility threshold and do not include the CHIP-specific policy dummy variables. In the main specification, COVARIATES includes the state quarter-specific unemployment rate and year-state child population estimates that are log transformed.
53 The simulated CHIP eligibility threshold is used for states with separate CHIP programs and the simulated child Medicaid eligibility threshold is used for all other states. In sensitivity models in which we focus on separate CHIP only, COVARIATES includes the CHIP eligibility threshold and CHIP-specific administrative simplification dummy variables.