7.1 Multiple Linear Regression, OLS
First, I present the OLS results. These results were estimated to show how the causal effects in the RD design compares to the statistical correlations. Table 2 below contains OLS coefficients for the treatment variable and the control variables. Most control variables significantly correlate to the outcome. As expected, higher ages are correlated with worse SRH, unhealthier BMI and higher probabilities of acquiring chronic health conditions. The sign of the other controls varies somewhat across the different dependent variables.
The treatment group correlates significantly with all outcomes. As expected, the signs indicate that being born after the treatment cutoff relates to better SRH at 5% significance and
healthier BMI at 1% significance. However, the correlation with CC is negative at 10%
significance, indicating that the treatment group experiences more chronic health conditions than the control group.
Table 2 Multiple linear regression (OLS)
Self-reported health
Body mass index Chronic health conditions
Constant -6.053 37.17*** -11.86*
(9.631) (7.907) (7.116)
Implementation 1986 0.038** 0.046*** -0.024*
(0.016) (0.013) (0.012)
(0.00009) (0.00007) (0.00007)
Settlement-type 0.019*** -0.030*** 0.020***
(0.003) (0.003) (0.002)
Observations 24,220 23,308 22,896
Men 2,172 2,134 2,113
Women 2,204 2,188 2,128
a *Significant at 10%; **Significant at 5%; ***Significant at 1%. Standard errors in parentheses.
b Bandwidth = 3. Cohorts [1980,1982] in treatment group and [1977,1979] in control group.
c Gender: 1 = Male, 2 = Female. Settlement-type: 1 = Oblast center, 2 = Town, 3 = Urban-type, 4 = Rural d SRH: 1 = Very bad, 5 = Very good. BMI: 0 = Unhealthy, 1 = Healthy. CC: 0 = Diagnosed, 1 = Healthy.
27
7.2 Sharp Regression Discontinuity Design
Table 3 on the next page contains estimates from all the sharp RD regressions. As you can see, there are no coefficients for control variables. The software function for RD does not print these coefficients. However, their inclusion does affect the LATE.
The main results in the top row show that being assigned to treatment conditions does improve SRH at 10% significance and BMI at 1% significance, just as hypothesized. In contrast, treatment worsen the probability of acquiring CC at 10% significance. All three LATEs are consistent with the OLS coefficients with the same sign and almost equal size.
The RD conducted here explain most of the correlation observed in a regular OLS regression.
The first test of robustness is checking bandwidths of 2 and 4 cohorts on each side of the cutoff. The LATE stays stable for BMI at both bandwidths, but only at bandwidth 4 for SRH and CC. Nonetheless, the insignificant treatment effects are remarkably close to its
correspondence in the main model. My interpretation is that we have reason to believe the model specification is correct.
The second test of robustness is checking that the control and treatment groups are equal in observed variables. There are no discontinuities at the cutoff for age, gender or region, which is as expected. However, there is a strong significant discontinuity for settlement-type on all three outcomes. The sign is negative, indicating that the treatment group settles in urban areas more than the control group. It might be caused by an underlying trend. Something happened that made the 2-3 years younger generation attract towards cities, towns and urban-type areas, rather than rural areas. Though unexpected, I would not interpret it as damaging for the LATE of Reform 1986.
The last test of robustness is checking placebo cutoffs. Some of the LATEs on placebo cutoffs are insignificant, but some are significant. Usually, discontinuities at other cutoffs indicate that changes in the dependent variables may be caused by unobserved trends or other
happenings than the one we assumed would create discontinuity. However, have in mind that the treatment conditions are mixed around the cutoff and that the treatment probability is below one. The placebo discontinuities are not necessarily caused by other interventions than the school reform. It might be the school reform and school enrollment at age 6, because we know the cutoff is not sharp. Some pupils enrolled at age 6 in the years before 1980, and the proportion of six-year-old pupils enrolling after 1980 may have increased from year to year, resembling an intervention.
28 Table 3 Sharp regression discontinuity design
Self-reported health
Body mass index Chronic health conditions Treatment ≥ 1980
Implementation 1986b 0.034* 0.054*** -0.025*
(0.017) (0.014) (0.013)
Implementation 1986 0.029 0.067*** -0.025
bw = 2 (0.022) (0.018) (0.016)
Implementation 1986 0.036** 0.035*** -0.020*
bw = 4 (0.015) (0.012) (0.011)
Ageb -0.114 -0.131 -0.113
(0.114) (0.116) (0.117)
Genderb -0.001 0.0008 -0.001
(0.014) (0.014) (0.015)
Regionb 0.003 -0.336 0.123
(1.224) (1.248) (1.261)
Settlement-typeb -0.099*** -0.099*** -0.135***
(0.034) (0.035) (0.035)
Observations at c ≥ 1980 24,220 23,308 22,896
Placebo cutoffs
Placebo #1 0.037** -0.025* 0.019
(Treatment ≥ 1976) (0.016) (0.013) (0.012)
Placebo #2 -0.019 -0.030** -0.004
(Treatment ≥ 1978) (0.017) (0.014) (0.012)
Placebo #3 -0.027 0.019 0.028**
(Treatment ≥ 1982) (0.018) (0.015) (0.013)
Placebo #4 0.033* -0.031** -0.009
(Treatment ≥ 1984) (0.018) (0.015) (0.013)
a *Significant at 10%; **Significant at 5%; ***Significant at 1%. Standard errors in parentheses.
b Bandwidth = 3, cutoff ≥ 1980. Cohorts [1980,1982] in treatment group and [1977,1979] in control group.
c Gender: 1 = Male, 2 = Female. Settlement-type: 1 = Oblast center, 2 = Town, 3 = Urban-type, 4 = Rural d SRH: 1 = Very bad, 5 = Very good. BMI: 0 = Unhealthy, 1 = Healthy. CC: 0 = Diagnosed, 1 = Healthy.
29 Figure 2 Sharp RD on self-reported health
Birth year, cutoff at 1979.5
Self-reported health
Birth year, cutoff at 1979.5
Body mass index
Figure 3 Sharp RD on body mass index
Birth year, cutoff at 1979.5
Chronic health conditions
Figure 4 Sharp RD on chronic health conditions
30
Figures for the three main models in the RD design is seen on the previous page. First, look at figure 3. Since treatment improves BMI at 1% significance, the visual jump in BMI is large.
Relative to the LATE, the small standard error puts the confidence interval of the two OLS regressions far from each other with no overlap. Graphically, it looks like the linear model is a correct specification. The common trend assumption for the control and treatment group seem to hold.
In figure 2 and 4, we notice that the discontinuity is smaller and that the confidence intervals overlap slightly. Remember that these models are significant only at a 10% level. For SRH and CC, the standard error is closer to the LATE than in the BMI model. Nonetheless, the control and treatment groups in both models seem to follow a similar linear trend.
31