| . | Model 1 . | (Model 1) |$+ R_{j}^{y}$| . | (Model 1) |$+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 2) |$+ R_{j}^{y}+ R_{j}^{o}$| . |
|---|---|---|---|---|---|---|
| . | Test 1 . | Test 1b . | Test 1c . | Test 1d . | Test 2b . | Test 3b . |
| SE estimator . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=\gamma _{i}=0$| . | |$Null\colon \gamma _{i}=0$| . |
| Cluster: year of birth | 0.001|$^{***}$| | 0.002|$^{***}$| | 0.001|$^{***}$| | 0.132 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Cluster: t and a = 1 × 5 | 0.001|$^{***}$| | 0.115 | 0.001|$^{***}$| | 0.202 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Conley:tand c = 7 × 7 | 0.001|$^{***}$| | 0.060|$^{*}$| | 0.001|$^{***}$| | 0.148 | 0.001|$^{***}$| | 0.005|$^{***}$| |
| . | Model 1 . | (Model 1) |$+ R_{j}^{y}$| . | (Model 1) |$+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 2) |$+ R_{j}^{y}+ R_{j}^{o}$| . |
|---|---|---|---|---|---|---|
| . | Test 1 . | Test 1b . | Test 1c . | Test 1d . | Test 2b . | Test 3b . |
| SE estimator . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=\gamma _{i}=0$| . | |$Null\colon \gamma _{i}=0$| . |
| Cluster: year of birth | 0.001|$^{***}$| | 0.002|$^{***}$| | 0.001|$^{***}$| | 0.132 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Cluster: t and a = 1 × 5 | 0.001|$^{***}$| | 0.115 | 0.001|$^{***}$| | 0.202 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Conley:tand c = 7 × 7 | 0.001|$^{***}$| | 0.060|$^{*}$| | 0.001|$^{***}$| | 0.148 | 0.001|$^{***}$| | 0.005|$^{***}$| |
Notes: Model 1 is the baseline specification using year dummies. Here |$R_{j}^{y}$| adds interaction terms for the young ages below 25 and |$R_{j}^{o}$| adds interaction terms for ages above 60. All models use dummy variables for the age specification where the omitted category is at age 25. In Model 2 the coefficients for the interaction effects |$\rho _{i}$| are set to zero. Clustered SEs calculated at (i) cohort level (year of birth) and (ii) interval of a years in the age dimension for each year. Conley SEs using a Bartlett Kernel, where t indicates the number of years included in the time dimension and c is the number of cohorts included in the cohort dimension. *, ** and ** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
Source. Own calculations based on SOEP v33.1 long format.
| . | Model 1 . | (Model 1) |$+ R_{j}^{y}$| . | (Model 1) |$+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 2) |$+ R_{j}^{y}+ R_{j}^{o}$| . |
|---|---|---|---|---|---|---|
| . | Test 1 . | Test 1b . | Test 1c . | Test 1d . | Test 2b . | Test 3b . |
| SE estimator . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=\gamma _{i}=0$| . | |$Null\colon \gamma _{i}=0$| . |
| Cluster: year of birth | 0.001|$^{***}$| | 0.002|$^{***}$| | 0.001|$^{***}$| | 0.132 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Cluster: t and a = 1 × 5 | 0.001|$^{***}$| | 0.115 | 0.001|$^{***}$| | 0.202 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Conley:tand c = 7 × 7 | 0.001|$^{***}$| | 0.060|$^{*}$| | 0.001|$^{***}$| | 0.148 | 0.001|$^{***}$| | 0.005|$^{***}$| |
| . | Model 1 . | (Model 1) |$+ R_{j}^{y}$| . | (Model 1) |$+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 1) |$+ R_{j}^{y}+ R_{j}^{o}$| . | (Model 2) |$+ R_{j}^{y}+ R_{j}^{o}$| . |
|---|---|---|---|---|---|---|
| . | Test 1 . | Test 1b . | Test 1c . | Test 1d . | Test 2b . | Test 3b . |
| SE estimator . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=0$| . | |$Null\colon \rho _{i}=\gamma _{i}=0$| . | |$Null\colon \gamma _{i}=0$| . |
| Cluster: year of birth | 0.001|$^{***}$| | 0.002|$^{***}$| | 0.001|$^{***}$| | 0.132 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Cluster: t and a = 1 × 5 | 0.001|$^{***}$| | 0.115 | 0.001|$^{***}$| | 0.202 | 0.001|$^{***}$| | 0.009|$^{***}$| |
| Conley:tand c = 7 × 7 | 0.001|$^{***}$| | 0.060|$^{*}$| | 0.001|$^{***}$| | 0.148 | 0.001|$^{***}$| | 0.005|$^{***}$| |
Notes: Model 1 is the baseline specification using year dummies. Here |$R_{j}^{y}$| adds interaction terms for the young ages below 25 and |$R_{j}^{o}$| adds interaction terms for ages above 60. All models use dummy variables for the age specification where the omitted category is at age 25. In Model 2 the coefficients for the interaction effects |$\rho _{i}$| are set to zero. Clustered SEs calculated at (i) cohort level (year of birth) and (ii) interval of a years in the age dimension for each year. Conley SEs using a Bartlett Kernel, where t indicates the number of years included in the time dimension and c is the number of cohorts included in the cohort dimension. *, ** and ** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
Source. Own calculations based on SOEP v33.1 long format.
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