1 item has been added to your cart.
| Title | The relationship between the group variable and the treatment dummy variable in didregress and xtdidregress | |
| Author | Pei-Chun Lai, StataCorp |
The standard DID model for repeated cross-sectional data fit by didregress is given by
$$Y_{ist}=γ_s+γ_t+z_{ist}\beta+D_{st}\delta+\varepsilon_{ist}$$where \(i\) is the observation-level index, \(s\) is the group-level index, and \(t\) is the time-level index. \(γ_s\) denotes the group effects, \(γ_t\) denotes the time effects, and \(z_{ist}\) are the observation-level characteristics. The parameter of interest in this model is the average treatment effect on the treated (ATET), which is given by the (\(\delta\)). Note that there is no index (i) in the variable (\(D_{st}\)) because at a given point in time "all units" in group (s) are either subject to the treatment or are not. For example, if a specific tax policy is implemented in some states and not in others, all individuals in state (s) at a given point in time (t) are either subject to the tax policy (the treatment) or are not.
The standard DID models are generally used to study the effect of a policy in a setting where there is a world before and after the policy when controlling for group (\(\gamma_s\)) and time effects (\(\gamma_t\)). \(D_{st}\) is a binary variable that indicates the treated observations. For our state and time example, \(D_{st}=0\) for either the state in the treated group or the state in the control group before the treatment occurs for the first time. After the treatment occurs, \(D_{st}=1\) for the states in the treated group, but \(D_{st}=0\) for the states in the control group. \(D_{st}\) is put in the second set of parentheses of didregress. For didregress to work, we should have a control group that has at least one state for which all observations have \(D_{st}=0\) over years.
If no states have \(D_{st}=0\) over years, and all states have both observations of \(D_{st}=0\) and \(D_{st}=1\),
| treatment | ||||
| State | No treat Yes treat | Total | ||
| 0 | 405 1,029 | 1,434 | ||
| 1 | 2,343 2,265 | 4,608 | ||
| 2 | 784 973 | 1,757 | ||
| Total | 3,532 4,267 | 7,799 |
we cannot assign any state to the control group, and we will get the error message
invalid group specification None of the groups defined by state is a control. r(198)
after running didregress. In other words, we do not have a state that is never treated and that is in the control group in the sample.
If we examine the hospdd.dta used in the examples of the PDF manual entry for didregress, the group versus treatment table is
. use https://www.stata-press.com/data/r18/hospdd, clear (Artificial hospital admission procedure data) . tabulate hospital procedure
| Hospital | Admission procedure | |||
| ID | Old New | Total | ||
| 1 | 92 92 | 184 | ||
| 2 | 84 84 | 168 | ||
| 3 | 76 76 | 152 | ||
| 4 | 100 100 | 200 | ||
| 5 | 100 100 | 200 | ||
| 6 | 100 100 | 200 | ||
| 7 | 116 116 | 232 | ||
| 8 | 88 88 | 176 | ||
| 9 | 80 80 | 160 | ||
| 10 | 84 84 | 168 | ||
| 11 | 88 88 | 176 | ||
| 12 | 80 80 | 160 | ||
| 13 | 92 92 | 184 | ||
| 14 | 76 76 | 152 | ||
| 15 | 76 76 | 152 | ||
| 16 | 84 84 | 168 | ||
| 17 | 72 72 | 144 | ||
| 18 | 44 44 | 88 | ||
| 19 | 152 0 | 152 | ||
| 20 | 168 0 | 168 | ||
| 21 | 136 0 | 136 | ||
| 22 | 144 0 | 144 | ||
| 23 | 152 0 | 152 | ||
| 24 | 120 0 | 120 | ||
| 25 | 96 0 | 96 | ||
| 26 | 168 0 | 168 | ||
| 27 | 192 0 | 192 | ||
| 28 | 136 0 | 136 | ||
| 29 | 160 0 | 160 | ||
| 30 | 88 0 | 88 | ||
| 31 | 168 0 | 168 | ||
| 32 | 160 0 | 160 | ||
| 33 | 168 0 | 168 | ||
| 34 | 216 0 | 216 | ||
| 35 | 192 0 | 192 | ||
| 36 | 184 0 | 184 | ||
| 37 | 96 0 | 96 | ||
| 38 | 176 0 | 176 | ||
| 39 | 144 0 | 144 | ||
| 40 | 176 0 | 176 | ||
| 41 | 192 0 | 192 | ||
| 42 | 128 0 | 128 | ||
| 43 | 152 0 | 152 | ||
| 44 | 104 0 | 104 | ||
| 45 | 192 0 | 192 | ||
| 46 | 144 0 | 144 | ||
| Total | 5,836 1,532 | 7,368 |
Because the hospitals 1–18 have observations on both the Old and New procedures, we can assign them to the treated group. Because hospitals 19–46 only have observations on the Old procedure, we can assign them to the control group.
We can also check time versus treatment as in this table,
. use https://www.stata-press.com/data/r18/hospdd, clear (Artificial hospital admission procedure data) . tabulate month procedure
| Admission procedure | ||||
| Month | Old New | Total | ||
| January | 1,842 0 | 1,842 | ||
| February | 921 0 | 921 | ||
| March | 921 0 | 921 | ||
| April | 538 383 | 921 | ||
| May | 538 383 | 921 | ||
| June | 538 383 | 921 | ||
| July | 538 383 | 921 | ||
| Total | 5,836 1,532 | 7,368 |
This table reports that all observations are on the Old procedure before April, and that some observations are on the Old procedure and some are on the New procedure beginning in April.
Note that the explanations above also apply to xtdidregress, which handles panel/longitudinal data.
