User-level method to implement staggered difference-in-difference estimations a la Sun and Abraham (Journal of Econometrics, forthcoming).

sunab( cohort, period, ref.c = NULL, ref.p = -1, bin, bin.rel, bin.c, bin.p, att = FALSE, no_agg = FALSE ) sunab_att(cohort, period, ref.c = NULL, ref.p = -1)

cohort | A vector representing the cohort. It should represent the period at which the treatment has been received (and thus be fixed for each unit). |
---|---|

period | A vector representing the period. It can be either a relative time period (with negative values representing the before the treatment and positive values after the treatment), or a regular time period. In the latter case, the relative time period will be created from the cohort information (which represents the time at which the treatment has been received). |

ref.c | A vector of references for the cohort. By default the never treated cohorts are taken as reference and the always treated are excluded from the estimation. You can add more references with this argument, which means that dummies will not be created for them (but they will remain in the estimation). |

ref.p | A vector of references for the (relative!) period. By default the first relative period (RP) before the treatment, i.e. -1, is taken as reference. You can instead use your own references (i.e. RPs for which dummies will not be created -- but these observations remain in the sample). Please note that you will need at least two references. You can use the special variables |

bin | A list of values to be grouped, a vector, or the special value |

bin.rel | A list or a vector defining which values to bin. Only applies to the relative periods and |

bin.c | A list or a vector defining which values to bin. Only applies to the cohort. Please refer to the help of the argument |

bin.p | A list or a vector defining which values to bin. Only applies to the period. Please refer to the help of the argument |

att | Logical, default is |

no_agg | Logical, default is |

If not used within a `fixest`

estimation, this function will return a matrix of interacted coefficients.

This function creates a matrix of `cohort x relative_period`

interactions, and if used within a `fixest`

estimation, the coefficients will automatically be aggregated to obtain the ATT for each relative period. In practice, the coefficients are aggregated with the `aggregate.fixest`

function whose argument `agg`

is automatically set to the appropriate value.

The SA method requires relative periods (negative/positive for before/after the treatment). Either the user can compute the RP (relative periods) by his/her own, either the RPs are computed on the fly from the periods and the cohorts (which then should represent the treatment period).

The never treated, which are the cohorts displaying only negative RPs are used as references (i.e. no dummy will be constructed for them). On the other hand, the always treated are removed from the estimation, by means of adding NAs for each of their observations.

If the RPs have to be constructed on the fly, any cohort that is not present in the period is considered as never treated. This means that if the period ranges from 1995 to 2005, `cohort = 1994`

will be considered as never treated, although it should be considered as always treated: so be careful.

If you construct your own relative periods, the controls cohorts should have only negative RPs.

You can bin periods with the arguments `bin`

, `bin.c`

, `bin.p`

and/or `bin.rel`

.

The argument `bin`

applies both to the original periods and cohorts (the cohorts will also be binned!). This argument only works when the `period`

represent "calendar" periods (not relative ones!).

Alternatively you can bin the periods with `bin.p`

(either "calendar" or relative); or the cohorts with `bin.c`

.

The argument `bin.rel`

applies only to the relative periods (hence not to the cohorts) once they have been created.

To understand how binning works, please have a look at the help and examples of the function `bin`

.

Binning can be done in many different ways: just remember that it is not because it is possible that it does makes sense!

Laurent Berge

# Simple DiD example data(base_stagg) head(base_stagg) #> id year year_treated time_to_treatment treated treatment_effect_true #> 2 90 1 2 -1 1 0 #> 3 89 1 3 -2 1 0 #> 4 88 1 4 -3 1 0 #> 5 87 1 5 -4 1 0 #> 6 86 1 6 -5 1 0 #> 7 85 1 7 -6 1 0 #> x1 y #> 2 -1.0947021 0.01722971 #> 3 -3.7100676 -4.58084528 #> 4 2.5274402 2.73817174 #> 5 -0.7204263 -0.65103066 #> 6 -3.6711678 -5.33381664 #> 7 -0.3152137 0.49562631 # Note that the year_treated is set to 1000 for the never treated table(base_stagg$year_treated) #> #> 2 3 4 5 6 7 8 9 10 10000 #> 50 50 50 50 50 50 50 50 50 500 table(base_stagg$time_to_treatment) #> #> -1000 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 #> 500 5 10 15 20 25 30 35 40 45 45 40 35 #> 3 4 5 6 7 8 #> 30 25 20 15 10 5 # The DiD estimation res_sunab = feols(y ~ x1 + sunab(year_treated, year), base_stagg) etable(res_sunab) #> res_sunab #> Dependent Var.: y #> #> (Intercept) 0.0063 (0.0443) #> x1 0.9883*** (0.0166) #> year = -9 0.3971 (0.4643) #> year = -8 -0.4161 (0.3306) #> year = -7 -0.0348 (0.2710) #> year = -6 -0.0863 (0.2359) #> year = -5 -0.3221 (0.2120) #> year = -4 -0.1375 (0.1939) #> year = -3 -0.0834 (0.1805) #> year = -2 0.0754 (0.1693) #> year = 0 -5.129*** (0.1604) #> year = 1 -3.451*** (0.1698) #> year = 2 -2.035*** (0.1803) #> year = 3 -0.6104** (0.1950) #> year = 4 1.147*** (0.2121) #> year = 5 2.287*** (0.2359) #> year = 6 4.559*** (0.2729) #> year = 7 5.207*** (0.3301) #> year = 8 6.958*** (0.4676) #> _______________ __________________ #> S.E. type IID #> Observations 950 #> R2 0.89654 #> Adj. R2 0.88676 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 # By default the reference periods are the first year and the year before the treatment # i.e. ref.p = c(-1, .F); where .F is a shortcut for the first period. # Say you want to set as references the first three periods on top of -1 res_sunab_3ref = feols(y ~ x1 + sunab(year_treated, year, ref.p = c(.F + 0:2, -1)), base_stagg) # Display the two results iplot(list(res_sunab, res_sunab_3ref)) # ... + show all refs iplot(list(res_sunab, res_sunab_3ref), ref = "all") # # ATT # # To get the total ATT, you can use summary with the agg argument: summary(res_sunab, agg = "ATT") #> OLS estimation, Dep. Var.: y #> Observations: 950 #> Standard-errors: IID #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.006306 0.044297 0.142359 0.88683 #> x1 0.988344 0.016624 59.452798 < 2.2e-16 *** #> ATT -1.016516 0.083251 -12.210183 < 2.2e-16 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> RMSE: 0.987344 Adj. R2: 0.88676 # You can also look at the total effect per cohort summary(res_sunab, agg = "cohort") #> OLS estimation, Dep. Var.: y #> Observations: 950 #> Standard-errors: IID #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.006306 0.044297 0.142359 0.88683 #> x1 0.988344 0.016624 59.452798 < 2.2e-16 *** #> cohort::2 3.082786 0.160917 19.157673 < 2.2e-16 *** #> cohort::3 1.429502 0.169888 8.414383 < 2.2e-16 *** #> cohort::4 0.001684 0.180523 0.009328 0.99256 #> cohort::5 -1.702666 0.194170 -8.768955 < 2.2e-16 *** #> cohort::6 -3.082949 0.211683 -14.564003 < 2.2e-16 *** #> cohort::7 -4.859333 0.235792 -20.608551 < 2.2e-16 *** #> cohort::8 -5.239574 0.272440 -19.232013 < 2.2e-16 *** #> cohort::9 -7.760783 0.330684 -23.468871 < 2.2e-16 *** #> cohort::10 -8.627732 0.465247 -18.544396 < 2.2e-16 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> RMSE: 0.987344 Adj. R2: 0.88676 # # Binning # # Binning can be done in many different ways # binning the cohort est_bin.c = feols(y ~ x1 + sunab(year_treated, year, bin.c = 3:2), base_stagg) # binning the period est_bin.p = feols(y ~ x1 + sunab(year_treated, year, bin.p = 3:1), base_stagg) #> NOTE: 1 observation removed because of NA values (RHS: 1). # binning both the cohort and the period est_bin = feols(y ~ x1 + sunab(year_treated, year, bin = 3:1), base_stagg) #> NOTE: 1 observation removed because of NA values (RHS: 1). # binning the relative period, grouping every two years est_bin.rel = feols(y ~ x1 + sunab(year_treated, year, bin.rel = "bin::2"), base_stagg) etable(est_bin.c, est_bin.p, est_bin, est_bin.rel, keep = "year") #> est_bin.c est_bin.p est_bin #> Dependent Var.: y y y #> #> year = -9 0.4122 (0.4893) #> year = -8 -0.3966 (0.3484) #> year = -7 -0.0163 (0.2856) -0.1185 (0.3807) -0.1151 (0.3807) #> year = -6 -0.0678 (0.2486) -0.2126 (0.3318) -0.2085 (0.3318) #> year = -5 -0.3037 (0.2234) -0.6283* (0.2984) -0.6241* (0.2984) #> year = -4 -0.1208 (0.2043) -0.4039 (0.2722) -0.4007 (0.2722) #> year = -3 -0.0660 (0.1902) -0.4842. (0.2529) -0.4811. (0.2529) #> year = -2 0.1564 (0.1690) -0.1895 (0.2375) -0.1863 (0.2375) #> year = 0 -4.865*** (0.1690) -6.429*** (0.2529) -6.427*** (0.2529) #> year = 1 -3.478*** (0.1789) -4.881*** (0.2729) -4.879*** (0.2729) #> year = 2 -1.928*** (0.1901) -3.429*** (0.2971) -3.427*** (0.2971) #> year = 3 -0.3391. (0.2053) -1.986*** (0.3325) -1.985*** (0.3325) #> year = 4 1.409*** (0.2234) -0.0616 (0.3812) -0.0599 (0.3812) #> year = 5 2.514*** (0.2490) 0.7065 (0.4649) 0.7081 (0.4649) #> year = 6 4.827*** (0.2869) 2.886*** (0.6556) 2.886*** (0.6557) #> year = 7 5.740*** (0.3494) #> year = 8 #> _______________ __________________ __________________ __________________ #> S.E. type IID IID IID #> Observations 950 949 949 #> R2 0.88394 0.78670 0.78713 #> Adj. R2 0.87427 0.77482 0.77528 #> #> est_bin.rel #> Dependent Var.: y #> #> year = -9 0.3946 (0.4773) #> year = -8 -0.1772 (0.2182) #> year = -7 #> year = -6 -0.2086 (0.1656) #> year = -5 #> year = -4 -0.1044 (0.1396) #> year = -3 #> year = -2 0.0764 (0.1740) #> year = 0 -4.344*** (0.1242) #> year = 1 #> year = 2 -1.384*** (0.1401) #> year = 3 #> year = 4 1.645*** (0.1656) #> year = 5 #> year = 6 4.804*** (0.2190) #> year = 7 #> year = 8 6.929*** (0.4805) #> _______________ __________________ #> S.E. type IID #> Observations 950 #> R2 0.88667 #> Adj. R2 0.88037 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1