Dear all,
I would like to compute Wald estimator to examine the plausibility of instrumental variables. Following (Angrist and Evans, 1998) the Wald estimator can be expressed as follows:
where where y is a health outcome measure, and IC is the endogenous binary variable of interest, whether the respondent provided any informal care. Let α be the constant term and β be the coefficient of interest and the random error is ε.
I now consider a binary instrument (z)—whether parents need care (z = 1 if need care, 0 if otherwise). The IV-Wald estimate of β is the ratio of two differences. The numerator is the difference between the expected value of y for those whose parents need care (y1 bar) and for those whose parents do not need care (y0 bar). The denominator is the difference between the expected value of informal care for those whose parents need care (IC1 bar) and for those whose parents do not need care (IC0 bar). Robust standard errors for these Wald estimators can be obtained by running regression models with the only endogenous explanatory variable of informal care for parents and one IV of whether parents need care (Angrist and Evans, 1998).
Here is an example of my data
where the out come is depression, endogenous variable is informal caregiving and proposed IV is careneed.
(Angrist and Evans, 1998): https://www.jstor.org/stable/116844?...o_tab_contents
Any help is much appreciated.
Thanks
I would like to compute Wald estimator to examine the plausibility of instrumental variables. Following (Angrist and Evans, 1998) the Wald estimator can be expressed as follows:
where where y is a health outcome measure, and IC is the endogenous binary variable of interest, whether the respondent provided any informal care. Let α be the constant term and β be the coefficient of interest and the random error is ε.
I now consider a binary instrument (z)—whether parents need care (z = 1 if need care, 0 if otherwise). The IV-Wald estimate of β is the ratio of two differences. The numerator is the difference between the expected value of y for those whose parents need care (y1 bar) and for those whose parents do not need care (y0 bar). The denominator is the difference between the expected value of informal care for those whose parents need care (IC1 bar) and for those whose parents do not need care (IC0 bar). Robust standard errors for these Wald estimators can be obtained by running regression models with the only endogenous explanatory variable of informal care for parents and one IV of whether parents need care (Angrist and Evans, 1998).
Here is an example of my data
Code:
clear input int id float(caregiving careneed depression) 1 0 0 12 3 0 0 12 4 0 0 13 5 0 0 33 6 0 0 11 7 0 0 7 8 0 0 11 9 0 0 12 10 0 0 13 11 0 0 26 13 0 0 3 15 0 0 12 16 0 0 8 17 0 0 12 18 0 0 10 19 0 0 10 20 0 0 4 21 0 0 11 22 0 0 9 23 0 0 10 24 0 0 7 25 0 0 12 26 1 1 12 27 0 0 10 28 0 0 12 29 0 0 12 30 0 0 12 31 0 0 12 33 0 0 12 34 0 0 12 35 0 0 18 36 0 1 10 37 0 0 11 38 0 0 17 39 0 0 15 40 0 0 3 41 0 0 9 42 0 0 5 43 0 0 10 44 0 0 17 45 1 1 35 46 0 0 13 47 1 1 10 48 0 0 12 49 0 0 12 50 0 0 9 51 0 0 8 52 0 0 18 53 0 0 35 54 0 0 12 55 0 0 12 56 0 0 13 58 0 0 13 59 0 0 12 61 0 0 13 62 0 0 15 63 0 0 12 64 0 0 9 65 0 0 14 66 0 0 14 67 1 1 12 68 0 0 12 70 0 0 10 71 0 0 13 72 0 0 25 73 1 1 15 74 0 0 12 76 0 0 12 77 0 0 18 78 0 0 14 79 0 0 12 80 0 0 10 81 1 1 9 82 0 0 14 83 0 0 5 84 0 0 17 85 0 0 14 86 0 0 13 87 0 0 12 88 0 0 3 89 0 0 25 90 0 0 6 91 0 0 13 92 0 0 10 93 0 0 45 94 0 0 0 95 0 0 6 96 0 0 5 97 0 0 12 98 0 0 44 99 0 0 12 100 0 0 10 102 0 0 9 103 0 1 12 104 0 0 6 105 0 0 9 106 0 0 7 107 0 0 20 108 0 0 12 109 0 0 12 end label values caregiving p_caregiving label def p_caregiving 0 "No", modify label def p_caregiving 1 "Yes", modify label values careneed p_careneed label def p_careneed 0 "No", modify label def p_careneed 1 "Yes", modify
(Angrist and Evans, 1998): https://www.jstor.org/stable/116844?...o_tab_contents
Any help is much appreciated.
Thanks
