# Wald test in Stata

Apr 13th, 2019
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1. * Note that x = 1993 and y = 1998.
2.
3. cap drop Insample
4. mark Insample if logpay93 !=. & logpay98 != .
5. summ Insample
6. scalar N = r(sum)
7.
8. * 1st entry of covariance matrix
9. corr logpay93 logpay98, cov
10. scalar var_mu93_minus_mu98 = (r(Var_1)*(r(N) - 1)/r(N) + r(Var_2)*(r(N)-1)/r(N) - 2*r(cov_12)*(r(N)-1)/r(N))/N
11. // Stata computes the sample estimates, but we are working with MLEs
12.
13. * 2nd and 3rd entries (cov_mus_vars)
14. foreach y in 93 98 {
15. summ logpay`y', detail
16. scalar mu_`y' = r(mean)
17. scalar var_`y' = r(Var)*(r(N) - 1)/r(N)
18. gen logpay`y'deviation2 = (logpay`y' - mu_`y')^2
19.
20. correlate logpay`y' logpay`y'deviation2, covariance
21. scalar cov_`y'_`y'deviation2 = r(cov_12)*(r(N) - 1)/r(N)
22. scalar var_`y'deviation2 = r(Var_2)*(r(N)-1)/r(N) // comes in handy for the final entry
23. display cov_`y'_`y'deviation2
24. }
25.
26. corr logpay93 logpay98deviation2, cov
27. scalar cov_93_98deviation2 = r(cov_12)*(r(N) - 1)/r(N)
28. display cov_93_98deviation2
29.
30. corr logpay98 logpay93deviation2, cov
31. scalar cov_98_93deviation2 = r(cov_12)*(r(N) - 1)/r(N)
32. display cov_98_93deviation2
33.
34. scalar cov_mus_vars = ( cov_93_93deviation2 - cov_93_98deviation2 - cov_98_93deviation2 + cov_98_98deviation2 )/N
35. display cov_mus_vars
36.
37.
38. * 4th entry
39. correlate logpay93deviation2 logpay98deviation2, cov
40. scalar cov_dev2s = r(cov_12)*(r(N) - 1)/r(N)
41.
42. scalar var_vars = ( var_93deviation2 + var_98deviation2 - cov_dev2s )/N
43.
44. di var_mu93_minus_mu98
45. cap drop Cov_theta
46. matrix define Cov_theta = ( var_mu93_minus_mu98 , cov_mus_vars \ cov_mus_vars, var_vars )
47. matrix list Cov_theta, nohalf // note that only the lower triangle will be printed if "nohalf" is not specified, as this matrix is symmetric
48.
49. matrix inv_Cov_theta = invsym(Cov_theta)
50. matrix list inv_Cov_theta
51.
52. matrix define theta = ( mu_93 - mu_98 \ var_93 - var_98 )
53. mat thetarow = theta'
54.
55. matrix Wald_joint_matrix = thetarow*inv_Cov_theta*theta
56. scalar Wald_joint = Wald_joint_matrix[1, 1]
57. di Wald_joint // Wald statistic
58. di chi2tail(2, Wald_joint) // p-value
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