If an employee has a tax deferred deduction (health insurance) then the total amount for this deduction is not included in Box 1 of the W2. It's my understanding that Box 3 of the W2 “Social Security Wages” and Box 5 “Medicare Wages” would include this amount.
Example
Total wages: $40,000
Tax deferred amount for health insurance: $2,000
Then -> Box 1: $38,000 - Box 3: $40,000 - Box $40,000
If an employer does report $38,000 (refer to example above) on all 3 boxes wouldn't they have to correct W2 because Social Security and Medicare is under paid by $153 ($2,000 * 7.65%) - Employee Responsibility and the employer match of $153 for a total of $306? ------ Or is there a particular circumstance in which the employer is allowed to report $38k vs $40k on Box 1, Box 3 and Box 5; although there was a $2,000 tax deferred deduction?
You have to ask your employer. Medical insurance premiums are not only exempt from income tax but from Social Security and Medicare taxes as well. Consequently these premiums will not be included in either boxes 1, 3, or 5.
Your assumption here is incorrect because medical insurance premiums are subtracted from your income before income tax and before Social Security and Medicare tax. Certain other benefits are also subtracted from box 1, 3, and 5 wages, most notably, benefits provided under a “cafeteria“ plan under section 125. This includes daycare benefits, a health savings account or HSA, and a few other things. (Medical insurance premiums are also technically deducted under section 125.)
The logic of the section 125 cafeteria plan is that you agree to a reduction in salary, and your employer provides certain benefits to you in return. That is why those benefits are not subject to Social Security or Medicare tax, because they aren’t part of your salary.
Retirement contributions, on the other hand, are still considered earned income and are subject to Social Security and Medicare tax even though they may be excluded from income tax. This would include a 401(k), 403(b), and other qualified pension plans.