A Study of Baricitinib and Birth Control Pills in Healthy Females

Inclusion Criteria: * Premenopausal females currently successfully using non-hormonal methods of contraception including tubular ligation, cervical vault cap, diaphragm, or non-hormonal coil with spermicide will be required in addition to use a second approved method of contraception for the duration of the study \[that is (i.e.), a male sexual partner who agrees to use a male condom with spermicide; a sterile sexual partner; or abstinence (participants reporting abstinence who become sexually active while on the study must agree to use other additional barrier methods of contraception)\]. The pregnancy test result must be negative at screening and at each check-in visit. Participants must have a regular menstrual cycle of approximately 28 days duration for at least 4 previous cycles prior to screening * Postmenopausal females, or women not of child-bearing potential due to surgical sterilization (at least 3 months after surgical hysterectomy, or at least 3 months after bilateral oophorectomy or bilateral tubal occlusion with or without hysterectomy) confirmed by medical history, or menopause. Menopausal women include women with spontaneous amenorrhea for at least 12 months or amenorrhea not induced by a medical condition such as anorexia nervosa and/or not taking medications during that time of amenorrhea \[example (e.g.), oral contraceptives (OCs), hormones, gonadotropin releasing hormone, anti-estrogens, selective estrogen receptor modulators, or chemotherapy\]. Postmenopausal status should be confirmed by a serum follicle-stimulating hormone level at screening greater than 40 international units per liter (IU/L) * Have a body mass index of 18 to 30 kilograms per square meter (kg/m\^2), inclusive Exclusion Criteria: * Have a positive pregnancy test or are lactating * Are currently enrolled in, have completed or discontinued within the last 90 days from a clinical trial involving a study drug; or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * Are persons who have previously completed or withdrawn from this study or any other study investigating baricitinib, and have previously received the study drug * Have known allergies to baricitinib or Microgynon (containing ethinyl estradiol and levonorgestrel) or related compounds * Have used or intend to use drugs or substances that are known to be inducers or inhibitors of cytochrome P450 3A (eg, St. John's wort, rifampin, ketoconazole) within 30 days prior to the first dose * Have taken OCs within 3 months, implanted contraceptives within 6 months, injectable contraceptives within 12 months, or topical controlled delivery contraceptives (patch) or hormonal coils within 3 months prior to the study * Have a history or presence of any thromboembolic disease, recurrent jaundice, acute or chronic liver disease, hormonally-induced migraines, undiagnosed vaginal bleeding, significant hyperlipidemia, and mammary, endometrial, or hepatic carcinoma (known or suspected) * Smokes more than 10 cigarettes per day