Efforts to establish the play's date of composition are complicated by its uncertain relationship with another Elizabethan play with an almost identical plot but different wording and character names, A Pleasant Conceited Historie, called the taming of a Shrew.[d] The Shrew 's exact relationship with A Shrew is unknown. Different theories suggest A Shrew could be a reported text of a performance of The Shrew, a source for The Shrew, an early draft (possibly reported) of The Shrew, or an adaptation of The Shrew. A Shrew was entered in the Stationers' Register on 2 May 1594, suggesting that whatever the relationship between the two plays, The Shrew was most likely written somewhere between 1590 (roughly when Shakespeare arrived in London) and 1594 (registration of A Shrew).
However, it is possible to narrow the date further. A terminus ante quem for A Shrew would seem to be August 1592, as a stage direction at 3.21 mentions "Simon," which probably refers to the actor Simon Jewell, who was buried on 21 August 1592. Furthermore, The Shrew must have been written earlier than 1593, as Anthony Chute's Beauty Dishonoured, written under the title of Shore's wife (published in June 1593) contains the line "He calls his Kate, and she must come and kiss him." This must refer to The Shrew, as there is no corresponding "kissing scene" in A Shrew. There are also verbal similarities between both Shrew plays and the anonymous play A Knack to Know a Knave (first performed at The Rose on 10 June 1592). Knack features several passages common to both A Shrew and The Shrew, but it also borrows several passages unique to The Shrew. This suggests The Shrew was on stage prior to June 1592.
In his 1982 edition of the play for The Oxford Shakespeare, H.J. Oliver suggests a date of composition of 1591/1592. His argument is based upon the title page of A Shrew, which mentions the play had recently been performed by Pembroke's Men. When the London theatres were closed on 23 June 1592 due to an outbreak of plague, Pembroke's Men went on a regional tour to Bath and Ludlow. The tour was a financial failure, and the company returned to London on 28 September, financially ruined. Over the course of the next three years, four plays with their name on the title page were published; Christopher Marlowe's Edward II (published in quarto in July 1593), and Shakespeare's Titus Andronicus (published in quarto in 1594), The True Tragedy of Richard Duke of York (published in octavo in 1595) and The Taming of a Shrew (published in quarto in May 1594). Oliver concludes that these four publications were reported texts sold by members of Pembroke's Men who were broke after the failed tour. If one accepts A Shrew is a reported version of The Shrew (which Oliver believes it is), it means The Shrew must have been in their possession when they began their tour in June, as they didn't perform it upon returning to London in September, nor would they have taken possession of any new material at that time. As such, Oliver concludes The Shrew must have been written prior to June 1592, and it was one of the performances during the Bath/Ludlow tour which gave rise to the A Shrew text.
Ann Thompson, who also believes A Shrew to be a reported text, suggests a similar theory in her 1984 and 2003 editions of the play for the New Cambridge Shakespeare. She too focuses on the closure of the theatres on 23 June 1592, arguing, like Oliver, that the play must have been written prior to June 1592 for it to have given rise to A Shrew. She also cites the reference to "Simon" in A Shrew, Anthony Chute's allusion to The Shrew in Beauty Dishonoured and the verbal similarities between The Shrew and A Knack to Know a Knave as supporting a date of composition prior to June 1592. Stephen Roy Miller, in his 1998 edition of A Shrew for the New Cambridge Shakespeare, agrees with the Oliver/Thompson date of late 1591/early 1592, as he too believes The Shrew preceded A Shrew (although he rejects the reported text theory in favour of an adaptation/rewrite theory).
Kier Elam, however, has argued for a terminus post quem of 1591 for The Shrew, based on Shakespeare's probable use of two sources published that year; Abraham Ortelius' map of Italy in the fourth edition of Theatrum Orbis Terrarum, and John Florio's Second Fruits. Firstly, Shakespeare errs in putting Padua in Lombardy instead of Veneto, probably because he used Ortelius' map of Italy as a source, which has "Lombardy" written across the entirety of northern Italy. Secondly, Elam suggests that Shakespeare derived his Italian idioms and some of the dialogue from Florio's Second Fruits, a bilingual introduction to Italian language and culture. Elam argues that Lucentio's opening dialogue,
Tranio, since for the great desire I had To see fair Padua, nursery of arts, I am arrived for fruitful Lombardy, The pleasant garden of great Italy.
is an example of Shakespeare's borrowing from Florio's dialogue between Peter and Stephan, who have just arrived in the north:
PETER I purpose to stay a while, to view the fair Cities of Lombardy. STEPHAN Lombardy is the garden of the world.
If one accepts Elam's arguments, it would suggest The Shrew could not have been written any later than 1591, which would place the date of composition as somewhere in the period 1590–1591.
The 1594 quarto of A Shrew was printed by Peter Short for Cuthbert Burbie. It was republished in 1596 (again by Short for Burbie), and 1607 by Valentine Simmes for Nicholas Ling. The Shrew was not published until the First Folio in 1623. The only quarto version of The Shrew was printed by William Stansby for John Smethwick in 1631 as A Wittie and Pleasant comedie called The Taming of the Shrew, based on the 1623 folio text. W.W. Greg has demonstrated that A Shrew and The Shrew were treated as the same text for the purposes of copyright, i.e. ownership of one constituted ownership of the other, and when Smethwick purchased the rights from Ling in 1609 to print the play in the First Folio, Ling actually transferred the rights for A Shrew, not The Shrew.