There appears to be some disagreement whether there is a teacher shortage in New York City. Sure, there is a shortage of ESL, Math, Science, and Special Education teachers, especially in the high poverty communities in the Bronx and Brooklyn. However, in those schools many of these shortages areas are covered by uncertified teachers in that subject and the DOE looks the other way Since its not about what's best for the students.
For the rest of the subjects, like English, Foreign Language, Physical Education, Social Studies, and the Arts (Art, Music, Technology) there is no teacher shortage. New York City is a magnet for newly minted teachers from the rest of the country due to higher salaries, a vibrant City lifestyle, and fringe benefits like a pension and health benefits. For example, come June 16th 2018, the minimum teacher salary is $56,711 for a "newbie", with no classroom experience. Compare that to the average starting teacher salary nationwide is $36, 141 and the maximum is $64,820, compared to New York City's $119,565 and you can see that New York City is a mecca for "newbies"..
Of course, 50% of these "newbies: will be leaving the NYC public schools within 5 years and only 33% will ever last long enough to be vested for a pension and even less for retiree health benefits. Moreover, 80% of these "newbies" will leave their hiring school before they achieve tenure. The numbers I have cited was primarily based on Tier IV teachers and before there was a teacher evaluation system, complete with the punitive Danielson rubric. Therefore, I suspect there will be even less Tier VI teachers making it to their 10-year vesting period for a pension and even less for the 15 years for retiree health benefits.
The DOE policies encourage the recruitment of "newbie" teachers by their "fair student funding" formula, the teacher excess policy, and their encouragement to hire the most inexpensive teachers for schools. What about the children you say? The DOE cares little about high teacher turnover, an unstable school environment, and large class sizes. Their policies are not geared to retention but recruitment and its up to the schools to deal with teacher dissatisfaction and in turn, hurts student academic achievement.
Add to the retention issue the much weakened student discipline policy and low teacher morale and you have the ingredients for failing schools and a transient teaching staff and a major reason for a school system in chaos.