An outer bound for the degrees of freedom (DoF) region of the K-user multiple-input single-output (MISO) broadcast channel (BC) is developed under the hybrid channel state information at transmitter (CSIT) model, in which the transmitter has instantaneous CSIT of channels to a subset of the receivers and delayed CSIT of channels to the rest of the receivers. For the 3-user MISO BC, when the transmitter has instantaneous CSIT of the channel to one receiver and delayed CSIT of channels to the other two, two new communication schemes are designed, which are able to achieve the DoF tuple of $\left(1,\frac{1}{3},\frac{1}{3}\right)$, with a sum DoF of $\frac{5}{3}$, that is greater than the sum DoF achievable only with delayed CSIT. Another communication scheme showing the benefit of the alternating CSIT model is also developed, to obtain the DoF tuple of $\left(1,\frac{4}{9},\frac{4}{9}\right)$ for the 3-user MISO BC.

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