The Solution of Singular Linear Difference Systems under Rational Expectations

  title={The Solution of Singular Linear Difference Systems under Rational Expectations},
  author={R. G. King and Mark W. Watson},
  journal={International Economic Review},
  • R. KingM. Watson
  • Published 1 November 1998
  • Mathematics
  • International Economic Review
Many linear rational expectations macroeconomic models can be cast in the first-order form, AE[subscript t]y[subscript t + 1] = By[subscript t] + CE[subscript t]x[subscript]t, if the matrix A is permitted to be singular. The authors show that there is a unique stable solution under two requirements: (1) the determinantal polynomial Az - B is not zero for some value of z, and (2) a rank condition. The unique solution is characterized using a familiar approach: a canonical variables… 

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“The Solution of Linear Di¤erence Models Under Rational Expectations

  • ” Econometrica
  • 1980

The Econometric Analysis of Non-Uniqueness in Rational Expecations Models, Amsterdam: North-Holland

  • Szafarz
  • 1991