Abstract This paper shows how to impose parametric restrictions in conjunction with sign restrictions to separate the shocks in SVARs. In sign restrictions, it is common to rotate an initial set of orthogonal shocks by utilising a Givens rotation matrix. In this paper, we show how to construct the Givens rotation matrix when parametric restrictions are part of the identification in sign restricted SVARs. The properties of Givens matrices are such that the parametric restrictions imply a system of equations which can be solved for the unknown parameters (or “angles”) in a rotation matrix, conditional on the values of the parameters which are drawn. The Givens rotation matrix formed in this manner is such that the parametric restrictions on the impulse responses are satisfied on each draw in sign restrictions. The method is demonstrated in an influential SVAR and is shown to generate results similar to those from a recent method which imposes the orthogonality and zero parametric restrictions on the columns of the rotation matrix in sign restrictions.

中文翻译：

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利用 Givens 旋转在 SVAR 中结合符号和参数限制

摘要 本文展示了如何结合符号限制施加参数限制以分离 SVAR 中的冲击。在符号限制中，通常使用 Givens 旋转矩阵来旋转一组初始正交冲击。在本文中，我们展示了当参数限制是符号限制 SVAR 中识别的一部分时如何构造 Givens 旋转矩阵。Givens 矩阵的性质使得参数限制意味着一个方程组，该方程组可以求解旋转矩阵中的未知参数（或“角度”），条件是绘制的参数值。以这种方式形成的 Givens 旋转矩阵使得在每次绘制符号限制时满足对脉冲响应的参数限制。