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The reduced form of the system is: = + = +, with vector of reduced form errors that each depends on all structural errors, where the matrix A must be nonsingular for the reduced form to exist and be unique. Again, each endogenous variable depends on potentially each exogenous variable.
A matrix is in reduced row echelon form if it is in row echelon form, with the additional property that the first nonzero entry of each row is equal to and is the only nonzero entry of its column. The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it.
For example, in the following sequence of row operations (where two elementary operations on different rows are done at the first and third steps), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form.
For example, a regression is often called a reduced-form equation even when no standard economic model would generate it as the reduced form relationship between variables. These conflicting distinctions between structural and reduced form estimation arose from the increasing complexity of economic theory since the formalization of simultaneous ...
A Latin square is said to be reduced (also, normalized or in standard form) if both its first row and its first column are in their natural order. [4] For example, the Latin square above is not reduced because its first column is A, C, B rather than A, B, C. Any Latin square can be reduced by permuting (that is, reordering) the rows and columns ...
This problem can be overcome by rewriting the VAR in reduced form. From an economic point of view, if the joint dynamics of a set of variables can be represented by a VAR model, then the structural form is a depiction of the underlying, "structural", economic relationships.
A traditional snickerdoodle recipe includes unsalted butter, granulated sugar, eggs, all-purpose flour, cream of tartar, baking soda and salt.
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction".