# Karl Schmedders (editor), Kenneth L. Judd (editor)'s Handbook of Computational Economics, Volume 3 PDF

By Karl Schmedders (editor), Kenneth L. Judd (editor)

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However, it remains to be seen whether or not that difference is substantial and what dimensions of the models are most important in determining this relative efficiency. It may be that it is not the number of state variables or control variables that is the crucial measure of size here but rather the number of parameters that are treated as unknown. For example, a relatively large model might have only a few parameters that need to be learned and thus the least efficient of the three methods will still be very useful for that model.

Pk−1,t −Pk,t ⎢ I 0 ... 0 0 ⎥ ⎢ ⎥ ⎢ 0 ⎥ I . . 0 0 =⎢ ⎥, ⎢ .. ⎥ .. ⎣ . 0 0 ⎦ 0 ... I 0 ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 0 ... 0 Bt Ct I ⎥ 0 . . 0⎥ ⎢0⎥ ⎢0⎥ ⎢0⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ I 0⎥ ⎥ 2,t = ⎢ .. ⎥ 3,t = ⎢ .. ⎥ 4 = ⎢ .. ⎦ .. ⎦ 0 0 0 0 I and the augmented state vector ⎡ ⎢ ⎢ ⎢ πt = ⎢ ⎢ ⎣ xt Ext+1 Ext+2 .. ⎤ ⎥ ⎥ ⎥ ⎥. ⎥ ⎦ (20) Ext+k−1 Taking the generalized eigenvalues of (19) allows us to decompose the system matrices 0,t and 1,t in the following manner, viz. Coleman and Van Loan (1988) or Moler and Stewart (1973), t = Qt 0,t Zt t = Qt 1,t Zt 23 Learning About Learning in Dynamic Economic Models with Zt Zt = I and Qt Qt = I .

In contrast the estimated value tracks the actual very closely in the known parameters case but does not track and indeed does not change in the deterministic case. So for the example at hand, the scenario of known parameters is better than the scenario of ignoring the fact of the unknown parameters in the deterministic case. Thus the Lucas critique is valid in this case. Ignoring the fact that the parameters are drifting and changing in response to policy pronouncements results in higher loss functions for the performance of the economy.