Palgrave Handbook of Econometrics: Applied Econometrics

78 How much Structure in Empirical Models?

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β = 0.985

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All shocks, π^

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Figure 2.1 Shape of the distance function

very little, suggesting that the problems present in Figure 2.1 are not specific to the
selected parameter vectors.
Since Figure 2.1 considers one dimension at a time, partial identification prob-
lems, where only combinations of parameters are identifiable, cannot be detected.
Figure 2.2 shows that ridges indeed exist: for example, responses to monetary
shocks carry little information about the correct combination ofλyandλπ;IS
shocks cannot separately identify the risk aversion coefficientφand the habit
persistence parameterh, while Phillips curve shocks have little information about
the discount factorβ. What is interesting is that when the responses to all shocks
are considered, some problems are reduced. For example, there appear to be fewer
difficulties in identifying the parameters of the policy rule when all the responses to
all shocks are considered – the distance function is more bell-shaped even though
there is a significantly large flat area. However, even in this case, the true values of
β,φandhare difficult to pin down.
This model, in addition to partial, weak and underidentification problems, faces
generic observational equivalence problems. For example, it would be hard to
detect whether the data are generated by an indeterminate version of the model
(which would be the case ifλπ <1) or a determinate one (λπ >1), so long