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3.5. TESTING MONETARY MODEL PREDICTIONS 95These restrictions are tested for a given value of the interest semielasticityof money demand, λ = ψ/(1 − ψ). To set up the Wald test,let π 0 =(β 0 , δ 0 ) be the grand coefficient vector from the OLS regressions, ⇐(70)R =(I 8 : I 8 ) be the restriction matrix and r 0 =(0, 0, 0, 0, (1/ψ), 0, 0, 0),Ω T = Σ T ⊗ Q −1T ,whereΣ T = 1 P²t ² 0 T t, Q T = 1 Pxt x 0 T t. Then asT →∞, the Wald statisticW =(Rπ − r) 0 [RΩ T R 0 ] −1 (Rπ − r) D ∼ χ 2 8 .Here are the results. The Wald statistics and their associated valuesof λ are W = 284, 160(λ = 0.02), W = 113, 872(λ = 0.10), W =44, 584(λ =0.16), and W =18, 291(λ =0.25). The restrictions arestrongly rejected for reasonable values of λ.One reason why the model fares poorly can be seen by comparing thetheoretically implied deviation of the spot rate from the fundamentals˜ζ t = e 1 ψB(I − ψB) −1 Y t ,which is referred to as the ‘spread’ with the actual deviation, ζ t = s t −f t .ThesearedisplayedinFigure3.5whereyoucanseethattheimpliedspread is much too smooth.Long-Run Evidence for the Monetary Model fromPanel DataThe statistical evidence against the rational expectations monetarymodel is pretty strong. One of the potential weak points of the modelis that PPP is assumed to hold as an exact relationship when it isprobably more realistic to think that it holds in the long run.Mark and Sul [101] investigate the empirical link between the monetarymodel fundamentals and the exchange rate using quarterly observationsfor 19 industrialized countries from 1973.1 to 1997.4 and thepanel exchange rate predictive regression⇐(72)s it+k − s it = βζ it + η it+k , (3.26)where η it+k = γ i + θ t+k + u it+k has an error-components representa- ⇐(73)tion with individual effect γ i ,commontimeeffect θ t and idiosyncratic