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250 CHAPTER 8. THE MUNDELL-FLEMING MODELest rates are in logarithms. Let y t be US industrial production, p t be theUS consumer price index, nbr t be the log of non-borrowed bank reservesdivided by the log of total bank reserves, i t − i ∗ t be the 3 month USforeignnominal interest rate differential, q t be the real exchange rate,and s t be the nominal exchange rate. 11 For each US—foreign countrypair, two separate VARs were run–one using the real exchange rateand one with the nominal exchange rate. In the Þrst system, the VARis estimated for the 5-dimensional vector x t =(y t ,p t ,nbr t ,i t − i ∗ t ,q t ) 0 .In the second system, we used x t =(y t ,p t ,nbr t ,i t − i ∗ t ,s t ) 0 . 12The Þrst row of plots in Figure 8.8 shows the impulse response ofthe log real exchange rate for the US-UK, US-Germany, and US-Japan,following a one-standard deviation shock to nbr t . An increase in nbr tcorresponds to a positive monetary shock. The second row shows theresponses of the log nominal exchange rate with the same countries toa one-standard deviation shock to nbr t .Both the real and nominal exchange rates are found to depreciateupon impact but the maximal nominal depreciation occurs somemonths after the initial shock. The impulse response of both exchangerates is hump-shaped. There is evidently evidence of overshooting, butit is different from Dornbusch overshooting which is instantaneous. Thisunrestricted VAR response pattern has come to be known as delayedovershooting.Long-horizon (36 months ahead) forecast-error variance decompositionsof nominal exchange rates attributable to orthogonalized monetaryshocks are 16 percent for the UK, 24 percent for Germany, and10 percent for Japan. For real exchange rates, the percent of varianceattributable to monetary shocks is 23 percent for the UK and Germany,and 9 percent for Japan. Evidently, nominal shocks are prettyimportant in driving the dynamics of the real exchange rate.11 Interest rates for the US and UK are the secondary market 3-month TreasuryBill rate. For Germany, I used the interbank deposit rate. For Japan, the interestrate is the Japanese lending rate from the beginning of the sample to 1981.8, andis the private bill rate from 1981.9 to 1998.112 Using BIC (Chapter 2, equation 2.3) with the updated data indicated that theVARs required 3 lags. To conform with Eichenbaum and Evans, I included 6 lagsand a linear trend.