RDP 9307: Explaining Forward Discount Bias: Is it Anchoring? Appendix D: Augmented Dickey-Fuller Tests on 3-Month Nominal Interest Differentials

The ADF tests are conducted on the weekly data, assuming a constant and no time trend. The null hypothesis of a unit root is rejected when the ADF statistic is more negative than the critical value. For a sample size of 500, 1%, 5% and 10% critical values are −3.44, −2.87 and −2.57 respectively. We include 20 autoregressive lags on the differenced interest differential and sequentially reduce the number of lags when the last lag has a t-statistic less than 2 in absolute value.

Deriving values for λ from Fair (1987)

Using quarterly data, Fair estimates a money demand function of the form

where POP_t is the population in quarter t. The parameter values we use for (D1) are the average of Fair's estimates for Canada, France, Germany, Japan and Italy (US and UK are excluded because Fair chooses a different specification for the US and finds (D1) mis-specified for the UK). Assuming Y_t and POP_t are fixed, we consider a once-off 1% shock to the nominal money supply at the beginning of a quarter. Given θ, assuming prices evolve according to our model (Δp_τ+1 = ( _τ − p_τ)/θ, with τ measured in 4-week periods) the chosen value of λ minimises the mean squared difference between the simulated interest rate path in our model and in Fair's estimated model when the two simulations are compared over 3 years.