The attached figure graphs the velocity of money and the interest rate in the period since 1959. The thing to note is that the two series move reasonably closely together. Velocity is defined as nominal gdp divided by the money supply (here measured by the St. Louis Federal Reserve bank’s measure called MZM). Note that when the interest rate is high, velocity is high, suggesting that money demand is low then.
The second attached figure displays further evidence in favor of our money demand specification, using data for the period 1900 to 1988. The top right picture shows that real balances move closely with real income. The bottom left graph shows that generally velocity has been low when interest rates were high, and velocity has been low otherwise (careful, the figure displays –log velocity which goes down when velocity goes up). Finally, the bottom right figure shows that money demand is pretty stable when you split the 20th century in half. In the later period, interest rates were generally low, and real money balances were low as theory predicted. Indeed, if we fit a money demand equation to data for the fist half of the century and extrapolated to the 2nd half, we would have had a pretty decent fit.
The analysis in all but the top left figure uses a short term rate of interest. The top left figure shows that the short rate and long rate behave similarly, so the analysis would yield roughly the same results if long rates had been used.