Why does a decrease in interest rate reduces the velocity of money circulation?

Why does a decrease in interest rate reduces the velocity of money circulation?

Keep in mind that money circulation and velocity of money circulation are different concepts. The relation you point out in your 2nd paragraph applies to money circulation, not its velocity: A high interest rate renders saving more attractive and thus reduces money circulation. Also, it is more useful to think of this in terms of "increase of money supply" rather than "decrease in interest rate".

The Wikipedia article you cite defines velocity of money circulation as

the frequency at which the average same unit of currency is used to purchase [something] within a given time period.

The key term is "average same unit of currency". An analogy with drivers and cars is illustrative:

Drivers demand cars (currency) so they can "visit destinations" (purchase goods and services). Suppose the central bank releases additional cars, thereby making them more affordable during a given period.

The release of additional cars will lead to an increase of drivers' aggregate mileage, but the frequency and average usage of one same car within that given period will decrease because now drivers have more cars (units of currency) to choose from [to perform their transactions]: If now you have access to five cars instead of just one, you might certainly end up driving more than you used to, but you are very unlikely drive five [, six, seven, ...] times more than when you had access to just one car. That means that, in average, your usage of one same car will be lower than that from when you only had one.

The implication on the frequency of average usage of the same unit follows directly from the above argument.

An increase of money supply reduces the velocity of money circulation also from the standpoint that economic agents will not necessarily spend all the additional money available. They will save a portion. That portion pushes down the frequency at which the average same unit currency is used for purchasing goods and services.

Lastly, the Wikipedia section of Relation to money demand is flawed. It states in relevant part:

Given the nominal flow of transactions using money, if the interest rate on alternative financial assets is high, people will not want to hold much money relative to the quantity of their transactions—they try to exchange it fast for goods or other financial assets, and money is said to "burn a hole in their pocket" and velocity is high.

That argument is flawed because it implicitly assumes that a low interest rate associated to money supply can coexist with a high interest rate on alternative financial assets: That creates arbitrage opportunities. In reality, both rates have a positive correlation. When alternative rates are high, people could not hold much money anyway because the interest rate associated to money supply is also high.

I would just like to share my take on your question and to rebuttal some of the comments already made. In particular, the analogy given by Mr. Inaki Viggers.

Currently, the way people view rate cuts is it stimulates the economy because a lower rate enables businesses and people to borrow cheaper. This is supposed to increase spending/consumption and thus increases GDP. (Obviously there are other impacts to currency/inflation but let's just stick to this.)

We have been in one of the longest bull markets in history from '09-'19 (2020 currently getting crushed by corona virus) but within that time, growth has been evident. However, I am actually very unsure of how much of this growth you can attribute to pumping liquidity into the market relative to things like technological growth.

To get back to the car analogy, yes you may have went from 1 car to 4 cars, but the entire point of giving you more cars is to increase your OVERALL mileage. If on average you were driving 2 times with the one car, and now you drive 1.2 with 2 cars (assuming the same distance per trip) then yes, your usage per car is going down. HOWEVER, the overall affect on the mileage is not very large. And what if you originally had 5 trips with one car, and now you only have 0.5x trips with 9 cars? Sure, the velocity takes a beating, but you are actually driving LESS.

My problem with Mr. Viggers analogy isn't the analogy itself, but the fact that people think it is set in stone you will increase your mileage by having more cars. There is a point of diminishing returns when you keep pumping liquidity into the markets, because you have a risk of deflation. And eventually, you won't have any cars left to give people which could be a really bad scenario if everyone loses the cars they originally have (i.e. if you enter a recession with very low rates, you can't provide monetary stimulus).

Think of the velocity going down as a dampening affect on GDP when rates are cut. If you keep giving people cars to drive around the world, people are gonna travel and visit everything. The second there is nothing else to see, they might just be comfortable with staying in their own home. (Trying to say that there may come a point in time where more money enters the market, but people don't spend it...perhaps they lock their cash into mortgages because rates are so low, etc.)

Another interesting aspect is when the government tries to take the cars they gave you back and you get angry about it...but that's a whole other topic haha.

Low velocity results in low interest rates - not the other way around. And with a higher demand for money, there is a lower need to economize on your holdings.

And the principal reason why velocity has fallen is the impoundment and idling of savings in our payment's system. Banks are "Black Holes". Banks do not loan out existing deposits. Banks pay for their earning assets with new money. All bank-held savings (funds held beyond the income period in which received), are lost to both consumption and investment, indeed to any type of payment of expenditure.

“Why are the time deposits not invested? Simply because the commercial banks are carrying on their balance sheet a liability that is owned by the nonbank public (not the commercial banks), that cannot be used unless the nonbank public decides to use it, and by definition it is not being used. You cannot write a draft against it, the banks cannot use it, the public is not using it, so it is not being used.”

It is no happenstance that velocity has fallen when non-M1 components relative to total checkable deposits rose from a proportion of 3.23 to 1 in Dec. 1993 to 13.76 to 1 by Feb. 2008 thereby destroying money velocity.

People fall down the rabbit hole. Income velocity may be a "fudge factor," but the transactions velocity of circulation is a tangible figure. Vi is a “residual calculation - not a real physical observable and measureable statistic.”

I.e. Dr. Milton Friedman's income velocity, Vi, is endogenously derived and therefore contrived (N-gDp divided by M) whereas Vt, is an “independent” exogenous force acting on prices.

As Dr. Philip George posits: “Changes in velocity have nothing to do with the speed at which money moves from hand to hand but are entirely the result of movements between demand deposits and other kinds of deposits.”

See: G.6 Debits and Deposit Turnover at Commercial Banks http://bit.ly/2pjr81u

The decline in income velocity, MZM velocity, since 1981 parallels the decline in the transactions’ velocity. The decline in velocity was directly caused by the impoundment of monetary savings in the payment's system, i.e., caused by the FDIC raising deposit insurance levels from 40,000 dollars to 250,000 dollars and the complete deregulation of interest rates for specifically the member banks.

Link: http://www.philipji.com/item/2014-04-02/the-velocity-of-money-is-a-function-of-interest-rates