What is Your Rate of Time Preference?

To determine your rate of time preference, perform the following thought experiment :

Assume that there is no Fed monetary supply inflation or deflation and that the supply and variety of future consumer goods in one year's time will not have appreciably changed from today. Also assume that there is no reason to expect the demand for money to increase or decrease over the next year.

There are two envelopes on the table.

Envelope A contains $1000 and can be opened at any time. But the $1000 must be spent immediately and not invested. Nor can another investment be made that depends on the acquisition of the $1000.

Envelope B can only be opened one year from today and will then contain $1000 plus a dollar amount that you write on the outside of the envelope today.

After you write the dollar amount on envelope B, I will choose either envelope A or envelope B, leaving the other for you.

If you have no knowledge of my rate of time preference, then your rate of time preference should be the dollar amount that you write on the envelope divided by 10 to give an annual percentage rate.

What dollar amount would you write on envelope B?

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I don't follow the logic of

I don't follow the logic of your claim, perhaps because I don't know what "no knowledge of my rate of time preference" means. In order to make a decision I need some opinion about what your rate of time preference is, and different opinions lead to different answers.

Suppose, for instance, we interpret "no knowledge" as meaning "a uniform prior distribution from zero to infinity," which makes as much sense to me as any alternative. In that case the probability that your discount rate is lower than 1000%/annum is zero, so I am perfectly safe writing $8000 on the envelope. You will take the other envelope, and I will get $9000 in a year instead of $1000 now.

Of course, I would be equally safe with a much larger number.

So far as I can tell, your conclusion makes no sense with any assumption short of "his discount rate has zero probability of being higher than mine." To see why, suppose my discount rate is 10% and I am considering, as per your conclusion, writing $100 on the envelope. If I do so, I am indifferent between the two envelopes. Instead I write $101. If you take Envelope A, I am better off than if I had written $100, since B is better than A (for me). If you take Envelope B, I am no worse off than if I had written $100, since A is as good as B would have been under those circumstances. So as long as the probability that your discount rate is above 10% is greater than zero, I should write a number larger than $100 on envelope B.

David, Thank you. Would it

David,

Thank you. Would it help if the person who ends up with envelope A becomes responsible for filling envelope B?

Thanks, Don

why "divided by 10", not

why "divided by 10", not divided by 1,000?

Write "infinity" on the

Write "infinity" on the envelope and before putting it on the table proclaim "dude, lets make a deal!" If he says no and just takes the envelope then hunt him down using the other $1000 to buy a nice snipper riffle.

What you are really doing is

What you are really doing is bidding $1000-n on the second envelope, where n is the interest amount (actually you're "bidding" on what you're willing to accept a year from now for $1000 now, but this only changes the numbers, not the strategies). You will bid at most what you're willing to pay for $1000 a year from now, but you will *try* to bid less if you think you can get away with it, since it's not a proxy bid like eBay where you (theoretically) only pay what you need to to beat the next highest bidder.

Very interesting thought

Very interesting thought experiment... I wonder, do you get to know what dollar amount I put on the back?

Plus...I agree that its problematic in the sense that you are not asking me to figure out my time preference, but rather, to try and gauge what yours would be, so that I can benefit by undercutting you by just a hair....afterall, I would want to maximize my own return, regardless of what my actual time preference is.

why do I have to spend the

why do I have to spend the 1000 dollars from envelope right away?

I might rather have 1000$ in a year with no stupid rules attached to it.

Although I'd probably just rules lawyer my way around that. "Spend it" on a money order, or foriegn currency, or gold bullion, cigarretes .... whatever ... just he most liquid commodity I could find that still counted as "spending" and not as "investing" or "saving". So the actual present value depends on the transaction costs associated with wherever you draw that arbitray line between spending and investing.

Here's my restatement of

Here's my restatement of your problem:

1. Someone (X) is giving each of us ("you" and "me") a gift which has a present value to me of at least $1,000 -- if I play my cards right.

2. One gift is $1,000 today, which must be consumed today.

3. The other gift is $1,000 plus an amount (A) that I get to designate. This gift ($1,000 + A) will be distributed a year from today.

4. After I have designated A, you get to choose between consuming $1,000 today and receiving $1,000 + A a year from today.

5. My designation of A leads to three possible outcomes:

a. A is (coincidentally) the same as the value (B) that you would have designated, in which case you will be indifferent between consuming $1,000 today and receiving $1,000 + A a year from today. But you might elect the $1,000 today, leaving me with $1,000 + A a year from today. In this case, I would want to choose a value for A that reflects my time preference, so that I am left with a gift that has a present value of at least $1,000.

b. A is less than B, in which case you will choose $1,000 today, and leave me with $1,000 + A a year from today. Again, I should choose a value for A that reflects my time preference, so that I am left with a gift that has a present value of at least $1,000.

c. A is greater than B, in which case you will choose to receive $1,000 + A a year from today, and I will be left with $1,000 to be consumed today. Given this possibility, I have nothing to lose by designating a value for A that reflects my time preference, and that is what I should do because outcomes (a) and (b) are also possible.

Is that it?

Even if I'm forced to spend

Even if I'm forced to spend the $1000 today, I can spend it on something that frees $1000 (or slightly less) of my OTHER money to invest. If I'm forced to spend it on something ephemeral which I wouldn't otherwise buy, it's not $1000 I'm measuring, it's that other thing.

Also, I don't think my (or most people's) time preference is linear over time, nor over size of asset. I have a different internal discount rate for $1000 next year than I have for $10M next year, and a different one still for either sum in 10 years.

Tom, I think that your

Tom,

I think that your formulation is equivalent to what I was originally thinking of, but that David's critique still applies. No matter how big a number you write down, you still won't be worse off than $1000 in the present, and maybe much better off.

I was actually interested in what people would choose for a time preference or discount rate with no effect from the market of any kind.

Maybe the problem should have been :

Write down a rate of interest. I will then choose which of us is the borrower of $1000 and which is the lender.

Please give me an actual rate.

Regards, Don

Just for the record I would

Just for the record I would write "infinity". :end:

For your original problem, I

For your original problem, I would probably write any number higher than say, $5000, per David Friedman's reply. I am a student currently and next year I will be working, so I'd be roughly indifferent between those two endowments.

But for:

"Write down a rate of interest. I will then choose which of us is the borrower of $1000 and which is the lender.

Please give me an actual rate."

My answer would be thanks, but no thanks. With no information about your preferences, the only way I could lessen the risk of being forced to lend (when I could hardly muster the resources) is by writing down a rate of interest that increasingly eclipses any rate that I'd be willing to pay.

Except infinity isn't a

Except infinity isn't a number. It's a concept.

My first thought was $100 (that is, $1100 total). I'm amused that nobody would come out with a number, preferring to discuss the question from every possible angle instead.

Two possibilities: #1 His

Two possibilities:
#1 His time preference matches or is less than mine, at which point only writing a number less than my preference could earn me the +1 year envelope. At which point, the optimal outcome is me getting the immediate envelope and he getting the +1 year envelope, I do not care what is written on it but should make sure that he takes it :wink:

#2 His time preference is greater than mine, at which point the optimal outcome is me taking the +1 year envelope, I should bid a number greater than mine but less than his.

We do not know which is the scenario. We do not have any idea what the other players time preference is. As such, I should write a number just slightly above my preference because his might just be slightly above mine and I don't want to bust him, and if his preference is below mine it doesn't matter to me what I write he is probably going to take it.

Don, Yes, I now see where I

Don,

Yes, I now see where I went off track. At my discount rate, $1,000 today is (for me) equivalent to $1,000 x (1 + rate) a year from now. Therefore, if I write an amount that reflects my discount rate, the outcome is the same for me no matter which envelope you choose.

Given that, I might as well write a larger amount because, if you have a higher discount rate than me, you may reject the larger amount (depending on your discount rate) and I'll be better off. (Which I think is what David said, in effect.) Therefore, I will not write an amount that reflects my time preference; I will write a higher amount.

To get an answer to your original question (What is my rate of time preference?), you reformulate the problem:

"Write down a rate of interest. I will then choose which of us is the borrower of $1000 and which is the lender."

If I write down a rate that reflects my actual time preference -- and if I'm indifferent as between lending, borrowing, or doing neither (an important caveat) -- then I'll be indifferent to your choice, no matter which way it goes.

If I write down a rate that's lower than my actual time preference, I'm worse off if you make me the lender, but better off if you make me the borrower. If I write down a rate that's higher than my actual time preference, I'm better off if you make me the lender, but worse off if you make me the borrower. Given that I have no information about your time preference, I have no idea what choice you will make. Prudence therefore dictates that I write down a rate that reflects my actual time preference. Seem right to me.

As for an actual number, I can't give you that. Why? For one thing, I don't know your creditworthiness, which I need to know if I commit to the possibility of being a lender. My time preference doesn't exist in a vacuum, so to speak. It depends on the risk associated with a particular course of action. That's why U.S. Treasury bonds carry lower interest rates than AAA corporate bonds, which carry lower interest rates than BBB corporate bonds, and so on.

Tom, As for an actual

Tom,

As for an actual number, I can’t give you that. Why? For one thing, I don’t know your creditworthiness, which I need to know if I commit to the possibility of being a lender. My time preference doesn’t exist in a vacuum, so to speak. It depends on the risk associated with a particular course of action. That’s why U.S. Treasury bonds carry lower interest rates than AAA corporate bonds, which carry lower interest rates than BBB corporate bonds, and so on.

That was the reason for all my initial qualifications. I wanted the number that would reflect only the time preference for present consumption over future consumption with all other factors neutral. If inflation were expected to be significant, for example, both lenders and borrowers would take into account the fact that the paid off dollars would have less purchasing power and adjust their nominal interest rate requirements as appropriate.

Regards, Don

When you're done conducting

When you're done conducting this experiment measuring your time preference, you might next want to measure your hunger, alertness, velocity, and elevation, since they are all similarly dependent upon circumstances and likely to change from measurement to measurement in ways that are difficult to predict or draw meaningful conclusions from.