In Step #1 we established that the “tightness” or “looseness” of an employer’s wage policy involved the absolute level of wages, relative to what was previously expected. Changes in the expected future movement of wages was incidental, and indeed could give you the wrong answer, in cases where it went the opposite way from movements in the actual payment levels, relative to the original baseline path.
Now we have a similar scenario. As it turns out, not only does this particular company pay wages, but it also lets its employees borrow money. Employees can take loans from the company on either one-month or one-year terms, with corresponding (annualized) interest rates. Originally, here is the rate structure that Bobby and Davie expect to face in the coming year:
So starting next year, Bobby and Davie think that if they borrow money in the beginning of a month and have to pay it back at the end of that month, then the annualized interest rate they pay on such loans is 4% for any loan taken out from January through June, and 8% for any loan taken out from July through December. However, if they just decide in the beginning of the year to borrow the money for the whole year, then they can do that too, at an interest rate of 6%.
Notice that the one-year interest rate is the average of the individual monthly rates. That’s not a coincidence. Knowing the short-term rates ahead of time, someone could just roll over the loan month-to-month. (The math isn’t exact, but it’s pretty close: Rolling over a loan month-to-month works out to a cumulative interest rate for the year of about 5.98%.)
OK, now the boss comes in during the Christmas party and says, “Guess what folks? Our credit department didn’t do too much business this past year, and nobody in here defaulted, so starting next year, we’re going to loosen things up. Here is the new schedule of loan rates for next year, starting in January when you come back to work.”
Naturally, Bobby is very pleased by the news. He says to his buddy Davie, “This is great! With this looser, easier loan policy, it will be easier for me to swing that plasma screen TV I wanted to buy on credit. Relative to what I expected to pay in interest charges, now I am unambiguously better off. Whether I borrow in any given month, or whether I take out a loan for the whole year, I am always paying a lower interest rate than I had expected, before this announcement. Clearly this indicates that our credit department is loosening. Merry Christmas!”
Davie is not so keen on the news. He explains, “Bobby, you made the same mistake as you did with that Grinch wage announcement a couple of months ago. Look: The spread between the one-year rate and January’s one-month rate has increased. Before the announcement, it was 2 percentage points. But now it’s increased to 3 percentage points. And as we all know, the one-year interest rate always works out to the average of the expected short rates over that period. So if the spread jumps from 2 percentage points to 3 percentage points, it can only mean that we are expecting a bigger rate hike in the future, than we were before the announcement. Indeed, I can tell you specifically what it is: Short-term rates are going to jump up a whopping 6 percentage points in the second half of this year. Before the boss made his announcement, we were only expecting a 4 percentage point jump. So I don’t know how in the world you’re calling this increase in expected future rate hikes a ‘loosening’ of policy. These fiends are clamping down good and tight. Fits right in with their $300 wage cut this month, ya know?”
So who is right in this new dispute between Bobby and Davie?