# Hacking Economics? Predicting Changes in Unemployment and Stock Indexes Given Changes in GDP Growth

It was about a year ago that I first began to test an idea that’d been rolling around in my head for months.  There seemed to be a simple proportionality between changes in NGDP growth and the unemployment rate.

Very roughly, when there’s a recession, one can often predict the peak unemployment rate that will occur given a specific drop in NGDP by simply adding the change in GDP to the pre-recession baseline unemployment rate.  Specifically, when measuring the change in GDP, do so as the pecent difference between the pre-recession trendline and the trough of a recession.

Let’s take the Great Recession, to illustrate.  The pre-recession was about 4.7%.  NGDP fell about 6.3% below the pre-recession growth trendline.  Add those numbers together and you get an unemployment rate of 10.5%.  This is about .5% higher than the rate that actually occured, but not a bad rule of thumb calculation.

It doesn’t work as well, however, when trying to calculate the peak unemployment rate during the Great Depression.  Unemployment is widely cited to have peaked at about 25%, but GDP fell about 30%.  The baseline unemployment rate was 3.14%.  Obviously 33.14% is considerably off from 25%, so the rule of thumb doesn’t work well for really large recessions.

Even before I’d checked the Great Depression data though, I thought I’d have to cap the change predicted by that simple formula to account for the possibility that the unemployment rate could exceed 100%.  Hence, I adjusted the formula to have the U3 rate hyperbolically approach 100% unemployment.  This solved the problem.

The new formula looked like this:

U3  = 1 – [1 / (1 + Ub + ΔGDP)],

where ΔGDP actually refers to change in GDP growth and Ub refers to the baseline U3 rate.

Now, testing the Great Recession and Depression data:

Great Recession:

U3  = 1 – [1 / (1 + .047 + .063)] = ~9.9%

Great Depression:

U3  = 1 – [1 / (1 + .0314 + .3)] = ~24.9%

Okay, about .1% off again.  I’ll take it.  But, the above little rule of thumb doesn’t apply to the rate at which unemployment falls during recoveries, for example.  I’ve begun trying to model that, but I’ll leave that for a future post.

Besides, predicting the unemployment rate that will occur given a change in NGDP growth is boring compared to predicting what will happen to prices of investment assets, for example.

While thinking about the above, I was also thinking about how large changes in stock indexes seemed to be in relation to changes in expected NGDP.  Why were stock prices so volatile?  I believe, consistent with market monetarism, that when the money supply isn’t expected to grow as quickly as the demand for money, the expected rate of return on cash and close equivalents increases proportionately, reflecting an increased demand for money. Demand for money apparently is usually determined by the expected supply.

It then dawned on me that the expected increase in the value of the dollar versus consumption and investment would directly subtract from the expected rate of return on most non-fixed income investments.

So, how does this idea work out for predicting how changes in NGDP  affects stock prices?  Apparently, pretty well.

The little model below simply divides the expected change in NGDP  by the implicit yield on a broad representative stock index, such as the S&P 500:

The model could simply be stated as P/E ratio x ΔGDP, but 500 stock prices can’t fall to zero unless the companies all go out of business, so I make an adjustment for this fact, resulting in:

ΔS&P 500 = 1 – [1 / (1 + P/E ratio x ΔGDP)]

Again, this is a rule of thumb, because the temporal structure of the expected changes in GDP are mirrored in the discounted earnings flow, which are reflected in part in yield curves.  However, watch how accurate it can be: *Note: P/E ratios referred to are those immediately prior to the recessions.

Great Recession:

GDP change from trend line: -6.3% (3% peak-to-trough, but it’s the trend line that matters)

Change in S&P 500: ~-53%

P/E ratio: ~18.5

Calculation: ΔS&P 500 = 1 – [1 / (1+18.5 x .063)] = ~ -.54

Great Depression:

GDP change from trend line: ~-30%

Change in S&P 500 Index: ~ -82%

P/E ratio: ~17

Calculation: ΔS&P 500 = 1 – [1 / (1+17 x .30)] = ~ -.83

Recession of 2001:

GDP change from trend line: ~-2.8%

Change in S&P 500 Index: ~ -46%

P/E ratio: ~32

Calculation: ΔS&P 500 = 1 – [1 / (1+32 x .028)] = ~ -.46

U3  = 1 – [1 / (1 + .04 + .028)] = ~6.4%

Recession of 1981-1982:

GDP change from trend line: ~-4.8%

Change in S&P 500 Index: ~ -46%

P/E ratio: ~10

Calculation: ΔS&P 500 = 1 – [1 / (1+10 x .048)] = ~ -.46

U3  = 1 – [1 / (1 + .073 + .048)] = ~10.8%

You may have noticed I left out the 1990-1991 recession.  This is because this simple rule of thumb doesn’t apply to that one.  As it turns out, the stock and Treasury markets underestimated the degree to which the Fed would let NGDP fall below trend.

It’s obvious markets were overly optimistic, especially considering what was going on with Treasury yield curves at the time.  The markets were simply persistently predicting a higher path of post-recession NGDP  during much of that recession than actually occurred. This underlines the point that it is important to pay attention to market expectations for changes in NGDP growth when trying to determine the effects they’ll have on asset prices.

I will probably go into this in more detail in a future post, because this one is long enough.  But, here’s the 1990-1991 recession data fit to the model anyway:

GDP change from trend line: ~-3.2%

Change in S&P 500 Index: ~ -15%

P/E ratio: ~13

Calculation: ΔS&P 500 = 1 – [1 / (1+13 x .032)] = ~ -.29

I may get to posting the data of prior recessions to these models in the near future.

PS: If you think this little rule of thumb is a hack job, blame me.  If you like it, special thanks goes to Scott Sumner and other market monetarists who taught me far more about economics than I ever learned taking a few college courses.