Previously on OCE
If you caught my last posting and are back for more... thank you! I'm really happy with how many returning visitors the blog is getting. If you didn't catch my last post, this one is basically an addition to it. You are welcome to go back and check it out in full, or be happy with this short synopsis:- An influential set of researchers (we'll call them RR) poured over historical data and claimed to observe a correlation between the amount of debt a country had (as a percent of their GDP), and what kind of growth (increase in GDP) they experienced. As the debt got to be greater than 90% of GDP, there was a precipitous drop off in average growth, going from the 3-4% range down to negative 0.1% growth (recession).
- A second set of researchers (that we'll call HAP) looked at the same data and found many flaws, from the actual data, to the averages, to the typos in their Excel worksheets, which made HAP's version of the growth number 2.2% under the high debt conditions.
So why is this important? Again stealing from last week:
- In 2010, when the first set of research came out, the US was nearing that magical 90% debt mark, and had just tried to stimulate its economy. Parts of Europe wanted to as well. Some RR believers argued that stimulus was a bad idea as it would lead to even more debt. Others even went the opposite direction and called for austerity in hopes of balancing the budgets and lowering debt.
- The idea behind stimulus is that a government can borrow money (adding to debt) and spend it right away on improving the economy (adding it to GDP). Because it is affecting both the numerator and the denominator of debt/GDP it has a dampened effect on the ratio. The bonus is that all that money you paid this year to build bridges, give tax refunds, or even landscape the national mall goes to people who can spend it again, increasing GDP next year.
The hope is that you can "grow your way out of debt" with the debt/GDP denominator gradually increasing and the debt becoming less burdensome as inflation eats away at it. But will it work? That is today's test. We are going to model a high-debt national economy and see how different conditions affect it.
Stimulation Simulation
Right off the bat I should point out that I'm making this model as simple as possible. We will have three columns (lets call them F, G, and H) that will be the year, GDP, and Debt, respectively. We'll add one extra column that we can define right now as Debt as a percent of GDP (by typing the [In Brackets] portion):
Great, we're done! Except for that pesky NAME! error we get for not having put anything into G2. Ok, lets fill it. For the year column, make a series of numbers F2:F32 that are 0 through 30. I'm including a year "0" so that at year "1" we can type in an equation that affects the previous year and can be dragged down to complete the column. Keeping with the "simple" theme, lets define some terms so that we can use them to fill our Debt and GDP columns.
Initial Values:
Initial GDP (in dollars) = C2 = 1000
Initial Debt (% of GDP) = C3
I think these are easy to justify. I'm going to use an arbitrary value of 1000 for the initial GDP because actual GDP values make for extra large cells, and honestly, we're going simple. The "% of GDP" for Initial Debt means we will have to use "C3*0.01*C2" quite a bit (which is annoying), but it makes the presentation look prettier and is more intuitive for some folks. I'll let people play around with the initial debt levels, keeping in mind that we were at 80ish % right before the crisis. As a background, we averaged 60ish % over the 1990s and 2000s.
Crisis and Stimulation:
Financial Crisis Hit (% of GDP) = C6
Stimulus (% of GDP) = C7
Percent of Stimulus Respent = C8
The idea here is that the financial crisis basically made about 5% of our GDP evaporate. I say "about" because it is tough to determine, as we did a lot of mitigation and don't actually have any real-time measurements. You could make a good argument for any number from 2-10 (and probably some bad ones too) so lets set this as a movable target as well. This will also let us set up scenarios in the absence of Crisis Hit. Same thing with the Stimulus. Technically there are still some remnants of stimulus dollars out there, but for the most part they were contained in the 5% of GDP injection of 2009. Some people thought we needed more, some less. Heck, lets make all the numbers from here on out movable values.
Speaking of values, when I say stimulus it means either tax breaks or spending. They are (basically) the same. Both are debts the government takes on so that spending in the economy will rise. Once spent, that money goes to someone else who can choose to spend it again or save it. The savings rate in the US is about 5%, making the Percent of Stimulus Respent theoretically about 95%. But since the European savings rate is higher (10-20%) and Asian rates higher still we might as well let this be anything.
Speaking of values, when I say stimulus it means either tax breaks or spending. They are (basically) the same. Both are debts the government takes on so that spending in the economy will rise. Once spent, that money goes to someone else who can choose to spend it again or save it. The savings rate in the US is about 5%, making the Percent of Stimulus Respent theoretically about 95%. But since the European savings rate is higher (10-20%) and Asian rates higher still we might as well let this be anything.
A Two State Solution:
Interest Rate on Debt (%) for Low Debt = C11, for High Debt = D11
Inflation Rate (%) for Low Debt = C12, for High Debt = D12
Deficit (-) or Surplus (+ % GDP) for Low Debt = C13, for High Debt = D13
Real GDP Growth Rate (%) for Low Debt = C14, for High Debt = D14
For this model we'll set up two states (where we look at the year before). If the previous year's debt is less than (or equal to) 90% of GDP we'll use the low debt values. Alternatively for greater than 90% of GDP we'll use the high debt values.
The interest rate on debt is really tough to pin down. In trying to be simple we are now confounded by the fact that you can hold a 1-year treasury bill which pays you for what you thought of the government's riskiness this year or hold a 30-year treasury bond which pays you for what you thought of the government waaaaaay in the past. An alternative, all-encompasing, way to think about the interest on our debt is that in 2011 we spent $251 Billion in interest on somewhere around $16 Trillion which is only... like 1.5% interest? And don't forget, that is nominal interest. If inflation right now is at 2% then loaning the US government money for 1 year gets you a negative return. But imagine you are an Greece, which as recently as last year had some 10-year notes as high as 30%, and now issues at around 8%. What do you pay for your debt? I'm going to leave this up to the reader and let them insert values for interest between 0 - 5%.
Inflation is a bit easier to track. For one thing, we have good numbers:
Long-term, the inflation rate has been semi-volitile (averaging 3.37%), but if you had to pin down one or two numbers I'd go with periods of 2.5%, which is about what the Fed targets, and periods of >5% when people get very unhappy. Looking back up at the debt graph again, it is tough to say that high inflation really correlates with debt (and if anything our lowest recent debt was when we had highest inflation). Lets give people the chance to make up their own minds and go with a range of 2.5%-10%.
Running a deficit or surplus is completely out of the scope of this experiment, but it happens so I guess we should model it. Whether or not the current level of debt encourages deficits or surpluses (surpli?) is an argument that I'd encourage in the comments. As a reference, our deficits in the 80s were about -2% GDP, and in the mid 00s neared -3%. Our surplus in the late 90s was near +2%.
Finally, we get to the point of this: GDP growth. Our real GDP growth has averaged about 3% since 1945, with an average of about 3.8% in the good times. As I mentioned earlier, RR and HAP differed on their value for countries at > 90% debt (finding -0.1 and +2.2% respectively).
Nominal Growth for Low Debt: (C15) [=((C14*.01+1)*(C12*.01+1)-1)*100]
Nominal Growth for High Debt: (D15) [=((D14*.01+1)*(D12*.01+1)-1)*100]
Inflation Rate (%) for Low Debt = C12, for High Debt = D12
Deficit (-) or Surplus (+ % GDP) for Low Debt = C13, for High Debt = D13
Real GDP Growth Rate (%) for Low Debt = C14, for High Debt = D14
For this model we'll set up two states (where we look at the year before). If the previous year's debt is less than (or equal to) 90% of GDP we'll use the low debt values. Alternatively for greater than 90% of GDP we'll use the high debt values.
The interest rate on debt is really tough to pin down. In trying to be simple we are now confounded by the fact that you can hold a 1-year treasury bill which pays you for what you thought of the government's riskiness this year or hold a 30-year treasury bond which pays you for what you thought of the government waaaaaay in the past. An alternative, all-encompasing, way to think about the interest on our debt is that in 2011 we spent $251 Billion in interest on somewhere around $16 Trillion which is only... like 1.5% interest? And don't forget, that is nominal interest. If inflation right now is at 2% then loaning the US government money for 1 year gets you a negative return. But imagine you are an Greece, which as recently as last year had some 10-year notes as high as 30%, and now issues at around 8%. What do you pay for your debt? I'm going to leave this up to the reader and let them insert values for interest between 0 - 5%.
Inflation is a bit easier to track. For one thing, we have good numbers:
Long-term, the inflation rate has been semi-volitile (averaging 3.37%), but if you had to pin down one or two numbers I'd go with periods of 2.5%, which is about what the Fed targets, and periods of >5% when people get very unhappy. Looking back up at the debt graph again, it is tough to say that high inflation really correlates with debt (and if anything our lowest recent debt was when we had highest inflation). Lets give people the chance to make up their own minds and go with a range of 2.5%-10%.
Running a deficit or surplus is completely out of the scope of this experiment, but it happens so I guess we should model it. Whether or not the current level of debt encourages deficits or surpluses (surpli?) is an argument that I'd encourage in the comments. As a reference, our deficits in the 80s were about -2% GDP, and in the mid 00s neared -3%. Our surplus in the late 90s was near +2%.
Finally, we get to the point of this: GDP growth. Our real GDP growth has averaged about 3% since 1945, with an average of about 3.8% in the good times. As I mentioned earlier, RR and HAP differed on their value for countries at > 90% debt (finding -0.1 and +2.2% respectively).
Nominally Keeping it Real
Because we pulled out inflation as a separate variable, we need to make sure that we change the real GDP growth to nominal growth (otherwise we'd be losing growth to inflation twice!) The readers won't be able to change this, but it will be listed so that they can see it.Nominal Growth for Low Debt: (C15) [=((C14*.01+1)*(C12*.01+1)-1)*100]
Nominal Growth for High Debt: (D15) [=((D14*.01+1)*(D12*.01+1)-1)*100]
Time For Sum Fun
For year zero, the GDP value will be the initial GDP minus whatever financial hit we take from the crisis, plus any additional amount from a stimulus. The debt value will be initial debt plus any additional stimulus. While I'm at it lets make a second model with no stimulus and a third with no crisis.
For year 1, the GDP will have three components. There is the GDP from last year plus the GDP growth plus respent stimulus (which is dependent on the year number so it decays exponentially). Divide by the inflation. Set it up as an "if" statement so it uses the correct variables.
For debt, we will add last year's debt plus interest on last year's debt plus (minus) any deficits (surpluses) and divided by inflation. Again, we will set it up as an "if" statement.
Now Complete the columns. I put a little ratio in to see which scenario has the larger GDP after 30 years, but other than that the model is pretty much made. Lets take it for a test drive!
Check Please
The first thing we should check for is what happens to the output during a normal amount of time. Lets take the years 1955-1970. We had decent growth, declining debt, and if we cut off in '70 we don't have to deal with the inflation spike:
With that info, I put in these inputs and got these results:
So we have about a 75% increase in real GDP and a drop in debt (as a % of GDP) from the low 60s to the low 30s. This matches the actual data very closely. This also tells us that in good times (if we are actually interested in it) we can decrease the debt (without running a surplus) by about 2% a year. This is the idea in "growing out of debt".
Crisis and Stimulus
So lets look at 2008 in the model. These are the starting points I'll assume.
If you replace the GDP lost in crisis with debt fueled stimulus (that is not propagated by re-spending it), you end up with the same amount of GDP as if you had no crisis at all. This is kind of cheating though because the debt never went above 90%. Lets try it again with a little nudge to the original debt.
While the stimulus replaced the GDP lost in the crisis, we also lost some GDP growth when we were above 90% debt for two years. Importantly, we are still much better off than if we had crisis but no stimulus. Because the crisis removed some GDP from the denominator of our debt/GDP ratio, even our no-stimulus model ended up going over 90% debt. Stimulus becomes progressively more needed as the crises get worse. This is my best guess at what the real conditions might be:
Here the stimulus definitely helped, but we still feel the pain. Interestingly in this scenario the stimulus model experienced 3 years above 90% debt but the no-stimulus model experienced 6 years. One big question (and possible flaw) with these circumstances is what the "re-spend" is on stimulus dollars. If it is set to 95%, like I'd expect from our savings rate, you end up with impossibly rosy situations where we are better off than if there was no crisis. Granted this takes 5-10 years to notice:
So yeah, I think I'll keep the re-spend toned down. Lets see what changing to the RR high debt growth rate and higher inflation would do to the model:
Not Pretty. In this instance the inflation actually helps with the debt (which otherwise goes spiraling out of control), and you can see that while it doesn't get us back to no-crisis, the stimulus definitely is better than no-stimulus. Anyways, you are probably tired looking at my tables.
Please do keep in mind that this is a communal google spreadsheet, and other people may be working on it at the same time. Don't mess up someone else's work until they have had a chance to see their answer (unless you really really know that they are a doo doo face that you want to mess with). Many of the cells are locked, and the variable ones only accept certain values. If you would like to recommend a different value please submit your idea in the comments and I will add it.
Take Home Message
So what have we learned? Well, for the most part, stimulus is a good way to squeeze out extra GDP from your economy. It takes very specific characteristics when you have high debt (high interest rates, low inflation, low growth, little re-spending) for stimulus to be worse than no stimulus. Can we grow out of debt (regardless of stimulus)? Absolutely. The big helper here is inflation. With moderate inflation and low interest it is possible to continually run a deficit and still decrease your real debt. That said, I'd much rather we were at a debt level where no one even questioned our credit-worthyness. At 2% decrease a year we could even get there in my lifetime!
-----
No comments:
Post a Comment