A Really Big Number

Way back in the early to mid 1980s I began my professional IT career working in higher education. Back then our administrative computer, which cost on the order of a quarter of a million early-1980s dollars, had two "hard drives" with a storage capacity of 300 megabytes (MB) each. That means each drive could store around 300 million characters, or "bytes", of data.

Each drive was in its own standalone cabinet about the size and appearance of a slightly undersized washing machine. The storage media was a "disk pack" consisting of a stack of ten "platters" the size of extra-large dinner plates, all attached to a central spindle. There was a space between one platter and the next so that read-write heads could track across each platter's surface. Data was magnetically encoded on both the upper and lower surface of each platter, meaning there were twenty  (ninteen actually, but never mind) data surfaces in the pack. The entire disk pack assembly was perhaps 12 to 14 inches in diameter and maybe 10 inches tall, and weighed a fair number of pounds. A pack could be removed from its cabinet by opening the "washing machine" lid, engaging a special holder, and screwing the pack off the drive mechanism.

That computer, with its 600 MB of data storage, ran the entire business of the university: purchasing and billing, payroll, student transcripts, course schedules, class rosters, and so on.

Although we would certainly have been happy for a little more, 600 MB of storage seemed perfectly acceptable. We might have been able to conceptualize a few gigabytes (GB) of capacity, but we didn't have occasion to do so. (Whereas a megabyte is approximately one million characters of data, a gigabyte is about one billion: a thousand times as much. So 600 MB is approximately 0.6 GB.) And while 600 MB seems paltry by today's standards, it was extraordinarily large by the standards of personal computers (PCs) of the day, which typically didn't have hard drives at all. So for us, gigabyte-denominated storage was conceivable but out of reach. Terabyte (TB) denominated storage was unimaginable, the stuff of futuristic science fiction. (A terabyte is approximately a trillion characters, or 1,000 GB, or 1,000,000 MB).

As everybody knows, things changed rapidly. By the mid to late 1990s, storage capacity of multiple gigabytes became common. A computer system with a terabyte of storage was conceivable, sometimes talked about reverently, but was very uncommon. You might find one in a supercomputer center modeling large scale weather patterns, esoteric chemical reactions, or nuclear explosions.

Without us hardly noticing, something extraordinary happened. Today my personal laptop computer has two hard drives, each with 750 GB of capacity, for a total of 1.5 TB. That's 2,560 times the storage of that 1980s quarter-of-a-million dollar enterprise computer.

I have a variety of external hard drives, in the range of 1 TB to 4 TB, used for doing backups. A 4 TB external drive can be had today for perhaps 150 dollars. An early 1980s 300 MB hard drive would have been priced in the tens of thousands of dollars, back when that was real money.

Just as remarkable, my hand-held digital voice recorder has a solid state memory card (microSD) providing 32 GB of nonvolatile storage on a card smaller than my little fingernail! That's around 70 times the capacity of one of those 300 MB washing machines. I could easily swallow it like an aspirin tablet. Your smart phone probably has one too.

Times change. Our conception of size and scale changes. Numbers that seemed astronomical then are commonplace now.

It's the same with lots of things. Unfortunately, people don't always know how to think about what they perceive to be large numbers, and what those numbers mean. Scales that are not familiar or are not commonplace can seem exotic and extreme, even unimaginable.

For example, consider the national debt. The official debt of the United States is currently on the order of 18 trillion dollars. Many consider that number to be so unimaginably huge that all they need do is utter it to "prove" the U.S. is on the road to ruin, and will arrive there soon. Persons hearing that utterance will nod in unison with tightened lips and grim faces. Oh, the horror!

You see, people just know that the debt is completely out of control and is utterly unsustainable. Why? Because $18 trillion is a really big number. And true enough, we have never before seen anything like it. Something has to be done, and soon.

But is that so? Are we really thinking correctly when we talk about scale as an absolute, outside of some context, with no reference point, no understanding of what it means or how it fits with the scale of other things to which it is related? Could it be that the notion of a really big number is arbitrary, or at least relative and subject to change? Could it be that those who try to persuade us by doing nothing more than bandying about really big numbers are pulling a fast one on us, or are perhaps even profoundly ignorant themselves about what those numbers mean?

So let's provide some context, beginning with another story from way back.

In the early 1980s I visited the very large and expensive home of a high-powered business executive, and overheard in conversation that the mortgage payments on that home were something like $3,000 per month. That was an extraordinary number back then, by the standards of workaday Americans. I could barely fathom how anybody could manage a $3,000 mortgage payment every month. My dad's (who was himself in management, in the upper middle class of society) mortgage payments on his nice large house were probably not more than a couple of hundred dollars.

The first thing to notice is something that everybody understands implicitly: scale does change over time. The notion of a $3,000 per month mortgage just doesn't boggle the mind today quite like it did back then.

There's a second thing that's just as important. The amount of debt a person can comfortably carry is highly dependent upon the size of that person's economy. In the case of individuals and families, the size of one's economy usually has to do with the amount of employment and investment income that person or family receives. As a general rule, the more you earn, the more debt you can service without difficulty. There isn't really an absolute amount of debt that is reasonable in every situation; it just depends.

It's the same for governments and national economies—although please note there are important differences between governments and families, differences which politicians routinely misunderstand in other contexts. It is nevertheless generally the case that the amount of debt a government can comfortably carry is highly dependent upon the size of the economy in which that government operates. In the government's case, income comes mainly from tax revenue, and tax revenue increases as the economy's size increases.

So the amount of debt a modern country with a large economy can carry is greater than the amount of debt that a country with a small economy can carry—just like how the much smaller size of my dad's economy meant his mortgage payments necessarily had to be far smaller than that of the rich executive.

Two things are thus happening simultaneously that affect how we think about the scale in which we describe debt. First, the real value of debt erodes (decreases) whenever the rate of inflation is greater than zero, as it almost always is. The inflation effect is one reason $3,000 mortgage payments don't seem so unusual today as they did three decades ago.

Second, whenever an economy's growth rate is greater than zero, that economy's size increases, and, as we have seen, the amount of debt that can be carried increases as well.

Because inflation and economic growth are both happening more or less continuously, it can be hard to say what we mean by a dollar of debt at some particular point in time. A dollar isn't a fixed quantity of value; its purchasing power is almost always declining, but this is compensated by the fact that incomes (personal and national) are always, for the most part, increasing.

Because a dollar's value is always changing, it can be hard to compare dollar-denominated quantities across time. For example, in the 1940s the price of a movie ticket was less than a quarter; today it can be ten dollars. Economists compare quantities denominated in "nominal" dollars (the dollars at a particular point in time) over different time periods by converting them to "constant", or "real", or "inflation-adjusted" dollars. So one way to compare the size of dollar-denominated debts from different periods is to convert those nominal debt quantities to constant dollars.

But because national economies don't get bigger by just inflating—they actually grow in productive capacity and, indeed, raw size (for example, an increasing population means more workers and more consumers)—a useful way to compare national debt over time is to state that debt as a ratio, with the debt (in nominal dollars) as the numerator, and the economy's size (also in nominal dollars) as the denominator. The economy's size is usually referred to as Gross Domestic Product, or "GDP".  GDP is just the total dollar value of all the goods and services the economy produces in a year. The ratio is thus a percentage, often referred to as "debt-to-GDP". Although there are other factors worth considering (such as prevailing interest rates), GDP is a useful indication of the debt-carrying capacity of a country, and the debt-to-GDP ratio allows us to compare a country's debt burden over time.

So how has U.S. debt looked over time? As a fraction of the economy, U.S. debt was at its highest point ever at the end of World War II. That's not surprising, because the U.S. borrowed heavily to fund the war effort, and even before that was doing a good bit of deficit spending during the Great Depression. In 1945, at war's end, the public debt was 112% of GDP. That's by far the highest debt burden in all of U.S. history. By contrast, the public debt for 2014 was a bit over 70% of GDP.

Remarkably, that historically high debt was never paid off; it was never even materially reduced! The 1945 debt was $258 billion. It ticked down ever so slightly for a few years, but by 1953 it was $266 billion. By 1955 it was $274 billion. 1960: $286 billion. 1965: $317 billion. 1970: $370 billion. Up, up and away!

If the debt in 1945 was the highest (relative to the economy) it has ever been, and was never reduced (in nominal dollars), how is it that we're not constantly bemoaning that immense WWII debt burden that we're still dragging around to this very day?

The answer is simple. The post-war economy entered a period of explosive growth. The two decades after World War II were a period of rapidly increasing prosperity and economic expansion. It is no exaggeration to say this was the period when the modern American middle class came into being. The resulting "baby boom" is just one indication of how things were changing. Because the economy (that is, GDP), was growing so rapidly, the debt-to-GDP ratio was constantly falling despite the fact that the debt was increasing in nominal dollars. (That is, the ratio's denominator was growing far faster than its numerator, so the ratio was shrinking.) A person of that time looking worriedly at the growing debt was obviously missing something crucially important. That should tell you that nominal dollars don't say much about the burden of debt, and the same lesson applies to today as well. Just as you could afford a more expensive house if your income was surging, the U.S. could comfortably carry a larger debt as its economy was rapidly growing.

Debt can be counter-intuitive; that war debt—huge at the time—was never paid off: It just withered away to insignificance.

If you're interested in knowing the actual post-war debt-to-GDP ratios of the United States, here are some. As already stated, the ratio was 112% in 1945. By 1947 it was already down to 90%. By 1950 it was in the mid-70s. Within a decade after the war it was in the mid-50s. It bottomed out in 1974 in the mid-20s. From there it began to tick up again.

We have recently experienced a period of rapid change. The U.S. debt-to-GDP ratio has doubled since the beginning of the financial crisis (a.k.a. the "Great Recession") of 2008. That should not be surprising to anybody. The period 2008 to the present has been a true economic depression—eclipsed only by the "Great Depression" of the 1930s—for the U.S. and, especially, the world. (Some countries, including some in Europe, have actually experienced greater economic devastation than they did in the 1930s.) "Economic depression" is defined informally as a prolonged downturn in economic activity. Or, alternatively, as a prolonged period of below normal economic activity. In such circumstances, the debt-to-GDP ratio increases due to effects on both the ratio's numerator and denominator. The denominator shrinks because economic activity—GDP—declines. The numerator grows because the government cannot sustain its operations without increased borrowing, due to decreased tax receipts from the weak economy (including no taxes paid by millions of laid-off workers), and increased social safety net expenditures. An increasing debt-to-GDP ratio is an expected consequence of economic recessions and especially depressions.

But the U.S. debt-to-GDP ratio is still well below what it was at the end of World War II. That should give you an indication of the comparative debt burden between now and then. And as the post-war experience shows, the best way to decrease the burden of debt is not to decrease the nominal amount of debt itself (because, paradoxically, government debt can actually be beneficial to the economy during periods of profound economic weakness), but instead to restore and sustain economic growth. Trying to shrink the debt by shrinking government has the perverse effect of shrinking the economy, and thus worsening the debt burden.

The annual budget deficit has declined dramatically from the trillion+ dollar deficits during the depression's worst years. That's exactly what you'd expect as the economy once again begins to grow. A growing economy (denominator) and slower debt growth (numerator) will both favorably affect the debt-to-GDP ratio, but future prospects depend on many factors—some with currently unknown trajectories—such as the rate of increase in health care costs. (Health care spending is the single biggest factor that will affect the government's fiscal position going forward.)

I'm not going to advance an opinion about the future, but I do want you to think about the past and the present. This all began as a story about scale and, especially, really big numbers. Is $18 trillion a really big number? Does that question even have a meaningful answer? Compared to what? In what context? If somebody tries to tell you that the U.S. national debt is unsustainable because it's $18 trillion, and, by implication, $18 trillion is a really big number, it's a strong clue that he doesn't actually know what he's talking about.

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Postscript - Here are 2014 public debt-to-GDP ratios for select countries, according to the CIA's The World Factbook. Japan: 228. Greece: 175. Italy 134. Ireland: 119. Spain: 98. France: 96. Canada: 93. United Kingdom: 87. Germany: 75. United States: 71. Israel: 67. Finland: 60. Brazil: 59. Venezuela: 51. Poland: 46. Denmark: 44. Mexico: 41. Argentina: 38. South Korea: 37. Taiwan: 37. Switzerland: 35. Australia: 35. Norway: 30. China: 22. Russia: 13. Iran: 11. Saudia Arabia: 2.

Copyright (C) 2015 James Michael Brennan, All Rights Reserved

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