When President Obama unveiled his $3.77 trillion budget, a key selling point relied on a somewhat arcane economic indicator: the ratio of federal debt to GDP (the goods and services the nation produces).

How much debt can the nation manage? The United States was at about 102 percent in 2012, with the amount of debt held by the public closer to 75 percent. To some, that signals danger. Others say we could handle even more. In certain wonky circles, the debate over what ratio is sustainable is almost endless. And yet, serious people assess the president’s budget, indeed any budget, by how it decreases this ratio in years to come.

This ratio, however, is nothing more or less than a statistic, and it highlights how our entire economic system today depends on the way we read such statistics. As the U.S. budget wars repeatedly demonstrate, GDP (gross domestic product), unemployment, inflation and trade statistics determine how the government spends (or does not spend) trillions of dollars. These numbers also shape whether large businesses invest or don’t, and whether small businesses spring to life or remain ideas to be acted on later.

Our debates, however, are based on a simple assumption that the set of numbers we use to measure the economy are accurate, or at least close enough. But what if they aren’t? What if we are making powerful assumptions about the economy based on statistics that are at best half-right?

Consider this, the Congressional Budget Office — which is responsible for “scoring” budgets and analyzing their long-term effects — only came into existence in 1974. Now, however, major spending bills in the United States must be justified based on statistics and formulas, and those become the basis of partisan commentary and ideological debates about what we spend and how we pay for it. You would think that there is a long history here, that the relationship between debt, economic growth and spending can be charted with a heap of statistics so that we can determine the effects with some certainty.

WonkBlog’s Neil Irwin and Brad Plumer discuss Carmen M. Reinhart’s findings in her book “This Time is Different,” and the right conclusions to draw on national debt. (The Washington Post)

That isn’t the case. GDP has only existed as a reliable statistic since the 1930s (and even then, more attention was paid to national income and then to gross national product ; GDP didn’t become the first among equals among economic statistics until 1991). Given that deficits, other than in times of war, were not much a part of U.S. policy until the 1970s, understanding the relationship between debt and GDP, therefore, is largely guesswork based on a limited amount of data for a very short time.

Other countries have even less history of collecting these numbers. Global financial markets were roiled recently by the announcement that China’s official GDP came in at 7.7 percent instead of the expected 8 percent. But the whole idea of using these numbers as absolute gauges of China’s economic health is barely 20 years old. Given that Beijing’s Five Year Plans set growth targets, many think political pressures make these numbers less reliable. Even without those pressures, considerable portions of China’s economy (and those of other countries as well) do not exist statistically: Private loans, for instance, fuel part of China’s economy, but they rarely show up in national accounts.

Today’s economic debates are central to every country in the world. But what if the world we are living in is not the world the numbers say we are living in?

Indicators such as GDP and the consumer price index offer insight into what is going on in this complicated set of exchanges we call “the economy.” But as the world has become infinitely more global and three-dimensional, these statistics have not kept pace. They were all developed more than a half-century ago, to measure a world of nation-states, of war and Great Depression. They have been tweaked and refined, but they remain products of a different world. The result is that we are using a 1950s dashboard to operate a 21st-century machine.

The iPhone and the trade deficit

Take trade statistics. These strongly shape our sense of whether the United States is competing effectively in the global economy. The most sensitive of these is the annual trade deficit with China, which has led to considerable animosity and hand-wringing over the past decade and has yawned wider as the U.S. economy has sagged.

Apple, that icon of American innovation, famously does not make its devices in America. It outsources production to factories in southern China, where its largest contractor, Foxconn, has come in for significant international criticism over the way it treats workers. And each time an iPhone is shipped from those factories to the Port of Long Beach, it adds about $200 to the trade deficit between the United States and China.

Or so the official statistics tell us. But are they right?

Surely, they are correct about the $200, which is — give or take — the declared wholesale value of the phone. Surely, that is correctly ascribed to China under the rules of the World Trade Organization, which dictate that a country of origin for a manufactured product is the place where it has undergone its last “major transformation.” But does that mean, as the numbers say, that $200 has simply left American shores to end up in the pockets or vaults of the Chinese? No, it does not.

Trade statistics, compiled in the United States by the Census Bureau, are based on straightforward reporting on customs forms, adhering to standards that have evolved over decades and are now codified by the WTO. But they stem from an earlier era, when something made in country X was, indeed, made in country X.

Today, however, many intricate manufactured goods are made in multiple countries. As companies such as Apple seek the least expensive and most efficient supply chain, various components and parts are made all over, shipped to a factory where they are put together and then sent to their final destinations. Foxconn may run the factories where the iPhone is assembled, and it may operate in China, but only in the world of static trade statistics is China where the iPhone is “made.”

In recent years, various academics and trade groups have attempted to break down the components of an iPhone and an iPad to determine where the money goes. The estimates vary but all indicate that only a fraction of the final price tag goes to China, as little as $10 per device, and those devices retail for more than $500 (before carrier rebates). The rest of the money goes to a web of suppliers based in Germany, Taiwan, Malaysia, Korea and the United States — and above all to Apple, the creator of the idea and provider of the intellectual property that made the devices possible. Almost none of that complexity, however, is visible in trade statistics. Worse, those numbers make it seem as if China is accruing advantages that it is, in fact, not.

Statistically, of course, these devices do benefit China. Every iPhone sold in the United States adds about $200 to the U.S.-China trade deficit, and each iPad adds $275, at least according to economists who looked at the issue in 2010. That means that Apple sales of the iPhone in the United States add billions of dollars to the trade deficit with China every year. But if the numbers reflected the complexity of the supply chain as well the intellectual property provided by Apple, much of this benefit would evaporate.

According to the Asia Development Bank, if the official figures incorporated a more accurate measure of value added, the balance of trade for the iPhone alone would be a paltry $73 million for China instead of billions. Similar studies have been done by the WTO and Organization for Economic Cooperation and Development.

And this is only for one product. Imagine if similar breakdowns were done for hundreds of thousands of other products that are traded. What might that do to our perceptions of where value is flowing and who is benefitting? The OECD is attempting to reframe global trade data to take such factors into account, but that remains a long way off. Imagine what would happen if better information revealed that the U.S. trade deficit with China was a fraction of what we thought. What would that do to the politics of blame or to the assertions by economists everywhere that global imbalances are imperiling the future? What if the imbalances are a statistical mirage?

What’s left out of GDP

This isn’t just a hypothetical “what if.” More research and increasing efforts by academics and organizations such as the OECD and economists at various U.S. Federal Reserve banks point unequivocally in that direction. And it’s true not just for trade numbers, but also for the granddaddy of all economic indicators: GDP.

Gross domestic product is a universal numerical proxy for the economy (well, except in Bhutan, which uses “gross national happiness” instead). Politicians worldwide use GDP as a gauge of whether their countries are doing well or badly, and the number is deeply woven into our collective understanding of economic health.

Its weaknesses are well known yet bear repeating: It measures only output, and only output whose worth is recorded. So, it misses domestic work, volunteer work and black-market activities; none of those count toward GDP. Output is measured regardless of whether it improves quality of life, and contraction of output is counted as negative even if it improves quality of life. A factory that pollutes a river and whatever local or national government spends to clean it up add to GDP. Buying long-lasting light bulbs that use less energy detracts from it.

Perhaps more important, GDP also falls short as a measure of all sorts of “free goods” that manifestly improve daily life and make both work and play more efficient and less expensive. At MIT, Erik Brynjolfsson and his colleagues have been doing groundbreaking work studying such free goods, especially services readily available on the Web: Google, Wikipedia, LinkedIn and a host of others. (Although much of the time spent using these tools goes to entertainment, they clearly facilitate commerce as well.)

Because the effect of free goods is virtually invisible to the calculation of GDP, statistically, they add almost nothing. Yet by helping us find what we want and need, they clearly add something to our daily lives. How you calculate what they add is a matter both arcane and complex, and, therefore, scholars like Brynjolfsson work to find ways to account for what is currently uncounted.

Brynjolfsson’s conclusion is that we may be doing somewhat better than GDP numbers suggest, to the tune of tens or even hundreds of billions of dollars a year. That benefit, however, isn’t distributed evenly. Those with smartphones and computers who use their tools most effectively benefit disproportionately.

The result is that GDP may simultaneously underestimate how well some people are doing – those with the means and the savvy to buy and use technology – and how much others are struggling. The limitations of trade statistics also undermine GDP. Negative trade balances subtract from GDP, and if American trade deficits are, in fact, substantially less than calculated, then GDP is significant higher.

The entire lattice of numbers we use to determine our economic health is subject to similar limitations. That would be of only academic interest if it didn’t matter so much to our collective sense of how we are doing and if that impression, in turn, didn’t shape so intimately our perception of what we can do, what we might spend, and what the future might hold.

If you were given a 1950s road map to get from point a to point b, you would either get hopelessly lost or take an inordinately long time to reach your destination. New roads wouldn’t be marked, and old ones wouldn’t be relevant. Yet in fundamental ways, we navigate the global economy of the early 21st century with an equally antiquated statistical map, and it’s no wonder that so often events unfold in ways we didn’t expect with consequences we didn’t anticipate.

Karabell is president of River Twice Research, where he analyzes economic and political trends. His next book “The Leading Indicators,” will be published by Simon and Schuster in 2014.