It has been a roller coaster ride for the stock market lately. On August 1, the United States government avoided a default by a last minute deal to raise the debt limit. A few days later, we witnessed the first ever downgrade of U.S. credit by Standard & Poor’s.

Using Mathematica‘s TradingChart command, we can witness the stock market’s immediate negative reaction to the downgrade. Note: Mouse over the chart to see the daily open, high, low, and closing price of the S&P 500 index.

Now that the world’s largest economy has lost its AAA status, what does it mean for the rest of the world? Will the debt downgrade spread? What is the implication to the bond market and the economic recovery? Can our economic well-being be measured by the amount of debt that we carry?

Indeed, there is much to think about. To fully understand the economic landscape, we first need to take a look at the U.S. fiscal situation. Wolfram|Alpha can be a handy entry point:

It is alarming to see a 14 trillion figure for our total government debt. However, we should understand the composition of the U.S. debt to make a meaningful judgment. We can ask Wolfram|Alpha to show a breakdown of the debt figure:

Note: Wolfram|Alpha provides a convenient way to generate this subpod without coding. You can do so by clicking the “+” sign on the top right-hand corner of the desired subpod from a full Wolfram|Alpha output. Please see the instructions here.

The subpod above shows a general breakdown of who owns the U.S. government securities. The amount held by the public is the amount held by Federal Reserve and government accounts. The amount held by agencies and trusts is the amount that is privately held.

Usually economists will look at the debt-to-GDP ratio as one of the indicators of the health of an economy. The debt-to-GDP ratio is the amount of national debt of a country as a percentage of its gross domestic product (GDP).

The two most commonly used debt-to-GDP ratios are total debt-to-GDP ratio, which reflects the indebtedness of a nation, and the public debt-to-GDP ratio, which reflects the government’s finances. We can ask Wolfram|Alpha for these two ratios:

The units are quoted in years, indicating the amount of debt as a percent of one year’s GDP.

Since the government is responsible for the public debt and not the accumulated private debt, the (U.S. debt held by public)/GDP is the ratio to consider for U.S. government securities’ credit worthiness.

Besides asking for the value of debt-to-GDP ratio, we can take a look at the time series of such ratios to see the change of the debt level as a percent of GDP.

We notice that the public debt soared after the 2008 financial crisis. This increase can be due to an increase in government insurance programs such as unemployment insurance, Medicare, and Medicaid.

The problem with obsessing about debt is that it ignores that there are two sides to any ledger, and that someone’s debt is another person’s asset. The problem with debt is not its size, but the uneven distribution among income classes. Basically 95% of the U.S. is in debt to the top 5% in terms of income distribution. If the debt is unevenly distributed, then income is unevenly distributed.

The Gini index is a common measure of such distortion of income distribution. A value of 0 means total equality and a value of 1 means total inequality. On consulting Wolfram|Alpha, we discover that the U.S. has a Gini index of 0.408, ranked 69th highest in the world. While we are not at either extreme in the Gini index distribution, this implied distortion of income could explain why there has been a lack of income, therefore demand, from the middle class.

Another major drive for the increase of our debt is the use of deficit spending to stimulate the economy, known as Keynesian economics. Wolfram|Alpha provides the amount of deficit as a percentage of GDP. By plotting the time series of the deficit percentage, we can clearly see the most recent (since 2008 financial crisis) increase in our deficit. Therefore, most of the stimulus program is deficit spending.

The basic point is that if government spends $1, albeit a borrowed dollar, to stimulate the economy, the national income may grow by more than $1. We can use the ratio of national income versus government spending, called the fiscal multiplier, to see the effect. If the fiscal multiplier is greater than 1, then the overall increase in national income is greater than the initial incremental amount of spending. However, if the fiscal multiplier is less than 1, the government spending might not have been as effective.

Another consequence to consider as a result of government borrowing is a concept called crowding out. It refers to a reduction in private consumption or investment due to government borrowing. The assumption is that there is a limited amount of available loanable funds in the market. The increase in government borrowing pushes up the demand for loanable funds and therefore increases the real interest rate. The result is a decrease in interest-sensitive expenditures from the private sector.

Note that crowding out only happens when the economy is at full capacity with negligible unemployment and above zero interest rates. So did the government’s stimulus program create crowding out in the U.S. economy? If the answer to this question is yes, then the demand for money and hence bond yields would increase. Many pundits predicted such an outcome, but the results as indicated below were in keeping with Keynesian predictions, and bond yields have dropped dramatically.

We can ask Wolfram|Alpha for an up-to-date unemployment rate:

Below is the unemployment rate of the last five years:

And the treasury yield:

With a 9.1% unemployment rate and 10-year treasury note yields at a 50 year low, we can safely conclude that the recent deficit spending did not crowd out the private expenditure.

So if crowding out is not a factor, why is it that we have yet to see the economic recovery?

When the monetary policy of increasing money supply (lowering interest rates) fails to stimulate the economy, a liquidity trap might be to blame. In John Maynard Keynes’ words in The General Theory of Employment, Interest and Money: “There is the possibility… that after the rate of interest has fallen to a certain level, liquidity preference is virtually absolute in the sense that almost everyone prefers cash to holding a debt at so low a rate of interest. In this event, the monetary authority would have lost effective control.”

How do we know if we are in a liquidity trap?

In macroeconomics, the identity:

means monetary base times the velocity of money is equal to the price level times real output. The right-hand side of the equation is the dollar value of GDP. If we divide both sides by the monetary base, we get a definition of the velocity of money:

We can think of the velocity of money as the average annual frequency a dollar turns over to purchase goods and services. If we believe that an increase in money supply results in an increase in GDP, we need to assume that the velocity of money does not decline.

You can interact with the dynamic Computable Document Format (CDF) file below to investigate the relation between 3-Month Treasury Bill Yield versus the Velocity of Monetary Base. The bottom left-hand corner of the graph shows a combination of low interest rate and a declining velocity of money. That is where the liquidity trap happens.

As of 2010, it seems that we are in a liquidity trap. We await the data from 2011 to see a complete picture.

You can download the full source code and descriptive details of the Demonstration above at the Wolfram Demonstrations Project, which is an excellent source of interactive knowledge apps on finance and economics.

It is not the amount of debt that is the concern for economic well-being, it is how we spend our borrowed money. If the borrowed funds are spent in a productive way, it is good for our economy. Otherwise, they are just wasted funds that our future generations will have to pay for.

How to tell if the funds are used wisely? One way is to calculate the stimulus multiplier. Another way to have a quick gauge is to see our nation’s labor productivity and inventiveness. Let’s save that for another post.