The Taylor rule, proposed by John Taylor, is a formula for determining the target Fed Funds rate. In the Taylor Rule, the Fed Funds rate baseline is set to the target nominal rate (target real rate plus target inflation), and then adjusted based on economic conditions. The rule states that the Fed Funds rate should be raised when inflation is higher than target inflation (“Inflation Gap”), and lowered when economic output is lower than potential output (“Output Gap”). The equation for the Taylor rule is shown below:

Target Fed Funds = Inflation + Target Real Rate + a1(Inflation Gap) + a2(Output Gap)

Though the rule itself is relatively simple, there are many different interpretations of how to implement it. There are of course multiple measures of inflation, and multiple measures of the output gap. In the chart, we use the Core Personal Consumption Expenditures (PCE) deflator, one of the measures favored by the Fed, as our measure of inflation. To measure the output gap, we use the CBO real potential GDP series, a trend line estimate, less actual real GDP.

The other two important components of the Taylor rule are the “weights” placed on the inflation gap and the output gap. These are the terms a1 and a2 in the formula. The larger the weighting, the more the prescribed Fed Funds rate moves in response to changes in inflation and output. In his original formulation, Taylor proposed weights of 0.5 for both inflation and output.

While the Fed does not explicitly follow the Taylor rule, it has proved to be a reasonable approximation of Fed policy. However, the Fed has indicated that it places more “weight” on the output gap than Taylor originally suggested. The graph shows the “original” Taylor rule, as well as an “alternate” Taylor rule with more weight placed on the output gap. In normal times these rules track fairly closely, however, when the output gap is large the alternate rule prescribes a much lower Fed Funds rate than the original rule. This formulation currently suggests a negative Fed Funds rate. Because the Fed Funds rate is up against a zero lower bound, this explains why the Fed engaged in unconventional monetary policy actions such as quantitative easing.

The graph projects out the target Fed Funds rate based on both formulations of the Taylor rule. Real GDP is projected using Bloomberg consensus estimates, and a constant 1.5% inflation rate based on the PCE deflator is assumed. This inflation rate is lower than the 2% target, but higher than the recent reading of 0.9%. Given these assumptions, the alternate rule does not imply an increased Fed Funds rate until 3Q 2012. This is roughly in line with the futures market, which suggests a greater than 50% chance of an increased Fed Funds rate in 2Q 2012.

Finally, this chart is not intended as a forecast, but merely as a template for understanding Fed policy. Any large surprise either to the upside or downside for GDP could impact Fed policy. The more important indicator to watch may be measures of core inflation. The Fed has stated that it favors measures of core inflation (inflation less food and energy), and has described the current commodities led uptick in CPI as “transient.” As long as measures of core inflation remain subdued there is little pressure on the Fed to raise rates until the output gap narrows. Economists should debate why the Fed makes its decisions; investors should only be concerned with how the Fed makes its decisions to determine likely outcomes.

The Fed recently completed its latest stress tests on banks. Based on the results, many banks were given the green light to increase dividend payouts as well as announce share buybacks. With this in mind, our chart of the week looks at the charge off rates and delinquency rates of loans at all commercial banks.

The Federal Reserve calculates these rates based on quarterly reports by all banks. The charge-off rate is defined as the flow of a bank’s net charge-offs during the quarter divided by the average level of loans outstanding. The delinquency rate is the ratio of the dollar amount of a bank’s delinquent loans to the dollar amount of total loans. Loans include real estate, agricultural, commercial & industrial, and consumer.

Prior to the official start of the recession, in the 2nd of quarter 2006, both rates began to increase, serving as a sign of things to come. In 2008, with the financial industry in danger of collapsing, the Fed stepped in and imposed tight restrictions on banks which led to dividends being slashed or all together eliminated. As banks struggled through the crisis, charge-off and delinquency rates climbed through 2009. During the official recession period between the 4th quarter of 2007 and 2nd quarter of 2009, the charge off rate increased by 255% and the delinquency rate increased by 160%. Perhaps as a sign that lending standards have improved and the economy has strengthened, both rates began to fall in 2010 and have been on a consistent decline the last four quarters. However, both rates are still well above pre-recession levels and undoubtedly haunted by continued high unemployment and a struggling housing market.