The greatest economic scholar of the first-half of the 20th century, Professor Irving Fisher, was born in 1867 and served as a professor of economics at Yale University during the years 1900 to 1935. He was the first celebrity economist who was venerated and often quoted by the media of his time. Unfortunately, his credibility and celebrity status came to a thunderous end around the stock market meltdown of 1929. Just before the crash, Irving Fisher announced to the media and world at large that "stock prices are at a permanently high plateau" and that he was quite bullish.
Alas, it was not just his intellectual reputation that took a hit; so did his personal finances. He actually put his money where his mouth was, and lost $10 million — which in today's inflation-adjusted values would be close to $140 million. Now, you may wonder why anyone might take retirement planning advice from someone who blew up so spectacularly. But his contributions to retirement economics deserve serious consideration.
Irving Fisher was likely the first economist to actually create an inflation index, by averaging the prices of thousands of goods and services and tracking them over time. He debated many different ways and methodologies for creating these indices and was well aware of the fact that if a particular index was biased towards the spending habits of the population as a group, it might not necessarily reflect the experiences of a subgroup, for example retirees. In many ways the elderly spend differently and their inflation might be higher.
It was thus Irving Fisher who first brought attention to the difference between a real interest rate and a nominal interest rate. In fact, he actually wrote down an equation that relates the two, which is called Fisher's inflation equation.
Fisher's Optimal Retirement Plan
If you haven't heard of the infamous 4% rule of retirement income planning, it's probably for the better. Most economists do not take kindly to this rule and the source of their discomfort can be traced directly to Irving Fisher's ideas about lifecycle consumption smoothing. Fisher's philosophy was that there was no universal spending or consumption rate and that everyone should pick a number that would best smooth their consumption. It does not have to be fixed or flat over time, and really depends on your personal preferences and especially your attitude towards risk. 
The chart (left) displays some actual data on retirement expenditure rates for retirees at various ages, in the years 1990, 2000 and 2010. Notice how the overall expenditure rates start to decline around the age of 50. By the age of 65 they are spending between 50% and 70% of what they did at age 50. And, by the age of 80 it has dropped to under 60%.
So, here is Fisher's insight: There is roughly a 10% chance you will live to the age of 95 and spend 30 years in retirement. This also means that 90% of retirees will never live to enjoy and appreciate that age. I personally am not willing to starve myself for the next 30 years — on a reduced standard of living — on the off chance that I make it to 95. Others might worry about living to age 95, and are not willing to reduce their standard of living if that happens. So, they must spend less today in order to build up enough of a reserve.
Here is a detailed example of how to apply Fisher's equation with some actual numbers. Start by assuming that you are nearing retirement with a nest egg worth approximately $500,000 and are entitled to a pension annuity that pays $25,000 per year, adjusted for inflation.
The question that Fisher's equation helps you address is how you should spend down the nest egg as you age. To keep things simple, let's further assume that your subjective discount rate (think patience) is equal to the prevailing market interest rate, which I take to be exactly 3%.
