The Hypothesis of “Big Government” – Disposable Income

In the first two parts of the “Hypothesis of Big Government” series, I got my hands on federal employment and employee income data, and also on median family income data, from about 1947 to 2007. A commenter on the second part of the series noted that

” . . . an intelligent conservative might post this question: ‘Even if I accept the idea that income is a good measure of quality of life, what matters is how much income I spend (after taxes), not how much I earn. Bigger government usually leads to more taxes and less disposable income. Are your income numbers gross or disposable?'”

This is an excellent point – disposable (post-tax) income is a MUCH better measure of quality of life than gross income. The median family income quoted was gross (at least, the Census Bureau does not indicate otherwise). I decided to hunt around for median pre- and post-tax income to see what I could learn.

I was only able to find this data for 1980-2003 [1]. Since there are already interesting trends in those two decades (large growth of govt. size and continued growth of deficit in the 1980s, followed by rapid shrinking govt. size and deficit in the 90s, followed by slight growth in size and large growth in deficit in the 2000s), this period could already be informative. In addition, it has the benefit of political party flipping – three terms of Republican presidents in the 80s, two terms of a Democrat in the 90s, and most of one term of a Republican president in the 2000s (up through 2003, when the data ends).

One important note: the data available is median HOUSEHOLD, not family, income. These are not the same. I will therefore show median pre-tax family income as well as median pre-tax household income. The family income is a control; if household income tracks family income, we should see this and then consider the post-tax household income as a reliable measure of post-tax family income.


First, let us compare the control (pre-tax family income) to the new data (pre-tax household income). They track beautifully. The slope of the ratio of these two data sets is 0.002 (2007 Dollars)/year, which is essentially zero. Therefore, pre-tax household income measures the same trends as pre-tax family income.

The pre- and post-tax household incomes are clearly different, and that difference varies with time.  The difference, divided by the gross, is a measure of the median tax burden. From 1980-1992, this (as a percentage of gross income) was 17.7%; from 1993-2000, this was 17.1%; from 2001-2003, this was 15.9%. So on average it’s been dropping by about 1% per decade.

The trends in disposable income largely track those in gross income, except after 2000, when disposable income flattens out while gross income drops. The opinion of the author is that here we are seeing the effect of the Bush tax cuts, since government spending was very much on the rise (along with deficit spending) while disposable income seems to hold against those pressures.

The tables illustrate the slopes in the size of government, government spending/deficits, and household and family income. We see that the trends in household and family incomes largely track, as expected. The caveat is that in the first and last periods studied (where household data is available), there is LESS household data, so one cannot expect the slope measured with fewer points to perfectly track the slope in the family income data. In between, where there is just as much data in both samples, we can make more reliable observations.

Considering the relationship between the size of government and disposable income, the conclusion is that the pace of increase in disposable income is largely unaffected by the large changes in the size of government from 1980-2000. Disposable income grows, but by less, after 2000 (until 2003, when the data ends) There are definitely internal variations that seem largely to coincide with recessions, but overall the trend is up and doesn’t seem all that connected to swings in the size of government.

The relationship between federal deficits and disposable income seems to be inverted, as it was with gross income. When deficits grow at a large rate, the rate of increase in disposable income is slowed. This is most apparent in the 2000s, but also clearly visible in the 1980s.


Disposable income is a more realistic measure of the quality of life in an American household. Trends in disposable income largely track those of gross income, except in the early 2000s. The author attributes this to the effect of the Bush tax cuts, but that is an opinion. In general, when federal deficit spending increases, the pace of disposable income growth decreases.

[1] SOURCE:  U.S. Census Bureau, Current Population Survey, Annual Social and Economic Supplements

Yes, in my back yard

I think a lot of people like to pick on places like Texas because of the very public way in which religion, politics, history, and science have been mixed up in discussions of education and teaching standards. An article I received today in the mail [1] suggests that we shouldn’t pretend that issues about science, religion, and education are isolated to places like Texas, Kansas, and Pennsylvania.

Let me begin this discussion of the article by stating two of my own personal beliefs regarding issues of science, religion, and education. First, everybody is entitled to their opinion about the origin of the universe and/or life – liberty is the essence of democracy. However (and second), opinions that are either irrelevant to a scientific understanding of nature, or which contradict observations of the natural world, have no place in shaping science education policy.

The news article discusses a new school board member in my hometown school district who explicitly denies that evolution has a role in shaping human development. Quoting from the article,

“To him, the idea that humans and apes share a common ancestor takes ‘a whole lot more faith than believing there was a creator who set all these things in motion and allows us to operate under free will.'” [1]

“‘I sort of got stuck on one thing with [several high school science teachers and school administrators], which was basically the teaching of evolution in the schools and how it tends to ride roughshod over the fact that various religions — Christian, Hebrew, Muslim — hold a theistic world view . . . Evolution is basically an assumption that there is no God.'” [1]

Let’s start by asking whether or not any of these views matter. To first order, the answer is “no,” so long as this isn’t the beginning of an attempt to alter science teaching in my home district. Personally, I don’t care if these views result in the creation of a theology/philosophy curriculum that gives students the chance to explore different theological world views, creation myths, and their impact on history and society. But, if this is the start of an attempt to put pressure on science teachers in my home district, I take SERIOUS issue.

I, like many others, am a product of the excellent science education offered by the Region 17 public school district. I began a love of physics as a freshman in high school, thanks in large part to my physics teacher, my father, and a NOVA episode entitled “The Creation of the Universe.” It was in the science classes where I found that I could “do” and “explore.” In physics, I could do great experiments and had the freedom to write lab reports with a computer (in 1992!). In chemistry, there were the usual smelly labs but also the chance for to be a lab assistant for two semesters. In biology, there was the usual biology class but also a special “DNA” class sponsored by Pfizer and run by one of the science faculty. That class actually let me run my own DNA tests, make new bacteria, etc. My concern, therefore, is only that the quality of the science education is under threat by theological ideology which fundamentally misunderstands science and mislabels it as arbitrary philosophy.

Science is the process of making observations of the natural world, offering hypotheses that explain those observations, testing those hypotheses with further observation or controlled experimentation, and the development of theories from successful hypothesis testing. This is a messy, non-linear business, where theories are not just “ideas,” but battle-tested predictive frameworks that develop new knowledge from previously disconnected observations.

What worries me most is the characterization both of science and evolution illustrated by the quotes above. Science and evolution don’t require the non-existence of a creator, and to say that is to pretty much fundamentally make-up stories about science. Science is only a means by which explanations of the natural world can be formulated, tested, and propagated. Scientific truths are those things which are apparent to any observer under the same conditions, usually written as mathematical statements. God can still have started the whole thing, and God can still have a role in the universe. But the point is that if God is in there mucking about with things as he pleases, that’s neither reproducible (in the observing) nor relevant.  Therefore, science and evolution don’t deny the existence of a God  – they merely don’t require it. That’s a very different statement.

I also find it a little funny that the district that started a DNA class now has a school board member who believes that it’s more likely that humans appeared fully formed in their present state and can’t be a variation on apes. To deny things like evolution and the observed age of the universe is, to me, to deny the work of the creator and is thus an affront to that creator. But the nice thing about science is that it frees me from worrying about such things.

It’s too bad this newest school board member so misunderstands the role and nature of science, because there is unique self-enlightenment in a scientific understanding of nature. There is deep beauty in the simple fact that Chimpanzee DNA is 99% similar to human DNA. There is real wonder – real child-like mind-numbing wonder – in how so little a set of variations is needed to create a species like ours . . .  one which can evolve over thousands of years only to convince itself of the opinion that the whole thing never happened.


The Hypothesis of “Big Government” – Part 2

There is one more study that is of interest in testing the hypothesis that big government is bad for America. While there appears to be no negative effect of the physical size of government on incomes [1], there is the potential that government spending has a negative impact on incomes. To study this, I obtained U.S. Federal spending numbers from [2]. I then plotted family income, total federal spending (in 2007  millions of dollars), and federal deficit spending (in 2007 millions of dollars). The trends here were MUCH more interesting, and do speak to the trade-off between government outlays and family income.

The data are shown here:

Quantitative Analysis of Trends

Let us first consider TOTAL government spending. In both family incomes and total government spending, the trends are overall positive (although slopes do change at times). There is a long period from about 1950-1992 where the slope of total govt. spending is nearly unchanged, while family incomes experience large growth, then slower growth after 1969.  Later, when the government spending slope lessens in 1992-2001, family incomes trend upward with an improved slope. When total federal spending increases sharply again 2001, family incomes do waver here. For the period after 2001, the trend in federal spending is due to war spending, while the trend in stagnating incomes is connected to the recession that started around that time and worsened later when housing speculation collapsed.

If one computes the correlation coefficient for family income and total government spending, the value returned is 0.94. That is, they both strongly trend positive over the period from 1947-2007.

Government deficit spending is much more complicated. Let us break the problem into four periods, where the slopes in government deficit spending  appear constant (though different in each period): 1947-1969, 1970-1992, 1993-2000, and 2001-2007. The table in the image above shows what the slopes in deficit spending (in millions of 2007 dollars per year) and family income (in 2007  dollars per year) look like during these periods. The trend is clear: when deficits trend strongly upward, incomes don’t trend upward as quickly. During periods when deficits are more flat or trend downward, incomes do trend upward MORE strongly. Clearly, there is a correlation (not necessarily causation) between the two, and while numerically it is positive it is far less than one – 0.48. It’s between a strong correlation and no correlation, due to the fact that while incomes trend positive overall they do so more strongly when deficits are flat or trending downward.


There is no overall negative correlation between incomes and total government spending. For whatever reason (my own speculation is GDP), they both trend strongly upward over time. However, periods of strong deficit spending correlate highly with periods of more slowly increasing income. Whatever the common cause (this study cannot pinpoint causation), there are clearly inverse impacts on deficits and income.



The Hypothesis of “Big Government”

Updated 3/20/2010: added a reference for the median family income data. Corrected the table of trends, removing an incorrect cell-by-cell normalization (division by the number of years over which the slope was measured). Slope is ALREADY in units of “per year,” so an additional division was not needed. This in no way alters the conclusions, it only changed numbers by a positive multiplicative factor.

A recurring theme from the conservatives in government is that big government is bad for America. The flip side of that statement is that smaller government must be better for America. This has especially come up in the recent debate about health care reform.  For instance, from the RNC website [1],

“We won’t continue to support big spending, big government, liberal ideas that are going to destroy the foundation and the fabric of America.” – Congressman Connie Mack

“Presidents during most of the late nineteenth century and the early part of the twentieth century were Republicans. The White House was in Republican hands under Presidents Dwight D. Eisenhower, Richard Nixon, Gerald Ford, Ronald Reagan, George H.W. Bush and George W. Bush. Under Presidents Ronald Reagan and George H.W. Bush, the United States won the Cold War, releasing millions from Communist oppression, in true anti-big government Republican spirit.” – From “Who We Are” on the GOP website [2].

I have, of late, begun to wonder: is big government good or bad? How would one judge this? The GOP likes to conflate big government with a negative impact on the American people. I decided to conduct my own study of the data and see what I could learn. So, here is my hypothesis: the size of government is correlated with income, and the correlation will be negative (that is, increasing government size will correspond to decreasing median income).

This hypothesis does not imply causation, only correlation.

To begin the study, I needed to obtain data on the size of government. I wound up contacting the U.S. Census Bureau and obtained this data for the period 1947-2007.  The office was EXTREMELY helpful and immediately responsive. I obtained the data as a Microsoft database, which I could then import into Excel.

I then needed income data [3]. I decided to start with the income data provided by the census bureau. The best and most complete data I had was the average December salary of a federal employee. I multiplied this by 12 in order to obtain an estimated average yearly income. I took inflation into account and corrected all dollar amounts to 2007 dollars.

In addition, I went online and obtained census bureau data for median family income. This was a check against the federal employee data, in case their incomes don’t track with median family income.  I also used this data normalized to 2007 dollars.

The results of a raw plot of the data is shown below:

Trends in Government

If the number of federal employees can be taken as a measure of “the size of government,” then there are periods of trending that are of interest. The government was its largest in the last 70 years during World War II, with about 3.5 million federal employees. That number then dropped after World War II (1947) to about 2/3 that number.  The size of government then gently or rapidly grew from 1947 to 1967, reaching 3 million employees.

From 1967-1981, the size of government decreased slightly or stagnated, reaching a low of  2.75 million during that period – never as low as post-WWII U.S. From 1981-1989, the federal government increased steadily and rapidly in size, from 2.8 to 3.1 million employees. During the 1990s, the size of government declined again to below the levels it achieved in the 1960s, except for a slight up-tick around 2000-2001. In the 2000s, the size of government stagnated, remaining approximately fixed at 2.7 million employees.

So, the size of the federal government was never as big as during WWII. Excluding WWII, the federal government achieved its maximum during this period in 1989.

Relationship between size of government and income

To explore the hypothesis, we can qualitatively compare the trends in government employee and family incomes to the size of government. Let’s begin with periods of increase in the size of government.

The size of government steadily increased from 1947-1967. During that same period, federal salary went from $24k to $46k and family income went from $25k to $43k. The next period of slow increase was from 1972-1981, during which time the average federal salary went from $61k to $55k and family salary went from $49k to $49k.  The next period of more rapid increase in the size of government from from 1981-1989. During that period, federal salary went from $50k to $55k, and family income went from $50k to $54k.

Let’s then consider periods of decline in the size of government. The first of these is a short period from 1953-1954, during which time federal salaries went from $31.0k to $30.5k and family incomes went from $28.8k to $28.0k. The next period of decline is from 1967-1971, during which time federal salaries went from $45.9k to  $54.1k and family incomes went from $43.1k to $47.0k. The next period of decline was from 1990-2002 (with the exception of a small spike upward in 2000). During that period, federal salaries went from $55.3k to $59.5k and family income went from $54.4k to $59.6k.

With the exception of the federal salaries from 1972-1981, salaries generally increased throughout the entire period. We should then look at the rate of overall increase as compared to the change in the size of government.

Quantitative Exploration of Government Size and Incomes

We can now look at the relationship between the change in the size of government and the rate of change in salary during the same periods.

Trends (slopes) in the size of government and income, as a function of time. The previous plot incorrectly divided by the number of years represented.

The table shows the slope of a line-fit to the data in each period (representing change in the number of employees per year, or change in income per year). Looking at the table, we observe the following:

  • Family income nearly always trends upward, largely independent of changes in the size of government.
  • When government size trends down (highlighted in purple), family incomes trended UPWARD  two out of three times. During the remaining period (’53-’54) there was a decline in family income.
  • When government size trends upward, there are interesting income trends. Family income always trends upward during these periods; federal work income trends upward in all but two of these periods.

Computing the correlation coefficient of the family income numbers and the government employment numbers, the correlation is 0.78. It is positive, meaning positive increases in government size correlate with positive increases in salary. It is significantly larger than 0, meaning that there is a strong positive correlation. Naively, these sets of data ARE positively correlated.

Other Trends

In addition, the chart of the data shown earlier has two variations. In one, the same data are shown with periods of recession overlaid in green. In the other, the same data are shown with periods of Republican control of the White House overlaid (since a Republican idea is at the heart of this study).

Let’s look at the recession data first [4]. Periods of long recession (more than 1 year) correspond very highly to periods when family income declines or stagnates. This isn’t a surprise, and is a good control for the data (you expect salaries to decline or stagnate during recessions). What happens to the size of government around recessions? Recessions do seem to correspond to times when there are changes in the size of government, but not clearly upward or downward changes. For instance, in the 1940s-1950s, recessions relate both to increases and decreases in the size of government. In later periods, changes in government size in either direction happen around the times of recessions.

What about party control of the White House [5]? Well, here there are some clear trends. Except for Reagan’s and G. H. W. Bush’s Presidencies, Republicans tend to preside over periods when the size of government is flat or slightly declining. So, of the six Republican Presidents from 1944-2007, 4/6 presided over such periods. Reagan presided over the largest increase in the size of the federal government since 1965, when Lyndon Johnson was President.  No Republican President presided over a large decline.

When Democrats are President, there are also clear trends. Truman presided over post-WWII America and, largely because of that, saw the single LARGEST decline in the size of government during ANY time from 1944-2007. His Presidency also saw an increase in the size of government after WWII. Kennedy saw a slight increase in the size of government, while Johnson presided over the next largest increase in the size of government. Carter presided over flat government size, while Clinton presided over the largest DECREASE in the size of the federal government since 1945. Of the five Democratic Presidents from 1944-2007, two presided over increases in the size of government, two presided over huge declines (Truman and Clinton, though Truman’s period was mixed), and one over a stagnant government size (Carter). So Democrats are more mixed, but at the extremes presided over the two largest declines in the size of government (Truman, Clinton) and two of the largest inclines in the size of government (Truman, Johnson).


There is a strong, positive correlation between the size of government and family income. This does not imply causation, only correlation; likely, there are external causes for these effects (e.g. growth in GDP), but this is only speculation. Periods of decline in the size of government correspond to increasing family income 66% of the time, while periods of increase in the size of government correspond to increasing family income 100% of the time. So income tends to increase regardless of the sign of change in the size of the government.

In addition, the income data seems to track recession data very well. Regarding the Presidential data, Democratic Presidents have presided over the two largest decreases in the size of government (Truman and Clinton), and Truman presided over a period of sharp increase in the size of government later in his Presidency. Presidents from both parties have presided over large increases in the size of government: Truman, Johnson, and Reagan. Republican Presidents tend to preside over periods of no, little, or slightly declining government growth, while for Democratic Presidents it’s more mixed.

The statement in the “Who We Are” section of the GOP website – “Under Presidents Ronald Reagan and George H.W. Bush, the United States won the Cold War, releasing millions from Communist oppression, in true anti-big government Republican spirit.” – is partly a falsehood. The data indicates that Reagan was, in reality, pro-government-growth. In addition, the statement that ” . . . big government . . . [is] going to destroy the foundation and the fabric of America” is also a falsehood. Based on incomes, big government isn’t destroying the foundation and fabric of America. The hypothesis that big government is bad for America, interpreted to mean “bad for incomes” and thus quality of life,  appears to be false. They are both strongly positively correlated; or, perhaps, more accurately income goes up largely independent of what government size does. What the real cause of growth in either might be is left to a different study.