Category Archives: Allmänt

Two quotes from two WWII figures

“Dear Bessie:
… I certainly enjoyed myself the evening I was there and you may be assured I shall repeat the offense as often as I can or you will allow me. That cake and coffee couldn’t be beat. I am like a girl that once boarded where I did. She said there was nothing better than cake but more cake. I heartily agree with her. It makes no difference about the variety just so it’s cake.”
– Harry S. Truman


“Meeting Roosevelt was like uncorking your first bottle of champagne.”
– Winston Churchill

From a Linear Algebra textbook

“A group X of students a group Y of professors stand in the yard. Each student throws a tomato at one of the professors (and each tomato hits its intended target). Consider the function y= f(x) from X to Y that associates with each student x the target y of his or her tomato. The image of f consists of those professors that are hit.”

The name Mudd

Many students at American universities are familiar with the name Mudd. Not only is there the Harvey Mudd College; there are also numerous Seeley G. Mudd buildings, libraries, and centers named after Harvey’s brother. At the University of Southern California and Columbia University there are also the Seeley W. Mudd buildings, named after their father (although it was actually Harvey Mudd who attended Columbia and later was a dean at the University of Southern California).

You must certainly at least once have wondered: are Harvey S., Seeley G., and Seeley W. Mudd related to Samuel A. Mudd, who treated John Wilkes Booth’s leg? The answer is: yes. Seeley G. and Harvey S. Mudd are great-great-great-great-great-grandsons and Seeley W. Mudd great-great-great-great-grandson of Henry “Harry” Mudd. Samuel A. Mudd is the great-great-great-grandson of Henry Mudd’s older brother, Thomas Mudd, Jr. It is a small world after all.

Simon Hedlin

Homo sapiens

During a seminar on climate change and optimal discount rates, professor Joseph Stiglitz reminds himself of an anecdote:

“Two planets meet. The first one asks: ‘How are you?’

‘Not so well,’ the second planet replies. ‘I’ve got the Homo sapiens.’

‘Don’t worry,’ the first planet says, ‘I’ve had it before. It doesn’t last long.'”

Income per capita and female labor force participation rates

The Financial Times has a great and highly recommended data blog for those of us who are interested in statistics and quantitative analysis. Its biggest disadvantage is that it is not updated frequently enough. The posts give much food for thought and a subject that was discussed last month is worth exploring further. The post was about the relationship between income per capita and the  female labor force participation rate and it can be found here.

Valentina Romei asks whether women in the workforce help boost economic growth. While it may or may not be true that female labor force participation is not an important determinant of growth, the graph that she presents in the post is not entirely convincing. It shows the relationship between the female labor force participation rate and income per capita in 2010. And a scatter plot without any control variables essentially assumes either that there are no fixed effects/other omitted variables or that the potential effect of the female labor force participation rate is so strong that it weighs more than all possible countering effects from other variables (this would still be a bias though, as we would underestimate the actual effect).

Romei concludes that her graph “shows a poor correlation between female labour participation and GDP per capita.” And yes, it does. But does that prove that the proportion of the women who take part in the workforce is unimportant? Not necessarily. Here is the relationship between income per capita and the unemployment rate based on data for all countries that are available in the World Bank’s database for 2010:

PPP and labor force participation rate

This graph does also show a weak relationship. But most people would probably agree that lower unemployment generally is good for economic growth. The point is: scatter plots are great because they are easy to comprehend, but they do not necessarily prove or disprove potential quantitative relationships. This is true in particular when countries and other bigger entities are being compared because they are already have such big initial differences.

Romei’s graph shows a weak relationship between female labor force participation rates and income per capita. One reason for that is that most of the countries with the highest female labor force participation rates do also happen to be poor. These are the ten countries in the world (according to the World Bank) with highest female labor force participation rates: Tanzania, Mozambique, Rwanda, Malawi, Burundi, Madagascar, Zimbabwe, Equatorial Guinea, Nepal, and Togo. Except for the extraction-based economy Equatorial Guinea, these are not precisely the richest countries in the world. One potential explanation is that in poor countries, many women have no choice but to work. This would be a case of reverse causation (where the dependent variable has an effect on the independent variable), and is one of those countering effects that was previously mentioned as a potential source of bias if we try to interpret Romei’s graph without further analysis.

What we are really interested in here is the counter-factual scenario. We know that Tanzania, Malawi and Zimbabwe are poor countries with high female labor force participation rates. What we want to know is whether they would higher, the same, or lower levels of income with a higher female labor force participation rate. Whether the United States has higher or lower income or/and female labor force participation rate than Spain is not particularly insightful; the interesting question is whether higher female labor force participation rate in the United States will boost American growth or not, everything else equal. And a cross-country scatter plot will not answer that question.

The following are a few very simple regression specifications. They are not meant to prove that higher female labor force participation causes higher income levels. The point is rather to show that an initially negative relationship quite easily can be turned into a positive relationship by taking some omitted variables into account.

ppp and fempar 1*** p<0.01. Robust (clustered where appropriate) standard errors in parentheses.

The dependent variable is income per capita in international dollars in terms of purchasing power parity (PPP). The main independent variable is female labor force participation rate in percent. The first column shows the result from the simplest of linear regressions. This result is different from the one depicted in Romei’s graph, because she finds a positive relationship between female labor force participation rate and income per capita whereas here the correlation is clearly negative. The result here implies that a one-percent increase in the female labor force participation rate is on average associated with a 51.91-dollar decrease in average annual income per capita. The reason that this result is negative whereas Romei’s is positive is probably because the data here is not only for 2010, but from 1990 to 2010 and it contains all observations available in the World Bank’s database for those years. See the following graph for comparison with Romei’s (although income per capita is the dependent variable, the axes are purposely swapped below for easier comparison with Romei’s original chart):

Female labor force participation rate and PPP per capita, 2010

The three other columns in the table show regressions that include different combinations of fixed effects. The result in the third column in the table is insignificant. The results in the two other columns, however, show a fairly large and highly significant relationship between income per capita in terms of PPP and female labor force participation. This implies that when we allow for differences between countries that are more or less constant over time (such as culture and geography) the initially negative relationship becomes positive such that higher female labor force participation rates are associated with higher levels of income.

Now, these results are not really proof of anything that concerns the main hypothesis about causality, because the analysis here lacks both a causal identification strategy and robustness tests. The table above simply shows that many important economic questions – such as the one related to female labor force participation and economic development – are not easy to answer. Scatter plots and regression outputs may look convincing, but sometimes they cannot, regrettably, tell us much. This is true in particular when we compare big and vastly different entities, such as countries.

Simon Hedlin

PhD or MBA?

Three recommended papers on top economics journal in the latest issue of Journal of Economic Literature.

According to David Card and Stefano DellaVigna, submission to top-five journals has increased over past two decades whereas the total number of articles published actually has declined; the acceptance rate is now roughly the same as for top PhD programs at about six percent. Citations are rising for recent papers in the fields Development and International, and falling for papers in Econometrics and Theory.

Daniel Hamermesh finds that the fraction of older authors (50+) in top-three journals has almost quadrupled in past two decades. Experimental research has become increasingly popular at the expense of papers on pure theory.

And as David Stern writes, academic economists are intensely interested in journal rankings, but except for some top-ten and bottom-four ranked journals, the rankings are quite uncertain with overlapping confidence intervals.

Conclusion: if you are young, interested in pure econometric theory, have not yet started a PhD program, and want to publish only in top journals, you should consider business school.

Simon Hedlin

What Heritage does not make clear about federal spending

A popular chart by the conservative think tank The Heritage Foundation is shared by thousands of people on Facebook every now and then. The chart is titled “Federal Spending Grew Nearly 12 Times Faster than Median Income.” The problem with this chart is that it does not paint a nuanced picture of how much the federal spending in the United States actually has grown. This is because one of the two plots is an aggregate number (total federal spending in dollars) and the other plot is a median value (median household income).

The fact that total federal spending has grown twelve times faster than median household income since 1970 is quite irrelevant if we do not take into account the growth in the number of households. If the number of households had grown faster than federal spending, the size of the federal government would actually have shrunk (Sweden has one of the largest public expenditures per capita in the world, but imagine how small the American federal government would be if its total federal spending equaled that of Sweden). So what did the household growth in America look like?

more people, more spending

As can be seen, federal spending grew faster than the number of households. But the number of households grew substantially, and this need to be deducted from the federal spending curve in the Heritage chart if a sensible comparison is to be made.

A caveat to be mentioned before showing the next graph is that it has not been possible to exactly replicate the numbers used by The Heritage Foundation. The calculations used here reaches the same number for federal spending of $3.6 trillion for 2010, but while Heritage estimates that the inflation-adjusted federal spending in 1970 was $926 billion, the number used here is $1.1 trillion. Similarly, both estimate median household income to be about $51,000 in 2010, but this blog (which copied numbers straight from the referred U.S Census Bureau report) uses a much greater number ($45,146 compared to $41,358) for 1970. So The Heritage Foundation finds that both federal spending and median income has grown at a faster rate than what this blog estimates. It is not clear from their chart which inflation-adjusted numbers they used or what price index they used to adjust for inflation, but overall this should not make too much of a difference. The general tendencies will still be the same. Especially since they find greater growth both in federal spending and in income.

When using federal spending per household instead of total federal spending, the graph looks very different. Here is a comparison to mean household income (which might better illustrates tax-paying abilities than median income). It turns out that federal spending still has grown considerably – but much less than what the Heritage chart shows.

growing government

So while The Heritage Foundation is correct that federal spending has grown quite rapidly – also in per-capita terms – the magnitude is much smaller than what their chart shows. And this would be the same case if one used their exact numbers as well, simply because the number of households has grown at a fast pace. Another measure of federal spending that might add some perspective to the debate on this issue is federal spending as a fraction of GDP.

big government

The chart made by The Heritage Foundation is often referred to as a long-term trend, and one of the main reasons why the United States has piled up so much debt. But this argument seems too simplified. In terms of share of GDP, there is no trend. Federal spending was actually lower in 2008 than in 1975, and lower in 2001 than in 1970.

Now, there are still good reasons to cut federal spending, but it is hard to make an argument that federal spending has grown at an explosive rate compared to income.

Simon Hedlin