Statistics

# How To Cheat With Graphics: Paul Krugman Style

Thanks to reader Doug Magowan for bringing this to our attention.

In his New York Times blog “The Conscience of a Liberal“, the far-left economist Paul Krugman presented these graphs and this story (which I quote in full so that there is no ambiguity):

Special Bulletin: Fractions Have Denominators

I’ve been getting some mail over yesterday’s column, with angry correspondents posting charts like this, showing government spending as a percentage of GDP, to claim that government spending has too surged:

But if you look at the raw numbers on government spending, here’s what you see:

Feel the surge!

What’s going on? Yes, that’s right: itâ€™s what happens when you divide by GDP in a time of terrible economic performance. Spending hasn’t surged; in fact, it grew more slowly in the two years after Lehman collapsed than in the two previous years, despite a sharp rise in spending on safety-net programs. Instead, GDP growth has plunged.

Notice anything funny about that second graph? Compare the vertical axis of it with that of the first graph. The first graph (spending as percentage of GDP) lets the data choose the range of the axis, from 30% to 37%. In the second graph, Krugman selects the axis range himself, from 0 to 6 trillion.

Here’s an estimate of that same second graph again, replotted letting the data chose the axis limits:

Feel the surge!

Why did Krugman—or whatever flunky he has plotting data for him—start at 0 trillion dollars for the second graph? Spending must, of course, start at zero dollars, but there is no good reason to do start the figure at that number except to hide a dramatic change in the data, and make it seem small or negligible.

Starting at 0 is a well known trick, and a good one. So wily it is that I don’t know why Krugman (or his flunky) didn’t try the same sleight of hand on the first graph, too. If he did, he could have got something like this:

Percentages start at 0, do they not? And they end at 100. Might as well set the limits of our graphs at these numbers, especially if we want to mask significant changes through time.

Sometimes it makes sense to start at percentage graph at 0, particularly when small percent changes translate into tiny actual-dollar shift. But here, a six-percentage point change is humongous because we’re talking trillions of dollars. Only a socialist would think this small change.

Of course, both of my recreations are estimates because I do not have the raw data to recreate them exactly. I do not capture the exponential percentage increase from 2009 to 2010, for example. But the actual-dollar spending graph is not too far off.

Krugman said, “Spending hasn’t surged; in fact, it grew more slowly in the two years after Lehman collapsed than in the two previous years…” He can make that statement only if tricked himself—or wants to tricks others. That is, either he’s lying to us, or is easily fooled by cheesy statistical tricks. There is no third explanation.

Note: at least one of the people commenting on Krugman’s blog noticed the shenanigans with the graphs, implying there is hope.

Categories: Statistics

### 38 replies »

1. @Cris Darrel Huff did an excellent book on this very subject: How to Lie With Statistics. It covers pretty much what was covered here and more.
Coupled with Edward Tufte’s “Visual Display of Quantitative Information”, together they make a great set for learning about how other distort numbers with statistics and graphs, and how to not do so yourself.

2. Pete says:

The How to Lie with Statistics book by Huff said that modifying the axes to start with ANYTHING OTHER THAN ZERO IS THE FOUNDATION OF LYING. See pages 63-64 in Huff’s book.

3. Also, to be fair: he is saying he is shown graphs like the first one to say how government spending has increased in comparison to GDP (which is natural during a recession). The latter shows this compared to the overall trend.

The idea behind both graphs have merit: the former is useful for showing change of some proportion over time, while the latter is useless for showing that change in relation to the overall picture.

4. Luis Dias says:

You missed the point, the point was to illustrate where did that spike in 2009 really come from: from the economic collapse, not from the “now the government is spending like hell”.

You erected a false strawman. But since you’ve done so, I urge you to graph those graphs with exactly those values but with the aesthetic “feel” that you are so fond of. You’ll also see the spike existing in the first graph and not existing in the second.

…. and the series of erecting strawmans continues unabated! Don’t miss the next episodes because we… we won’t!

5. Briggs says:

Sam,

Right. Both graphs are useful and serve different purposes. And both show, with some pluses and minuses, an inexorable increase in government spending. Didn’t matter who was president, or what party dominated Congress. Spending keeps going up and up and up….

Krugman should have also shown the “numerator” graph, too.

Right, Luis?

The spike present in the percentage graph is there in the second graph. Your criticism comes from not looking at Krugman’s graph carefully. Part of this isn’t your fault, because Krugman put the squeeze on that picture.

In 2009, the second graph is about 4,700 or 4,800. It increases to 5,100 or so by the end of 2010. That’s a spike: a six to nine percent increase. It just appears less dramatic because of the poor way the data is presented.

Does anybody have access to the raw data so I can replot cleanly?

I was taught that you should start graphs at 0 (or similar base reference) so that your audience is not misled.

However, both graphs look very similar to me. If I was shown both without commentary, I wouldn’t draw any conclusions, other than spending has increased. I disagree with Luis Dias above, I think that there IS a spike in the second graph, it’s just not as pronounced because of the scale. To really compare the two you need to make them the same scale.

Good work stating the obvious, Briggs. I can only wish that it weren’t necessary…

7. Briggs says:

Pete,

If that’s so, then it is a rare case of Huff making a mistake. Starting at zero does not make sense for many, even most graphs.

Take our case: it’s possible that government spending is actually negative. It has been so in times historical. This of course means those rare instances when the government takes in more than it spends. Since it is possible that our numbers could be negative, and very large negative, we could start the plot at, say, -10 trillion, or even smaller.

8. Pete says:

“If thatâ€™s so…”

I gave the exact page. Go to Amazon or Google Books and look inside the book.

“Starting at zero does not make sense for many, even most graphs.”

Too bad that this is not the case for *this* graph. Actually the example of Huff is for a very very similar case. (Increase of earnings.)

The starting point really just needs to be consistent and logical. Krugman’s comparison was horribly misleading because it was not consistent. I agree with Briggs that the most useful starting point of the graph would not be zero.

10. Pat Moffitt says:

We who cannot print money must take into account declining revenues in our spending habits. So should those that can print money.

11. Doug M says:

GDP (nominal) has increased about 2% despite the recession. So, Krugman’s main point, that the growth of government speding as a % of GDP has accelerated because GDP has contrated, is COMPLETELY FALSE!

Government spending in these charts looks like it includes state and local. Federal spending has increased at about 25% in the last 2 years. State and Local has grown at about half that pace.

12. Doug M says:

Take our case: itâ€™s possible that government spending is actually negative. It has been so in times historical.

Spending is never negative (or I suppose it always is, depending on your point of view).
Don’t get spending confused with the deficit.

13. Jerry says:

Krugman seems to be attempting to defend the current admin by showing that government spending in absolute terms has not “surged” but has actually maintained a nice steady increase. But the 800 pound gorilla is simply this: the government is spending over 36% of GDP. That’s a disaster no matter how you graph it!

14. Bernie says:

Where government spending has a lower multiplier effect than the equivalent private sector spending then government spending can suppress the growth of GDP. Economic multipliers are key to driving economic growth. The robust growth in the 80s and 90s was in large measure driven by significant infrastructure investment in areas that depended heavily on US made investment goods such as telecomm. The 90s and early 2000s saw excessive investment in housing which though it led to a lot of growth because of the large multiplier, is now a definite drag on the economy – there is unlikely to be a housing led recovery.

Current spending by the government has very low multipliers either because nobody wants to actually buy or pay for the stuff that is being invested in or the payments go essentially to consumption goods that are made in China.

We would have been far better off if the government had simply enabled and encouraged the private sector to invest in new US energy technology and US energy resources. A US oil and nuclear boom could refloat this economy and allow us to avoid a Japanese decade.

15. Johan says:

Pete
I”m sorry, my copy of Huff’s “How to Lie with Statistics” (Penguin Books, 1991) doesn’t mention this “start-at-0” rule anywhere. All chapter 5 “The Gee-Whiz Graph” says is: 1) choice of ranges on graphs can have a huge impact on interpretation (e.g. percent change); 2) the choice of proportion of the y-axis to the x-axis can distort as well ; and 3) one can distort bar charts by having them start at positive values and / or trimming below an artificial baseline to 0.
Anders Wallgren in his “Graphing statistics & data: creating better charts ” wrongly linked this absurd “start-at-0” rule to Huff, and now it’s all over the Internet.

16. Les Johnson says:

It may not be Krugman, or his flunky. It might be Bill Gates.

I get nearly identical graphs (fonts, line color, and y-axis start/end points) when I plot estimates in Excel 2007.

I was trying to look at the slopes, but without the underlying data for the % of GDP, that is a pointless task.

17. Les Johnson says:

Or not. If I use % of GDP 31% and 36% as start and end points, and Gov spending as 4000 and 5100, then calculate GDP, I get 12903 and 14166 for GDP.

The slopes? For GDP growth its 1263, vs 1100 for spending.

I would call use those identical, seeing as I use estimates and two point graphs.

18. Noblesse Oblige says:

Let me tell my own Krugman story. A few years ago he published a column in which he referred to figures showing that California’s growth in per capita electricity use since 1970 was significantly less than the national average. The conclusion to be derived from this was that California’s energy policy is working. (I am not making this up). Being interested in this, I checked into the EIA figures for various states and found that all states in the region have similar or better records, including even Nevada. Not surprisingly the hot humid Southeast led the nation. I sent him a private email calling attention to this and suggesting that perhaps climate factors may have more of a bearing than government policy.

I wrote him off.

19. Pete says:

Oh Johan, please stop lying. Copy & paste from the book below. Pick a phrase from the passage below and search it on Google Books to identify and see the exact page.

“Well let our graph show how national income increased ten per cent in a year. Begin with a paper ruled into squares. Name the months along the bottom. Indicate billions of dollars up the side. Plot your points and draw your line, and your graph will look like this.

[Graph starting at 0 up to 24. Line starts at 20 ends up at 22]

Now that’s clear enough. It shows what happened during the year and it shows it month by month. He who runs may see and understand, because the whole graph is in proportion and there is a zero line at the bottom for comparison. Your ten per cent looks like ten per cent — an upward trend that is substantial but perhaps not overwhelming.

This is very well if all you want to do is convey information. But suppose you want to win an argument, shock a reader, move him into action, sell him something. For that, this chart lacks schmaltz. Chop off the bottom.

[Graph starting at 20 up to 24. Line starts at 20 ends up at 22]

Now that’s more like it. (You have saved paper too, something to point out if any carping fellow objects to your misleading graphics.) The figures are the same and so is the curve. It is the same graph. Nothing has been falsified-except the impression it gives. But what the hasty reader sees now is a national income line that has climbed halfway up the paper in twelve months, all because most of the chart isn’t there any more. Like the missing parts of speech in sentences that you met in grammar classes, it is “understood”. Of course, the eye does not “understand” what isn’t there and a small rise became, visually, a big one.

Now that you have practiced to deceive, why stop with truncating? ….”

[discussion continues with changing the scale of x and y axis]

You may continue the argument about GDP, spending, etc. I do not care about that. But please stop distorting what somebody said (in that case Huff) in order to support your arguments.

The case of Huff was SO similar to the one mentioned here, that citing Huff in *support* of what is being said here would have him turning into his grave.

20. Pete says:

And by reviewing Huff a little bit more, I find him condemning exactly the same graph. In Huff’s book, the graph is about “Government Payrolls”. From 1938. Some things never change.

Simply Google [“government payrolls up” “government payrolls stable”] (with the quotes) and you will find he example in Huff’s book.

21. Paul Krugman is an intellectually dishonest gargoyle. Thank you Mr. Briggs for unmasking his trickery

22. Alex Heyworth says:

Jerry says:
18 October 2010 at 1:54 pm

…. But the 800 pound gorilla is simply this: the government is spending over 36% of GDP. Thatâ€™s a disaster no matter how you graph it!

Just be thankful it hasn’t reached over 50% of GDP like the UK. Although it may only be a matter of time.

23. AusieDan says:

I am an outsider, and so not a partisan in this particular arguement
The proper presentation of the data depends on the purpose.

You may want to know if the government is taking a greater or lesser share of the pie as the years go by.
In that case you need to measure Gov spend as a percentage of FULL employement GDP.

You may wish to know if the governemnt spending is increasing the level of government debt.
Or if it is filling in for falling private demand and hence at least partly helping to curb increasing under use of resources, human and otherwise.
There are a number of other things you could seek to discover.

Each has a correct method, but there are many other methods that are designed to decieve, or just happen to do so by mistake.

If you want to look at proportions, you MUST start a zero.

If you are charting two things similtaneously ( say goverrnment spending vs private consumption) then you can get a better comparison by filling the screen with the data from bottom to top. That showns more clearly how they mover relative to each other.

Just don’t think you can get the best trend indications (rate of increase and so forth) if you start the graph above absolute zero.

HINT – if you want to see how quickly the temperature has been rising over the last 100 years, convert all temperatures to degrees absolute and graph fom zero up.
See the increase? I thought not.

24. Hasdrubal says:

This is probably a case where a numerical example might be better than a graphical one, from the census page linked above:

Year – Total Expenditures – Change compared to the previous year
2000 – 3021.5
2001 – 3220.8 – 199.3 (6.6%)
2002 – 3422.9 – 202.1 (6.3%)
2003 – 3624.6 – 201.7 (5.9%)
2004 – 3827.0 – 202.4 (5.6%)
2005 – 4109.9 – 282.9 (7.4%)
2006 – 4319.8 – 209.9 (5.1%)
2007 – 4636.9 – 317.1 (7.3%)
2008 – 5020.2 – 383.3 (8.2%)
2009 – 5344.9 – 324.7 (6.5%)

It’s a bit easier to look at those numbers and say there wasn’t much of a surge in spending: If you’re looking for a surge compared to the trend in growth, that came in 2007. And you can even look at that and say it’s only \$100 billion over the trend.

On the other hand, if you look at the actual increases or the sum of the increases, spending grew by over 300 billion in 2007 and 2009, and almost 400 billion freaking dollars in 2008. That’s a pretty darn huge surge: Government spending jumped by over a trillion dollars, _25%, in the course of three years!_ And it’s still growing, maybe not as quickly, but it’s certainly not falling nor did it fall in any of the past 10 years.

It’s hard to see on the graph that it increased by 25% in three years, you have to guesstimate the values and the rate of change isn’t intuitive for me at least. But when you put the actual numbers down, it’s much easier to see.

25. You seem to be interested in plotting data along lines from one reference to another. You assert that Paul Krugman is a “far-left economist.” Question: From what data point do you begin your plotting of his thinking? Milton Friedman? Jeffrey Sachs? John Williamson? Greenspan?

26. Pete says:

Hasdrubal, thanks! This is a plot in which there will be no arguments about the axes.

Adjusting for inflation we have the following:

2001 3.77%
2002 4.68%
2003 3.62%
2004 2.90%
2005 4.00%
2006 1.87%
2007 4.49%
2008 4.42%
2009 6.81%

We have two outliers: 6.81% in 2009 (up), and 1.87% in 2006 (down).

The worrisome part is that the increases happen throughout the last decade (and may be earlier).

27. Speed says:

Percentages start at 0, do they not? And they end at 100.

Percentages can exceed 100. Even (especially?) government spending as a percent of GDP.

28. Johan says:

Pete
I don’t have to copy-paste anything – I have Huff’s book right next to me. And I repeat, all Huff says is that the choice of ranges on graphs can have a huge impact on interpretation. That is a) true, and b) something entirely different than saying that you always have to start-at-0. Period.

29. Don Felix says:

The statement that starting the y-axis at 0 is a way to mask changes is a weird way of restating the fact that starting a something greater than 0 is a well-known way to exaggerate changes. The problem with Krugman’s piece is that he performed 2 transformations (from % of GDP to dollars as units, and changing the y axis to start at 0), then implied it was the only change he’d made, so one would conclude that the decrease in the denominator due to the recession was the entire reason for the visual difference. If he’d explicitly said that starting at 30% of GDP was deceitful and shown a graph ranging from 0-100% first, commented on that and then went on to show the change to dollars and the difference it made it would have been a fair piece, though not particularly newsworthy.

30. ecjs says:

How did you get a non-differential curve transform into a straight line using dilatation of the y-axis? This is incredibly wrong.

31. Pete says:

Johan, yes, Huff says that changing the axes changes the interpretation. But he is not saying “pick whatever you prefer”. He takes explicitly sides.

You do not understand the sarcasm in “This is very well if all you want to do is convey information. But suppose you want to win an argument, shock a reader, move him into action, sell him something. For that, this chart lacks schmaltz. Chop off the bottom.”?

Or you do not see the more explicit statement “Now that you have practiced to deceive, why stop with truncating?”

Finally, google the following: [“government payrolls up” “government payrolls stable”] (with the quotes) and you will find the exact same example that we discuss here in Huffâ€™s book.

Again: I do not care about the whole GDP issue. I am not a US citizen and how the US government spends money is of no interest to me. Take off your partisan glasses and try to read the actual arguments about presenting information.