"Rising earnings leads to rising dividends". I've read that in many articles. I've even written that myself many times.
Is it true? How direct is the relationship? If earnings rise by 10%, do dividends rise by 10%? Do companies that grow earnings faster than others, grow dividends faster than others?
Please read part 1 for definitions of "compound annual growth rate," "bumpiness," and "correlation."
What is the correlation between earnings growth and dividend growth?
My dividend website tracks 886 companies, comprising all of David Fish's lists of Dividend Champions, Contenders, and Challengers, and more.
I chose to start with the year 2000, as since then the market has experienced two recessions:
and the U.S. Government lost its AAA rating in 2011.
351 companies out of 886 had sufficient earnings data and dividend data to be worth comparing. The raw data can be found here. The correlation was 0.406901, which is positive, but not significant.
I used Excel to create a scatter plot with a trendline (see below). The trendline (a "best fit" line) has an Rsquared of 0.16557, so it is not a good fit.
Column D in the raw data is the ratio of dividend CAGR over earnings CAGR. A ratio of greater than 1 means dividends grew faster than earnings; I call that generous. A ratio of less than 1 means earnings grew faster than dividends; I call that stingy.
155 out of 351 were stingy, 196 were generous. The distribution looks like this:

It's tempting to simply buy the most generous companies, but this might not be a good idea. The 4 most generous companies (O, ratio = 28; CCL, ratio = 24.5; MPR, ratio = 22.7; MCY, ratio = 18.2) had high ratios not because of high dividend CAGR but because of low earnings CAGR: all 4 companies had an earnings CAGR of less than 0.5% per year, over 13 years. For example, O's 2000 earnings were $0.845, its 2012 earnings were $0.86 (with 7 years of earnings increases and 6 years of earnings decreases in between), so its earnings CAGR was a very low 0.147% (but its earnings bumpiness was very high).
Another issue with generous companies is that when dividend growth rises faster than earnings growth, the payout ratio (of dividends over earnings) also rises, and it can't "rise to the sky." Similarly, for stingy companies, when the earnings growth rises faster than dividend growth, the payout ratio falls. For example, NSC's payout ratio was 60% in 2000 but was only 23% in 2012.
David Van Knapp wrote an article about the most widelyheld dividend growth companies. How generous or stingy are they? Here are the ones I have data for:

I'm not surprised that GE had an earnings CAGR of 0  it earned $1.29 in 2000, and $1.29 in 2012. No growth, no CAGR.
I am surprised that EMR, INTC, SO, KMB, LEG, and O had such low earnings CAGRs.
I am surprised that MMM, O, SO, and GE had such low dividend CAGRs.
I'm not surprised that DRI, MCD, PAYX, WAG, WMT, UTX, PEP, CL, MDT, and BDX were generous.
I'm not surprised that PG has a ratio so close to 1 that it looks like they planned it that way. In my opinion, PG is the most shareholderfriendly company of all (except for recently transferring their transfer agency to ComputerShare).
I am surprised that GIS, AFL, JNJ, CVX, PFE, KO, CSX, XOM, CAT, APD, NSC, and RTN were stingy.
Conclusion
Regarding the questions at the top of this article:
How direct is the relationship? If earnings rise by 10%, do dividends rise by 10%?
The answer is "not in any significant way." If one rises, the other may or may not rise, by that amount or by a different amount.
Do companies that grow earnings faster than others, grow dividends faster than others?
The answer is "not in any significant way," which means you don't have to give up earnings growth in order to get dividend growth, or vice versa.
Another way to see that earnings growth and dividend growth are not strongly correlated is to look at the scatter chart above. Pick any point on the x axis (dividend CAGR), and look up  you will have many earnings CAGRs to choose from. Similarly, pick any point on the y axis (earnings CAGR), and look right  you will have many dividend CAGRs to choose from.
What I do is: first, sort the raw data by earnings CAGR, then eliminate all the rows where the number is below my minimum; second, sort the remaining rows by dividend CAGR, then eliminate all the rows where the number is below my minimum; now I have a list of companies that meet or exceed both minima. I consider all of them for further due diligence.
Acknowledgements
SA members David Fish, David Van Knapp, and richjoy403 (in alphabetical order) made significant and helpful suggestions on a first draft of this article. I am glad to thank each of them for their help.
David Van Knapp kindly pointed out his earlier article on a similar topic, which I was unaware of until after this article was written.
Disclosure: I am long AFL, CVX, DRI, INTC, JNJ, KO, PEP, WAG, WMT. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.