As I have said, the empirical evidence on sales tax volatility has shown sales taxes to be not significantly less volatile than income taxes in the short-run. These estimates come from deviations around a trend. So sales tax revenues seem to stray from their long-run trends about as much as income taxes do. Income taxes have steeper trends though, meaning they tend to rise faster then do sales tax revenues as aggregate incomes increase. The best estimates I have seen are about a 1.8 long-run elasticity for income taxes and a 0.8 elasticity for sales (see this post). Many public economists argue that short-run volatility is what we should be focusing on - how quickly to the revenues crash due to a sudden downturn in the economy - and I agree that this is an essential component. However, I also think the long-run elasticities are very important as well and have said so, but perhaps have been not as clear as I would have liked as to why. The basic point is that since income tax revenues grow faster in the long-run, they will slow down faster as well when income growth slows down.
To make this point more clearly using a real recent episode in Oregon's economic history, I did a quick little back-of-the-envelope calculation based on the actual State of Oregon quarterly personal income figures from the Bureau of Labor Statistics. First off, understand that, in general, aggregate personal incomes increase over time due to inflation, population increases, productivity improvements, etc. So long-run trends in incomes are always positive as are tax receipt growth figures. But in 2001 and 2002 Oregon experienced a very significant slow down of income growth, so I decided to see what receipts of the two types of taxes would look like using those national estimates of elasticities. Based on the average growth rate over the period 1987 to 2007 we could have expected personal income to grow by about 9.2% over that two year span (2001-2002), in reality it grew 3.6%. So from the estimates elasticities we find that based on these expectations v. reality figures, income tax revenue would have fallen about 10% below 'normal', while sales tax revenue would have fallen 4.5% short of 'normal'. This seems quite a significant difference. Of course you can make the opposite argument as well, that once personal incomes started growing at normal rates again the income tax would have more quickly regained the lost revenues than would a sales tax. But, it would have more ground to make up anyway. So though I think the short-run is quite important, I think this long-run differential is important too.
Finally, two comments on the previous post. First, a few people, I think, misunderstand the quote from the Feldstein and Wrobel paper. It does not say anything about whether a progressive tax structure is good or bad - it simply says that the US job market is quite fluid and so employers have to compensate for high taxes. Full stop. So if your aim is to reduce inequality in a state through a highly progressive income tax, it won't work. It has nothing to say on whether inequality reduction is a good goal, or on who should or shouldn't pay tax, or whether the relatively wealthy should pay more, etc. I found this an absolutely fascinating paper - who would have thought that the US job market is that fluid, or that employees respond so strongly to net incomes, not just gross? Wow. But I guess the fact that I find this so fascinating is why I am an economist that does not get invited to many parties...
Second, if you care about poverty and unemployment you should care deeply about economic growth.