gc-  
 
You are absolutely correct. This paper is total nonsense. You can't naively chain the correlations. 
 
Out of curiousity I just created a python script to generate sample data. Just using very basic assumptions, I was able to create a dataset of 500 parent child pairs where the following was true: 
 
Parental IQ and wage had a .23 correlation. 
Child IQ and wage had a .51 correlation 
Parent IQ and Child IQ had a .33 correlation 
Parent earnings and child earnings had a .15 correlation. 
 
If you simply multiply the values, you get .23*.33*.55 = .02 
 
Thus naively multiplying the correlations can make the results go off by an order of magnitude! 
 
Here is the code I used to generate the dataset ( note, I made IQ linear for simplicity, all I wanted to prove was that just multiplying the correlations will not work in all circumstances): 
 
def runtest(): 
parent_iq = random.randint(85, 115) 
child_iq = parent_iq+random.randint(-40, 40) 
parent_earnings = parent_iq * 600 + random.randint(-40000, 40000) 
child_earnings = child_iq * 600 + random.randint(-40000, 40000) 
print parent_iq,",",child_iq,",",parent_earnings,",",child_earnings 
 
for x in range(0, 500):  
runtest()

One more note - 
 
A lot of what we perceive as decline in the U.S. is the dramatically increased crime rate in the major northern cities. One theory I've heard promoted is that this was less the result of a breakdown in governance, and more the result of the great migration of poor, African-American sharecroppers from the south to the north. The southern cities ( Atlanta, Savannah, St. Louis, New Orleans ) always had a very high homicide rate ( as high as Cleveland or Baltimore has today). And that was under the ultimate, law and order, Jim Crow regime. As the African-American lower class moved from the southern cities to the northern cities, the crime came with them. The decline in crime rate in some American cities during the 1990's ( such as New York and Boston), can be attributed to dramatically rising real estate prices that pushed the lower classes into ring cities such as Newark.

Mencius - 
 
It seems likely to me that a significant portion of the reported increase in violence is due to increased reporting. Britain in 1900 was before the day of telephones in every home, pay phones on every street corner, and 911. My roommate works in social service, and works a child service department hotline and notes that people call up about all kinds of random crap. A fair amount is made up - a woman trying to get her boyfriend in trouble for instance. And given the civil service state's pension for paperwork, it all gets filed. 
 
I also recall reading ( I wish I could find the source) that in the 1800's New York it was far more common for murder to go unreported. Bodies would end up in the river and no one would notice. This was a time when the city was filled with gangs. Now the Irish are peaceful and even Southie in Boston is gentrifying. Read Angela's Ashes or All Soul's should disabuse yourself of the notion that the past 30 years has been all decline. 
 
As for the recent drop in crime, Peter Moskos (an example of a sociologist doing things the right way) spent a year in the Baltimore police department and reported that there was very little fudging of statistics. I do think that better trauma care has played a significant role in lowering the murder rate. I remember coming across a Boston Globe article a few years ago that said that the rate of knife wounds and gun shot wounds was the same over the past few decades, but that the survival rate had gone significantly up.

TGGP - statistics that are a straight recording of what people observed are useful in giving history a dimension of quantity. Those are the kind of number Mencius cites. It's the historical record of how many murders the police observed. 
 
What the "social scientist" does is create equations, models, charts etc with these figures in trying to divine cause and effect. The process is complete numerology. There are always far, far more variables than available data. Furthermore, the process of selecting and weighting the variables introduces innumerable fudge factors. The result thus becomes extremely susceptible to the biases of the academic.  
 
There is no easy way to determine cause and effect. You have to read the history. For instance, if you read crime reports from the 1920's and notice that a lot of murders occurred between gangs of bootleggers, that might indicate that prohibition was a cause of the increase in crime.