How good are people at guessing the ages of their respective ethnic group? I have a Chinese friend and she says that she has a much harder time guessing Western people's ages than Eastern people's ages. No particular surprise here. For me it's the opposite. I have the feeling that Eastern people look younger longer and then "suddenly" look older.

To have a comparison, I wonder if there is a study on "Western people guessing Western people's ages" vs. "Eastern people guessing Eastern people's ages".
Cross-race effect in facial processing

As @analystic has noted, there is substantial research documenting what is sometimes called the "cross-race effect":


  Cross-race effect (sometimes called cross-race bias, other-race bias
  or own-race bias) is the tendency for people of one race to have
  difficulty recognizing and processing faces and facial expressions of
  members of a race or ethnic group other than their own.


For an overview of research see the meta-analysis by Meissner and Brigham (2001). To quote parts of the abstract:


  Data were analyzed from 39 research articles, involving
  91 independent samples and nearly 5,000 participants. Measures of hit
  and false alarm rates, and aggregate measures of discrimination
  accuracy and response criterion were examined, including an analysis
  of 8 study moderators. ... Overall, results indicated a "mirror effect" pattern in which own-race faces yielded a higher proportion of hits and a lower
  proportion of false alarms compared with other-race faces. 


Note that the effect is probably related to degree of interaction with the  racial group. Thus, it is not so much a fixed genetic difference, but rather that in many societies we tend to interact more with our own racial group.

It would not be surprising if part of the cross-race effect would be reflected in poorer performance in rating the age of people from a different race relative to one's own race.

General skill in estimating ages

You can find a nice review of the age estimation literature in Rhodes (2009).
The author suggests that a general in group bias may exist in skill in age estimation. I.e., that prediction is not just better for the same race but also for people of similar age.


  Taken together, data on group biases in age estimation must be
  regarded as suggestive that in-group age estimation is superior to
  that of out-group age estimation. This may include more accurate age
  estimates for individuals of one’s own ethnicity or age group (but see
  Burt &amp; Perrett, 1995). However, given the dearth of data, the full
  range and impact of group biases on age estimation has yet to be
  explored.


Estimating ages of own versus other race

I also found a specific study by Dehon and Bredart (2001) which specifically looked at accuracy in cross-racial age estimation.

Citing the abstract:


  In the present study, we investigated whether this finding extends to
  age perception. Caucasian and African participants were asked to
  estimate the age of Caucasian and African faces. The main result of
  this experiment was a significant race of 'subject $\times$ race of face'
  interaction showing that Caucasian participants performed better at
  evaluating Caucasian faces than African faces. However, African
  participants performed equally with both type of faces. This result is
  explained by the Africans' time of residence in Belgium


They used  72 Caucasian and 72 African photographs as stimuli. Actual ages of faces ranged between 20 and 45 years. In terms of absolute deviation in years between actual age and estimated age, thy found that:


  Caucasian participants were better at estimating the age of
  Caucasian faces (mean = 6.35 years, SD=3.13 years) than African
  faces (mean= 7.79 years, SD= 2.96 years) whereas the performance of
  African participants did not differ with the kind of face (mean =6.98
  years, SD =3.25 years and mean =  6.79 years, SD= 2.86 years for
  Caucasian and African faces, respectively).


Note of course that these differences in age accuracy are not that large.

References


Dehon, H. &amp; Bredart, S. (2001). An 'other-race' effect in age estimation from faces. Perception, 30, 1107-1114.
Meissner, C.A. &amp; Brigham, J.C. (2001). Thirty years of investigating the own-race bias in memory for faces: A meta-analytic review.. Psychology, Public Policy, and Law, 7, 3. PDF
Rhodes, M.G. (2009). Age estimation of faces: A review. Applied Cognitive Psychology, 23, 1-12.