賃金の伸びに物価の変動を反映した実質賃金
Does this mean "the real wages which reflect the fluctuation of price amid the wages increase"?
厚生労働省は８日午前、１月の毎月勤労統計調査（速報）を発表した。賃金の伸びに物価の変動を反映した実質賃金は前年同月比０・４％増と、５か月ぶりに上昇した。労働者１人あたりの平均賃金を示す現金給与総額（名目賃金）は、同０・９％増の２７万４１７２円だった。
I don't quite understand it especially 伸び and に in that sentence.
The issue here appears to be the usage of the word 反映. Since you seem to be familiar with the core meaning of the word, let's look at the structures this word occurs in. It has several "patterns", if you will. First, let's look at what dictionaries have to say: デジタル大辞泉（小学館）
１ 光や色などが反射して光って見えること。「夕日が雪山に―する」
２ 対照的に色がうつり合って美しさを増すこと。「壁と床 (ゆか) の色が面白く―し合っている」
３ あるものの性質が、他に影響して現れること。反影。また、それを現すこと。「住民の意見を政治に―させる」
The first two senses obviously are more literal and closely related to words that talk about physical phenomena like 反射. Our focus is the third one, the figurative usage of 反映.
This 反映 chiefly has these patterns that you will likely encounter:
- 1 Aを/はBに反映する
- 1a Cが/はAをBに反映する
- 1b AをBに反映するC
- 2 Aが/はBに反映される
- 2a Aが反映されるB
- 3 Aを/はBに反映させる
- 4 Bが/はAを反映する
- 4a Aを反映するB
Here apparently we are dealing with 1, more specifically, 1b. How the actual sentence is best rendered in English depends on context and style. に doesn't always have to become "in", but "in" is a good place to start. I am going to give you a couple more examples before we move on to your sentence at issue.
趣旨(A)を素案(B)に反映した意見(C) (source: 西宮市 official website)
(literally) Opinions that reflect the main point(s) in the draft
(Or in other words) Suggestions that allow the main points to be reflected in the draft; suggestions that show the main points reflected in the draft
レンタル傘の利用情報(A)をＳＮＳ(B)に反映するシステム(C) (特許庁 registered patent JP2012008614A)
System for incorporating usage information of rental umbrella into SNS (official translation)
長年培ってきた電源のアプリケーションを含めたノウハウ(A)を設計(B)に反映したプラズマ負荷に最適な信頼性の高い電源(C)です。 (source)
These highly reliable power generators have been optimized for plasma loads with a design that reflects our many years of knowledge that includes power generator applications. (official translation)
I understand where your confusion is coming from. When you try to render a sentence following this structure in a different language, B and C both seem to do the "reflecting" or at least both seem capable of reflecting A. But as you can see from the examples, C always has more of an active role than B in causing or allowing the reflection of A.
賃金の伸びに物価の変動を反映した実質賃金
real wages that reflect price fluctuations in/in terms of/in the manner of/as indicated by wage growth
By the way, I disagree with the other answer. Pretty sure this に is a 格助詞.
Eddie Kal explained the word 反映する and associated に very well. I just would like to add a few points.
First, 伸び means increase or growth.
Second, I would say that the original text,
賃金の伸びに物価の変動を反映した実質賃金は前年同月比０・４％増と、５か月ぶりに上昇した。
is logically incorrect, strictly speaking, but that this template is commonly used in news reports. To be logically correct, it must be said as
名目賃金に物価の変動を反映した実質賃金は前年同月比０・４％増と、５か月ぶりに上昇した。
where 名目（めいもく）賃金 means the nominal wages (i.e., the face value of wages, or unadjusted raw data of wages), or as
賃金の伸びに物価の変動を反映した実質賃金の増加額は前年同月比０・４％であった。実質賃金は５か月ぶりに上昇した。
In other words, the increase of the wages face value should correspond to the increase of the real wages, rather than the real wages itself. I'm afraid that, if you analyzed the text carefully and rigorously, then you might have got stuck at this type of skewing of logic.
Third, you could translate 反映した as 'adjusted' in this case. I think you can translate, for example, '実質賃金とは、名目賃金に物価の変動を反映したものである。' to 'Real wages is the nominal wages adjusted by changes of the prices.'
