Attributive だろう


I came across this sentence (下町ロケット, p.239):

> 「どうだ、そろそろウチに戻ってこないか」  
>  そんなことをいいはじめたのは、六十五歳を過ぎ、体力的な衰えを **感じはじめただろう頃だ** 。

Meaning-wise, it seems hard to imagine it means anything other than
感じはじめた頃だろう. However, I wonder, is there is a slight difference in nuance, or
something else that would have made the author choose this rare (at least I
don't think I've seen it before) usage of だろう?

* * *

**和訳**

この文章に出くわしました：（下町ロケットp.239）

> 「どうだ、そろそろウチに戻ってこないか」  
>  そんなことをいいはじめたのは、六十五歳を過ぎ、体力的な衰えを **感じはじめただろう頃だ** 。

意味的には、「感じはじめた頃だろう」と同じだと思っていますが、これほど珍しい（少なくとも私は見たことのない）「だろう」の使い方をする理由（ニュアンスの違いなど）はありますか。




I think there is a slight difference in what the uncertainty is about:

>   1. … 六十五歳を過ぎ、<unsure>体力的な衰えを感じはじめた</unsure> **だろう** 頃だ。
>   2. … <unsure>六十五歳を過ぎ、体力的な衰えを感じはじめた頃</unsure> **だろう** 。
>

In #1, the uncertainty is less about the actual time frame, and more about
what their physical condition had been. In #2, it seems that the uncertainty
is mainly about the time frame.

Likewise, in the sentences below, #1 is unsure whether the children were
hungry, while #2 is unsure whether these children had it worst:

>   1. いちばん大変だったのは、お腹が空いていた **であろう** 子供たちだ。
>   2. いちばん大変だったのは、お腹が空いていた子供たち **であろう** 。
>

* * *

I did not know that this use of `だろう` is technically incorrect and should be
`であろう` instead (as brought up by xeta217 in the comments). I could also find
[one page](http://www2.dokkyo.ac.jp/~japan/japanese/sub1/sub1-8.htm) online
that agrees with this rule. However, there are probably
[many](https://goo.gl/dQ2dg1) [other](https://goo.gl/HvYzDd)
[books](https://goo.gl/Sd5096) that use phrases like だろう頃に, so it may be that
this rule is not widely known, or debatable.




I think there is a slight difference in what the uncertainty is about:

>   1. … 六十五歳を過ぎ、<unsure>体力的な衰えを感じはじめた</unsure> **だろう** 頃だ。
>   2. … <unsure>六十五歳を過ぎ、体力的な衰えを感じはじめた頃</unsure> **だろう** 。
>

In #1, the uncertainty is less about the actual time frame, and more about
what their physical condition had been. In #2, it seems that the uncertainty
is mainly about the time frame.

Likewise, in the sentences below, #1 is unsure whether the children were
hungry, while #2 is unsure whether these children had it worst:

>   1. いちばん大変だったのは、お腹が空いていた **であろう** 子供たちだ。
>   2. いちばん大変だったのは、お腹が空いていた子供たち **であろう** 。
>

* * *

I did not know that this use of `だろう` is technically incorrect and should be
`であろう` instead (as brought up by xeta217 in the comments). I could also find
[one page](http://www2.dokkyo.ac.jp/~japan/japanese/sub1/sub1-8.htm) online
that agrees with this rule. However, there are probably
[many](https://goo.gl/dQ2dg1) [other](https://goo.gl/HvYzDd)
[books](https://goo.gl/Sd5096) that use phrases like だろう頃に, so it may be that
this rule is not widely known, or debatable.

