Record three quotations from a study Bible and a commentary or two from your Five Horizons bibliography to help you interpret the phrase “paneled houses” (Hag 1:4).
"Possibly internal wood lining walls or ceilings (cf. 1 Kgs 6:9; 7:3,7; Jer 22:14)" (NIV Zondervan Study Bible, 1853).
"In v. 4 Haggai speaks of the “covered” houses in which the people live. The specific nuance of sĕpûnîm in this description is not entirely clear. Is the prophet referring to lavish expenditures for houses with interior paneling made of costly material (so apparently NIV), and if so, how does this relate to the economic hard times in which they were living? Given the mess the economy was in, as described in vv. 5–11, one wonders where money for such elaborate spending would have come from. Or does Haggai merely mean houses that are “roofed,” in contrast to the demolished temple structure that had no such cover? The Hebrew word sĕpûnîm in v. 4 has been understood both ways. ... The word sĕpûnîm in Hag 1:4 likely refers to the covering of interior walls with paneling, having in mind primarily the practice of the well-to-do few rather than that of the financially hard-pressed majority. It may be significant in this regard that it is the governor and the high priest who are specifically singled out in this first sermon (1:1). Haggai’s point is that while some of the people live in comfortable, convenient, and even lavishly appointed dwellings, the temple of God by contrast lies in rubble and is the object of disinterest and neglect on the part of the people" (Taylor and Clendenen, Haggai, Malachi, 123-24).
"A major problem concerns the meaning of sep̱ûnîm. The word is a Qal passive participle from the root sāp̱an, which means 'to cover,' 'to roof in,' 'to panel.' Thus the expression beḇāttêḵem sep̱ûnîm can be rendered: 'your houses (that are) covered/roofed/paneled.' The first and last possibilities suggest the adorning of the houses with wood paneling. In this sense the word is used in 1 K. 7:7 (Solomon’s throne hall was 'covered' [NIV], 'finished' [RSV], had 'cedar panels' [TEV]) and Jer. 22:14.
"Concerning Jehoahaz, one of the evil kings of Judah, Jer. 22:14 states that he built himself a palace with spacious rooms and large windows, 'paneling it with cedar' (RSV). In 1 K. 6:15 it is said that Solomon decorated the interior walls of the temple, 'paneling them from the floor of the temple to the ceiling' (NIV). The word translated 'paneling,' however, is not sāp̱an but sāp̱â. The custom of decorating the inner walls by applying panels of cedar to cover them cannot be denied, although it seems that it was restricted to large and expensive buildings, for example, the temple and the palaces of kings. In Haggai the point of reference could have been either the decoration or the finishing of the houses. On the one hand the people could have decorated their houses with excessive wood supplies, while that specific commodity was totally absent as far as the temple was concerned (cf. v. 8). On the other hand the point of comparison could have been the completion of the houses, by providing the necessary roofs, while the temple still remained a ruin. The ancient versions (Aquila, LXX, Vulg.) seem to support the notion of the roofing-in of the houses. Perhaps both points of reference must be considered in trying to explain the prophet’s argument. He is contrasting their total lack of concern in regard to the house of the Lord with their zeal for their own houses. They had both the time and the means to decorate (to cover/ panel) or to complete (to roof-in) their houses, while the required building material for the temple still had to be gathered, and the temple itself remained a ruin!
"We agree with some scholars that we must not overestimate the general conditions of the dwellings at that time. The people were experiencing adverse economical circumstances; Jerusalem seemed to have had only a small number of inhabitants (Zech. 1:16), even seventy-five years later (Neh. 7:4). The point of the argument, however, is that the people have exerted themselves literally to 'run' on behalf of their own houses (v. 9), while nothing was done to rebuild the temple" (Verhoef, The Books of Haggai and Malachi, 58-59).
Summarize what you conclude that "paneled houses" refers to.
Whether or not it refers to extremely ornate decorating, clearly the people prioritized using wood to complete or beautify their houses rather than the temple. So it least refers to completed houses—while the temple lay in ruins.