If you need the variable spacing from row to row, then add an extra column to hold the line spacing commands:

\documentclass{article}
\usepackage{array}
\begin{document}
\begin{table}[htp]
\begin{center}
\caption{Data Units, Sources, and Dates}
\begin{tabular}{| *4{>{\centering\arraybackslash}m{1in}|} @{}m{0pt}@{}}
\hline
\textbf{Variable} & \textbf{Dates} & \textbf{Units} &
\textbf{Source} &\\[2ex]
\hline
\textbf{Nominal Physical Capital Stock} & 1950-1990 & Billions
US\$ & Nehru and Dhareshwar (1993) &\\[0ex]
\hline
\textbf{Total Population} & 1950-1990 & Billions & Nehru and
Dhareshwar (1993) &\\[0ex]
\hline
\textbf{Nominal GDP} & 1950-1990 & Billions US\$ & PWT &\\[5ex]
\hline
\textbf{Real GDP per capita} & 1950-1990 & 2005 US\$ per capita &
PWT &\\[5ex]
\hline
\end{tabular}
\label{tabular:UKJPNdata}
\end{center}
\end{table}
\end{document}
You can visualise why this is helping by placing a \vrule at the end of each final cell:

\documentclass{article}
\usepackage{array}
\newcommand{\myrule}{\vrule width 3pt}
\begin{document}
\begin{table}[htp]
\begin{center}
\caption{Data Units, Sources, and Dates}
\begin{tabular}{| *4{>{\centering\arraybackslash}m{1in}|}}
\hline
\textbf{Variable} & \textbf{Dates} & \textbf{Units} &
\textbf{Source} \myrule\\[2ex]
\hline
\textbf{Nominal Physical Capital Stock} & 1950-1990 & Billions
US\$ & Nehru and Dhareshwar (1993) \myrule\\[0ex]
\hline
\textbf{Total Population} & 1950-1990 & Billions & Nehru and
Dhareshwar (1993) \myrule\\[0ex]
\hline
\textbf{Nominal GDP} & 1950-1990 & Billions US\$ & PWT \myrule\\[5ex]
\hline
\textbf{Real GDP per capita} & 1950-1990 & 2005 US\$ per capita &
PWT \myrule\\[5ex]
\hline
\end{tabular}
\label{tabular:UKJPNdata}
\end{center}
\end{table}
\begin{table}[htp]
\begin{center}
\caption{Data Units, Sources, and Dates}
\begin{tabular}{| *4{>{\centering\arraybackslash}m{1in}|} @{}m{0pt}@{}}
\hline
\textbf{Variable} & \textbf{Dates} & \textbf{Units} &
\textbf{Source} &\myrule\\[2ex]
\hline
\textbf{Nominal Physical Capital Stock} & 1950-1990 & Billions
US\$ & Nehru and Dhareshwar (1993) &\myrule\\[0ex]
\hline
\textbf{Total Population} & 1950-1990 & Billions & Nehru and
Dhareshwar (1993) &\myrule\\[0ex]
\hline
\textbf{Nominal GDP} & 1950-1990 & Billions US\$ & PWT &\myrule\\[5ex]
\hline
\textbf{Real GDP per capita} & 1950-1990 & 2005 US\$ per capita &
PWT &\myrule\\[5ex]
\hline
\end{tabular}
\label{tabular:UKJPNdata}
\end{center}
\end{table}
\end{document}
From this you can see that the extra depth being added by at the end of lines is on the final line of the cell's paragraph.
This solution is a variation of https://tex.stackexchange.com/a/94717/15925 by David Carlisle; in particular a different format for the last column is given, as the other solution adding an l column happens not to work in this case.
\bf, please see Does it matter if I use\textitor\it,\bfseriesor\bf, etc. and Will two-letter font style commands (\bf,\it, …) ever be resurrected in LaTeX? Also, in terms of horizontal alignment, see Should I use\centeror\centeringfor figures and tables? – Werner Aug 07 '13 at 05:09