How do I align my column values so that they are all under each other without the negative shifting the number values?

You should use booktabs for better rules and above all siunitx for numeric tables.

I guessed at a possible definition of \scell.

\documentclass{article}
\usepackage{siunitx,booktabs,caption}
\usepackage{rotating}

\newcommand{\scell}[1]{{\begin{tabular}[t]{@{}c@{}}#1\end{tabular}}}

\begin{document}

\begin{sidewaystable}
\footnotesize

\caption{Estimated Production Elasticities, Returns to Scale, and Rates of Techni Variables)}
\label{t52}

\begin{tabular*}{\textwidth}{
  @{\extracolsep{\fill}}
  l
  S[table-format=-1.1]
  *{8}{S[table-format=-1.2]}
  @{}
}
\toprule
\scell{Period 2 vs. \\ Period 1} &
\scell{Difference\\ in Growth\\ Rate} &
\scell{Change in \\Elasticity\\ of Output\\ wrt K} &
\scell{Change in \\Elasticity\\ of Output\\ wrt L} &
\scell{Change in \\Elasticity\\ of Output\\ wrt H} &
\scell{Change in \\ Growth Rate\\ of K} &
\scell{Change in\\ Growth Rate \\ of L} &
\scell{Change in \\Growth Rate\\ of H} &
\scell{dy/dx \\ oil} &
\scell{Local\\ Technical\\ Process} \\
\midrule
Canada     & -1.4 & -0.22 &  0.18 & -0.08 & -0.36 & -0.21 & -0.14 & -0.31 & -0.24\\
France     & -3.1 & -0.44 & -0.02 & -0.09 & -0.70 & -0.65 & -0.01 & -0.43 & -0.80\\
W. Germany & -2.9 & -0.44 & -0.06 & -0.04 & -0.90 & -0.30 &  0.12 & -0.42 & -0.87\\
Italy      & -2.4 & -0.40 &  0.01 & -0.07 & -0.82 &  0.54 &  0.06 & -0.94 & -0.75\\
Japan      & -5.6 & -0.89 &  0.07 & -0.11 & -1.25 & -0.28 & -0.17 & -1.78 & -1.15\\
U.K.       & -2.1 & -0.09 & -0.01 & -0.03 &  0.08 & -0.59 &  0.04 & -0.95 & -0.52\\
U.S.       & -1.5 & -0.19 &  0.15 & -0.06 & -0.52 &  0.18 &  0.00 & -0.61 & -0.41\\
\midrule
\scell{Period 3 vs. \\ Period 2} &
\scell{Difference\\ in Growth\\ Rate} &
\scell{Change in \\Elasticity\\ of Output\\ wrt K} &
\scell{Change in \\Elasticity\\ of Output\\ wrt L} &
\scell{Change in \\Elasticity\\ of Output\\ wrt H} &
\scell{Change in \\ Growth Rate\\ of K} &
\scell{Change in\\ Growth Rate \\ of L} &
\scell{Change in \\Growth Rate\\ of H} &
\scell{dy/dx \\ oil} &
\scell{Local\\ Technical\\ Process} \\ \hline
Canada     & -0.6 & -0.16 &  0.14 & -0.07 & -0.40 & -0.14 & -0.03 &  0.31 & -0.26\\
France     & -0.4 & -0.30 & -0.02 & -0.08 & -0.18 &  0.69 & -0.07 &  0.43 & -0.82\\
W. Germany &  1.1 & -0.17 &  0.00 & -0.03 &  0.10 &  1.29 & -0.07 &  0.42 & -0.47\\
Italy      & -0.8 & -0.29 &  0.05 & -0.08 & -0.25 & -0.14 & -0.10 &  0.94 & -0.90\\
Japan      & -1.1 & -0.58 &  0.01 & -0.05 & -0.50 & -0.47 & -0.13 &  1.78 & -1.19\\
U.K.       &  1.0 & -0.16 & -0.01 & -0.04 &  0.19 &  0.76 & -0.03 &  0.95 & -0.64\\
U.S.       & -0.1 & -0.12 &  0.13 & -0.05 &  0.06 & -0.31 & -0.07 &  0.61 & -0.35\\
\bottomrule
\end{tabular*}

\end{sidewaystable}

\end{document}

As starting point is used @egreg answer ... with employed two additional packages: makecell and multirow and a little bit different table design:

\documentclass{article}
\usepackage{rotating}
\usepackage{booktabs, makecell, multirow}
\usepackage{siunitx}

\begin{document}
\begin{sidewaystable}
    \centering
\caption{Estimated Production Elasticities, Returns to Scale, and Rates of Techni Variables}
\label{t52}
    \renewcommand{\arraystretch}{1.4}
    \sisetup{table-format=-1.2, table-column-width=4em}
\begin{tabular}{ @{} l *{9}{S}  @{}}
    \toprule
\multirow{2.4}{*}{State}   
    &   
{\multirow{2.4}{*}{\makecell{Difference\\ in Growth\\ Rate}}} 
        &   \multicolumn{3}{c}{Change in Elasticity of Output}
            &   \multicolumn{3}{c}{Change in Growth Rate}
                &   {\multirow{2.4}{*}{\makecell{dy/dx\\ oil}}} 
                    &   {\multirow{2.4}{*}{\makecell{Local\\ Technical\\ Process}}}    \\
    \cmidrule(lr){3-5}\cmidrule(lr){6-8}
    &   &   {wrt K}
            &   {wrt L} 
                &   {wrt H} 
                    &   {of K}
                        &   {of L}
                            &   {of H}
                                &   &           \\
    \midrule
\multicolumn{10}{c}{Period 2 versus Period 1}   \\ 
    \midrule
Canada      & -1.4  & -0.22 &  0.18 & -0.08 & -0.36 & -0.21 & -0.14 & -0.31 & -0.24\\
France      & -3.1  & -0.44 & -0.02 & -0.09 & -0.70 & -0.65 & -0.01 & -0.43 & -0.80\\
W. Germany  & -2.9  & -0.44 & -0.06 & -0.04 & -0.90 & -0.30 &  0.12 & -0.42 & -0.87\\
Italy       & -2.4  & -0.40 &  0.01 & -0.07 & -0.82 &  0.54 &  0.06 & -0.94 & -0.75\\
Japan       & -5.6  & -0.89 &  0.07 & -0.11 & -1.25 & -0.28 & -0.17 & -1.78 & -1.15\\
U.K.        & -2.1  & -0.09 & -0.01 & -0.03 &  0.08 & -0.59 &  0.04 & -0.95 & -0.52\\
U.S.        & -1.5  & -0.19 &  0.15 & -0.06 & -0.52 &  0.18 &  0.00 & -0.61 & -0.41\\
    \midrule
\multicolumn{10}{c}{Period 3 versus Period 2}   \\
    \midrule
Canada      & -0.6  & -0.16 &  0.14 & -0.07 & -0.40 & -0.14 & -0.03 &  0.31 & -0.26\\
France      & -0.4  & -0.30 & -0.02 & -0.08 & -0.18 &  0.69 & -0.07 &  0.43 & -0.82\\
W. Germany  &  1.1  & -0.17 &  0.00 & -0.03 &  0.10 &  1.29 & -0.07 &  0.42 & -0.47\\
Italy       & -0.8  & -0.29 &  0.05 & -0.08 & -0.25 & -0.14 & -0.10 &  0.94 & -0.90\\
Japan       & -1.1  & -0.58 &  0.01 & -0.05 & -0.50 & -0.47 & -0.13 &  1.78 & -1.19\\
U.K.        &  1.0  & -0.16 & -0.01 & -0.04 &  0.19 &  0.76 & -0.03 &  0.95 & -0.64\\
U.S.        & -0.1  & -0.12 &  0.13 & -0.05 &  0.06 & -0.31 & -0.07 &  0.61 & -0.35\\
    \bottomrule
\end{tabular}
    \end{sidewaystable}
\end{document}