I am trying to estimate a partial adjustment model but my book doesn't give any guidance.
Do I need another variable for Y_t-Y_{t-1} if so how is it used in the regression?

<br />
Y^{*}_{i}=\alpha+\beta_{0}X_t+u_t<br />

The data set I am working with is:
<br />
\begin{bmatrix}<br />
YR       &     Y     &       X\\<br />
1970	  &   36.99	& 52.805\\<br />
1971	 &    33.6    & 55.906\\<br />
1972	  &   35.42	& 63.027\\<br />
1973	  &   42.35	& 72.931\\<br />
1974   &    52.48	& 84.79\\<br />
1975	 &    53.66	& 86.589\\<br />
1976	 &    58.53	& 98.797\\<br />
1977	 &    67.48	& 113.201<br />
\end{bmatrix}<br />
<br />
\begin{bmatrix}<br />
1978	  &   78.13	& 126.905\\<br />
1979	  &   95.13	& 143.936\\<br />
1980	  &   112.6	& 154.391\\<br />
1981	 &   128.68	& 168.129\\<br />
1982	 &   123.97	& 163.351\\<br />
1983   &   117.35	& 172.547\\<br />
1984	  &  139.61	& 190.682\\<br />
\end{bmatrix}<br />
<br />
\begin{bmatrix}<br />
1985	  &  152.88	& 194.538\\<br />
1986	  &  137.95	& 194.657\\<br />
1987	   & 141.06	& 206.326\\<br />
1988	 &   163.45	& 223.541\\<br />
1989	  &  183.8	& 232.724\\<br />
1990	 &   192.61 &	239.459\\<br />
1991    &  182.81 &	235.142<br />
\end{bmatrix}<br />