Not that I put a great deal of confidence in regression analysis,
but I still thought that these results that I got on U.S.
inflation and unemployment data since 1961 were kind of
interesting.  Most of this should be pretty self-explanatory
(if you are familiar with regression analysis, at least);
the Party variable =1 in years with Democratic presidents and
=0 in years with Republican presidents.

Overall, they all seem to indicate a vertical long-run Phillips curve,
with the "long-run" being about a year.

Comments, anyone?
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Regressing unemployment on constant and inflation yields
Beta           =  5.617   0.105 
Standard errors=  0.522   0.088 
R-squared      =  0.045 

Regressing inflation on constant and unemployment yields
Beta           =  2.382   0.431 
Standard errors=  2.288   0.361 
R-squared      =  0.045 

Regressing unemployment on constant, inflation,
            lagged inflation, and lagged unemployment yields
Beta           =  1.372  -0.171   0.364   0.620 
Standard errors=  0.532   0.066   0.067   0.082 
R-squared      =  0.853 
Implicit estimate of natural rate of unemployment =   3.611 

Regressing unemployment on constant, inflation, and lagged inflation
Beta           =  5.003  -0.347   0.573 
Standard errors=  0.402   0.108   0.105 
R-squared      =  0.540 

Regressing unemployment on constant, inflation, and lagged unemployment
Beta           =  0.561   0.127   0.805 
Standard errors=  0.727   0.053   0.106 
R-squared      =  0.691 
Implicit estimate of natural rate of unemployment =   2.870 

Regressing unemployment on constant, inflation, inf(t-1), and inf(t-2)
Beta           =  4.512  -0.197   0.197   0.321 
Standard errors=  0.405   0.108   0.156   0.106 
R-squared      =  0.660 

Regressing unemployment on constant and lagged unemployment
Beta           =  1.247   0.800 
Standard errors=  0.720   0.114 
R-squared      =  0.628 
Implicit estimate of natural rate of unemployment =   6.219 

Regressing unemployment on constant, inflation, Party, inf(t-1), un(t-1)
Beta           =  1.563  -0.153  -0.297   0.338   0.612 
Standard errors=  0.556   0.068   0.261   0.070   0.082 
R-squared      =  0.860 
Implicit estimate of natural rate of unemployment =   4.026 

Regressing unemployment on constant, Party, and lagged unemployment
Beta           =  1.831  -0.744   0.747 
Standard errors=  0.726   0.355   0.109 
R-squared      =  0.677 
Implicit estimate of natural rate of unemployment =   7.240 

Regressing unemployment on constant, Party, lagged Party, inflation, and
lagged
 unemployment
Beta           =  1.346  -0.308  -0.505   0.127   0.726 
Standard errors=  0.777   0.545   0.557   0.051   0.108 
R-squared      =  0.742 
Implicit estimate of natural rate of unemployment =   4.915 

Regressing inflation on constant, lagged inflation, and unemployment
yields
Beta           =  4.762   1.016  -0.780 
Standard errors=  1.249   0.120   0.242 
R-squared      =  0.735 

Regressing unemployment on constant, inflation-lagged inflation,
 and lagged unemployment yields
Beta           =  2.091  -0.263   0.664 
Standard errors=  0.703   0.087   0.112 
R-squared      =  0.722 
Implicit estimate of natural rate of unemployment =   6.224 

Regressing unemployment on constant, inflation(t), inflation(t-1),
            inflation(t-2), unemployment(t-1), and unemployment(t-2)
yields
Beta           =  1.255  -0.210   0.420  -0.019   0.521   0.122 
Standard errors=  0.636   0.083   0.114   0.102   0.230   0.175 
R-squared      =  0.857 
Implicit estimate of natural rate of unemployment =   3.508