Solutions to Computer Exercises in Assignment 4

C10.10
(i)

. tsset t
        time variable:  t, 1948 to 2003

. correlate inft deft
(obs=56)

             |     inft     deft
-------------+------------------
        inft |   1.0000
        deft |   0.0975   1.0000

The correlation is small (.098). From a statistical point of view, this implies that the parameters of the model can be estimated more
precisely.

(ii)

. gen inft1 = L.inft

. gen deft1 = L.deft

. reg i3t inft deft inft1 deft1

      Source |       SS       df       MS              Number of obs =      55
-------------+------------------------------           F(  4,    50) =   27.18
       Model |  299.516929     4  74.8792323           Prob > F      =  0.0000
    Residual |  137.722545    50   2.7544509           R-squared     =  0.6850
-------------+------------------------------           Adj R-squared =  0.6598
       Total |  437.239474    54   8.0970273           Root MSE      =  1.6597

------------------------------------------------------------------------------
         i3t |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        inft |   .3426159   .1253973     2.73   0.009      .090748    .5944837
        deft |  -.1896663   .2212844    -0.86   0.395    -.6341291    .2547964
       inft1 |   .3819795   .1335847     2.86   0.006     .1136667    .6502922
       deft1 |   .5692731   .1967706     2.89   0.006     .1740477    .9644985
       _cons |   1.611482   .4007615     4.02   0.000     .8065291    2.416435
------------------------------------------------------------------------------

 

(iii) The estimated long-run propensity is .343 + .382 = .725 which is larger than .606.

(iv)

. test inft1 deft1

 ( 1)  inft1 = 0
 ( 2)  deft1 = 0

       F(  2,    50) =    5.22
            Prob > F =    0.0087

The F-statistic is 5.22 (p-value = .009). Therefore, the lagged values of inflation and deficit are joinlty significant at 5% level.
 

C11.8
(i)

. tsset t

. gen unemt1 = L.unemt

. gen inft1 = L.inft

. reg unemt unemt1


      Source |       SS       df       MS              Number of obs =      55
-------------+------------------------------           F(  1,    53) =   69.17
       Model |  69.0545684     1  69.0545684           Prob > F      =  0.0000
    Residual |  52.9097954    53  .998298026           R-squared     =  0.5662
-------------+------------------------------           Adj R-squared =  0.5580
       Total |  121.964364    54  2.25859933           Root MSE      =  .99915

------------------------------------------------------------------------------
       unemt |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      unemt1 |   .7425353   .0892793     8.32   0.000     .5634636     .921607
       _cons |   1.488356   .5199931     2.86   0.006     .4453819     2.53133
------------------------------------------------------------------------------

The predicted unemployment rate for 2004 is 1.49 + .742*6 = 5.94, which overpredicts the actual rate of 5.5.

(ii)

. reg unemt unemt1 inft1

      Source |       SS       df       MS              Number of obs =      55
-------------+------------------------------           F(  2,    52) =   59.57
       Model |  84.9046984     2  42.4523492           Prob > F      =  0.0000
    Residual |  37.0596653    52  .712685871           R-squared     =  0.6961
-------------+------------------------------           Adj R-squared =  0.6845
       Total |  121.964364    54  2.25859933           Root MSE      =  .84421

------------------------------------------------------------------------------
       unemt |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      unemt1 |   .6496298   .0779645     8.33   0.000     .4931825     .806077
       inft1 |   .1829481   .0387936     4.72   0.000     .1051029    .2607932
       _cons |   1.295166   .4412616     2.94   0.005     .4097097    2.180622
------------------------------------------------------------------------------

The regression results show that lagged inflation is statistically significant.

(iii) Predicted unemployment rate for 1997 is 1.295 + .650*6 + .183*2.3 = 5.62 which still overpredicts the actual rate but the magnitude of overprediction is slightly smaller.