-------------------------------------------------------------------------------- log: C:\Documents and Settings\Patricia_Anderson\My Documents\ECON 20\In > Class\nov22.log log type: text opened on: 22 Nov 2002, 11:14:19 . use intdef . desc Contains data from intdef.dta obs: 49 vars: 13 24 Jan 2000 22:55 size: 2,499 (100.0% of memory free) ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- year int %9.0g 1948-1996 i3 float %9.0g 3 mo. T bill rate inf float %9.0g CPI inf. rate rec float %9.0g fed. receipts, % GDP out float %9.0g fed. outlays, % GDP def float %9.0g out - rec i3_1 float %9.0g i3[_n-1] inf_1 float %9.0g inf[_n-1] def_1 float %9.0g def[_n-1] ci3 float %9.0g i3 - i3_1 cinf float %9.0g inf - inf_1 cdef float %9.0g def - def_1 y77 byte %9.0g =1 year >= 1977; change in FY ------------------------------------------------------------------------------- Sorted by: . **look at receipts and outlays over time . graph rec out year . reg out rec Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 1, 47) = 28.49 Model | 114.5505 1 114.5505 Prob > F = 0.0000 Residual | 188.946255 47 4.02013308 R-squared = 0.3774 -------------+------------------------------ Adj R-squared = 0.3642 Total | 303.496755 48 6.32284906 Root MSE = 2.005 ------------------------------------------------------------------------------ out | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- rec | 1.458954 .2733148 5.34 0.000 .9091151 2.008792 _cons | -6.334109 4.884008 -1.30 0.201 -16.15947 3.491249 ------------------------------------------------------------------------------ . **create a simple time trend . gen t=year-1947 . **add a trend . reg out rec t Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 2, 46) = 62.41 Model | 221.769792 2 110.884896 Prob > F = 0.0000 Residual | 81.7269626 46 1.7766731 R-squared = 0.7307 -------------+------------------------------ Adj R-squared = 0.7190 Total | 303.496755 48 6.32284906 Root MSE = 1.3329 ------------------------------------------------------------------------------ out | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- rec | .5950867 .2130249 2.79 0.008 .1662898 1.023884 t | .1226329 .0157861 7.77 0.000 .0908572 .1544087 _cons | 6.010395 3.614837 1.66 0.103 -1.265893 13.28668 ------------------------------------------------------------------------------ . **let's detrend the data . reg out t Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 1, 47) = 102.22 Model | 207.905197 1 207.905197 Prob > F = 0.0000 Residual | 95.5915578 47 2.03386293 R-squared = 0.6850 -------------+------------------------------ Adj R-squared = 0.6783 Total | 303.496755 48 6.32284906 Root MSE = 1.4261 ------------------------------------------------------------------------------ out | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- t | .1456531 .0144061 10.11 0.000 .1166716 .1746345 _cons | 16.05051 .413785 38.79 0.000 15.21808 16.88294 ------------------------------------------------------------------------------ . predict outdetrend, resid . reg rec t Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 1, 47) = 17.60 Model | 14.6649795 1 14.6649795 Prob > F = 0.0001 Residual | 39.1513471 47 .833007385 R-squared = 0.2725 -------------+------------------------------ Adj R-squared = 0.2570 Total | 53.8163266 48 1.12117347 Root MSE = .91269 ------------------------------------------------------------------------------ rec | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- t | .0386837 .0092196 4.20 0.000 .0201363 .0572311 _cons | 16.87168 .2648124 63.71 0.000 16.33895 17.40442 ------------------------------------------------------------------------------ . predict recdetrend, resid . reg outdetrend recdetrend Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 1, 47) = 7.97 Model | 13.864595 1 13.864595 Prob > F = 0.0069 Residual | 81.7269627 47 1.73887155 R-squared = 0.1450 -------------+------------------------------ Adj R-squared = 0.1268 Total | 95.5915577 48 1.99149079 Root MSE = 1.3187 ------------------------------------------------------------------------------ outdetrend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- recdetrend | .5950867 .2107465 2.82 0.007 .1711194 1.019054 _cons | -2.88e-09 .1883804 -0.00 1.000 -.3789725 .3789725 ------------------------------------------------------------------------------ . **suppose the trend is quadratic . reg out rec t Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 2, 46) = 62.41 Model | 221.769792 2 110.884896 Prob > F = 0.0000 Residual | 81.7269626 46 1.7766731 R-squared = 0.7307 -------------+------------------------------ Adj R-squared = 0.7190 Total | 303.496755 48 6.32284906 Root MSE = 1.3329 ------------------------------------------------------------------------------ out | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- rec | .5950867 .2130249 2.79 0.008 .1662898 1.023884 t | .1226329 .0157861 7.77 0.000 .0908572 .1544087 _cons | 6.010395 3.614837 1.66 0.103 -1.265893 13.28668 ------------------------------------------------------------------------------ . gen tsq=t^2 . reg out rec t tsq Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 3, 45) = 48.25 Model | 231.523178 3 77.1743925 Prob > F = 0.0000 Residual | 71.9735772 45 1.59941283 R-squared = 0.7629 -------------+------------------------------ Adj R-squared = 0.7470 Total | 303.496755 48 6.32284906 Root MSE = 1.2647 ------------------------------------------------------------------------------ out | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- rec | .4430179 .2112917 2.10 0.042 .0174545 .8685813 t | .2589588 .0572011 4.53 0.000 .1437499 .3741678 tsq | -.0026089 .0010565 -2.47 0.017 -.0047367 -.000481 _cons | 7.467283 3.480143 2.15 0.037 .4579156 14.47665 ------------------------------------------------------------------------------ . gen tcub=t^3 . reg out rec t tsq tcub Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 4, 44) = 36.75 Model | 233.574941 4 58.3937352 Prob > F = 0.0000 Residual | 69.921814 44 1.58913214 R-squared = 0.7696 -------------+------------------------------ Adj R-squared = 0.7487 Total | 303.496755 48 6.32284906 Root MSE = 1.2606 ------------------------------------------------------------------------------ out | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- rec | .5016181 .2168339 2.31 0.025 .0646182 .938618 t | .10843 .1442246 0.75 0.456 -.1822357 .3990956 tsq | .0046039 .0064345 0.72 0.478 -.008364 .0175718 tcub | -.000095 .0000836 -1.14 0.262 -.0002636 .0000735 _cons | 7.144954 3.480519 2.05 0.046 .1304279 14.15948 ------------------------------------------------------------------------------ . log close log: C:\Documents and Settings\Patricia_Anderson\My Documents\ECON 20\I > nClass\nov22.log log type: text closed on: 22 Nov 2002, 12:24:56 -------------------------------------------------------------------------------