Macroeconomic Analysis
Econ 506, Nov. 3, 1998
C. Swanson
The econometrics of Output growth, money, interest rates and a
little bit of forecasting.
We begin with a procedure that picks out the important variables.
Throw everything in--RATS picks of the relevant variables:
The input:
stwise yg
#constant yg{1 to 6} m1g{1 to 6} m2g{1 to 6}
The output:
Dependent Variable YG - Estimation by Stepwise
Quarterly Data From 1963:04 To 1992:04
Usable Observations 117 Degrees of Freedom 110
Centered R**2 0.277103 R Bar **2 0.237672
Durbin-Watson Statistic 1.917220
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. YG{1} 0.158981115 0.087491983 1.81709 0.07192530
2. YG{2} 0.211943591 0.084501264 2.50817 0.01359496
3. YG{8} -0.191542655 0.084819503 -2.25824 0.02590364
4. YG{10} 0.203002078 0.084779910 2.39446 0.01833583
5. M1G{9} 0.016974769 0.011546261 1.47015 0.14437491
6. M1G{10} -0.027680742 0.011972755 -2.31198 0.02264085
7. M2G{1} 0.035696419 0.008326309 4.28718 0.00003898
Conclusion: M2 money growth, and output growth at one and two period lags seem
to be the most important variables. M1 growth at 9 and 10 quarter lags remain,
but these seem rather obscure, so we don't place a huge amount of weight on them.
********
Checking what factors that affect investment. Notice that investment growth
(ig) has been used (set ig = log(in)-log(in{1}) ).
We would find that current output growth is everthing. Note that for
forecasting, current values are useless.
Input:
linreg ig
#constant yg{0 to 6} ig{0 to 6}
Output (most of it):
Dependent Variable IG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 107
Centered R**2 0.740381 R Bar **2 0.708839
Durbin-Watson Statistic 2.002667
Q(30) 29.928220
Significance Level of Q 0.46933437
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant -0.01318823 0.00575869 -2.29015 0.02397416
2. YG 33.59040725 2.26966995 14.79969 0.00000000
3. YG{1} 4.86264822 4.10721448 1.18393 0.23906481
4. YG{2} -3.93515648 4.13146537 -0.95248 0.34299804
5. YG{3} -5.52380416 4.24074190 -1.30256 0.19552292
6. YG{4} 5.52212167 4.20045489 1.31465 0.19143893
7. YG{5} -6.97224349 4.09054239 -1.70448 0.09119376
8. YG{6} -4.90978894 4.18301968 -1.17374 0.24310405
9. IG{1} -0.00356343 0.09705684 -0.03671 0.97078075
10. IG{2} 0.01083358 0.09408760 0.11514 0.90854711
11. IG{3} 0.12251097 0.09612022 1.27456 0.20522608
12. IG{4} -0.11206451 0.09524194 -1.17663 0.24195424
13. IG{5} 0.03895678 0.09408902 0.41404 0.67967234
14. IG{6} 0.06873222 0.09543675 0.72019 0.47298076
**
Input:
Exclude
#yg{1 to 6} ig{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
YG Lag(s) 1 to 6
IG Lag(s) 1 to 6
F(12,107)= 1.77011 with Significance Level 0.06235343
*****
Let's get rid of current output growth.
Input:
linreg ig
#constant yg{1 to 6} ig{1 to 6}
Output:
Dependent Variable IG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 108
Centered R**2 0.208937 R Bar **2 0.121041
Durbin-Watson Statistic 1.975046
Q(30) 32.910890
Significance Level of Q 0.32642243
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant -0.00134704 0.00990851 -0.13595 0.89211528
2. YG{1} 22.00761323 6.84641888 3.21447 0.00172369
3. YG{2} 7.85600178 7.04356199 1.11535 0.26717824
4. YG{3} -9.28249352 7.35493831 -1.26208 0.20964001
5. YG{4} 7.97405339 7.29248705 1.09346 0.27662418
6. YG{5} -6.71661880 7.10713297 -0.94505 0.34674122
7. YG{6} -10.55778477 7.23756276 -1.45875 0.14753652
8. IG{1} -0.24501680 0.16623387 -1.47393 0.14340976
9. IG{2} -0.13818313 0.16253563 -0.85017 0.39711068
10. IG{3} 0.16396623 0.16693511 0.98222 0.32818898
11. IG{4} -0.12793384 0.16546957 -0.77316 0.44111880
12. IG{5} -0.05056366 0.16313871 -0.30994 0.75720176
13. IG{6} 0.25501475 0.16437005 1.55147 0.12371529
Some tests:
Input:
Exclude
#yg{2 to 6} ig{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
YG Lag(s) 2 to 6
IG Lag(s) 1 to 6
F(11,108)= 1.46775 with Significance Level 0.15421845
*****
Let's take a look at the effect of interest rates on investment.
Input:
linreg ig
#constant yg{1 to 6} ig{1 to 6} rr{1 to 6}
Output:
Dependent Variable IG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 102
Centered R**2 0.345224 R Bar **2 0.229675
Durbin-Watson Statistic 1.962602
Q(30) 35.638727
Significance Level of Q 0.22014314
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant 0.01845130 0.02261002 0.81607 0.41636322
2. YG{1} 14.40063804 6.83281573 2.10757 0.03751958
3. YG{2} 5.04938857 6.85354136 0.73676 0.46296189
4. YG{3} -7.45150848 7.15071605 -1.04206 0.29984530
5. YG{4} 8.10440540 7.08108036 1.14452 0.25508858
6. YG{5} -5.22626874 7.01298845 -0.74523 0.45784823
7. YG{6} -9.77930460 7.20487351 -1.35732 0.17767590
8. IG{1} -0.17971307 0.16457461 -1.09199 0.27741210
9. IG{2} -0.03732212 0.15901590 -0.23471 0.81490679
10. IG{3} 0.17758528 0.16248596 1.09293 0.27700043
11. IG{4} -0.06088759 0.16021006 -0.38005 0.70469965
12. IG{5} -0.06163377 0.15885388 -0.38799 0.69883175
13. IG{6} 0.22837208 0.15847224 1.44109 0.15262335
14. RR{1} 0.00808209 0.00523910 1.54265 0.12601288
15. RR{2} -0.02882940 0.00804348 -3.58419 0.00052043
16. RR{3} 0.01824888 0.00873132 2.09005 0.03910033
17. RR{4} -0.01064938 0.00890105 -1.19642 0.23430699
18. RR{5} 0.01228774 0.00869040 1.41394 0.16042322
19. RR{6} -0.00150768 0.00590593 -0.25528 0.79901883
***
We repeat some of the above tests, but this time with the real interest rate
included.
Input:
Exclude
#yg{3 to 6} ig{1 to 6} rr{4 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
YG Lag(s) 3 to 6
IG Lag(s) 1 to 6
RR Lag(s) 4 to 6
F(13,102)= 1.22833 with Significance Level 0.27048481
Conclusion: The significance level is well above 0.05. Tossing out all of
these variables is not a big problem, so we will, in the interest of
parsimony (whatever that is).
****
Testing whether money affects output.
First we kitchen sink the model--throw in everything.
Input:
linreg yg
#constant yg{1 to 6} m1g{1 to 6} m2g{1 to 6}
Output:
Dependent Variable YG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 102
Centered R**2 0.243530 R Bar **2 0.110035
Durbin-Watson Statistic 1.965984
Q(30) 33.302651
Significance Level of Q 0.30955941
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant -0.000299231 0.000388760 -0.76971 0.44325233
2. YG{1} 0.194366200 0.099143155 1.96046 0.05266961
3. YG{2} 0.184410580 0.103297670 1.78523 0.07719555
4. YG{3} 0.017008881 0.104636333 0.16255 0.87119251
5. YG{4} 0.037225282 0.103837898 0.35849 0.72071443
6. YG{5} -0.065251781 0.105420731 -0.61897 0.53731913
7. YG{6} 0.138689747 0.102157119 1.35761 0.17758279
8. M1G{1} 0.006317516 0.016650001 0.37943 0.70515706
9. M1G{2} 0.017006142 0.018917155 0.89898 0.37078069
10. M1G{3} -0.011649790 0.018972516 -0.61404 0.54055927
11. M1G{4} -0.006741859 0.018886219 -0.35697 0.72184992
12. M1G{5} 0.001094670 0.019106422 0.05729 0.95442364
13. M1G{6} 0.006963570 0.017539429 0.39702 0.69217948
14. M2G{1} 0.048737347 0.022093912 2.20592 0.02963381
15. M2G{2} -0.014904458 0.025296429 -0.58919 0.55703506
16. M2G{3} -0.001109713 0.025421411 -0.04365 0.96526660
17. M2G{4} -0.001861751 0.024805510 -0.07505 0.94031879
18. M2G{5} 0.011212289 0.024942275 0.44953 0.65400351
19. M2G{6} -0.014452395 0.022573061 -0.64025 0.52344593
**
Some exclusion tests.
Input:
Exclude
#m1g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M1G Lag(s) 1 to 6
F(6,102)= 0.30824 with Significance Level 0.9313860
Conclusion: There does not seem to be much of problem with tossing out
M1 growth.
***
Let's try M2 growth.
Input:
Exclude
#m2g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M2G Lag(s) 1 to 6
F(6,102)= 1.24125 with Significance Level 0.29162938
Conclusion: There does not seem to be a problem with ignoring M2 growth
either.
***
Okay, let's toss out all forms of money and see if we have a problem.
Input:
Exclude
#m1g{1 to 6} m2g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M1G Lag(s) 1 to 6
M2G Lag(s) 1 to 6
F(12,102)= 1.22450 with Significance Level 0.27677641
Conclusion: That is not a problem either. The significance
level is well above 0.05. The data could have been generated
with probability 0.27 even if all the money coefficents had
been zero. It seems that money is not much help in making
forecasts.
***
So, we'll have the best model for forecasting:
Input:
linreg yg
#constant yg{1 2}
Output:
Dependent Variable YG - Estimation by Least Squares
Quarterly Data From 1961:04 To 1992:04
Usable Observations 125 Degrees of Freedom 122
Centered R**2 0.127974 R Bar **2 0.113678
Durbin-Watson Statistic 1.985505
Q(31) 38.676179
Significance Level of Q 0.16169264
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant 0.0005018088 0.0001345099 3.73065 0.00029121
2. YG{1} 0.2635343468 0.0891317841 2.95668 0.00373443
3. YG{2} 0.1695922382 0.0888708277 1.90830 0.05870213
***
It behooves us to go back and check the whether M1 and M2 have any effect when
the number of lags on yg have been truncated down to two lags.
Input:
linreg yg
#constant yg{1 2} m1g{1 to 6} m2g{1 to 6}
Output:
Dependent Variable YG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 106
Centered R**2 0.226389 R Bar **2 0.124213
Durbin-Watson Statistic 1.978717
Q(30) 36.845628
Significance Level of Q 0.18168538
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant -0.000168678 0.000366097 -0.46075 0.64592476
2. YG{1} 0.191298495 0.096273790 1.98703 0.04949961
3. YG{2} 0.203848468 0.099117238 2.05664 0.04217661
4. M1G{1} 0.006845084 0.016306450 0.41978 0.67549745
5. M1G{2} 0.018975583 0.018175969 1.04399 0.29886371
6. M1G{3} -0.018604742 0.018116394 -1.02696 0.30677889
7. M1G{4} -0.006057601 0.018468291 -0.32800 0.74355858
8. M1G{5} -0.003354411 0.018506761 -0.18125 0.85651492
9. M1G{6} 0.011372769 0.016951114 0.67092 0.50373353
10. M2G{1} 0.044500837 0.020411543 2.18018 0.03145610
11. M2G{2} -0.020608328 0.024451719 -0.84282 0.40122846
12. M2G{3} 0.005327909 0.024634404 0.21628 0.82918580
13. M2G{4} 0.000444107 0.024297733 0.01828 0.98545168
14. M2G{5} 0.011296284 0.024351843 0.46388 0.64368636
15. M2G{6} -0.011950021 0.021453718 -0.55701 0.57869211
***
The same tests from above are repeated.
Input:
Exclude
#m1g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M1G Lag(s) 1 to 6
F(6,106)= 0.41954 with Significance Level 0.86459778
Comment. M1 still seems unimportant.
***
Input:
Exclude
#m2g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M2G Lag(s) 1 to 6
F(6,106)= 1.23979 with Significance Level 0.29197607
Comment. M2 is also unimportant, it seems.
***
Now let's kill both together.
Input:
Exclude
#m1g{1 to 6} m2g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M1G Lag(s) 1 to 6
M2G Lag(s) 1 to 6
F(12,106)= 1.24443 with Significance Level 0.26314146
Conclusion. As before, lagged money does not seem to aid in forecasting
lagged values of output growth are included.
***
So did Uncle Milton just make up all this business about money
and output? Does money help forecast output?
Let's see what happens when we don't put in lagged values of
output growth.
Input:
linreg yg
#constant m1g{1 to 6} m2g{1 to 6}
Output:
Dependent Variable YG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 108
Centered R**2 0.147550 R Bar **2 0.052833
Durbin-Watson Statistic 1.495765
Q(30) 39.191761
Significance Level of Q 0.12149051
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant -0.000236412 0.000379841 -0.62240 0.53499235
2. M1G{1} 0.003483707 0.016645240 0.20929 0.83461494
3. M1G{2} 0.022422121 0.018776156 1.19418 0.23502356
4. M1G{3} -0.015057290 0.018765239 -0.80240 0.42408187
5. M1G{4} -0.006538259 0.019002213 -0.34408 0.73145601
6. M1G{5} -0.008810040 0.019072973 -0.46191 0.64507336
7. M1G{6} 0.010492937 0.017617961 0.59558 0.55270068
8. M2G{1} 0.039847026 0.021174743 1.88182 0.06255284
9. M2G{2} -0.010123374 0.025043441 -0.40423 0.68684111
10. M2G{3} 0.012032554 0.025363356 0.47441 0.63616749
11. M2G{4} 0.003732914 0.025240549 0.14789 0.88270255
12. M2G{5} 0.013047996 0.025317761 0.51537 0.60734831
13. M2G{6} -0.006091553 0.022223830 -0.27410 0.78453129
***
On to our tests.
Input:
Exclude
#m1g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M1G Lag(s) 1 to 6
F(6,108)= 0.39657 with Significance Level 0.87982803
Comment. M1 still seems uninterestin.
***
Input:
Exclude
#m2g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M2G Lag(s) 1 to 6
F(6,108)= 1.99675 with Significance Level 0.07231296
Comment. Look at that! M2 growth is now signficant at the 7.5 percent
level. That is not overwhelming, but it is something.
***
Now let's see what happens if all the coefficients on money are zero.
Input:
Exclude
#m1g{1 to 6} m2g{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
M1G Lag(s) 1 to 6
M2G Lag(s) 1 to 6
F(12,108)= 1.55780 with Significance Level 0.11506902
Comment. The significance drops from the previous regression.
This suggests that money may not be that important. However, M2
growth, by itself, does seem to be a significant predicter of
output growth.
****
Let's turn to some other variables, inflation and nominal
stock returns (with dividends omitted).
Input:
linreg yg
#constant inf{1 2} m1g{1 to 6} nsr{1 to 6}
Output:
Dependent Variable YG - Estimation by Least Squares
Quarterly Data From 1962:04 To 1992:04
Usable Observations 121 Degrees of Freedom 108
Centered R**2 0.281099 R Bar **2 0.201221
Durbin-Watson Statistic 1.727861
Q(30) 33.548131
Significance Level of Q 0.29925577
Variable Coeff Std Error T-Stat Signif
*******************************************************************************
1. Constant 0.001546616 0.000221676 6.97692 0.00000000
2. INF{1} -0.030063156 0.021962628 -1.36883 0.17389201
3. INF{2} -0.019091901 0.026058899 -0.73264 0.46536257
4. INF{3} 0.010249792 0.026188412 0.39139 0.69628264
5. INF{4} -0.030664694 0.026639369 -1.15110 0.25223138
6. INF{5} 0.007927760 0.026788592 0.29594 0.76784578
7. INF{6} 0.002833655 0.022231021 0.12746 0.89881019
8. NSR{1} 0.002986793 0.001813602 1.64688 0.10248860
9. NSR{2} 0.002280375 0.001828598 1.24706 0.21507243
10. NSR{3} 0.000554906 0.001789416 0.31010 0.75707887
11. NSR{4} 0.000792579 0.001818918 0.43574 0.66389357
12. NSR{5} -0.000764126 0.001825919 -0.41849 0.67642118
13. NSR{6} -0.001656564 0.001732784 -0.95601 0.34120071
***
Input:
Exclude
#nsr{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
NSR Lag(s) 1 to 6
F(6,108)= 1.40049 with Significance Level 0.22103786
Comment. Nominal stock returns do not seem to help forecast
output growth.
***
Now check the effect of inflation.
Input:
Exclude
#inf{1 to 6}
Output:
Null Hypothesis : The Following Coefficients Are Zero
INF Lag(s) 1 to 6
F(6,108)= 3.49762 with Significance Level 0.00336255
Comment. High inflation is a bad omen (we look to the sign of the
coefficients for this conclusion). Furthermore, inflation is a good predicter
of output growth. Low inflation is a good sign.
Your assignment.
1. Find which variables will best help predict stock returns. Use variables
in growth form (stock price growth, output growth, etc., all variables except
the interest rate). Be sure to test for proper exclusions, and other possible
problems.
2. Test the Fisher equation proposition. (Nominal interest rates equal
the real interest rate plus inflation.) For the real interest rate use
(a) a constant and (b) some constant times the growth rate of consumption.
3. Test the proposition that money growth causes inflation. (Again, do lots
tests. You may want to include output.) Be clear about your final results.
4. Which variables help forecast investment? How well does durable
consumption do?