ARMA and VAR modelling of Industrial Production in America

JOHNS HOPKINS AAP AUGUST 2016
Modeling ARMA and VAR
MACROECONOMETRICS FINAL PROJECT
Johns Hopkins AAP Matías Costa – Maegan Hawley – Emilio José Calle

MACROECONOMETRICS FINAL PROJECT AUGUST 2016
Modeling ARMA and VAR 2
Introduction of Main Variable: Industrial Production Index (IPI)
Section 1: Modelling IPI as an ARMA Process
Section 2: Modelling of IPI with other Explanatory Variables
Section 3: Unemployment Forecasting in VAR

The monthly Industrial Production Index (IP) is an economic indicator from the Federal Reserve
Board that measures the real production of output from manufacturing, mining, and utilities such
as electric and gas.
Data for the index are pulled from the Bureau of Labor Statistics and various trade associations
on a monthly basis. IP is computed as a Fisher index with weights based on annual estimates of
value added and the base year (currently 2012) set to 100.
The Fisher index is calculated by taking the geometric mean of the Laspeyres and Paasche indices:
where is Laspeyres' index and is Paasche's index. And P is the Industrial Price Index.
Many investors use the IP index of several industries in order to examine the growth in the
industry. Generally, when the indicator grows every month, it is a positive sign that shows the
industry is performing well.
Source: http://www.federalreserve.gov/Releases/g17/About.htm

1a. PLOT THE DATA FOR THE INDUSTRIAL PRODUCTION INDEX:
-20
-15
-10
-5
0
5
10
1975 1980 1985 1990 1995 2000 2005 2010 2015
ip

1b. PLOT THE CORRELOGRAM FOR THE INDUSTRIAL PRODUCTION INDEX:

2. COMMENT ON THE DATA:
This time series appears stationary as it reflects a constant variance and mean over time.
Specifically, the data appear to fluctuate along a constant mean of 0. The floor and ceiling of
these series range from 5 to -5, except when you look at the 2008 financial recession you can
see that the IP dropped down past -15.
This is consistent with the way this variable is built, as explained in the introduction at the
beginning of this report.
3. DECIDE ON AN ARMA(P,Q) MODEL BASED ON _T (SIC, BIC) AND SIMPLICITY
We selected an ARMA(4,11) for our model based on low SIC and BIC values as well as the simplicity
of the p,q values.
As demonstrated in the “ARMA Criteria Table” below, an ARMA(4,11) has both the lowest SIC(AIC)
and BIC values of all the ARMA(p,q) combinations.
Additionally, the ARMA(4,11) is the simplest model when compared to other ARMA models that
have similar, but slightly higher SIC and BIC values. If one of the other ARMA combinations
revealed slightly higher SIC and BIC values, but offered a lower-order model, we would have
considered that one over the ARMA(4,11).
In this case, however, the ARMA(4,11) offers us the best fit based on all three SIC, BIC and model
simplicity criteria. The reason for the high-order MA component in this model is because the
Industrial Production variable is defined as the growth rate year on year, leading to a strong MA
presence.
SUMMARY:
Automatic ARIMA Forecasting
Selected dependent variable: IP
Date: 08/06/16 Time: 10:39
Sample: 1973M01 2019M12
Included observations: 510
Forecast length: 0
Number of estimated ARMA models: 169
Number of non-converged estimations: 0
Selected ARMA model: (4,11)(0,0)
AIC value: 1.34747400898

Equation Output
Dependent Variable: IP
Method: ARMA Maximum Likelihood (BFGS)
Date: 08/06/16 Time: 10:39
Sample: 1973M01 2015M06
Convergence achieved after 93 iterations
Coefficient covariance computed using outer product of gradients
Variable Coefficient Std. Error t-Statistic Prob.
C 1.443722 0.781700 1.846900 0.0654
AR(1) 0.164718 0.036776 4.478924 0.0000
AR(2) 0.153853 0.050182 3.065880 0.0023
AR(3) 0.186425 0.042044 4.434039 0.0000
AR(4) 0.124788 0.046207 2.700646 0.0072
MA(1) 0.975557 1.190018 0.819783 0.4127
MA(2) 0.984597 1.512608 0.650926 0.5154
MA(3) 0.986381 1.967560 0.501322 0.6164
MA(4) 0.978262 1.717025 0.569742 0.5691
MA(5) 0.993363 1.208197 0.822186 0.4114
MA(6) 0.993364 0.929092 1.069177 0.2855
MA(7) 0.978258 1.607138 0.608696 0.5430
MA(8) 0.986382 1.815927 0.543184 0.5872
MA(9) 0.984599 1.700871 0.578879 0.5629
MA(10) 0.975557 1.431133 0.681668 0.4958
MA(11) 0.999988 1.463988 0.683058 0.4949
SIGMASQ 0.222078 0.712393 0.311735 0.7554
R-squared 0.980388 Mean dependent var 1.466513
Adjusted R-squared 0.979751 S.D. dependent var 3.368342
S.E. of regression 0.479308 Akaike info criterion 1.490148
Sum squared resid 113.2599 Schwarz criterion 1.631295
Log likelihood -362.9877 Hannan-Quinn criter. 1.545487
F-statistic 1540.278 Durbin-Watson stat 1.986116
Prob(F-statistic) 0.000000
Inverted AR Roots .83 -.09-.55i -.09+.55i -.48
Inverted MA Roots .87+.50i .87-.50i .50-.86i .50+.86i
.00+1.00i .00-1.00i -.49-.87i -.49+.87i
-.87+.50i -.87-.50i -1.00

ARMA Criteria Table
Model Selection Criteria Table
Date: 08/06/16 Time: 10:39
Sample: 1973M01 2019M12
Model LogL AIC* BIC HQ
(4,11)(0,0) -362.987671 1.347474 1.478141 1.398480
(6,12)(0,0) -360.245493 1.348388 1.502114 1.408395
(5,11)(0,0) -362.526922 1.349386 1.487739 1.403393
(7,11)(0,0) -361.413988 1.352532 1.506257 1.412539
(6,11)(0,0) -362.454659 1.352676 1.498715 1.409683
(7,12)(0,0) -360.813764 1.353950 1.515361 1.416957
(8,11)(0,0) -361.383645 1.355970 1.517382 1.418978
(3,11)(0,0) -366.428370 1.356129 1.479109 1.404135
(1,12)(0,0) -367.962481 1.358023 1.473317 1.403028
(9,11)(0,0) -361.072661 1.358414 1.527512 1.424421
(12,11)(0,0)-358.088969 1.358472 1.550628 1.433480
(10,12)(0,0)-359.112917 1.358556 1.543027 1.430565
(8,12)(0,0) -361.338976 1.359358 1.528456 1.425366
(11,12)(0,0)-358.350739 1.359400 1.551556 1.434409
(10,11)(0,0)-361.001097 1.361706 1.538490 1.430714
(9,12)(0,0) -361.050238 1.361880 1.538664 1.430888
(11,11)(0,0)-360.282989 1.362706 1.547176 1.434714
(2,11)(0,0) -376.873152 1.389621 1.504915 1.434626
(3,12)(0,0) -375.880800 1.393194 1.523861 1.444200
(12,10)(0,0)-373.851643 1.410821 1.595292 1.482830
(10,10)(0,0)-376.744712 1.413988 1.583086 1.479996
(11,10)(0,0)-376.670631 1.417272 1.594056 1.486280
(1,11)(0,0) -388.914152 1.428774 1.536381 1.470778
(7,10)(0,0) -383.986963 1.429032 1.575071 1.486038
(8,10)(0,0) -383.033685 1.429197 1.582923 1.489204
(6,10)(0,0) -387.199921 1.436879 1.575232 1.490885
(0,12)(0,0) -395.155250 1.450905 1.558513 1.492910
(4,10)(0,0) -399.991194 1.475146 1.598126 1.523152
(0,11)(0,0) -408.435179 1.494451 1.594372 1.533456
(12,8)(0,0) -408.595301 1.526934 1.696032 1.592941
(10,8)(0,0) -411.767177 1.531089 1.684815 1.591096
(6,9)(0,0) -415.770467 1.534647 1.665314 1.585653
(12,9)(0,0) -409.891168 1.535075 1.711859 1.604083
(5,9)(0,0) -418.053636 1.539197 1.662178 1.587203
(9,8)(0,0) -415.496945 1.540769 1.686808 1.597776
(7,9)(0,0) -417.201359 1.543267 1.681620 1.597274
(12,6)(0,0) -417.673147 1.552032 1.705758 1.612039
(8,8)(0,0) -421.800649 1.559577 1.697930 1.613583
(5,10)(0,0) -425.000821 1.567379 1.698045 1.618385
(7,8)(0,0) -425.492159 1.569121 1.699788 1.620127
(4,9)(0,0) -427.848888 1.570386 1.685680 1.615391
(5,8)(0,0) -429.681638 1.576885 1.692179 1.621890
(6,8)(0,0) -428.706766 1.576974 1.699955 1.624980
(3,9)(0,0) -432.941175 1.584898 1.692506 1.626903
(10,9)(0,0) -426.119242 1.585529 1.746941 1.648537
(3,10)(0,0) -432.941020 1.588443 1.703737 1.633449
(11,7)(0,0) -428.799780 1.591489 1.745214 1.651496
(11,9)(0,0) -427.454443 1.593810 1.762908 1.659818
(8,7)(0,0) -437.246023 1.610801 1.741468 1.661807
(9,7)(0,0) -437.222781 1.614265 1.752618 1.668271
(11,6)(0,0) -436.747639 1.616126 1.762165 1.673133
(12,5)(0,0) -438.214578 1.621328 1.767367 1.678335
(11,5)(0,0) -439.370939 1.621883 1.760236 1.675889
(9,9)(0,0) -438.047082 1.624280 1.778006 1.684287
(8,9)(0,0) -440.375478 1.628991 1.775030 1.685998
(10,6)(0,0) -442.859748 1.634254 1.772607 1.688261
(12,4)(0,0) -444.107642 1.638680 1.777032 1.692686
(3,8)(0,0) -451.578838 1.647443 1.747364 1.686447
(2,10)(0,0) -451.966498 1.652363 1.759971 1.694368
(11,8)(0,0) -445.304276 1.653561 1.814973 1.716569
(1,10)(0,0) -454.864348 1.659093 1.759015 1.698098
(2,8)(0,0) -456.084675 1.659875 1.752110 1.695879
(10,5)(0,0) -452.676231 1.665519 1.796185 1.716524
(11,4)(0,0) -453.171503 1.667275 1.797941 1.718281
(7,6)(0,0) -460.072167 1.684653 1.799947 1.729658
(8,6)(0,0) -459.774204 1.687143 1.810123 1.735148
(2,9)(0,0) -462.792840 1.687209 1.787130 1.726213
(9,6)(0,0) -459.654250 1.690263 1.820930 1.741269
(6,5)(0,0) -464.269208 1.692444 1.792365 1.731449
(9,5)(0,0) -461.461571 1.693126 1.816106 1.741132
(7,5)(0,0) -463.789247 1.694288 1.801896 1.736293
(6,6)(0,0) -463.844291 1.694483 1.802091 1.736488
(6,7)(0,0) -463.278773 1.696024 1.811318 1.741029
(10,4)(0,0) -462.306959 1.696124 1.819104 1.744130
(7,7)(0,0) -462.518762 1.696875 1.819855 1.744881
(1,9)(0,0) -467.157535 1.699140 1.791375 1.735144
(12,3)(0,0) -463.820215 1.705036 1.835703 1.756042
(7,4)(0,0) -469.082479 1.709512 1.809434 1.748517
(10,7)(0,0) -463.127710 1.709673 1.855712 1.766679
(10,3)(0,0) -467.268605 1.710172 1.825466 1.755178
(8,4)(0,0) -468.340025 1.710426 1.818033 1.752431
(9,4)(0,0) -467.707488 1.711729 1.827023 1.756734
(11,3)(0,0) -467.257505 1.713679 1.836659 1.761685
(8,5)(0,0) -469.530024 1.718192 1.833486 1.763197
(9,3)(0,0) -474.725815 1.733070 1.840678 1.775075
(4,7)(0,0) -476.268471 1.734995 1.834916 1.773999
(5,4)(0,0) -480.203934 1.741858 1.826407 1.774862
(5,6)(0,0) -478.850795 1.744152 1.844073 1.783156
(6,4)(0,0) -480.203295 1.745402 1.837637 1.781406
(5,5)(0,0) -480.203357 1.745402 1.837637 1.781406
(5,7)(0,0) -479.726171 1.750802 1.858410 1.792807
(10,2)(0,0) -480.226765 1.752577 1.860185 1.794582
(11,2)(0,0) -480.087788 1.755630 1.870924 1.800636
(1,8)(0,0) -485.085941 1.759170 1.843719 1.792174
(2,7)(0,0) -485.869889 1.761950 1.846499 1.794954
(9,2)(0,0) -484.582778 1.764478 1.864399 1.803482
(5,3)(0,0) -488.789099 1.768756 1.845618 1.798759
(8,2)(0,0) -487.804321 1.772356 1.864591 1.808360
(3,7)(0,0) -492.800820 1.790074 1.882309 1.826078
(8,3)(0,0) -494.943302 1.801217 1.901139 1.840222
(4,5)(0,0) -497.227028 1.802224 1.886772 1.835227
(4,4)(0,0) -498.701906 1.803907 1.880770 1.833911
(4,6)(0,0) -497.466900 1.806620 1.898855 1.842624

(4,2)(0,0) -503.400878 1.813478 1.874968 1.837481
(3,6)(0,0) -500.463029 1.813699 1.898248 1.846703
(3,4)(0,0) -502.589754 1.814148 1.883324 1.841151
(4,3)(0,0) -504.470318 1.820817 1.889993 1.847820
(2,6)(0,0) -504.432467 1.824229 1.901091 1.854232
(3,3)(0,0) -506.461382 1.824331 1.885821 1.848334
(12,1)(0,0) -502.733729 1.835935 1.951229 1.880940
(3,2)(0,0) -513.642005 1.846248 1.900052 1.867251
(2,3)(0,0) -516.568962 1.856628 1.910431 1.877630
(2,4)(0,0) -515.947286 1.857969 1.919459 1.881972
(5,1)(0,0) -516.265679 1.859098 1.920588 1.883101
(6,0)(0,0) -516.282596 1.859158 1.920648 1.883161
(4,1)(0,0) -517.445740 1.859737 1.913541 1.880739
(2,2)(0,0) -518.589611 1.860247 1.906364 1.878249
(2,5)(0,0) -515.666931 1.860521 1.929697 1.887524
(5,0)(0,0) -517.673534 1.860544 1.914348 1.881547
(7,0)(0,0) -516.199895 1.862411 1.931587 1.889414
(6,1)(0,0) -516.212731 1.862456 1.931633 1.889460
(5,2)(0,0) -516.220101 1.862483 1.931659 1.889486
(3,1)(0,0) -519.231552 1.862523 1.908641 1.880525
(1,7)(0,0) -515.466520 1.863356 1.940219 1.893360
(3,5)(0,0) -515.942954 1.865046 1.941909 1.895049
(8,0)(0,0) -516.193849 1.865936 1.942798 1.895939
(7,1)(0,0) -516.197813 1.865950 1.942812 1.895953
(6,2)(0,0) -516.208187 1.865986 1.942849 1.895990
(2,1)(0,0) -521.327816 1.866411 1.904842 1.881412
(1,6)(0,0) -517.441093 1.866812 1.935989 1.893816
(9,0)(0,0) -516.154370 1.869342 1.953891 1.902346
(8,1)(0,0) -516.192084 1.869475 1.954024 1.902479
(6,3)(0,0) -516.213180 1.869550 1.954099 1.902554
(10,0)(0,0) -515.401466 1.870218 1.962453 1.906222
(11,0)(0,0) -515.346987 1.873571 1.973492 1.912575
(10,1)(0,0) -515.381501 1.873693 1.973615 1.912698
(12,0)(0,0) -515.318104 1.877015 1.984622 1.919019
(11,1)(0,0) -515.346486 1.877115 1.984723 1.919120
(1,5)(0,0) -523.894381 1.886150 1.947640 1.910153
(4,0)(0,0) -526.078151 1.886802 1.932920 1.904804
(1,4)(0,0) -528.725419 1.899736 1.953539 1.920738
(0,9)(0,0) -530.709045 1.920954 2.005503 1.953958
(3,0)(0,0) -538.362824 1.926819 1.965250 1.941820
(1,3)(0,0) -545.539618 1.955814 2.001932 1.973816
(0,10)(0,0) -541.688277 1.963434 2.055669 1.999438
(0,8)(0,0) -547.649724 1.977481 2.054344 2.007485
(1,2)(0,0) -553.672424 1.981108 2.019539 1.996110
(2,0)(0,0) -555.119109 1.982692 2.013437 1.994693
(0,7)(0,0) -551.626866 1.988039 2.057215 2.015042
(0,6)(0,0) -559.042711 2.010790 2.072280 2.034793
(1,1)(0,0) -563.691553 2.013091 2.043836 2.025092
(1,0)(0,0) -580.820379 2.070285 2.093344 2.079286
(0,5)(0,0) -620.959701 2.226807 2.280611 2.247810
(0,4)(0,0) -666.562008 2.384972 2.431089 2.402974
(0,3)(0,0) -773.653139 2.761181 2.799613 2.776183
(2,12)(0,0) -815.501117 2.948586 3.071566 2.996591
(0,2)(0,0) -886.835544 3.158991 3.189736 3.170993
(9,10)(0,0) -902.277268 3.274033 3.435444 3.337040
(0,1)(0,0) -1044.900153 3.715958 3.739017 3.724959
(7,3)(0,0) -1062.858918 3.811556 3.903792 3.847561
(4,12)(0,0) -1091.544748 3.934556 4.072909 3.988562
(4,8)(0,0) -1105.261357 3.969012 4.076620 4.011017
(12,12)(0,0)-1131.375671 4.104169 4.304012 4.182178
(12,7)(0,0) -1139.412641 4.114938 4.276350 4.177946
(5,12)(0,0) -1177.395555 4.242537 4.388576 4.299544
(9,1)(0,0) -1198.855069 4.293812 4.386047 4.329816
(7,2)(0,0) -1207.550137 4.321100 4.405649 4.354104
(0,0)(0,0) -1342.512689 4.767775 4.783148 4.773776
(12,2)(0,0) -1328.701646 4.768446 4.891426 4.816451
ARMA Criteria Graph
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
(4,11)(0,0)
(6,12)(0,0)
(5,11)(0,0)
(7,11)(0,0)
(6,11)(0,0)
(7,12)(0,0)
(8,11)(0,0)
(3,11)(0,0)
(1,12)(0,0)
(9,11)(0,0)
(12,11)(0,0)
(10,12)(0,0)
(8,12)(0,0)
(11,12)(0,0)
(10,11)(0,0)
(9,12)(0,0)
(11,11)(0,0)
(2,11)(0,0)
(3,12)(0,0)
(12,10)(0,0)
Akaike Information Criteria (top 20 models)

ARMA Comparative Tables
4. SHOW RESIDUAL DIAGNOSTICS THAT VALIDATE YOUR CHOICE OF MODEL (RESIDUAL
CORRELOGRAMS, Q-TEST, ETC).
The plot of the residuals (below) shows no discernable pattern, a constant variance and an expected
mean of zero. In other words, the residuals look like white noise, which is an indication that our
chosen model is a good fit to the data. The plot also shows that the actual vs. fitted values are a very
close match.
The correlogram of the residuals show that the bars for both the Autocorrelation Function (ACF) and
the Partial Autocorrelation Function (PCF) are close to zero with no pattern to them. These results
suggest that there is no correlation between the residuals, which further supports our chosen model.
Lastly, when we look at the Q-stats, we can see that all the associated p-values are all much greater
than 0.05 meaning we fail to reject the null hypothesis that there is no serial correlation between
residuals. These results are good news for our model since failing to reject the null hypothesis
supports the case that there is no serial correlation between the residuals. If the p-values had been
less than 0.05, it would have suggested there was serial correlation between the residuals thus
indicating a need to reevaluate our model.
SIC/AIC AR
MA
-Values- 4 5 6
10 1.475 1.567 1.437
11 1.347 1.349 1.353
12 3.935 4.243 1.348
BIC AR
MA
-Values- 4 5 6
10 1.598 1.698 1.575
11 1.478 1.488 1.499
12 4.073 4.389 1.502

Actual vs. Fitted Graphs
-4
-3
-2
-1
0
1
2
-20
-15
-10
-5
0
5
10
1975 1980 1985 1990 1995 2000 2005 2010 2015
Residual Actual Fitted
Residual Correlograms and Q-Test

5. ESTIMATE THE MODEL UP TO THE LATEST OBSERVATION. THEN DO A DYNAMIC FORECAST
FOR THE NEXT 5 YEARS. INCLUDE CONFIDENCE INTERVALS.
-8
-6
-4
-2
0
2
4
6
8
10
II III IV I II III IV I II III IV I II III IV I II III IV
2015 2016 2017 2018 2019
IPF ± 2 S.E.
Forecast: IPF
Actual: IP
Forecast sample: 2015M06 2019M12
Root Mean Squared Error 0.085313
Mean Absolute Error 0.085313
Mean Abs. Percent Error 32.51241
A dynamic forecast is one that does not update its knowledge after each period, which is why we
see here that the forecast trends back towards the mean.

6. Next, include the other 4 variables as explanatory variables. You will need to decide on
model { how many lags (p) of each variable, and how many MA components (q) to keep. Here
is my suggestion, start with the p and q you used in step 2 on this list. For example, if you
modeled your main variable as an ARMA(6,2), then use 6 lags for all of the explanatory
variables and keep the MA(2) structure. Use the same lag p for all the explanatory variables.
Then, as usual, try different p's and q's and see how SIC and BIC change. Decide on a model.
What can be seen below is the different AR-MA combinations that were tried out to select the best-
fitting model for the data set.
The first one tested was the base AR(4) MA(11) found in the previous section using only IPI and its
autoregressions. Registering the results it can be seen that the AIC is 1.617118 and SIC 1.892762, but
other combinations of AR and MA gave better fitting results.
AR(5) MA(12) being the best fitting one with AIC = 1.470070 and SIC= 1.796323.Thus this model was
selected for the multivariable case.

Method: ARMA Maximum Likelihood (OPG - BHHH)
Date: 08/06/16 Time: 12:49
Sample: 1973M05 2015M06
Convergence not achieved after 500 iterations
IP(-1) 1.626231 0.063603 25.56848 0.0000
IP(-2) -1.139602 0.094570 -12.05032 0.0000
IP(-3) 0.827362 0.086416 9.574186 0.0000
IP(-4) -0.401640 0.043961 -9.136367 0.0000
FFR(-1) 0.052233 0.035180 1.484727 0.1383
FFR(-2) -0.093678 0.059476 -1.575072 0.1159
FFR(-3) 0.038771 0.059255 0.654306 0.5132
FFR(-4) 0.020148 0.033260 0.605755 0.5450
PCEINFLATION(-1) 0.132827 0.079418 1.672495 0.0951
PCEINFLATION(-2) -0.325140 0.170335 -1.908830 0.0569
PCEINFLATION(-3) 0.253194 0.180984 1.398984 0.1625
PCEINFLATION(-4) -0.091053 0.088184 -1.032543 0.3023
EBP(-1) -0.182081 0.054737 -3.326446 0.0009
EBP(-2) -0.004094 0.080632 -0.050777 0.9595
EBP(-3) -0.136642 0.077741 -1.757671 0.0795
EBP(-4) 0.013316 0.062077 0.214512 0.8302
UNEMP(-1) -0.216873 0.123165 -1.760830 0.0789
UNEMP(-2) 0.058144 0.185887 0.312792 0.7546
UNEMP(-3) -0.085399 0.185975 -0.459193 0.6463
UNEMP(-4) 0.256941 0.111862 2.296934 0.0221
C 0.094166 0.107693 0.874395 0.3823
MA(1) -0.789370 3.128521 -0.252314 0.8009
MA(2) 0.911486 8.758849 0.104065 0.9172
MA(3) -0.762165 9.246236 -0.082430 0.9343
MA(4) 0.753322 2.200428 0.342353 0.7322
MA(5) -0.693954 1.843193 -0.376496 0.7067
MA(6) 0.750070 7.817659 0.095946 0.9236
MA(7) -0.756369 8.002078 -0.094522 0.9247
MA(8) 0.901179 10.02509 0.089892 0.9284
MA(9) -0.723709 8.908408 -0.081239 0.9353
MA(10) 0.972506 9.834049 0.098892 0.9213
MA(11) -0.715011 6.092958 -0.117350 0.9066
SIGMASQ 0.244935 1.517994 0.161354 0.8719
Inverted MA Roots .84-.43i .84+.43i .82 .51+.86i
.51-.86i -.00-1.00i -.00+1.00i -.48-.86i
-.48+.86i -.88-.48i -.88+.48i

Method: ARMA Maximum Likelihood (OPG - BHHH)
Date: 08/06/16 Time: 13:11
Sample: 1973M06 2015M06
Convergence not achieved after 500 iterations
IP(-1) 0.913110 0.082557 11.06042 0.0000
IP(-2) 0.040925 0.071919 0.569050 0.5696
IP(-3) 0.084352 0.065527 1.287287 0.1986
IP(-4) -0.007017 0.071552 -0.098065 0.9219
IP(-5) -0.166242 0.047232 -3.519662 0.0005
FFR(-1) 0.044872 0.036526 1.228493 0.2199
FFR(-2) -0.037171 0.050673 -0.733540 0.4636
FFR(-3) -0.032724 0.055312 -0.591622 0.5544
FFR(-4) 0.037727 0.052131 0.723701 0.4696
FFR(-5) 0.013049 0.035630 0.366232 0.7144
PCEINFLATION(-1) 0.180072 0.085817 2.098311 0.0364
PCEINFLATION(-2) -0.314919 0.142431 -2.211022 0.0275
PCEINFLATION(-3) 0.101583 0.158060 0.642687 0.5207
PCEINFLATION(-4) -0.019244 0.157139 -0.122464 0.9026
PCEINFLATION(-5) 0.006674 0.093755 0.071181 0.9433
EBP(-1) -0.121419 0.053367 -2.275163 0.0233
EBP(-2) -0.154980 0.054988 -2.818403 0.0050
EBP(-3) -0.129754 0.054132 -2.396980 0.0169
EBP(-4) -0.045976 0.066354 -0.692891 0.4887
EBP(-5) -0.007993 0.065681 -0.121692 0.9032
UNEMP(-1) -0.252105 0.122004 -2.066363 0.0393
UNEMP(-2) -0.024110 0.154271 -0.156285 0.8759
UNEMP(-3) -0.120512 0.148132 -0.813548 0.4163
UNEMP(-4) 0.315541 0.157243 2.006708 0.0454
UNEMP(-5) 0.106194 0.131280 0.808910 0.4190
C 0.112507 0.180260 0.624140 0.5328
MA(1) 0.147980 2.012039 0.073547 0.9414
MA(2) 0.134471 2.536965 0.053005 0.9578
MA(3) 0.065694 2.774316 0.023679 0.9811
MA(4) 0.030319 3.187323 0.009512 0.9924
MA(5) 0.068029 1.720054 0.039551 0.9685
MA(6) 0.045049 4.041056 0.011148 0.9911
MA(7) 0.034612 2.344236 0.014765 0.9882
MA(8) 0.125890 2.544531 0.049475 0.9606
MA(9) 0.179498 2.715202 0.066109 0.9473
MA(10) 0.195885 2.713438 0.072191 0.9425
MA(11) 0.249114 1.867220 0.133415 0.8939
MA(12) -0.786232 2.823196 -0.278490 0.7808
SIGMASQ 0.203604 0.728346 0.279542 0.7800
Inverted MA Roots .85+.45i .85-.45i .85 .51-.86i
.51+.86i -.00-1.00i -.00+1.00i -.49-.87i
-.49+.87i -.87+.50i -.87-.50i -1.00

7. ESTIMATE THE MODEL UP TO 2013M12. THEN, DO A DYNAMIC FORECAST, WITH
CONFIDENCE INTERVALS, FROM 2014M1 UP TO THE LATEST OBSERVATION IN THE SAMPLE.
COMMENT ON THE FITTED VALUES VS THE ACTUAL. NOTE: THE FITTED VALUES WON'T
NECESSARILY BE GOOD," DON'T WORRY TOO MUCH ABOUT THAT. BUT IT'D BE GOOD IF YOU
CAN PROVIDE SOME EXPLANATION FOR THE BEHAVIOR OF THE FORECASTS BASED ON YOUR
KNOWLEDGE OF ARMA FORECASTING.
-1
0
1
2
3
4
5
6
7
8
I II III IV I II III IV I II III IV I II III IV I II
2011 2012 2013 2014 2015
ip IPF UP_IP LB_IP
The model fits the actual data pretty well for 2014, but in 2015 there is a big divergence between the
two.
While the forecasted IPI aimed towards a stabilization in 2014 around the 3% range, the actual data
shows that IPI declined steeply during this year.
What this data says is that the forecast wanted to go back to the momentum it had during the recovery
from the last financial crisis, however, there have been several shocks to the American economy that
have pushed IPI down such as the crash of oil prices, that delayed or cancelled many manufacturing
projects related to the oil industry such as building wells, refineries, pipelines and the like.

1. ESTIMATE A VAR(12) FROM THE START OF THE SAMPLE UP TO 2013M12.
Vector Autoregression Estimates
Date: 08/02/16 Time: 21:10
Sample (adjusted): 1974M01 2013M12
Included observations: 480 after adjustments
Standard errors in ( ) & t-statistics in [ ]
IP UNEMP FFR EBP PCEINFLATION
IP(-1) 0.851393 -0.044540 0.040490 -0.031468 0.004500
(0.05057) (0.01322) (0.03269) (0.02038) (0.02897)
[ 16.8351] [-3.36958] [ 1.23855] [-1.54411] [ 0.15533]
IP(-2) 0.060732 0.022166 -0.002550 0.036315 0.094686
(0.06483) (0.01694) (0.04191) (0.02612) (0.03714)
[ 0.93684] [ 1.30819] [-0.06084] [ 1.39018] [ 2.54951]
IP(-3) 0.035230 -0.019469 -0.103080 0.000366 -0.051264
(0.06512) (0.01702) (0.04210) (0.02624) (0.03731)
[ 0.54099] [-1.14386] [-2.44868] [ 0.01395] [-1.37408]
IP(-4) 0.051243 0.028111 -0.053365 0.001081 -0.068647
(0.06580) (0.01720) (0.04253) (0.02651) (0.03770)
[ 0.77880] [ 1.63458] [-1.25465] [ 0.04075] [-1.82109]
IP(-5) -0.041405 0.008578 0.056458 -0.017309 -0.027652
(0.06622) (0.01731) (0.04281) (0.02668) (0.03794)
[-0.62529] [ 0.49565] [ 1.31896] [-0.64867] [-0.72892]
IP(-6) -0.119765 0.002692 0.011976 -0.002298 0.071720
(0.06627) (0.01732) (0.04284) (0.02671) (0.03797)
[-1.80720] [ 0.15539] [ 0.27954] [-0.08607] [ 1.88902]
IP(-7) -0.010616 0.025011 0.034650 -0.005396 0.004344
(0.06608) (0.01727) (0.04272) (0.02663) (0.03786)
[-0.16065] [ 1.44811] [ 0.81116] [-0.20266] [ 0.11474]
IP(-8) 0.011232 -0.021978 0.048107 -0.027821 0.018151
(0.06597) (0.01724) (0.04265) (0.02659) (0.03780)
[ 0.17025] [-1.27456] [ 1.12801] [-1.04647] [ 0.48023]
IP(-9) 0.063944 -0.022422 -0.020916 0.054467 -0.083133
(0.06591) (0.01723) (0.04260) (0.02656) (0.03776)
[ 0.97023] [-1.30164] [-0.49095] [ 2.05085] [-2.20177]

IP(-10) 0.034822 -0.003893 -0.061968 0.020144 0.036988
(0.06640) (0.01736) (0.04292) (0.02676) (0.03804)
[ 0.52441] [-0.22431] [-1.44367] [ 0.75283] [ 0.97231]
IP(-11) -0.031145 0.024663 -0.034609 -0.020389 -0.018554
(0.06572) (0.01718) (0.04248) (0.02648) (0.03765)
[-0.47390] [ 1.43578] [-0.81463] [-0.76989] [-0.49278]
IP(-12) -0.069127 -0.012722 0.037971 -0.015907 0.034440
(0.04781) (0.01250) (0.03091) (0.01927) (0.02739)
[-1.44583] [-1.01806] [ 1.22855] [-0.82562] [ 1.25733]
UNEMP(-1) -0.598125 0.918932 -0.693061 -0.033260 0.046232
(0.19721) (0.05155) (0.12748) (0.07947) (0.11298)
[-3.03292] [ 17.8276] [-5.43650] [-0.41853] [ 0.40920]
UNEMP(-2) 0.286472 0.093895 0.671587 0.147966 0.018104
(0.25885) (0.06766) (0.16733) (0.10431) (0.14829)
[ 1.10672] [ 1.38784] [ 4.01361] [ 1.41855] [ 0.12209]
UNEMP(-3) -0.260702 0.043898 -0.263159 -0.122576 -0.172910
(0.26515) (0.06930) (0.17140) (0.10685) (0.15190)
[-0.98324] [ 0.63343] [-1.53537] [-1.14723] [-1.13830]
UNEMP(-4) 0.472855 0.006869 0.054260 -0.110365 0.047042
(0.26579) (0.06947) (0.17181) (0.10710) (0.15227)
[ 1.77908] [ 0.09888] [ 0.31581] [-1.03046] [ 0.30894]
UNEMP(-5) -0.041823 0.003221 -0.073770 0.113528 -0.077982
(0.26597) (0.06952) (0.17193) (0.10718) (0.15237)
[-0.15725] [ 0.04633] [-0.42908] [ 1.05927] [-0.51179]
UNEMP(-6) -0.179830 -0.045788 0.515437 -0.009545 0.234649
(0.26409) (0.06903) (0.17071) (0.10642) (0.15130)
[-0.68095] [-0.66335] [ 3.01930] [-0.08969] [ 1.55093]
UNEMP(-7) 0.558519 -0.037256 -0.182075 -0.108196 0.088861
(0.26519) (0.06931) (0.17143) (0.10686) (0.15193)
[ 2.10608] [-0.53749] [-1.06210] [-1.01246] [ 0.58489]
UNEMP(-8) -0.073989 0.012878 -0.146226 0.093537 -0.202034
(0.26474) (0.06920) (0.17114) (0.10668) (0.15167)
[-0.27947] [ 0.18611] [-0.85443] [ 0.87678] [-1.33205]
UNEMP(-9) -0.293459 -0.038214 -0.087360 0.103114 0.067725
(0.26291) (0.06872) (0.16995) (0.10594) (0.15062)
[-1.11619] [-0.55609] [-0.51402] [ 0.97328] [ 0.44964]
UNEMP(-10) 0.565578 -0.013516 -0.018288 -0.021731 -0.050617
(0.26223) (0.06854) (0.16952) (0.10567) (0.15023)
[ 2.15677] [-0.19720] [-0.10788] [-0.20565] [-0.33692]
UNEMP(-11) -0.153923 0.130231 0.070839 -0.110795 -0.083607
(0.26034) (0.06804) (0.16829) (0.10491) (0.14915)
[-0.59125] [ 1.91391] [ 0.42094] [-1.05613] [-0.56057]

UNEMP(-12) -0.312412 -0.095599 0.123860 0.041358 0.086348
(0.19704) (0.05150) (0.12737) (0.07940) (0.11288)
[-1.58556] [-1.85631] [ 0.97245] [ 0.52089] [ 0.76495]
FFR(-1) 0.088422 -0.001493 1.318494 -0.030926 0.029397
(0.07829) (0.02046) (0.05061) (0.03155) (0.04485)
[ 1.12945] [-0.07296] [ 26.0535] [-0.98031] [ 0.65545]
FFR(-2) 0.013910 -0.021672 -0.585717 0.057440 0.075469
(0.12869) (0.03364) (0.08319) (0.05186) (0.07373)
[ 0.10809] [-0.64431] [-7.04078] [ 1.10764] [ 1.02363]
FFR(-3) -0.234409 0.055010 0.246952 -0.090196 -0.126679
(0.13578) (0.03549) (0.08777) (0.05472) (0.07779)
[-1.72638] [ 1.55005] [ 2.81355] [-1.64847] [-1.62851]
FFR(-4) 0.043279 -0.032452 -0.108431 0.061046 0.096011
(0.13869) (0.03625) (0.08966) (0.05589) (0.07946)
[ 0.31205] [-0.89521] [-1.20941] [ 1.09227] [ 1.20833]
FFR(-5) 0.023618 0.024341 0.266295 -0.001805 -0.108299
(0.13904) (0.03634) (0.08988) (0.05603) (0.07966)
[ 0.16986] [ 0.66977] [ 2.96272] [-0.03222] [-1.35955]
FFR(-6) 0.183743 -0.036458 -0.406481 -0.018628 0.121207
(0.13832) (0.03615) (0.08942) (0.05574) (0.07924)
[ 1.32838] [-1.00842] [-4.54599] [-0.33420] [ 1.52954]
FFR(-7) -0.073072 0.026365 0.182253 -0.015174 -0.145740
(0.13585) (0.03551) (0.08782) (0.05474) (0.07783)
[-0.53787] [ 0.74252] [ 2.07533] [-0.27718] [-1.87255]
FFR(-8) 0.030783 -0.031094 0.079722 0.078025 0.245225
(0.13235) (0.03459) (0.08556) (0.05333) (0.07583)
[ 0.23258] [-0.89884] [ 0.93179] [ 1.46294] [ 3.23408]
FFR(-9) 0.054236 0.034269 0.059074 -0.079237 -0.214497
(0.13266) (0.03467) (0.08576) (0.05346) (0.07600)
[ 0.40883] [ 0.98832] [ 0.68886] [-1.48222] [-2.82230]
FFR(-10) -0.139419 -0.000365 -0.146021 0.052756 0.181223
(0.13117) (0.03428) (0.08479) (0.05286) (0.07514)
[-1.06292] [-0.01066] [-1.72217] [ 0.99813] [ 2.41167]
FFR(-11) -0.102025 0.007592 0.090381 -0.061406 -0.200825
(0.12128) (0.03170) (0.07840) (0.04887) (0.06948)
[-0.84121] [ 0.23951] [ 1.15281] [-1.25643] [-2.89028]
FFR(-12) 0.141403 -0.024211 -0.016346 0.053652 0.055412
(0.07245) (0.01894) (0.04683) (0.02920) (0.04151)
[ 1.95169] [-1.27853] [-0.34900] [ 1.83766] [ 1.33499]
EBP(-1) -0.284737 0.021877 0.096712 0.618518 -0.154135
(0.12126) (0.03169) (0.07839) (0.04886) (0.06947)
[-2.34816] [ 0.69028] [ 1.23380] [ 12.6580] [-2.21876]
EBP(-2) -0.237933 0.022770 -0.208478 0.276333 0.084403

(0.14267) (0.03729) (0.09222) (0.05749) (0.08173)
[-1.66776] [ 0.61064] [-2.26057] [ 4.80665] [ 1.03267]
EBP(-3) -0.144058 -0.026394 0.159302 0.042714 0.095309
(0.14738) (0.03852) (0.09527) (0.05939) (0.08443)
[-0.97744] [-0.68519] [ 1.67207] [ 0.71921] [ 1.12879]
EBP(-4) 0.058897 0.037660 -0.088509 0.086876 -0.038061
(0.14738) (0.03852) (0.09527) (0.05939) (0.08443)
[ 0.39963] [ 0.97765] [-0.92902] [ 1.46283] [-0.45078]
EBP(-5) -0.042054 0.035788 -0.268393 -0.127089 -0.044290
(0.14732) (0.03851) (0.09523) (0.05937) (0.08440)
[-0.28546] [ 0.92940] [-2.81823] [-2.14073] [-0.52476]
EBP(-6) 0.034258 0.015063 0.226434 0.042509 0.030936
(0.14901) (0.03895) (0.09633) (0.06005) (0.08537)
[ 0.22990] [ 0.38676] [ 2.35068] [ 0.70792] [ 0.36238]
EBP(-7) 0.144006 -0.040832 -0.025906 -0.096827 0.038252
(0.14942) (0.03905) (0.09659) (0.06021) (0.08560)
[ 0.96376] [-1.04552] [-0.26821] [-1.60810] [ 0.44685]
EBP(-8) -0.111826 -0.003604 0.073836 -0.055785 -0.002022
(0.14920) (0.03900) (0.09644) (0.06012) (0.08547)
[-0.74952] [-0.09242] [ 0.76558] [-0.92787] [-0.02365]
EBP(-9) -0.118310 -0.049560 0.080355 0.022489 -0.011884
(0.14867) (0.03886) (0.09611) (0.05991) (0.08517)
[-0.79578] [-1.27539] [ 0.83612] [ 0.37539] [-0.13952]
EBP(-10) -0.030263 0.007163 -0.162486 -0.031050 0.035931
(0.14828) (0.03876) (0.09586) (0.05975) (0.08495)
[-0.20408] [ 0.18481] [-1.69512] [-0.51964] [ 0.42296]
EBP(-11) 0.188911 0.071567 -0.027153 0.080050 -0.045516
(0.14449) (0.03777) (0.09340) (0.05822) (0.08278)
[ 1.30745] [ 1.89505] [-0.29071] [ 1.37486] [-0.54986]
EBP(-12) -0.040634 -0.034595 -0.018233 0.000132 0.054917
(0.12920) (0.03377) (0.08352) (0.05206) (0.07402)
[-0.31450] [-1.02443] [-0.21831] [ 0.00254] [ 0.74193]
PCEINFLATION(-1) 0.172466 0.009833 0.077708 0.006539 1.372125
(0.08503) (0.02222) (0.05496) (0.03426) (0.04871)
[ 2.02837] [ 0.44245] [ 1.41379] [ 0.19085] [ 28.1682]
PCEINFLATION(-2) -0.293351 0.033352 -0.124313 0.027653 -0.457107
(0.14298) (0.03737) (0.09242) (0.05761) (0.08191)
[-2.05175] [ 0.89248] [-1.34504] [ 0.47996] [-5.58056]
PCEINFLATION(-3) 0.179532 -0.082357 0.112884 -0.034881 0.015379
(0.14772) (0.03861) (0.09549) (0.05953) (0.08463)
[ 1.21531] [-2.13299] [ 1.18211] [-0.58596] [ 0.18172]
PCEINFLATION(-4) -0.078973 0.121111 -0.196572 -0.008432 0.132875
(0.14562) (0.03806) (0.09413) (0.05868) (0.08342)

[-0.54233] [ 3.18209] [-2.08829] [-0.14369] [ 1.59278]
PCEINFLATION(-5) -0.048402 -0.128904 0.286528 0.079450 -0.153009
(0.14293) (0.03736) (0.09239) (0.05759) (0.08188)
[-0.33865] [-3.45061] [ 3.10123] [ 1.37946] [-1.86865]
PCEINFLATION(-6) -0.010267 0.090114 -0.257716 -0.054016 0.102585
(0.14358) (0.03753) (0.09281) (0.05786) (0.08225)
[-0.07151] [ 2.40133] [-2.77676] [-0.93362] [ 1.24716]
PCEINFLATION(-7) 0.163069 -0.030910 0.299275 -0.069599 0.057099
(0.14443) (0.03775) (0.09337) (0.05820) (0.08275)
[ 1.12903] [-0.81880] [ 3.20541] [-1.19583] [ 0.69005]
PCEINFLATION(-8) -0.152756 -0.013118 -0.151375 0.123073 -0.153506
(0.14576) (0.03810) (0.09422) (0.05874) (0.08351)
[-1.04800] [-0.34433] [-1.60656] [ 2.09534] [-1.83827]
PCEINFLATION(-9) 0.065207 -0.014182 -0.016128 -0.085528 0.152079
(0.14646) (0.03828) (0.09468) (0.05902) (0.08391)
[ 0.44523] [-0.37048] [-0.17035] [-1.44918] [ 1.81249]
PCEINFLATION(-10) -0.312193 0.033804 -0.065411 0.017477 0.032650
(0.14637) (0.03826) (0.09462) (0.05898) (0.08385)
[-2.13292] [ 0.88361] [-0.69133] [ 0.29630] [ 0.38936]
PCEINFLATION(-11) 0.279984 -0.034635 0.139895 -0.005028 -0.162414
(0.14075) (0.03679) (0.09098) (0.05672) (0.08063)
[ 1.98924] [-0.94148] [ 1.53757] [-0.08865] [-2.01420]
PCEINFLATION(-12) -0.004658 0.022750 -0.074462 0.005815 0.038126
(0.08382) (0.02191) (0.05418) (0.03378) (0.04802)
[-0.05557] [ 1.03842] [-1.37425] [ 0.17215] [ 0.79395]
C 0.477025 0.124342 0.218264 0.087025 0.018364
(0.17635) (0.04609) (0.11400) (0.07106) (0.10103)
[ 2.70504] [ 2.69769] [ 1.91467] [ 1.22463] [ 0.18177]
R-squared 0.972998 0.991346 0.988547 0.813500 0.988997
Adj. R-squared 0.969132 0.990107 0.986907 0.786793 0.987421
Sum sq. resids 153.1446 10.46209 63.99462 24.86804 50.26377
S.E. equation 0.604566 0.158016 0.390809 0.243620 0.346354
F-statistic 251.6433 799.9726 602.7531 30.46074 627.6738
Log likelihood -406.9137 237.1562 -197.4936 29.35810 -139.5301
Akaike AIC 1.949640 -0.733984 1.077057 0.131841 0.835542
Schwarz SC 2.480059 -0.203566 1.607475 0.662260 1.365961
Mean dependent 1.376945 6.513542 5.127667 0.051699 4.274951
S.D. dependent 3.441029 1.588675 3.415417 0.527610 3.088147
Determinant resid covariance (dof adj.) 8.39E-06
Determinant resid covariance 4.25E-06
Log likelihood -437.0429
Akaike information criterion 3.091845
Schwarz criterion 5.743939

2. DO IMPULSE RESPONSE FUNCTIONS USING THE CHOLESKY DECOMPOSITION, FOR 60 LAGS.
ORDER THIS WAY: UNEMPLOYMENT RATE, PCE INFLATION, INDUSTRIAL PRODUCTION, EXCESS
BOND PREMIUM, THE 3-MONTH RATE.
-1.2
-0.8
-0.4
0.0
0.4
0.8
5 10 15 20 25 30 35 40 45 50 55 60
Response of IP to UNEMP
-1.2
-0.8
-0.4
0.0
0.4
0.8
5 10 15 20 25 30 35 40 45 50 55 60
Response of IP to PCEINFLATION
-1.2
-0.8
-0.4
0.0
0.4
0.8
5 10 15 20 25 30 35 40 45 50 55 60
Response of IP to IP
-1.2
-0.8
-0.4
0.0
0.4
0.8
5 10 15 20 25 30 35 40 45 50 55 60
Response of IP to EBP
-1.2
-0.8
-0.4
0.0
0.4
0.8
5 10 15 20 25 30 35 40 45 50 55 60
Response of IP to FFR
Response to Cholesky One S.D. Innovations ± 2 S.E.

3) EXPLAIN WHAT THE ORDERING IMPLIES REGARDING THE CORRELATION OF SAME-PERIOD
INNOVATIONS TO EACH OF THE VARIABLES.
Because the Cholesky decomposition method imposes a recursive structure on the variables, the
contemporary relationships of the variables is going to be affected by their ordering.
In this case, the first variable is unemployment rate, which means it is going to be affected by its
current innovation only and not by any of the subsequent variables’ current innovations.
Innovations to the second variable, pce inflation, will be affected by its current innovations, plus
those of the preceding unemployment rate variable. Innovations to the third variable, industrial
production, will be affected by its current innovations plus the current innovations of the preceding
two variables.
This pattern will continue all the way through to the last variable ordered. Therefore, the recursive
nature of Cholesky decomposition means the variable that is ordered first is going to have effects on
all the subsequent variables.
Thus, it makes sense to order the variables from most exogenous to least exogenous. In contrast, the
residual method sets the impulses to one standard deviation of the residuals, which ignores the
correlations in the VAR residuals. Therefore, when using the residual method, the order of the
impulse variables is not going to matter.
4) PLOT THE RESPONSE OF THE UNEMPLOYMENT RATE TO STANDARDIZED SHOCKS TO THE 5
VARIABLES.

The only shock that will affect the unemployment rate in the same period is a shock to itself - the
unemployment rate.
A shock to pceinflation will start to significantly affect the unemployment rate a few months after the
initial shock. Peak effects of the shock are felt after 30 months after which they slowly start to wear
off. This suggests that the unemployment rate will feel effects from a shock in pceinflation for at least
5 after the fact.
A shock to ip will be felt by unemp soon after the initial shock. In this case, unemployment rate will
actually go down until about the 15th
month when it will start trending back to its pre-shock level.
Unemp responds to a shock in ebp by rising sharply soon after the initial shock, peaking after about 17
months. The effects from the shock then begin to decrease, finally arrive back at zero between 50-55
months after the initial shock.
Ffr is the last impulse variable in this Cholesky impulse response function, which means it’s going to
include innovations from all the previous variables as well. A shock to the ffr will slowly start to
impact the unemployment rate after about 1 year. The effect will continue slowly climbing then start
to level off after about 35 months.

5) THE UNEMPLOYMENT RATE TENDS TO GO UP WHEN THE EBP GOES UP. HOW DOES THE EBP
AFFECT OTHER VARIABLES? PLOT THE IRF OF EACH OF THE 5 VARIABLES TO A STANDARDIZED
SHOCK TO THE EBP.
-.2
-.1
.0
.1
.2
.3
5 10 15 20 25 30 35 40 45 50 55 60
Response of UNEMP to EBP
-.6
-.4
-.2
.0
.2
.4
5 10 15 20 25 30 35 40 45 50 55 60
Response of PCEINFLATION to EBP
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
5 10 15 20 25 30 35 40 45 50 55 60
Response of IP to EBP
-.1
.0
.1
.2
.3
5 10 15 20 25 30 35 40 45 50 55 60
Response of EBP to EBP
-.5
-.4
-.3
-.2
-.1
.0
.1
.2
5 10 15 20 25 30 35 40 45 50 55 60
Response of FFR to EBP
Response to Cholesky One S.D. Innovations ± 2 S.E.

Explanation:
When you look at the effect that EBP has on unemp, pceinflation, IP, and FFR you can see that the
initial shock on these 4 variables is zero.
When you look at the response of the unemployment rate to a shock in EBP, a change of EBP
today has a peak effect on unemp around the 20th
month of about .18. This illustrates how when
credit conditions tighten, unemployment rate goes up. After this, the effects of the initial EBP’s
shock start to wear off and unemp has a gradual decrease back towards zero, and finally reaches
zero around the 52nd
month.
When credit conditions tighten, pceinflation will not immediately respond in that same period,
but shortly after pceinflation begins to drop and reaches a negative-peak effect around the 16th
month of about -.2. It takes about 55 months for inflation to return to pre-shock levels.
A shock on EBP today leads to a subsequent negative response by IP that continues to decline
until about the 10th
month where it hits a negative peak effect of -.75. At this point, IP begins to
rise back up until it reaches a positive peak effect on the 32nd
month of about .22. After the 32nd
month the effect of the ebp shock on ip stabilizes as it drifts closer towards zero.
The response of FFR due to a shock to EBP has a small but positive peak effect of about .015 during
the first month (which may or may not be statistically significant) and then drops to a negative
peak effect of about -.25 in the 17th
month. Subsequently the effect on FFR remains negative
however it gradually drifts back towards zero.
Additionally the effect of EBP on EBP has a positive initial effect of about .24, and then later
decreases towards zero by the 25th
month. In the periods after the initial EBP shock, EBP drops to
negative figures, and remain fairly constant around -.02.

6) LASTLY, SOLVE THE MODEL UP TO 2019 M12. FORECAST THE UNEMPLOYMENT RATE,
INCLUDING CONFIDENCE INTERVALS.
2
3
4
5
6
7
8
9
10
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
unemp unemp (Baseline Mean)
U_LB U_UB
The forecasted unemployment rate is pretty similar to that of the actual unemployment rate until
about the middle of 2014. At this time, the actual path of the unemployment rate continues its
downward trend while the forecasted unemployment rate starts declining at a slower rate until
the end of 2015 when we see the forecast starts to go back up as it heads back towards the mean.
7) REFERENCES
1, Investopedia. "Industrial Production and Capacity Utilization - G.17." Industrial Production and
Capacity Utilization. Investopedia, 2016. Web. 08 Aug. 2016.
2, The Federal Reserve. "Industrial Production and Capacity Utilization - G.17."Industrial Production
and Capacity Utilization. The Federal Reserve, 1 Apr. 2016. Web. 08 Aug. 2016.

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