This document presents a statistical analysis examining the impact of fiscal and monetary policies on the economy and stock market, using various macroeconomic variables as dependent measures. It concludes that empirical evidence does not support previously established 'truths' regarding positive correlations between these policies and economic indicators like RGDP, CPI, unemployment, and stock performance. The analysis reveals a divergence between expected and actual relationships, showing many correlations to be weak or of the wrong sign, raising doubts about the effectiveness of traditional quantitative models in accurately predicting economic behavior.

1. Statistical Analysis measuring the
impact of Fiscal and Monetary Policy
on the Economy and the Market
Gaetan Lion, September 29, 2021
1

2. Content
2
1. Introduction
2. What we know to be “true”
3. Defining the variables
4. Data Analysis
5. RGDP
6. CPI
7. Unemployment Rate
8. Stock Market
9. Conclusion

3. 1. Introduction
3
This is a study attempting to statistically measure the impact of Government policies on the economy and
the stock market. The “causal” Government policies considered will include:
• Fiscal Policy, entailing Budget Deficit spending;
• Monetary Policy with the Federal Reserve managing the Federal Funds rate; and
• Monetary Policy with the Federal Reserve conducting large purchases of securities (Treasuries, MBS);
The dependent or impacted macroeconomic variables affected by the above Government policies will
include:
• The overall economy (RGDP);
• Inflation (CPI);
• Unemployment Rate; and
• Stock market.

4. 2. What we know to be “true”
4

5. What we know to be “true” statements
5
• Fiscal Policy characterized by Budget Deficit spending stimulates the economy, reduces the
unemployment rate, increases inflation, and boosts the stock market;
• Monetary Policy-Federal Funds Rate. A decrease in the Federal Funds Rate (FF) stimulates the economy,
reduces the unemployment rate, increases inflation, and boosts the stock market, and vice versa;
• Monetary Policy-Quantitative Easing. When the Federal Reserve purchases securities (Treasuries,
Agencies securities), referred to as Quantitative Easing (QE), it stimulates the economy, reduces the
unemployment rate, increases inflation, and boosts the stock market, and vice versa.
We do not call any of the above “hypotheses” but instead “truths”; as each statement is backed up by some
empirical evidence and the foundation of Keynesian economics and modern economy management. Some of the
statements also relate to the Federal Reserve mandates of maintaining stable prices and sustainable low
unemployment rate.

6. “What we know to be true” table
6
RGDP CPI Unemployment Stock
Fiscal + + - +
Monetary-FF - - + -
Monetary-QE + + - +
Dependent Variables
Causal
Variables
The above table summarizes the objective of our statistical analysis; which is to confirm the directional impact of
the Government policy causal variables on the macroeconomics dependent variables.
The signs reflect the directional sign that the causal variables should have in any model that explains the behavior of
the macroeconomic dependent variable. We note that both Fiscal (an increase in Deficit Spending) and Monetary-
QE (Fed purchasing securities) have the same directional sign. Monetary-FF has the opposite sign as an increase in
FF will lower RGDP, CPI, and Stock market valuation, and increase the unemployment rate. This is all part of the
“truths” we know.

7. 3. Defining the Variables
7

8. The Dependent Variables:
RGDP, CPI, Unemployment Rate, Stock Market
8
RGDP: quarterly % change in Real GDP. Seasonally adjusted.
Source: FREDS (original data BEA).
CPI: quarterly % change in CPI (All Urban Consumers). Seasonally adjusted.
Source: FREDS (original data BLS).
Unemployment Rate: quarterly first difference in unemployment rate. Seasonally adjusted.
Source: FREDS (original data BLS).
Stock Market: quarterly % change in market value of total corporate equities (probably the most
encompassing measure of stock market cap).
Source: Table L.213 from the Z.1 Financial Accounts of the United States.

9. Fiscal Policy variable: Budget Deficit Spending
9
We measure Budget Deficit Spending by looking at the difference in total US Treasuries outstanding on
a quarterly basis. We look at this difference in two different ways:
a) Quarterly % change. In such case, we call this variable within our models just “fiscal”;
b) Quarterly first difference in Treasuries/GDP ratio. In this case, we call this variable “fiscal_gdp.” If
the Treasury to GDP ratio changes from 60% in Q1 to 70% in Q2, this variable value in Q2 would be:
70% - 60% = 10%.
The data source for US Treasuries is L.209 from the Z.1 Financial Accounts of the United States.
The data source for GDP (seasonally adjusted) is FREDS (original source BEA).

10. Monetary Policy Variable - QE
10
We measure Quantitative Easing (QE) conducted by the Federal Reserve in two different ways:
a) Quarterly % change in Federal Reserve holdings of Treasuries and Agency securities. In such case,
we call this variable within our models just “qe”;
b) Quarterly first difference in Federal Reserve holdings of Treasuries and Agency securities/GDP ratio.
In this case, we call this variable “qe_gdp.” If the Treasury to GDP ratio changes from 15% in Q1 to
20% in Q2, this variable value in Q2 would be : 20% - 15% = 5%.
The data source for QE related securities is L.109 from the Z.1 Financial Accounts of the United States.
The data source for GDP (seasonally adjusted) is FREDS (original source BEA).

11. Monetary Policy – Federal Funds Rate (FF)
11
We look at the quarterly first difference in FF. If FF increased from 1% in Q1 to 2% in
Q2, the variable value in Q2 will be: 2% - 1% = 1%.
Source: FREDS

12. 4. Data Analysis
12
The data runs from 1952Q1 to 2021Q1

13. 13
Scatter Plot Matrix
As shown, the
relationships between
the dependent
variables and the
causal variables look
for the most part
pretty weak, and near
random.

14. 14
Scatter Plot Matrix
1985Q4 – 2021Q1
We used a truncated
shorter time series to
observe if the effects
of Budget Deficit
Spending and QE,
when such
Government policies
had been more active
would leave a more
pronounced footprint
in the data. It did not.
Near randomness still
prevails when
assessing the
relationships between
the dependent
variables and the
causal ones.

15. 15
Scatter Plot Matrix with
more details using the
entire data set
The additional details include
split regression trendlines (red
lines), histogram showing the
statistical distributions of
variables (blue) and actual
correlation coefficients. As
shown, there is much
divergences within the causal
vs. dependent variables
relationships when compared
to the expected narrative
“truths” disclosed earlier.

16. 16
Scatter Plot Matrix with more
details using the data set from
1985Q4 to 2021Q1
Using the truncated time series did
not help in uncovering more
convergent linear relationships
between the causal and the
dependent variables.

17. Fiscal and Monetary Policies very active since the Great Recession
17
The graph on the left shows Fiscal Policy/GDP or our defined measure of Budget Deficit Spending/GDP. The one on the
right shows our defined measure of QE also scaled to GDP. The X-axis shows an Index reflecting the observation number
out of 274 (last data point being 2021Q1). Both graphs show how much more active has the Government and the
Federal Reserve been in their attempts to stimulate the economy during the Great Recession, the ensuing slow recovery,
and the recent COVID recession. See yellow highlighted area.

18. 18
The rhythm of the variables
based on % change (Fiscal
Policy and QE) vs. the ones
based on first difference in
the GDP ratio have a bit of
a different rhythm during
the recent period (Great
Recession onward).
This is simply due to the
different variable
transformations.
v

19. 19
Correlations with RGDP
FF Fiscal Fiscal/GDP QE QE/GDP
Spot 0.20 0.10 -0.43 -0.05 -0.26
Lag 1 -0.07 0.05 0.06 0.14 0.24
Lag 2 -0.10 0.03 -0.01 0.13 0.10
Lag 3 -0.03 0.09 0.13 0.08 0.09
Lag 4 -0.17 0.03 0.06 0.08 0.07
Correlations with CPI
FF Fiscal Fiscal/GDP QE QE/GDP
Spot 0.14 0.02 -0.18 -0.08 -0.15
Lag 1 0.18 0.05 -0.10 -0.02 -0.06
Lag 2 0.15 0.12 -0.04 0.02 -0.03
Lag 3 0.14 0.12 -0.04 0.00 -0.03
Lag 4 0.15 0.09 -0.05 -0.02 -0.03
We looked at correlations with the causal
variables lagged up to 4 quarters.
Most of the correlations between RGDP
and the causal variables are either really
weak or of the wrong sign.
Same comments for the correlations
between CPI and the causal variables.
The blue table indicates the respective
correlation sign, we would expect
between the causal and dependent
variables.

20. 20
The blue table indicates the respective
correlation sign, we would expect
between the causal and dependent
variables.
Most of the correlations between
Unemployment Rate and the causal
variables are either really weak or of the
wrong sign.
Correlations with Unemployment Rate
FF Fiscal Fiscal/GDP QE QE/GDP
Spot -0.22 -0.09 0.41 0.19 0.43
Lag 1 -0.06 -0.08 -0.06 -0.14 -0.29
Lag 2 -0.02 -0.01 -0.05 -0.13 -0.23
Lag 3 0.07 -0.14 -0.18 -0.11 -0.12
Lag 4 0.06 -0.10 -0.12 -0.09 -0.08
Correlations with Stock
FF Fiscal Fiscal/GDP QE QE/GDP
Spot -0.02 0.11 -0.10 0.09 0.01
Lag 1 -0.16 0.15 0.15 0.17 0.15
Lag 2 -0.07 0.06 0.10 0.16 0.12
Lag 3 -0.04 0.08 0.14 0.11 0.13
Lag 4 -0.02 0.11 0.15 0.04 0.07
Same comments for the correlations
between Stock and the causal variables.

21. Data Analysis section conclusion
21
The data analysis uncovered a huge divergence between “what we know to be true” and the actual
correlations between the mentioned causal variables and the dependent variables. In just about all
instances, none of the macroeconomic relationships that we expected to be pretty strong turned out to be
so. As shown many of the correlations had the wrong directional sign or were really weak.
Thus, it is unlikely that we will be able to develop quantitative models (various regression types) that do
any of the following acceptably well:
a) Include each type of the causal variables to explain the behavior (variance) of the dependent variable;
b) Fit the historical data;
c) Predict and forecast well;
d) Reduce materially the estimates error relative vs. using the average value as a sole estimate;
e) Demonstrate any explicit and explanatory (Granger) causality between the causal variables and the
dependent variables.
None of the above will preclude us from moving forward on this project. At times, what you can’t confirm
is just as informative as what you can.

22. 5. RGDP
22

23. RGDP OLS Regression
23
qe_gdpL1, ffL4, ffL2 were the 3 best
variables we could include in this RGDP
Model that had the correct sign and
were statistically significant at the Alpha
0.10 level. We could not include a single
variable related to Fiscal – Budget Deficit
Spending that had the appropriate sign
and adequate stat. significance.
The R Squares are very close to Zero. It
does not fit the historical data well. And,
can’t predict well.

24. 24
-10.0%
-8.0%
-6.0%
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
1953Q1
1955Q2
1957Q3
1959Q4
1962Q1
1964Q2
1966Q3
1968Q4
1971Q1
1973Q2
1975Q3
1977Q4
1980Q1
1982Q2
1984Q3
1986Q4
1989Q1
1991Q2
1993Q3
1995Q4
1998Q1
2000Q2
2002Q3
2004Q4
2007Q1
2009Q2
2011Q3
2013Q4
2016Q1
2018Q2
2020Q3
RGDP
quarterly
%
change
RGDP Model Estimate vs. Actual
Actual Estimate
-12.0%
-10.0%
-8.0%
-6.0%
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
1953Q1
1955Q2
1957Q3
1959Q4
1962Q1
1964Q2
1966Q3
1968Q4
1971Q1
1973Q2
1975Q3
1977Q4
1980Q1
1982Q2
1984Q3
1986Q4
1989Q1
1991Q2
1993Q3
1995Q4
1998Q1
2000Q2
2002Q3
2004Q4
2007Q1
2009Q2
2011Q3
2013Q4
2016Q1
2018Q2
2020Q3
RGDP
quarterly
%
change
RGDP Model Residual
RGD St. deviation 1.13%
Stand. Error 1.07%
Error reduction -5.2%
RGDP OLS Model
visual output
The RGDP OLS Model visual output confirms
that it is absent any material data fitting
information. The residuals, as shown, on
the bottom graphs are very large.
The standard error of the model (1.07%) is
nearly as large as RGDP’s standard deviation
(1.13%), resulting in an immaterial error
reduction (-5.2%) vs. just using an average
value to fit the historical data set.

25. RGDP VAR model
25
Estimate Std. Error t-stat p-value
ff.l1 -0.129 0.061 -2.121 0.035
ff.l2 -0.161 0.063 -2.577 0.011
ff.l3 -0.025 0.064 -0.393 0.695
ff.l4 -0.138 0.062 -2.229 0.027
-0.454
fiscal_gdp.l1 0.030 0.092 0.331 0.741
fiscal_gdp.l2 -0.231 0.093 -2.482 0.014
fiscal_gdp.l3 0.106 0.094 1.13 0.259
fiscal_gdp.l4 -0.073 0.094 -0.773 0.440
-0.167
qe_gdp.l1 0.441 0.089 4.947 0.000
qe_gdp.l2 -0.093 0.108 -0.858 0.391
qe_gdp.l3 0.033 0.109 0.299 0.765
qe_gdp.l4 0.022 0.100 0.219 0.827
0.403
rgdp.l1 0.248 0.082 3.035 0.003
rgdp.l2 0.126 0.084 1.505 0.133
rgdp.l3 0.033 0.084 0.39 0.697
rgdp.l4 0.030 0.086 0.347 0.729
0.437
Coef. Sums
ff -0.454
fiscal_gdp -0.167
qe_gdp 0.403
rgdp 0.437
We built a RGDP Vector Autoregression (VAR) model, using
standardized variables (for equal scale) to explore Granger
Causality. The causal variables using GDP ratios worked better
than the ones using quarterly % change. We used information
criteria to select the best number of lags.
Goodness-of-fit
Adj. R Square 0.147
Standard Error 0.920
Error reduct. -8.0%
Even though VAR is not focused on
statistical significance, notice the majority
of causal variables are not stat. significant.
When we sum the coefficients of all 4 lags,
the Fiscal_GDP variable has the wrong sign
(-). It confirms how we could not find a
Fiscal variable with the proper sign (+) in
the OLS regression.
Despite this RGDP VAR model including 16 different variables,
including 4 autoregressive one, this VAR Goodness-of-fit
measures are bad, including an Adjusted. R Square of only
0.147, associated with an error
reduction of – 8.0% vs. a model that
uses the average as a single output
(with a standardized standard
deviation of 1.0).

26. RGDP Granger Causality Test
26
RGDP is Granger caused by:
F p-value
ff 4.0 0.004
fiscal_gdp 1.7 0.148
qe_gdp 7.0 0.000
RGDP Granger causes:
F p-value
ff 8.7 0.000
fiscal_gdp 4.7 0.001
qe_gdp 2.0 0.097
These two tables allow you to figure out the direction of the causality. A causal
variable should Granger cause the dependent variable RGDP much more than the
reverse. However, as we can see for 2 out of the 3 causal variables this is not the case.
The Granger Causality F test values are a lot higher for RGDP “causing” the causal
variable than the reverse for both FF and Fiscal_GDP. Well, at least for FF, as observed
within the VAR model, the direction of the FF causality (negative) was correct. For
Fiscal_GDP, it was incorrect.
As shown, only the QE_GDP variable passes this Granger Causality test in terms of
direction (it Granger causes RGDP much more than the reverse. And, its related VAR
coefficients directional sign is correct (positive).
The results of our VAR & Granger Causality test
are consistent with our OLS Regression. In the
latter, we could not include a single Fiscal
variable with the correct sign. And, as shown
the QE_GDP variable was the most stat.
significant with the highest standardized
coefficient.

27. RGDP Cumulative Impulse Response Function
27
Cumulative Impulse Response Functions (IRFs) are an interesting output of VAR. Here, we show what is the impact of an
upward unanticipated shock of + 1 standard deviation in the causal variable on RGPD over the next 8 quarters (or 2 years).
The IRF graphs make good sense. A + 1 standard deviation shock in FF causes a – 0.5 standard deviation drop in RGDP phased
in over the next 8 quarters.
A similar shock in Fiscal_GDP causes a + 0.15 standard deviation increase in RGDP. Although the effect is weak, surprisingly it
has the correct sign.
A similar shock in QE_GDP causes a + 0.5 standard deviation increase in RGDP. Very similar to the FF shock, but in opposite
direction, which makes sense.

28. RGDP. Forecast Error Variance Decomposition (FEVD)
28
Forecast Error Variance Decomposition
Quarter rgdp ff fiscal_gdp qe_gdp
1 1.00 0.00 0.00 0.00
2 0.88 0.02 0.02 0.08
3 0.85 0.03 0.02 0.10
4 0.84 0.04 0.03 0.09
5 0.82 0.06 0.03 0.09
6 0.82 0.06 0.03 0.09
7 0.82 0.06 0.03 0.09
8 0.82 0.06 0.03 0.09
The FEVD indicates the amount of information each variable contributes to the other variables in the
autoregression. It determines how much of the forecast error variance of each of the variables can be explained by
exogenous shocks to the other variables.
The table above does not support “what we know to be true”, as over 80% of the information, as defined above, is
generated by the lags of RGDP.

29. RGDP section - Conclusion
29
As reviewed, the majority of quantitative tools we used did no support “what we know to
be true” regarding the relationship between RGDP and the causal variables.
A very interesting exception was the IRF related to the fiscal variable that at least confirms
a positive sign with RGDP. Why this was the case is challenging to explain.
Given the negative sum of coefficients within the VAR
model, we expected the IRF graph to show a negative
impulse shock. As shown on the graph, it was not the case.

30. 6. CPI
30

31. CPI OLS Regression
31
All R Squares are close to zero. After
including the best variable, Fiscal Lag 3
quarters (fiscalL3), we could not add any
other variables. Thus, we could not build
an adequate model to explain the
behavior of the CPI using our
Government policy causal variables.
In other words, regarding CPI “what we
know to be true” is not supported by the
data and the related quantitative
method.
The model resulting error reduction as
shown below is very close to Zero.
CPI St. deviation 0.800%
Stand. Error 0.796%
Error reduction -0.5%

32. CPI OLS Regression visual output
32
-3.0%
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
1953Q1
1955Q4
1958Q3
1961Q2
1964Q1
1966Q4
1969Q3
1972Q2
1975Q1
1977Q4
1980Q3
1983Q2
1986Q1
1988Q4
1991Q3
1994Q2
1997Q1
1999Q4
2002Q3
2005Q2
2008Q1
2010Q4
2013Q3
2016Q2
2019Q1
CPI
quarterly
%
change
CPI Model Estimates
Estimate Actual
-4.0%
-3.0%
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
4.0%
1953Q1
1955Q4
1958Q3
1961Q2
1964Q1
1966Q4
1969Q3
1972Q2
1975Q1
1977Q4
1980Q3
1983Q2
1986Q1
1988Q4
1991Q3
1994Q2
1997Q1
1999Q4
2002Q3
2005Q2
2008Q1
2010Q4
2013Q3
2016Q2
2019Q1
CPI Model Residual
As shown, this CPI OLS Regression model is really
bad; and is not statistically different from just using
the average quarterly % change in the CPI as a
single estimate.

33. CPI VAR model
33
Estimate Std. Error t-stat p-value
ff.l1 0.166 0.044 3.825 0.000
ff.l2 0.130 0.046 2.849 0.005
ff.l3 0.061 0.046 1.328 0.185
ff.l4 0.026 0.045 0.572 0.568
0.383
fiscal.l1 -0.059 0.054 -1.09 0.277
fiscal.l2 0.076 0.052 1.464 0.144
fiscal.l3 0.053 0.053 0.995 0.321
fiscal.l4 -0.025 0.055 -0.456 0.649
0.044
qe.l1 0.065 0.055 1.177 0.240
qe.l2 0.107 0.059 1.817 0.070
qe.l3 -0.057 0.058 -0.991 0.323
qe.l4 -0.023 0.054 -0.43 0.667
0.091
cpi.l1 0.228 0.065 3.521 0.001
cpi.l2 0.158 0.062 2.528 0.012
cpi.l3 0.372 0.063 5.889 0.000
cpi.l4 0.050 0.065 0.766 0.444
0.807
Sum of coefficients
ff 0.383
fiscal 0.044
qe 0.091
cpi 0.807
Using quarterly % change variables worked
a bit better than using GDP ratio variables.
Following information criteria, using 4 lags
was best.
Note that the sum of the FF coefficients have the wrong sign (-).
And, very few causal variables have both the correct sign and are
statistically significant.
This model has a relatively good R Square
of 0.53, associated with a good error
reduction of – 31.6%. However, this is
due to the autoregressive variables (cpi.l1, etc.). The causal
variables impart very little information into this CPI VAR model.
Adj. R Square 0.533
Standard Error 0.684
Error Reduction -31.6%

34. CPI Granger Causality Test
34
As shown, CPI Granger causes the Fiscal and QE variables a lot
more than the reverse. The causality goes in the wrong
direction.
FF Granger causes CPI much more than the reverse, which is a
good thing. But, as we know it has the wrong directional sign
(+) within the VAR*, which makes this a bad test outcome.
This test is consistent with our inability to develop a descent
CPI OLS Regression earlier.
* The directional sign is derived from the VAR, not the Granger
Causality test.
CPI is Granger caused by:
F p-value
ff 5.2 <.001
fiscal 1.3 0.28
qe 2.2 0.07
CPI Granger causes:
F p-value
ff 1.6 0.2
fiscal 6.3 <.001
qe 3.8 0.01

35. CPI Cumulative Impulse Response Function
35
FF -> CPI Fiscal -> CPI QE -> CPI
An upward shock in FF causing a
positive upward response in CPI
contradicts “what we know to be true.”
Both the shock in Fiscal and QE variables causing an upward response in CPI
make good sense. When either of those causal variables would incur an upward
shock of + 1 standard deviation, the CPI would respond with an upward increase
of + 0.3 standard deviation over the next 8 quarters. This response is not that
strong, but is actually surprisingly high given the very low sum of the VAR
coefficients of such causal variables (both much under 0.1).

36. CPI. Forecast Error Variance Decomposition (FEVD)
36
The FEVD indicates the amount of information each variable contributes to the other variables in the
autoregression. It determines how much of the forecast error variance of each of the variables can be explained by
exogenous shocks to the other variables.
The table above does not support “what we know to be true”, as over 85% of the information, as defined above, is
generated by the lags of RGDP. And, another 10% is generated by the FF variable that has the wrong sign.
Forecast Error Variance Decomposition
Quarter CPI FF Fiscal QE
1 1 0 0 0
2 0.95 0.05 0.00 0.00
3 0.89 0.08 0.01 0.03
4 0.87 0.08 0.01 0.03
5 0.86 0.09 0.01 0.03
6 0.86 0.10 0.01 0.03
7 0.86 0.10 0.02 0.03
8 0.85 0.10 0.02 0.03

37. CPI section - Conclusion
37
As reviewed, the majority of quantitative tools we used did no support “what we know to
be true” regarding the relationship between CPI and the mentioned causal variables.
A very interesting exception were the IRFs related to the Fiscal and QE variables that
generated convergent results. Why this was the case is challenging to explain.
Given the very low sum of
coefficients within the VAR
model, we expected the IRF
graphs to show an impact on
CPI a lot closer to Zero (the
horizontal red line). As shown
on the graph, it was not the
case.

38. 7. Unemployment Rate
38

39. Unemployment
OLS Regression
39
All R Squares are close to zero. After
including the best variable, QE/GDP Lag
1 quarter (qe_gdpL1), we could not add
any other variables. This is obviously a
really poor model that indicates we can’t
readily build an adequate model to
explain the behavior and forecast
Unemployment Rate using our
Government policy causal variables.
Again. “what we know to be true” is not
supported by the data and the related
quantitative method.
Y St. deviation 0.86%
Stand. Error 0.83%
Error reduction -3.3%

40. Unemployment Rate
OLS Regression visual output
40
As shown, this Unemployment Rate OLS Regression
model is really bad; and is not statistically different
from just using the average quarterly first
difference in the Unemployment Rate as a single
estimate.

41. Unemployment VAR model
41
Using GDP ratio variables worked a bit
better than quarterly % change variables.
Following information criteria, using 4 lags
was best.
Note that the sum of the FF coefficients and QE_GDP coefficients
have the wrong sign. And, very few causal variables have both
the correct sign and are statistically significant.
The R Square is close to Zero. The related
error reduction of – 4.9% vs. just using
the Average as a single estimate is
immaterial. This is especially true given
that the Fiscal_GDP variable has the
wrong sign (when summing coefficients
for all the lags).
Estimate Std. Error t-stat p-value
ff.l1 -0.087 0.063 -1.382 0.168
ff.l2 -0.015 0.064 -0.240 0.811
ff.l3 0.085 0.065 1.315 0.190
ff.l4 0.100 0.063 1.580 0.115
0.083
fiscal_gdp.l1 0.160 0.087 1.843 0.066
fiscal_gdp.l2 0.213 0.089 2.387 0.018
fiscal_gdp.l3 -0.121 0.090 -1.340 0.181
fiscal_gdp.l4 -0.054 0.090 -0.603 0.547
0.197
qe_gdp.l1 -0.231 0.114 -2.024 0.044
qe_gdp.l2 -0.213 0.138 -1.551 0.122
qe_gdp.l3 -0.015 0.137 -0.110 0.912
qe_gdp.l4 -0.040 0.123 -0.328 0.744
-0.500
unemp.l1 -0.136 0.100 -1.359 0.175
unemp.l2 -0.086 0.100 -0.863 0.389
unemp.l3 0.069 0.102 0.680 0.497
unemp.l4 0.090 0.100 0.898 0.370
-0.064
Sum of coefficients
ff 0.083
fiscal_gdp 0.197
qe_gdp -0.500
unemp -0.064
Adj. R Square 0.107
Standard Error 0.951
Error Reduction -4.9%

42. Unemployment Rate Granger Causality Test
42
The only variable that appears to have an adequate Granger
causality is QE_GDP. Both the direction of the causal
relationship and its directional sign (-) are correct*. This is not
the case for the other two variables.
The result of this Granger Causality test explains why we could
include just a single variable (a QE_GDP one) within our OLS
Regression with the correct sign that was statistically
significant.
* The directional sign is derived from the VAR, not the Granger
Causality test.
Unemp. rate is Granger caused by:
F p-value
ff 1.4 0.235
fiscal_gdp 3.8 0.005
qe_gdp 4.8 <.001
Unemp. rate Granger causes:
F p-value
ff 3.8 0.005
fiscal_gdp 0.6 0.669
qe_gdp 0.8 0.504

43. Unemployment Rate Cumulative Impulse Response Function
43
Somewhat consistent with the sum of the coefficients of the VAR model, only the IRF for the QE_GDP variable (right
hand graph) makes good sense. QE does indeed reduce the unemployment rate as it should. And, the impact of an
upward shock in QE is fully digested after 6 quarters resulting in a – 0.4 standard deviation in unemployment rate
after an upward shock of + 1 standard deviation in QE (measured as first difference in QE/GDP ratio).
FF -> Unemployment Rate Fiscal_GDP -> Unemployment Rate QE_GDP -> Unemployment Rate

44. Unemployment Rate. Forecast Error Variance Decomposition (FEVD)
44
The FEVD indicates the amount of information each variable contributes to the other variables in the
autoregression. It determines how much of the forecast error variance of each of the variables can be explained by
exogenous shocks to the other variables.
The table above does not support “what we know to be true”, as over 88% of the information, as defined above, is
generated by the lags of Unemployment Rate. And, the remainder is in part provided by one causal variable
(Fiscal_GDP) that has the wrong directional sign.
Forecast Error Variance Decomposition
Quarter unemp ff fiscal_gdp qe_gdp
1 1 0 0 0
2 0.968 0.011 0.006 0.015
3 0.933 0.012 0.015 0.040
4 0.908 0.016 0.032 0.043
5 0.894 0.018 0.044 0.045
6 0.892 0.019 0.044 0.045
7 0.890 0.020 0.045 0.045
8 0.885 0.021 0.049 0.045

45. Unemployment Rate section - Conclusion
45
As reviewed, for the most part the quantitative methods we used did no support “what we
know to be true” regarding the relationship between Unemployment Rate and the
mentioned causal variables.
One worthy exception was the relationship between QE and Unemployment Rate that
made good sense. A boost in QE reduces the Unemployment Rate.

46. 8. Stock Market
46

47. Stock Market
OLS Regression
47
All R Squares are close to zero. This
indicates we can’t readily build an
adequate model to explain the behavior
of the Stock Market using our
Government policy causal variables.
Again. “what we know to be true” is not
supported by the data and the related
quantitative method.
Y St. deviation 8.2%
Stand. Error 8.0%
Error reduction -2.1%

48. Stock Market
OLS Regression visual output
48
As shown, this Stock Market OLS Regression model
is really bad; and is not that different from just
using the average quarterly % change in the Stock
Market total capitalization as a single estimate. -30%
-20%
-10%
0%
10%
20%
30%
1953Q1
1955Q3
1958Q1
1960Q3
1963Q1
1965Q3
1968Q1
1970Q3
1973Q1
1975Q3
1978Q1
1980Q3
1983Q1
1985Q3
1988Q1
1990Q3
1993Q1
1995Q3
1998Q1
2000Q3
2003Q1
2005Q3
2008Q1
2010Q3
2013Q1
2015Q3
2018Q1
2020Q3
Stock
quarterly
%
change
Stock Market Model Estimates
Estimate Actual
-4%
-3%
-2%
-1%
0%
1%
2%
3%
4%
1953Q1
1955Q3
1958Q1
1960Q3
1963Q1
1965Q3
1968Q1
1970Q3
1973Q1
1975Q3
1978Q1
1980Q3
1983Q1
1985Q3
1988Q1
1990Q3
1993Q1
1995Q3
1998Q1
2000Q3
2003Q1
2005Q3
2008Q1
2010Q3
2013Q1
2015Q3
2018Q1
2020Q3
Stock
quarterly
%
change
Stock Market Model Residual
Residual

49. Stock Market VAR model
49
Using quarterly % change variables worked
a bit better. Following information criteria,
using 4 lags was best.
Note that only one causal variable is stat.
significant out of 12 (when you include all the
lags).
The R Square is close to Zero. The related
error reduction of – 0.6% vs. just using
the Average as a single estimate is
immaterial.
Estimate Std. Error t-stat p-value
ff.l1 -0.157 0.064 -2.450 0.015
ff.l2 -0.079 0.065 -1.214 0.226
ff.l3 -0.037 0.065 -0.574 0.567
ff.l4 0.011 0.065 0.166 0.868
-0.262
fiscal.l1 0.080 0.076 1.052 0.294
fiscal.l2 -0.048 0.074 -0.648 0.517
fiscal.l3 0.007 0.077 0.092 0.927
fiscal.l4 0.043 0.081 0.533 0.594
0.082
qe.l1 0.077 0.079 0.974 0.331
qe.l2 0.072 0.085 0.843 0.400
qe.l3 0.065 0.084 0.772 0.441
qe.l4 -0.015 0.079 -0.187 0.852
0.199
stock.l1 -0.016 0.062 -0.253 0.800
stock.l2 -0.035 0.065 -0.529 0.598
stock.l3 -0.002 0.067 -0.026 0.979
stock.l4 -0.028 0.065 -0.430 0.668
-0.080
Sum of coefficients
ff -0.262
fiscal 0.082
qe 0.199
stock -0.080
Adj. R Square 0.024
Stand. Error 0.994
Error Reduct. -0.6%

50. Stock Market Granger Causality Test
50
For all three causal variables, the Stock Market Granger
causes them a lot more than the reverse. Again, the Granger
Causality goes in the wrong direction.
Stock Market is Granger caused by:
F p-value
ff 1.73 0.143
fiscal 0.53 0.712
qe 1.44 0.221
Stocke Market Granger causes:
F p-value
ff 5.63 <.001
fiscal 4.89 <.001
qe 3.92 0.004

51. Stock Market Cumulative Impulse Response Function
51
Consistent with the sum of the coefficients of the VAR model, all the IRF graphs make good directional sense.
Nevertheless, notice that all the respective shocks’ impacts are rather weak (around 0.3 standard deviation in Stock
Market movement for a 1 standard deviation shock in the causal variable).
FF - > Stock Market Fiscal- > Stock Market QE - > Stock Market

52. Stock Market. Forecast Error Variance Decomposition (FEVD)
52
The FEVD indicates the amount of information each variable contributes to the other variables in the
autoregression. It determines how much of the forecast error variance of each of the variables can be explained by
exogenous shocks to the other variables.
The table above does not support “what we know to be true”, as over 94% of the information, as defined above, is
generated by the lags of the Stock Market variable. And, the remainder is in good part provided by two causal
variables that have the wrong directional sign.
Forecast Errror Variance Decomposition
Quarter stock ff fiscal qe
1 1 0 0 0
2 0.967 0.025 0.004 0.004
3 0.957 0.029 0.004 0.010
4 0.953 0.029 0.005 0.013
5 0.950 0.029 0.008 0.013
6 0.948 0.029 0.010 0.013
7 0.946 0.029 0.010 0.014
8 0.944 0.029 0.010 0.016

53. Stock Market – section Conclusion
53
As reviewed, the quantitative tools we used did no support “what we know to be true”
regarding the relationship between Stock Market and the mentioned causal variables.
The adjusted R Square of both the OLS Regression and VAR were close to Zero. And, most
often, the Granger causality was going in the wrong direction.

54. 9. Conclusion
54

55. The “truths”
55
RGDP CPI Unemployment Stock
Fiscal + + - +
Monetary-FF - - + -
Monetary-QE + + - +
RGDP CPI Unemployment Stock
Fiscal NA + NA +
Monetary-FF - NA NA -
Monetary-QE + NA - +
RGDP CPI Unemployment Stock
Fiscal - + + +
Monetary-FF - + + -
Monetary-QE + + - +
RGDP CPI Unemployment Stock
Fiscal + + - +
Monetary-FF - + - -
Monetary-QE + + - +
IRFs
OLS
Regression
VAR
In many
instances, the
statistical
methods
(OLS, VAR,
IRFs) do not
support the
“truths”

56. The models do not explain the behavior of Y
56
RGDP CPI Unemployment Stock
OLS Regression 0.08 0.01 0.08 0.03
VAR 0.15 0.53* 0.11 0.02
Adjusted R Square
* This relatively high R Square is entirely due to the autoregressive CPI variables, and
not due to any of the causal variables.

57. Other Causality related measures
57
RGDP CPI Unemployment Stock
FEVD explained
by Y
82% 85% 88% 94%
Granger Causality
wrong direction
2 out 3 2 out 3 1 out 3 3 out 3
Invariably, the autoregressive Y variables account for over 80% to close to 100% of the Forecast Error Variance
Decomposition (FEVD) within the VAR models. In turn, this means that the 3 causal variables (FF, Fiscal, QE)
explain very little of the mentioned FEVD.
As shown, the Granger causality often runs in the wrong direction where the Y variable Granger causes the causal
variable much more than the reverse.

58. Correlations are most informative
58
Correlations with RGDP Correlations with CPI
FF Fiscal Fiscal/GDP QE QE/GDP FF Fiscal Fiscal/GDP QE QE/GDP
Spot 0.20 0.10 -0.43 -0.05 -0.26 Spot 0.14 0.02 -0.18 -0.08 -0.15
Lag 1 -0.07 0.05 0.06 0.14 0.24 Lag 1 0.18 0.05 -0.10 -0.02 -0.06
Lag 2 -0.10 0.03 -0.01 0.13 0.10 Lag 2 0.15 0.12 -0.04 0.02 -0.03
Lag 3 -0.03 0.09 0.13 0.08 0.09 Lag 3 0.14 0.12 -0.04 0.00 -0.03
Lag 4 -0.17 0.03 0.06 0.08 0.07 Lag 4 0.15 0.09 -0.05 -0.02 -0.03
Average -0.03 0.06 -0.04 0.08 0.05 Average 0.15 0.08 -0.08 -0.02 -0.06
Correlations with Unemployment Rate Correlations with Stock
FF Fiscal Fiscal/GDP QE QE/GDP FF Fiscal Fiscal/GDP QE QE/GDP
Spot -0.22 -0.09 0.41 0.19 0.43 Spot -0.02 0.11 -0.10 0.09 0.01
Lag 1 -0.06 -0.08 -0.06 -0.14 -0.29 Lag 1 -0.16 0.15 0.15 0.17 0.15
Lag 2 -0.02 -0.01 -0.05 -0.13 -0.23 Lag 2 -0.07 0.06 0.10 0.16 0.12
Lag 3 0.07 -0.14 -0.18 -0.11 -0.12 Lag 3 -0.04 0.08 0.14 0.11 0.13
Lag 4 0.06 -0.10 -0.12 -0.09 -0.08 Lag 4 -0.02 0.11 0.15 0.04 0.07
Average -0.03 -0.08 0.00 -0.06 -0.06 Average -0.06 0.10 0.09 0.11 0.10
The simplest tool (correlation) is also the most informative. As reviewed earlier, just about all the correlations are
either of the wrong sign (orange) or very weak (close to Zero), and not supportive of “what we know to be true.”

59. Considerations
59
In plain English, none of the statistical methods we used could confirm “what we know to be true”
regarding well accepted macroeconomic relationships.
It is possible that other quantitative approaches could be more successful relying on data usingnon
detrended variables at their respective nominal levels. This may allow for Cointegration and Error
Correction model structures. However, such attempt would raise the following issues: variable
cointegration, non stationarity & unit roots, Y autocorrelation, etc.
Given the divergent underlying nature of the variables considered within our models, the mentioned
issues may be challenging to overcome.