Impact of Fiscal and Monetary Policy on the Economy and the Market PowerPoint Presentation

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

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2 Content Introduction What we know to be “true” Defining the variables Data Analysis RGDP CPI Unemployment Rate Stock Market Conclusion

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3 1. Introduction 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.

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4 2. What we know to be “true”

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5 What we know to be “true” statements 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.

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6 “What we know to be true” table 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.

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7 3. Defining the Variables

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8 The Dependent Variables: RGDP, CPI, Unemployment Rate, Stock Market 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.

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9 Fiscal Policy variable: Budget Deficit Spending 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: Quarterly % change. In such case, we call this variable within our models just “fiscal”; 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).

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10 Monetary Policy Variable - QE We measure Quantitative Easing (QE) conducted by the Federal Reserve in two different ways: Quarterly % change in Federal Reserve holdings of Treasuries and Agency securities. In such case, we call this variable within our models just “qe”; 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).

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11 Monetary Policy – Federal Funds Rate (FF) 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

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

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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.

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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.

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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.

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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.

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17 Fiscal and Monetary Policies very active since the Great Recession 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.

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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

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The blue table indicates the respective correlation sign, we would expect between the causal and dependent variables. 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. 19

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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. Same comments for the correlations between Stock and the causal variables.

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21 Data Analysis section conclusion 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: Include each type of the causal variables to explain the behavior (variance) of the dependent variable; Fit the historical data; Predict and forecast well; Reduce materially the estimates error relative vs. using the average value as a sole estimate; 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.

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22 5. RGDP

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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.

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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 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 6.0% 4.0% 2.0% 0.0% -2.0% -4.0% -6.0% -8.0% -10.0% -12.0% 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.

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RGDP VAR model 25 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. 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).

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RGDP Granger Causality Test 26 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.

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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.

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28 RGDP. Forecast Error Variance Decomposition (FEVD) 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.

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29 RGDP section - Conclusion 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.

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30 6. CPI

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31 CPI OLS Regression 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.

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32 CPI OLS Regression visual output 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% -3.0% 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 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 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% -3.0% -4.0% 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.

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33 CPI VAR model 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.

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34 CPI Granger Causality Test 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.

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35 CPI Cumulative Impulse Response Function 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).

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36 CPI. Forecast Error Variance Decomposition (FEVD) 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.

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37 CPI section - Conclusion 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.

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38 7. Unemployment Rate

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39 Unemployment OLS Regression 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.

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40 Unemployment Rate OLS Regression visual output 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.

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41 Unemployment VAR model 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).

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42 Unemployment Rate Granger Causality Test 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.

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43 Unemployment Rate Cumulative Impulse Response Function 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

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44 Unemployment Rate. Forecast Error Variance Decomposition (FEVD) 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.

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45 Unemployment Rate section - Conclusion 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.

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46 8. Stock Market

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47 Stock Market OLS Regression 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.

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48 Stock Market OLS Regression visual output 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 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 4% 3% 2% 1% 0% -1% -2% -3% -4% Residual

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49 Stock Market VAR model 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.

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50 Stock Market Granger Causality Test 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: Stocke Market Granger causes:

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51 Stock Market Cumulative Impulse Response Function 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

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52 Stock Market. Forecast Error Variance Decomposition (FEVD) 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.

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53 Stock Market – section Conclusion 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.

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54 9. Conclusion

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The “truths” 55 IRFs OLS Regression VAR In many instances, the statistical methods (OLS, VAR, IRFs) do not support the “truths”

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56 The models do not explain the behavior of Y 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.

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57 Other Causality related measures 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.

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58 Correlations are most informative 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.”

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59 Considerations 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.