*A Mark Sadowski post*

In this post we are going to add US stock market indices to the baseline VAR which I developed in these three posts. (1, 2, 3).

In particular, we are going to add the Dow Jones Industrial Average (DJIA) and the S&P 500 Index (SP500).

The first thing I want to do is to demonstrate that the monetary base Granger causes stock market indices during the period from December 2008 through May 2015. Here is a graph of the natural log of SBASENS and DJIA.

And here is a graph of the natural log of SBASENS and SP500.

The following analysis is performed using a technique developed by Toda and Yamamoto (1995).

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for all three series. I set up two two-equation VARs in the log levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of two for the VAR that includes the Dow Jones Industrial Average as a variable. An LM test suggests that there is no problem with serial correlation at this lag length. The AR roots table suggests that the VAR is dynamically stable, and the Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that the two series are not cointegrated at this lag length.

Most information criteria suggest a maximum lag length of five for the VAR that includes the S&P 500 Index as a variable. An LM test suggests that there is no problem with serial correlation at this lag length. The AR roots table suggests that the VAR is dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that the two series are not cointegrated at this lag length.

Then I re-estimated the two level VARs with one extra lag of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 3, I left the intervals at 1 to 2 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, the results are as follows:

- I fail to reject the null that the Dow Jones Industrial Average does not Granger cause the monetary base, but I reject the null that the monetary base does not Granger cause the Dow Jones Industrial Average at the 1% significance level.
- I fail to reject the null that the S&P 500 Index does not Granger cause the monetary base, but I reject the null that the monetary base does not Granger cause the S&P 500 Average at the 1% significance level.

In other words there is strong evidence that the monetary base Granger causes stock market indices, but not the other way around.

Since the monetary base Granger causes stock market indices they should probably be added to our baseline VAR model. This is because, under these circumstances, we might expect shocks to the monetary base in the VAR model to lead to statistically significant changes in the stock market indices.

With the Dow Jones Industrial Average added to the baseline VAR model, most information criteria suggest a maximum lag length of three. However, an LM test suggests that there is problem with serial correlation at this lag length. Increasing the lag length to four eliminates this problem. An AR roots table shows the VAR to be dynamically stable.

With the S&P 500 Index added to the baseline VAR model, most information criteria suggest a maximum lag length of three. However, an LM test suggests that there is problem with serial correlation at this lag length. Increasing the lag length to four eliminates this problem. An AR roots table shows the VAR to be dynamically stable.

The Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that there exists one cointegrating equation at this lag length in both VARs. But this is expected, since we already have evidence that the monetary base is cointegrated with industrial production. This matter is addressed in greater detail in the three posts where the baseline VAR is developed.

I am using a recursive identification strategy (Choleskey decomposition), which is the dominant practice in the empirical literature on the transmission of monetary policy shocks. Such a strategy means that the order of the variables affects the results. For the four-variable VARs I am arranging the output level first, the price level second, the monetary policy instrument third, and the financial variable last in the vector. This ordering assumes that the Federal Open Market Committee (FOMC) sees the current output level and price level when it sets the policy instrument, and that the output level and price level respond to a policy shock with one lag, but that financial markets respond to a policy shock with ** no lag**.

As before, the response standard errors I will show are analytic, since Monte Carlo standard errors change each time an Impulse Response Function (IRF) is generated. Here are the responses to the monetary base and the stock market indices in the four-variable VARs.

The response of the Dow Jones Industrial Average to a positive shock to the monetary base is significantly positive from month one through month three. The instantaneous response of the S&P 500 Index is positive but statistically insignificant. This is followed by a statistically significant positive response in month two. Furthermore a positive shock to the Dow Jones Industrial Average in month one leads to a statistically significant positive response in the level of industrial production in months four through eight, and a positive shock to the S&P 500 Index in month one leads to a statistically significant positive response in the level of industrial production from months five through eight.

The IRFs show that a positive 2.3% shock to the monetary base in month one leads to a peak increase in the Dow Jones Industrial Average of 1.6% in month three. In turn, a positive 2.3% shock to the Dow Jones Industrial Average in month one leads to a peak increase in industrial production of 0.15% in month five.

The IRFs also show that a positive 2.2% shock to the monetary base in month one leads to a peak increase in the S&P 500 Index of 1.5% in month three. In turn, a positive 2.7% shock to the S&P 500 Index in month one leads to a peak increase in industrial production of 0.17% in month eight.

That Quantitative Easing (QE) raises stock prices is probably one of the least controversial claims about it. In fact, perhaps one of the most iconic images in the age of zero interest rate policy (ZIRP) is the series of graphs concerning the relationship between the S&P 500 Index and QE posted by Bill McBride of Calculated Risk, such as this one. (The references to “Operation Twist” are, if anything, a distraction.)

Nominal stock prices have probably risen in response to positive shocks to the monetary base due to higher Nominal GDP (NGDP) expectations.

So the real question is why might higher stock prices lead to higher output?

James Tobin’s q theory provides one mechanism through which increased NGDP expectations may increase output through its effects on the prices of stocks. Tobin defines q as the market value of corporations divided by the replacement cost of their physical capital. If q is high the market price of corporations is high relative to the replacement cost of their physical capital, and new equipment and structures is cheap relative to the market value of corporations. Corporations can then issue stock and get a high price for it relative to the cost of the equipment and structures they are buying. Thus nominal investment spending will rise because corporations can purchase new equipment and structures with only a small issue of stock.

Franco Modigliani’s life-cycle theory of consumption provides another mechanism through which increased NGDP expectations may increase output through its effects on the prices of stocks. In the life-cycle model, consumption spending is determined by the expected resources of consumers, which are made up of human capital, physical capital and financial wealth. A major component of financial wealth is the holdings of stock shares. When stock prices increase, the value of financial wealth increases, thus increasing the expected resources of consumers, and nominal consumption spending rises.

**The bottom line is, in the Age of ZIRP, positive shocks to the monetary have probably raised NGDP expectations, which has raised stock prices, which has increased nominal investment and consumption spending, which has raised real output.**

Next time I shall add a measure of the value of the dollar to the baseline VAR. How has QE affected the value of the dollar, and how have changes in the value of the dollar impacted the economy?

Tune in next time and find out.

Mark,

Thanks for the continuing posts. The stock market variables effects look as expected. A few ideas, again from more of a forecasting perspective vs. effect testing. It’s ironic, but sometimes measures other than the market itself are helpful in measuring expectations and connecting financial market impacts to the “economy” (which from a modeling perspective, I have found difficult to achieve). To wit, the dividend yield and consumption/wealth (“Cay”) ratio have been used as measures of the equity premium, which may reflect expectations “better” than the market itself! Robert Shiller maintains a database of monthly dividend yields (real or nominal) at http://www.econ.yale.edu/~shiller/data.htm. Cay is from Lettau and Ludvigson 2001 http://www.econ.nyu.edu/user/ludvigsons/eqprem1.pdf. It is somewhat controversial, and there has been a lot of work in this area since, but it may in some way, fit in with your Modigliani reasoning.

Perhaps the main thing that your modeling has me thinking about is whether or not this type of model needs to be done in terms of (or at least augmented by) UNEXPECTED changes in the monetary base and its impacts on expectations and nominal financial and economic variables. This of course requires a model for expected changes to the monetary base 🙂 . Forward guidance? Fed fund futures? Adaptive expectations ? Announcement effects? Maybe the VECM after all? Phew! What do you think?

I look forward to your extensions you mentioned regarding fiscal and currency variables.

gofx,

1) I shall add Cay to the list of variables that I need to check. Thanks!

2) Romer and Romer developed a measure of unanticipated federal funds rate changes that showed that monetary policy had stronger effects on output and prices than previously estimated.

http://eml.berkeley.edu/~dromer/papers/AER_September04.pdf

And there are several studies (e.g. Bernanke and Kuttner, 2005) that show that most of the effect of monetary policy on financial markets is from unanticipated changes. So there is good precedence for what you are suggesting.

However, in the limited number of papers that have done what I am attempting to do here (five, counting Hayashi and Koeda, 2014) none try to estimate the unexpected change of the monetary base (or however the stock of QE is measured). It may be because it is difficult to estimate, or it may simply be because nobody has tried to do it yet.

So you have given me a lot more to chew on.

Mark,

Thanks for those references,Those look really helpful and I will give them a look. Expectations are important—-and hard to measure. Keep up the good work!