2018-03-15Macro `n Cheese

# What if the stock market is the economy?

Despite demonstrating a complete lack of green thumbs (we have experts taking care of his office plants), in this edition of Macro-n-cheese Roger(squared) try to sow a new seed in the flora of business cycle models. A futile endeavor? You’ll be the judge.

In the barren fields of economic research, there are only a handful of academics devoted to cultivating fundamentally new ideas. One of those is Professor Roger Farmer (of Warwick, UCLA etc.), who has long questioned central tenets of the new-Keynesian heterodoxy. Among other things, he has written on ‘Endogenous Business Cycles’ (with steady state indeterminacy) and wants to replace New-Keynesian sticky prices with what he calls a ‘belief function’. Speaking as a layman I would label Farmer’s work as essays for developing a macro framework in Behavioral Economics, despite Farmer’s assertion that he’s an old-school (or perhaps ‘right-school’) Keynesian. Now, I must admit to not seeing eye to eye with all I have read of Farmer, but today I thought we would study an interesting alternative hypothesis to business cycles, in particular the Global Financial Crisis that he has put forward.

Note: In the graph above I, like Farmer, use the logs of Real S&P500 (deflated by the ‘money wage’, which is compensation of employees divided by FTE number of employees) and UNR (defined as (100*UNR)/(100-UNR )). These transformations produce new variables that are unbounded above and below, which is important since there is evidence that the two transformed variables are non-stationary but cointegrated. In order for a series to be non-stationary it must be able to increase or decrease without limit, independently of its current value.

##### Chart 1: There is some correlation…

In short, what we will have a look at is how well asset prices, in particular stock markets, explain the real economy; in particular, the unemployment rate. Below is a bivariate VAR(2) estimated for two periods, pre- and post-Volcker (i.e. a variant of “the great moderation”).

Dependent
variable
1953 Q1-1979 Q3 1979Q4-2017 Q4
p u p u
R2: 0.95 R2: 0.98
p(-1) 1.42
(0.0000)
-0.35
(0.0001)
1.29
(0.0000)
-0.22
(0.0000)
p(-2) -0.44
(0.0000)
0.26
(0.0127)
-0.30
(0.0000)
0.21
(0.0000)
u(-1) 0.14
(0.0419)
1.43
(0.0000)
-0.07
(0.5471)
1.56
(0.0000)
u(-2) -0.12
(0.0487)
-0.55
(0.0000)
0.08
(0.4330)
-0.60
(0.0000)
c -0.13
(0.1844)
-0.20
(0.0709)
0.06
(0.1499)
0.02
(0.4939)

Note: VAR(2) in levels. Probabilities within parenthesis.

##### Table 1: Quite steady coefficients, especially for the unemployment equation.

One thing that Farmer points out is that the coefficients seem quite stable, suggesting that the relation between stock markets and the real economy are also quite stable. This is an attractive feature in comparison to many other economic relationships that tend to break down during/after the great moderation. Admittedly, the coefficient stability is somewhat less remarkable in my calculations (then Farmer’s ditto) but, nonetheless, still decent. Farmer seems to suggest that this is a proof of no structural breaks in our series, though in my opinion this is an altogether different question.

Under any circumstances, when I proceed with putting the data into the Macrobond VECM-framework, cointegration rank tests are automatically computed. These indicate both that there is a unit root and that the series are cointegrated (1), over the full sample as well as in the two subsamples (pre-/post-Volcker) suggested by Farmer.

1953 Q1-1979 Q3 1979 Q4-2017 Q4 1953 Q1-2017 Q4
0 rank
(no coint.)
1 rank
(coint.)
0 rank
(no coint.)
1 rank
(coint.)
0 rank
(no coint.)
1 rank
(coint.)
Trace test 0.0002 0.8767 0.0000 0.4736 0.0000 0.7320
Maximum
Eigenvalue
0.0000 0.8767 0.0000 0.4736 0.0000 0.7320

Note: The fact that the Johansen test points to one cointegrating vector means, by default, that there indeed exists a unit root (which is why a unit root test is more nice than necessary).

##### Table 2: Cointegration is present

We cannot yet perform causality tests in Macrobond (keep’em support tickets coming!), but even main stream economists admit that empirical studies mostly support the idea that asset prices cause real economy responses. The fact that Farmer (and others) finds that stock markets cause unemployment does not, as Granger himself pointed out1, imply a means of control. For this, we need an economic model that chisels out the mechanism of the causal chain. And this is where Farmer gets interesting.

According to the traditional – fundamental – view of the business cycle, the GFC was caused by an event that signaled depressed earnings and, hence, increased unemployment for an extended period of time (at least until the next fundamental signal)2. Furthermore, according to this view, policy intervention is (or rather, would be) futile as it cannot stave off the fundamental causes of forward looking, unique equilibrium, market behavior.

1Granger (1980): “Testing for causality: a personal viewpoint”. Journal of Economic Dynamics and Control, p. 329–352.

2Absent any clear-cut event, the traditional model completely fails to explain the depth, breadth and longevity of the GFC.

Invoking Keynes “Animal Spirits”, Farmer instead paints the causal chain thus: For some reason, the perceived risk of doing business increased, and lower earnings were anticipated. As a result, market participants sold off shares in the belief that future market prices would be lower. Stock markets and the price of paper assets dropped, causing households to curtail spending, which in turn lead to worker lay-offs; and the reduced level of economic activity caused a self-fulfilling drop in company earnings.

In addition, and in contrast to the fundamental view, Farmer’s ‘animal spirits’ is also able to explain why large-scale asset purchases are an effective way of restoring confidence and resurrecting the economy. From a monetary policy perspective, this is an attractive and truly important feature of Farmer’s work.

– This begs the question: Is the stock market really the economy?

Granted, it would be easier to just apply Farmer’s model and run with it. However, due to lingering doubts of the stability of the VECM, or rather the stability of the cointegrating relationship3 I have nonetheless chosen to also estimate a simple bivariate VAR in levels4.

3Doubts that are only augmented when studying the out-of-sample performance when using the pre-Volcker or full sample coefficients.

4This is also suggested by the MB-application as the cointegrating relation with other specifications and (shorter) samples often is full rank (implying the variables are close to stationary).

$\left[\begin{array}{c}\Delta {u}_{t}\\ \Delta {p}_{t}\end{array}\right]=\left[\begin{array}{cc}0.57& -0.50\\ 0.06& 0.41\end{array}\right]\left[\begin{array}{c}\Delta {u}_{t-1}\\ \Delta {p}_{t-1}\end{array}\right]+\left[\begin{array}{c}-0.13\\ 0.00\end{array}\right]\left[\begin{array}{ccc}1& 1.71& 1.72\end{array}\right]\left[\begin{array}{c}{u}_{t-1}\\ {p}_{t-1}\\ c\end{array}\right]$

(VECM estimated Pre-Volcker)

As you will see, the Bivariate VAR outperforms the VECM during the GFC quite handsomely as the latter model seems to suggest considerably more persistence in unemployment than what post-GFC experiences de facto indicate.

That said the coefficient of the cointegrating vector, ‘α’, has the expected negative sign, albeit only insignificantly so in the stock market equation. As ‘α’ is -0.13 (and significant) in the unemployment equation it nonetheless suggests that unemployment adjusts toward the long run solution, the cointegrating equation, with some 13% per year. Encouragingly, independent of specifications, the parameter values for ‘α’, remain close to -0.1 (in a range of -0.13 to -0.09).

Now, turning to using stock markets as a forecasting tool for the real economy I have studied the out-of-sample5 performance of Farmer’s model for various horizons but here, for lack of space, I will focus on one multi-period forecast surrounding the GFC, in particular the period after the FED initiated the large scale asset purchases, LSAP by the end of 2008. Also, as my aim here is to find a functional forecast model, I have chosen to let the application find the best possible model6.

5Out-of-sample model evaluations is another feature I urge you to send us support tickets on!

6Using the Bayesian Information Criteria (BIC/Schwartz) and the default maximum of three lags and regressors.

##### Chart 2 a & b: Unemployment and the stock market, out of sample performance

Albeit far from perfect, the Bivariate VAR handsomely outperforms Farmer’s VECM-model, and this holds true even for different lag structures or estimation windows. Despite seemingly stable coefficients in Farmer’s model (the cointegrating vector), the generally poor out-of-sample fit suggests that the VECM is indeed mis-specified as discussed above. This, in turn, puts into question the idea that low-frequency movements of the stock market matter for the real economy.

That said, the occurrence of breaks in cointegrating equations are known to make ordinary VARs generate better forecasts even if the underlying data generating process is a VECM. Also, the lion’s share of model specifications I (incl. sample windows) suggest that the data is indeed cointegrated, implying there is some Granger causality, even if the direction is unclear.

In conclusion, and with the important caveat that Farmer’s claim of causality is correct, the statement that the stock market is the economy is at least plausible. Furthermore, the causal chain Farmer has laid out suggests that it can also be controlled, with the large-scale asset purchases from FED and other central banks being glaring examples. Hence, the apparent success of these policies should come as no surprise to those adhering to Farmer’s Keynesian interpretations (‘Farmerism’?).

To the rest of us– if nothing else – it increases the anxiety levels connected to the FED’s quantitative tightening process. Let’s hope our anxiety won’t instigate too much stock market volatility though. The economy depends upon it.

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