# Origins of Stock Market Fluctuations

*Daniel Greenwald, Martin Lettau, Sydney Ludvigson*
Link

Abstract

Three mutually uncorrelated economic disturbances that we measure empirically explain 85% of the quarterly variation in real stock market wealth since 1952. A model is employed to interpret these disturbances in terms of three latent primitive shocks. In the short run, shocks that affect the willingness to bear risk independently of macroeconomic fundamentals explain most of the variation in the market. In the long run, the market is profoundly affected by shocks that reallocate the rewards of a given level of production between workers and shareholders. Productivity shocks play a small role in historical stock market fluctuations at all horizons.

Summary

Overall a very interesting paper showing that most of the growth in the detrended value of the stock market over time is attributable to changes in the labor share. Important to my own efforts, demonstrates a decomposition of a non-stationary series into components attributable to various orthogonal shocks using a Cholesky decomposition within a VAR approach. Also includes some helpful discussion of the moving average representation of the VAR.

This uses a very similar methodology to the one I use in Don’t Discount Interest Rates to decompose the level of stock market wealth into various drivers. Notably, the authors argue for using separate regressions when regressing the outcome variable on the shocks, using a different regression for each shock rather than stuffing them all into the same regression. This works since all the shock are uncorrelated by assumption. This is obviously an important assumption, but clearly it can be rigorously justified.

Since $e_{c,t}$, $e_{y,t}$ and $e_{a,t}$ are mutually uncorrelated and i.i.d., we estimate these equations separately by OLS with L = 16 quarters.

They do the same thing I do where I get the cumulative decomposition by summing up the effects on the first differences.

The effect on the log levels of stock wealth of each disturbance is obtained by summing up the effects on the log differences

The one area where they do differ is that they include a deterministic linear trend in stock market wealth (edit: not sure this is actually different from my approach, it’s implicit since the underlying regressions are on first differences), which of course soaks up some of the non-stationarity and leaves less room to be explained by the shocks. However, it seems in reporting their results they report the explained variance of the detrended series, so it’s still possible for the shocks to “fully explain” stock market wealth over time. This feels OK – it makes sense in the context of the stock market to have a deterministic term since there does seems to be a strong force driving the market up over time that’s probably out of scope of this paper to explain.

One interesting chart was one showing the detrended stock market value against the cumulated factor share shock. They move very closely together, suggesting a tight relationship. Perhaps interesting for Don’t Discount Interest Rates, though I have a feeling this kind of chart would be tricky to explain to folks (cumulated shock? detrended stock market?):