A new paper proposes a practical method for identifying asset price bubbles. First, one estimates deviations of prices from fundamentals based on three different approaches: a structural model, an econometric data-rich regression, and a purely statistical trend filter. Then one computes the first principal component of the three deviation series as an estimate for the common component behind them. As a general approach the method holds promise for detecting price distortions in financial markets and setback risk for ongoing trends.

*The post ties in with SRSV’s summary lecture on price distortions, particularly the section on detecting price distortions.
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*The below are excerpts from the paper. Emphasis and cursive text have been added.*

### What are bubbles and why do we need to identify them?

“Bubbles rely on the notion of a fundamental value and on excessive movements of prices without reference to the fundamental value. Thus, Fama (2014) defines bubbles as ‘an __irrational strong price increase that implies a predictable strong decline__’.”

*From a more technical angle bubbles are defined as ‘episodes of unsustainable and quickening asset price growth with accelerating corrections and rebounds’. View SRSV post on causes and pattern recognition of such bubbles here.*

“In a rational bubble model…the __asset price is decomposed into a fundamental value, equal to the sum of expected cash-flows, and a bubble component__, which is a rational stochastic deviation from the fundamental value growing with the discount factor…rational bubbles have explosive conditional expectations.”

“It is __crucial to disentangle asset price movements driven by fundamentals from movements resulting from the bubble component__. First, [*bubbles*] may generate a misallocation of capital. Second, [*bubbles*] entail risk for financial stability jeopardizing the functioning of the financial system. Third, bubble bursts are associated with financial crises and with deeper and longer recessions. Fourth, the transmission of monetary policy may be impaired if the dynamic of bubbles goes against the response of fundamentals to monetary policy.”

“Asset price bubbles are unobserved and there is no consensus on the most appropriate way to identify them empirically. This reflects theoretical controversies.”

### What are the key methods for estimating bubbles?

“We first estimate fundamental or trend values and compute deviations of asset prices from these fundamental and trend values. We do so for stock and housing prices in the United States… Data are available from January 1986 to August 2016 …The residuals capture the component of the asset price unrelated to macroeconomic and financial fundamentals.”

“Three empirical approaches – structural, econometric and statistical – may be considered to identify bubbles…

- According to a
**structural model**, the__bubble is a deviation of the asset price from expected discounted cash flows__…The fundamental value is related to the cash-flows and the discount factor only…Assuming risk- neutral agents, a constant discount factor and constant cash-flows [*this model*] determines the fundamental value as…the ratio of the real dividend..[*and*] the discount factor captured by long-term sovereign interest rates. - A data-rich
**‘econometric’ approach**…[*uses*] a__larger set of information to estimate the fitted value of the____fundamenta__l [*and*] may provide a better proxy in-sample…Asset prices are represented by projections against a wide range…of macroeconomic and financial variables…[*These are*] macroeconomic (rents and dividends, industrial production, GDP, real disposable income, inflation, confidence indicators and oil prices) and financial variables (real long term interest rate, monetary and credit aggregates, other asset prices and the VIXindicator). Lags of the endogenous variable are also included in the estimation…[*This approach*] provides ordinary least squares regression estimates of the best in-sample prediction of a given asset .. - We also consider a model corresponding to the
**‘statistical’ approach**where__bubbles are defined as significant deviations from a trend__. Most of the papers in the [*academic*] literature have relied on a statistical filter to decompose asset prices between trend and cycle…Our [*statistical*] model…identifies bubbles with a dummy taking the value 1 (-1) when asset prices are more than 1.5 standard deviation superior (inferior) to the Christiano-Fitzgerald trend (view paper here) and the value 0 when asset prices are within these bounds, so 87% of the data lies within them.”

### How to gather all estimates into one?

“We develop a new bubble indicator using a __Principal Component Analysis (PCA) to extract the common denominator of structural, econometric and statistical approaches__…The first principal component boils down to a model averaging of the structural, econometric and statistical approaches and maximizes their common variance, whereas the idiosyncratic dynamics of each approach will be dropped. So the first principal component can be considered as a robust measure of the bubble component.”

“Stock and housing bubble indicators…capture 58 and 57% of the variance of their respective three bubble components… The individual bubble components for each approach together with the bubble indicator, the first principal component, are plotted in [*the figure below*]”