There are different methodologies to detect a change in the market efficiency, both in the market and firm-specific cases.
In the FIRM-SPECIFIC case, the most common procedure is the event study methodology; you can find how to construct an event-study case explained in Kothari & Warner (2006), who collected all the event study methodology implemented till 2006 in the academic literature; below, you can find the paper reference and relative link:
Kothari, S. P., and Jerold B. Warner. "The econometrics of event studies." > Available at SSRN 608601 (2004).
In the BROAD MARKET case, there exist different measures/proxy for the market efficiency exploited in the academic literature to test and measure the effects of the change in market efficiency on the markets.
Below, you can find a list of the proxies developed in the academic literature to test/measure the level of market efficiency and the relative references in chronological order.
As regards the review about market efficiency test and measuring:
Bollerslev, Tim, and Robert J. Hodrick. Financial market efficiency tests. No. w4108. National bureau of economic research, 1992.
Lim, Kian‐Ping, and Robert Brooks. "The evolution of stock market
efficiency over time: a survey of the empirical literature." Journal
of Economic Surveys 25.1 (2011): 69-108.
As regards the market efficiency test:
Amihud, Yakov, and Haim Mendelson. "Trading mechanisms and stock returns: An empirical investigation." The Journal of Finance 42.3 (1987): 533-553.
- Variance Ratio Test/MEC()
Lo, Andrew W., and A. Craig MacKinlay. "Stock market prices do not follow > random walks: Evidence from a simple specification test." Review of financial > studies 1.1 (1988): 41-66.
Peters, Edgar E. Fractal market analysis: applying chaos theory to
investment and economics. Vol. 24. John Wiley & Sons, 1994.
Cajueiro, Daniel O., and Benjamin M. Tabak. "The Hurst exponent over
time: testing the assertion that emerging markets are becoming more
efficient." Physica A: Statistical Mechanics and its Applications
336.3 (2004): 521-537.
As regards the market efficiency measures:
Pincus, Steven M. "Approximate entropy as a measure of system complexity." Proceedings of the National Academy of Sciences 88.6 (1991): 2297-2301.
Look at here to know more about the statistical properties of the approximate entropy measure.
L. Kristoufek and M. Vosvrda. Measuring capital market efficiency:
Global and local correlations structure. Physica A, 392:184–193, 2013.
Bramante, Riccardo, Diego Zappa, and Giovanni Petrella. "On the interpretation and estimation of the market model R-square." Electronic Journal of Applied Statistical Analysis 6.1 (2013): 57-66.
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