Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank) = a − b log(Size), and take b as an estimate of the ...Pareto exponent. The reason for this popularity is arguably the simplicity and robustness of this method. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and propose that, if one wants to use an OLS regression, one should use the Rank −1 / 2, and run log(Rank − 1 / 2) = a − b log(Size). The shift of 1 / 2 is optimal, and reduces the bias to a leading order. The standard error on the Pareto exponent ζ is not the OLS standard error, but is asymptotically (2 / n)
1 / 2
ζ. Numerical results demonstrate the advantage of the proposed approach over the standard OLS estimation procedures and indicate that it performs well under dependent heavy-tailed processes exhibiting deviations from power laws. The estimation procedures considered are illustrated using an empirical application to Zipf's law for the United States city size distribution.
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Diversification disasters Ibragimov, Rustam; Jaffee, Dwight; Walden, Johan
Journal of financial economics,
02/2011, Volume:
99, Issue:
2
Journal Article
Peer reviewed
The recent financial crisis has revealed significant externalities and systemic risks that arise from the interconnectedness of financial intermediaries’ risk portfolios. We develop a model in which ...the negative externality arises because intermediaries’ actions to diversify that are optimal for individual intermediaries may prove to be suboptimal for society. We show that the externality depends critically on the distributional properties of the risks. The optimal social outcome involves less risk-sharing, but also a lower probability for massive collapses of intermediaries. We derive the exact conditions under which risk-sharing restrictions create a socially preferable outcome. Our analysis has implications for regulation of financial institutions and risk management.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
3.
INFERENCE WITH FEW HETEROGENEOUS CLUSTERS Ibragimov, Rustam; Müller, Ulrich K.
The review of economics and statistics,
03/2016, Volume:
98, Issue:
1
Journal Article
Peer reviewed
Open access
Suppose estimating a model on each of a small number of potentially heterogeneous clusters yields approximately independent, unbiased, and Gaussian parameter estimators. We make two contributions in ...this setup. First, we show how to compare a scalar parameter of interest between treatment and control units using a two-sample t-statistic, extending previous results for the one-sample t-statistic. Second, we develop a test for the appropriate level of clustering; it tests the null hypothesis that clustered standard errors from a much finer partition are correct. We illustrate the approach by revisiting empirical studies involving clustered, time series, and spatially correlated data.
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The paper focuses on econometrically justified robust analysis of the effects of the COVID-19 pandemic on financial markets in different countries across the World. It provides the results of robust ...estimation and inference on predictive regressions for returns on major stock indexes in 23 countries in North and South America, Europe, and Asia incorporating the time series of reported infections and deaths from COVID-19. We also present a detailed study of persistence, heavy-tailedness and tail risk properties of the time series of the COVID-19 infections and death rates that motivate the necessity in applications of robust inference methods in the analysis. Econometrically justified analysis is based on heteroskedasticity and autocorrelation consistent (HAC) inference methods, recently developed robust t-statistic inference approaches and robust tail index estimation.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The paper focuses on econometrically justified robust analysis of the effects of the COVID-19 pandemic on financial markets in different countries across the World. It provides the results of robust ...estimation and inference on predictive regressions for returns on major stock indexes in 23 countries in North and South America, Europe, and Asia incorporating the time series of reported infections and deaths from COVID-19. We also present a detailed study of persistence, heavy-tailedness and tail risk properties of the time series of the COVID-19 infections and death rates that motivate the necessity in applications of robust inference methods in the analysis. Econometrically justified analysis is based on heteroskedasticity and autocorrelation consistent (HAC) inference methods, recently developed robust t-statistic inference approaches and robust tail index estimation.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
We show that diversification does not reduce Value-at-Risk for a large class of dependent heavy tailed risks. The class is characterized by power law marginals with tail exponent no greater than one ...and by a general dependence structure which includes some of the most commonly used copulas.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary ...and sufficient conditions for Markov processes of a given order to exhibit m-dependence, r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness with m-dependence or r-independence in time series.
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We develop a general approach to robust inference about a scalar parameter of interest when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the ...following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q≥2 groups, estimate the model for each group, and conduct a standard t-test with the resulting q parameter estimators of interest. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.
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Focusing on the model of demand-driven innovation and spatial competition over time in Jovanovic and Rob (1987), we study the effects of the robustness of estimators employed by firms to make ...inferences about their markets on the firms’ growth patterns. We show that if consumers’ signals in the model are moderately heavy-tailed and the firms use the sample mean of the signals to estimate the ideal product, then the firms’ output levels exhibit positive persistence. In such a setting, large firms have an advantage over their smaller counterparts. These properties are reversed for signals with extremely heavy-tailed distributions. In such a case, the model implies anti-persistence in output levels, together with a surprising pattern of oscillations in firm sizes, with smaller firms being likely to become larger ones next period, and vice versa. We further show that the implications of the model under moderate heavy-tailedness continue to hold under the only assumption of symmetry of consumers’ signals if the firms use a more robust estimator of the ideal product, the sample median.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Excess volatility in main emerging and developed stock markets is carefully analysed in this study. Tail distribution of returns of both stock market index and individual stocks is evaluated and ...compared with the theoretical distribution found by Gabaix et al. (2003, 2006). For stock market index, recursive and rolling estimation are used. In recursive estimation, we find that all the developed markets obey “the Cubic Law of the Stock Returns”, while most of the emerging countries exhibit heavier tail with a tail index lower than 3 at 95% significance level. In rolling estimation, the tail index in the developed markets does not stabilise around 3, and after 2008 financial crisis, all the developed markets and most emerging ones suffer a drop in the tail index. For individual stocks, the tail distributions of stock returns, trading volume, and the number of trades in each emerging country behave quite differently from the theoretical model by Gabaix et al. (2006), especially the stock returns.
•We present a detailed empirical analysis of heavy-tailedness in emerging and developed markets.•All the developed markets appear to obey the “cubic law of stock returns”.•Many emerging markets have heavier tails with a tail index lower than 3.•Heavy-tailedness of other financial variables differs from developed markets.•The degrees of heavy-tailedness exhibit structural breaks due to 2008 crisis.•The degrees of heavy-tailedness exhibit structural breaks due to 2008 crisis.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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