Since the establishment of neoclassical economics in the nineteenth century, there has been a debate in the economics profession over the role played by mathematics. Mathematics can add precision to discussion of real-world empirical problems in economics, but care needs to be taken when formalizing a problem to ensure that errors of translation are not made. Formalism allows one to be sure that a chain of reasoning is correct but applying conclusions back to an empirical science problem is fraught if an error of translation has been made. We illustrate such a difficulty in the context of Arrow’s impossibility theorem, specifically the mistranslation of the non-dictatorship condition. The notion of dictatorship entails causality, but causality does not correspond to the usage of the implication sign in mathematics or logic. We use the rules of logic to illustrate that the way that dictatorship is rendered mathematically in the impossibility theorem makes the existence of a dictator (or dictators) not only reasonable but likely.

Calculating the amount of regulatory capital to cover unexpected losses due to operational events in the upcoming year has caused problems because of difficulties in fitting probability distributions to data. It is consequently difficult to judge an appropriate level of capital that reflects the risk profile of a financial institution. We provide theoretical and empirical analyses to link the calculated capital to the sum of losses using appropriate statistical approximations. We conclude that, in order to reasonably reflect the associated risk, the capital should be approximately half the sum of losses, with a wide bound for the ratio of capital to sum.

This paper shows mainly the following results. 1) The debt to GDP ratio cannot diverge to infinity, that is, fiscal collapse is impossible. The necessary condition for this result is that the propensity to consume from the asset is positive. 2) The divergence of the debt to GDP ratio is prevented by inflation when the interest rate on government bonds is considerably higher than the real growth rate, and the inflation rate which is sufficient to prevent divergence of the debt to GDP ratio is smaller than the interest rate on government bonds. Only an inflation rate slightly greater than the difference between the interest rate on government bonds and the sum of the real growth rate and the propensity to consume from the asset is required. This inflation is not caused by policy but occurs naturally.

Liquidity can be a real phenomenon for execution of the financial holding. Its risk falls in debate to impose a conditional cost on the counterparty. The time-varying liquidity is often linked to the expected fundamental value of an investment. In this work, the microblogging-based informed transaction is examined as a determinant of the liquidity-facilitating cost. Most importantly, this study investigates the economic blockade era and post-pandemic uncertainty. The sentiment indicators were found to be determinants of liquidity. These findings were consistent in the post-pandemic period. However, the investor pessimistic sentiment was a priced risk factor in liquidity during the economic blockade period. Based on the Bayesian theorem, a relativeness was reported between sentiment indicators and the liquidity-facilitating cost. The same findings were depicted in environments of the pandemic era. Nevertheless, the posterior probability indicated an occurrence of the liquidity-associated cost in response to the pessimistic sentiments during the economic blockade period. This quantification may have potential implications in terms of exploring liquidity from the microblogging perceptive.

In this study, the time-varying pattern of returns with the trading cost is assessed in light of sanctions on the Russia’s economy. The analysis is performed on the Moscow Exchange Index (MOEX) using the ordinary least squares (OLS) method, Bayes’ Theorem technique, and vector error correction model (VECM). Firstly, the transparency of asset’s value in the same trading period was noted to execute the trade with a limited price impact. Thus, the liquidity seems not priced in returns. In addition, the posterior probability of the transparent asset’s value stabilized the market at a limited transaction cost. In this case, there is less likelihood of liquidity acting as a risk element in returns during the same trading session. These results correspond to the era without sanctions, as well as economic restrictions period. Before the economic restrictions, the execution of investment occurred on its real or close value due to the market transparency in the following trading period. This implies, that the past trading cost series is not priced in yields on investment. During the Russia-related sanctions, a higher price impact of transaction was noted due to the ambiguity in the future asset’s value. Therefore, the past liquidity series is a pricing element in the short run and long run. The analysis suggests a potential inference of trading cost to determine the yield on investment.