Every metric space is separable in function realizability

We first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with synthetic topology, every $T_0$-space is separable and every discrete space is countable. It follows that intuitionistic logic does not show the existence of a non-separable metric space, or an uncountable set with decidable equality, even if we assume principles that are validated by function realizability, such as Dependent and Function choice, Markov's principle, and Brouwer's continuity and fan principles

District digest : Economic trends across the region

"The Roles of New and Existing Establishments in Employment in the Fifth District," article by R. Andrew Bauer, pg. 36-39Federal Reserve District, 5th ; Economic conditions ; Economic indicators

Examining contributions to core consumer inflation measures

The purpose of this paper is to examine the composition of inflation over time. The authors calculate the contributions to inflation for individual series of the consumer price index (CPI) and personal consumption expenditures price index (PCEPI) and then aggregate those contributions into major consumer expenditure categories. This technique provides a wealth of information concerning aggregate inflation behavior in a concise way, enabling the authors to describe the composition of inflation at any point in time. A particularly important benefit of this method is that it allows them to distinguish broad-based changes in inflation from changes due to relative price movements of a few components. The authors examine long-term trends in contributions to PCEPI core inflation and make inferences about the direction of inflation in the near term. In addition, they examine the decline in CPI core inflation over the 2002–03 period and find that the decline was largely driven by relative price changes of two components.

Decomposing inflation

As U.S. core inflation measures have declined in recent years, analysts have renewed their efforts to understand inflation dynamics. A common approach to this issue is to make inferences about how price changes of major components affect the aggregate inflation rate. This article takes a more rigorous approach, calculating and plotting the precise contributions of major consumer expenditure categories to core inflation measures over time. ; This technique has distinct advantages. It highlights the underlying trends in inflation, enabling analysts to make more informed inferences about the near-term direction of inflation. It also allows analysts to distinguish broad-based changes in inflation from changes due to relative price movements of a few components. ; The analysis focuses on the core components of the consumer price index (CPI) and the personal consumption expenditures price index (PCEPI). Over the long term, the authors note, the composition of core services inflation has remained relatively stable while the composition of core goods inflation has changed dramatically. Over the 2002–03 period, movements in core inflation measures resulted mainly from significant relative price changes of two components that were persistent enough to alter the path of core inflation for a sustained period, the authors conclude. ; The results of this study highlight the importance of gauging the impact of relative changes in a low-inflation environment and suggest that recent concern about overall price deflation was perhaps overstated.Inflation (Finance)

Smoothing the shocks of a dynamic stochastic general equilibrium model

In some ways, the recession of 2001 and the recovery that followed it were unique: During the recession, the contraction in measured output was driven almost entirely by a retrenchment in business capital spending while consumer spending and residential investment remained positive. And the recovery was marked by moderate, uneven gross domestic product growth and job market weakness that were historically unusual. These events raise questions about the conventional wisdom on post–World War II business cycles. ; To help answer these questions, the authors use a general equilibrium model with sticky prices and sticky wages as a framework for exploring the effects of structural shocks to the U.S. economy. Using the Kalman filter, the authors estimate the parameters of the model and then back out the unobservable shocks that make the model’s observed variables match the observable data. ; The model shows that during the 1990–91 and 2001 recessions demand shocks turned sharply negative as output growth weakened. However, the model attributes the relatively small decline in output during the 2001 recession to a positive productivity shock. Both the 1990–91 and 2001 recessions exhibited a sudden loosening of monetary policy greater than would be predicted by a Taylor rule. The model does not capture inflation dynamics during these periods and attributes frequent changes in inflation to the markup shock.Business cycles ; Econometric models

Transparency, expectations, and forecasts

In 1994 the FOMC began to release statements after each meeting. This paper investigates whether the public’s views about the current path of the economy and of future policy have been affected by changes in the Federal Reserve’s communications policy as reflected in private sector’s forecasts of future economic conditions and policy moves. In particular, has the ability of private agents to predict where the economy is going improved since 1994? If so, on which dimensions has the ability to forecast improved? We find evidence that the individuals’ forecasts have been more synchronized since 1994, implying the possible effects of the FOMC’s transparency. On the other hand, we find little evidence that the common forecast errors, which are the driving force of overall forecast errors, have become smaller since 1994. JEL Classification: E59, C33common errors, idiosyncratic errors, transparency

Internal Control Quality as an Explanatory Factor of Tax Avoidance

Internal control disclosures mandated by section 404 of the Sarbanes-Oxley Act (SOX) are designed to provide information about a firm’s financial reporting quality and in doing so may offer information on firm-specific tax planning activities. Internal control weaknesses disclosed under SOX are frequently related to a firm’s tax function (Ge and McVay, 2005; Gleason, Pincus and Rego, 2010) and thus raise the question of whether or not these frequent problems affect corporate tax avoidance. In this thesis, I test hypotheses that tax-related disclosures, particularly those that contain company-level internal control weaknesses (ICWs), provide information with respect to long-run tax avoidance. Furthermore, I test hypotheses that the combination of internal control quality and aggressive tax avoidance aid in assessing shareholder returns. To conduct these tests, I collect and construct firm-level SOX disclosure data from 2004 to 2006 across 1,286 publicly-owned corporations. I begin with an empirical analysis of the association between tax avoidance and firm-level ICWs and generally find that the presence of tax ICWs and company-level tax ICWs constrain long-run tax avoidance. For firms with low cash constraints however, company-level tax ICWs appear to lead to an increase in tax avoidance. Nevertheless, subsequent analysis of monthly abnormal returns implies that the stock market reacts negatively to the disclosure of company-level tax ICWs, regardless of whether or not tax aggressiveness is also present. This thesis contributes to the literature by documenting the first evidence that internal control disclosures provide information regarding firm-level tax planning. Although the number of internal control weakness disclosures is decreasing over time, the availability of these SOX disclosures represents a previously unavailable opportunity to examine and further understand internal governance mechanisms within the firm and their influence on tax planning. In addition, this thesis further corroborates prior literature that argues for the importance of the pervasiveness of internal control weaknesses by showing that the pervasive, company-level tax internal control weaknesses are associated with tax avoidance and lower shareholder returns. Finally, my dissertation implies that the presence of tax internal control weaknesses constrains tax avoidance and thus a focus on improving internal controls could help improve the tax planning function. However, my firm-level analysis also implies that effective tax planning is a sustainable process and thus a firm and its stakeholders may require several periods before the full benefits of these improvements are realized