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This paper considers the problem of estimating a linear model between two heavy-tailed variables if the explanatory variable has an extremely low (or high) value. We propose an estimator for the model coefficient by exploiting the tail dependence between the two variables and prove its asymptotic properties.

Worst-case analysis is used among financial regulators in the wake of the recent financial crisis to gauge the tail risk. We provide insight into worst-case analysis and provide guidance on how to estimate it. We derive the bias for the non-parametric heavy-tailed order statistics and contrast it with the semi-parametric extreme value theory (EVT) approach.

We present the annual update of the Bank of Canada staff estimates for global potential output growth. These estimates served as key inputs to the analysis supporting the April 2026 Monetary Policy Report.

This article provides an overview of the growth of Canadian-dollar-denominated assets in official foreign reserves. Based on International Monetary Fund data and on internal Bank of Canada analysis, we estimate that the total reserve holdings of Canadian-dollar assets increased from negligible levels before 2008 to around US$200 billion in the third quarter of 2013. We discuss the determinants of this increase, as well as its potential impact on Canadian debt markets, for example, lower yields and therefore reduced financing costs for the Government of Canada, and the possible negative impact on market liquidity.

This paper analyzes the optimal quantity of central bank reserves in an economy where reserves and other financial assets provide liquidity benefits. Using a static model, I derive a constrained Friedman rule that characterizes the socially optimal level of reserves, demonstrating that this quantity is neither necessarily large nor small but depends on the marginal benefits of reserves relative to alternative safe assets.

The authors present the four common cyclical vulnerabilities that appear in financial systems, providing examples of qualitative and quantitative indicators used to monitor these vulnerabilities across different sectors. They also discuss other inputs to the vulnerability assessment and to the internal process used at the Bank of Canada for identifying, evaluating and communicating vulnerabilities and risks, and highlight some of the key challenges in assessing financial system vulnerabilities and risks.

Central banks play a pivotal role in well-functioning payments systems by providing liquidity via collateralized lending. This article discusses the role of collateral and haircut policy in central bank lending, as well as the distinguishing features of the central bank’s policy relative to private sector practices. It presents a model that explicitly incorporates the unique role of central banks in the payments system and argues that central banks must consider how their haircut policies affect the relative price and liquidity of assets, the market’s asset allocation, and the likelihood of participants to default. Furthermore, under extraordinary circumstances, there is a rationale for the central bank to temporarily reduce haircuts or broaden the list of eligible collateral to mitigate the shortage of liquidity in the market.

We propose a macroeconomic model with a nonlinear Phillips curve that has a flat slope when inflationary pressures are subdued and steepens when inflationary pressures are elevated. Our model can generate more sizable inflation surges due to cost-push and demand shocks than a standard linearized model when inflation is high.

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Canada's First Coinage

Photography by Gord Carter, Ottawa.