Negative Interest Rates on Central Bank Digital Currency

Paying negative interest rates on central bank digital currency (CBDC) becomes increasingly relevant to monetary operations, since several major central banks have been actively exploring both negative interest rate policy and CBDC after the Great Recession. This paper provides a formal analysis to evaluate the macroeconomic impact of negative interest rates on CBDC through the lens of a neoclassical general equilibrium model with monetary aggregates. In the benchmark model, agents have access to two types of assets: CBDC and productive capital. The demand for digital currency is motivated by a liquidity constraint. I show that paying negative interest on CBDC induces agents to save less and consume more via a substitution effect. A drop in savings in turn causes a fall in capital investment, subsequent output, and real money balances. To clear the money market, the price level increases. I then extend the model to include government bonds which deliver a positive return. This allows me to study a non-trivial portfolio effect: when the government pays a negative interest rate on CBDC, the tax on agents' capital spending increases, inducing a decrease in capital investment and an increase in government bonds in agents' portfolio. Such a policy causes a drop in investment and output. However, there is a transitory decline in the price level due to a "flight to quality"

Null Space Removal in Finite Element Discretizations

Partial differential equations are frequently utilized in the mathematical formulation of physical problems. Boundary conditions need to be applied in order to obtain the unique solution to such problems. However, some types of boundary conditions do not lead to unique solutions because the continuous problem has a null space. In this thesis, we will discuss how to solve such problems effectively. We first review the foundation of all three problems and prove that Laplace problem, linear elasticity problem and Stokes problem can be well posed if we restrict the test and trial space in the continuous and discrete finite element setting. Next, we introduce methods to solve the linear system and obtain a numerical solution.Finally, we will present the numerical experiments conducted in the finite element library deal.II. We compare the numerical and graphical output to evaluate the performance of each method, providing a more comprehensive understanding of the strengths and limitations

Dynamic Temperature Modulation Sensing Technique of Electronic Nose: A Review

Electronic nose (E-nose) is a simulation of human nose, which consists of a gas sensor array and an artificial intelligent algorithm. The gas sensing properties of semiconductor sensors are affected by the heating temperature. For most gases, there exists the optimum oxidation temperature. If sensor response is recorded, we can obtain the data with abundant information at different working temperatures. The selectivity and sensitivity of a gas sensor array are the bottleneck of its development. Dynamic temperature modulation sensing technique is a use of semiconductor sensor temperature modulation characteristics by modulating its heating voltage to realize the heating temperature in a range of changes, people can record the corresponding response. The temperature modulation sensing technique can effectively improve the sensitivity of E-nose and realize the detection of low concentration gas, so it is of great practical significance to development technique of E-nose, which is based on temperature modulated sensing system for promoting the detection speed. But so far, the technique is only used for the detection of several common gases (such as methanol, ethanol, carbon monoxide, et al). The aim of this review is to supply a summary of the development and significant achievements of dynamic temperature modulation sensing technique used in E-nose in recent years. We are also looking forward to seeing dynamic temperature modulation sensing technique to accomplish more breakthroughs and get more achievements

Background Elimination in Wound Infection by Electronic Nose Based on Adaptive Noise Cancellation System and Genetic Algorithm

when electronic nose (E-nose) is used to diagnose the wound infection of mice, there exists strong background interference which reduces the accuracy of the E-nose. An adaptive noise cancellation system (ANCs) based on adaptive filters is introduced into denoising the wound infection data, and the genetic algorithm (GA) is used to reduce the redundancy of the Multi-channel data. The method using ANCs combined with GA has achieved good performance, and the accuracy of LRLS-GA is 100% with less calculated amount

A Novel Feature Extraction Technique of Electronic Nose for Detecting of Wound Infection Based on Phase Space

Rapid and timely monitoring of traumatic inflammation is conducive to doctors? diagnosis and treatment. It has been proved that electronic nose (E-nose) is an effective way to predict the bacterial classes of wound infection by smelling the odor produced by the metabolites, and it has also been found thatthe classification accuracy of E-nose is very different when different feature is extracted and put into the classifier. The gas sensor array of E-nose can be seen as a dynamic system whose response temporally evolves following the concentration of the odors. As the central concept in the analysis of dynamic systems, phase space is the first time to be employed by us to construct the feature matrix of wound infection data in this paper. Dynamic moments, the functions of time delay in phase space, is used as the feature of wound infection. The odors of four different classes of wound (wound uninfected, and infected withP. aeruginosa, E. coliandS. aureus) are used as the original response of E-nose.Experimental results prove that the classification accuracy of test data set is 96.43% when R2 is used as the feature, which is much better than M2P, M3P (other two dynamic moments), maximum value of the steady-state response and maximum value of the first-order derivative (two traditional feature of E-nose)

Understanding a New Keynesian Model with Liquidity

The Global Financial Crisis of 2007--2009 and its aftermath have called for a rethink of the role of money in shaping business cycle fluctuations. To this end, this paper studies a New Keynesian model with money (liquidity). In the model, agents hold government money and other financial assets. However, there is a "short rate disconnect" (i.e., an interest rate spread) between the policy rate on money and the interest rate on household's savings. The paper shows that there exists a meaningful "liquidity effect" that is quantitatively significant for the macroeconomy. As the spread increases, so does the price of liquidity. In a model where consumption and money are complements, such an increase in the opportunity cost of money induces agents to consume less and work less. Both the effects imply that the real wage can fall, which in turn puts downward pressures on inflation via the New Keynesian Phillips curve. The fall in inflation makes the monetary authority cut the nominal interest rates by more, but at the cost of increasing the spread even further. In addition, the paper compares the dynamic responses to technology shocks and monetary policy shocks for the model with liquidity and the standard New Keynesian model. The results show that the responses can be quantitatively different for the two models. Finally, this paper studies the interaction between the liquidity effect and monetary policy, highlighting the liquidity effect that can play in business cycles

Trust Shocks, Financial Crises, and Money

A precondition for a well-functioning monetary system is trust. This paper develops a neoclassical general equilibrium model in which public and private money coexist and the impact of trust shocks on the macroeconomy is examined. In this paper, trust is modelled as limited commitment between borrowers and lenders. A borrower who issues private money can credibly commit to repay at most a fraction of his or her future output. The paper shows that a lack of trust can engineer a financial crisis, with substantial effects on both the real and monetary variables. In the model, an unexpected drop in the trust parameter causes young workers to divert less of their savings into investment goods and more of their savings into consumption goods. A fall in capital investment in turn leads to a decline in real output. I also show that trust shocks can have detrimental effects on both workers and entrepreneurs. In addition, the model shows that, to clear the money market, an increase in the real demand for government money causes the price level to fall, inducing transitory deflation. This is in line with the low inflation episodes during and following the Great Recession. The decline in capital investment and the price level also implies that the amount of deposits has to shrink in a financial crisis. Finally, once trust shocks hit the economy, the money multiplier drops. This is due to the decrease in capital investment and the increase in the real demand for government money