scholarly journals Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 846 ◽  
Author(s):  
Yingkang Xie ◽  
Zhen Wang ◽  
Bo Meng
Keyword(s):  
Business Cycle ◽  
Fractional Order ◽  
Preference Function ◽  
Positive Equilibrium ◽  
Proposed Model ◽  
Investment Function ◽  
Business Cycle Model ◽  
The Business Cycle ◽  
Positive Equilibrium Point ◽  
Delayed Time

In this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee that the positive equilibrium point of DTFOM is locally stable. In addition, Hopf bifurcation is obtained by a new method, where the time delay is regarded as the bifurcation parameter. Finally, a numerical example of DTFOM is given to verify the effectiveness of the proposed model and methods.

scholarly journals Study on the Business Cycle Model with Fractional-Order Time Delay under Random Excitation

Entropy ◽  
2017 ◽  
Vol 19 (7) ◽  
pp. 354 ◽  
Author(s):  
Zifei Lin ◽  
Wei Xu ◽  
Jiaorui Li ◽  
Wantao Jia ◽  
Shuang Li
Keyword(s):  
Time Delay ◽  
Business Cycle ◽  
Fractional Order ◽  
Random Excitation ◽  
Cycle Model ◽  
Business Cycle Model ◽  
The Business Cycle

scholarly journals Investment Dispersion and the Business Cycle

2014 ◽  
Vol 104 (4) ◽  
pp. 1392-1416 ◽  
Author(s):  
Rüdiger Bachmann ◽  
Christian Bayer
Keyword(s):  
Business Cycle ◽  
Adjustment Costs ◽  
Firm Risk ◽  
Firm Level ◽  
Cross Sectional ◽  
Capital Adjustment ◽  
Investment Rates ◽  
Business Cycle Model ◽  
The Business Cycle ◽  
Heterogeneous Firm

The cross-sectional dispersion of firm-level investment rates is procyclical. This makes investment rates different from productivity, output, and employment growth, which have countercyclical dispersions. A calibrated heterogeneous-firm business cycle model with nonconvex capital adjustment costs and countercyclical dispersion of firm-level productivity shocks replicates these facts and produces a correlation between investment dispersion and aggregate output of 0.53, close to 0.45 in the data. We find that small shocks to the dispersion of productivity, which in the model constitutes firm risk, suffice to generate the mildly procyclical investment dispersion in the data but do not produce serious business cycles. (JEL D42, D92, E32, G31, G32)

scholarly journals ARE UNIT ROOT TESTS USEFUL IN THE DEBATE OVER THE (NON)STATIONARITY OF HOURS WORKED?

2013 ◽  
Vol 19 (1) ◽  
pp. 167-188
Author(s):  
Amélie Charles ◽  
Olivier Darné ◽  
Fabien Tripier
Keyword(s):  
Monte Carlo ◽  
Business Cycle ◽  
Monte Carlo Simulations ◽  
Unit Root ◽  
Unit Root Tests ◽  
Cycle Model ◽  
Hours Worked ◽  
Simulated Series ◽  
Business Cycle Model ◽  
The Business Cycle

The performance of unit root tests on simulated series is compared, using the business-cycle model of Chang et al. [Journal of Money, Credit and Banking39(6), 1357–1373 (2007)] as a data-generating process. Overall, Monte Carlo simulations show that the efficient unit root tests of Ng and Perron (NP) [Econometrica69(6), 1519–1554 (2001)] are more powerful than the standard unit root tests. These efficient tests are frequently able (i) to reject the unit-root hypothesis on simulated series, using the best specification of the business-cycle model found by Chang et al., in which hours worked are stationary with adjustment costs, and (ii) to reduce the gap between the theoretical impulse response functions and those estimated with a Structural VAR model. The results of Monte Carlo simulations show that the hump-shaped behavior of data can explain the divergence between unit root tests.

Stability and Hopf Bifurcation of a Fractional-Order Food Chain Model With Disease and Two Delays

2020 ◽  
Vol 15 (3) ◽  
Author(s):  
Xinhe Wang ◽  
Zhen Wang ◽  
Xiao Shen
Keyword(s):  
Fractional Order ◽  
Food Chain ◽  
Positive Equilibrium ◽  
Chain Model ◽  
Two Delays ◽  
Existence Conditions ◽  
Positive Equilibrium Point ◽  
The Stability ◽  
Food Chain Model ◽  
Bifurcation And Stability

Abstract In this study, a fractional-order food chain model with disease and two delays is proposed. The existence conditions for a positive equilibrium point are given, and the stability conditions without the effects of delays are established. The effects of a single time delay and two time delays are discussed, the bifurcation and stability criteria are obtained, and the bifurcation points are calculated. To support the theoretical analysis, numerical simulations are presented.

Python and Dynare Code

2020 ◽  
pp. 258-266
Author(s):  
Harold L. Cole
Keyword(s):  
Business Cycle ◽  
Open Source ◽  
Cycle Model ◽  
Main Text ◽  
Matlab Code ◽  
Business Cycle Model ◽  
The Business Cycle

In this chapter a variety of different sample codes are provided in Python, complementing the Matlab code in the main text. In addition, Dynare (an open source add-on to Matlab) code is provided for the business cycle model.

scholarly journals Inventories and the Business Cycle: An Equilibrium Analysis of (S, s) Policies

2007 ◽  
Vol 97 (4) ◽  
pp. 1165-1188 ◽  
Author(s):  
Aubhik Khan ◽  
Julia K Thomas
Keyword(s):  
Business Cycle ◽  
Equilibrium Analysis ◽  
Aggregate Fluctuations ◽  
Cycle Model ◽  
Delivery Costs ◽  
Inventory Investment ◽  
Cyclical Variability ◽  
Business Cycle Model ◽  
The Business Cycle ◽  
Inventory Accumulation

We develop an equilibrium business cycle model where nonconvex delivery costs lead firms to follow (S, s) inventory policies. Calibrated to postwar US data, the model reproduces two-thirds of the cyclical variability of inventory investment. Moreover, it delivers strongly procyclical inventory investment, greater volatility in production than sales, and a countercyclical inventory-to-sales ratio. Our model challenges several prominent claims involving inventories, including the widely held belief that they amplify aggregate fluctuations. Despite the comovement between inventory investment and final sales, GDP volatility is essentially unaltered by inventory accumulation, because procyclical inventory investment diverts resources from final production, thereby dampening fluctuations in sales. (JEL E22, E32).

scholarly journals Interação dos Dispêndios de Publicidade com Ciclos Econômicos e o Valor da Empresa: Análise Empírica das Empresas Norte-Americanas do Setor de Bens de Consumo

2010 ◽  
Vol 8 (3) ◽  
pp. 283
Author(s):  
Graziela Fortunato ◽  
Walter Ness ◽  
Arilton Teixeira ◽  
Paulo Cesar Motta
Keyword(s):  
Stochastic Process ◽  
Panel Data ◽  
Business Cycles ◽  
Business Cycle ◽  
Multiple Regression ◽  
Firm Value ◽  
Proposed Model ◽  
The Business Cycle

This study aims to verify the contribution of advertising expenditures to firm value. To reach this goal, we considered business cycles, which follow a stochastic process and may influence the decision as to the amount to be spent in advertising. With the optimization of these expenditures under the business cycle effect, it is, in fact, possible to analyze whether the results positively contribute to firm value. Data from US companies of the consumer staples sector from 1997 to 2008 were employed to test the proposed model through multiple regression and panel data. The results indicate favorable evidences which confirm the proposed model.

scholarly journals Hopf Bifurcation in an Augmented IS-LM Linear Business Cycle Model with Two Time Delays

2020 ◽  
Vol 5 (3) ◽  
pp. 518-528
Author(s):  
Firdos Karim ◽  
Sudipa Chauhan ◽  
Sumit Kaur Bhatia ◽  
Joydip Dhar
Keyword(s):  
Hopf Bifurcation ◽  
Business Cycle ◽  
Capital Accumulation ◽  
Local Stability ◽  
Time Delays ◽  
Equilibrium Points ◽  
Scale Production ◽  
Cycle Model ◽  
Investment Function ◽  
Business Cycle Model

This paper deals with the amalgamated basic IS-LM business cycle model with Kaldor’s growth model to form an augmented model. Pertaining to substantial evidence, IS-LM model in paradigm with a specific economic extension (Kaldor-Kalecki Business cycle model in our case) provides an adept explanation of a developing but strong economy like that of our country. Occurring in the equation of capital accumulation, the two time delays are a result of the assumption in the investment function being both income and capital stock dependent in past period and maturity period. Investigating a model combined with capital accumulation is both interesting and important. From economist point of view, production without capital is impossible to even imagine. Moreover capital accumulation is impeccable to large-scale production, specialisation and creation of employment opportunities. In our model ‘I’ the investment function, ‘S’ the savings function and ‘L’ the demand for money are depending linearly on their arguments. We adhere to a linear model, contrary to the popular belief of non- linear models being the undisputed style for modern economics. The model is first shown to be mathematically and economically poised. The local stability of boundary and interior equilibrium points has been investigated. Three cases arise, pertaining to two time delays. System dynamics exhibits mutation under the influence of time delays and may clinch or discharge its local stability when subjected to the latter. Hopf bifurcation occurs when the delay parameter crosses a critical value.

scholarly journals Economic Fluctuations in Turkey in the Light of Business Cycle Theories

2012 ◽  
Author(s):  
Emine Fırat
Keyword(s):  
Business Cycle ◽  
Market Failure ◽  
Free Market ◽  
Economic Fluctuations ◽  
Past Century ◽  
Business Cycle Theory ◽  
Macroeconomic Policies ◽  
Business Cycle Model ◽  
The Business Cycle ◽  
The Right

Some economists have tried to demonstrate the cause of economic fluctuations and its solution with business cycle theories. The classical school emphasizes the efficiency of free market economy and the optimization of private economic factors. The Keynesian school believes that the causes of economic fluctuations arise from not only just the deviations from market equilibrium but also market failure on a grand scale. The debate over the source and propagation of economic fluctuations rages as fiercely today as it did in the Great Depression that began in 1929. Economic Fluctuation models investigate to answer the question of why economies go through boom and bust and why economies experience cycles of recession and recovery. In the economic literature, based on the Business Cycle Theories many different approaches have been proposed. While economists discuss the ultimate form of the right business cycle model, they must take into consideration the decisive factors of economic fluctuations in the past century. In this study, the local economic crisis occurred in Turkey in recent years are investigated in the light of Business Cycle Theory and also the effects of macroeconomic policies are evaluated on the basis of economic fluctuations models.

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