On the macroeconomic effects of heterogeneous productivity shocks

2016 ◽  
Vol 16 (1) ◽  
pp. 1-23
Author(s):  
Christian Jensen
Keyword(s):  
Asymptotic Distribution ◽  
Moment Generating Function ◽  
Aggregate Productivity ◽  
Productivity Shocks ◽  
Representative Agent ◽  
Agent Model ◽  
Macroeconomic Effects ◽  
The Moment ◽  
Heterogeneous Productivity ◽  
Entire Distribution

AbstractThe conventional wisdom that producer heterogeneity washes out, and is therefore irrelevant for the aggregate economy, does not apply when producers compete monopolistically. Despite this, the effects of such heterogeneity can be reproduced with an appropriately redefined representative-agent framework where the equilibrium values of aggregates are expressed in terms of the moment generating function of the distribution of heterogeneity, or its asymptotic distribution. Increased heterogeneity raises aggregate productivity and production, more so the fiercer competition is. We propose a framework where the entire distribution of heterogeneity matters, yet computationally requires no more than a representative-agent model.

scholarly journals A Theory of Demand Shocks

2009 ◽  
Vol 99 (5) ◽  
pp. 2050-2084 ◽  
Author(s):  
Guido Lorenzoni
Keyword(s):  
Business Cycles ◽  
Aggregate Demand ◽  
Aggregate Productivity ◽  
Productivity Shocks ◽  
Demand Shocks ◽  
The Public ◽  
Long Run ◽  
Short Run ◽  
Public Signal ◽  
Heterogeneous Productivity

This paper presents a model of business cycles driven by shocks to consumer expectations regarding aggregate productivity. Agents are hit by heterogeneous productivity shocks, they observe their own productivity and a noisy public signal regarding aggregate productivity. The public signal gives rise to “noise shocks,” which have the features of aggregate demand shocks: they increase output, employment, and inflation in the short run and have no effects in the long run. Numerical examples suggest that the model can generate sizable amounts of noise-driven volatility. (JEL D83, D84, E21, E23, E32)

scholarly journals The ruin problem for a Wiener process with state-dependent jumps

2020 ◽  
Vol 16 (1) ◽  
pp. 13-23
Author(s):  
M. Lefebvre
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Jump Diffusion ◽  
Moment Generating Function ◽  
Continuous Part ◽  
State Dependent ◽  
The Moment ◽  
First Time

AbstractLet X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

scholarly journals Tornumonkpe Distribution: Statistical Properties and Goodness of Fit

2021 ◽  
pp. 12-22
Author(s):  
Barinaadaa John Nwikpe
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Mathematical Expression ◽  
Information Criterion ◽  
Moment Generating Function ◽  
Data Sets ◽  
The Moment ◽  
The One ◽  
Coefficient Of Skewness ◽  
New Distribution

A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2,  and gamma(3  distributions. The shape of its density for different values of the parameter has been shown.  The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

scholarly journals Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1149 ◽  
Author(s):  
Hyojin Lee ◽  
Kyeongjun Lee
Keyword(s):  
Scale Parameter ◽  
Moment Generating Function ◽  
Likelihood Inference ◽  
Exponential Parameter ◽  
Hybrid Censoring ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
New Type ◽  
The Moment ◽  
Censoring Scheme

In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.

scholarly journals Exact Performance Analysis of Amplify-and-Forward Bidirectional Relaying over Nakagami-m Fading Channels with Arbitrary Parameters

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1277
Author(s):  
Dong Qin ◽  
Yuhao Wang ◽  
Tianqing Zhou
Keyword(s):  
Fading Channels ◽  
Signal To Noise Ratio ◽  
Ergodic Capacity ◽  
Moment Generating Function ◽  
Amplify And Forward ◽  
Relay Systems ◽  
Signal Error ◽  
Bidirectional Relaying ◽  
Fading Parameter ◽  
The Moment

The exact performance of amplify-and-forward (AF) bidirectional relay systems is studied in generalized and versatile Nakagami-m fading channels, where the parameter m is an arbitrary positive number. We consider three relaying modes: two, three, and four time slot bidirectional relaying. Closed form expressions of the moment generating function (MGF), higher order moments of signal-to-noise ratio (SNR), ergodic capacity, and average signal error probability (SEP) are derived, which are different from previous works. The obtained expressions are very concise, easy to calculate, and evaluated instantaneously without a complex summation operation, in contrast to the nested multifold numerical integrals and truncated infinite series expansions used in previous work, which lead to computational inefficiency, especially when the fading parameter m increases. Simulation results corroborate the correctness and tightness of the theoretical analysis.

On the linear exponential family

1968 ◽  
Vol 64 (2) ◽  
pp. 481-483 ◽  
Author(s):  
J. K. Wani
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Scalar Product ◽  
Exponential Family ◽  
Characterization Theorem ◽  
Random Variable ◽  
Moment Generating Function ◽  
The Moment ◽  
Image Position

In this paper we give a characterization theorem for a subclass of the exponential family whose probability density function is given bywhere a(x) ≥ 0, f(ω) = ∫a(x) exp (ωx) dx and ωx is to be interpreted as a scalar product. The random variable X may be an s-vector. In that case ω will also be an s-vector. For obvious reasons we will call (1) as the linear exponential family. It is easy to verify that the moment generating function (m.g.f.) of (1) is given by

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