Log-linearisation in Short

Log-linearisation in Short with an example

There exist many different types of models of equations for which there exists no closed form solution. In these cases, we use a method known as log-linearisation. One example of these kinds of models are non-linear models like Dynamic Stochastic General Equilibrium (DSGE) models. DSGE models are non-linear in both parameter and in variables. Because of this, solving and estimating these models is challenging.

Hence, we have to use approximations to the non-linear models. We have to make concessions in this, as some features of the models are lost, but the models become more manageable.

In the simplest terms, we first take the natural logs of the non-linear equations and then we linearise the logged difference equations about the steady state. Finally, we simplify the equations until we have linear equations where the variables are percentage deviations from the steady state. We use the steady state as that is the point where the economy ends up in the absence of future shocks.

Usually in the literature, the main part of estimation consisted of linearised models, but after the global financial crisis, more and more non-linear models are being used. Many discrete time dynamic economic problems require the use of log-linearisation.

There are several ways to do log-linearisation. Some examples of which, have been provided in the bibliography below.

One of the main methods is the application of Taylor Series expansion. Taylor’s theorem tells us that the first-order approximation of any arbitrary function is as below.

We can use this to log-linearise equations around the steady state. Since we would be log-linearising around the steady state, x* would be the steady state.

For example, let us consider a Cobb-Douglas production function and then take a log of the function.

The next step would be to apply Taylor Series Expansion and take the first order approximation.

Since we know that

Those parts of the function will cancel out. We are left with –

For notational ease, we define these terms as percentage deviation of x about x* where x* signifies the steady state.
Thus, we get

At last, we have log-linearised the Cobb-Douglas production function around the steady state.

Bibliography:
Sims, Eric (2011). Graduate Macro Theory II: Notes on Log-Linearization – 2011. Retrieved from https://www3.nd.edu/~esims1/log_linearization_sp12.pdf


Zietz, Joachim (2006). Log-Linearizing Around the Steady State: A Guide with Examples. SSRN Electronic Journal. 10.2139/ssrn.951753.


McCandless, George (2008). The ABCs of RBCs: An Introduction to Dynamic Macroeconomic Models, Harvard University Press


Uhlig, Harald (1999). A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily, Computational Methods for the Study of Dynamic
Economies, Oxford University Press

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How to Design a Novel Replicative Study?

“A replication study attempts to validate the findings of a published piece of research. By doing so, that prior research is confirmed as being both accurate and broadly applicable”

A replication process generally consists of two parts. The first part is concerned with reproducing key findings from the original study. If this step was successful, the next part will be performing robustness checks. Meta-analysis reveals another side of replicating published research. Meta-based studies survey the empirical results of a group of published papers attempting to test three key dimensions— statistical power, selective reporting bias, and between-study heterogeneity.

From the perspective of contributing to scientific research, replication studies are important for the continued progress of science. Given the relative scarcity of replication studies and in recognition of the importance of these methods, there has been increasing attention by editors of A-class journals (American Economic Review, Journal of Political Economy, Review of Economic Studies, Journal of Applied Econometrics) in publishing replicative studies.

The one-day intensive online workshop on 29 June 2020 by “Econometric Replication: Methods & Guidelines for Designing a Replicated Study” will teach you theoretically and practically how to design a novel replicated study.

Learn about the workshop and moderator at https://www.ms-researchhub.com/home/events/workshops/econometric-replication.html

References:

http://www.economics-ejournal.org/special-areas/replications-1

https://www.deakin.edu.au/__data/assets/pdf_file/0007/1198456/WhatMeta-AnalysesReveal_WP.pdf

https://link.springer.com/article/10.1007/s11301-018-0149-3

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Now the World Witnesses the True Value of Science & Researching

The world is cruel!


Actors, football players, and models are millionaires and their monthly paychecks can sometimes exceed some developing countries’ annual budgets., while doctors, researchers, and teachers in the majority of countries earn only what is enough for living.


In such times, when the entire humankind is at threat and faces a global crisis, everyone stands at the researchers’ and doctors’ doorsteps waiting for them to develop a cure or a vaccine to save the world. In such times, the true value of science and researching emerges and the significance of investing in knowledge and education becomes evident and nonnegligible.
Our vision at MSR HUB “Bridging Knowledge between those who have it and those who need” derives our team and defines our mission, accordingly and as a part of our contribution in alleviating and supporting the world in the forthcoming global recession.


MS Research Hub institute will administrate and fund the first research project that will be moderated by selected team members to empirically investigate and predict how economies behave – and should behave- in times of the Coronavirus. Using historical data of similar epidemics that have hit the humankind, starting from the Spanish flu at the beginning of the 19 century, passing by MARS and MERS, our objective will be to develop a prescription that the world can use to mitigate the recessionary spillovers.


This research project will be the official launching of our institute’s “Research Grant Program” that aims to fund independent researchers from the least developed countries to carry on their planned human-related research projects in all scientific fields.


We believe first and always in mighty Allah, human-kind, and the power of knowledge and science in facing the current crises.


Dr. Sherif Hassan CEO & Academic Division director at MSR HUB- Germany

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General guidelines of scientific writing

An excerpt from Manikw’s blog 

When I was CEA chair, I sent the following guidelines to my staff as they started drafting the Economic Report of the President. A friend recently emailed me a copy, and I thought I would share them with blog readers. They are good rules of thumb, especially for economists writing for a general audience.

ERP Writing Guidelines

· Stay focused. Remember the take-away points you want the reader to remember. If some material is irrelevant to these points, it should probably be cut.

· Keep sentences short. Short words are better than long words. Monosyllabic words are best.

· The passive voice is avoided by good writers.

· Positive statements are more persuasive than normative statements.

· Use adverbs sparingly.

· Avoid jargon. Any word you don’t read regularly in a newspaper is suspect.

· Never make up your own acronyms.

· Avoid “of course, “clearly,” and “obviously.” Clearly, if something is obvious, that fact will, of course, be obvious to the reader.

· The word “very” is very often very unnecessary.

· Keep your writing self-contained. Frequent references to other works, or to things that have come before or will come later, can be distracting.

· To mere mortals, a graphic metaphor, a compelling anecdote, or a striking fact is worth a thousand articles in Econometrica.

· Keep your writing personal. Remind readers how economics affects their lives.

· Remember two basic rules of economic usage: o “Long run” (without a hyphen) is a noun. “Long-run” (with a hyphen) is an adjective. Same with “short(-)run.” o “Saving” (without a terminal s) is a flow. “Savings” (with a terminal s) is a stock.

· Buy a copy of Strunk and White’s Elements of Style. Also, William Zinsser’s On Writing Well. Read them—again and again and again.

· Keep it simple. Think of your reader as being your college roommate who majored in English literature. Assume he has never taken an economics course, or if he did, he used the wrong textbook.

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