Questions tagged [log-linearization]

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log linearize exponential expressions

How do I log-linearize an expression like: $e^{(\theta*(x_t-\bar{x}))}$ Where $\theta$ is any constant and $\bar{x}$ is the steady-state of $x$ Generally when we log-linearize say $x_t$, we write it ...
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1answer
92 views

New Keynesian Phillips Curve: log-linearization

I am facing some problems in log-linearizing the following equation: which is the New Keynesian Phillips Curve (NKPC). The expected result, once log-linearized, is: which is described by equation 46 ...
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1answer
27 views

Linear version of Taylor type rule

I have a problem with linearization of Taylor rule from monetary policy. How can I linearize this equation I dont know how I should treat R, pi and y, as parameters?
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46 views

Percent change vs difference in logs: Which to prefer when forcasting non-stationary series with rare large excursions?

One of the most common ways to convert a non-stationary time series into a stationary one is to take the difference in logs. This is approximately equal to the percentage change for small changes, and ...
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Log-linearization of CES production function

I am trying to recover the Log-linearisation of a CES production function in a paper. Although I am fairly confident with Log-linearisations, I simply do not find the supposed result. The production ...
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2answers
291 views

First order condition of log functions in general and interpretation

In the following, a first order condition for a log function is calculated. I know how the left part was calculated, however, I am a little bit confused where the gamma on the right site comes from ...
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10 views

log-linearize a forward looking variable (P/D) with recursive expression

I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, ...
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0answers
39 views

Log deviation from steady state - understanding a journal paper

I hope a question like this is fair game on this website! I'm doing some research for my thesis, and have come across what seems to be a pretty simple model - two countries, A (representing the USA) ...
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11 views

Using Ordinal (Star Rating) variables to predict outcomes in Log lin regressions + Taking Median significant coefficients of multiple regressions

Framing the regression I am attempting to analyze the effects of several variables on clicks for Google My Business listings. Currently I'm using a Log-Lin regression model to predict the % increase ...
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34 views

Linearization around the steady state (Asset pricing application)

I am working through a linearization example from Colacito and Croce (2011). In the paper the following expression is derived: \begin{align} & (v^{i}_{c,t})^{\theta}=E_{t}[\delta e^{\Delta c^{i}_{...
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23 views

Deriving log-linearized equilibrium in Galí (2019)

I am reading the Paper "The effects of a money-financed fiscal stimulus" by Galí (2019). I am trying to derive the log-linearized equilibrium as given in equations (15)-(22). I believe I am ...
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77 views

Log- Linearization of equations

can somebody help me understand how it is possible to log-linearize this equation? $$\frac{1}{1+i_{t}}=\beta E^i_{t}\left[\frac{P_{t}}{P_{t+1}} \cdot \frac{U_{c}\left(C_{t+1}^{i}, \xi_{t+1}\right)}{U_{...
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1answer
216 views

Log linearising EUler equation

I am trying to solve a problem that asks to log linearise following Euler equation of the New Keynesian model: $$C^{-\sigma}_t=\beta E_tC^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1}).$$ The solution is ...
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15 views

Are typical macro DSGE (RBC or New Keynesian DSGE) models linear, non-linear, or log (linearized)?

In Carl Hommes 2015 book on Expectations, it seems he considers DSGE models (being it either RBC DSGE or New Keynesian DSGE) to be linear, or (log)linearized models, on page 3 of the introduction. He ...
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159 views

Log-linearizing a non-separable utility function around the steady state

I've started reading Jordi Galí's Monetary Policy, Inflation and the Business Cycle (2nd ed., 2015). In section 2.5.2, Galí considers an example with the following non-separable period utility ...
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1answer
620 views

Constant elasticity proof for log-linear demand curve

From Perloff 2008e solved 2.2: Q: Show that the elasticity of demand is a constant e if the demand function is log-linear, ln Q=ln A+e ln p. A: Differentiating with respect to p, we find that (dQ/dp)/...
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1answer
227 views

How do you use a Log-linear model when you have negative Xs?

I am trying to us a Log-linear model to derive an elasticity. However, some of my Xs are negative numbers. Being as the model relies on the natural log of the Ys and the Xs, how can this model work ...
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44 views

log linearization around steady state (price dynamics)

I'm stuck with a derivation from Gali's book. In the version 2008, I can't get eq. (7) from chapter 3. All is ok until the following: $$ (1-\epsilon)\log\pi_{t}=\log(\theta+(1-\theta)\exp[(1-\...