Questions tagged [log-linearization]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
0 answers
35 views

Log-linearisation of the Euler equation

I am struggling to log-linearize the following around the steady state: $ U'\left(e^{z_t} F(k_t, 1) + (1 - \delta)k_t - k_{t+1}\right) - \beta E_{z_t}U'\left(e^{z_{t+1}} F(k_{t+1}, 1) + (1 - \delta)k_{...
cluelessMacro's user avatar
0 votes
1 answer
30 views

a question about second-order log-linear approximation

I have a very simple question. I don't understand OA6 equation. Where is the 2, the denominator of $\frac{v_{11}}{2}$, gone?
user14261785's user avatar
1 vote
0 answers
30 views

Help with the log-linearization of a difficult term

I'm currently trying to retrace a log-linearization done in this paper. I want to log-linearize around the steady-state, as it is commonly done for DSGE models (see here). $\bar{x_t}$ are steady-state ...
mindandfields's user avatar
1 vote
1 answer
32 views

Log-linearizing a second order term around the steady-state

I'm currently trying to retrace a log-linearization done in a paper. I want to log-linearize around the steady-state, as it is commonly done for DSGE models (see here) and I want to disregard all ...
mindandfields's user avatar
2 votes
1 answer
69 views

Log-linearization in RBC model

Can anyone show how by applying log-linearization we can turn this equation: $\frac{X_t}{C_t} = \left( (1 - \vartheta) + \vartheta \left( \frac{L_t}{C_t} \right)^{1-\nu} \right)^\frac{1}{1-\nu}$ into ...
NC520's user avatar
  • 125
0 votes
0 answers
61 views

how to log-linearize a utility function?

This is a part of Online Appendix to Business Cycle Dynamics under Rational Inattention (Mackowiak and Wiederholt, 2015). I don't understand why C_j is supposed to be a denominator. Could anyone give ...
user14261785's user avatar
1 vote
0 answers
40 views

Log-linearization with first-order Taylor approximation

I am having trouble with a log-linearization replication that I stumbled across in the appendix of the Chari, Kehoe & McGrattan paper "Business Cycle Accounting". More specifically the ...
Nedralixx's user avatar
2 votes
1 answer
198 views

Log linearization with sums

I have the following equation for a variable $s$: $$ s = -\beta\frac{\alpha(1-w)^{\zeta-1}-(1-\alpha)w^{\zeta-1}}{\alpha(1-w)^{\zeta}+(1-\alpha)w^{\zeta}} $$ where $\zeta$, $\alpha$, and $\beta$ are ...
D.J. P.'s user avatar
  • 21
1 vote
0 answers
62 views

What is the typical utility function of the standard loglinear demand function?

What is the typical utility function of this demand function? $$x_1 = \ln(x_2) - \beta \ln(p_1) + \gamma \ln(y).$$ With budget constraint $y = p x_1 + x_2.$
Victor Nielsen's user avatar
3 votes
1 answer
349 views

Log Linearising CES demand

I have been trying to log-linearise the demand function that follows from a standard two-good CES-utility maximamalisation problem. That is: Maximise \begin{eqnarray} U(h,c)= \left(G_1^{\rho}+ G_2^{\...
An economict's user avatar
0 votes
1 answer
188 views

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 ...
john smith's user avatar
1 vote
1 answer
288 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 ...
AVR's user avatar
  • 23
1 vote
0 answers
169 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 ...
andrewH's user avatar
  • 253
2 votes
0 answers
484 views

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 ...
EconRider's user avatar
3 votes
2 answers
676 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 ...
randomname's user avatar
2 votes
0 answers
68 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) ...
user3822171's user avatar
2 votes
0 answers
49 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}_{...
David Lim's user avatar
2 votes
0 answers
104 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_{...
bdvse's user avatar
  • 69
2 votes
1 answer
1k 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 ...
randomname's user avatar
2 votes
0 answers
50 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 ...
Beck Batucada's user avatar
3 votes
0 answers
256 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 ...
chsk's user avatar
  • 263
0 votes
1 answer
1k 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)/...
huppuguga's user avatar
1 vote
1 answer
455 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 ...
Maddy's user avatar
  • 19
1 vote
0 answers
87 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-\...
felipe's user avatar
  • 11