# Questions tagged [log-linearization]

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### 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 ...
• 11
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### 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 $y = p x_1 + x_2.$
123 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^{\...
• 33
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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 ...
1 vote
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### 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 ...
• 23
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### 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 ...
• 195
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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 ...
441 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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### 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) ...