<p>On the empirical side, there might be answers for you in the national accounts. I only know about the french case : the french statistical institute (INSEE) has different depreciation data for different types of capital (e.g. buildings, machines, patents) and for different sectors. These data are supposed to reflect both physical depreciation and "normal obsolescence". The only reference I can give you is in french : Jean-François Baron, "Les comptes de patrimoine et de variation de patrimoine, base 2000", INSEE, 2008, <a href="http://www.insee.fr/fr/indicateurs/cnat_annu/base_2000/documentation/methodologie/nb10.pdf" rel="nofollow noreferrer">http://www.insee.fr/fr/indicateurs/cnat_annu/base_2000/documentation/methodologie/nb10.pdf</a> , but I suspect you can find similar data in other national accounts.</p>

<p>On the theoretical side, if I understand you, you mean that a capital good can become economically obsolete before it is physically out of use. I see three possible reasons (possibly overlapping) for this :</p>

<ol>
<li><p>the price of inputs (e.g. the wage rate) rises so that this capital good is not profitable any more</p></li>
<li><p>the price of output falls but not the price of inputs, so that it is not profitable</p></li>
<li><p>production is demand constrained <em>and</em> there other more productive ("new") capital goods available, so that our capital good will remain idle (although it could be profitable if there were a higher demand)</p></li>
</ol>

<p>To account for this problem, you have to drop the representation of capital as a single homogeneous magnitude (the number "K") and have different capital goods with different properties (productivity and input requirements). This is called a "vintage capital" model. I don't know if this has been done in an RBC or DSGE framework, but a quite complete neoclassical paper dealing with these issues is :
Solow, Yaari, Tobin, Weiszäcker (1966), "Neoclassical growth with fixed factor proportions" 
<a href="http://sites-final.uclouvain.be/econ/DW/DOCTORALWS2004/bruno/vintage/solow%20yaari%20tobin.pdf" rel="nofollow noreferrer">http://sites-final.uclouvain.be/econ/DW/DOCTORALWS2004/bruno/vintage/solow%20yaari%20tobin.pdf</a> </p>

CC BY-SA 3.0
2017-01-04T18:32:07.643Z
2017-01-04T18:32:07.643Z
user11629
<p>A common calibration for depreciation rates within RBC models is to assume 10% depreciation rate (based on NIPA stats, for instance). This implies a half-life of about 6.5 years. But this estimate seems a little low for advanced economies where capital is often in the form of computerized technology etc, which would seem to depreciate at a much faster rate (say 25% pa, implying a half-life of more like 2.5 yrs). Further, with technological advance you have the problem of obsolescence - the useful life of a capital good may end long before it depreciates away fully using the 10% pa rate. There is an element of unpredictability around obsolescence as well.   </p>

<p>How can this be accounted for within RBC and DSGE models? Would obsolescence pose a problem for calibrating a model assuming delta is approx. 10%? </p>

<p>Thanks in advance, </p>

<p>R. </p>

CC BY-SA 3.0
2017-01-04T15:22:18.750Z
I would be surprised if a large fraction of capital (weighted by cost) were comprised by computerized technology, even in advanced economies. Computers are quite cheap compared to container ships, highways, bridges, buildings,  factories, etc.
dismalscience
<dsge><rbc>
Depreciation vs. obsolescence in RBC and New Keynesian DSGE models
Robert Brown
# Depreciation vs. obsolescence in RBC and New Keynesian DSGE models

(Asked by: username_0 on 2017-01-04)

A common calibration for depreciation rates within RBC models is to assume 10% depreciation rate (based on NIPA stats, for instance). This implies a half-life of about 6.5 years. But this estimate seems a little low for advanced economies where capital is often in the form of computerized technology etc, which would seem to depreciate at a much faster rate (say 25% pa, implying a half-life of more like 2.5 yrs). Further, with technological advance you have the problem of obsolescence - the useful life of a capital good may end long before it depreciates away fully using the 10% pa rate. There is an element of unpredictability around obsolescence as well.

How can this be accounted for within RBC and DSGE models? Would obsolescence pose a problem for calibrating a model assuming delta is approx. 10%?

Thanks in advance,

R.

**Tags:** dsge, rbc

> **Comments:**
> **username_1**: I would be surprised if a large fraction of capital (weighted by cost) were comprised by computerized technology, even in advanced economies. Computers are quite cheap compared to container ships, highways, bridges, buildings,  factories, etc.  

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## 1 answers

### Answer by username_2 on 2017-01-04. Score: 2 | Accepted answer

On the empirical side, there might be answers for you in the national accounts. I only know about the french case : the french statistical institute (INSEE) has different depreciation data for different types of capital (e.g. buildings, machines, patents) and for different sectors. These data are supposed to reflect both physical depreciation and "normal obsolescence". The only reference I can give you is in french : Jean-François Baron, "Les comptes de patrimoine et de variation de patrimoine, base 2000", INSEE, 2008, <http://www.insee.fr/fr/indicateurs/cnat_annu/base_2000/documentation/methodologie/nb10.pdf> , but I suspect you can find similar data in other national accounts.

On the theoretical side, if I understand you, you mean that a capital good can become economically obsolete before it is physically out of use. I see three possible reasons (possibly overlapping) for this :

1. the price of inputs (e.g. the wage rate) rises so that this capital good is not profitable any more
2. the price of output falls but not the price of inputs, so that it is not profitable
3. production is demand constrained *and* there other more productive ("new") capital goods available, so that our capital good will remain idle (although it could be profitable if there were a higher demand)

To account for this problem, you have to drop the representation of capital as a single homogeneous magnitude (the number "K") and have different capital goods with different properties (productivity and input requirements). This is called a "vintage capital" model. I don't know if this has been done in an RBC or DSGE framework, but a quite complete neoclassical paper dealing with these issues is :
Solow, Yaari, Tobin, Weiszäcker (1966), "Neoclassical growth with fixed factor proportions"
<http://sites-final.uclouvain.be/econ/DW/DOCTORALWS2004/bruno/vintage/solow%20yaari%20tobin.pdf>


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