Capital depreciation rate increases with Capital stock

On most macro models we assume that there is a depreciation rate (delta) that is constant. The depreciation is proportional to the capital stock. A lot of important qualitative conclusions would change we if we assumed this not to be the case.

I argue there is a god reason to assume that the depreciation rate increases with the aggregate capital stock. 

The main reason for this increasing rate theoretical, however.

a) The theoretical reason:

Why do we assume diminishing marginal returns to any factor of production (and capital in particular)? The main reason is because we assume there is choice in what to work, invest, etc. You start to allocate resources where they have the highest return, and only then you go for those with a a lower return. 

Now if you assume that, by definition, any possible investment must have the same depreciation rate, you will get the current model. But if you consider that there might be different depreciation rates and different return rates, and that investors always prefer to invest on the highest r-d available (r: gross return of investment, d: delta, depreciation rate), you will get the familiar decreasing r with capital, and also an increasing delta.

This argument, will be made formally, in mathematical terms.

b) Empirical clues:

There are a lot of empirical "clues" that this is the case. Although a formal "proof" using data could be complicated, we may present some of this clues:

b1) In the US the depreciation has steadily increased during the 60s, 70s and 80s (I've shown this graph to Fahiz). Is was a significant increase. It is safe to say that capital stock has increased considerably during this period.

b2) In developing countries, it is possible to see that some where the economy develops the depreciation rate has also increased, and some where war and other problems led to a reduction in the size of the economy, there was a reduction in the depreciation rate.

b3) The depreciation rate for R&D is higher than for most of other kinds of investment. Again, the higher the capital stock, the higher the proportion of it that is R&D.

b4) Some work about "endogenous deprecation" shows higher depreciation when investment increases (as a cyclical phenomena), although they give a different explanation for it (the cost of adjusting the capital stock makes it that during times of increasing aggregate demand it compensates to use a higher utilization capacity and this depreciates capital faster). I am not saying in this regard that our explanation is better (I believe both mechanisms play a role), I am just saying that the cyclical data is also quite compatible with this idea.

c) Consequences

One important consequence of this idea (there may be others) is that decreases in labor supply end up increasing wages not only on the short term, but also in the steady state (as opposed to what happens if the depreciation rate is constant). 

Other much important consequences may be derived once this "increasing depreciation function" is estimated (we would not be doing this estimation, but maybe challenging others to do it?)