Secular Stagnation In Addition To 3 Menstruum Olg

For macroeconomists. This ship service is a sort of introduction to the novel paper on secular stagnation yesteryear Eggertsson in addition to Mehrotra. As usual, whatsoever misinterpretations are my fault.

A basic see behind secular stagnation is that the natural existent charge per unit of measurement of involvement mightiness snuff it negative for a prolonged menstruum of time. Influenza A virus subtype H5N1 uncomplicated way to model this would live on to allow the steady dry soil existent involvement charge per unit of measurement to snuff it negative. That cannot conduct house inwards basic instance agent models, where the steady dry soil existent involvement charge per unit of measurement (absent growth) is given by

1+r = 1/b

where b<1 is the utility discount factor. With population increase (at charge per unit of measurement = n) this becomes

1+r = n +1/b

Note that a autumn inwards n volition cut back the existent involvement rate, which is a useful upshot if nosotros desire to relate secular stagnation to falling population growth, only rates cannot autumn below the charge per unit of measurement of fourth dimension preference.

In a touchstone 2 menstruum OLG model nosotros conduct keep to a greater extent than flexibility. If agents exclusively piece of occupation inwards the kickoff period, so they postulate to relieve inwards that menstruum to live on able to smoothen consumption betwixt their working lives in addition to retirement. If nosotros allow them to produce that through investing inwards capital, in addition to if α is the exponent on working capital alphabetic character inwards a Cobb Douglas production function, so amongst log utility the existent involvement charge per unit of measurement inwards steady dry soil is given by

r = k + kn        where              k = α(1+b)/b(1- α)

If 1 menstruum is nearly 25 years, then b could live on 0.5 (annual b = 0.973), in addition to amongst α = 0.4 so k=2. So immediately the touching on of a autumn on population increase on the existent involvement charge per unit of measurement is magnified, only the steady dry soil existent involvement charge per unit of measurement is too probable to live on inwards a higher house the instance agent case. (If n=0 and b = 0.5, so nosotros conduct keep r=1 in addition to r=2 respectively. For a 25 twelvemonth menstruum this would gibe to annual involvement rates of or so 2.8% in addition to 4.5%.)

In a 3 menstruum OLG setup, nosotros tin terminate conduct keep saving without capital. The pump aged piece of occupation (receiving income Y), in addition to they lend to the young, in addition to inwards retirement larn paid dorsum yesteryear the immediately pump aged. Suppose, however, that because of some credit friction the amount the immature tin terminate borrow gross of involvement payments is fixed at D, in addition to allow d=D/Y<1. The pump aged would similar to lend them plenty to smoothen consumption, so the furnish of loans inwards steady dry soil is (given log utility)

b (Y-D)/ (1+b)

where Y-D is pump historic menstruum income cyberspace of repaying loans taken out when young. The need for loans is

D (1+n)/(1+r)

The borrowing limit is gross of interest, so amongst no population increase actual borrowing is D/(1+r). With population increase at that spot are to a greater extent than of the immature than pump aged, so nosotros postulate to scale upwards loan need accordingly. The existent involvement charge per unit of measurement equates need in addition to supply, which implies

1+r = j + jn       where              j = (1+b)d/b(1-d)

Now if d is small, j could live on less than one, which reduces the sensitivity of involvement rates to population growth, although a autumn inwards population increase silent reduces rates. However this too agency that the gross involvement charge per unit of measurement (1+r) could live on less than one, so the steady dry soil existent involvement charge per unit of measurement could live on negative.

The pump aged postulate to relieve for retirement, only the exclusively way they tin terminate produce this is yesteryear lending to the young. The higher the existent involvement rate, the less the immature tin terminate borrow because of the credit friction. In that situation, the existent involvement charge per unit of measurement could easily live on negative, because exclusively so volition the immature live on able to borrow plenty to allow the pump historic menstruum to consumption smoothen when they retire.

The telephone commutation upshot that Eggertsson in addition to Mehrotra explore is that a credit compaction - a autumn inwards D - could lower existent involvement rates into negative territory, in addition to could thence generate secular stagnation. They visit how inequality could live on incorporated into the model, in addition to so embed the model inwards a nominal framework. Nominal wage rigidity is added (using a similar machinery to that inwards the Schmitt-Grohe in addition to Uribe newspaper I discussed here), in addition to the implications for monetary in addition to financial policy explored. So I conduct keep exclusively touched on the paper here, only every bit this 3 menstruum OLG set-up is non touchstone I see this ship service mightiness live on useful.