Rules Of Thumb (Ellison & Fudenberg) (Technology Convergence)

Question 1

Rules of thumb in Ellison and Fudenberg in whether to adopt a new technology or not. (2)

Answer 1

Not forward looking or consider historical returns, only last periods returns!

Popularity weighting

Question 2

Consider two technologies g and f with returns ug and uf . We know g is better in expectation, but may be worse in bad years:

How can we express the return

Answer 2

ugt - uft = ø+εt

Ø is difference between the 2 techs
E.g for HYV seeds, generally returns better, however in bad weather returns become worse than the normal seeds! (Accounted for in the error term, which can be negative!)

Question 3

Xt = people using technology g in period t.

And a share α of population can switch technologies each period.

So, under Ellison and Fudenberg, when do people switch technology?

Answer 3

Switch technology that performs better in the last period (since not forward looking, or not historical looking!)

Question 4

If ugt > uft (last period), write

Expression for the next period (t+1) for people who switch to g.

Answer 4

Xt+₁ = (1-α)Xt + α with probability p

(1-α)Xt is people that already use tech g so can’t switch, a is people that can switch!

Question 5

If ugt < uft (in the last period), write

Expression for the next period (t+1) for people who switch to f

Answer 5

Xt+1 = (1-a)Xt with probability 1-p

(People using g so can switch!)

Question 6

What does the long run equilibrium get us?

And the meaning

Answer 6

Setting Xt+1 = Xt (since next period based of previous)

Gets us long run equilirbium
E(Xt) = p

Means no convergence. Share X will fluctuate forever, since using last years returns which is forever unstable (since we have the error term ut which accounts for being g being generally better but CAN have worse returns in some periods! (not efficient because we know g is better!)

Question 7

If individuals CAN observe E(xt) = p , how can they infer g is better than f?

Answer 7

If Xt > 0.5 it means g is better than f!!

(ONLY IF OBSERVABLE IS KEY!)

Question 8

So we pick G if Xt>0.5

What is this known as

Answer 8

Full popularity weighting. Where we can observe E(xt)=P

Since we only consider popularity, not past returns

Question 9

So why is full popularity weighting bad:

Answer 9

uninformative - all copy each other so no information to gain. instantly herd and converge to g or f, depending on the starting value I.e if Xt>0.5 then converges to g! Regardless of returns!

Question 10

So we need to consider returns: what measures this?

Answer 10

Intermediate popularity weighting

Question 11

Intermediate popularity weighting - what does it do

Answer 11

Combines past returns AND popularity

Question 12

Intermediate popularity weighting: choose g if…

Answer 12

Ugt - Uft >= m(1-2xt)

m is population weighting e.g m=0 dont care about popularity, solely base of returns

Question 13

Important:
What if m=0

What if m = infinity

What if m is intermediate

Answer 13

If m=0 only returns matter i.e choose if Ugt>uft

If m = infinity: Full popularity weighting (if X<0.5 RHS is +infinity, if X>0.5 RHS is -infinity, so returns have to be > +infinity which is never the case, or > -infinity which is always the case, HENCE OUR INEQUALITY IS NO LONGER INFORMATIVE, PURELY BASED ON POPULARITY!

If m is intermediate… there is a threshold Xg where above it we converge to g, and a threshold Xf where below means we we converge to f.

Question 14

Even in the worse case scenario we will still choose g if…

Answer 14

Xt>Xg = m-Ø+σ /2m

Population is above the threshold to converge
I.e if population share is sufficiently high, returns do not matter and we will still converge to 1. So still increase g despite low returns

Question 15

What if Xt < Xf = m-Ø+σ/2m

Answer 15

Share using g will converge to 0, since we are below the threshold

Even if returns are highest, we will still use the worse technology (f) since population share is so low

Question 16

So 4 possible scenarios of thresholds

Xf>0 and Xg<1
Xf<0 and Xg<1
Xf>0 and Xg>1
Xf<0 and Xg>1

Answer 16

Xf>0 and Xg < 1 : means convergence to either technology is possible, depending on the shocks received.

Xf<0 and Xg<1 - means g is on average much better than f, so never converge towards f since always above the threshold since it is <0! and eventually trend towards g.

Xf>0 and Xg>1 Inverse of second, we converge to f

Xf<0 and Xg>1 not much popularity weighting. Share keeps fluctuating.

Question 17

If we want economy to converge to g as quickly as possible, what do we do, and how is there a risk

Answer 17

Higher m (weight population more)>higher Xf, lower Xg>faster convergence (Xg threshold is lower so easier to reach to go above)

Risk: if m=infinity we get xf=xg=0.5 , so risk of converging to Xt=0

Question 18

So what is there a trade of between

Answer 18

Speed of convergence and probability of convergence.

Lower m gives better probability of converging to g, however slower.

Question 19

Effect of higher Ø (difference between the 2 technologies to begin with: a high Ø means a technology is way better on average)

Answer 19

Faster convergence (positive returns are more frequent)

Question 20

What technologies is faster convergence harder for?

Answer 20

Technologies which are generally a little worse, but sometimes a lot better e.g seatbelts, insurance (positive returns ø are infrequent so convergence and adoption of technology may be slow!!!)