Aiyagiri Memory Consumption

1

Hi,

I am working through the Aiyagiri example and it ran fine (if a bit slowly). Now I am trying to extend it by endogenizing labour. The issue here is that the R and Q matrices become too large (I think) and as a result python keeps throwing a memory error after a couple of iterations.

I am using python 64 bit on a 64 bit machine. I have 8 GB of Ram. I am using windows 10.

I have modified the code to be that it iterates through a range of r_values to get the equilibrium level of interest rate and capital stock. I read an issue with the discrete DP quant econ package that for larger problems the fact that we need to specify R and Q before hand could prove to be to be too memory intensive (ref: https://github.com/QuantEcon/QuantEcon.py/issues/185). I am not sure if this was fixed or not.

At this point I am contemplating if coding it all from scratch would prove to be a better option. Something along the lines of this: https://lectures.quantecon.org/py/optgrowth.html

Would slightly complicated to code up but I feel like it won’t be as memory intensive? I am going to try it today, but I was wondering if anyone else had any tips here which may save me some unnecessary effort.

Thank you to anyone who might reply.

2

Hi @Hariharan_Jayasankar, this is indeed a known issue with the way the DP routines are written. But there are advantages to pre-building R and Q in other situations, so it’s a trade off.

@oyama.daisuke is the author of the code and might have further thoughts.

You can write your own version of the DP routines, certainly, and that’s probably a good option in a high dimensional setting. Here’s some jitted, parallelized optimal savings code that might help get you started:

Regards, John.

3

As discussed at https://github.com/QuantEcon/QuantEcon.py/issues/185 which you already referred to, it is an inherent limitation of the way in which DiscreteDP is implemented, which assumes that P and Q are stored in RAM upfront. The best you can do currently is to use a sparse matrix format for Q (if your problem is sparse enough).

It would be interesting to see if the Blaze ecosystem would help, which can handle “larger-than-memory” arrays. (I have never used it yet though.)

4

Thank you @john.stachurski. That notebook seems helpful!

5

I will see if the sparse matrix option works for me.

@john.stachurski, if I may ask, whats the difference between the model you posted and the Aiyagari model? It seems like the only difference from the lecture notes and this is how z is defined. Or am I wrong?

Thanks

6

Yes that’s right, @Hariharan_Jayasankar. But it’s solved with a much lower memory footprint. Of course that only gives you the household problem. For the equilibrium problem you can follow the Aiyagari lecture.

Good luck, John.

7

Hi,

Sorry if this is too much to ask, but it’s a related question which I am not able to figure out.

Is it possible to use a jitted function to loop over parameter values in these scenarios? For example in the notebook you posted, you loop over values of r to compute the capital supply for different levels of interest rates.

I find a normal loop to be far too slow, but jitting it in a straightforward manner throws too many errors. This is the baseline code for it:

def get_eq(r_min = 0.02, r_max = 0.04, r_size = 1, tol = 1e-3, n_iter = 100):

r_range = np.linspace(r_min, r_max, r_size)
iter = 0
error = tol + 1
n = 0

while error > tol and iter < n_iter:
    
    r_i = r_range[0]
    # Figure out firm problem
    
    w_i = r_to_w(r_i)
    
    # Solve agents problems
    mod = AiyagariProb(r = r_i, w = w_i)
    T = mod.bellman_operator()
    v_init = np.ones((mod.a_size, mod.z_size))
    v_star, pol = vfi(T, v_init)
    
    k_s = prices_to_capital_stock()
    
    # get back how much the firm is willing to pay for that K_s
    r_star = rd(k_s)
    
    # Error
    error = np.absolute(r_star - r_i)
    
    n = n + 1
    

return r_i, k_s

What this is doing is looping over different values of r, getting a value of w, inserting w and r into the consumer problem, getting a level of capital stock, then seeing what interest rate (r_star) firms are willing to pay for that level of capital stock. If r_i and r_star aren’t close enough, the loop goes to the next value of r.

8

@Hariharan_Jayasankar: I suggest you practice with Numba to get a sense of what’s possible and what’s not. Have a read of the documentation to see what can be just in time compiled. But in this case, there won’t be much speed gain to jitting the outer loop — given that the inner loops are already jitted. I don’t usually do it myself. I try to make the inner loop as fast as possible and then after that it just depends on your hardware.

Good luck solving your problem.

9

Alright. That makes sense.

Thanks for all the help John. And the lectures!