Econ-ARK for Central Banks

Microfoundations in a Nutshell (1/2)

Prehistory

• Modigliani and Brumberg (1954), Friedman (1957), Diamond (1964)
• Perfect Foresight models: 1960s-70s

Bewley (1977)

• Formalization of Friedman PIH
• Rigorous treatment of uncertainty, liq constr
• Entirely qualitative/analytical

Microfoundations in a Nutshell (2/2)

Early 1990s: Numerical computation of SS dist’n of wealth

• Life Cycle / OLG:
  • Zeldes (1989); Hubbard, Skinner, and Zeldes (1994, 1995);
  • Huggett (1996); Carroll (1997)
• Infinite Horizon
  • Deaton (1991); Carroll (1992); Aiyagari (1994)
• Aggregate dynamics? Hopeless:
  • requires predicting evolution of entire distribution

Dynamics

Krusell-Smith (1998):

• mean of distribution \(\bar{k}\) is good enough!
• still excruciatingly slow

Reiter (2010):

• SS Micro and Dyn Macro can be solved independently
  • Why? Idiosyncratic shocks 100x larger than agg
  • So agg shocks cause ‘small’ perturbation of dstn
• \(\Rightarrow\) Reiter Singularity: 2014-2018
  • Culmination: “Sequence Space Jacobian” Toolkit:
  • Bring us your micro SS and Jacobians wrt PF aggregate shocks
    • …We’ll give you the dynamic macro

Where Does Econ-ARK Fit? (1/2)

Rich Set of Tools for SS Micro …

• Consumption/Saving
• Portfolio Choice
• Discrete-Continuous Problems: DC-EGM tool
• Labor Supply: Keane and Imai
• Medical Expense Risk
• Life Cycle Modeling: solutions and datasets
• Sophisticated Liquidity Constraints
  • Higher rate for borrowing vs saving
  • Withdrawal penalties for retirement saving
• Etc etc

But Wait, There’s More: Indirect Inference

Life Cycle Model (Gourinchas-Parker; Cagetti)

• SolvingMicroDSOPs

• With Bequests? (DeNardi)

  • TRP Model Notebook

But Wait, There’s More: REMARKS

• An easy-to-use standard for guaranteed replicability

  • on any computer (Mac, Win, Linux)
  • using any open-source language: Python, R, Julia, …
  • About 26 of them

• Builds on industry standards: Docker, cff, conda, pip, …

• Aim:

  • Set a standard for journals
    • Now every journal has different requirements
  • Results should be replicable on submission
    • Editors, referees can “kick the tires”
    • Readers can easily stand on your giant shoulders
    • Central banks can exchange and compare models

Where Are We Going? ‘DYNARK’:

• Model specification tools for any Bellman Problem (mockup)
• Three layers:
  1. Abstract mathematical description
     • The symbolic version that appears in the text
     • Describes the “Platonic Ideal” of the model
     • What you would solve with \(\infty\) computing power
  2. Numerical/approximation details
     • Metaparameters like # of gridpoints for approx
     • Restrictions on ranges of parameters (e.g. 1 < CRRA < 10)
  3. Specify your claims:
     • Concrete assertion about results
     • “Model requires CRRA > 8 to match portfolio share”

Why These Elements?

• 2 and 3 allow AUTOMATIC robustness testing
• For each approx:
  • does claim fail as gridpoints increase?
• For each restriction:
  • ‘parameter sweep’ of values in allowed ranges

Underlying Motivation

Tower of Babel problem

1. Lack of transparency: What exactly is your model?
   • Lots of buried assumptions: gridpoints, boundaries, dstns
2. Lack of replicability
   • Some notorious stories (only runs on Win 8.1 w/ Matlab 8.7.6.5)

Causes:

• Everyone writes their own code
  • Often inherited from advisor
  • Barriers to entry
• Can take months just to get someone else’s model working
  • Quicker to build on your own Byzantine legacy code

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