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What are State Space Models?

What are State Space Models?. Andrew P. Blake CCBS/HKMA May 2004. Model form. Introduced into the rational expectations literature by Blanchard and Kahn (1980) Develops a model form used in much of the optimal control literature

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What are State Space Models?

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  1. What are State Space Models? Andrew P. Blake CCBS/HKMA May 2004

  2. Model form • Introduced into the rational expectations literature by Blanchard and Kahn (1980) • Develops a model form used in much of the optimal control literature • Later generalised to handle slightly more complicated economic models

  3. Linear stochastic model • We consider a model in state space form: • u is a vector of control instruments, s a vector of endogenous variables, ε is a shock vector • The model coefficients are in A, B and C

  4. Properties of the model • Linear, time invariant • System of first order equations • Is this restrictive? • May be of any size, and may be quite sparse • Superficially like a first order VAR

  5. Properties of the model (2) • Companion form • What if the model is (ignoring stochastics): • We can write in first order form as:

  6. What happens with RE? • Modify the model to: • Now we have z as predetermined variables and x as jump variables • Model has a saddlepath structure • Solved using Blanchard & Kahn (1980)

  7. What happens with RE? (2) • What if we have a feedback rule for u? • The model ‘under control’ is:

  8. Generalized BK • Now modify the model to: • May be that E21 = 0 and E22 is singular • Can be solved using Klein (1997), Soderlind (1999)

  9. How does this compare with other forms? • Binder & Pesaran, Sims, Dennis have used RE models of the form: • Sometimes called semi-structural form • How do they compare?

  10. How does a BK model fit into this? • We can rewrite our BK form model as: • Larger, sparser, redundant future terms • Can be more compact • Still requires ‘companion form’ type transform for further lags

  11. Why use state-space? • Trivially: Most of the literature does • Our Ox programs/WinSolve use SS • SS requires us to identify the variables as predetermined or not • This is advantageous for understanding models • Understand role of states and co-states

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