📖 Update manual

doc/manual/source/bibliography.rst

@@ -44,6 +44,7 @@ Bibliography
 * Kim, Jinill and Sunghyun Kim (2003): “Spurious welfare reversals in international business cycle models,” *Journal of International Economics*, 60, 471–500.
 * Kanzow, Christian and Stefania Petra (2004): “On a semismooth least squares formulation of complementarity problems with gap reduction,” *Optimization Methods and Software*, 19, 507–525.
 * Kim, Jinill, Sunghyun Kim, Ernst Schaumburg, and Christopher A. Sims (2008): “Calculating and using second-order accurate solutions of discrete time dynamic equilibrium models,” *Journal of Economic Dynamics and Control*, 32(11), 3397–3414.
+* Komunjer, Ivana and Ng, Serena (2011): ”Dynamic identification of dynamic stochastic general equilibrium models”, *Econometrica*, 79, 1995–2032.
 * Koop, Gary (2003), *Bayesian Econometrics*, John Wiley & Sons.
 * Koopman, S. J. and J. Durbin (2000): “Fast Filtering and Smoothing for Multivariate State Space Models,” *Journal of Time Series Analysis*, 21(3), 281–296.
 * Koopman, S. J. and J. Durbin (2003): “Filtering and Smoothing of State Vector for Diffuse State Space Models,” *Journal of Time Series Analysis*, 24(1), 85–98.
@@ -52,13 +53,16 @@ Bibliography
 * Liu, Jane and Mike West (2001): “Combined parameter and state estimation in simulation-based filtering”, in *Sequential Monte Carlo Methods in Practice*, Eds. Doucet, Freitas and Gordon, Springer Verlag.
 * Lubik, Thomas and Frank Schorfheide (2007): “Do Central Banks Respond to Exchange Rate Movements? A Structural Investigation,” *Journal of Monetary Economics*, 54(4), 1069–1087.
 * Murray, Lawrence M., Emlyn M. Jones and John Parslow (2013): “On Disturbance State-Space Models and the Particle Marginal Metropolis-Hastings Sampler”, *SIAM/ASA Journal on Uncertainty Quantification*, 1, 494–521.
+* Mutschler, Willi (2015): “Identification of DSGE models - The effect of higher-order approximation and pruning“, *Journal of Economic Dynamics & Control*, 56, 34-54.
 * Pearlman, Joseph, David Currie, and Paul Levine (1986): “Rational expectations models with partial information,” *Economic Modelling*, 3(2), 90–105.
 * Planas, Christophe, Marco Ratto and Alessandro Rossi (2015): “Slice sampling in Bayesian estimation of DSGE models”.
 * Pfeifer, Johannes (2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”.
 * Pfeifer, Johannes (2014): “An Introduction to Graphs in Dynare”.
+* Qu, Zhongjun and Tkachenko, Denis (2012): “Identification and frequency domain quasi-maximum likelihood estimation of linearized dynamic stochastic general equilibrium models“, *Quantitative Economics*, 3, 95–132.
 * Rabanal, Pau and Juan Rubio-Ramirez (2003): “Comparing New Keynesian Models of the Business Cycle: A Bayesian Approach,” Federal Reserve of Atlanta, *Working Paper Series*, 2003-30.
 * Raftery, Adrian E. and Steven Lewis (1992): “How many iterations in the Gibbs sampler?,” in *Bayesian Statistics, Vol. 4*, ed. J.O. Berger, J.M. Bernardo, A.P. * Dawid, and A.F.M. Smith, Clarendon Press: Oxford, pp. 763-773.
 * Ratto, Marco (2008): “Analysing DSGE models with global sensitivity analysis”, *Computational Economics*, 31, 115–139.
+* Ratto, Marco and Iskrev, Nikolay (2011): “Identification Analysis of DSGE Models with DYNARE.“, *MONFISPOL* 225149.
 * Schorfheide, Frank (2000): “Loss Function-based evaluation of DSGE models,” *Journal of Applied Econometrics*, 15(6), 645–670.
 * Schmitt-Grohé, Stephanie and Martin Uríbe (2004): “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function,” *Journal of Economic Dynamics and Control*, 28(4), 755–775.
 * Schnabel, Robert B. and Elizabeth Eskow (1990): “A new modified Cholesky algorithm,” *SIAM Journal of Scientific and Statistical Computing*, 11, 1136–1158.

doc/manual/source/the-model-file.rst

@@ -9154,15 +9154,27 @@ Performing identification analysis
             * minimal system as in *Komunjer and Ng (2011)*
             * reduced-form solution and linear rational expectation model
               as in *Ratto and Iskrev (2011)*
+            Note that for orders 2 and 3, all identification checks are based on the pruned
+            state space system as in *Mutschler (2015)*. That is, theoretical moments and 
+            spectrum are computed from the pruned ABCD-system, whereas the minimal system
+            criteria is based on the first-order system, but augmented by the theoretical
+            (pruned) mean at order 2 or 3.
 
-         2. Identification strength analysis based on sample information matrix as in
-            *Ratto and Iskrev (2011)*
+         2. Identification strength analysis based on (theoretical or simulated) curvature of
+            moment information matrix as in *Ratto and Iskrev (2011)*
 
          3. Parameter checks based on nullspace and multicorrelation coefficients to
             determine which (combinations of) parameters are involved
 
 *General Options*
 
+    .. option:: order = 1|2|3
+
+        Order of approximation. At orders 2 and 3 identification is based on the
+        pruned state space system. Note that the order set in other functions does
+        not overwrite the default.
+        Default: ``1``.
+
     .. option:: parameter_set = OPTION
 
         See :opt:`parameter_set <parameter_set = OPTION>` for
@@ -9220,13 +9232,15 @@ Performing identification analysis
             * ``0``: efficient sylvester equation method to compute
               analytical derivatives
             * ``1``: kronecker products method to compute analytical
-              derivatives
+              derivatives (only at order=1)
             * ``-1``: numerical two-sided finite difference method
-              to compute all identification Jacobians
+              to compute all identification Jacobians (numerical tolerance
+              level is equal to ``options_.dynatol.x``)
             * ``-2``: numerical two-sided finite difference method
               to compute derivatives of steady state and dynamic
               model numerically, the identification Jacobians are
-              then computed analytically
+              then computed analytically (numerical tolerance
+              level is equal to ``options_.dynatol.x``)
 
         Default: ``0``.
 
@@ -9297,7 +9311,7 @@ Performing identification analysis
     .. option:: no_identification_spectrum
 
         Disables computations of identification check based on
-        Qu and Tkachenko (2012)'s G, i.e. Gram matrix of derivatives of
+        *Qu and Tkachenko (2012)*'s G, i.e. Gram matrix of derivatives of
         first moment plus outer product of derivatives of spectral density.
 
     .. option:: grid_nbr = INTEGER
@@ -9311,7 +9325,7 @@ Performing identification analysis
     .. option:: no_identification_minimal
 
         Disables computations of identification check based on
-        Komunjer and Ng (2011)'s D, i.e. minimal state space system
+        *Komunjer and Ng (2011)*'s D, i.e. minimal state space system
         and observational equivalent spectral density transformations.
 
 *Misc Options*