diff --git a/doc/manual/source/bibliography.rst b/doc/manual/source/bibliography.rst
index dce3c0d89e226077f9dfc6be0ae74fe78e52bb9c..a8442cbca60a93bdf191fb3a18fc756775c804d4 100644
--- a/doc/manual/source/bibliography.rst
+++ b/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.
diff --git a/doc/manual/source/the-model-file.rst b/doc/manual/source/the-model-file.rst
index 096ebbf34bec601eaa792a6d3533ad4bb47cbfe0..e465161e571b3bb2a5137e2fdaa4f80eabdce6fa 100644
--- a/doc/manual/source/the-model-file.rst
+++ b/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 ` 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*