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We consider a bootstrap estimator of the parameters of state space models and show that the bootstrap realizations of this estimator, usually employed to approximate asymptotic confidence intervals,<jats:italic>p<\/jats:italic>\u2010values, and critical values of tests, can be also constructively used to build a test for forms of misspecifications which invalidate asymptotic normality. The test evaluates how \u201cclose or distant\u201d the estimated state space model is from the case where asymptotic inference based on the Gaussian distribution applies. We derive sufficient conditions on the number of bootstrap repetitions,<jats:italic>B<\/jats:italic>, relative to the number of sample observations,<jats:italic>T<\/jats:italic>, for the test statistic to have a well\u2010defined asymptotic distribution under the null. Throughout the paper, we focus on the state space form of small\u2010scale monetary dynamic stochastic general equilibrium (DSGE) models and investigate the usefulness of our approach through Monte Carlo experiments and empirical illustrations based on US quarterly data. Results show that (i) bootstrapping the state space form provides highly reliable inference and (ii) the suggested test detects weakly identified parameters reasonably well in finite samples.<\/jats:p>","DOI":"10.1002\/jae.2843","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T09:32:48Z","timestamp":1625823168000},"page":"3-22","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models"],"prefix":"10.1002","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3000-9885","authenticated-orcid":false,"given":"Giovanni","family":"Angelini","sequence":"first","affiliation":[{"name":"Department of Economics University of Bologna Bologna Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2856-0005","authenticated-orcid":false,"given":"Giuseppe","family":"Cavaliere","sequence":"additional","affiliation":[{"name":"Department of Economics University of Bologna Bologna Italy"},{"name":"Department of Economics University of Exeter Business School Exeter UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5351-2876","authenticated-orcid":false,"given":"Luca","family":"Fanelli","sequence":"additional","affiliation":[{"name":"Department of Economics University of Bologna Bologna Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474930701220071"},{"key":"e_1_2_10_3_1","volume-title":"Optimal filtering","author":"Anderson B. 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