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Using Monte Carlo experiments, we examine the performance of indirect inference tests of DSGE models in small samples, using various models in widespread use. We compare these with tests based on direct inference (using the Likelihood Ratio). We find that both tests have power so that a substantially false model will tend to be rejected by both; but that the power of the indirect inference test is by far the greater, necessitating re-estimation to ensure that the model is tested in its fullest sense. We also find that the small-sample bias with indirect estimation is around half of that with maximum likelihood estimation.

Using Monte Carlo experiments, we examine the performance of Indirect Inference tests of DSGE models, usually versions of the Smets-Wouters New Keynesian model of the US post-war period. We compare these with tests based on direct inference (using the Likelihood Ratio), and on the Del Negro-Schorfheide DSGE-VAR weight. We find that the power of all three tests is substantial so that a false model will tend to be rejected by all three; but that the power of the indirect inference tests are by far the greatest, necessitating re-estimation by indirect inference to ensure that the model is tested in its fullest sense.

We extend the method of indirect inference testing to data that is not filtered and so may be non-stationary. We apply the method to an open economy real businss cycle model on UK data. We review the method using a Monte Carlo experiment and find that it performs accurately and has good power.

We propose a numerical method, based on indirect inference, for checking the identification of a DSGE model. Monte Carlo samples are generated from the model’s true structural parameters and a VAR approximation to the reduced form estimated for each sample. We then search for a different set of structural parameters that could potentially also generate these VAR parameters. If we can find such a set, the model is not identified.

We investigate the relative roles of monetary policy and shocks in causing the Great Moderation, using indirect inference where a DSGE model is tested for its ability to mimic a VAR describing the data. A New Keynesian model with a Taylor Rule and one with the Optimal Timeless Rule are both tested. The latter easily dominates, whether calibrated or estimated, implying that the Fed's policy in the 1970s was neither inadequate nor a cause of indeterminacy; it was both optimal and essentially unchanged during the 1980s. By implication it was largely the reduced shocks that caused the Great Moderation - among them monetary policy shocks the Fed injected into inflation.

We review the methods used in many papers to evaluate DSGE models by comparing their simulated moments with data moments. We compare these with the method of Indirect Inference to which they are closely related. We illustrate the comparison with contrasting assessments of a two-country model in two recent papers. We conclude that Indirect Inference is the proper end point of the puzzles methodology.

We evaluate the Smets-Wouters model of the US using indirect inference and the bootstrap with a VAR representation of the main US data series. We find that the New Keynesian SW model is strongly rejected by the data’s dynamic properties and in particular cannot match the variability of the data. An alternative (New Classical) version of the model with flexible wages and prices and a one-period information lag fares no better. A ‘weighted’ model (mostly New Classical but part New Keynesian) is better able to match the data variability, though it too is rejected overall. Allowing for structural breaks in the monetary regime we find a model from 1984 onwards fits fairly well dynamically; this has a high New Keynesian weight, suggesting much greater nominal stickiness during the ‘great moderation’. Our results are robust to a variety of concerns about the bootstrap, parameter uncertainty, and numerical procedures.

We examine a two country model of the EU and the US. Each has a small sector of the labour and product markets in which there is wage/price rigidity, but otherwise enjoys flexible wages and prices with a one quarter information lag. Using a VAR to represent the data, we find the model as a whole is rejected. However it is accepted for real variables, output and the real exchange rate, suggesting mis-specification lies in monetary relationships. The model highlights a lack of spillovers between the US and the EU.

We use the method of indirect inference, using the bootstrap, to test the Smets and Wouters model of the EU against a VAR auxiliary equation describing their data. We find that their model generates excessive variance compared with the data. But their model fits the dynamic facts quite well if the errors have the properties assumed by SW but scaled down. We compare a New Classical version of the model which also performs reasonably if error properties are chosen using New Classical priors (notably excluding shocks to preferences). Both versions have (different) difficulties fitting the data if the actual error properties are used. A model combining rigid and flexible-wage/price sectors, with a weight of around 5% on the rigid sector, does best in fitting the data.

A Real Business Cycle model of the UK is developed to account for the behaviour of UK nonstationary macro data. The model is tested by the method of indirect inference, bootstrapping the errors to generate 95% confidence limits for a VECM representation of the data; we find the model can explain the behaviour of main variables (GDP, real exchange rate, real interest rate) but not that of detailed GDP components. We use the model to explain how ‘crisis’ and ‘euphoria’ are endemic in capitalist behaviour due to nonstationarity; and we draw some policy lessons.

We review the methods used in many papers to evaluate DSGE models by comparing their simulated moments and other features with data equivalents. We note that they select, scale and characterise the shocks without reference to the data; crucially they fail to use the joint distribution of the features under comparison. We illustrate this point by recomputing an assessment of a two-country model in a recent paper; we find that the paper's conclusions are essentially reversed.

In this paper we propose an index of the fiscal stance suitable for practical use in short-term policy making. The index is based on a comparison of a target level of the debt-GDP ratio for a given finite horizon with a forecast of the debt-GDP ratio based on a VAR formed from the government budget constraint. This approach to measuring the fiscal stance is different from the literature on fiscal sustainability. We emphasise the importance of having a forward-looking measure of the fiscal stance for the immediate future rather than a test for fiscal sustainability that is backward-looking, or based just on past behaviour which may not be closely related to the current fiscal position. We use our methodology to construct a time series of the indices of the fiscal stances of the US, the UK and Germany over the last 25 or more years. We find that both the US and UK fiscal stances have deteriorated considerably since 2000 and Germany's has been steadily deteriorating since unification in 1989, and worsened again on joining EMU.