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Indirect Inference has been found to have much greater power than the Likelihood Ratio in small samples for testing DSGE models. We look at asymptotic and large sample properties of these tests to understand why this might be the case. We find that the power of the LR test is undermined when re-estimation of the error parameters is permitted; this offsets the effect of the falseness of structural parameters on the overall forecast error. Even when the two tests are done on a like-for-like basis Indirect Inference has more power because it uses the distribution restricted by the DSGE model being tested.

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.

This lecture is about how best to evaluate economic theories in macroeconomics and finance, and the lessons that can be learned from the past use and misuse of evidence. It is argued that all macro/finance models are `false' so should not be judged solely on the realism of their assumptions. The role of theory is to explain the data, They should therefore be judged by their ability to do this. Data mining will often improve the statistical properties of a model but it does not improve economic understanding. These propositions are illustrated with examples from the last fifty years of macro and financial econometrics

This paper argues that the crisis was an outcome of EMU: setting a common monetary policy for countries with different initial inflation rates. The crisis countries were those with high inflation rates which then had negative real interest rates and consequently over-borrowed. Current policy discussions focus on crisis measures: fiscal, banking and political union, not avoiding another crisis. This paper suggests two ways to avoid a future crisis: offset an inappropriate monetary policy using fiscal policy; markets could better price loan rates by taking into account default risk. The paper shows that neither was done prior to the crisis.

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.

The immediate background to this paper is the downgrade of the U.K.'s credit rating in February 2013, the market's view that this should have occurred earlier and the emphasis in fiscal policy on reducing debt rather than recovery from recession. We propose a measure of the U.K. sovereign credit rating based on an open economy macroeconomic model that is simple to compute and easily automated. Whether based on an ad hoc debt-GDP limit or a DSGE model of an open economy, our measure downgrades the U.K.'s sovereign credit rating from the middle of 2008. From 2010 the rating improves and is nearly restored to triple-A by 2012.

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 business 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 find that forecasts from DSGE models are not more accurate than either times series models or official forecasts, but neither are they any worse. We also find that all three types of forecast failed to predict the recession that started in 2007 and continued to forecast poorly even after the recession was known to have begun. We investigate why these results occur by examining the structure of the solution of DSGE models and compare this with pure time series models. We show that the main factor is the dynamic structure of DSGE models. Their backward-looking dynamics gives them a similar forecasting structure to time series models and their forward-looking dynamics, which consists of expected values of future exogenous variables, is difficult to forecast accurately. As a result we suggest that DSGE models should not be tested through their forecasting ability.

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 postwar 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.

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.

We evaluate the Smets-Wouters model of the US using indirect inference with a VAR representation of the main US data series. We find that the original New Keynesian SW model is on the margin of acceptance when SW's own estimates of the variances and time-series behaviour of the structural errors are used. However when the structural errors implied jointly by the data and the structural model are used the model is rejected. We also construct an alternative (New Classical) version of the model with flexible wages and prices and a one-period information lag. This too is rejected. But when small proportions of both the labour and product markets are assumed to be imperfectly competitive within otherwise flexible markets the resulting `weighted' model is accepted.

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 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 evaluate the Smets-Wouters New Keynesian model of the US postwar period, using indirect inference, the bootstrap and a VAR representation of the data. We find that the model is strongly rejected. While an alternative (New Classical) version of the model fares no better, adding limited nominal rigidity to it produces a `weighted' model version closest to the data. But on data from 1984 onwards - the `great moderation' - the best model version is one with a high degree of nominal rigidity, close to New Keynesian. Our results are robust to a variety of methodological and numerical issues.

In this paper we propose a new way to formulate optimal policy based on a quadratic intertemporal welfare function where the dynamic constraint is based on a VAR model of the economy which we call the PVAR method. We argue that the VAR under control should not be derived simply by replacing the VAR equation for the policy instruments by an optimal control rule because this alters the stochastic structure of the VAR. Instead, one should first transform the VAR in order to condition the non-policy variables on the policy instruments, then use the resulting sub-system as the dynamic constraint, and finally construct the VAR under control by combining this sub-system with the resulting optimal policy rule. In this way the original stochastic structure of the VAR is retained. In comparing the two approaches we explain the theoretical advantages of the PVAR over the standard method and we illustrate the methods by examining the formulation of optimal monetary policy for the US. We suggest that since the whole process is easily automated, the PVAR method may provide a useful benchmark for use in real time against which to compare other, probably far more labour intensive, policy choices.

It is widely recognised that the "one-size-fits-all" monetary policy of the euro-zone is a potential problem. How much of a problem has not been much investigated. It is argued in this paper that it may result in the euro not being sustainable in the longer term without drastic changes to other aspects of the EU and, in particular, to fiscal policy. The problem is not the fault of the ECB, but is due to having a single nominal interest rate. As a result, the evidence reveals that national price levels are diverging over time which is leading to a permanent and unsustainable loss of competitiveness. A formal theory of inflation in the euro-zone based on an open-economy version of the New Keynesian model is used to analyse the problem. Although the euro system has automatic stabilising mechanisms arising from the changes in competitiveness and from absorbtion effects, these are shown to be not strong enough. The model is then modified to allow for fiscal transfers between countries and the size of the transfers required to produce a euro that may be sustainable are derived. It is shown that, in effect, this is an inflation tax, requiring high inflation countries to make transfers to low inflation countries as often happens within a single country in the form of unemployed benefits to low activity regions. Ultimately, the choice may lie between closer political union and a break-up of the euro-zone.

We propose an index of the fiscal stance that is convenient for practical use. It is based on a finite time horizon, not on an infinite time horizon like most tests. As it employs VAR analysis it is simple to compute and easily automated. We also show how it is possible to analyse a change of policy within a VAR framework. We use this methodology to examine the effect on fiscal sustainability of a change in policy. We then conduct an empirical examination of the fiscal stances of the US, the UK and Germany over the last 25 or more years, and we carry out a counter-factual analysis of the likely consequences for fiscal sustainability of using a Taylor rule to set monetary policy over this period. Among our findings are that the recent fiscal stances of all three countries are not sustainable, and that using a Taylor rule in the past would have improved the fiscal stances of the US and UK, but not that of Germany.

Surprisingly there are very few estimates of the equity risk premium period-by-period that satisfy a no-arbitrage condition, despite the vast literature on the subject. This is mainly due to the difficulties of estimation. Using the stochastic discount factor (SDF) model based on observable macroeconomic factors - as opposed to unobservable (latent) affine factors - and a new econometric methodology, we provide new estimates of the equity risk premium for the US and the UK based on monthly data 1975-2001. We obtain estimates of the risk premium for many of the best-known versions of consumption CAPM including time-separable power utility and time-nonseparable Epstein-Zin utility. We also show why many of the formulations of these models are unable to provide estimates of the risk premium. A related, and rapidly growing, literature that adopts a more statistical approach focuses on the empirical relation between the return on equity (or the Sharpe ratio) and return volatility. We argue that SDF theory implies that this relation is misconceived.

This Paper is an exploration into the links between macroeconomics and finance as they affect the FOREX risk premium. SDF theory is used in which the factors are observable macroeconomic variables. Three SDF theories are compared: a benchmark model based on traditional tests of FOREX efficiency; consumption-based CAPM; and the monetary model of the exchange rate. The theory takes account of both domestic and foreign investors. The joint distribution of the excess return to FOREX and the macro factors satisfies the no-arbitrage assumption, and is a suitably restricted version of multivariate GARCH-in-mean. Monthly data for the sterling-dollar exchange rate 1975-97 are used. The results suggest that the FOREX risk premium is best modelled by CAPM based and the factors that determine next period’s exchange rate.

A measure of the credibility of monetary policy is the inflation risk premium embodied in nominal yields. This will be time varying and can be estimated by combining the information contained in the nominal term structure of interest rates with that in the real term structure of inflation-indexed bonds. Information can also be obtained about the real risk premium, and about expected inflation. We estimate these risk premia using a generalization of the Cox-Ingersoll-Ross (CIR) affine-yield model. We use a one-factor model of the real term structure based on monthly observations on two-year, five-year and ten-year UK index-linked debt, and a two-factor model of the nominal term structure for the corresponding nominal yields. Our estimates show that the inflation risk premium contributes on average about 100 basis points to nominal yields. Since the exit from the Exchange Rate Mechanism (ERM) this has fallen to about 70 basis points. This shows the greater credibility of monetary policy in recent years. The real risk premium is much higher, and has fluctuated between 170 and 260 basis points since exit from the ERM, reflecting uncertainty about the real economy. The inflation risk premium provides a correction to the break-even method of forecasting inflation and produces an unbiased forecast.

Recent concern about the difficulty of obtaining structurally stable models of money demand combined with the removal of capital controls have drawn attention to the theory of currency substitution (CS). The purpose of this paper is to examine whether CS is a relevant factor in the demand for currency. A number of different theories are considered. The traditional approach to the demand for money focuses on the domestic holding. In contrast CS is concerned with both domestic and foreign holding of domestic currency, and with the substitutability between domestic and foreign currencies. Often it is not realized that there are various CS theories and they give different predictions. CS theories can be supplemented by the theory of vehicle currencies which emphasizes the use of a currency in international transactions by third-party countries. In this paper all of these theories are tested using alternative definitions of money, including both resident and non-resident holding, for data on the US dollar, the yen and the deutschmark. The evidence provides support for both CS and vehicle-currency effects but more in non-resident than resident currency holdings.

If a nation fails to satisfy its intertemporal budget constraint (IBC) then, like a government or a household, either it will become insolvent or it can consume more of its income. The main purpose of this paper is to establish necessary and sufficient conditions for a nation to satisfy its IBC, and to use these to carry out a test of whether the United States is violating its IBC. After suitable modifications the techniques used in the literature in testing the government IBC can be used; for example, the balance of payments replaces the government budget constraint. The analysis provides a number of new results and generalizations of existing results.

Dornbusch's overshooting model of the exchange rate has proved a very influential alternative to the monetary model. The original Dornbusch model was specified in continuous time and assumed perfect foresight. It also imposed the restriction of a sticky price level which does not respond instantaneously to new information. While convenient for analytic purposes, this particular model is less suitable for empirical analysis in which the data are aggregated over time and expectations are not formed perfectly. This paper presents a discrete time, rational expectations version of the Dornbusch model in which the price level is permitted to respond immediately, but not necessarily fully, to new information. The resulting dynamic behaviour of the exchange rate is analysed and interpreted. The conditions under which exchange rate overshooting occurs are derived and the effect of pre-announced policy changes are studied. Although the main purpose of the paper is expositional, an interesting feature of the results is that price stickyness is shown to be neither a necessary nor a sufficient condition for a change in monetary policy to bring about exchange rate overshooting.

This paper examines the appreciation of the dollar over the period 1980-85. The standard theories try to explain the increased demand for dollar assets by differential rates of return on bonds or by "safe-haven" arguments associated with the lower riskiness of United States assets. Neither of these explanations has proved satisfactory, however, and this has led to the search for other theories, including non-rational theories such as speculative bubbles and chartism. This paper proposes an alternative explanation, based on the role of the dollar as a vehicle currency and, in particular, the dominance of interbank transactions. It is shown that, in the years when the dollar appreciated most, changes in banks' assets and liabilities dominated the United States capital account. These were also years when United States banks were locked into large long-term foreign dollar loans to developing countries which, to make matters worse, were highly risky and often required further loans to help service the debt. Since deposits are mainly short-term and loans are long-term, the short-run demand for dollars is inelastic. In our view a decrease in the supply of dollar deposits at various times was a major cause of the dollar's appreciation. A formal model of exchange rate determination, based on the portfolio behaviour of banks, is developed and the predictions are shown to be consistent with the available evidence.

This paper analyses the effects of monetary shocks in the determination of exchange rates in economies where banks play a central role in providing finance for domestic investment and in international capital transactions. This is a situation that prevails in many countries, both developed and developing. For such countries the standard models of exchange rate determination are not strictly appropriate. As there are six state variables, a rational expectations simulation model is constructed and is used to carry out the dynamic analysis. In addition to the exchange rate there are two other jump variables in the model: Tobin's q and the shadow price of bank debt, which depends on expectations of future interest rates. It is shown that financing investment through intermediation helps to stabilize the economy following a domestic monetary shock but makes the economy more vulnerable to a foreign monetary shock.

This paper considers the estimation of a number of commonly used single-equation linear models, all of which have rationally expected future explanatory variables. Fully efficient and less efficient instrumental variable estimators are proposed in each case. The choice of estimation method is usually represented as a trade-off between efficiency on the one hand and robustness and computational convenience on the other. It is shown in this paper that there is a more fundamental issue which must influence the choice of estimator, namely the type of solution that the model possesses. The construction of an efficient estimation method depends on whether or not the model has a unique solution and often this will not be known a priori. Preliminary estimation by instrumental variable methods can be used to resolve this question. Various tests are proposed in the paper. Whiteman's solution method is used to determine the types of solution that are possible for each model. It is shown how these solutions can be written as both backwards and forwards solutions and the parameter restrictions which are required to obtain unique solutions.

It is widely thought that neither the foreign exchange markets nor equity markets are efficient, in the sense that tests of the unbiasedness hypothesis and of the present value relationship, respectively, typically lead to rejection. Interest has therefore turned to whether a risk premium exists. This paper provides non-parametric estimates of the foreign exchange and equity risk premia, i.e., estimates that do not depend on any particular model of risk. The average risk premia for three exchange rates (the DM, Yen, Pound are all against the Dollar) and for four stock markets (West Germany, Japan, the United Kingdom and United States) over 1973-88 are shown to be quite small. In contrast, considerable variation is discovered in these risk premia during this period.

This paper discusses the best way to formulate and estimate a dynamic econometric model when interest focuses mainly upon its long-run properties. Using results derived for the more general context of transformed regression models, it is shown how point estimates and the standard errors of long-run multipliers and long-run structural coefficients can be obtained using standard estimation methods. It is argued that such formulations are preferable to other specifications such as the error correction model. If the explanatory variables that enter the long-run solution are trend-stationary then it is found that no harm is done to the asymptotic properties of the long-run coefficients by omitting short-run dynamics entirely, though this is not recommended in practice. The results of this paper are related to the concept of co-integration and to the work of Engle and Granger. Finally, a new methodology for the construction of dynamic models is proposed.

Previous empirical studies of international CAPM models have not found much evidence to support the model. In this paper we suggest reasons why this might have happened and perform new tests using improved models and data. A range of monthly CAPM models are estimated for 1973-87 for aggregate equities and bonds in Germany, Japan, the United States and United Kingdom. The models are an improvement on earlier work in that we integrate equity markets into the analysis instead of focusing exclusively on government bond stocks, and we carefully measure the rates of return for both bonds and equities. In particular, bond returns reflect changes in the price of bonds as well as coupons. Despite this wider portfolio and the introduction of ARCH effects in the conditional covariance matrix of errors, our model still yields implausible estimates of the coefficient of relative risk aversion and provides very little explanatory power for expected relative rates of return. Correcting the ICAPM for these major deficiencies does not reverse earlier conclusions in the literature.

A well known characteristic of flexible exchange rates is their volatility, with result that their movement can be closely approximated by a random walk. One of the attractions of the monetary model of the exchange rate is its ability to offer an explanation of this volatility. A major drawback is that empirical tests of the exchange rate equation arising from the monetary model very often lead to rejection of the model. The blame for this is usually attributed to the breakdown of the purchasing power parity assumption. The main purpose of this paper is to attempt to provide measures of the relative importance of the likely principal causes of the failure of the monetary model. A second objective is to test the random walk hypothesis for exchange rates. The methodology employed is new and has wide application elsewhere. It involves explicitly modelling the misspecification by time series techniques. The results, which are for the sterling-United States Dollar and Deutschemark-United States Dollar exchange rates, confirm the importance of the breakdown of the PPP assumption but they also show that misspecification of the money market is equally important. Whilst a random walk model is found to provide a very good fit, it is shown that lagged information can be used to improve the explanation of the spot exchange rate and hence the random walk hypothesis can be rejected.