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Cet article etudie l’incorporation des mesures non conventionnelles de politique monetaire dans les modeles d’equilibre general stochastiques et dynamiques. La these principale de cet article est qu’il n’y a aucune dimension de la politique monetaire, conventionnelle ou pas, qu’il soit impossible de modeliser dans ce type de cadre.

We address this question using an estimated New Keynesian DSGE model of the Euro Area with trend inflation, imperfect indexation, and a lower bound on the nominal interest rate. In this setup, a decrease in the steady-state real interest rate, increases the probability of hitting the lower bound constraint, which entails significant welfare costs and warrants an adjustment of the monetary policy strategy. Under an unchanged monetary policy rule, an increase in the inflation target of eight tenths the size of the drop in the real natural rate of interest is warranted. Absent an increase in the inflation target, and assuming the effective lower bound prevents the ECB from implementing more aggressive negative interest rate policies, adjusting the monetary strategy requires considering alternative instruments or policy rules, such as committing to make-up for recent, below-target inflation realizations. Galí acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S) and from the Generalitat de Catalunya, through CERCA and SGR Programme (2017-SGR-1393).

We construct, and then estimate by maximum likelihood, a tractable dynamic stochastic general equilibrium model with incomplete insurance and heterogenous agents. The key feature of our framework is that cross‐sectional heterogeneity remains finite dimensional. The solution to the model thus admits a state‐space representation that can be used to recover the distribution of the model's parameters. Household heterogeneity expands the set of observables to cross‐sectional moments available at the business‐cycle frequency (in addition to the usual macro and monetary time series). Incomplete insurance gives rise to a precautionary motive for holding wealth that propagates aggregate shocks via (i) a stabilizing aggregate supply effect, working through the supply of capital, and (ii) a destabilizing aggregate demand effect coming from the feedback loop between unemployment risk and precautionary saving. Using the estimated model to measure the contribution of precautionary savings to the propagation of recent recessions, we find strong aggregate demand effects during the Great Recession and, to a lesser extent, during the 1990–1991 recession. In contrast, the supply effect at least offsets the demand effect during the 2001 recession. DSGE incomplete insurance heterogenous agents Bayesian estimation C32 E12 E21 E52

We study how changes in the steady-state real interest rate (henceforth r*) affect the optimal inflation target in a New Keynesian dynamic stochastic general equilibrium (DSGE) model with trend inflation and a lower bound on the nominal interest rate. In this setup, a lower r* increases the probability of hitting the lower bound. That effect can be counteracted by an increase in the inflation target, but the resulting higher steady-state inflation has a welfare cost in and of itself. We use an estimated DSGE model to quantify that trade-off and determine the implied optimal inflation target, conditional on the monetary policy rule in place before the financial crisis. The relation between r* and the optimal inflation target is downward sloping. While the increase in the optimal inflation rate is in general smaller than the decline in r*, in the currently empirically relevant region the slope of the relation is found to be close to −1. That slope is robust to allowing for parameter uncertainty. Under makeup strategies such as price level targeting, the optimal inflation target is significantly lower and less sensitive to r*.

We study how changes in the value of the steady-state real interest rate affect the optimal inflation target, both in the U.S. and the euro area, using an estimated New Keynesian DSGE model that incorporates the zero (or effective) lower bound on the nominal interest rate. We find that this relation is downward sloping, but its slope is not necessarily one-for-one: increases in the optimal inflation rate are generally lower than declines in the steady-state real interest rate. Our approach allows us not only to assess the uncertainty surrounding the optimal inflation target, but also to determine the latter while taking into account the parameter uncertainty facing the policy maker, including uncertainty with regard to the determinants of the steady-state real interest rate. We find that in the currently empirically relevant region for the US as well as the euro area, the slope of the curve is close to -0.9. That finding is robust to allowing for parameter uncertainty

In a neoclassical growth model with incomplete markets and heterogeneous, liquidity-constrained agents, the properties of the Laffer curve depend on whether debt or transfers are adjusted to balance the government budget constraint. The Laffer curve conditional on public debt is horizontally S-shaped. Two opposing forces explain this result. First, when government wealth increases, the fiscal burden declines, calling for lower tax rates. Second, because the interest rate decreases when government wealth increases, fiscal revenues may also decline, calling for higher taxes. For sufficiently negative government debt, the second force dominates, leading to the odd shape of the Laffer curve conditional on debt.

In response to the 2008–2009 crisis, faced with distressed financial intermediaries, the European Central Bank (ECB) embarked in longer term refinancing operations (LTROs) with full allotment. Using an estimated DSGE model with a frictional banking sector, we find that such liquidity injections have played a key role in averting a major credit crunch. A counterfactual analysis suggests that, absent these nonconventional measures, output, consumption, investment, and the GDP deflator would have been 2.5%, 0.5%, 9.7%, and 0.5% lower on average over 2009, respectively.

This paper studies the local dynamic properties of a simple general equilibrium model with Social vat. Strict balanced budget rules often lead to real indeterminacy of aggregate equilibrium, leaving room for « sunspots » fluctuations. In a closed-economy setup, social vat escapes this property and only reduces the aggregate labor supply elasticity. However, the quantitative effects are weak. Classification JEL : E32, E62

In this paper, using U.S. as well as French sectoral data and indicators of price rigidity, we reexamine the (lack of) relation between price stickiness and inflation persistence. This has recently been put forward by Bils and Klenow (2004) as evidence against time-dependent price setting models. We obtain that, when filtering out sector-specific shocks along the lines of Boivin, Giannoni, and Mihov (2009), and allowing for an alternative assumption on the marginal cost process, the case against the time-dependent Calvo model is substantially weakened.

Cet article etudie les effets des politiques de desin?ation sur la dynamique macroeconomique americaine. Les politiques de desin?ation sont identifiees a l’aide d’une technique d’episode comme des chocs reduisant de facon permanente le niveau d’in?ation de long terme. Nous montrons que ces epidodes sont suivis d’une periode de recession persistente. L’in?ation augmente a court terme au dessus de son niveau de long terme et presente une dynamique en cloche. Cette dynamique se retrouve sur l’evolution du taux d’interet. Ces resultats sont robustes a des changements dans l’ensemble d’information utilise, ainsi qu’a des changements de specification du modele.

Standard business cycle models face difficulties generating (i) government spending multipliers exceeding unity and (ii) stabilizing effects of government size. Using a simple model with externality in labor supply, we show that a sufficient degree of complementarity between aggregate and private labor supplies is key to reproducing these stylized facts.

In this paper, we ask whether a small structural model with sticky prices and wages, embedding various modelling devices designed to increase the degree of strategic complementarity between price-setters, can fit postwar U.S. data. To answer this question, we resort to a two-step empirical evaluation of our model. In a first step, we estimate the model by minimizing the distance between theoretical autocovariances of key macroeconomic variables and their VAR-based empirical counterparts. In a second step, we resort to Watson's [Watson, M.W., 1993. Measures of fit for calibrated models. Journal of Political Economy 101, 1011–1041.] procedure [Measures of fit for calibrated models. Journal of Political Economy 101 (6), 1011.1041] to quantify the model's goodness-of-fit. Our main result is that the combination of sticky prices and sticky wages is central in order to obtain a good empirical fit. Our analysis also reveals that a model with only sticky wages does not perform well according to Watson's criterion [Watson, M.W., 1993. Measures of fit for calibrated models. Journal of Political Economy 101, 1011–1041.].

This article assesses monetary policy’s performances in the Euro zone in the face of supply shocks. We determine the responses of output, inflation, labor share and the nominal interest rate to a supply shock as identified through a structural var model. We then develop a dsge model with nominal rigidities subject to the optimal monetary policy. The model is estimated and tested on the basis of its ability to reproduce the responses drawn from the var model. Our results suggest that assuming optimal monetary policy allows for a satisfying fit to the data. Classification JEL : E31, E32, E52.

This paper examines the ability of Structural Vector Autoregressions (SVARs) to properly uncover the impulse response functions of hours after a technology improvement. Using a simple model in which hours do not react to technology shocks, we determine the main sources of distortions in an SVAR model which includes labor productivity growth and labor input in first difference.

We investigate identification issues in estimated Taylor rules. Embedding two alternative views about monetary policy, inertia versus serially correlated shocks, in a single equation, we show that using euro data, it is impossible to discriminate between these two competing representations.

Structural Vector Autoregressions with a differenced specification of hours (DSVAR) suggest that productivity shocks identified using long-run restrictions lead to a persistent and significant decline in hours worked. Economists have interpreted this evidence as showing that standard business cycle models in which a positive technology shock leads to a rise in hours are inconsistent with the data. In this paper we argue that such a conclusion is unwarranted because model's data and actual data are not treated symmetrically. To illustrate this problem, we estimate and test a flexible-price DSGE model with non-stationary hours using Indirect Inference on impulse responses of hours and output after technology and non-technology shocks. We find that, once augmented with a moderate amount of real frictions, the model can mimic well impulse responses obtained from a DSVAR on actual data. Using this model as a data generating process, we show that our estimation method is less subject to bias than a method that would directly compare theoretical responses with responses from the DSVAR.

Would the U.S. economy's dynamic response to permanent technology shocks have been different from the actual responses if monetary authorities' systematic response to these shocks had been optimal ? To answer this question, we characterize the dynamic effects of permanent technology shocks and the way in which U.S. monetary authorities reacted to these shocks over the sample 1955(1)-2002(4) using a structural VAR. A sticky price-sticky wage model is developed and estimated to reproduce these responses. We then formally compare these responses with the outcome of the optimal monetary policy.

We construct, and then estimate by maximum likelihood, a tractable dynamic stochastic general equilibrium model with incomplete insurance and heterogenous agents. The key feature of our framework is that cross-sectional heterogeneity remains finite dimensional. The solution to the model thus admits a state- space representation that can be used to recover the distribution of the model's parameters. Household heterogeneity expands the set of observables to cross- sectional moments available at the business-cycle frequency (in addition to theusual macro and monetary time series). Incomplete insurance gives rise to a precautionary motive for holding wealth that propagates aggregate shocks via (i) a stabilizing aggregate supply effect, working through the supply of capital, and (ii) a destabilizing aggregate demand effect coming from the feedback loop between unemployment risk and precautionary saving. Using the estimated model to measure the contribution of precautionary savings to the propagation of recent recessions, we find strong aggregate demand effects during the Great Recession and, to a lesser extent, during the 1990-1991 recession. In contrast, the supply effect at least offsets the demand effect during the 2001 recession.

This paper quantifies the welfare cost of monopolistic competition in a simple parametric class of endogenous growth models, embedding the neoclassical growth framework as a special case. We put particular emphasis on taking transitional dynamics into account. In doing so, we develop an original two-step numerical procedure to compute the value function. We find for conservative calibrations that the welfare cost of monopolistic competition can be anywhere between 0.4 and 1.2% of consumption, depending on whether labor is elastically or inelastically supplied.

This paper studies the dynamic properties of the labor market search model using three alternative sources of growth. Deterministic and stochastic exogenous growth specifications are compared with an endogenous growth specification, which is based on an external learning-by-doing mechanism. We apply Watson's (J. Political Economy 101 (6) (1993) 1011) test to assess the models’ performances over different frequency ranges. It is shown that the endogenous growth specification can bring the labor market search model into closer conformity with the data than its exogenous counterparts.

We consider the empirical consequences for generalized method of moments (GMM) estimates of the New Keynesian Phillips Curve (NKPC) of allowing for a more refined supply-side than conventionally postulated. Under our production structure, both labor share and the output gap explain inflation dynamics.

Les modeles de cycles reels (RBC) avec chocs technologiques permanents ne parviennent generalement pas a reproduire les faits stylises du cycle economique. Il en decoule qu’avec un a priori favorable a la presence d’une marche aleatoire dans les principales series macroeconomiques, nous devons rejeter la methodologie RBC. Dans ce papier, nous montrons que la prise en compte d’une forme particuliere de croissance endogene dans un modele RBC par ailleurs standard permet d’echapper a ce dilemme. En particulier, elle permet d’obtenir une marche aleatoire realiste dans le produit national, sans pour autant sacrifier a la reproduction des faits stylises du cycle.

Most RBC models need deterministic technical progress to account for the business cycle stylized facts. Does this mean that we are to dismiss the evidence in favor of a unit root in output when we have a prior in favor of RBC models? To answer this question, we explore the usefulness of introducing an endogenous source of growth in a standard RBC model. Using a formal measure of fit, we show that doing so permits us both to reproduce some key business cycle facts and to obtain a unit root in output.

This paper quantifies the welfare cost of monopolistic competition in a human-capital-based endogenous growth model with analytical solution. For conservative calibrations, it is shown that this welfare cost may be 2% of consumption, well beyond conventional estimates.

In response to the 2008-2009 crisis, faced with distressed financial intermediaries, the ECB embarked in long-term refinancing operations (LTROs). Using an estimated DSGE model with a frictional banking sector, we find that such liquidity injections can have large macroeconomic effects, with multipliers up to 0.5. However, the latter depend in an important way on how standard monetary policy is adjusted in conjunction with these non-standard measures. We find that the effects are larger when the separation principle is breached, that is to say when we force monetary policy not to react to the stimulative effects of LTROs.

This paper assesses the time series properties of rational expectations models with news shocks. We show that news shocks allows to substantially improve the dynamic behavior of such models in generating higher persistence. We also warn the use of SVAR models to uncover news shocks.

Les regles fiscales auto–financees conduisent souvent a une indetermination reelle de l’equilibre macroeconomique, laissant ainsi la place a des fluctuations de type «taches solaires». Dans le cadre d’une economie fermee, la TVA sociale echappe a cette propriete et reduit uniquement l’elasticite de l’offre de travail. Cependant, les effets quantitatifs sont modestes.This paper studies the local dynamic properties of a simple general equilibrium model with Social VAT. Strict balanced budget rules often lead to real indeterminacy of aggregate equilibrium, leaving room for «sunspots» fluctuations. In a closed-economy setup, social VAT escapes this property and only reduces the aggregate labor supply elasticity. However, the quantitative effects are weak.

This paper is a quantitative investigation into the characteristics of the Laffer curve in a neoclassical growth model with incomplete markets and heterogeneous, liquidity-constrained agents. We show that the shape of the Laffer curves related to taxes on labor, capital and consumption dramatically changes depending on which of transfers or government debt are adjusted to make the government budget constraint hold. When transfers are adjusted, the Laffer curve has the traditional shape. However, when debt is adjusted, the Laffer curve looks like a horizontal S, in which case fiscal revenues can be associated with up to three diferent levels of taxation. This finding occurs because the tax rates change non monotonically with public debt when markets are incomplete.

This paper examines issues related to the estimation of the government spending multiplier (GSM) in a DSGE context. We stress a source of bias in the GSM arising from the combination of endogenous government expenditures and Edgeworth complementarity between private consumption and government expenditures. Due to cross-equation restrictions, omitting the endogenous component of government policy at the estimation stage would lead an econometrician to underestimate the degree of Edgeworth complementarity and, consequently, the long-run GSM. An estimated version of our model with US postwar data shows that this bias matters quantitatively. The results are robust to a number of perturbations. (JEL E13, E23, E32, E62, H50)

This paper examines issues related to the estimation of the government spending multiplier (GSM) in a Dynamic Stochastic General Equilibrium context. We stress a potential source of bias in the GSM arising from the combination of Edgeworth complementarity/substitutability between private consumption and government expenditures and endogenous government expenditures. Due to cross-equation restrictions, omitting the endogenous component of government policy at the estimation stage would lead an econometrician to underestimate the degree of Edgeworth complementarity and, consequently, the long-run GSM. An estimated version of our model with US postwar data shows that this bias matters quantitatively. The results prove to be robust to a number of perturbations.

In this paper, we study issues related to the estimation of long–run government spending multiplier (GSM) in a Dynamic Stochastic General Equilibrium (DSGE) context. We stress a potential source of bias in the GSM arising from the combination of (i) Edgeworth complementarity between private consumption and government expenditures and (ii) countercyclical government expenditures. We find that the degree of Edgeworth complementarity and the cyclicality of policy interact through cross–equation restrictions, paving the way for potential biases. It turns out that the GSM increases with the degree of Edgeworth complementarity between private consumption and government expenditures. Thus, any bias in the degree of Edgeworth complementarity translates into a biased GSM.

The aim of this paper is to complement the MDE-SVAR approach when the weighting matrix is not optimal. In empirical studies, this choice is motivated by stochastic singularity or collinearity problems associated with the covariance matrix of Impulse Response Functions. Consequently, the asymptotic distribution cannot be used to test the economic model's fit. To circumvent this difficulty, we propose a simple simulation method to construct critical values for the test statistics. An empirical application with US data illustrates the proposed method.

This paper characterizes the short- and long-run effects of overtime de-taxation. A dynamic general equilibrium with overtime hours is first developed and calibrated to French data. A fiscal shock consisting of a complete de-taxation of overtime hours is then implemented in the model. Several fiscal scenarios are considered, depending on the pace of public debt and depending on whether consumption taxes or lump-sum taxes are adjusted. In each case, the welfare gains of the fiscal reform are computed. Overtime de-taxation is found to have very limited aggregate effects on output and the labor supply. It also generates a small welfare gain or even a welfare loss, depending on the on the fiscal scenario.

The present paper investigates the dynamic effects of disinflation shocks for a number of real macroeconomic variables in the euro area. Using structural VARs, we identify disinflation shocks as the only shocks that can exert a long-run effect on inflation as well as other nominal variables cointegrating with inflation. These shocks are found to generate large recessionary effects, notably when it comes to investment, and triggers a persistent rise in unemployment and in the real interest rate. The analysis is complemented by computing inefficiency measures on goods and labor markets. We show that, after a disinflation shock, inefficiencies in the labor market seem to prevail. These conclusions are robust to modifications of our baseline identification scheme.

The quantitative and dynamic consequence of a social VAT reform, i.e. a fiscal reform consisting in substituting VAT for social contributions, is assessed using two general equilibrium models. The first one is a Walrasian model with no other frictions than distortionary taxation of labor and capital incomes and consumption. The second one introduces in addition matching frictions in the labor market. Two alternative financing schemes are considered for the practical details of implementing the social VAT. In all cases, the fiscal reform turns out to generate a small, positive long-run effect on aggregate variables and yields a modest welfare gain. In the no-friction model, this welfare gain is substantially reduced when the reform is pre-announced six quarters prior to implementation. The effect of such a pre-announced reform are smaller when labor market frictions are taken into account.

The Euro area as a whole has experienced a marked downward trend in inflation over the past decades and, concomitantly, a protracted period of depressed activity. Can permanent and gradual shifts in monetary policy be held responsible for these dynamics? To answer this question, we embed serially correlated changes in the inflation target into a DSGE model with real and nominal frictions. The formal Bayesian estimation of the model suggests that gradual changes in the inflation target have played a major role in the Euro area business cycle. Following an inflation target shock, the real interest rate increases sharply and persistently, leading to a protracted decline in economic activity. Counter--factual exercises show that, had monetary policy implemented its new inflation objective at a faster rate, the Euro zone would have experienced more sustained growth than it actually did.

The euro area as a whole has experienced a marked downward trend in inflation over the past decades and, concomitantly, a protracted period of depressed activity. Can permanent and gradual shifts in monetary policy be held responsible for these dynamics? To answer this question, we embed serially correlated changes in the inflation target into a DSGE model with real and nominal frictions. The formal Bayesian estimation of the model suggests that gradual changes in the inflation target have played a major role in the euro area business cycle. Counter-factual exercises show that, had monetary policy implemented its new inflation objective at a faster rate, the euro zone would have experienced more sustained growth than it actually did.

This paper characterizes the short- and long-run effects of overtime de-taxation. A dynamic general equilibrium with overtime hours is first developed and calibrated to French data. A fiscal shock consisting of a complete de-taxation of overtime hours is then implemented in the model. Several fiscal scenarios are considered, depending on the pace of public debt and depending on whether consumption taxes or lump-sum taxes are adjusted. In each case, the welfare gains of the fiscal reform are computed. Overtime de-taxation is found to have very limited aggregate effects on output and the labor supply. It also generates a small welfare gain or even a welfare loss, depending on the on the fiscal scenario.

The authors use two general-equilibrium models to assess the quantitative and dynamic impact of “ social VAT”, i.e., a tax reform that would substitute a value-added tax for employers’ social contributions. The first model is a Walrasian model with no frictions other than distortionary taxes on labor income, capital income, and consumption. The second model adds labor-market matching frictions. We examine two scenarios for social-VAT implementation. In both scenarios, the tax reform generates a small, long-term effect on levels of aggregate variables and a modest welfare gain. In the no-friction model , the gain is substantially reduced when the reform is pre-announced six quarters prior to enactment. The announcement effect is milder in the model with labor-market frictions., L’impact quantitatif et dynamique de la TVA sociale, i.e. une réforme fiscale consistant à substituer de la TVA aux charges patronales, est évalué à l’aide de deux modèles d’équilibre général dynamique. Le premier est un modèle walrasien sans autres distorsions que des taxes sur les revenus du travail et du capital et sur la consommation. Le second introduit en plus des frictions d’appariement sur le marché du travail. Deux scenarii de mise en œuvre de la TVA sociale sont envisagés. Dans tous les cas, la réforme fiscale se traduit par un effet de long terme de faible ampleur sur le niveau des variables agrégées et une amélioration modeste du bien-être. Dans le modèle sans frictions, ces gains sont substantiellement réduits lorsque la réforme est pré-annoncée six trimestres avant sa mise en oeuvre effective. L’effet d’une préannonce est moindre dans le modèle avec frictions sur le marché du travail., Sahuc Jean-Guillaume, Matheron Julien, Fève Patrick. La TVA sociale : bonne ou mauvaise idée ?. In: Économie & prévision, n°193, 2010-2. pp. 1-19.

Estimation of the Implicit Inflation Target in the Euro Area. Euro area countries as a whole have experienced a marked downward trend over the 1980s. Over this period, the unemployment rate has increased and economic activity has been sluggish. Changes in the implicit inflation target, viewed as low frequency movements of inflation, might possibly explain these developments. To highlight this issue, the present study estimates the dynamics of the implicit inflation target in the euro zone over the period 1970-2004. Based on a small macroeconometric model, the implicit target, not known by the econometrician, is identified through a minimal set of theoretical restrictions : (i) the inflation target is a non stationary process, (ii) inflation is a monetary phenomenon in the long-run, and (iii) changes in the implicit target have no long-run effects whatsoever on real variables. The model is estimated so as to match output growth, changes in inflation and the ex post real interest rate. Our main results are : (i) inflation target shocks account for the bulk of nominal fluctuations ; (ii) due to monetary policy inertia and nominal stickiness, changes in the target generate large swings in the real interest rate translating into substantial short-run effects on real variables ; (ii) in spite of this inflation target shocks moderately impact on output dynamics., Le taux d'inflation dans l’ensemble des pays qui constituent la zone euro a fortement diminué au cours des années 1980. Durant cette période, le taux de chômage a significativement augmenté et l'activité économique a notablement ralenti dans la zone. Les variations de la cible implicite d’inflation des banques centrales, assimilées aux mouvements de basse fréquence de l’inflation, sont potentiellement un facteur d’explication de ces évolutions. Afin d’éclairer cette question, cette étude propose d’estimer les évolutions dynamiques de la cible implicite d’inflation dans la zone euro au cours de la période 1970(1)-2004(4) à l’aide d’une petite maquette macroéconométrique. Cette cible implicite d’inflation, inobservée de l’économiste, est identifiée à l’aide d’un ensemble minimal de restrictions théoriques : (i) la cible implicite d’inflation suit un processus non stationnaire (ii) l’inflation est un phénomène exclusivement monétaire à long terme et (iii) les variations de la cible implicite d’inflation n’ont pas d’effet réel à long terme. Le modèle est estimé de façon à reproduire le taux de croissance du PIB, la variation de l’inflation et le taux d’intérêt réel ex post. Les résultats principaux qui se dégagent de l’analyse empirique sont les suivants : (i) les chocs sur la cible implicite d’inflation expliquent l’essentiel des fluctuations des variables nominales, même à court terme ; (ii) leurs effets réels à court terme transitent par l’inertie du taux d’intérêt nominal et la forte hausse du taux d’intérêt réel qui en découle ; (iii) en dépit de cela, ces chocs n’affectent que modestement la dynamique du PIB., Sahuc Jean-Guillaume, Matheron Julien, Fève Patrick. Une estimation de la cible implicite d’inflation dans la zone euro. In: Revue française d'économie, volume 24, n°2, 2009. pp. 39-56.

The aim of this paper is to complement the minimum distance estimation–structural vector autoregression approach when the weighting matrix is not optimal. In empirical studies, this choice is motivated by stochastic singularity or collinearity problems associated with the covariance matrix of impulse response functions. Consequently, the asymptotic distribution cannot be used to test the economic model's fit. To circumvent this difficulty, we propose a simple simulation method to construct critical values for the test statistics. An empirical application with US data illustrates the proposed method.