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This paper explores the successes and failures of the new open economy macroeconomics more critically by addressing the performance of the model at all frequencies along the line of Watson's [Watson, M.W., 1993. Measures of Fit for Calibrated Models, Journal of Political Economy 101, 1011-1041] measures of fit. This paper shows that the NOEM model with either PCP or PTM is not successful in generating the spectral density of the selected variables calculated from the data. In particular, the model cannot generate mass spectra of the exchange rates at low frequencies as in the data. It shows that the NOEM model with either separable preference or incomplete asset market cannot generate the typical hump-shaped spectra of exchange rates.

In recent years, a proliferation of new monetary models that incorporate imperfect competition and nominal rigidities into a dynamic stochastic general equilibrium have surfaced in macroeconomics.1 This kind of research program is closely linked to the recent theoretical development of international finance, which has become known as the new open economy macroeconomics. New open economy macroeconomics, embedding imperfect competition and nominal rigidities in a dynamic general equilibrium open economy attempts to explore empirical issues, such as the excessive exchange rate movements and liquidity effects which had been unaccounted for previously. In the theoretical development of international finance, Obstfeld and Rogoff (2000) argue that the assumption of sticky prices in the producer's currency is important for matching the behavior of the terms of trade. Their Redux model assumes no international market segmentation, favoring the producer–currency–pricing (hereafter PCP) approach in the exchange rate fluctuations. However, there is a large body of evidence against the law of one price. In particular, Engel (1999) and Chari, Kehoe, and McGrattan (2000) hereafter Chari et al. (2000)) have documented that the international deviations in tradable prices are responsible for the violation of the law of one price. In line with this empirical evidence, many authors, presuming that international markets for manufacturing goods are sufficiently segmented, have introduced the so-called ‘pricing-to-market (hereafter PTM)’ approach into the new open economy macroeconomic (hereafter NOEM) model. PTM with local-currency sticky prices breaks the link between home and foreign price levels and allows the real exchange rates to fluctuate.2 In particular, Betts and Devereux, 1999 and Betts and Devereux, 2000 set up a full-fledged PTM model and show that the model outperforms the PCP model in tracking the real exchange rate movements. Notwithstanding these theoretical developments in international finance, relatively little empirical or quantitative studies have been done. Some studies have attempted to evaluate the quantitative importance of the mechanisms emphasized in the NOEM model either via calibration exercises or VAR econometric models. In important quantitative applications of the NOEM model in dynamic general equilibrium settings, Betts and Devereux (1999), Chari et al. (2000), and Kollman (1997) show the potential of the model to replicate international business cycle regularities including the variability of real and nominal exchange rates. In calibration exercises, Chari et al. (2000), and Kollman (1997) have evaluated the NOEM model with PTM by comparing the unconditional moments generated by the model with the unconditional moments observed in the data. In the econometric investigation, Betts and Devereux (1999) have shown that the NOEM model with PTM performs well in matching the stylized facts of the international monetary transmission mechanism as documented by VAR results. In frequency domain, King and Watson (1996), Stock and Watson (1999), and Watson (1993) document interesting stylized facts over business cycles. The selected real macroeconomic variables have common, hump-shaped growth rate spectra. That is, the spectra are relatively low at low frequencies, rise at middle frequencies, and then decline at high frequencies. However, no one in international finance has explored whether the current NOEM models can generate the dynamics of the selected variables at low and high frequencies in addition to business cycle frequencies. Because the height of the spectral density of the selected variable at each frequency indicates the extent of that frequency's contribution to the variance of the corresponding variable, the variance of the corresponding variable occurring between any two frequencies is given by the areas under the spectrum between those two frequencies. Therefore, one cannot argue that the NOEM model performs well in matching the volatile exchange rate movements by comparing only the unconditional moments generated by the model with the unconditional moments observed in the data in a specific frequency band. Chari et al. (2000) and Kollman (1997) are no exception. Their quantitative evaluation of the NOEM model is insufficient in obtaining an overall fit of the model because they evaluate the performance of the model only at business cycle frequencies. Even if the spectral density of exchange rates constructed from the model has the inverse shape of the spectral density calculated from the data, the variance of exchange rates generated from the model can be equal to the variance of the exchange rates in the data because the variance is the area under the spectrum between 0.03 = 1/32 and 0.16 = 1/6 cycles per period. Therefore, to address more precisely and critically the NOEM model's performance, it is necessary to use more general measures of fit such as the spectral density and the spectrum of the error required to reconcile the model and the data as in Watson (1993). In this respect, the recent studies by Ellison and Scott (2000), and Jung (2004) deserve attention. Ellison and Scott (2000) examine the performance of a Calvo-type sticky price model with an exogenous monetary policy at both high frequencies and business cycle frequencies. Jung (2004) goes one step further to explore the role of external habit formation in the Calvo-type and Taylor-type sticky price models with an endogenous monetary policy. Both point out that the sticky price model fails because it generates insufficient output fluctuations at business cycle frequencies as well as excessive output volatility at high frequencies. In addition, they argue that it is desirable and necessary to address more critically the quantitative performance of the model with more general measures of fit if one wishes to gain more fruitful intuitions about the model. This paper critically examines the successes and failures of the NOEM model by addressing the performance of the model at all frequencies along the line of Watson (1993)'s measure of fit. For this purpose, I first set up a benchmark quantitative NOEM model with complete asset markets as in Chari et al. (2000). Then I evaluate the performance of the model with either PCP or PTM in terms of second moments over the business cycle frequencies as in Betts and Devereux (1999), and Chari et al. (2000). After that, I extend the evaluation to the overall fit of the model by comparing the spectral densities of the selected variables calculated from the model with those of the data. To address quantitative evaluation of the model more critically, I also discuss the performance of the model using Watson (1993)'s RMSAE. Finally, I perform sensitivity analysis with different assumptions about preference, asset market structure, shocks, and market frictions following Chari et al. (2000), Christiano, Eichenbaum and Evans (2003 hereafter CEE (2003)), and Smets and Wouters (2002) to obtain more robust results. The main findings of this paper can be summarized as follows. First, the NOEM model with either PCP or PTM is not successful in generating the hump-shaped spectral density for the selected variables calculated from the data. Watson (1993)'s RMSAE for output and price is greater than one, showing the poor performance of the model. The most dramatic failure of the model is the business cycle frequency fluctuation in exchange rates. The NOEM model with either PCP or PTM cannot explain the hump-shaped spectral density of exchange rates. Second, the model generates far too much volatility of the selected variables at high frequencies compared to the data. This fact mirrors Ellison and Scott (2000)'s findings in the closed economy model. Third, the introduction of separable preference into the model is not successful in generating the typical hump-shaped spectra of exchange rates whether one assumes either incomplete asset market or other shocks such as uncovered interest parity shocks and preference shocks. Finally, the extended NOEM model with more diverse market frictions such as habit persistence, capital adjustment cost in investment changes, and indexation in prices and wages as in CEE (2003) and Smets and Wouters (2002) is successful in generating the typical hump-shaped spectral density of the some selected variables including consumption. However, the model still fails in replicating the hump-shaped spectral density of exchange rates. Even if the uncovered interest parity condition holds, the monetary policy shock cannot lead to a hump-shaped response of exchange rate as long as the elements that disconnect the tight relation between interest differentials and expected exchange rate depreciation do not dominate the effect on interest rate differentials on the expected exchange rate depreciation. This paper is composed as follows. Section 2 discusses the features of the data, focusing on the fluctuations of exchange rates. Section 3 specifies the benchmark NOEM model with PCP as well as the NOEM model with PTM, and discusses the properties of the equilibrium. Section 4 discusses regarding the quantitative implications of the model. Section 5 performs a sensitivity analysis with the extended NOEM model and Section 6 contains concluding remarks.

This paper investigates whether the NOEM model with either PCP or PTM can generate the typical hump-shaped spectra of exchange rate changes as in the data. The paper shows that the NOEM model is not successful in generating the spectral density of the selected variables calculated from the sticky price model, though NOEM model with separable preferences does generate volatile exchange rate movements as in the data. Specifically, the model cannot generate mass spectra of exchange rates at low and business cycle frequencies as in the data. The NOEM model displays a flat spectrum for exchange rates and output without a noticeable business cycle peak, while the spectral density of output and nominal exchange rates of the data displays a peak at business cycle frequencies. These are the dramatic failures of the NOEM model. The NOEM model either with other shocks or an incomplete asset market fails to produce the typical hump-shaped spectral density of output and exchange rates at low and business cycle frequencies. The extended NOEM model with the market frictions suggested by CEE (2003) and Smets and Wouters (2002) generates the typical hump-shaped spectral density of output, but it still fails in generating the hump-shaped spectral density of exchange rates. In future research, it would be desirable to explore elements that can improve the performance of the model at low and business cycle frequencies. Essentially, it would be necessary to find elements that endogenously disconnect the close relation between the interest rate differentials and the expected exchange rate depreciation, i.e. the uncovered interest parity.