Skip to main content

Advertisement

SpringerLink
Log in

Nowcasting GDP Growth for Small Open Economies with a Mixed-Frequency Structural Model

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

This paper proposes a mixed-frequency small open economy structural model, in which the structure comes from a New Keynesian dynamic stochastic general equilibrium (DSGE) model. An aggregation rule is proposed to link the latent aggregator to the observed quarterly output growth via aggregation. The resulting state-space model is estimated by the Kalman filter and the estimated current aggregator is used to nowcast the quarterly GDP growth. Taiwanese data from January 1998 to December 2015 are used to illustrate how to implement the technique. The DSGE-based mixed-frequency model outperforms the reduced-form mixed-frequency model and the MIDAS model on nowcasting Taiwan’s quarterly GDP growth.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. Some other recent studies with the mixed-frequency strategy include the fixed-frequency VAR model in Schorfheide and Song (2015) and Rondeau (2012). The latter combines quarterly series with annual series in an effort to estimate a DSGE model for emerging economies.

  2. The constant term in (1) is ignored because we demean all the variables in the empirical work.

  3. The coefficient \(\omega \) is obtained under the assumption that the elasticities of substitution between domestic and foreign goods and between goods produced in different foreign countries are both equal to one, i.e., the functions have a Cobb–Douglas form.

  4. In the model, technology is not separately specified and is therefore imbedded in the real output.

  5. In this DSGE model, the firms’ staggered price-setting scheme is adopted from Calvo (1983). That is, each intermediate firm faces a constant probability (\(1-\phi \)) to re-optimize its price within a period. The index of openness, \(0 \le \alpha \le 1\), is the ratio of domestic consumption allocated to imported goods. In equilibrium, the domestic CPI is a CES function of the price level of domestic goods and the price level of imported goods.

  6. A similar problem was previously diagnosed in Lubik and Schorfheide (2007) when they estimated Gali and Monacelli’s (2005) model based on data for Australia, Canada, New Zealand and the U.K.

  7. The most popular solution methods are Blanchard and Kahn (1980), Klein (2000), Sims (2002), and Uhlig (1999).

  8. In the state-space representation, (1) is rewritten as: \(y_t-\bar{y}_t=E_t(y_{t+1}-\bar{y}_{t+1})-\frac{1}{\sigma }[R_t-E_t \pi _{t+1}] -\left[ \frac{\alpha \sigma _\alpha (\omega -1)}{\sigma _\alpha +\varphi }\right] \;E_t\Delta y^*_{t+1}\).

  9. The monthly observations in this paper are year-on-year percentage changes. As an alternative, we have estimated models with these observables constructed as month-on-month percentage changes. However, these series contain high degrees of noise and cause the maximum likelihood estimates to be poor. In the paper, the real GDP growth is constructed as the quarter-on-quarter growth rate to avoid further enlarging the dimension of the state-space model. If instead year-on-year real output growth is used, we need to include additional lagged variables in the state vector.

  10. Estimates in Teo (2009) are obtained using the Bayesian method for the sample period of 1992Q1–2004Q4.

  11. With \(\hat{\phi }=0.945\), the estimated pricing adjustment behavior is highly sluggish for it implies that on average each firm waits 18 months before resetting prices. As discussed in Kim (2010), the estimates of price stickiness could be very sensitive to the estimation strategies and model specifications. The range in the estimates of the price stickiness duration in some U.S. studies is wide too, being as short as 8 months and as long as 24 months.

  12. In Taiwan, no real-time data on quarterly national accounts are available. Given that policy evaluation is not the main purpose of the current paper, our second-best choice is to use the pseudo real-time data. A number of empirical studies have conducted model comparisons based on the pseudo real-time data; see, for example, Schumacher and Breitung (2008), Giannone et al. (2008), and Foroni and Marcellino (2014a).

  13. The mixed-frequency model is a flexible model that can incorporate any timely information that proves to be useful for nowcasting, such as survey data from experts or a monthly industrial production index. Because the current paper focuses on a structural model, it only includes variables that are considered in the DSGE framework. For comparison purposes, it is only fair if we use the same set of observables as in other models.

  14. The Augmented Dickey Fuller (ADF) test is applied to the dependent variable (GDP growth rate) and the null of a unit root is rejected at the conventional significance level. For the explanatory variables, the ADF tests reject the null of a unit root for the domestic and foreign inflation rates, the changes in the terms-of-trade, and the changes in the exchange rate. The test shows that the skip-sampled monthly interest rate series contains a unit root. The ADF test results are available from the authors upon request.

References

  • Aadland, D., & Huang, K. X. D. (2004). Consistent high-frequency calibration. Journal of Economic Dynamics and Control, 28, 2277–2295.

    Article  Google Scholar 

  • Aruoba, B., Diebold, F., & Scotti, C. (2009). Real-time measurement of business conditions. Journal of Business Economics and Statistics, 27(4), 417–427.

    Article  Google Scholar 

  • Bernanke, B. S., Gertler, M., & Watson, M. W. (1997). Systematic monetary policy and the effects of oil price shocks. Brookings Papers on Economic Activity, 1, 91–157.

    Article  Google Scholar 

  • Blanchard, O., & Kahn, C. (1980). The solution of difference equations under rational expectations. Econometrica, 48, 1305–1311.

    Article  Google Scholar 

  • Boivin, J., & Giannoni, M. (2006). DSGE models in a data-rich environment. NBER Working Paper.

  • Calvo, G. (1983). Staggered prices in a utility maximizing framework. Journal of Monetary Economics, 12, 383–398.

    Article  Google Scholar 

  • Christiano, L. J., & Eichenbaum, M. (1987). Temporal aggregation and structural inference in macroeconomics. Carnegie-Rochester Conference Series on Public Policy, 26, 64–130.

    Article  Google Scholar 

  • Clarida, R., Gali, J., & Gertler, M. (2000). Monetary policy rules and macroeconomic stability: Evidence and some theory. Quarterly Journal of Economics, 115(1), 147–180.

    Article  Google Scholar 

  • Clements, M. P., & Galvao, A. B. (2008). Macroeconomic forecasting with mixed-frequency data: Forecasting US output growth. Journal of Business and Economic Statistics, 26, 546–554.

    Article  Google Scholar 

  • Durbin, J., & Koopman, S. J. (2001). Time series analysis by state space methods. Oxford: Oxford University Press.

    Google Scholar 

  • Edge, R., Kiley, M., & Laforte, J. (2008). A comparison of forecast performance between federal reserve staff forecasts, simple reduced-form models, and a DSGE model. Federal Reserve Board of Governors: Manuscript.

  • Foroni, C., & Marcellino, M. (2014a). A comparison of mixed frequency approaches for nowcasting Euro area macroeconomic aggregates. International Journal of Forecasting, 30, 554–568.

    Article  Google Scholar 

  • Foroni, C., & Marcellino, M. (2014b). Mixed-frequency structural models: Identification, estimation, and policy analysis. Journal of Applied Econometrics, 29, 1118–1144.

    Article  Google Scholar 

  • Foroni, C., Marcellino, M., & Schumacher, C. (2015). Unrestricted mixed data sampling (MIDAS): MIDAS regressions with unrestricted lag polynomials. Journal of the Royal Statistical Society, Series A (Statistics in Society), 178(1), 57–82.

    Article  Google Scholar 

  • Gali, J., & Monacelli, T. (2005). Monetary policy and exchange rate volatility in a small open economy. Review of Economic Studies, 72, 707–734.

    Article  Google Scholar 

  • Ghysels, E., Santa-Clara, P., & Valkanov, R. (2004). The MIDAS touch: Mixed data sampling regression models. Chapel Hill, N.C.: Mimeo.

    Google Scholar 

  • Ghysels, E., Sinko, A., & Valkanov, R. (2006). MIDAS regressions: Further results and new directions. Econometric Reviews, 26(1), 53–90.

    Article  Google Scholar 

  • Giannone, D., Monti, F., & Reichlin, L. (2009). Incorporating conjunctural analysis in structural models. In V. Wieland (Ed.), The science and practice of monetary policy today (pp. 41–57). Berlin: Springer.

  • Giannone, D., Reichlin, L., & Small, D. (2008). Nowcasting: The real-time informational content of macroeconomic data. Journal of Monetary Economics, 55, 665–674.

    Article  Google Scholar 

  • Kim, T. B. (2010). Temporal aggregation bias and mixed frequency estimation of New Keynesian model. Mimeo: Duke University.

    Google Scholar 

  • Klein, P. (2000). Using the generalized Schur form to solve a multivariate linear rational expectations model. Journal of Economic Dynamics and Control, 24, 1405–1423.

    Article  Google Scholar 

  • Liu, H., & Hall, S. G. (2001). Creating high-frequency national accounts with state-space modelling: A Monte Carlo experiment. Journal of Forecasting, 20, 441–449.

    Article  Google Scholar 

  • Lubik, T., & Schorfheide, F. (2007). Do central banks respond to exchange rate movements? A structural investigation. Journal of Monetary Economics, 54, 1069–1087.

    Article  Google Scholar 

  • Mariano, R., & Murasawa, Y. (2010). A coincident index, common factors, and monthly real GDP. Oxford Bulletin of Economics and Statistics, 72, 27–46.

    Article  Google Scholar 

  • Mariano, R. S., & Murasawa, Y. (2003). A new coincident index of business cycles based on monthly and quarterly series. Journal of Applied Econometrics, 18(4), 427–443.

    Article  Google Scholar 

  • Rondeau, S. (2012). Sources of fluctuations in emerging markets: DSGE estimation with mixed frequency data. Ph.D. thesis, Columbia University.

  • Rubaszek, M., & Skrzypczynski, P. (2008). On the forecasting performance of a small-scale DSGE model. International Journal of Forecasting, 24, 498–512.

    Article  Google Scholar 

  • Schorfheide, F., Sill, K., & Kryshko, M. (2010). DSGE model-based forecasting of non-modelled variables. International Journal of Forecasting, 26, 348–373.

    Article  Google Scholar 

  • Schorfheide, F., & Song, D. (2015). Real-time forecasting with a mixed frequency VAR. Journal of Business and Economic Statistics, 33, 366–380.

    Article  Google Scholar 

  • Schumacher, C., & Breitung, J. (2008). Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data. International Journal of Forecasting, 24(3), 386–398.

    Article  Google Scholar 

  • Sims, C. A. (2002). Solving linear rational expectations models. Computational Economics, 20, 1–20.

    Article  Google Scholar 

  • Stock, J. H., & Watson, M. W. (1989). New indexes of coincident and leading economic indicators. NBER Macroeconomics Annual, 4, 351–409.

    Article  Google Scholar 

  • Stock, J. H., & Watson, M. W. (1991). A probability model of the coincident economic indicators. In K. Lahiri & G. H. Moore (Eds.), Leading economic indicators (pp. 63–89). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Teo, W. L. (2009). Estimated dynamic stochastic general equilibrium model of the Taiwanese economy. Pacific Economic Review, 14, 194–231.

    Article  Google Scholar 

  • Uhlig, H. (1999). A toolkit for analyzing nonlinear dynamic stochastic models easily. In R. Marimon & A. Scott (Eds.), Computational methods for the study of dynamic economies (pp. 114–142). Oxford: Oxford University Press.

    Google Scholar 

Download references

Acknowledgements

The authors are grateful for helpful comments from Kenneth West, Barbara Rossi, Frédérique Bec, Yu-Ning Huang, Yi-Ting Chen, and participants at the 2016 International Symposium in Computational Economics and Finance (ISCEF) in Paris.

Author information

Authors and Affiliations

  1. Department of Economics, National Central University, Taoyuan, 32001, Taiwan, ROC

    Ruey Yau

  2. Department of Economics, Western Michigan University, Kalamazoo, MI, 49008, USA

    C. James Hueng

  3. School of Economics, Zhongnan University of Economics and Law, Hubei, 430073, China

    C. James Hueng

Authors
  1. Ruey Yau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. James Hueng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ruey Yau.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yau, R., Hueng, C.J. Nowcasting GDP Growth for Small Open Economies with a Mixed-Frequency Structural Model. Comput Econ 54, 177–198 (2019). https://doi.org/10.1007/s10614-017-9697-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-017-9697-1

Keywords

JEL Classification

Search

Navigation