Abstract
In this article, we present a new approach based on dynamic factor models (DFMs) to perform accurate nowcasts for the percentage annual variation of the Mexican Global Economic Activity Indicator (IGAE), the commonly used variable as an approximation of monthly GDP. The procedure exploits the contemporaneous relationship of the timely traditional macroeconomic time series and nontraditional variables as Google Trends with respect to the IGAE. We evaluate the performance of the approach in a pseudo real-time framework, which includes the pandemic of COVID-19, and conclude that the procedure obtains accurate estimates, for one and two-steps ahead, above all, given the use of Google Trends. Another contribution for economic nowcasting is that the approach allows to disentangle the key variables in the DFM by estimating the confidence interval for the factor loadings, hence allows to evaluate the statistical significance of the variables in the DFM. This approach is used in official statistics to obtain preliminary and accurate estimates for IGAE up to 40 days before the official data release.
Keywords
References
1.
Ahn, S. and A. Horenstein, 2013. “Eigenvalue ratio test for the number of factors.” Econometrica 81(3): 1203–1227. DOI: https://doi.org/10.3982/ECTA8968.
2.
Ali, U., Herbst, C.M., and C.A. Makridis. 2021. “The impact of COVID-19 on the US child care market: Evidence from stay-at-home orders.” Economics of Education Review 82: 102094. DOI: https://doi.org/10.1016/j.econedurev.2021.102094.
3.
Antolin-Diaz, J., Drechsel, T., and I. Petrella. 2017. “Tracking the slowdown in long-run GDP growth.” Review of Economics and Statistics 99(2): 343–356. DOI: https://doi.org/10.1162/REST_a_00646.
4.
Aprigliano, V., and L. Bencivelli. 2013. Ita-coin: a new coincident indicator for the Italian economy. Banca D’Italia. Working papers: 935: DOI: https://dx.doi.org/10.2139/ssrn.2405416v.
5.
Bai, J. 2003. “Inferential theory for factor models of large dimensions.” Econometrica 71(1): 135–171. DOI: https://doi.org/10.1111/1468-0262.00392.
6.
Bai, J. 2004. “Estimating cross-section common stochastic trends in nonstationary panel data.” Journal of Econometrics 122(1): 137–183. DOI: https://doi.org/10.1016/j.jeconom.2003.10.022.
7.
Bai, J., and S. Ng. 2002. “Determining the number of factors in approximate factor models.” Econometrica 70(1): 191–221. DOI: https://doi.org/10.1111/1468-0262.00273.
8.
Bai, J., and S. Ng. 2004. “A PANIC attack on unit roots and cointegration.” Econometrica 72(4): 1127–1177. DOI: https://doi.org/10.1111/j.1468-0262.2004.00528.x.
9.
Bai, J., and S. Ng. 2007. “Determining the number of primitive shocks in factor models.” Journal of Business & Economic Statistics 25(1): 52–60. DOI: https://doi.org/10.1198/073500106000000413.
10.
Bai, J., and S. Ng. 2013. “Principal components estimation and identification of static factors.” Journal of Econometrics 176(1): 18–29. DOI: https://doi.org/10.1016Zj.jeconom.2013.03.007.
11.
Baríbura, M., Giannone, D., and L. Reichlin. 2011. “Nowcasting”, In Oxford Handbook of Economic Forecasting edited by Michael P. Clements and David F. Hendry: 193–224. DOI: https://doi.org/10.1093/oxfordhb/9780195398649.013.0008.
12.
Barigozzi, M., Lippi, M., and M. Luciani. 2015. Dynamic factor models, cointegration, and error correction mechanisms . arXiv preprint arXiv:1510.02399. DOI: https://doi.org/10.48550/arXiv.1510.02399.
13.
Barigozzi, M. Lippi, and M. Luciani. 2016. Non-Stationary Dynamic Factor Models for Large Datasets. SSRN 2741739. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.2741739.
14.
Benchimol, J., S. Kazinnik, and Y. Saadon. 2021. “Federal Reserve communication and the COVID-19 pandemic.” Covid Economics 71: 218. DOI: https://cepr.org/content/-covid-economics-vetted-and-real-time-papers-0 (accessed January 2022).
15.
Boivin, J., and S. Ng. 2006. “Are more data always better for factor analysis?” Journal of Econometrics 132(1): 169–194. DOI: https://doi.org/10.1016/j.jeconom.2005.01.027.
16.
Buono, D., Mazzi, G., M. Marcellino, and G. Kapetanios. 2017. “Big data types for macroeconomic nowcasting.” Eurostat Review on National Accounts and Macroeconomic Indicators 1(2017): 93–145. Available at: https://ec.europa.eu/eurostat/-cros/content/big-data-types-macroeconomic-nowcasting-dario-buono-gian-luigi-mazzi-george-kapetanios_en (accessed October 2021).
17.
Caperna, G., Colagrossi, M., A. Geraci, and G. Mazzarella. 2022. “A Babel of web-searches: Googling unemployment during the pandemic.” Labour Economics (74). DOI: https://doi.org/10.1016/j.labeco.2021.102097.
18.
Caruso, A. 2018. “Nowcasting with the help of foreign indicators: The case of Mexico.” Economic Modelling 69: 160–168. DOI: https://doi.org/10.1016Zj.econmod.2017.09.017.
19.
Choi, H. and Varian. 2012. “Predicting the present with Google Trends.” Economic record 88: 2–9. DOI: https://doi.org/10.1111/j.1475-4932.2012.00809.x.
20.
Choi, I. 2017. “Efficient estimation of nonstationary factor models.” Journal of Statistical Planning and Inference 183: 18–43. DOI: https://doi.org/10.1016/j.jspi.2016.10.003.
21.
Corona, F., G. González-Farías, and P. Orraca. 2017a. “A dynamic factor model for the Mexican economy: Are common trends useful when predicting economic activity?” Latin American Economic Review 27(1). DOI: https://doi.org/10.1007/s40503-017-0044-7.
22.
Corona, F., P. Poncela, and E. Ruiz. 2017b. “Determining the number of factors after stationary univariate transformations.” Empirical Economics 53(1): 351–372. DOI: https://doi.org/10.1007/s00181-016-1158-5.
23.
Corona, F., P. Poncela, and E. Ruiz. 2020. “Estimating Non-stationary Common Factors: Implications for Risk Sharing.” Computational Economics 55(1): 37–60. DOI: https://doi.org/10.1007/s10614-018-9875-9.
24.
De Valk, S., D. de Mattos, and P. Ferreira. 2019. “Nowcasting: An R Package for Predicting Economic Variables Using Dynamic Factor Models.” The R Journal 11(1). DOI: https://doi.org/10.32614/RJ-2019-020.
25.
Delajara, M., F.H. Alvarez, and A.R. Tirado. 2016. “Nowcasting Mexico’s short-term GDP growth in real-time: A factor model versus professional forecasters.” Economia 17(1): 167–182. DOI: https://muse.jhu.edu/article/634035.
26.
Diebold, F. and R. Mariano, 1995. “Comparing Predictive Accuracy.” Journal of Business & Economic Statistics 13(3): 253–263. DOI: https://doi.org/10.1080/07350015.1995.10524599.
27.
Doz, C., D. Giannone, and L. Reichlin. 2011. “A two-step estimator for large approximate dynamic factor models based on Kalman filtering.” Journal of Econometrics 164(1): 188–205. DOI: https://doi.org/10.1016/j.jeconom.2011.02.012.
28.
Doz, C., D. Giannone, and L. Reichlin. 2012. “A quasi maximum likelihood approach for large, approximate dynamic factor models” The Review of Economics and Statistics 94(4): 1014–1024. DOI: https://doi.org/10.1162/REST_a_00225.
29.
Forni, M., M. Hallin, M., Lippi, and L. Reichlin. 2000. “The generalized dynamic-factor model: identification and estimation.” Review of Economics and Statistics 82(4): 540–554. DOI: https://doi.org/10.1162/003465300559037.
30.
Galbraith, J. and G. Tkacz. 2018. “Nowcasting with payments system data.” International Journal of Forecasting 34(2): 366–376. DOI: https://doi.org/10.1016/j.ijforecast.2016.10.002.
31.
Gálvez-Soriano, O. 2020. “Nowcasting Mexico’s quarterly GDP using factor models and bridge equations.” Estudios Economicos 35(2): 213 –265. DOI: https://doi.org/10.24201/ee.v35i2.402.
32.
Gamboa, J.C.B. 2017. Deep learning for time-series analysis . arXiv:1701.01887. DOI: https://doi.org/10.48550/arXiv.1701.01887.
33.
Giannone, D., M. Lenza, and G.E. Primiceri. 2021. Economic predictions with big data: The illusion of sparsity . ECB Working Paper: 2021/2542, SSRN. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.3835164.
34.
Giannone, D., L. Reichlin., and D. Small. 2008. “Nowcasting: The real-time informational content of macroeconomic data”. Journal of Monetary Economics 55(4): 665–676. DOI: https://doi.org/10.1016/j.jmoneco.2008.05.010.
35.
Goldsmith-Pinkham, P. and A. Sojourner. 2020. “Predicting Initial Unemployment Insurance Claims Using Google Trends.” Technical report, Working Paper. DOI: https://paulgp.github.io/GoogleTrendsUINowcast/google_trends_UI.html.
36.
González-Astudillo, M. and D. Baquero. 2019. “A nowcasting model for Ecuador: Implementing a time-varying mean output growth.” Economic Modelling 82: 250–263. DOI: https://doi.org/10.1016/j.econmod.2019.01.010.
37.
Graff, M., D. Moctezuma, S. Miranda-Jiménez, S., E.S. Tellez. 2022. “A Python library for exploratory data analysis and knowledge discovery on Twitter data.” Computers & Geosciences, 159: 105012 . DOI: https://doi.org/10.1016Zj.cageo.2021.105012.
38.
Guerrero, V.M., A.C. García, A. C., and E. Sainz. 2013. “Rapid Estimates of Mexico’s Quarterly GDP.” Journal of Official Statistics 29(3): 397–423. DOI: https://doi.org/10.2478/jos-2013-0033.
39.
Harvey, A., and G. Phillips. 1979. “Maximum Likelihood Estimation of Regression Models With Autoregressive-Moving Averages Disturbances.” Biometrika 152: 49–58. DOI: https://doi.org/10.1093/biomet/66.1.49.
40.
Hewamalage, H., C. Bergmeir, and K. Bandara. 2021. “Recurrent Neural Networks for Time Series Forecasting: Current status and future directions.” International Journal of Forecasting : 37(1): 388–427. DOI: https://doi.org/10.1016/j.ijforecast.2020.06.008.
41.
Huang, G.B., Q.Y. Zhu, and C.K. Siew. 2006. “Extreme learning machine: Theory and applications.” Neurocomputing 70(1–3): 489–501. DOI: https://doi.org/10.1016/j.neucom.2005.12.126.
42.
INEGI. a. Indicador Global de la Actividad Económica. Available at: https://www.inegi.org.mx/temas/igae/
43.
INEGI. b. Estimación Oportuna del PIB Trimestral. Available at: https://www.inegi.org.mx/temas/pibo/.
44.
INEGI. c. Indicador Oportuno de la Actividad Económica. https://www.inegi.org.mx/investigacion/ioae/
45.
INEGI. d. Indicador Mensual Oportuno de la Actividad Manufacturera. Available at: https://www.inegi.org.mx/investigacion/imoam/
46.
Kourentzes, N., Barrow, D.K., and S.F. Crone. 2014. “Neural network ensemble operators for time series forecasting.” Expert Systems with Applications 41(9): 4235–4244. DOI: https://doi.org/10.1016/j.eswa.2013.12.011.
47.
León, C., and F. Ortega. 2018. “Nowcasting economic activity with electronic payments data: A predictive modeling approach.” Revista de economia del Rosario 21(2): 381–407. DOI: https://dialnet.unirioja.es/servlet/articulo?codigo=7411408.
48.
Onatski, A. 2010. “Determining the number of factors from empirical distribution of eigenvalues.” The Review of Economics and Statistics : 92(4): 1004–1016. DOI: https://doi.org/10.1162/REST_a_00043.
49.
Ord, J., R. Fildes, and N. Kourentzes. 2017. Principles of Business Forecasting-2nd Ed. Wessex, Incorporated.
50.
Poncela, P. and E. Ruiz. 2016. “Small versus big data factor extraction in Dynamic Factor Models: An empirical assessment in dynamic factor models.” In Advances in Econometrics , edited by E. Hillebrand, and S.J. Koopman. 35: 401–434. DOI: https://doi.org/10.1108/S0731-905320150000035010.
51.
Sezer, O.B., M.U. Gudelek, and A.M. Ozbayoglu. 2020. “Financial time series forecasting with deep learning: A systematic literature review: 2005–2019.” Applied Soft Computing 90: 106–181. DOI: https://doi.org/10.1016/j.asoc.2020.106181.
52.
Shmueli, G. 2010. “To explain or to predict?” Statistical science 25(3): 289–310. DOI: https://doi.org/10.1214/10-STS330.
53.
Stephens-Davidowitz, S. and H. Varian. 2014. A hands-on guide to Google data . Technical report, Google Inc. Available at: https://people.ischool.berkeley.edu/,hal/Papers/2015/primer.pdf (accessed October 2021).
54.
Stock, J.H., and M.V. Watson. 2011. “Dynamic factor models.” In Oxford Handbook of Economic Forecasting . edited by M.P. Clements, and D.F. Hendry, Oxford: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780195398649.013.0003.
55.
Tibshirani, R. 1996. “Regression shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society. Series B (Methodological) 58(1): 267 – 288. DOI: https://doi.org/10.1111/j.2517-6161.1996.tb02080.x.
56.
Varian, H.R. 2014. “Big data: New tricks for econometrics.” Journal of Economic Perspectives 28(2): 3–28. DOI: https://doi.org/10.1257/jep.28.2.3.
57.
World Bank, World Bank national accounts data. Available at: https://data.worldbank.org/indicator/NY.GDP.MKTP.CD